Modeling Materila Failure in High Strain-Rate Problems

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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.