Low speed impact of laminated polymethylmethacrylate/adhesive/polycarbonate plates

We study three-dimensional finite transient deformations of transparent poly-methyl-methacrylate (PMMA)/adhesive/polycarbonate (PC) laminates impacted at low speed by a hemispherical nosed rigid cylinder using the commercial finite element (FE) software LS-DYNA. The two glassy polymers PMMA and PC are modeled as thermo-elasto-visco-plastic materials by using the constitutive relation proposed by Mulliken and Boyce and modified by Varghese and Batra. For the nearly incompressible viscoelastic bonding layer, the elastic response is modeled by the Ogden relation and the viscous response by the Prony series. Delamination at interfaces between the adhesive and the polymeric sheets is simulated by using the cohesive zone model incorporated in LS-DYNA. The effective plastic strain, the maximum principal stress, and the maximum stretch based failure criteria are used for delineating failure in PC, PMMA and the adhesive, respectively. Failed elements are deleted from the analysis domain. The three layers are discretized by using 8-node brick elements and integrals over elements are numerically evaluated by using a reduced Gauss integration rule. The coupled nonlinear ordinary differential equations obtained by the Galerkin approximation are integrated by using the conditionally stable explicit algorithm. Results have been computed for at least two different FE meshes. The computed number and configurations of cracks in the PMMA are found to qualitatively agree with the test observations. It is also found that the energy dissipated due to plastic deformations in the PC is considerably more than that due to cracks formed in the PMMA.