Dynamic fracture parameters and constraint effects in functionally graded syntactic epoxy foams

Functionally graded syntactic foam sheets are developed by dispersing microballoons in epoxy for studying dynamic fracture behavior under low velocity impact loading. The volume fraction of microballoons is graded linearly over the width of the sheets. The mode-I crack initiation and growth behaviors are studied using reflection coherent gradient sensing technique and high-speed photography in samples with crack on the compliant and stiff sides and oriented along the compositional gradient. Crack growth along the gradient in each case shows sudden acceleration followed by steady state growth and deceleration during the window of observation. In both cases, the crack accelerations are similar while crack decelerations show differences. The dynamic stress intensity factor history prior to crack initiation in each case shows a rapid increase at different rates with the crack on the compliant side of the graded sheet experiencing higher rate of loading relative to the one with the crack on the stiffer side. Post-crack initiation stress intensity factor histories suggest increasing fracture toughness with crack growth in the graded sample with the crack on the compliant side while a decreasing trend is seen when the crack is on the stiffer side.Optical measurements are supplemented by finite element simulations for studying crack tip constraint effects on fracture behavior of graded foam sheets. Computed plane strain constraints in graded configurations are essentially identical to the homogeneous counterpart and the computed stress intensity factors obtained from plane stress elasto-dynamic analyses of the graded foams correlate well with the experimental measurements prior to crack initiation. The computed T-stress histories however, show an earlier loss of negative crack tip constraint in case of the graded foam sample with a crack on the compliant side. This correlates well with the higher crack tip loading rate and earlier crack initiation suggesting a possible role of in-plane constraint on fracture of graded foam. The coincidence of the time rate of change of in-plane constraint parameter becoming stationary close to experimentally observed crack initiation times are noted.