A grain-scale study of spall in brittle materials

Abstract

The evolution of spall for a brittle material is investigated under variance of anisotropy, grain boundary fracture energy, and loading. Because spall occurs in the interior of the specimen, fundamental studies of crack nucleation and growth are needed to better understand surface velocity measurements. Within a cohesive approach to fracture, we illustrate that for anisotropic materials, increases in the fracture energy cause a transition in crack nucleation from triple-points to entire grain boundary facets. Analysis of idealized flaws reveals that while crack initiation and acceleration are strong functions of the fracture energy, flaws soon reach speeds on the order of the Rayleigh wave speed. Finally, simulated surface velocities of spalled configurations are correlated with microstructural evolution. These fundamental studies of nucleation, growth, and spall attempt to link atomic separation to the macroscopic spall strength and provide a computational framework to examine the evolution of spall and the impact on the simulated surface velocity field.

Mesoscale modeling of nonlinear elasticity and fracture in ceramic polycrystals under dynamic shear and compression

“…Many cohesive laws have been investigated in previous works on heterogeneous polycrystalline solids (Espinosa and Zavattieri, 2003a,b;Clayton and McDowell, 2004;Clayton, 2005a,b;Vogler and Clayton, 2008;Foulk and Vogler, 2010;Kraft et al, 2010). A simple irreversible cohesive law is prescribed in the present work, with the same functional form and parameters for normal and tangential separations d n and d t .…”

“…More complex cohesive laws incorporating piecewise-linear traction-separation relationships with various slopes were investigated; alternative formulations did not offer any apparent advantages with regards to numerical stability or representation of macroscopic fracture strength but often would require specification of experimentally unknown parameters. Differently from many previous studies (Espinosa and Zavattieri, 2003a,b;Clayton and McDowell, 2004;Clayton, 2005a,b;Vogler and Clayton, 2008;Foulk and Vogler, 2010), distinct cohesive finite elements are not used in the present numerical framework. In other words, finite element meshes are not seeded a priori with interfacial elements.…”

“…It is understood that real ceramic microstructures should exhibit variation among fracture behaviors (e.g., in functional forms of cohesive laws as well as in fracture strengths and energies) at interfaces depending on grain misorientation, grain boundary curvature, impurities, and pre-existing defects. Thus, the assumption of uniform grain boundary behavior is an idealization, albeit one that has been used frequently in other numerical studies of heterogeneous polycrystalline solids (Clayton and McDowell, 2004;Vogler and Clayton, 2008;Foulk and Vogler, 2010;Kraft et al, 2010). Variable grain boundary properties can strongly influence overall behavior of ceramics (Espinosa and Zavattieri, 2003b;; however, assignment of variable properties as an initial condition is problematic since experimental measurements of mesoscopic grain boundary strength distributions are scarce if not nonexistent.…”

“…More recently, mesoscale models, in which the behavior of each grain within a polycrystal is addressed explicitly, have provided insight into effects of microstructural properties -e.g., grain sizes and shapes, anisotropic elasticity and/or plasticity, local fracture properties, and distributions of second phases -on deformation and failure behavior of polycrystalline solids (Espinosa and Zavattieri, 2003a,b;Clayton and McDowell, 2004;Clayton, 2005aClayton, ,b, 2006aVogler and Clayton, 2008;Foulk and Vogler, 2010; Zhang et al, 2005b,a;Kraft et al, 2010;Gazonas et al, 2010). Much earlier work focused on twodimensional simulations; however, recent advances in computational hardware (e.g., processor speed and numbers of parallel processors), finite element software (Jung, 2010), and microstructure rendering and meshing technologies (Rollett and Manohar, 2004;Rollett et al, 2007) now enable fully resolved simulations of three-dimensional polycrystalline microstructures incorporating nonlinear material behavior, interfacial fracture, and multi-body contact Gazonas et al, 2010).…”

“…As discussed in more detail later, these microstructures are idealized in the sense that they do not correspond to reconstructions of actual specimens of the ceramics under present consideration; rather, they are synthesized from numerical algorithms incorporating grain growth or Voronoi methods. Synthetic microstuctures of this sort are typically used when digital reconstructions of actual microstructures are not available (Zhang et al, 2005b;Clayton, 2009b;Foulk and Vogler, 2010). Properties of SiC or AlON are assigned to each microstructure in different simulations, and results of various simulations enable comparison between materials holding grain morphology fixed.…”