von Mises true stress vs absolute true strain for atactic PS during extension (, “ext”) and compression (, “com”). The inset shows the von Mises stress as a function of , thereby showing a wider range for the compression data. Fitting the data in the inset by Eq. (2) in the range gives the value of the yield stress for extension and strain-hardening modulus , and for compression and .
von Mises equivalent true stress vs strain for atactic PS for two different cooling rates. The solid lines are fits of Eq. (2). There is no difference for the strain-hardening modulus and the extrapolated yield value. However, the initial yield peak is higher for the slowly cooled sample. Also there is a small difference in the strain at which the yield peak occurs (numerical values are given in Table I).
von Mises stress vs strain during uniaxial-stress extension for different external pressures at . Solid lines are fits to the simulation data as is done in Fig. 1. Observe that both the yield peak and the strain-hardening modulus turn out to increase with increasing external pressure.
von Mises true yield stress vs pressure near the yield point. The solid line is a fit to Eq. (3).
(a) Strain-hardening modulus vs pressure near yield. (b) The ratio of strain-hardening modulus to von Mises true yield stress vs field pressure. Considère’s limit for necking, , is also shown.
(a) Applied work and increase in internal energy vs strain. (b) Various contributions to the internal energy as a function of strain during uniaxial-stress extension.
Plotted is an energy vs engineering strain for atactic PS produced with two different cooling rates. The insets show the difference. (a) Total potential energy. The initial difference in potential energy does not vanish entirely upon deformation. The main decrease occurs up until shortly after the yield point . In the strain-hardening regime the difference stays approximately the same. (b) Total interchain energy (both in units of and , see text). The interchain energy behaves very similar to the potential energy.
Density vs strain for atactic PS for two different cooling rates during uniaxial-stress extension. The inset shows the difference. The initial difference in density disappears after yield.
Root-mean-square displacement of united atoms for the slowly cooled, fast-cooled, and high-pressure samples in the undeformed (“iso,” closed markers) and the deformed (“def,” open markers) cases as a function of strain (for the deformed samples) and time.
True stress in the extension direction vs strain during uniaxial-stress extension, for different stress contributions. The hardening is mainly due to intrachain interactions. Interchain stress decreases after the yield peak, likely caused by the simultaneous decrease in density after yield. The yield tooth (peak and further softening) is caused by a combination of intrachain and interchain interactions.
True stress in the active direction vs strain for different stress contributions. The stress at is subtracted and a separation of 50 MPa between the different contributions is added for clarity. (a) Slowly (with markers, upper curve near yield) vs fast-cooled (without markers, lower curve near yield) sample. One can see that both the interchain and intrachain stresses are higher for the slowly cooled sample. (b) Compression (with markers) vs extension (without markers). The absolute Gaussian strain is used for the -axis and for compression the stresses have been multiplied by −1 to allow for a better comparison with extension. While for extension the interchain stress decreases after initial yielding, it is for compression fairly constant in the displayed range after initial yielding.
True intrachain stress in the active direction vs absolute true strain for (▵) compression and (×) extension. The stress at is subtracted. For compression the stresses have been multiplied by −1 to allow for a better comparison with extension. The inset shows the same as a function of . Results of fitting the data by the Gaussian-based constitutive Eq. (2) are that (compression) and (extension).
Results from simulation and literature experiments of various mechanical properties of PS.
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