Modeling Materila Failure in High Strain-Rate Problems

高应变率问题中材料失效的建模[j]。C.弗吉尼亚理工学院和州立大学将使用双曲热方程以及表示热粘塑性材料的质量、线性动量和动量矩平衡的方程来描述此类材料在高应变率变形期间绝热剪切带（asb）的产生和传播。ASB是一个狭窄的强塑性变形区域，通常发生在大多数金属和某些聚合物在高应变率下变形的延性破坏之前。由于材料的塑性变形、热传导和热应力引起的热将被考虑在内。对控制方程的伽辽金近似得到的耦合非线性常微分方程进行积分时所使用的时间增量自适应调整，从而计算出在规定精度内的稳定解。在剪切带的发展过程中，将计算剪切带状材料内部的能量耗散率、带边缘的能量传导率和用于提高剪切带状材料温度的能量。它的速度将通过在不同时间定位它的边缘来确定。通过将ASB建模为奇异曲面，我们将确定其传播速度，并将其与上述数值计算结果进行比较。应该注意的是，ASB不是经典意义上的波，它沿边缘传播，而不是与表面垂直传播。该速度将与ASB边缘内和边缘附近材料的变形状态有关。

Modeling Material Failure in High Strain Rate ProblemsR. C. BatraVirginia Polytechnic Institute and State UniversityAn hyperbolic heat equation along with the equations expressing thebalance of mass, linear momentum and moment of momentum forthermoviscoplastic materials will be used to delineate the initiationand propagation of adiabatic shear bands (ASBs) during high strain ratedeformations of such materials. An ASB is a narrow region of intenseplastic deformation that usually precedes the ductile failure of mostmetals and some polymers deformed at high strain rates. The heatgenerated due to plastic deformations of the material, heat conductionand thermal stresses induced will be accounted for. The finite elementmesh will be refined adaptively and the time increment used to integratethe coupled nonlinear ordinary differential equations obtained by theGalerkin approximation of the governing equations will be adjustedadaptively so as to compute the stable solution within the prescribedaccuracy. The energy dissipation rate within the shear banded material,rate of energy conducted out of the edges of the band, and the energyused to raise the temperature of the shear banded material will becomputed during the development of the shear band. Its speed will beascertained by locating its edges at different times.By modeling an ASB as a singular surface, we will determine its speed ofpropagation and compare it with that computed above numerically. Itshould be noted that an ASB is not a wave in the classical sense and itpropagates edgewise rather than normal to its surface. This speed willbe related to the state of deformation of the material within andadjacent to the edge of the ASB.