**3.1 Properties of PET**

PET is a thermoplastic with high resistance to most solvents, weak acids, and bases; strength; gloss; high impact resistance; and hardness [73]. It is also resistant to many other chemicals such as hexane, methanol, sulfur dioxide, and solutions with low acid concentrations [74–76]. The physical and chemical properties of PET are examined in **Table 3**; it is a valuable hydrocarbon containing 62% C, 4% H, and 34% O and has a high calorific value. PETs are self-extinguishing and have very low gas permeability, good adhesion and weldability, high hardness, good refractive index, and good resistance to ultraviolet [89]. They have very low O2 and water permeability

#### **Table 3.**

*Physical and thermal properties of PET.*

## *Mechanical and Thermal Properties of HDPE/PET Microplastics, Applications, and Impact… DOI:http://dx.doi.org/10.5772/intechopen.110390*

compared to most plastics (PS, PVC, etc.) [97]. The thermal conductivity of PET is also very low compared to PLA, ABS, HDPE, PP, and PA. Although it is a fairly transparent and colorless material, it usually appears opaque and off-white as the thickness increases. Depending on the thermal and process conditions, it can be found in semicrystalline or amorphous form. Because of this, it may appear dull, white, or glassy. It depends on process parameters such as crystal structure, processing temperature, cooling rate, and stretching. Crystallization is an important parameter that affects the properties of polymers. The benzene ring in the main chain of PET provides both slow crystallization during cooling and hardness. This adversely affects the spinning process of high-speed fibers [98]. Glass transition temperature (Tg) is an important value that affects the material properties and potential applications of a polymer [99]. Mechanical properties (deformation modulus, etc.) and physical properties (density, volume, specific heat, etc.) of polymers in glass transition state are not. Due to the Tg temperature, PET loses its glassy property and becomes viscous at 67–80°C; its cold crystallization (Tcc) is in the range of 115–140°C, melting temperature is 248–250°C, and enthalpy of melting (∆Tm) is 35–50 J/g; its hot crystallization temperature (Tc) is 194–205°C, and its enthalpy (∆Tc) is 29–55 J/g (**Table 3**) [100]. PETs begin to thermally degrade at temperatures above 340°C [101]. Although the melting temperature (Tm) of PET is not as high as PEEK (334°C), it is higher than that of PP (170°C), LDPE (134°C), PS (106°C), and PVC (199°C) [102].

PETs have excellent mechanical properties, creep resistance, fatigue resistance, friction resistance, and dimensional stability over wide temperature ranges (**Table 4**) [99, 110]. However, the disadvantages of slow crystallization rate, machining difficulties, high molding temperature, and poor impact

#### **Table 4.** *Mechanical and electrical properties of PET.*

performance limit their use [111]. The storage modulus of PET, which is the plastic deformation energy of a polymeric material, is 2000–4200 MPa at 25°C and 242 MPa at 80°C [112]. Tensile strength, flexural strength, Young's modulus, elongation at break, impact strength, flexural modulus, and hardness of PET are approximately 40–60 MPa, 55–100 MPa, 1000–3500 MPa, 19–46 MPa, 4.6 kJ/m2 , 2000–3500 MPa, and 96, respectively (**Table 4**). PET's tensile strength (26 MPa) at 77 K is higher than PA (14.5 MPa), PC (13.5 MPa), Teflon (4.3 MPa), and PVC (9.5 MPa), and its elongation at break value is higher than theirs [113].

Dielectric is an important property of insulating materials. When an ever-increasing voltage is applied to an insulating material, it eventually reaches a point where its electrical properties deteriorate, causing a drop in resistance, and it begins to lose dielectric strength. PET shows a dielectric property of 150–200 kV/cm (**Table 4**).

### **3.2 PET applications**

PET has wide use in many fields (packaging, textile, medical, etc.) due to its satisfactory properties [114–116]. In fact, PETs that have completed their useful life (waste) are ground to micron sizes and used as concrete additives [117]. Micro PETs are generally produced and used in spherical and fibrous structures [118]. They are used in protective fabrics, filters, wound dressings, drug delivery, and scaffolds [119–121]. Because of PET's properties such as biocompatibility, high uniformity, mechanical strength, and chemical resistance, it has been successfully used in vascular prostheses for large vascular grafts and in various surface modification methods to improve the cell adhesion properties (**Figure 4a**) [127]. PETs are also used in a variety of biomedical applications such as implants, heart valves, sutures, scaffolds, surgical nets, and urinary and blood circulation catheters [122, 128]. Micro PET fibers are the most widely used synthetic fibers in textile yarn production, and their consumption is expected to be 50 Mton/year by 2050 (**Figure 4b**) [129, 130]. However, although PET's usage has become widespread in many special applications (**Figure 4a** and **b**), it is mostly used in food and beverage packaging (**Figure 4c** and **d**) [131].

**Figure 4.**

*PET applications (a) vascular prostheses [122, 123] (b) carpet [124] (c) beverage bottles [125] (d) food packaging [126].*

*Mechanical and Thermal Properties of HDPE/PET Microplastics, Applications, and Impact… DOI:http://dx.doi.org/10.5772/intechopen.110390*

### **4. The formation of mHDPE and mPET in nature**

HDPE microplastics (mHDPE) and PET microplastics (mPET) are discharged into the environment in two ways [132]. The first of these is that they are fabricated by producers in <5 mm dimensions in the form of granules, powders, or pellets for later use in applications [133]. During the production process and during their use in the application areas, they are discharged into the environment through the disposal in air, wastewater, and other waste. The second is formed by the degradation of HDPEs and PETs under environmental conditions, which have reached the end of their useful life and are collected directly into the environment as waste or in municipal waste collection areas [134]. In nature, HDPE and PETs are resistant to chemical degradation and take decades for theenvironmental residues to decompose completely [135]. This degradation is the reduction of molecular weight as a result of chemical changes in the structure of the polymer [136]. Waste HDPE and PET exposed to sunlight undergo photooxidation as a result of the absorption of high-energy wavelengths of the ultraviolet (UV) spectrum [137]. As long as decomposition continues in the presence of oxygen, temperature-dependent thermo-oxidative reactions may occur. In addition, degradation may occur due to both biological and mechanical stresses. As a result, these decomposed HDPE and PET wastes become brittle and gradually break up into smaller pieces of micron size [138].

Photodegradation is one of the common degradation processes of polymers, which provokes cross-linking and chain scission reactions [139]. In the photooxidation mechanism that occurs during the UV-irradiation period, first carbonyl groups are formed; then, vinyl and hydroxyl/hydroxyperoxide groups are formed, and these chemical changes can be observed by FTIR spectroscopy [140, 141]. In the FTIR spectra of HDPE, its peaks are occurred at 3300–3600 cm−1 of hydroxyl groups (∙OH), 1700–1800 cm−1 of carbonyl groups (>C〓O), and 1600–1650, 989 and 908 cm−1 of vinyl groups (∙C〓C∙) [142, 143]. The effect of UV irradiation on polymers, carbonyl, vinyl, and hydroxyl groups is studied as an indicator of polymer basic scission [144]. Since the main photooxidation product groups of HDPE are carbonyl and vinyl, the effect of UV radiation can be examined by looking at the carbonyl index and vinyl index [145]. When HDPEs in thin film form are exposed to UV irradiation at 280 nm at a light intensity of 500 W/m2 at 25°C and 50% constant relative humidity, the carbonyl and vinyl indexes increase over time [139, 142]. After 30 days, the carbonyl and vinyl indexes of HDPE increase significantly [61, 140, 144]. As a result, it can be said that waste HDPEs, which are exposed to UV irradiation in nature, start to decompose after 30 days and turn into smaller particles. However, the carbonyl index of PET does not change significantly over time [146]. It can be said that PET is more resistant to UV irradiation than HDPE. In short, waste PETs take more time to decompose in nature by UV irradiation compared to HDPE.

The degradation of plastics, which exist as waste in nature, by using microorganisms is of great interest. Biological agents (bacterial and fungal species) and their metabolic enzymes, which are abundant in nature, have different degradation abilities for natural and synthetic polymers [147]. The biodegradation process of HDPE in nature is quite slow [148]. Therefore, it is necessary to recover HDPE wastes by appropriate methods such as physical, chemical, and biological processes [149]. Moog et al. [150] highlighted the potential for biodegradation of waste PETs and stated that PET substrates under varying conditions have enzyme functionality, secretion, and production of recombinant proteins. Shabbir et al. [151], in their experimental

study with PE, PET, and PP microplastics, stated that there was weight loss in all MPs, indicating structural, morphological, and chemical changes, and confirmed this situation with SEM and FTIR analyses. Farzi et al. [152] investigated the biodegradation of mPETs by streptomyces bacterial species at laboratory scale and stated that the degradation is slow compared to physicochemical methods, and additional physical/ chemical methods should be applied to increase the degradation rate. The biodegradation of 500 m particle size HDPE under laboratory conditions is approximately 10% in 24 days [153].

Mechanical degradation of polymers is typically limited to chain scission [154]. As given in **Tables 2** and **4**, due to the good mechanical properties of PET and HDPE such as tensile strength and elongation at break, they are slow to decompose as waste by mechanical forces in nature.

However, although the mechanical, biological, and chemical degradation times of mPET and mHDPE, which exist as waste in nature, are long separately, this time becomes shorter when it is considered that they occur together. As the use of PET and HDPE increases day by day, it creates more waste in nature, and accordingly, more microplastics are formed.

### **4.1 The effect of mHDPE and mPET on nature and life**

Plastics are the most useful synthetic polymers used in packaging industries, agriculture, household applications, and many similar applications [155]. The unpredictable use of these synthetic polymers leads to an ever-increasing accumulation of solid waste in the natural environment [156]. This causes soil and water pollution at alarming rates, affecting the natural system and creating various environmental hazards [157]. Plastics, which are resistant to environmental influences, are seen as an environmental threat. MPs, both leaching into the environment in micron sizes during the production and usage processes by the manufacturers and occurring as small-sized plastic particles by the degradation of plastics found as waste in the environment, can lead to potential ecotoxicological effects [158, 159]. In general, the densities of microplastics found in nature vary in the range of 0.8–2 gcm−3. The microplastic particle has the average weight of 12.5 μg, volume of 0.011 mm3 , and density of 1.14 gcm−3 [160]. Therefore, MPs can enter the body through airborne inhalation and food intake, which exist in many places in atmospheric environments today. When inhaled, they may cause inflammation or other biological responses in the lung [161]. In addition, they can cause health effects such as genotoxicity, which is due to the desorption of pollutants associated with polycyclic aromatic hydrocarbons (PAH); reproductive toxicity, which is due to the plastic itself and additives (plasticizers, dyes, etc.); mutagenicity; and carcinogenicity [161, 162]. Khalid et al. [163] stated that there are various inorganic and organic chemicals absorbed on MPs and that this poses a greater threat to living things than to MPs. In addition, MPs affect some plant community structure [164]. Issac et al. [165] stated that PE (about 54%) is the most abundant microplastic floating in the ocean.

Cheng et al. [166] investigated the effect of HDPE (25 μm) and PP (13 μm) microplastics on earthworms (*Metaphire guillelmi*) using Nile red fluorescent staining and observed ingestion by earthworms exposed to HDPE and PP microplastics. PP microplastics significantly reduced bacterial diversity and changed the bacterial community structure in the soil. Bringer et al. [167] exposed oyster embryos to different sizes of mHDPE for 24 hours and observed that the mHDPEs bind to the locomotor eyelashes of oyster D-larvae, influencing the swimming activity and development

*Mechanical and Thermal Properties of HDPE/PET Microplastics, Applications, and Impact… DOI:http://dx.doi.org/10.5772/intechopen.110390*

of oyster D-larvae. Kim et al. [168] conducted an experimental study using the *nematode caenorhabditis elegans* and zebra fish to determine the effects of mHDPEs on human health. They stated that it affected *caenorhabditis elegans* reproduction and zebra fish larval death at a concentration of more than 200,000 particles/mL. Jemec et al. [169] observed that mpETs, formed by abrasion and washing of textiles, were ingested by daphnia magna and increased the death rate of daphnia magna in their guts. Shen et al. [170] observed that the higher the concentration of mPETs, the more pronounced was the negative effect on *Drosophila*, with reduced egg production of the female flies and lower lipid, glucose content, and starvation resistance of the male flies. Najahi et al. [170] studied the effects of mPETs on human bone marrow mesenchymal stromal cells and adipose mesenchymal stromal cells. They found that it caused an approximate 30% reduction in proliferating cells associated with the onset of senescence or an increase in apoptosis.

Existing studies on mPETs and mHDPEs show that there is a lot of evidence that these wastes have a negative impact on living life. However, this does not cover all living things. Weber et al. [171] investigated the effect of the freshwater invertebrate amphipod *Gammarus pulex* exposed to mPETs for 48 hours and observed that the survival, development, metabolism, and nutritional activity of *Gammarus pulex* did not change significantly depending on the amount of mPET and the age of *Gammarus pulex*.

### **5. Conclusions**

Microplastics are pollutants that accumulate in large quantities in the environment with each passing day and cause significant pollution. In addition to leaking into the environment during the production and usage processes of MPs, they can be formed by the mechanical, thermal, and biological decomposition of plastics, which are discharged into the environment after the completion of their useful life. HDPE and PETs, which have significant usage and application areas among plastics, have a very long life in the natural environment due to their chemical and mechanical resistance. In the current studies, it was seen that mHDPEs and mPETs indirectly or directly affect the habitat characteristics of living things and basic ecosystem functions. mHDPEs and mPETs can affect the living organism in which they are infested directly with their function and properties, as well as with the impurities they absorb. Although mPETs and mHDPEs do not cover all living organisms in the world, they adversely affect life and the environment. However, more scientific studies are needed to predict this situation.

### **Conflict of interest**

The authors declare no conflict of interest.

*Advances and Challenges in Microplastics*


**4. IFEM**

According to the concept of CM, the residual stress existing in welded specimens can be calculated through the measured out-of-plane displacement normal to a plane of interest. Several assumptions are made in the linear elastic finite element analysis: (1) small displacements or deformations of the welded components or structures, (2) linear elastic behavior during the material removal, and (3) unchanged boundary conditions during loading process. Therefore, it can be defined as an inverse finite element method (IFEM). In general, a set of linear equation below describes the welded components or structures in the linear elastic finite element:

$$[K][\mu] = [F] \tag{4}$$

ensuring computation accuracy when carrying out transient welding temperature

*Simulation model and weld sequence of butt welded joint: (a) without considering back-gouging; (b) with*

*Residual Stress Evaluation with Contour Method for Thick Butt Welded Joint*

*DOI: http://dx.doi.org/10.5772/intechopen.90409*

In principle, plastic strain is the generation source of welding residual stress, which is mainly determined by the maximum welding temperature and restraint condition. Here, the restraint condition is not considered, and the maximum welding temperature distribution is used to describe the features of welding temperature field of the butt welded joint. During the thermal analysis of the butt welded joint, the initial temperature is assumed to be 20°C. To simulate the heat input of moving welding arc during welding, the volumetric heat source with uniform density distribution is employed. For this heat source, the welding arc energy is dependent on the welding current, voltage, speed, and arc efficiency. When the welding process is SMAW, the arc heat efficiency is 0.6 and the welding arc length is 30 mm. And the heat source volume denoted the considered weld pool volume and can be obtained by calculating the volume fraction of the elements in currently being welded zone. The nonlinear isotropic Fourier heat flux was also employed for heat conduction. The temperature-dependent thermal properties such as thermal conductivity, specific heat, and density are considered. **Figure 9** presents the fusion zone in middle cross-section of the butt welded joint with or without considering back-gouging. The simulated fusion zone is slightly greater than the Xgroove area, while the maximum temperature is approximately 2300°C. Comparing to the macrostructure of the butt welded joint, the fusion zone with considering back-gouging agrees better than that without considering back-gouging. Therefore,

nonlinear heat transfer computation.

*5.1.1 Root weld*

**115**

*considering back-gouging.*

**Figure 8.**

$$\begin{array}{c} |K| = \\\\ \frac{E}{(1-2\nu)(1+\nu)} \begin{bmatrix} \frac{\partial^{2}(1-\nu)}{\partial x^{2}} + \left(\frac{\partial^{2}}{\partial y^{2}} + \frac{\partial^{2}}{\partial x^{2}}\right) \frac{(1-2\nu)}{2} & \frac{\partial^{2}}{2\partial x\partial y} & \frac{\partial^{2}}{2\partial x\partial x} \\\\ \frac{\partial^{2}}{2\partial x\partial y} & \frac{\partial^{2}(1-\nu)}{\partial y^{2}} + \left(\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial x^{2}}\right) \frac{(1-2\nu)}{2} & \frac{\partial^{2}}{2\partial y\partial x} \\\\ \frac{\partial^{2}}{2\partial x\partial x} & \frac{\partial^{2}}{2\partial y\partial x} & \frac{\partial^{2}(1-\nu)}{\partial x^{2}} + \left(\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}}\right) \frac{(1-2\nu)}{2} \end{array}$$

where *E* is the Young's modulus, 210 GPa, *υ* is Poisson's ratio, 0.3, ½ � *K* is the stiffness matrix of the welded component or structure, ½ � *u* is the matrix of nodal displacements, and ½ � *F* is the matrix of external nodal force.


*1.4. Contributions*

This work tries to answer these research questions from the development of a novel multi-objective approach where the robots, when selecting their targets, are always considering travelling costs and the opportunity cost of keeping connected or regaining connectivity. A simple yet useful model for the signal strength and attenuation effects provide the robots with connectivity awareness. Thereupon, connectivity level measurements and path costs are considered together into a *task utility* function for finding solutions with a right balance between the benefit of visiting the closer targets and the usefulness of keeping the team connectivity level as high as possible.

For the sake of robustness, a decentralised approach is followed. Robots make decisions asynchronously addressing coordination implicitly through localisation and mapping data exchanging. The human operator is asked to use his application-field expertise to play a part in the task assessment process.

The main contributions of this proposal can be summarised as follows.


**13. β-fibrinogene 455G/A gene polymorphism**

Various studies have been conducted to investigate the relationship between β-fibrinogen 455G/A polymorphism and ischemic stroke in different populations. In a study conducted by Kessler et al., the AA genotype of the β-fibrinogen 455G/A polymorphism was more observed in patients with major vascular infarction. In a study conducted by Nishiuma et al., in a Japanese population, A allele of β-fibrinogen 455G/A polymorphism was identified as an independent risk factor for hypertensive patients. In a study conducted by Martiskainen et al., a significant association was found between the A-allele and the lacunar infarction susceptibility in the β-fibrinogen 455G/A polymorphism. In a study conducted by Zhang et al., in the Chinese population, β-fibrinogen 455G/A polymorphism was found to be a genetic risk factor in the development of ischemic stroke. There are some meta-analysis studies showing that β-fibrinogen 455G/A polymorphism is associated with ischemic stroke in Chinese or Asian populations. A number of studies have been conducted to determine the association between this polymorphism and ischemic stroke, but no study has shown genetic effects in the pathogenesis of cardioembolic stroke in AF patients. The role of β-fibrinogen 455G/A polymorphism in cardioembolic stroke pathology is unclear. Promoter elements play an important role in regulating gene transcription. Transcription factor binding sites and transcription initiation rates can be varied by a promoter variant. β-fibrinogen 455G/A polymorphism has an important stimulatory effect on the rate of basal and induced transcription rate of the β-fibrinogen gene. There is a significant association between A allele of this polymorphism and increased promoter activity. β-Fibrinogen 455G/A polymorphism is one of the genetic polymorphisms associated with an increase in plasma fibrinogen. The increase in fibrinogen levels of individuals with A allele is greater than the increase in fibrinogen levels of individuals with G allele. Therefore, A allele of β-fibrinogen 455G/A polymorphism was found to be associated with higher fibrinogen level. Platelet aggregation, fibrinogen, an important determinant of blood viscosity, is a component that plays a role in the coagulation cascade. As a result of elevated fibrinogen levels, thrombosis progresses and coagulation increases. In animal studies, fibrinogen applications have been shown to increase thrombosis and embolic status at increasing doses. In addition, it is known that fibrinogen has been implicated in triggering various inflammatory processes. As a basic component of inflammation, fibrinogen can cause impairment of thrombus plaque and is effective in the development of ischemic stroke. As a result of all these events, hemorheological disorders occur. As a result of all these events, hemorheological disorders occur. Other polymorphisms that occur in the fibrinogen gene may also cause high fibrinogen concentrations such as β-fibrinogen 455G/A polymorphism β-fibrinogen 455G/A polymorphism has also been proven to be ineffective in the development of thrombotic events. In a study carried out by Xiaofeng Hu et al., in Chinese AF patients, proved that there is a relationship between increased risk of cardioembolic stroke and β-fibrinogen 455G/A polymorphism [30].

homocysteine metabolism. These polymorphisms are thought to be effective in the development of nonvalvular AF, which is the most common arrhythmia in clinical practice. Homocysteine is a highly reactive, sulfur-containing amino acid that occurs as a product of the essential amino acid methionine. Gene polymorphisms known to be associated with homocysteine occur in genes encoding enzymes that play a role in the metabolism of homocysteine. Of these polymorphisms, MTHFR C677T and A1298C gene polymorphisms are associated with a decrease in MTHFR enzyme activity. In addition to these polymorphisms, there is also the MTR A2756G gene polymorphism. Homocysteine plays an important role in the pathogenesis of AF and there are studies showing that there is a significant relationship between increased homocysteine levels and AF. In some studies, there was a significant relationship between MTHFR C677T gene polymorphism and increased plasma homocysteine levels in patients with low folate levels. There are few studies related to MTHFR A1298C and MTR A2756G polymorphisms. In a study conducted by Betti Guisti et al., there was a significant relationship between plasma total homocysteine levels and MTHFR C677T gene polymorphism genotype distributions in patients with nonvalvular AF. Furthermore, no significant relationship was observed between plasma total homocysteine levels and MTHFR 1298AA and MTR 2756GG genotypes in nonvalvular AF patients. Given the combined genotype distributions, it is known that the MTHFR C677T and A1298C gene polymorphisms are related to each other [31]. It is presented primer sequences that used to determine MTHFR

MTR A2756G CATGGAAGAATATGAAGATATTAGAC biotinGAACTAGAAGACAGAAATTCTCTA PCR, polymerase chain reaction; SNP, single nucleotide polymorphism; MTHFR, methylenetetrahydrofolate reductase;

Gene Polymorphisms Associated with Atrial Fibrillation http://dx.doi.org/10.5772/intechopen.76920 19

**Genes Forward primer (5′–3′) Reverse primer (5′–3′)**

**Table 9.** Primer sequences used in PCR for MTHFR C677T and A1298C, MTR A2756G.

MTHFR C677T biotinTGAAGGAGAAGGTGTCTGCGGGA CCACTCCAGCATCACTCACT MTHFR A1298C biotinCAAGGAGGAGCTGCTGAAGA CTTGAGAAAAGGCAAAGCAGAC

(C677T and A1298C) and MTR A2756G gene polymorphisms in **Table 9**.

Different results have been obtained in gene polymorphism studies to explain the pathogenesis of AF in which environmental and genetic factors play a role together. Differences in the results of these studies may result from different selection criteria for patients and control groups. Moreover, the findings obtained from these studies are different from each other because they are carried out with different races and populations. Identification of genes associated with AF and polymorphisms that occur in these genes will allow us to have information about the underlying mechanisms of the disease in susceptibility to this disease. Identification of candidate genes that play a role in genetic susceptibility to AF will be mentor to the prevention of this disease and the development of new therapies for disease. In order to be able to explain the pathogenesis of AF and to develop appropriate therapies for this disease, comprehensive studies should be conducted with different populations and with a large number of patients and control groups.

**15. Conclusion**

MTR, methionine synthase reductase.


2.2.3. Step 3. Boron Transport Parameter Estimation

The transport coefficients of boron can be estimated based on the following equation suggested by Hyung and Kim which accounts for the transport of boric acid (H3BO3) and borate ion (H2BO3 −) [24]:

$$B\_{\rm B} = \alpha\_0 B\_{\rm (H\_3BO\_3)} + \alpha\_1 B\_{\rm (H\_2BO\_3{-})} \tag{29}$$

In this equation, *α*0 and *α*1 represent the fractions of boric acid and borate ion which can be estimated using the apparent dissociation constant *K*a1 and the *H*+ ion concentration [24]:

$$\mathfrak{a}\_{\mathbf{0}} = \frac{\{H^{+}\}}{\{H^{+}\} + \mathrm{K}\_{\mathbf{a}1}} \tag{30}$$

$$\alpha\_1 = \frac{K\_{\rm a1}}{\{H^+\} + K\_{\rm a1}} \tag{31}$$

The value of *K*a1 can be determined by a correlation in terms of salt concentration and temperature as given by the correlation of Edmond and Gieskes as presented by Nir and Lahav [38]:

$$
\log\_{10}{K\_{\rm a1}} = \frac{2291.90}{T} + 0.01756 \, T - 3.3850 - 0.32051 \left( \frac{\text{S}}{1.80655} \right)^{1/3} \tag{32}
$$

where *T* is the temperature in kelvin, and *S* is the concentration of salt in g/L. It was also noted by Nir and Lahav [38] that a number of authors have missed the temperature dependence from the 0.01756 *T* term when writing this correlation.

Although in principle the temperature dependent factors can also be estimated here through fitting expressions similar to Equation (27), the temperature-dependent expressions determined by Hyung and Kim can also be used since they show that their fitted parameters fit well for a number of different membranes tested [24]. The work of Hyung and Kim also gives values for the boric acid and borate ion transport coefficients for those types of membranes, and these values are used by Mane et al. as part of their numerical simulation model [23]. However, the simulation results of Mane et al. underpredict the rejection of boron for higher pH values (8.5 and 9.5) compared with their experimental results [23]. This difference could be due to the fact that the transport coefficient values determined by Hyung and Kim were based on a flat sheet membrane [24] while Mane et al. utilized a spiral wound module with the same material [23]. To account for this, it is suggested here that the values of *B*(H3BO3)0 and *B*(H2BO3 −)0 should be fitted for each membrane material and for each design of membrane module.

The values of *B*B can be determined from experimental measurements and calculation with Equation (12) rearranged as (assuming that *k*B = *k*):

$$B\_{\rm B} = \frac{\mathsf{C\_{Bp}} \, f\_{\rm W}}{\left(\mathsf{C\_{Bb}} - \mathsf{C\_{Bp}}\right) \, e^{\left(f\_{\rm W}/k\right)}}\tag{33}$$

Since *α*0 + *α*1 = 1 then for each temperature measured the values of *B*B can be plotted against *α*0 which should give a linear fit with intercept *B*(H2BO3 −) and gradient equal to *B*(H3BO3) − *B*(H2BO3 −) so that the transport coefficients of boric acid and borate ion can be determined. If values are fitted at each temperature the temperature dependence can also be included.


**6. References**

**7**

*Brazil*

**Progressive Stiffness Loss Analysis**

**of Symmetric Laminated Plates due to**

**Transverse Cracks Using the MLGFM**

*Pontifical Catholic University of Parana, Mechanical Engineering Graduate Program,*

With the purpose to create high strength advanced structures, new materials are being developed presenting favorable characteristics for specific applications. Composite Materials are examples of these developments. They can be formed by high strength long fibers, conveniently oriented in a matrix, to form a lamina of composite material. The lamina presents high strength in the fiber direction, but, since it is slender, does not have enough rigidity, what makes impossible the use of an isolated lamina. Piling up and gluing a set of laminas, a laminate is formed which one presents better characteristics than original and isolated materials. The main strength of each lamina is oriented according to the fiber directions. Thus, micro cracks can be produced if sufficient tension is applied in the transverse direction of the fibers, as shown in figure 1, since the resistance of the lamina in these directions depends only on the matrix material. The rise of several transverse cracks

Several papers are found in technical literature dealing with the behavior of composite materials with transverse cracks. Vejen & Pyrz (2002) investigated the transverse crack growth in long fiber composites using the finite element method. Three criteria concerning pure matrix growth, fiber/matrix interface growth and crack kinking out of a fiber/matrix interface were implemented to form a software package for crack propagation calculus.

Cain and colleagues (2003) have studied unidirectional graphite bismaleimide composites to determine the effect of the matrix dominant properties on the failure of the material. The authors showed that the final fracture was caused by the development of a dominant matrix shear crack parallel to the fibers. They also concluded that the decrease in shear modulus of

Ogihara et al (1998) have proposed a two-dimensional model which considers that, in the case of displacements and stress fields in the interlaminar cross-play laminates, there is a prevalence of plane-strain case, even in the presence of transverse cracks. They have also commented that the failure process of cross-ply laminates is due an accumulation of

the composite was the most sensitive and best represented by damage evolutions.

**1. Introduction**

produces loss of stiffness in the laminate.

transverse cracks and delamination.

Roberto Dalledone Machado, Antonio Tassini Jr.,

Marcelo Pinto da Silva and Renato Barbieri