PSI - Issue 23

Yoshitaka Umeno et al. / Procedia Structural Integrity 23 (2019) 348–353 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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formed and grow during simulation. The voids decrease the effective section area against the external force, and consequently cause stress reduction. Note that it is only in the cases applying triaxial strain that the brittle fracture and void nucleation were observed. The uniform biaxial deformation does not result in brittle fracture although the tensile condition has a relatively strong multiaxial effect; it is possible that this feature contributes to ductility in PC.

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Fig. 3: Stress-strain relationships under various deformation types. Curves were smoothed by the Bezier approximation for clarity (a). Snapshots of simulation cell deformed under uniaxial stress (b) and uniaxial strain (c).

3.2. Yield Stress as a Function of Strain Rate Yield stresses as functions of strain rates evaluated at different temperatures are shown in Fig. 4 (a). The results are translated into Fig. 4 (b) by using the Williams-Landel-Ferry (WLF) equation,     s 2 s 1 10 log C T T a C T T T     , (3) where C 1 =  8.86 ， C 2 = 101.6 K (common values for various polymers). Experimental data (Bauwens-Crowet 1974) are also shown in the figure. We found that the data points collapsed onto one curve with T s = 900 K. This value is larger than the value often used in analysis of experimental results, T s = T g + 50 K ( T g =423 K is the glass transition temperature of PC), indicating room for further quantitative improvement in the modeling. Figure 5 shows yield stresses as a function of strain rate at a temperature of 300 K under the four loading modes. We found that the plots were classified into two groups; a pair of uniaxial stress and biaxial tension, and that of uniaxial strain and triaxial tension. The plots of each group were fitted to a curve of the Cowper-Symonds equation,        p 1/ 0 1       , (4) meaning that we obtained two master curves of yield stress-strain rate relation. These results are consistent with our former study (Kubo and Umeno 2016 (1)) where CGMD simulations demonstrated that qualitative aspects of the behavior of PC molecules at fracture were divided into two types depending on the stress triaxiality. In other words, the stress triaxiality was found to be a major factor determining deformation and fracture behavior of PC.              C Y Y