The overall deformation behavior of rubber-toughened polymers (e.g. PC/ABS blends) exhibits a pronounced plastic dilatancy. As this volume increase results from diverse micromechanisms the appropriate structure of a macroscopic model is not obvious. In this contribution, different material models featuring plastic dilatancy are compared with regard to their ability to capture the deformation behavior of PC/ABS in different loading situations. All models are calibrated to match experimental data under uniaxial tension in terms of true stress-strain curves and the evolution of volume strain. Afterwards they are employed in finite element (FE) simulations of single-edge-notch-tensile (SENT) tests. Patterns of plastic deformation computed from the different material models are compared to experimental findings.
Experimental studyUniaxial tensile tests on a commercial PC/ABS blend were carried out at different strain rates. Through the assumption of equal transverse and through-thickness strain, the true stress-strain response and the evolution of the volume strain was determined using digital image correlation (DIC). The stress-strain behavior features a small elastic range up to a distinct yield point at about 5 % strain (Fig. 1). Thereafter, the material exhibits intrinsic softening before progressively rehardening until failure takes place at a logarithmic strain of about 0.7. Moreover, it was found that a ten times higher strain rate leads to increased stress in the plastic range (Fig. 1). Owing to well known [1] yet here not further studied micromechanisms such as void growth and crazing, the overall response of PC/ABS under uniaxial tension exhibits a pronounced plastic dilatancy shown in Fig. 2. In order to analyze the behavior of the PC/ABS material in more complex loading situations SENT tests have been performed. Using DIC plastic deformations were found to localize in an elongated zone ahead of the notch (Fig. 3) which is typical for rubber-toughened polymers [1]. The notch radius in these tests was 1 mm while the specimen thickness was 3 mm.
Constitutive modelsThree different isotropic yield functions accounting for a dependence on hydrostatic stress and -in conjunction with an associated flow rule-giving rise to plastic volume strain are analyzed with respect to their capability to describe the behavior of PC/ABS. These are the Drucker-Prager (DP) and the Raghava (R) model featuring a linear and non-linear interrelation between von Mises σ e and hydrostatic stress σ m , respectively, and a simplified Gurson-type (or Green) model (G) where in addition the effect of an evolving porosity f is taken into account [2-4]. The corresponding yield functions readand the plastic part of the rate-of-deformation tensor is given by D p =ε p N with N = (∂Φ/∂σ) / ∂Φ/∂σ . Rate dependence is captured byε p =ε 0 g (Φ) whereε 0 is a reference strain rate and g (Φ) describes the influence of stress. The parameter α, which is different in each model, takes the specific pressure dependency into account and k(ε p ) represent...
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