{"content":[{"text":"International Journal of Plasticity 121 (2019) 227–243 \n F. Shen, et al. \n specific mechanical behavior such as strain softening for amorphous polymers under monotonic loading (Nguyen et al., 2016), \n Mullins effect for styrene-butadiene rubber under cyclic loading (Ayoub et al., 2011b) and stiffness reduction under repeated loading \n tests (Balieu et al., 2013). Besides, localized damage and plastic deformation lead to the onset of necking at high strain before the \n breaking of polymers. \n Loading conditions, especially temperature and strain rate, affect the mechanical response of thermoplastic polymers (Boyce \n et al., 1994; Chen et al., 2002, 2016; Hine et al., 2005). Temperature has a significant effect on the elastic modulus and yield stress of \n thermoplastic polymers. The mobility of amorphous chains increases significantly with an increase in temperature, especially in the \n rubber-glass transition region. It leads to a significant decrease of the elastic modulus and yield stress as the polymers change from \n the glassy state to the rubbery state. Moreover, volume increases in an increasing rate. For some amorphous polymers such as \n polycarbonate and polymethylmethacrylate, the stress-strain responses in the glassy and the rubbery states have obvious differences \n (Srivastava et al., 2010). Conversely, material temperature is influenced by its deformation. The energy dissipation due to the \n viscoplastic flow causes self-heating of thermoplastic polymers (Maurel-Pantel et al., 2015; Ovalle Rodas et al., 2014). The strain rate \n influences the yielding and viscoplastic flow behavior of thermoplastic polymers. The increase of strain rate leads to continuous \n hardening after yielding. Meanwhile, the self-heating phenomenon is also influenced by the strain rate (Maurel-Pantel et al., 2015). \n Higher strain rate leads to larger increment of the temperature. Therefore, there is competition between softening (caused by self- \n heating and damage) and hardening (induced by strain rate) during deformation. \n Thermo-mechanical constitutive models have been proposed to interpret the mechanical behavior of thermoplastic polymers with \n time and temperature dependencies. Arruda et al. (1995) modified an elastic-viscoplastic model (Boyce et al., 1988) originally for \n isothermal conditions to reproduce the temperature-dependent mechanical behavior of polymethylmethacrylate. The shear modulus \n was defined as a logarithmic function of temperature. Srivastava et al. (2010) developed a thermo-mechanical model to study the \n elastic-viscoplastic behavior of three thermoplastic polymers over a wide temperature range spanning their glass transition tem- \n peratures. In addition, the effect of rubber-glass transition on the thermo-mechanical behavior has been considered in the modeling of \n several amorphous polymers (Anand et al., 2009; Buckley and Jones, 1995; Dooling et al., 2002; Dupaix and Boyce, 2007; Mathiesen \n et al., 2014; Xiao et al., 2017). Bouvard et al. (2013) used three microstructure-based internal state variables in a thermo-mechanical \n model to describe the micro-mechanisms of chain deformation. Inspired by the model developed for isothermal condition (Polanco- \n Loria et al., 2010), Garcia-Gonzalez et al. (2017) developed a thermo-hyperelastic-viscoplastic model with consideration of strain \n rate-dependent material hardening, self-heating caused by plastic dissipation, and material expansion. Yu et al. (2017b) proposed a \n thermo-mechanical model to evaluate the cyclic viscoelastic-viscoplastic response of polyethylene with ultra-high molecular weight. \n More recently, Yu et al. (2017a) extended their previous model to consider the effect of chemical reaction and moisture diffusion on \n the cyclic mechanical behavior of polyamide 6. The multi-physical coupling relationship was considered in the proposed hydro- \n thermo-viscoelastic-viscoplastic model. \n Damage behavior can be included in the constitutive modeling for the mechanical behavior of thermoplastic polymers. These \n constitutive models generally can be categorized into two classes: micromechanics and continuum damage mechanics (CDM) \n methods. \n The micromechanics method considers the damage process as the growth of voids as well as their interactions within the material. \n The Gurson model and its modified versions (Gurson, 1977; Nahshon and Hutchinson, 2008; Tvergaard, 1982), originally for porous \n metallic materials, were extended to investigate void growth in thermoplastic polymers. The hydrostatic pressure dependency (Jeong \n and Pan, 1995; Lazzeri and Bucknall, 1995) and the strain rate sensitivity (Challier et al., 2006; Zaïri et al., 2005) were considered in \n the modeling. Zaïri et al. (2011) further considered voids growth with anisotropic behavior in rubber-toughened polymers at large \n deformation. The advantage of a micromechanics method is that it provides a connection between microstructures (voids, cracks and \n matrix) and mechanical behavior of polymers. However, the resulting models are complicated with material parameters regarding \n the distribution and evolution of microstructures, which are difficult to calibrate from the overall mechanical behavior. \n The CDM method, in contrast, introduces a damage variable (scalar or tensor) to represent the material degradation at the \n macroscopic scale induced by micro-voids and micro-cracks (Al-Rub and Voyiadjis, 2003; Haddag et al., 2009; Lemaitre and \n Chaboche, 1994; Shen et al., 2015, 2017; Voyiadjis and Dorgan, 2007). The coupling relationships between stress, elastic strain, \n plastic strain and damage can be considered intrinsically in the thermodynamic framework. Ayoub et al. (2011a) and Ayoub et al. \n (2011b) proposed visco-hyperelastic-damage models for high-cycle and low-cycle fatigue behavior of styrene–butadiene rubber, \n respectively. The deterioration of mechanical behavior during cyclic loading was explained through the network alteration theory in \n which a damage variable was introduced to represent the change in the number of chain segments. Balieu et al. (2013) developed an \n elastic-viscoplastic-damage model for 20% mineral-filled polypropylene with consideration of the non-isochoric deformation and the \n hydrostatic pressure dependency. Two methods to calculate the evolution of damage during deformation were proposed, one using \n the reduction of stiffness and the other using the variation of stresses under compressible and incompressible assumptions. Com- \n paring with the micromechanics method, damage variable and its evolution in the CDM method can be identified from the mac- \n roscopic mechanical behavior of thermoplastic polymers. \n It should be highlighted that hitherto the CDM-based models for the mechanical response of thermoplastic polymers are limited to \n isothermal conditions. Indeed, the damage should be appropriately incorporated in a thermo-mechanical model for a better de- \n scription of the mechanical response. The effect of damage on self-heating, although important, is yet to be considered in the \n constitutive modeling. Furthermore, the influence of temperature on the damage evolution of polymers has never been studied. \n Therefore, this study presents a thermo-elastic-viscoplastic-damage model to address the above shortcomings. The model aims to \n describe the thermo-mechanical response of thermoplastic polymers during finite deformation, taking into consideration of damage \n and self-heating. Based on thermodynamics, the coupling relationship between damage and elasticity as well as viscoplasticity is \n 228","bbox":{"left":0.071667,"top":0.031415,"width":0.863339,"height":0.936395}}],"images_bbox":[],"images_bbox_not_text_overlap":[]}