Computational Modeling of Adiabatic Heating in Triaxially Braided Polymer Matrix Composites Subjected to Impact Loading via a Subcell Based Approach

The high rate deformation of polymer matrix composites is often accompanied by significant local adiabatic heating; in the case of ballistic impact loading, heat is generated locally within the polymer matrix due to the conversion of plastic work to heat, but the rapid nature of the event does not allow sufficient time for heat transfer to occur. In this work, a user-defined material subroutine implemented into LS-DYNA® to facilitate the analysis of triaxially braided polymer matrix composites subjected to impact loading, including the effects of heat generation due to high rate inelastic deformation of the polymer matrix, is discussed. To approximate the triaxially braided architecture in finite element models in a computationally efficient manner, a subcell-based modeling approach is utilized whereby the mesoscale repeating unit cell of the triaxial braid is discretized in-plane into an assemblage of subcells. Each mesoscale subcell is approximated as a unique composite laminate with stacking sequence determined from the braid architecture and unidirectional layer thicknesses and fiber volume fractions determined from optical micrographs. Each laminate is modeled in LS-DYNA as a layered thick shell element, where integration point strain increments are taken as volume averaged strain increments applied to a doubly-periodic repeating unit cell with one fiber and three matrix microscale subcells. The generalized method of cells micromechanics theory is utilized to localize the globally applied strains to the constituent level to determine the local strains and stresses as well as the global response of the doubly-periodic repeating unit cell via homogenization. An existing unified pressure dependent viscoplastic constitutive model that was previously extended by the authors to nonisothermal conditions is utilized to model the rate, temperature, and pressure dependent polymer matrix. In the polymer constitutive model, the inelastic strain rate tensor components have been modified to explicitly depend on temperature; strain rate and temperature dependent shifts in matrix elastic properties are determined by shifting dynamic mechanical analysis data with the integration point effective strain rate. Since the subroutine is micromechanical in nature, constitutive models are only applied at the lowest (micro) length scale. Local temperature rises in the polymer matrix due to inelastic deformation are computed at the microscale via the heat energy equation, assuming adiabatic conditions. Simulations of quasi-static straight-sided coupon tests and flat panel impact tests on a representative [0°/60°/–60°] triaxially braided composite material system are conducted to validate the subcell methodology and study the effects of adiabatic heating on the simulated impact response. Time histories of simulated and experimentally measured out-of-plane displacement profiles during the impact event are compared; good agreement is found between experiments and simulations. Simulation results indicate significant internal temperature rises due to the conversion of plastic work to heat in an impact event.