Athermal shear-transformation-zone theory of amorphous plastic deformation. I. Basic principles

We develop an athermal version of the shear-transformation-zone (STZ) theory of amorphous plasticity in materials where thermal activation of irreversible molecular rearrangements is negligible or nonexistent. In many respects, this theory has broader applicability and yet is simpler than its thermal predecessors. For example, it needs no special effort to assure consistency with the laws of thermodynamics, and the interpretation of yielding as an exchange of dynamic stability between jammed and flowing states is clearer than before. The athermal theory presented here incorporates an explicit distribution of STZ transition thresholds. Although this theory contains no conventional thermal fluctuations, the concept of an effective temperature is essential for understanding how the STZ density is related to the state of disorder of the system.

Figure 1

(Color online) Upper panel: The normalized stress $s∕s_y$ as a function of strain $\gamma$ for different values of the normalized strain rate $2D^{\mathrm{tot}}{\tau }_0=\dot{\gamma }{\tau }_0$. The parameters used in integrating Eqs. (3.13, 3.14, 3.15, 3.16) are $\zeta =1$, ${\chi }_{\infty }=1$, ${\chi }_0=0.5$, $\tilde{\mu }=45$, ${ϵ}_0=1$, and $c_0=0.25$. The different values of the normalized strain rate (from top to bottom) are $2D^{\mathrm{tot}}{\tau }_0=\dot{\gamma }{\tau }_0=0.3,0.1,0.015$. The initial values used are $m(\gamma =0)=0$ (i.e., no previous deformation) and $\Lambda (\gamma =0)=\exp (-1∕{\chi }_0)$. Lower panel: The corresponding curves of $\chi$ as a function of $\gamma$ for the three cases. See text for discussion.

Figure 2

(Color online) The normalized stress $s∕s_y$ as a function of the strain $\gamma$ for the stress controlled loading shown in the inset. The parameters used are the same as those in Fig. 1. Note that, although the maximum absolute normalized stress is $\mid s∕s_y\mid =0.9$, significant subyield plastic deformation is visible, in addition to memory effects.