Thursday, December 6, 2012
Mechanical and Civil Engineering Seminar
Intrinsic Instability of Nonlinear Elastic Crystals and a Model for Boron Carbide
John Clayton, Impact Physics, ARL
A number of crystalline solids demonstrate amorphization or structure collapse associated with loss of shear stiffness at high pressure, including quartz, berlinite, garnet, and boron carbide. Loss of intrinsic stability can be associated with various forms of the so-called Born criteria. In this work, intrinsic stability is first analyzed for homogeneous deformations of several nonlinear elastic solids, including third-order Green elastic materials and compressible neo-Hookean materials. A third-order anisotropic elastic model for trigonal boron carbide crystals is then developed using experimental and DFT data. This model reproduces observed behaviors under hydrostatic and uniaxial (shock) compression, including the onset of instability at around 4% compression in the latter.
A primitive continuum amorphization model is implemented, wherein transformation is triggered upon attainment of stress-induced intrinsic instability. Polycrystal simulations demonstrate effects of impact stress, grain geometry, and crystal polytype in dynamic/shock compression. Directions for further research are outlined that could resolve ambiguities in the present approach.