TY - JOUR
T1 - An improved plastically dilatant unified viscoplastic constitutive formulation for multiscale analysis of polymer matrix composites under high strain rate loading
AU - Sorini, Christopher
AU - Chattopadhyay, Aditi
AU - Goldberg, Robert K.
N1 - Funding Information:
The first two authors gratefully acknowledge the support offered by the NASA Harriett G. Jenkins Graduate Fellowship Program Grant # NNX15AU36H . Appendix A A comparison of the E862 uniaxial tensile and compressive true stress-strain curves computed using Equations 36 and 37 is shown in Figs. A1 and A2 . The data used for the conversions from engineering to true stress-strain can be found in [ 35 , 36 ]. In Figs. A1 and A2 , the dashed curves were computed using Equation 36 and the solid (corrected) curves were computed using Equation 37 . Fig. A1 Comparison of experimental tensile true stress-strain response of Epon 862 epoxy using equations (36) and (37) at a) Room temperature (25 °C); b) 50 °C; c) 80 °C. Fig. A1 Fig. A2 Comparison of experimental compressive true stress-strain response of Epon 862 epoxy using Equations (36) and (37) at a) Room temperature (25 °C); b) 50 °C; c) 80 °C. Fig. A2
Funding Information:
The first two authors gratefully acknowledge the support offered by the NASA Harriett G. Jenkins Graduate Fellowship Program Grant #NNX15AU36H.
Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2020/3/1
Y1 - 2020/3/1
N2 - Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson's ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics framework to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate significant thermal softening due to the conversion of plastic work to heat in the composite for matrix dominated deformation modes.
AB - Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson's ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics framework to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate significant thermal softening due to the conversion of plastic work to heat in the composite for matrix dominated deformation modes.
KW - Adiabatic heating
KW - Micromechanics
KW - Plastically compressible
KW - Plastically dilatant
KW - Polymer matrix composites (PMCs)
KW - Tension-compression asymmetry
KW - Viscoplasticity
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U2 - 10.1016/j.compositesb.2019.107669
DO - 10.1016/j.compositesb.2019.107669
M3 - Article
AN - SCOPUS:85077395557
SN - 1359-8368
VL - 184
JO - Composites Part B: Engineering
JF - Composites Part B: Engineering
M1 - 107669
ER -