A constitutive model for non‐linear behavior of SMC accounting for linear viscoelasticity and micro‐damage

Abstract

An approach for modeling sheet molding compound (SMC) composites as viscoelastic damageable material is presented. Continuum damage mechanics theory by Chow and Wang (Int. J. Fract., 33, 3 (1987)) was used in combination with linear viscoelasticity. The model was applied to a modern SMC composite material containing both hollow glass spheres for low density and toughening additive for improved impact resistance. Tensile tests and uniaxial creep test were employed to build the constitutive model. Validation was done by comparing test data with simulations of uniaxial creep on material with different degrees of damage. The model has good accuracy at moderate damage levels under controlled time‐dependent crack propagation. Tensile testing at two different fixed strain rates was simulated using quasi‐elastic method to calculate relaxation modulus. The model predicts the stress‐strain curve with good accuracy until the region is close to failure, where new mechanisms not accounted for are taking place. Finally, a simulation of a cyclic tensile test with increasing maximum strain per cycle was performed, and since both damage and viscoelasticity are included in the model, the slope change, accumulation of residual strain, and hysteresis in the stress‐strain, loading‐unloading curve are predicted. POLYM. COMPOS., 26:84–97, 2005. © 2004 Society of Plastics Engineers

An incremental 2D constitutive model accounting for linear viscoelasticity and damage development in short fibre composites

“…Hystheresis loops and slope reduction are observed in tensile loading and unloading tests with increasing maximum strain, see Figure 1 (below). As it was demonstrated in Reference [7] the material model with the assumptions formulated in the Introduction section gives rather good approximation of the tensile test, slightly overestimating the non-linearity for high strain rates and underestimating it for slow strain rates. The reason for discrepancies is believed to be the time-dependent damage development which is not included in the model.…”

“…Equation (47) must be obtained experimentally and in previous work [7,11] it has been shown that, using uniaxial tensile loading data, an initially isotropic short fibre composite can be described with a linear relationship:…”

“…The reason for discrepancies is believed to be the time-dependent damage development which is not included in the model. The relaxation functions E(t) and (t) are calculated point by point using the quasi-elastic approach and uniaxial creep data from Reference [7]. The calculated E(t) and (t) curves are seen in Figure 2.…”

“…The objective of the present paper is to generalize the non-linear one-dimensional model developed previously [7] to the 2D case and to derive an incremental formulation suitable for FE-simulations using shell theory. It is implemented in a commercial FE-solver and is validated simulating (a) constant strain rate tensile test and comparing with an analytical solution; (b) fourpoint bending test and comparing with experimental data.…”

“…The state of damage is very complex and a development of micro mechanism-based damage models is a complex work for a future. Since the quantification of microdamage entities belonging to different damage modes (matrix cracks in 1511 composites has been demonstrated in unidirectional creep tests of samples with different degree of damage and in analytical modelling of tensile loading-unloading tests with different strain rates [7].…”