Mixed-Mode Dynamic Crack Growth in a Functionally Graded Particulate Composite: Experimental Measurements and Finite Element Simulations

Mixed-mode dynamic crack growth behavior in a compositionally graded particle filled polymer is studied experimentally and computationally. Beams with single edge cracks initially aligned in the direction of the compositional gradient and subjected to one-point eccentric impact loading are examined. Optical interferometry along with high-speed photography is used to measure surface deformations around the crack tip. Two configurations, one with a crack on the stiffer side of a graded sheet and the second with a crack on the compliant side, are tested. The observed crack paths are distinctly different for these two configurations. Furthermore, the crack speed and stress intensity factor variations between the two configurations show significant differences. The optical measurements are examined with the aid of crack-tip fields, which incorporate local elastic modulus variations. To understand the role of material gradation on the observed crack paths, finite element models with cohesive elements are developed. A user-defined element subroutine for cohesive elements based on a bilinear traction-separation law is developed and implemented in a structural analysis environment. The necessary spatial variation of material properties is introduced into the continuum elements by first performing a thermal analysis and then by prescribing material properties as temperature dependent quantities. The simulated crack paths and crack speeds are found to be in qualitative agreement with the observed ones. The simulations also reveal differences in the energy dissipation in the two functionally graded material (FGM) cases. $T$-stresses and hence the crack-tip constraint are significantly different. Prior to crack initiation, larger negative $T$-stresses near the crack tip are seen when the crack is situated on the compliant side of the FGM.