**Figure 6.50:** Tensile and compressive moduli of elasticity and tensile and compressive strength of continuous-discontinuous glass/carbon fibre SMC perpendicular to fibre direction, 90°, (• = median, + = mean, box = 25*th* to 75*th* percentile; lines indicate minimum and maximum or 1.5 interquartile range, respectively, ◦ = outlier).

Specimens featuring a higher tensile modulus of elasticity also tended to show increased tensile strength, and a slight positive correlation was observed in terms of tensile loading. No correlation was observed between compressive modulus of elasticity and compressive strength.

**Table 6.7:** Tensile and compressive properties of continuous-discontinuous glass/carbon fibre SMC in fibre direction of the continuous component with tensile and compressive modulus of elasticity (*E*), Poisson's ratio (*νt*), tensile and compressive strength (*R*), elongation at tensile or compressive strength (*εR*) and failure strain (*εmax*) corresponding to a decrease of sustained load to 0.8· preceding F*max*. Variable *n* indicates number of evaluated specimens.

**Table 6.8:** Tensile and compressive properties of continuous-discontinuous glass/carbon fibre SMC perpendicular to fibre direction of the continuous component with tensile and compressive modulus of elasticity (*E*), Poisson's ratio (*νt*), tensile and compressive strength (*R*), elongation at tensile or compressive strength (*εR*) and failure strain (*εmax*) corresponding to a decrease of sustained load to 0.8· preceding F*max*. Variable *n* indicates number of evaluated specimens.

Figure 6.51 shows representative tensile stress-strain curves of hybrid CoDico GF/CF SMC in 0° and 90°. In qualitative terms, uniaxial tension in the fibre direction of the continuous component (0°) led to a stress-strain evolution comparable to the behaviour of pure continuously carbon fibre reinforced SMC. Hence, the continuous component determined the evolution of the stress-strain response.  However, final failure was characterised by an abrupt and brittle fracture of the specimens.

**Figure 6.51:** Representative stress-strain curves resulting from uniaxial tension of continuous-discontinuous glass/carbon fibre SMC (CoDico GF SMC) in 0° and 90°.

Loaded perpendicular to the fibre direction of the continuous component (90°), the stress-strain curve of hybrid CoDico GF/CF SMC showed a linear evolution up to an elongation of *εt* ≈ 0.5 %, followed by a gradual decrease and brittle failure. The decrease in stiffness slightly reflected the behaviour of the discontinuous component. Assuming that the discontinuous core maintained tensile loads after failure of the continuous face sheets, hybridisation increased tensile strength and tensile failure strain compared to pure Co CF SMC (Figure 6.52).

**Figure 6.52:** Representative stress-strain curves resulting from uniaxial tension of continuous carbon fibre SMC (Co CF SMC), discontinuous glass fibre SMC (Dico GF SMC) and continuous-discontinuous glass/carbon fibre SMC (CoDico GF/CF SMC) in 90°.

In the following, the damage evolution of a hybrid CoDico GF/CF SMC loaded in fibre direction of the continuous component (0°) is considered in detail. For this purpose, Figure 6.53 depicts a representative tensile stress-strain curve, and strain fields corresponding to distinct points (A – H) are shown in Figure 6.54.

**Figure 6.53:** Representative *σ* − *ε* curve resulting from uniaxial tension of continuousdiscontinuous glass/carbon fibre SMC in 0°. Corresponding strain fields to points A – H are depicted in Figure 6.54.

As depicted in Figure 6.54, strains resulting from deformation in *x*− and *y*− directions (*εxx* and *εyy*) showed a homogeneous evolution at the beginning of loading (point A). As load increased, lateral strains (*εyy*) became highly heterogeneous (point B) and reflected the pattern of the stitching yarns (Figure 6.56). Strain localisations at the edges of the specimen indicate points of failure initiation (point C). In these mostly resin-rich regions, where continuous carbon fibre bundles were sheared and pushed apart during compression moulding such that the discontinuous glass fibre SMC was locally no longer reinforced, uniaxial tension led to elevated lateral strains.

Furthermore, the indicated sections were characterised by misaligned fibre bundles, coinciding with the edge of the specimen.

**Figure 6.54:** Evolving strain field resulting from uniaxial tension of continuousdiscontinuous glass/carbon fibre SMC.

Figure 6.55 shows a representative CoDico SMC tensile specimen, which is characterised by fibre misalignment in the face sheets and resin-rich regions at the surface resulting from manufacturing.

Initiated by inter-fibre fracture, the sudden appearance and growth of cracks was linked to small load drops in the stress-strain curve, indicating partial failure of the specimen (point D). However, the specimen was still able to maintain further load, and the stress-strain curve still showed an increasing evolution. In the following, interfibre fractures propagated easily (Figure 6.54 points E – H). Crack propagation and splitting between individual carbon fibre bundles was linked to a macroscopic interlaminar delamination between the discontinuous and continuous component. With a further increase in load, the hybrid continuous-discontinuous SMC specimen was thus partially weakened, and the final macroscopic failure was marked by a brittle fracture based on fibre fractures of the continuous component and local failure of the discontinuous part due to pseudodelamination (Figure 6.57).

Misaligned carbon fibres coincide with the edge 10 mm

**Figure 6.55:** Representative tensile specimen of hybrid continuous/discontinuous glass/carbon fibre SMC specimens showing misaligned carbon fibres and pushed apart of carbon fibre bundles.

**Figure 6.56:** Superposition of strain field resulting from uniaxial tension of continuousdiscontinuous glass/carbon fibre SMC with pattern of stitching yarns.

Figures 6.58 and 6.59 depict a side view and a top view of fractured (post-mortem) CoDico GF/CF SMC specimens. The multiple failure mechanisms described in the preceding section are clearly visible. In addition, delamination between the continuous and discontinuous component (interlaminar delamination) and within the continuous component (intralaminar delamination) can be clearly seen. In Figure 6.60, spalling of the matrix can also be identified as a result of evolving damage.

**Figure 6.57:** Damage evolution resulting from uniaxial tension of continuousdiscontinuous glass/carbon fibre SMC.

**Figure 6.58:** Fractured (post-mortem) hybrid continuous-discontinuous glass/carbon fibre SMC specimen which was exposed to uniaxial tension, side view.

10 mm

**Figure 6.59:** Fractured (post-mortem) hybrid continuous-discontinuous glass/carbon fibre SMC specimen which was exposed to uniaxial tension, top view.

**Figure 6.60:** Fractured (post-mortem) hybrid continuous-discontinuous glass/carbon fibre SMC specimen which was exposed to uniaxial tension, top view (2).

Scanning electron microscopy (SEM) investigations of a post-mortem specimen showed that macroscopically visible inter-bundle fractures were accompanied by inter-fibre fractures of the continuous material (Figure 6.61 and Figure 6.62). In addition, matrix cracks, which grow perpendicular to the tensile direction, were present (Figure 6.61).

Interface failure between fibres and matrix as well as breakage of individual glass fibres determined failure of the discontinuous component in the transition zone. Within the core, the discontinuous material mainly failed due to intralaminar pseudo-delamination, hence matrix cracking and interface failure. Figure 6.61 depicts a fractured CoDico SMC specimen with a higher magnification, which allows one to clearly identify inter-fibre fractures within the continuous component, not only present on a bundle scale but also separating individual carbon fibre filaments.

**Figure 6.61:** Detailed SEM observation of continuous component of fractured (postmortem) continuous-discontinuous glass/carbon fibre SMC which was exposed to uniaxial tension.

**Figure 6.62:** SEM investigation of fractured (post-mortem) continuous-discontinuous glass/carbon fibre SMC specimen which was exposed to uniaxial tension.

In the following, the damage evolution and failure mechanisms of hybrid CoDico SMC exposed to uniaxial compression are described. The representative stress-strain curve depicted in Figure 6.63 refers to the displacement of the crosshead. Due to the early and partial failure of the continuous face layers, strain measurement with the tactile clip-on extensometer was not possible until fracture.

Comparable to the presentation of damage evolution resulting from uniaxial tension, strain fields corresponding to significant points of the representative compressive stress-strain curve are shown in Figure 6.64.

If CoDico SMC (0°) was exposed to uniaxial compression, the resulting strain field was slightly heterogeneous before first failure was initiated (point A). In addition, the triangular shape of local strain concentrations reflected the pattern of the stitching yarns (Figure 6.65 point A). Damage was initiated by an abrupt failure of continuous carbon fibre bundles due to fibre fractures (point B) visible on the macroscopic scale. The fibre fractures were followed by an interfibre failure between different fibres, preferably between different fibre bundles (point B and C). Fractured fibres led to a local interlaminar delamination (point D), to a spalling of the matrix and to a progressive weakening of the specimen, which started to bend slightly (point E). If the applied load exceeded the residual compressive strength of the laminate, final failure was suddenly initiated. It could mainly be characterised by intralaminar pseudo-delamination of the discontinuous glass fibre SMC (point F). Localisation of fibre and inter-fibre fractures as well as crack propagation were linked to the pattern of the stitching yarns (Figure 6.65 point F).

**Figure 6.63:** Representative stress-strain curve resulting from uniaxial compression of continuous-discontinuous glass/carbon fibre SMC. Corresponding strain fields in points A – F depicted in Figure 6.64 and magnification of selected strain fields in Figure 6.65.

**Figure 6.64:** Evolving strain fields and damage evolution (side and top view) resulting from uniaxial compression of continuous-discontinuous glass/carbon fibre SMC.

10 mm

**Figure 6.65:** Strain field resulting from uniaxial compression of hybrid continuousdiscontinuous glass/carbon fibre SMC superposed by localisation and pattern of stitching yarns, magnification of selected images of Figure 6.64.

Post-mortem observations of hybrid CoDico SMC specimens enabled clear identification of the different stages of failure resulting from uniaxial compression.

In Figure 6.66, the location of fibre fractures and resulting crack propagation paths are clearly visible. Uniaxial compressive loading also led to a localised spalling of the matrix. A side-view of fractured specimens (Figure 6.67) clearly depicts delamination between the continuous and discontinuous component (interlaminar delamination), resulting from early fibre breakage of the continuous face layers (Figure 6.64: points D – F). Failure of the Dico GF SMC in the core of the hybrid CoDico was defined by shearing and pseudodelamination.

**Figure 6.66:** Fractured (post-mortem) continuous-discontinuous glass/carbon fibre SMC specimen, which was exposed to uniaxial compression, top view.

**Figure 6.67:** Fractured (post-mortem) continuous-discontinuous glass/carbon fibre SMC specimens, which were exposed to uniaxial compression, side view.

### **6.3.4 Out-of-plane loading of SMC composites**

The following section presents the flexural properties of discontinuous glass fibre SMC, continuous carbon fibre SMC and hybrid continuous-discontinuous glass/carbon fibre SMC.  Hence no difference in material stiffness compared to in-plane loadings was observed. With an average tensile strength of 283 MPa, *Rt*<*Rf* <*Rc* holds true. The superposition of tensile and compressive strains resulting from out-ofplane loadings explains this finding. Discontinuous glass fibre SMC exposed to three-point bending loadings was able to maintain high deflections. However, deviation between strain at flexural strength (*εR*, *f* ) and strain at failure (*εmax*, *f* ) was marginal (Table 6.5), indicating brittle failure.

Figure 6.68 shows a representative stress-strain response resulting from three-point bending of Dico GF SMC.

**Figure 6.68:** Representative stress-strain curve resulting from three-point bending of discontinuous glass fibre SMC.

In Figure 6.69, failure evolution shortly prior to final fracture is displayed. Flexural loading initially led to failure resulting from tensile strains at the lower side of the specimen (point b), characterised by a chipping off of the boundary layers (Chaturvedi et al., 1983) (point c). With a further increase in load, crack propagation preferably in the thickness direction of the specimen was observed (point d) leading to a loss of load-bearing capacities and a gradual stiffness decrease in the stress-strain curve. The formation of cracks within the specimen and an abrupt failure due to intra-laminar delamination (in-plane failure) (points e and f) marked the final failure of discontinuous glass fibre SMC specimens exposed to flexural loads.  For the considered span-to-thickness ratio of 32:1, investigations led to a flexural modulus which featured only approximately 0.9 of the stiffness resulting from tensile loadings (*x*¯ = 101.3 GPa). It is thus critical to say whether the determined value can be considered as flexural modulus of elasticity or should better be described as apparent flexural modulus of elasticity, with a higher span-to-thickness ratio possibly leading to a value closer to the tensile modulus of elasticity of the material. However, an increase in span-to-thickness ratio to 40:1 only slightly increased flexural modulus of elasticity, and given the observed variations, this increase was not significant. The flexural strength of continuous carbon fibre SMC was not as high as the tensile strength of the material, but it significantly exceeded compressive strength, indicating the simultaneous presence of tensile and compressive stresses and strains.

Figure 6.70 depicts representative stress-strain curves of continuous carbon fibre SMC exposed to three-point bending, and Figure 6.71 demonstrates significant points of failure evolution shortly prior to failure.

Continuous carbon fibre SMC exhibited generally a linear stressstrain response if exposed to bending loads, and failure was linked to an abrupt load drop. No significant variation between strain at flexural strength (*εR*, *f* ) and flexural failure strain (*εmax*, *f* ) was observed (Table 6.9). Failure was initiated by fibre fractures due to compressive stresses at the upper side of the specimen (point a). The initiation of failure was linked with a load drop in the stress-strain evolution; however, specimens were still able to maintain load. With increasing deflection and hence loading, fibre breakage and kinking became more important (point b). A crack below the loading nose formed (point c) and propagated in thickness direction of the specimen linked to localised delamination (points c – f).

**Table 6.9:** Flexural properties of continuous carbon fibre SMC in fibre direction (0°) for a span-to-thickness ratio of 32:1, with flexural modulus of elasticity (*Ef* ), flexural strength (*Rf* ), elongation at flexural strength (*εR*, *f* ) and flexural failure strain (*εmax*, *f* ) corresponding to a decrease of sustained load to 0.8· preceding F*max*. Variable *n* indicates number of evaluated specimens n.

**Figure 6.70:** Representative stress-strain curves resulting from three-point bending of continuous carbon fibre SMC in fibre direction (0°).

**Figure 6.71:** Failure evolution of continuous carbon fibre SMC exposed to three-point bending, side view.

### **<IP_ADDRESS> Flexural properties of continuousdiscontinuous glass/carbon fibre SMC**

The flexural properties of hybrid CoDico SMC were determined by means of three-point bending tests with the same test setup and specimen geometry considered for the individual materials. Mechanical material properties are summarised in Table 6.10. Figure 6.72 depicts representative stress-strain curves of CoDico GF/CF SMC resulting from three-point bending and Figure 6.73 presents significant points of failure evolution. Exposed to flexural loads, CoDico GF/CF SMC showed a linear stress-strain evolution comparable to continuous carbon fibre SMC; hence the continuous face layers dominated resulting material behaviour. After reaching flexural strength, specimens showed an abrupt damage, and strain at flexural strength (*εR*, *f* ) was approximately the same as the defined failure strain (*εmax*, *f* ). Flexural failure of hybrid CoDico SMC was initiated by fibre breakage of the continuous carbon fibres on the upper side of the specimen due to compressive stresses (point a). Failure progressed with local interlaminar delamination (point b) and fibre breakage on the lower surface (point c). The discontinuous glass fibre core layer partially failed (point d), most likely due to compressive failure, since it was locally no longer reinforced due to the failure and delamination of the continuous carbon fibre reinforced layer at the upper surface. Subsequently, tensile stresses led to tensile failure on the lower surface of the continuous carbon fibre SMC, which was also linked to delamination (Figure 6.73 d and e). At the end of the loading, the continuous component failed abruptly and in a highly localised manner, marked by fibre fractures and splitting in the lower surface. The glass fibre reinforced core layers remained almost intact, since the continuous carbon fibre reinforced shell layers received the majority of the load until failure (Dong and Davies, 2012).

**Table 6.10:** Flexural properties of continuous-discontinuous glass/carbon fibre SMC (0◦ ) for a span-to-thickness ratio of 32:1, with flexural modulus of elasticity (*Ef* ), flexural strength (*Rf* ), elongation at flexural strength (*εR*, *f* ) and flexural failure strain (*εmax*, *f* ) corresponding to a decrease of sustained load to 0.8· preceding F*max* (\*for one considered specimen load dropped only to 0.83·*Fmax*). Variable *n* indicates number of evaluated specimens.

**Figure 6.72:** Representative stress-strain curves resulting from three-point bending of continuous-discontinuous glass/carbon fibre SMC.

**Figure 6.73:** Failure evolution of continuous-discontinuous glass/carbon fibre SMC exposed to three-point bending, side view.

## **6.4 Mechanical properties and failure at the structure level**

In the following section, the mechanical properties and damage evolution resulting from quasi-static and dynamic puncture are presented. Attention falls mainly on the interaction of damage mechanisms and the stress-strain responses of the different SMC composites resulting from puncture loading. Puncture properties were evaluated in terms of maximum sustained load (referred to as maximum load or strength, *Fmax*) and puncture energy (*Ep*), which equals the absorbed energy of the specimen during quasi-static or dynamic loading. Puncture energy was computed as follows

$$E\_p = \int\_0^{\chi\_p} F d\chi \tag{6.2}$$

with the force *F* and the deflection *x*. A numerical approximation of this integration was completed by applying a trapezoid rule. To mitigate or eliminate the aspect of friction between the striker and the punctured surface, the puncture energy was calculated up to the puncture deflection (*xp*) according to EN ISO 6603-2 (2000). Within this ISO standard *xp* is defined as the position at which the instantaneous measured load is half of the precedent maximum load occurred during puncture. In addition, energy at maximum load (*EFmax* ) was calculated, taking into account Equation 6.2 within the bounds 0 < *x* < *xFmax* . In the dynamic loading case, the filtered forcedeflection response was considered to calculate puncture energy and to define the maximum sustained load of the specimen.

### **6.4.1 Puncture properties of discontinuous glass fibre SMC**

For structural observations, charge and flow region specimens of discontinuous glass fibre SMC have been considered. Investigations of rate dependent behaviour were based on puncture testing carried out in quasi-static and dynamic manner. Maximum load, puncture energy, energy at maximum load and corresponding deflections have been evaluated and are presented in Figure 6.74 and Table 6.11.

**Table 6.11:** Quasi-static and dynamic puncture properties of discontinuous glass fibre SMC.

**Figure 6.74:** Quasi-static and dynamic puncture properties of discontinuous glass fibre SMC (• = median, + = mean, box indicates 25*th* to 75*th* percentile; lines indicate minimum and maximum or 1.5 interquartile range, respectively; ◦ = outlier).

Maximum load and puncture energy of Dico GF SMC did not significantly differ for charge, as compared to flow region specimens. Mechanical performance showed higher scatter in terms of a dynamic puncture. With an increase of 60 % in maximum sustained load, Dico GF SMC exhibited positive rate dependence. Energy absorption capability (*Ep*) showed an increase of 48 % and 51 % for charge or flow region specimens, respectively. Specimens, which sustained a high load during quasi-static or dynamic puncture also showed higher energy absorption capability (Figure 6.74). No significant difference was observed considering deflection at maximum load and puncture deflection, regardless of puncture velocity and specimen type. The slope of the load-deflection response was fitted by a least squares fit (as presented in section <IP_ADDRESS>) in the range of 1 < *d* < 2 to evaluate the puncture stiffness (*S*). In the dynamic loading case, the slope of force-deflection response was fitted in the same manner, beyond the dynamic offset in the same deflection range. With an increase from 427 N mm−1 (*µ* = 48 N mm−1 , CV = 11.2 %) to 1001 N mm−1 (*µ* = 97 N mm−1 , CV = 9.7 %), Dico GF SMC exhibited a significant rate dependence in terms of puncture stiffness.

Figure 6.75 shows representative force-deflection as well as energydeflection responses resulting from quasi-static and dynamic puncture of charge and flow region Dico GF SMC specimens. In general, the force-deflection and energy-deflection response can be divided into six distinct regions, already defined by Kau (1990) and Knakal and Ireland (1986). In the following, the quasi-static material response is described in a detailed way. At the beginning of loading (section I), a common trend was seen for the Dico SMC specimen punctured in a quasi-static manner, and at lower contact forces, the contact response was of a power law form. Within this first part, indentation took place (Hertzian contact) (Sutherland and Soares, 2005). The following section was defined by a linear increase (section II) until a yield point. This point indicated a transition of the force-deflection curve from linear increase to an increase with reduced slope, due to initiation of failure. In the following, the force-deflection response was characterised by small load drops, which indicated evolving damage based on crack formation and growths. Force increased to peak load (section III), where peak was defined by a plateau rather than a distinct point if the specimens were punctured in a quasistatic manner. After peak, the load decreased gradually due to the formation and the growth of a widespread crack network; however, the specimen retained its structural integrity (section IV). In section V the striker penetrated through the punctured specimen, and the last section (section VI) of the force-deflection response resulted from friction between the striker and the specimen.

**Figure 6.75:** Force-deflection and energy-deflection curves resulting from quasi-static and dynamic puncture of discontinuous glass fibre SMC. Individual sections can be defined as follows: I: dynamic offset; II: yield; III: peak; IV: failure; V: penetration; and VI: friction.

The dynamic force-deflection response shows qualitatively the same characteristics. However, the initial part is defined by a dynamic offset (I) (Knakal and Ireland, 1986), which may have arisen from the apparatus and the specimen itself (e.g. influenced by its stiffness). Independent of loading rate, energy absorptions started beyond the yield point in a decisive way, since at the beginning of impact, elastic deformation did not contribute to energy absorption. As soon as cracks were initiated at the bottom side of the specimen, energy absorption became more important because of the formation of new surfaces, which absorbed energy induced by the striker. Energy absorption was most important beyond peak load until specimens were fully punctured by the striker (section IV and V). The energy-deflection curves reached a plateau, and in this phase energy was only dissipated due to frictional sliding between the specimen and shaft of the striker. Beyond maximum load, specimens punctured in a dynamic manner absorbed significantly more energy. Results presented by Trauth et al. (2018) indicate a rate dependence of interface properties of UPPH-based SMC composites reinforced with glass fibres enhancing energy absorption capability at higher loading rates.

Figure 6.76 depicts a representative force-deflection response of a Dico GF SMC specimen punctured in a quasi-static manner, in detail. Damage evolution was investigated through in-situ images captured with a camera positioned below the fixture. For significant steps in the force-deflection evolution, the corresponding images can be found in Figure 6.78. In addition crack growth was quantified by image processing (Figure 6.77).

**Figure 6.76:** Representative force-deflection response resulting from quasi-static puncture of a discontinuous glass fibre SMC flow region specimen.

**Figure 6.77:** Evolution of crack volume with increasing deflection and corresponding energy-deflection response of two representative discontinuous glass fibre SMC specimens.

50 mm

**Figure 6.78:** Failure evolution resulting from quasi-static puncture of discontinuous glass fibre SMC; flow region specimen, arrow indicating flow direction.

The rising portion of the force-deflection curve resulting from quasistatic puncture of Dico GF SMC started with a linear increase in deflection with increasing force, which was not linked to visible damage at the lower surface (point A and B). The decrease in stiffness in point C resulted from partial failure of the specimen at the lower surface due to the formation of cracks, tending to be oriented in flow direction, which was linked to first crack initiation events, as depicted in Figure 6.77. A further increase in force (points C – F, section III) led to crack growth and the continual formation of new (radial) cracks, but the crack-network was dominated by two major perpendicular radial cracks. Up to maximum load, the crack network further grew. From point F, the force significantly decreased as a result of important failure of the specimen, which was marked by abrupt crack growth (points G – I, section IV). Crack formation and growth rate increased significantly during this stage of puncture. In section V (points J – L) the specimen was penetrated. Penetration was linked to important further crack initiation and growth, before the shaft of the striker slid along the punctured surface in section VI. In this phase, energy was dissipated due to frictional sliding between the specimen and shaft of the striker. Post-mortem observation of the specimens highlighted some small circumferential cracks, which resulted from clamping.

In a comparable way, damage evolution resulting from dynamic puncture was captured by means of high-speed imagery during the impact event. Figure 6.79 highlights distinctive points of a representative force-deflection response, while Figure 6.80 depicts the corresponding high-speed images.

**Figure 6.79:** Representative dynamic force-deflection response of discontinuous glass fibre SMC flow region specimen.

50 mm

**Figure 6.80:** Damage evolution resulting from dynamic puncture of discontinuous glass fibre SMC flow region specimen; arrow indicating flow direction.

Considering dynamic puncture, the small drops in force in the rising part of the curve resulted from test setup and wave reflections; they do not reflect material behaviour, as the location of these load drops were reproducible for different specimens (Trauth et al., 2018). The first visible damage occurred in point C (at yield). In the following section, cracks started to grow, usually in flow direction. After reaching maximum force, load dropped due to sudden crack growth and formation at the lower surface (points E – G). In the following the striker penetrated through the specimen (points G – I).

## **6.4.2 Puncture properties of continuous carbon fibre SMC**

Continuous carbon fibre SMC exhibited a significant negative rate dependence. Maximum load (*Fmax*) and puncture energy (*Ep*) showed a characteristic decrease of −13 % and −21 %, respectively, if specimens were punctured in a dynamic manner (Table 6.12). No correlation between maximum sustained load and absorbed energy could be observed (Figure 6.81).

Different failure modes were observed for Co CF SMC punctured in a quasi-static manner, which significantly influenced damage absorption capability. As a consequence, puncture energy exhibited a very high scatter (Figure 6.81). A first failure type was characterised by an abrupt load drop after reaching maximum load to a force value, which was significantly lower than peak force and below *Fmax*/2. Considering the second type, load also abruptly decreased after peak load; however, force-deflection response showed a distinct plateau. For certain specimens, defined by the third failure type, load did not drop below 0.5· *Fmax*. These specimens have not been considered to calculate puncture energy or puncture deflection. Due to the early onset of failure, stiffness of continuous carbon fibre SMC was evaluated in the range of 0.25 < *d* < 1, with a least squares fit. In the dynamic loading case, the slope of the force-deflection response was fitted in the same manner for a deflection of ≈ 1 < *d* < 2, due to a dynamic offset. The stiffness of continuous carbon fibre SMC exposed to quasi-static or dynamic puncture did not show significant variation (Table 6.12).

**Figure 6.81:** Quasi-static and dynamic puncture properties of continuous carbon fibre SMC (• = median, + = mean, box indicates 25*th* to 75*th* percentile; lines indicate minimum and maximum or 1.5 interquartile range, respectively).

**Table 6.12:** Quasi-static and dynamic puncture properties of continuous carbon fibre SMC.

Figure 6.82 depicts representative force-deflection responses resulting from quasi-static and dynamic puncture of continuous carbon fibre SMC. The damage evolution of a selected continuous carbon fibre SMC punctured in a quasi-static manner is depicted in Figure 6.84, with corresponding images shown in Figure 6.83.

In general, first part of the force-deflection evolution was characterised by a steady (linear) increase in force for an increase of deflection up to peak load (sections I – III). A yield point could be identified at low deflections (section I, *d* ≈ 1 mm). After yield, a decrease in stiffness due to the onset of failure at the lower surface of the specimens was observed (section III). Gradual failure led to a further decrease in stiffness up to peak load. Peak was linked to marginally lower deflection in the dynamic loading case. Beyond peak load, the specimens failed abruptly and were suddenly no longer able to maintain loads (section IV). The prompt failure was also reflected by a kinking of the energy-deflection evolution. With only a slight increase from deflection at maximum load (*dFmax* ) to puncture deflection (*dp*), continuous carbon fibre SMC showed low damage tolerance, with a localised puncture loading independent from loading rate (Table 6.12). The end of the puncture event (sections V and VI) was defined by penetration of the striker and friction.

**Figure 6.82:** Representative force-deflection and energy-deflection response resulting from quasi-static and dynamic puncture of continuous carbon fibre SMC. Individual sections can be defined as follows: I: dynamic offset; II: yield; III: peak; IV: failure; V: penetration; and VI: friction.

**Figure 6.83:** Damage evolution resulting from quasi-static puncture of continuous carbon fibre SMC.

**Figure 6.84:** Representative force-deflection response resulting from quasi-static puncture of continuous glass fibre SMC.

Starting with a linear increase of the force-deflection response, an early formation of cracks in the fibre direction at the lower surface (points A – C, section I) slightly influenced the specimen's stiffness. In the beginning, damage was marginal, but as force increased, more cracks formed (starting from point C), and energy absorption became more important (section II). The small load drops in points D – H characterised abrupt, stepwise and instable crack growth linked to important energy absorption based in the formation of new surfaces (section III). Most important was the major crack in the middle of the specimen below the striker. Cracks grew easily in the fibre direction up to clamping (I), and the following load drop (I→J) was marked by a significant fracture of the specimen and the formation of inter-fibre cracks starting from clamping. The striker started to push through the specimen. Final failure was based on fibre breakage and linked to a significant load drop (point L).

The force-deflection evolution of a continuous carbon fibre SMC specimen punctured in a dynamic manner is qualitatively comparable to the quasi-static response (Figure 6.85 and 6.86).

**Figure 6.85:** Representative force-deflection response resulting from dynamic puncture of continuous glass fibre SMC.

The initial increase in load with increasing displacement led to the formation of numerous small cracks at the lower surface, oriented in the fibre direction (points A – C, section II). Fibre breakage and the formation of cracks perpendicular to fibre direction were more important if Co CF SMC was punctured in a dynamic manner, and the important load drop in point D was linked to fibre fracture in the bottom layer. As soon as peak load was reached, the specimen was no longer able to maintain loads and the force-deflection response dropped significantly. In the following, the striker penetrated through the specimen, and energy absorption mainly resulted due to friction.

50 mm

**Figure 6.86:** Damage evolution resulting from dynamic puncture of continuous carbon fibre SMC.

## **6.4.3 Puncture properties of continuousdiscontinuous glass/carbon fibre SMC**

Hybrid CoDico GF/CF SMC specimens were punctured in the same manner as the specimens made from the individual components, to enable evaluation of a hybridisation effect on structural properties. Charge and flow region specimens have been considered for evaluation, and Figure 6.87 and Table 6.13 depict the experimentally determined puncture properties of CoDico GF/CF SMC.

In contrast to Dico GF SMC, which showed no significant difference in mechanical performance of charge and flow region specimens (Figure 6.74 and Table 6.11), puncture energy (*Ep*) of CoDico GF/CF SMC was significantly lower for specimens extracted from flow region (Figure 6.87). The same trend was observed for maximum load; however, the difference was not significant for quasi-static puncture. With an increase of maximum load of 38 % and 28 % for charge and flow region specimens, CoDico GF/CF SMC exhibited a positive rate dependence, which was less distinct than for pure Dico GF SMC. Energy absorption capability increased for higher loading speeds 14 % and 23 % for charge and flow region specimens, respectively.

Stiffness of the CoDico GF/CF SMC specimens was evaluated in the range of 1 < *d* < 2 in the quasi-static and dynamic loading case by a least squares fit. If punctured in a quasi-static manner, the stiffness of the hybrid CoDico GF/CF SMC was in between the observed values of Dico GF and Co CF SMC. If punctured in a dynamic manner, stiffness increased (≈ 48 %). A positive correlation characterises the relation between maximum sustained load and absorbed energy for the two considered velocities (Figure 6.87).

**Table 6.13:** Quasi-static and dynamic puncture properties of continuous-discontinuous glass/carbon fibre SMC.

**Figure 6.87:** Quasi-static and dynamic puncture properties of continuousdiscontinuous glass/carbon fibre SMC (• = median, + = mean, box indicates 25*th* to 75*th* percentile; lines indicate minimum and maximum or 1.5 interquartile range, respectively, ◦ = outlier).

The force-deflection response, independent of loading rate, qualitatively showed the same evolution as defined for the Dico GF SMC and the Co CF SMC (Figure 6.88).

**Figure 6.88:** Representative force-deflection and energy-deflection responses resulting from quasi-static and dynamic puncture of continuous-discontinuous glass/carbon fibre SMC. Individual sections can be defined as follows: I: dynamic offset; II: yield; III: peak; IV: failure; V: penetration; and VI: friction.

After a linear increase up to yield (section I and II), stiffness started to decrease due to failure initiation at the lower surface (section III). From this point, damage of the specimen became evident due to numerous small load drops in the force-deflection response. Energy absorption became more important during this stage of loading, but did not quantitatively differ for different loading rates. The decreasing part of the force-deflection evolution was characterised by a stepwise decrease independent of loading rate, which indicated partial and subsequent failure of the specimen consisting of different layers (section IV). Energy-deflection responses beyond peak (section IV) indicated that specimens punctured in a dynamic manner were able to absorb more energy than was the case with a quasi-static loading of the material. This tendency was already observed for Dico GF SMC composites, and it is highly possible that failure mechanisms of CoDico GF/CF SMC also differ with respect to loading rate. It is conceivable that the difference in energy absorption capability most probably resulted from the rate dependent failure evolution of the Dico GF SMC composite or the interface properties between the continuous and discontinuous components. In the end, the striker penetrated the specimen (section V). Load did not decrease to zero due to frictional effects (section VI).

With a significant increase from deflection at maximum load (*dFmax* ) to puncture deflection (*dp*), CoDico GF/CF SMC featured better damage tolerance than did Co CF SMC (Table 6.13 and 6.12). The discontinuously reinforced core of the hybrid CoDico GF/CF SMC enhanced damage tolerance, preventing sudden failure of the specimen as soon as peak load was reached.

Figures 6.89 and 6.91 detail a representative force-deflection response and significant points in terms of damage evolution resulting from quasi-static puncture of the hybrid CoDico GF/CF SMC. Evolution of crack volume is depicted in Figure 6.90 to allow a quantitative evaluation of the evolving damage.

**Figure 6.89:** Representative force-deflection response resulting from quasi-static puncture of continuous-discontinuous glass/carbon fibre SMC. Images corresponding to points A – L appear in Figure 6.91.

**Figure 6.90:** Evolution of crack volume with increasing deflection and corresponding energy-deflection response of three representative continuous-discontinuous glass/carbon fibre SMC specimens.

50 mm

**Figure 6.91:** Damage evolution resulting from quasi-static puncture of hybrid continuous-discontinuous glass/carbon fibre SMC.

Starting with a steady (linear) increase (points A – C) due to the formation of small cracks at the lower surface in the direction of the fibres of the continuous carbon fibre SMC, failure became visible at lower deflections compared to the discontinuous glass fibre SMC. Nevertheless, the stiffness of the specimen was not affected during this stage of loading (yield corresponds to point C), in contrast to an early decrease in stiffness of the Co CF SMC. The small load drops in points C, D and E resulted from abrupt crack formation and growth, mainly in fibre direction of the continuous component. Compared to the pure Co CF SMC, the crack network which formed at the lower surface of the hybrid CoDico GF/CF SMC specimen consisted of a larger number of rather small cracks. The cracks parallel to the fibre direction of the continuous face sheets propagated easily up to clamping. This progression was linked to significant load drops in point G. Beyond peak the evolution of the force-deflection response was marked by fibre breakage (points H and I) and delamination between the continuously and discontinuously reinforced layers of the CoDico GF/CF SMC (point J). From point K to the end of the force-deflection curve, evolution was determined by the striker pushing through the specimen and friction.

Figure 6.92 presents the post-mortem observations of fractured CoDico GF/CF SMC specimens, which were punctured in a quasistatic manner. The failure of the discontinuous component was determined by pseudo-delamination. Interlaminar (interlayer) and intralaminar (intralayer) delamination within the continuous components were also important failure mechanisms accompanied by inter-fibre fractures within the continuous component.

10 mm

**Figure 6.92:** Damage region of a continuous-discontinuous glass/carbon fibre SMC specimen, punctured in a quasi-static manner.

The damage evolution of a representative hybrid CoDico GF/CF SMC specimen punctured in a dynamic manner is depicted in Figure 6.93, with corresponding images of damage evolution shown in Figure 6.94. Force-deflection evolution was characterised by a steady increase up to peak load. Several small cracks aligned in fibre direction of the continuous component formed (points A – C) and grew up to clamping. However, the formation of these cracks did not macroscopically influence the structural stiffness of the component. The significant load drop beyond peak load was characterised by a growth and spreading of the cracks formed within the continuous material. Delamination took place locally (points E – G). After reaching a small plateau (point G), the specimen suddenly failed due to the bursting of the continuous face sheet at the lower surface.

**Figure 6.93:** Representative force-deflection response resulting from dynamic puncture of continuous-discontinuous glass/carbon fibre SMC.

**Figure 6.94:** Damage evolution resulting from dynamic puncture of hybrid continuousdiscontinuous glass/carbon fibre SMC.

50 mm

Macroscopic post-mortem observation of hybrid CoDico GF/CF SMC specimens punctured in a dynamic manner (Figure 6.95) clearly indicated that interlaminar delamination played a more pronounced role than did damage mechanisms resulting from quasi-static puncture. In addition, pull-out of (glass) fibre bundles was the dominating failure mechanism of the discontinuous component (Figure 6.95).

Pulled-out glass fibre bundles

10 mm

**Figure 6.95:** Damage region of a continuous-discontinuous glass/carbon fibre SMC specimen, punctured in a dynamic manner showing interlaminar delamination between the continuous and discontinuous component as well as pulled-out fibre bundles of the discontinuous component.

## **6.5 Mechanical properties and failure at the component level**

Component properties were determined to investigate the effect of hybridisation on component scale, with load case simulating nearservice loadings. Having approximately the same density (as described in sections <IP_ADDRESS> and <IP_ADDRESS>), the component made from pure discontinuous glass fibre SMC and the locally reinforced parts realised with continuous carbon fibre SMC feature the same weight. In addition, the geometry was unchanged. As explained in section 4.4, the load data from the load cell and deflection data measured via a tactile transducer, positioned in the middle below the component, were recorded. Since all tests were carried out in a deflectioncontrolled manner, the deflection data of the specimens are identical with one another except for the maximum deflection at breakage. The measured force, however, differed and is considered in the following.

Figure 6.96 clearly shows that for components with local reinforcement the load increase over deflection was higher (i.e. the stiffness of the parts significantly increased due to the incorporation of a local reinforcement). At the last loading stage, corresponding to a maximum deflection of 5 mm, the specimens with continuous carbon fibre reinforcements carried an average load surplus of 946 N, in comparison to specimens without local reinforcement. That shift corresponds to an increase in strength of 32 %. Initial stiffness showed a more important scatter for the hybrid CoDico GF/CF SMC component (23 %) compared to the pure Dico SMC demonstrator parts, exhibiting a scatter in initial stiffness of only 3 %. The force-deflection response of the Dico and CoDico GF/CF SMC demonstrator parts were characterised by a gradual decrease, indicating a slight degradation of components' stiffness, resulting from increasing damage to the component due to loading. The force-deflection response of the hybrid CoDico GF/CF SMC demonstrator parts showed only a slight decrease within the first three cycles, then increased in a linear way up to cycle 8. Load at failure was significantly higher for locally reinforced components (739 N, increase of 17 %), but deflection at failure decreased from an average of 9.0 mm for purely discontinuous glass fibre SMC demonstrator parts to 7.6 mm if hybridisation took place (decrease of 1.4 mm, 15 %). In addition, the scatter of fracture strength was significantly reduced due to the local reinforcement (Dico GF SMC *µ* = 226 N, CoDico GF/CF SMC *µ* = 88 N).

**Figure 6.96:** Evolution of maximum force during four-point bending loading of discontinuously (Dico) and continuously-discontinuously (CoDico) reinforced demonstrator part evaluated at maximum deflection of each cycle.

Figure 6.97 depicts the stiffness of the components determined for every cycle according to Equation 4.5. In general, stiffness decreased for the Dico GF SMC and CoDico GF/CF SMC demonstrator parts with every cycle from the beginning of loading. Local reinforcement increased initial stiffness 23 % from an average value of 1247 N mm−1 to 1538 N mm−1 . However, initial stiffness of the hybrid CoDico GF/CF SMC demonstrator parts showed a significantly higher scatter, with CV = 9.5 %, compared to a variation of CV = 1.2 % for the purely discontinuous glass fibre SMC components.

**Figure 6.97:** Evolution of stiffness during four-point bending loading of discontinuously (Dico) and continuously-discontinuously (CoDico) reinforced demonstrator part evaluated at maximum deflection of each cycle.

Considering damage evolution, lower values of *D* (damage parameter) at equal stages for the locally reinforced components were observed (Figure 6.98). Comparably to stiffness evolution during cyclic loading, locally reinforced components showed a slightly higher scatter in evolving damage.

**Figure 6.98:** Evolution of damage during four-point bending loading of discontinuously (Dico) and continuously-discontinuously (CoDico) reinforced demonstrator part evaluated at maximum deflection of each cycle.

### **6.6 Analytical stiffness prediction**

In the following section, the results of analytical modelling to predict the stiffness of discontinuous glass fibre SMC, continuous carbon fibre SMC and continuous-discontinuous glass/carbon fibre SMC are presented.

## **6.6.1 Analytical stiffness prediction of discontinuous glass fibre SMC**

To analytically describe the stiffness of the discontinuous glass fibre SMC based on the Halpin–Tsai equations and Mori–Tanaka homogenisation approach (section <IP_ADDRESS>), the material properties listed in Table 6.14 have been taken into consideration.

**Table 6.14:** Input parameters and material data of discontinuous glass fibre SMC.

Figure 6.99 and Figure 6.100 depict the analytically determined tensile modulus of elasticity and shear modulus considering different aspect ratios of the fibrous reinforcement (*l*/*d*) and a fibre volume content of 20, 25 or 30 vol.%, respectively. These values reflect the variation of the experimentally determined fibre volume content of the sheets considered within this dissertation.

**Figure 6.99:** Tensile modulus of elasticity of discontinuous glass fibre SMC. Prediction based on Halpin–Tsai equations.

**Figure 6.100:** Shear modulus of discontinuous glass fibre SMC. Prediction based on Halpin–Tsai equations.

Considering the diameter of a glass fibre filament of 13.5 µm (Johns Manville, 2018) and the length of the filament in a standard SMC of 25.4 mm, the corresponding value of *l*/*d* equals 1881.5. For a fibre volume content of 26.6 vol.% (average value of all considered 1D Dico SMC sheets) predicted tensile modulus of elasticity and shear modulus equal 12.3 GPa and 4.4 GPa, respectively. Given the average fibre volume content of 2D Dico GF SMC sheets, predicted tensile modulus of elasticity and shear modulus are equal to 11.7 GPa and 4.2 GPa, respectively. Figures 6.102 and 6.103 demonstrate the analytically determined tensile modulus of elasticity of the discontinuous glass fibre SMC specimen extracted in flow direction and perpendicular to flow, based on the Mori–Tanaka approach. *E*0 and *E*90 consider the stiffness in the *y*− and *x*− directions according to the convention presented in Figure 6.101.

**Figure 6.101:** Orientation and convention of coordinate system to define elastic moduli based on Mori–Tanaka approach with fibre orientation tensors.

**Figure 6.102:** Modulus of elasticity of a specimen extracted in flow direction. Calculations based on Mori–Tanaka homogenisation and orientation averages.

**Figure 6.103:** Modulus of elasticity of a specimen extracted perpendicular to flow direction. Calculations based on Mori–Tanaka homogenisation and orientation averages.

The calculations depend on a fibre volume content of 24.2 vol.%. This value was experimentally determined by means of thermogravimetric analysis of specimens extracted from the same sheet as the investigated specimens. Accuracy of the Mori–Tanaka homogenisation approach was evaluated with a comparison of analytically determined and experimentally measured stiffness. For this purpose, the (scanned) specimens were mechanically loaded in uniaxial tension to determine an experimental value of the tensile modulus of elasticity. Specimens were mechanically clamped with a clamping distance of 50 mm. Gauge length was set to 20 mm, and strains were measured with an extensometer. Tensile modulus of elasticity was determined in the strain range of 0.05 % to 0.25 %. Each specimen was loaded three times, up to a maximum strain of 0.35 % and tensile modulus of elasticity was determined on the rising slope using Equation 4.10 presented in section 4.5. The experimentally determined values were 12.16 GPa (*µ* = 0.015 GPa, CV = 0.13 %) for the specimen extracted parallel to flow direction and 8.75 GPa (*µ* = 0.10 GPa, CV = 1.18 %) for the specimen perpendicular to flow direction. Table 6.15 lists the experimentally and analytically determined values of the tensile modulus of elasticity for the two considered specimens.

**Table 6.15:** Comparison of analytically (Mori–Tanaka approach) and experimentally determined tensile modulus of elasticity.

Stiffness of individual slices was estimated with the Mori–Tanaka approach combined with the parallel axis theorem, assuming that the neutral axis coincides with the central axis of the specimen, enabled to define a flexural modulus of elasticity. The accuracy of the estimated stiffness was also evaluated through an experimental comparison. For this purpose, the specimens were loaded in three-point bending (*L*/*h* = 20) up to a maximum deflection of 0.25 %, and flexural modulus of elasticity was determined three times for one specimen.

The experimentally determined values were 13.53 GPa (*µ* = 0.51 GPa CV = 3.74 %) for the specimen extracted parallel to flow direction and 9.05 GPa (*µ* = 0.20 GPa, CV = 1.12 %) for the specimen perpendicular to flow direction. In Table 6.16 the average mean value of the experimentally measured flexural modulus of elasticity is compared with the analytically determined value.

**Table 6.16:** Comparison of analytically (Mori–Tanaka approach and parallel axis theorem) and experimentally determined flexural modulus of elasticity.

## **6.6.2 Analytical stiffness prediction of continuous carbon fibre SMC**

The material properties listed in Table 6.17 have been considered to analytically describe the tensile modulus of elasticity in the fibre direction (0°). Figure 6.104 clearly shows that the RoM slightly overestimates elastic material behaviour in the fibre direction.

**Table 6.17:** Input parameters and material data of continuous carbon fibre SMC.

**Figure 6.104:** Longitudinal tensile modulus of elasticity of continuous carbon fibre SMC (0°) based on rule of mixtures.

Considering an FVC of 52.2 vol.% or 55.2 vol.% (sheet 1 and sheet 2) the predicted tensile modulus of elasticity is 128 GPa and 135 GPa, respectively. Taking into account the experimentally determined average value of 110.1 GPa this equals a deviation of 21.8 % and 15.5 %.

## **6.6.3 Analytical stiffness prediction of continuousdiscontinuous glass/carbon fibre SMC**

### **<IP_ADDRESS> Tensile and compressive modulus of elasticity**

The rule of hybrid mixtures (RohM) is an appropriate tool to predict the tensile modulus of elasticity of a hybrid composite. Since an analytical approach to predict the tensile modulus of elasticity of the continuous carbon fibre SMC composite (Figure 6.104) slightly overestimates material properties, the tensile and compressive modulus of the continuous carbon fibre SMC and the discontinuous glass fibre SMC were considered as input parameters.

The resulting stiffness of the hybrid laminate can be predicted by applying the RohM (Equation 5.44) as shown in Figure 6.105. To account for the scatter in material properties of SMC composites, calculation is based either on the arithmetic mean value or on the 25*th* and 75*th* percentile.

The experimental results depicted in Figure 6.105 depend on an average thickness of the hybrid specimens *h* = 2.91 mm and a thickness of the face sheets of *hf* = 0.33 mm. Hence, (2 · *hf* )/*h* ≈ 0.22-0.23.

**Figure 6.105:** Tensile modulus of elasticity in fibre direction of the continuous component. Calculations based on hybrid rule of mixtures.

#### **<IP_ADDRESS> Flexural modulus of elasticity**

The flexural stiffness of the hybrid CoDico GF/CF SMC laminate has been analytically modelled based on the classical laminate theory (CLT) (described in section 5.4.2). A symmetric and an asymmetric lay-up, due to the tension-compression anisotropy of the continuous material, were considered. Flexural rigidity resulting from a symmetric and an asymmetric lay-up are presented below. The analytical predictions based on the material parameters that appear in Table 6.18.

**Table 6.18:** Input parameters and material data of the discontinuous glass fibre SMC and continuous carbon fibre SMC considered for CLT.

In order to determine the shear modulus of the discontinuous glass fibre SMC (*G*12,*Dico*), results obtained by the Halpin–Tsai approach depicted in Figure 6.100 were considered. The analytically predicted value of *G*12,*Dico*= 4.37 GPa is within the boundaries described in CES EduPack (2017) considering a 40 wt.% glass fibre SMC (unsaturated polyester resin-based). Förster and Knappe (1971) presented a method to estimate the shear modulus of a unidirectionally carbon fibre reinforced lamina.

**Figure 6.106:** Flexural modulus of elasticity of continuous-discontinuous glass/carbon fibre SMC, predicted by classical laminate theory described in section 5.3.

As clearly depicted in Figure 6.106, the CLT based on a symmetric lay-up of the hybrid CoDico GF/CF SMC (assuming that tensile and compressive modulus of elasticity of the continuous component are equal) overestimates flexural stiffness (*Ef* ,*CLT*,*sym* = 64.06 GPa). Given the tension-compression anisotropy, the CLT (asymmetric lay-up) precisely predicts the resulting stiffness of the hybrid CoDico GF/CF SMC (*Ef* ,*CLT*,*asym* = 58.84 GPa). The experimentally determined arithmetic average equals *Ef* = 59.34 GPa, hence, deviation is below 1 %.

# **7 Discussion**

The following section discusses the results presented in chapter 6. First, an evaluation of experimental methods is offered. Next, the particularity of the unsaturated polyester-polyurethane two-step curing hybrid resin system is addressed. The third part is based on the vertical characterisation strategy defined in chapter 4 and focusses on micromechanical observations followed by reasons explaining the observed mechanical behaviour of the individual and hybrid material, always linked to failure evolution and damage mechanisms. Attention is drawn primarily to the effect of hybridisation. In addition, tools to model stiffness and strength of the individual material, but more important of the hybrid material in an analytical way are evaluated in terms of complexity and accuracy of predictions.

## **7.1 Testing methodology and preliminary studies**

This work has undertaken a deep investigation to determine the influence of the specimen's geometry on resulting mechanical properties. Tensile tests with different rectangular and dog-bone shaped specimens were carried out to define a possible influence of specimen geometry on the resulting material performance. Relative properties were compared to account for variations in the fibre volume content of different sheets and specimens, which were extracted from twodimensional (2D) flow sheets with planar isotropic fibre orientation (as shown in Figure 6.25). As stated in Marissen and Linsen (1999), smaller SMC specimens feature more cut fibres within the gauge section and less efficient reinforcement, deceasing the experimentally determined flexural stiffness and strength of the material. The relative stiffness of rectangular specimens featuring a width of 30 mm and a clamping distance of 100 mm (geometry R 2.1) was slightly lower than the stiffness of the same specimen type, clamped at a distance of 130 mm with the same gauge section (10 × 70 mm2 ). Calculations of technical strains by averaging local displacement values considering a larger surface of the specimen may falsify results due to local strain concentrations (overestimation of average strains) near clamping (St. Venant's principle). However, relative material properties determined with slightly different geometries of the specimens did not significantly differ, and small variations can be based on structural rather than on statistical effects, as indicated by Varna et al. (1992).

The effect of the specimen's geometry on the relative strength of the discontinuous SMC material was slightly more important with larger specimens featuring lower strength (specimen geometry R 2 and B 2 in Figure 6.2). However, decreases were marginal (below 5 %) and not significant if scatter is considered. A possible explanation of this finding might be a size effect, commonly known for composite materials (Sutherland et al., 1999). The microstructure of a composite is important in determining the defects that may give rise to a size effect. At the microlevel, a decrease in fibre diameter was observed to lead to higher strength values (Griffith, 1921). Size effects on the specimen scale indicated that in smaller specimens, the probability of the occurrence of internal flaws or defects is lower than in larger ones. Hence, material strength might increase due to a size effect (Wisnom, 1999), for example. Size effects may explain the findings of this present dissertation.

Due to the heterogeneous microstructure, mechanical characterisation of discontinuous SMC materials was generally determined by a significant scatter. Taking stereo digital image correlation into consideration helped to deduce global information on strains resulting from mechanical loads. Conventional strain measurement techniques, such as strain gauges or extensometers, determine only local displacements, and evaluated strains depend strongly on the local microstructure of the contact zone. A parameter study pointed out that within appropriate bounds, measuring of displacement fields by means of digital image correlation to deduce strains was robust and reliable (Table 6.3).

## **7.2 Material behaviour of unsaturated polyester-polyurethane two-step curing hybrid resin system**

The moulded unsaturated polyester-polyurethane two-step curing (UPPH) hybrid resin sheets exhibited high porosity, although the individual components were mixed in a vacuum to reduce the amount of air within the mixture. For this reason, tensile strength was characterised by a very high scatter, induced due to failure initiation at pores. Hence, the determined values should be considered with caution. Elastic properties (tensile modulus of elasticity and Poisson's ratio) which were important for modelling of material properties of the discontinuous and continuous SMC composites, however, could be determined precisely and matched very well with experimentally determined values of the same resin system presented by Kehrer et al. (2018).

Exposed to uniaxial compression, the rectangular specimens bent easily, and compressive failure strain could not be determined. Compressive strength was defined as the stress corresponding to the point in stress-strain response where the bending factor (*bf* ) reached a value of 0.1 (Figure 6.24).

**Figure 7.1:** Damaged unsaturated polyester-polyurethane hybrid resin specimens, exposed to tensile loadings showing numerous fractures (a) and exposed to compressive loadings showing high plastic deformation (b).

Considering the experimental results, the unsaturated polyesterpolyurethane hybrid two-step curing resin system exhibited a tensioncompression anisotropy. Tensile loading led to a brittle failure of the specimens due to cracking, most probably simultaneously at different points (Figure 7.1a), whereas specimens featured a high plastic deformation if loaded in compression (Figure 7.1b) and did not fail even for a very small clamping distance (≈ 5 mm).

## **7.3 Discontinuous glass fibre SMC**

## **7.3.1 Microstructural aspects of discontinuous glass fibre SMC**

The discussion of microstructural aspects is based on the results presented in section 6.2. In the following, process-induced characteristics of fibre volume content and fibre orientation of the discontinuous glass fibre SMC composite are discussed as a starting point to relate the characteristic microstructure to the observed material properties.

### **Fibre volume content**

Discontinuous glass fibre reinforced SMC sheets showed a higher average fibre volume content (26.6 vol.%) than the nominal fibre volume content of approximately 23 vol.%. The variation may be explained by the height of the resin film. Generally, it is calculated to lead, in combination with the adapted velocity of the conveyor belt and cutting unit, to a desired fibres-to-resin ratio and thus to a nominal fibre content. Variations in the film height of the resin between the theoretically calculated and real value resulting from a distinct viscosity and shear properties of the considered resin system are possible. Correction factors may be considered, based on detailed experience with the processing of a specific resin system to counteract the non-negligible amount of resin pressed out at the edges of the sandwiched SMC mat, due to calendaring and rolling-up of the semi-finished material. However, no correction factors were applied to adapt the film height of the resin to manufacture the materials considered within this dissertation. Investigations of the fibre volume content of the discontinuous (one-dimensional [1D]) glass fibre SMC material showed variations in average fibre volume content (FVC) within one campaign (21.5 vol.% to 28.2 vol.%). However, only one sheet featured an FVC below the nominal value of 23 vol.% (Figure 6.9). It is possible that this distinct sheet was moulded with a stack of semi-finished material which originated from the end or the edges of the SMC roll. This section might thus feature a process-related lower fibre content. Due to the characteristics of the SMC manufacturing process and the bundle structure of the fibrous reinforcement, a locally divergent FVC resulted from processing and was unavoidable. The heterogeneous microstructure and the length of the bundles, which clearly exceeded the diameter of the specimens considered for thermogravimetric analysis (TGA) examinations, may favour the observed variations in fibre volume content within one sheet, between approximately 4 vol.% and 10 vol.%.

Different regions of one sheet, for example charge and flow region, did not show a characteristic distribution of FVC (Figure 6.11). Therefore, a sufficiently large number of specimens extracted at different positions of one sheet precisely describes the average real fibre volume content and its variation within one sheet. This value is important to know in order to describe mechanical properties based on micromechanical approaches.

Computed tomography allowed for the definition of fibre volume content in a non-destructive manner. The determined values based on image processing of *µ* − *CT* data of two distinct specimens extracted from the same sheet, were equal to 33.7 vol.% and 34.5 vol.%, respectively. The experimentally determined FVC (TGA) of the considered sheet was equal to 24.2 vol.%. The difference in results between the two methods highlights an important point of microstructural analyses through image processing based on *µ*-CT data. If the resolution is not high enough or the thresholds are not appropriately defined, individual fibres within one bundle cannot be individually tracked. Instead, entire fibre bundles are considered to define the FVC, although the fibre volume fraction in a bundle is only 65 % on average (Orgéas et al., 2011).

Based on the same semi-finished material, variations in terms of FVC did not significantly differ between 1D and 2D flow sheets. In addition, as no distinct difference in average FVC and intra- as well as inter-plaque variation were observed for two manufacturing campaigns (Figure 6.10), the introduced process to manufacture nonfilled structural glass fibre SMC which premised on the hybrid resin system, is robust.

Standard SMC formulations consider a significant amount of fillers, which may be as high as 40 wt.% (Orgéas et al., 2011), to account for special requirements (e.g. flame retardancy or to improve surface quality). Fillers increase a material's density having no enhancing effect on the material properties in general. The discontinuous SMC composite considered within the present dissertation is referred to as structural SMC, featuring no fillers and a nominal fibre content of ≈ 41 wt.%. With an average density of 1.53 g cm−3 , it has a high lightweight potential since standard SMC formulations, based on comparable fibre content feature densities in the range of 1.75 g cm−3 to 1.95 g cm−3 (CES EduPack, 2017; Oldenbo et al., 2003).

### **Fibre orientation**

The investigated discontinuous glass fibre SMC exhibited a significant anisotropy in terms of fibre orientation with distinctly formed shell and core layers (Figure 6.14 and 6.15), as typically known for SMC materials and stated for example by Kim et al. (1992) or Le et al. (2008). It is highly possible that the discontinuous glass fibre SMC considered within this study deformed in uniform extension within the core layers, as described by Barone and Caulk (1985). The contact of the semi-finished material with the preheated mould led to faster movement of the material within the shell layers, usually in the bottom half, since the material's viscosity was decreased in the contact zone. Splitting of fibre bundles and curvature of fibres, observed within the shell layers, might be a result of the aforementioned flow phenomena and the severe shearing of the paste-rich boundary layers (Le et al., 2008). Furthermore, as stated by Odenberger et al. (2004) during the initial phase of flow, outer layers of the stack are not forced to remain outer layers and may also move axially. However, the investigated SMC was characterised by a slightly orthotropic fibre orientation, with a negligible amount of fibre bundles aligned in *z*-direction (*Ozz* ≈ 0). This fibre orientation indicates that shear deformation of the bundles due to flow was negligible and the compression moulding process was preferably defined by a plug-flow of the material. Resulting from one-dimensional (1D) flow, a preferred orientation with more fibre bundles aligned parallel to flow direction was observed. The ratio of *Oyy*/*Oxx*, given values averaged over the thickness of the specimen, was equal to 1.79 for the specimens extracted in flow direction. With a ratio of *Oyy*/*Oxx* = 1.18 (Le et al., 2008) observed for compression moulded sheets without significant flow, anisotropy in terms of fibre orientation becomes clear for the SMC composite investigated within this dissertation.

## **7.3.2 Mechanical behaviour and damage evolution of discontinuous glass fibre SMC**

#### **Coupon level: Tensile, compressive and flexural properties**

The mechanical properties of SMC composites depend strongly on manufacturing parameters and material flow (Taggart et al., 1979; Trauth et al., 2018, 2017a). The effect of fibre orientation was also observed within this dissertation, and 2D flown sheets featured planar isotropic material properties (Figure 6.25) with a factor of anisotropy of *fA* = 1.05 in terms of tensile modulus of elasticity (*Et*) and tensile strength (*Rt*). A 1D flow led to anisotropic material properties (Figure 6.26) and regardless of loading case, material properties in the flow direction (0°) were significantly enhanced, as compared to the material performance perpendicular to flow. Material flow during compression moulding aligned fibre bundles in the flow direction across the entire sheet, and no difference was observed in the mechanical material behaviour of charge and flow region specimens. Tensile, compressive and flexural modulus of elasticity featured a factor of anisotropy of *fA* = 1.38, 1.37 and 1.38, respectively.

Anisotropy of strength was more severe, with *fA* = 1.96 for tensile, *fA* = 1.33 for compressive and *fA* = 1.67 for flexural loads. In order to compare the effect of fibre orientation on different loading cases, it is important to consider, that free length (between the clamping) of specimens differed with respect to different testing procedures. Hence, the volume of the specimen exposed to load differed (especially in terms of uniaxial compression and tension). Variations in material properties (0°) were most important for tensile loads (CV was in the range of 17 % to 30 %, CV of *Rc* and *Rf* were below 15 % and 11 %, respectively). Especially in terms of strength, the observed anisotropy was more severe compared than the material investigated, for example, by Taggart et al. (1979) (tensile strength: *fA* = 1.32, compressive strength: 1.13 < *fA* < 1.26). However, a more significant effect of flow on anisotropy was stated by Boylan and Castro (2003), with *fA* ≈ 1.5 for stiffness and *fA* ≈ 2.6 for tensile strength.

The aforementioned findings highlight the importance of determining the mechanical material properties of an SMC composite in strong interaction with preceding flow during compression moulding. Depending on the resin system, fibre type and mould geometry, the influence of material flow on resulting mechanical performance may significantly differ and cannot be generalised.

In terms of tensile modulus of elasticity, the investigated Dico GF SMC composite showed lower mechanical properties, compared to a 45 wt.% polyester- based SMC material investigated by Chaturvedi et al. (1983). The aforementioned material featured an average tensile modulus of 14.7 GPa, but no details were presented on manufacturing parameters, nor mould coverage or flow condition. The Dico UPPH-based GF SMC composites considered within this dissertation, featuring a comparable fibre content, were characterised by a slightly lower average tensile modulus of elasticity (13.1 GPa in flow direction and 9.5 GPa perpendicular to flow direction). However, considering scatter in mechanical testing, this deviation is not significant. The tensile modulus of elasticity of a vinylester-based SMC composite with a fibre weight content of 41 wt.% investigated by Trauth et al. (2017a) was equal to 11 GPa in the manufacturing direction and 9.4 GPa perpendicular to the direction of manufacturing. Since the sheets investigated by Trauth et al. (2017a) did not flow, anisotropy was less severe (*fA* = 1.19). Featuring a comparable FVC, the presented UPPH-based 2D flow Dico SMC composites (*Rt* = 159 MPa) clearly outperformed the vinylester-based SMC composite in terms of tensile strength (*Rt* = 100 MPa, Trauth et al., 2017a). However, slightly smaller specimens have been considered within this dissertation, and due to a 100 % mould coverage realised by Trauth et al. (2017a), entrapped air might present an explanation of the SMC composite's lower strength.

Determination of compressive properties was rarely carried out on SMC materials in the past. Database values presented in the CES EduPack (2017) indicate a compressive modulus of elasticity of a 40 wt.% glass fibre SMC, based on an unsaturated polyester of 11.6 GPa. This value ranges between the experimentally determined value of compressive modulus of elasticity in 0° (*Ec* ≈ 12.6 GPa) and 90° (*Ec* ≈ 9.2 GPa) for the material considered within this dissertation. A polyester-based SMC investigated by Taggart et al. (1979) featured comparable stiffness (*Ec* = 12.4 GPa), but at a lower fibre content (25 wt.%). In terms of compressive strength, indicated values range between 204 MPa to 284 MPa for a fibre volume content from 25 wt.% to 65 wt.% (Table 2.3). Although the indicated values might be inferior to the results obtained for specimens aligned perpendicular to flow within this dissertation, experimentally determined strength values perpendicular to flow (≈ 225 MPa) were significantly lower than a 40 wt.% unsaturated polyester-based SMC (CES EduPack, 2017) due to a flow-induced anisotropic fibre orientation.

Compared to polyester-based SMC composites featuring a FWC of 25, 30 or 65 wt.% (investigated by Walrath et al., 1982) the UPPH-based material investigated within this dissertation showed a significantly higher flexural modulus of elasticity. However, compared to the flexural properties presented by Chaturvedi et al. (1983) (polyesterbased SMC, FWC: 45 %), flexural modulus of elasticity was slightly lower but flexural strength exceeded the values presented by Chaturvedi et al. (1983).

Generally, comparison of quantitative material data of different SMC composites is difficult, since mould coverage and flow, as well as specimen orientation, specimen geometry and testing parameters, may significantly vary.

The investigated discontinuous UPPH-based SMC composite did not show significant variation in terms of tensile, compressive or flexural modulus of elasticity. Nevertheless, as generally known for SMC materials and stated, for example, by Taggart et al. (1979), Mrkonjic et al. (2015) or Trauth et al. (2017a) – and as summarised in Table 2.3 – the investigated UPPH based discontinuous glass fibre SMC also exhibited a significant tensile-compression asymmetry in terms of strength, and *Rt* < *Rf* < *Rc* holds true. However, this finding has to be critically reflected with respect to specimen size. This special characteristic is important to consider when mechanical material properties are sought to be modelled (Feld et al., 2017; Oldenbo et al., 2004).

Exposed to tensile loads, damage of Dico GF SMC was characterised by a failure evolution well known for SMC materials, described by Derrien et al. (2000), Jendli et al. (2005) or Wang et al., 1983, for example. Nevertheless, the kinking of the stress-strain curve ('kneepoint') was not as pronounced as for standard SMC materials as defined by Chaturvedi et al. (1983), for instance. The absence of fillers or the special UPPH resin system might present possible explanations. Elastic deformation of the investigated Dico GF SMC was followed by the formation of interfacial cracks most likely perpendicular to loading direction. Microcracks within the matrix started to propagate, but fibre bundles aligned perpendicular to loading direction impeded further crack growth. Cracks were forced to propagate around the fibres, and crack growth was hence more likely to happen perpendicular to the loading direction. For this reason, earlier failure of specimens with fibres preferably aligned perpendicular to flow resulted, probably due to an easier spread of the cracks over the entire width of the specimen. This growth of cracks explains lower strength observed for 90° specimens (≈ 0.5·*Rt* of 0° specimens). Observation of post-mortem specimens exposed to tensile loads furthermore indicated a change from individual fibre failure in the shell layers to fibre bundle pull-out and pseudo-delamination within the core (Figure 6.37). As indicated, material flow during moulding led to a separation of individual filaments from the bundle structure of the shell. In this part of the specimen, fibres were also more likely to be characterised by a distinct curvature, which locally changed the orientation of the fibres in the shell layers with respect to the direction of loading (Figure 6.17). Fibres in the shell layers tended to break as soon as strength of an individual fibre was exceeded. Due to the slightly different orientation of the fibres, the possibility of breakage differed for different fibres. Within the core, fibre bundles could maintain higher loads, as stresses were transferred within the bundle and distributed between multiple fibres. For this reason, fibre bundles did not break as easily as single fibres, if exposed to tensile loads but interface failure was more likely to happen, resulting in pull-out of fibre bundles or pseudo-delamination.

Exposed to uniaxial compression, specimens mainly failed due to shearing. Pseudo-delamination was not as important as for tensile loadings. Compressive loads counteracted crack growth and debonding, leading to higher damage tolerance of the SMC composite and explaining higher the compressive strength of SMC materials, also linked to higher failure strains.

Exposed to out-of-plane loads, Dico SMC was not significantly sensitive to shear strains, and even for a span-to-thickness ratio of 4:1, no pure shear failure was observed. Dico GF SMC exhibited a high damage tolerance if loaded in three-point bending, and high deflections were possible before failure strain was reached. Failure was highly localised below the loading nose, based on chipping of (Chaturvedi and Sierakowski, 1983) and failure between fibre bundles.

#### **Modelling approaches**

Applying a generalised rule of mixtures (RoM) to estimate the stiffness of the discontinuous glass fibre SMC, according to Equation 5.23, resulted in a modulus of elasticity of 7.9 GPa for an average fibre content of 25.2 vol.% (average mean value of investigated 2D SMC sheets, depicted in Figure 6.10). Hence, the predicted value significantly underestimates (≈ −30 %) the experimentally determined stiffness of a 2D GF SMC, and it is not recommended to be considered to analytically predict the stiffness of chopped fibre SMC composites.

The Halpin–Tsai approach was based on a small number of input parameters. However, this method does not generally account for fibre orientation, and the predicted stiffness is most likely to represent the material behaviour of a planar-isotropic SMC with no preferred fibre orientation resulting from material flow. With an experimentally determined average value of *Et* = 11.6 GPa determined for 2D flow SMC sheets with an assumed planar-isotropic fibre orientation and no distinction made between charge and flow region specimens or 0° and 90°, the analytically determined value slightly (6 %) overestimated the stiffness of the material. However, this variation was not significant with respect to the intrinsic scatter of material properties of SMC composites and it is important to mention that the Halpin– Tsai approach is easy to apply to gain a basic understanding of the mechanical performance of SMC materials not exposed to uniaxial flow during compression moulding.

Predictions based on the Mori–Tanaka approach allowed for a description of longitudinal and transverse stiffness of the material through consideration of information on fibre orientation gained by *µ*-CT observations. Deviations between experimentally and theoretically predicted values were marginal (below 4 %) and may have resulted from the value of fibre volume content considered for modelling. The average fibre volume content (determined by TGA) of the sheets from which specimens have been extracted was consulted to calculate the stiffness of the specimens. However, in reality the FVC was characterised by variations with respect to the specimen's thickness. A precise determination of fibre volume content is important to consider for this homogenisation approach, and it would be best to consider local fibre volume contents within different layers of the specimen according to the components of the FOTs. This method implies, however, that only small volumes of the material could be considered to achieve a sufficiently high resolution of the *µ*-CT images. Nevertheless, with regard to the small deviations, the Mori–Tanaka approach was an appropriate tool to predict the tensile modulus of elasticity of the one-dimensionally flown sheets, even though only an average fibre volume content of the sheet was considered.

Given the layered structure of the SMC materials, which results due to stacking of multiple layers of the semi-finished material prior to moulding, a summation of the stiffness of individual layers with respect to the neutral axis and a parallel axis theorem enhanced the accuracy of the predicted flexural modulus (error decreased from 15.3 % based on a simple summation to 11.3 % based on a summation with parallel axis theorem). Nevertheless, variation between calculated and experimentally determined values was higher for flexural stiffness than for tensile properties. Observation by means of *µ*-CT was based on an alignment of the captured images to compensate for possible misalignment of the specimen within the computer tomograph. Hence, the surface layers were possibly (artificially) cropped for image processing and could not be evaluated in terms of fibre orientation. Since these layers most importantly influence flexural stiffness, the effect on estimated flexural modulus is more important compared to a possible induced error while predicting tensile modulus of elasticity.

#### **Structure level: Puncture properties**

Considering puncture properties of SMC composites, a wide literature review indicated that, so far, little attention has been paid to rate effects.

In Trauth et al. (2018), a positive rate dependence of puncture properties was observed for SMC composites based on the same UPPH resin system as considered within this dissertation with a comparable glass fibre reinforcement (41 wt.%, 25.4 mm long fibres). Maximum load and energy absorption capability significantly increased for higher loading rates for charge (65 % and 67 %) and flow region specimens (73 % and 64 %). The findings of Trauth et al. could be confirmed by the results of this study (section 6.4.1). Nevertheless, the increase in maximum load and puncture energy was slightly less important (increase in maximum load and puncture energy was ≈ 60 % and 50 %, respectively), which could be explained by the anisotropic fibre orientation of the 1D flow SMC sheets. In Trauth et al., 2018 2D flow sheets have been considered for experimental investigations. In addition, intrinsic scatter is again important to consider.

Due to manufacturing of the SMC sheets in a compression moulding process, variations in thickness are possible which may influence the resulting puncture properties, and an exponential correlation between maximum load or absorbed energy and thickness of the specimen was observed for SMC materials (Kau, 1990; Lee et al., 1999), as affirmed in EN ISO 6603-2 (2000). Given the results of the present study, no significant influence of specimens' thickness on dynamic impact properties could be observed (coefficient of regression *r* 2 < 0.5). Variations in fibre volume content, hence variation in density and thus mass of the specimens, also did not significantly influence dynamic puncture properties (*r* 2 < 0.3).

Considering quasi-static puncture loads, strength and puncture energy correlated with *h* 1.98 and *h* 2.0, respectively. However, regression coefficients (*r* 2 ) were only 0.6 and 0.7, and variations in terms of thickness of the Dico GF SMC sheets (¯*h* = 2.85 mm, *µ* = 0.11 mm, CV = 3.83 %) were too small to significantly affect puncture properties. Due to a very localised loading, the highly heterogeneous microstructure had a more important effect on puncture properties.

Damage of discontinuous glass fibre SMC exposed to quasi-static and dynamic puncture was characterised by a comparable damage evolution. In general, it was mainly based on the formation of radial cracks initiated below the striker. A yield point could be defined for both loading rates, characterised by a decrease in stiffness, followed by a second linear load-deflection response, with a reduced slope. Insitu image capturing allowed for investigation of damage evolution, and this yield point was linked to damage initiation on the lower surface, affecting the macroscopic stiffness of the material (Kau, 1990). Dico GF SMC specimens exposed to puncture loads did not fail abruptly, and no distinct point in the force-deflection response could be assigned to breaking. The failure was characterised by a gradual failure linked to a slight but steady decrease of the forcedeflection evolution due to successive crack formation and growth, strongly dependent on fibre distribution and orientation.

In the dynamic loading case, due to a relatively low stiffness of the material, oscillation of the specimen resulted due to the impacting energy. Although this effect is normally less severe for lower impacting speeds (Cheresh and McMichael, 1986), the initial part of the load-deflection curve of the Dico GF SMC was characterised by a dynamic offset. Hence, calculation of the material's puncture stiffness is complex. The presented method to define puncture stiffness within this dissertation accounted for a possible indentation of the striker at the beginning of loading (Hertzian contact) and did not consider deflections below 1 mm in the quasi-static loading case. The same deflection range was considered for dynamic puncture for the sake of comparability and to take the dynamic offset into consideration.

The increase in maximum load and energy absorption capability were most likely based on different failure mechanisms, which determined the damage evolution of the material. Failure modes of glass fibre reinforced polymers may change with increasing loading rate (Okoli, 2001). A transition in failure modes of Dico GF SMC exposed to puncture was already observed by Trauth et al. (2018), with fibre pullout and matrix cracking being more important at higher loading rates. In addition, the matrix properties significantly influence evolving damage, since the aforementioned failure mechanisms such as fibre pull-out, for example, strongly rely on the fibre-matrix interfacial strength (Mallick, 2007). Jendli et al. (2005) also concluded that, exposed to higher loading rates, the fibre-matrix interface failure strength of SMC composites significantly increased.

### **7.4 Continuous carbon fibre SMC**

### **7.4.1 Microstructural aspects of continuous carbon fibre SMC**

The fibre volume content (FVC) of continuous carbon fibre SMC was generally higher than the nominal fibre content for the same reasons as described in section 7.3.1. Due to the continuous reinforcement, which somehow eliminates the effect of TGA specimen size, intraplaque variations were lower than for the discontinuous material (below 5 % with the exception of one sheet). However, thinner sheets were characterised by a higher scatter. A possible explanation might be insufficient impregnation, which was most severe for the thinnest (*h* ≈ 1 mm) sheets, as depicted in Figure 7.2. Dry spots possibly resulted from a too small amount of resin on the upper and lower carrier foil during manufacturing of the semi-finished material. In addition, if pre-curing of the special UPPH resin system is not sufficiently controlled by heating and cooling down the SMC mat on the conveyor belt or due to a too long delay between manufacturing of the semi-finished material and the following compression moulding step, the material may be at risk to dry out. Since dry spots were not observed in such a significant amount on thicker Co CF SMC sheets, re-impregnation of thicker sheets (distribution of resin) might be possible during moulding.

**Figure 7.2:** Dry spots on compression moulded continuous carbon fibre SMC sheet featuring a nominal thickness of 1 mm.

## **7.4.2 Mechanical behaviour and damage evolution of continuous carbon fibre SMC**

### **Coupon level: Tensile, compressive and flexural properties**

Manufacturing of continuous carbon fibre SMC, based on an adopted SMC process, is reliable and leads to a continuous carbon fibre composite with properties comparable to those of conventional unidirectional carbon fibre reinforced polymers (Trauth and Weidenmann, 2016). However, resulting material properties were determined by a significant scatter. Inhomogeneities in the material due to locally insufficient impregnation and thus variations in fibre volume content and fibre misalignment were the most important reasons for the observed scatter. Considering tensile loads, an increasing FVC did not automatically lead to enhanced tensile properties due to the aforementioned detrimental properties of the Co CF SMC sheets. Furthermore, preliminary tests showed that mechanical performance tends to decrease if continuous carbon fibre SMC sheets were stored and mechanically loaded at a later time (Figure 6.4). The complex B-stage evolution combined with variable time frames between manufacturing of semi-finished materials and moulding or between testing campaigns may explain the observed tendencies. However, such investigations were not in the scope of this dissertation, and further investigation must be made to better understand the curing characteristics and ageing effects of Co CF SMC.

The mechanical material performance of the continuous carbon fibre SMC was significantly determined by a tension-compression anisotropy. As commonly stated in the literature (e.g. Serna Moreno et al., 2016; Soutis, 1997), compressive strength was significantly lower than tensile strength. The anisotropy most possibly resulted from shear mode deformation (fibre microbuckling or kinking) (Berbinau et al., 1999; Rosen, 1965). According to Naik and Kumar (1999) kinking is defined as a direct consequence of localised plastic microbuckling, coupled with low failure strain of the reinforcing material. This failure mode was first (analytically) described by Rosen (1965), who stated, that due to the small diameters of the individual fibres, described as slender columns, buckling is highly possible, although the composite may not tend to buckle on the macroscopic scale. A weak radial bond between the fibres further favours this failure mode if the composite is exposed to compressive loads (Hahn and Williams, 1986), and shear properties of the matrix become extremely important (Eyer et al., 2016). In contrast to tensile stiffness and strength, which are fibre-dominated properties of a continuous material, the matrix properties play a more decisive role if a unidirectional composite is loaded in compression. The low compressive strength of the continuous carbon fibre SMC is a limiting parameter in designing hybrid CoDico SMC structures. With a ratio of *Ec*/*Et* ≈ 0.8 and *Rc*/*Rt* ≈ 0.4, deviation between the tensile and compressive stiffness and strength of the investigated continuous carbon fibre SMC was more severe compared to values presented in the literature (e.g. *Rc*/*Rt* ≈ 0.6 (Budiansky and Fleck, 1993). Limited compressive strength also resulted in early failure initiation due to compressive strains during out-of-plane loading of continuous carbon fibre SMC.

As depicted in Figure 7.3, in some cases Co CF SMC was characterised by a significant misalignment of the fibres with respect to axis of the sheet, hence loading direction. Possible sources of the resulting fibre misalignment are the feeding of the dry non-crimp fabric at the beginning of the conveyor belt, a shifting during manufacturing of the semi-finished material or an inaccurate placement of the semifinished sheet on the cutting table or inside the mould, as well as stacking of different layers of the semi-finished material prior to moulding. In addition, extraction of the specimens for mechanical characterisation may also influence the fibre orientation within the specimens. Fibre misalignment significantly affects strength of unidirectionally reinforced composites, especially in terms of uniaxial compression (Wisnom, 1990). In addition, deviations from an ideal parallel fibre orientation of unidirectional fibre-reinforced composite with respect to loading direction reduces resistance to splitting (Hillig, 1994). Observation of failure evolution resulting from uniaxial tension indicated that Co CF SMC characterised by a distinct fibre misalignment likely failed due to the formation of inter-fibre cracks. Cracks were most likely initiated where misaligned fibre bundles met the edges of the specimens. The evolution of the stress-strain curve prior to final failure reflected successive crack formation and growth. If misalignment was not too pronounced, specimens likely failed due to fibre fractures and spontaneous bursting. The failure evolution of continuous carbon fibre reinforced materials usually depends heavily on the fibre matrix interface (Hamada et al., 1997), which might also play an important role in the evolving damage of the investigated Co CF SMC composites within this dissertation, since a weak interface might favour the formation and growth of inter-fibre fractures.

**Figure 7.3:** Macroscopic observation showing fibre misalignment of continuous carbon fibre SMC composite.

Additionally, the microstructure of continuous carbon fibre SMC was characterised by fibre waviness. It was defined by an out-of-plane ondulation resulting from the stitching yarns of the individual layers (Figure 7.4) and the stacking of several semi-finished sheets to obtain moulded plaques featuring different thicknesses. Fibre misalignment and fibre waviness (in- and out-of-plane misalignment) resulted from the organisation of fibres (multiple filaments) in bundles, which were held together by stitching yarns. Fibre waviness generally has a negative influence on material and laminate properties consisting of unidirectional carbon fibre reinforced layers (Adams and Hyer, 1994; Wisnom, 1990, 1999). It influences not only tensile but also compressive properties such that the greater the misalignment, the weaker and more compliant the laminate (Budiansky and Fleck, 1993; Mrse and Piggott, 1993). Simulation of tensile and compressive failure of continuous carbon fibre reinforced materials loaded perpendicular to the fibre direction reveal that the tension fracture initiates as interfacial debonding and evolves as a result of interactions between interfacial debonding and matrix plastic deformation, while the compression failure is dominated by matrix damage (Lei et al., 2012).

**Figure 7.4:** Microscopic observation of continuous carbon fibre SMC (axis 1 is parallel to the fibres) showing ondulation and fibre waviness.

#### **Modelling approaches**

With regard to the aforementioned microstructural particularities, analytical prediction of tensile modulus of elasticity in the fibre direction through the application of a rule of mixtures significantly overestimates the experimentally determined value by 20 %. Indeed, the Voigt bound is the upper bound of a predicted material property, assuming all fibres are perfectly aligned in the fibre direction. A misalignment of fibrous reinforcement decreases the resulting material stiffness, with an increasing misalignment angle. Taking into account that matrix failure strain (*εmax* ≈ 3 %) is higher than (carbon) fibre failure strain (*εmax* ≈ 2 % CES EduPack, 2017), and hence strength prediction according to Figure 2.5a, it was possible to estimate tensile strength of Co CF SMC featuring a FVC of 55 vol.%. With the described approach, analytically determined strength equals ≈ 2300 MPa. The average experimental value of 1424 MPa is 60 % lower. This significant deviation might underline the effect of fibre misalignment, ondulation and dry spots observed for the continuous carbon fibre SMC. In addition, the fibre strength defined by the supplier might be a result of fibre bundle and not single-fibre testing, hence deviating from real fibre properties. Considering the technical data sheet of the supplier, which lists the material properties of the non-crimp fabric in a unidirectional layup, as considered within this dissertation (Zoltek, 2018c), the average strength value of 1440 MPa (FVC of 55 vol.%) is in the same range as the experimentally defined value.

#### **Structure level: Puncture properties**

Puncture properties of carbon fibre reinforced composites show most likely no variation of mechanical performance due to a variation of loading rate (Caprino et al., 2003; Trauth et al., 2018), and a possible explanation might be the non-rate sensitivity of the carbon fibres (Zhou et al., 2010). The continuous carbon fibre SMC composite investigated within this dissertation even exhibited a slightly negative rate dependence in terms of strength and energy absorption capability. The parallel fibre bundles were no important obstacle for the striker, which easily punctured the specimen especially at higher loading rates, hence impacting energies, and failure was brittle and catastrophic.

The resulting force-deflection response, regardless of puncture velocity, was characterised by an increase to maximum load, which was followed by a sudden load drop. Failure was mainly based on the formation and growth of inter-fibre cracks. Once initiated, fractures grew easily and spontaneously. A yield point leading to a slightly decreased slope in the quasi-static loading case, was hence linked to very low deflections (below 1 mm) and indicated the early onset of failure. For this reason, stiffness was defined by fitting the slope of the force-deflection response below a deflection of 1 mm.

In general, impact or puncture testing of continuously reinforced materials is based on laminates featuring a stacking sequence which deviates from a purely unidirectional reinforcement with only 0° plies (e.g. Belingardi and Vadori, 2002 and Li et al., 2002). The architecture of fibrous reinforcement of the Co CF SMC considered within this dissertation is not suitable to sustain puncture loads. However, puncture testing of Co CF SMC within this dissertation aimed to define a reference of puncture properties and to evaluate the effect of hybridisation in a subsequent step. For this reason, the same layup of the continuous carbon fibre SMC, considered for hybridisation (only 0°) was taken into account to deduce puncture properties.

## **7.5 Continuous-discontinuous glass/carbon fibre SMC**

## **7.5.1 Microstructural aspects of continuousdiscontinuous glass/carbon fibre SMC**

The two different SMC composites (Dico GF and Co CF SMC) feature a comparable density of *ρDico* = 1.53 g cm−3 and *ρCo* = 1.50 g cm−3 . Hence, the density of the hybrid SMC had a similar magnitude. Scanning electron microscopy (SEM), *µ*-CT and macroscopic observations enabled investigation of the microstructure of the hybrid CoDico SMC composite (section 6.2). The results most importantly depicted a transition zone between the discontinuous and the continuous material, and no sharp or distinct interface was formed. The material flow of the discontinuous component locally pushed the continuous fibre bundles apart during moulding. The glass fibre bundles' individual fibres spread and separated from the bundles and showed a higher curvature in the transition zone, similar to the microstructure, which was observed for pure discontinuous glass fibre SMC. As known for standard SMC materials, bundle structure was not influenced in the core layers in terms of separation or curvature. Fibre orientation distribution within the discontinuous component of the hybrid SMC was comparable to the evolution of the components of the fibre orientation tensor over thickness of a pure discontinuous glass fibre material (Figure 6.19). Comparable average values were obtained (*Oyy* ≈ 0.6 [flow direction] and *Oxx* ≈ 0.4). The transition zone within the hybrid material featured a thickness of ≈ 0.5 mm (Figure 6.20).

As already discussed by Mallick (1986) and Corbridge et al. (2017), the misalignment of the continuous material, resulting from crossflow of the discontinuous component in a one-shot compression moulding process of hybrid SMC sheets, also negatively affected resulting material properties of the hybrid CoDico GF/CF SMC investigated within this dissertation. Failure evolution due to inter-fibre fracture was favoured by misaligned fibres meeting the edge of the specimen. Taking into account the manufacturing process presented within this dissertation, there was no significant cross-flow of the discontinuous material during moulding of the hybrid SMC sheets. However, hybrid SMC sheets were nevertheless characterised by a significant (local) spreading and fibre misalignment (Figure 6.22). Thus, although the stack of discontinuously reinforced semi-finished material featured the same width as the mould, local cross-flow occurred. Since there was no stabilising mechanism (fixation) perpendicular to the fibre axis, shearing and pushing apart usually occurred between different continuous carbon fibre bundles.

## **7.5.2 Mechanical properties, damage evolution and hybridisation effect**

### **<IP_ADDRESS> Coupon level**

The following section deals with the discussion of mechanical material properties and failure evolution of the CoDico GF/CF SMC at the coupon level. Different criteria to evaluate a hybridisation effect are discussed and the effect of hybridisation in terms of mechanical performance and damage evolution is considered.

#### **Evaluation of hybridisation effects**

The primary objective of hybrid composites is to enhance a distinct property of a material, structure or component which might be of mechanical, physical or thermal origin, for example. Within this dissertation, only mechanical properties were of interest. For this purpose, in terms of uniaxial loads, the effect of hybridisation was evaluated for material properties in the fibre direction of the continuous component. The arithmetic mean value of distinct properties was accounted for (with no difference between charge and flow region specimens) to evaluate the effect of hybridisation (*EoH*2), and the mechanical performance of the Dico GF SMC was considered as a reference. Due to the brittle nature of continuous fibre reinforced composites, failure strain and deflection at failure of the Co CF SMC were considered references to evaluate a possible enhancement of damage tolerance resulting from hybridisation.

Taking a deviation from the rule of mixtures into consideration to evaluate an effect of hybridisation (*EoH*1) is suitable only for uniaxial loadings. In addition, it is important to precisely describe the volume fractions occupied by the individual constituents, as stated by Phillips (1976). The thickness of the investigated hybrid CoDico GF/CF SMC sheets (¯*h* = 2.91 mm) featured only slight variations (*µ* = 0.06 mm, CV = 2.19 %). Nevertheless, the thickness of the continuous reinforcement was characterised by high variations. As depicted in Figure 6.22 and Figure 7.5, the pushing apart of the continuous carbon fibres in the transition zone, even locally, led to a disruption of the continuous reinforcement.

**Figure 7.5:** Section through a compression moulded continuous-discontinuous glass/carbon fibre SMC specimen to depict layered structure, spread carbon fibre bundles and variable thickness of the continuous reinforcement.

The inconsistency of continuous reinforcement, especially, complicated predictions of the material properties. Consequently, a thickness of 2 · 0.33 mm of the face sheets and *h* = 2.91 mm of the laminate was considered (hence (2 · *hf* )/*h* = 0.23) to apply a rule of hybrid mixtures according to Equation 5.44. Furthermore, a variation of ± 0.05 mm was considered to define scatter whilst modelling material properties.

### **Tensile modulus of elasticity and tensile strength**

When characterising hybrid composites, it is generally not recommended to measure displacements with strain gauges or an extensometer, since these techniques do not account for the variability of locally different material properties resulting from the anisotropic and heterogeneous microstructure of the material (Feraboli et al., 2009). Digital image correlation, however, provides an appropriate measurement technique to account for microstructural heterogeneities (Johanson et al., 2015; Selezneva and Lessard, 2015). It also offers a possibility to investigate damage evolution (Laurin et al., 2012). This contactless measurement technique also provides the important advantage, that a partial failure does not lead to distorted strain measurements which could result from a measurement with devices which have contact with the specimen (e.g. an extensometer). The following discussion of mechanical performance within this section is based on the results and findings presented in section 6.3.3.

As clearly indicated in Figure 7.6, which sums up the tensile properties of the two individual and the hybrid SMC composites, a linear correlation was observed for tensile modulus of elasticity and tensile strength due to hybridisation.

**Figure 7.6:** Tensile properties of continuous carbon fibre SMC, discontinuous glass fibre SMC and continuous-discontinuous glass/carbon fibre SMC to evaluate the hybridisation effect (• = median, box indicates 25*th* to 75*th* percentile; lines indicate minimum and maximum or 1.5 interquartile range, respectively).

Hybridisation of SMC composites within this study led to a significantly increased **tensile modulus of elasticity** (+169 %).

Earlier attempts to hybridise SMC materials also showed hybridisation effects in terms of tensile stiffness. With combined reinforcement based on chopped and continuous glass fibres, the tensile modulus of elasticity significantly increased with the increasing content of the continuous component. For a ratio of the two components comparable to the ratio of the hybrid SMC composites investigated within this dissertation, a unidirectional reinforcement resulted in an average stiffness increase of 57 % (Sridharan, 1982). The effect of hybridisation was less pronounced than in the results of the present study, since only glass fibres were considered as reinforcement, featuring a significantly lower tensile modulus of elasticity compared to carbon fibres.

Sridharan (1982) pointed out that the ratio of continuously and discontinuously reinforced plies forming an interlayer hybrid SMC is the factor most responsible for the resulting stiffness of the hybrid material. The increase of stiffness was proportional to the volume content of the continuous component. Investigations by Trauth and Weidenmann (2016) resulted in a stiffness increase of 284 % if the ratio of continuous/discontinuous SMC was 1:2 and the continuous material was placed in the middle. For a ratio of 2:1 with two continuously carbon fibre reinforced face sheets, the stiffness increase was more substantial (647 %). A two-sided reinforcement of a standard SMC composite (based on a mixture of thermoset and thermoplastic resin system with 30 wt.% of glass fibres and 46 wt.% of fillers) by non-crimp carbon fibre fabrics in ± 45° configuration, led to a stiffness increase of 125 % (Gortner et al., 2015a). The effect of continuous reinforcement of the hybrid CoDico SMC investigated within this dissertation was more distinct. With a nominal thickness of the hybrid SMC sheets of 2 – 3 mm considered by Gortner et al. (2015a) and the thickness of each layer of the ± 45° reinforcing layers of ≈ 400 µm, the ratio of (2 · *hf* )/*h* equalled 0.27 – 0.4 in the cited publication. Although this ratio of (2 · *hf* )/*h* was slightly higher compared to the hybrid material considered within this study, the lower increase of stiffness resulted from the orientation of the carbon fibres, which were not aligned in loading direction (± 45°).

A combination of a glass fibre SMC (based on an unsaturated polyester, with either 25 or 50 wt.% of glass fibres and a significant amount of fillers) with pre-impregnated carbon fibres, in a woven configuration, led to a stiffness increase of 20 % and 41 %, respectively. If unidirectional pre-impregnated carbon fibres were considered, the increase of tensile modulus was more distinct (100 %, 200 %) due to the alignment of carbon fibres in loading direction (Wulfsberg et al., 2014). No indication was made concerning ratio between the continuous and discontinuous components; hence, a direct comparison with the results obtained within the present dissertation is not possible.

The approach to hybridise SMC composites presented within this dissertation led furthermore to an almost tripled **tensile strength** (193 %, Figure 7.6). Given the aforementioned references, this effect was more distinct, as compared to a hybrid SMC composite reinforced solely by glass fibres (124 %, Sridharan, 1982). A hybridisation based on two ± 45° non-crimp fabrics increased tensile strength by 350 % (Gortner et al., 2015a). At a first glance, this value seems more remarkable compared to the results achieved by the hybridisation approach described within this dissertation, but with an average tensile strength of only ≈ 40 MPa of the pure discontinuous glass fibre SMC, the reference value to determine the effect of hybridisation was decisively lower.

A woven carbon fibre pre-impregnated fabric increased the tensile strength of discontinuous glass fibre SMC, featuring a fibre content of 25 wt.%/ 50 wt.%, respectively, 17 % and 33 %. A unidirectional carbon fibre pre-impregnated fabric increased tensile strength of the same discontinuous glass fibre SMC composites 167 % and 200 %. The architecture and orientation of the continuous reinforcement determined effect of hybridisation (Wulfsberg et al., 2014). Considering a unidirectional reinforcement and a discontinuous glass fibre SMC featuring a FWC of 50 %, hybridisation was in the same range as the results of mechanical characterisation of the UPPH-based CoDico GF/CF SMC.

### **Modelling of tensile properties**

A rule of hybrid mixtures (Equation 5.44), based on the properties of the individual components, was already frequently considered to determine and predict the stiffness of hybrid short fibre reinforced composites (Fu et al., 2000, 2001), particle-short fibre hybrid composites (Fu et al., 2002), hybrid composites based on a combination of unidirectional fibres and fabrics (Ikbal et al., 2016) and continuous fibre hybrids (Swolfs et al., 2014). As yet, little attention has been paid to analytical modelling of interlayer hybrid composites based on both continuous and discontinuous fibrous reinforcement.

Based on the experimental results of this dissertation, a rule of hybrid mixtures, presented in 5.44, enabled accurate prediction of the tensile stiffness of a hybrid CoDico SMC (Figure 6.105). If a ratio of (2 · *hf* )/*h* = 0.23 is considered, the analytically predicted stiffness value of 35.3 GPa matches very well with the experimentally determined value (Figure 6.49).

Presented by Zweben (1977), early attempts to predict the tensile strength of hybrid materials, derived from a combination of different fibre types in unidirectional configuration, were based on statistical analysis of failure mechanisms. A more basic estimation of the strength of a hybrid composite exposed to uniaxial loads may follow the rule of hybrid mixtures (presented in section 5.4.1), with the components *PC*1 and *PC*2 referring to the strength of the two individual fibre reinforced materials combined in a laminate. However, as stated by Manders and Bader (1981), for instance, it is highly possible that in hybrid composites which feature only a low amount of the stiffer and more brittle component, where the predominating fraction is based on the less stiff and more ductile component, the hybrid might be able to carry additional loads after the brittle component has failed. Hence, a bilinear rule of hybrid mixtures might be more appropriate to estimate the strength of hybrid interlayer composites.

A bilinear rule of mixtures was already successfully applied to predict strength of hybrid materials based on a combination of different unidirectionally arranged fibre types (Manders and Bader, 1981). Recently, it was also considered to predict strength of hybrid glass/carbon composites reinforced by two different types of woven fabrics (plain weave glass and twill weave carbon) (Zhang et al., 2012) or satin weave carbon and plain weave glass fibre fabrics (Pandya et al., 2011). The approach of a bilinear rule of hybrid mixtures is now extended to hybrid composites based on continuous and discontinuous fibre reinforcements. The homogenised properties of the two components are considered as input parameters. Basically, the strength of a hybrid composite (*σhyb*,*max*) exposed to uniaxial in-plane loads, can be described according to the model presented in Figure 2.5a. The tensile strength for low fractions of the low elongation fibrous reinforcement *C*1 (in the case of this dissertation corresponding to the Co CF SMC face sheets) equals

$$
\sigma\_{\text{hyb},\text{max}} = \sigma\_{\text{C2},\text{max}} \cdot (1 - \phi\_{\text{C1}}) \, \tag{7.1}
$$

with *σC*2,*max* the tensile strength of *C*2 and with *φC*1 the volume fraction of component *C*1. If the volume fraction of *C*1 increases, the strength of the hybrid composite is equal to

$$
\sigma\_{\text{hyb},\text{max}} = \sigma\_{\text{C1},\text{max}} \cdot \phi\_{\text{C1}} + \sigma\_{\text{C2}} (\varepsilon\_{\text{C1},\text{max}}) \cdot (1 - \phi\_{\text{C1}}).\tag{7.2}
$$

Generally, *C*1 features a lower failure strain than *C*2, and *εC*1,*max* represents the failure strain of the brittle component *C*1. The term *σC*2(*εC*1,*max*) refers to the stress within component *C*2 at the moment of failure of component *C*1, equal to the strain *εC*1,*max*, and is calculated by applying Hooke's law, hence assuming linear elastic behaviour of *C*2 up to failure of *C*1. This is an idealised assumption. The presented bilinear rule of hybrid mixtures predicted a tensile strength of 459 MPa of the CoDico GF/CF SMC. This value slightly underestimate the experimentally determined value, and a positive hybridisation effect (13 %) can be stated, as clearly depicted in Figure 7.7.

Analytically predicted tensile strength based on a linear rule of mixtures did not significantly differ from the strength value determined with a bilinear rule of mixtures since no important variation between failure strain of Dico GF and Co CF SMC resulted from uniaxial tension. The predicted tensile strength equalled 464 MPa (positive hybridisation effect of 12 %). The average value as well as the 25*th* and the 75*th* percentile are depicted to account for variations in mechanical performance and the strength of the individual components. For the sake of clarity, only average values are depicted to calculate the linear rule of hybrid mixtures.

**Figure 7.7:** Prediction of tensile strength of hybrid continuous-discontinuous glass/carbon fibre SMC based on a linear rule of hybrid mixtures (RohM) and a bilinear rule of hybrid mixtures (bilinear RohM) with rectangle and error bars indicating experimentally determined values.

The strength of CoDico GF/CF SMC composites was mainly determined by the continuous component. Minimal and critical content of the reinforcing continuous material (equivalent to minimal and critical fibre content in a composite, defined by Kelly and Davies (1965), were extremely low. As depicted in Figure 7.8, stress-strain evolution of the hybrid CoDico SMC composite was mainly determined by the continuous carbon fibre SMC and showed a linear increase up to brittle fracture.

**Figure 7.8:** Representative stress-strain curves of discontinuous glass fibre, continuous carbon fibre and continuous-discontinuous glass/carbon fibre SMC resulting from uniaxial tension.

Small load drops (Figure 6.51), which resulted from partial failure of some specimens, did not influence the overall evolution of the stress-strain curve. The **tensile failure strain** of CoDico SMC composites was increased (15 % compared to failure strain of continuous carbon fibre SMC). In terms of hybrid composites, this effect is often described as pseudo-ductility (Hayashi, 1972). According to Ikbal et al. (2016), the hybrid structures may show some ductility because of their mixture of a certain amount of brittle carbon fibres combined with ductile glass fibres. Exhibiting a slightly enhanced tensile failure strain of the discontinuous SMC composite, damage evolution in continuous carbon fibre reinforced parts of the material is constrained because of surrounding glass fibres. Hence, the carbon fibre reinforced part of the hybrid material may sustain greater strain before failure, and the (tensile) failure strain of hybrid configuration increases. However, ductility in general refers to a more gradual failure evolution. Considering that final failure of hybrid CoDico GF/CF SMC composites was still characterised by a catastrophic and brittle failure, pseudo-ductility, as defined by Swolfs et al. (2014), for example, might not be the appropriate term, and enhancement of failure strain is a better description of the observed effects.

### **Failure evolution resulting from uniaxial tension**

Fibre orientation (misalignment) and inconsistency of the continuous face layers (pushed apart, leading to resin-rich regions) significantly determined the failure evolution of hybrid CoDico GF/CF SMC composites. For the investigated hybrid CoDico SMC composites, tensile failure stems from on a combination of damage mechanisms, characteristic of the discontinuous and the continuous components. As clearly depicted in Figure 7.8, no stiffness degradation, characteristic of the discontinuous component and resulting from evolving damage, was observed for the hybrid CoDico GF/CF SMC. Failure within the discontinuous glass fibre SMC, hence crack formation and growth, which might nevertheless be possibly present within the specimen, did not influence the global stress-strain response of the hybrid CoDico GF/CF SMC in a significant way. In the end of loading, the discontinuous component failed due to pseudodelamination between different bundles, and the failure of the continuous phase was mainly defined by fibre fractures for small angles of misalignment. Damage was more likely to be defined by inter-fibre fractures and splitting for larger angles of misalignment. In addition, (intra- and interlayer) delamination occurred. The superposition of failure mechanisms, characteristic of the individual components of a hybrid material has already been observed for comparable hybrid materials (Selmy et al., 2011).

The specific carbon fibre bundle structure, hence the characteristic pattern of the stitching yarns, significantly influenced evolving strains of the continuous carbon fibre SMC (Figure 7.9) and led to a locally highly heterogeneous strain field if the pure Co CF was loaded in tension. In contrast, the strain field of hybrid CoDico GF/CF SMC could most likely be described as homogeneous in the loading direction.

The resulting strain field (*εxx*) was thus strongly influenced by the discontinuously reinforced core layers. Local crack initiation and growth, characteristic for the failure of Dico GF SMC (Figure 6.34 and 6.35), was not observed at the surface layer of the hybrid CoDico SMC, and the resulting strain field remained globally and qualitatively homogeneous up to fracture. In contrast, transverse strains (*εyy*) were characterised by a highly heterogeneous evolution. Driven by slightly different Poisson's ratios of the continuous and discontinuous material (Co CF SMC: *νt* = 0.32 and Dico GF SMC *νt* = 0.38), differences in transverse strain, as clearly depicted in Figure 7.9 might be explained, resulting furthermore from inconsistent continuous reinforcement in the shell layers. In addition, the pushing apart of the carbon fibre bundles resulted in locally not continuously reinforced specimens, so transverse strains in these locations depend on the properties of the discontinuous material.

**Figure 7.9:** Strain fields resulting from uniaxial tension of discontinuous glass fibre SMC, continuous-discontinuous glass/carbon fibre hybrid SMC and continuous carbon fibre SMC corresponding to a global average strain *εxx*,*global* ≈ 1 %.

#### **Compressive modulus of elasticity and compressive strength**

The compressive stiffness and strength of Dico GF SMC, Co CF SMC and CoDico GF/CF SMC are summarised in Figure 7.10.

The investigated hybrid CoDico GF/CF SMC composite exhibited a significant increase in **compressive modulus of elasticity** (143 %). The resulting stiffness could accurately be predicted by a rule of hybrid mixtures described in Equation 5.44 and depicted in Figure 6.105. The effect of hybridisation was less significant than for a vinylester-based discontinuous glass fibre SMC reinforced by layers of continuous carbon fibre SMC (based on unsaturated polyesterpolyurethane resin system). The described hybrid laminates, investigated by Trauth and Weidenmann (2016), were characterised by an increase of compressive modulus of elasticity of 240 % and 680 %, depending on the ratio of continuous-discontinuous material, respectively. Comparable to tensile properties, the effect of hybridisation on material's stiffness depended strongly on the ratio of the combined materials, with the continuous material dominating the enhancement of the global stiffness. In general, specimens investigated by Trauth and Weidenmann (2016) featured thicker continuous face layers with a ratio of (2 · *hf* )/*h* ≈ 0.3 – 0.6; therefore, enhancement of material's stiffness was more significant than in the results presented within this dissertation. Since the continuous carbon fibre SMC exhibited an anisotropy in terms of tensile and compressive properties, compressive modulus of elasticity of the hybrid CoDico GF/CF SMC was also slightly lower than the tensile counterpart, and *Ec* = 0.86· *Et* held true for the hybrid CoDico SMC.

A hybridisation of the investigated SMC composites did not affect the **compressive strength** of the discontinuous SMC. A similar effect was stated by Ikbal et al. (2016) considering the compressive strength of a hybrid (unidirectional) glass and carbon fibres reinforced composite. A slight decrease of 2 % of compressive strength was even observed (Dico GF SMC *Rc* = 298 MPa and hybrid CoDico GF/CF SMC *Rc* = 292 MPa). This difference, however, resulted more likely from scatter in material properties of the two components. In contrast, Trauth and Weidenmann (2016) reported an increase of 63 % and 136 % considering the compressive strength of a hybrid CoDico SMC laminate. The specific layup, which consisted of several layers of the continuous carbon fibre reinforced prepreg considered as face layers significantly increased compressive strength within the aforementioned study.

**Figure 7.10:** Compressive properties of discontinuous glass fibre SMC, continuous carbon fibre SMC and continuous-discontinuous glass/carbon fibre SMC (• = median, + = mean, box indicates 25*th* to 75*th* percentile; lines indicate minimum and maximum or 1.5 interquartile range, respectively, ◦ = outlier).

In contrast, face sheets within this present dissertation consisted of only one layer of continuous carbon fibre reinforced prepreg. This approach resulted in a lower damage tolerance of the Co CF SMC exposed to uniaxial compression. A positive hybridisation effect in terms of compressive strength (increase of ≈ 10 %) was also reported by Pandya et al. (2011), based on investigation of the mechanical performance of hybrid materials made from unidirectional glass and carbon fibres.

#### **Modelling of compressive properties**