Modeling Materila Failure in High Strain-Rate Problems

高应变率问题中的材料失效模型。C. BatraVirginia Polytechnic Institute and State University双曲型热方程沿着描述热粘塑性材料的质量平衡、线动量和动量矩的方程，将描述这种材料在高应变率变形过程中绝热剪切带（ASB）的产生和扩展。 ASB是一个狭窄的强塑性变形区域，通常先于大多数金属和某些聚合物在高应变率下变形的延性破坏。 由于材料的塑性变形产生的热量，热传导和热应力引起的将占。 有限元网格将自适应地加密，并且用于积分由控制方程的Galerkin近似得到的耦合非线性常微分方程的时间增量将自适应地调整，以便在规定的精度内计算稳定解。 在剪切带的发展过程中，剪切带内的能量耗散率、剪切带边缘的能量传导率以及用于提高剪切带材料温度的能量都将发生变化。 它的传播速度将通过在不同时刻定位它的边缘来确定，通过将ASB建模为奇异曲面，我们将确定它的传播速度，并将其与上面数值计算的速度进行比较。 应该注意的是，ASB不是经典意义上的波，它沿边缘传播，而不是垂直于其表面。 这个速度将与ASB边缘内和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.