An Image Based Inertial Impact Test to Extract Viscoelastic Constitutive Parameters

Abstract

Polymer matrix composites often exhibit a strong strain rate dependance in their mechanical response. In many of these materials, the viscoelastic behavior of the polymer matrix drives the rate dependence in the composite, however identifying these parameters at high strain rate presents a significant challenge. Common high-rate material characterization techniques such as the Kolsky (split-Hopkinson pressure) bar require a large test matrix across a range of strain rates. Kolsky bars also struggle to identify constitutive parameters prior to the yield due to inertial effects and the finite period of time required to reach force equilibrium. The Image Based Inertial Impact (IBII) test has been successfully used to identify linear elastic constitutive behavior of composites at high strain rates, but, to date, has only been used to extract constitutive properties at a single nominal strain rate in each test. Here, we propose an adaptation of the IBII test to identify viscoelastic parameters at high strain rates using full-field displacement data and the nonlinear virtual fields method (VFM). We validate the technique with finite element simulations of an IBII test on a model viscoelastic material that is characterized with a Prony series formulation of the generalized Maxwell model. The nonlinear VFM is then used to extract the Prony pairs for dynamic moduli and time constants from the full-field deformation data. The nonlinear viscoelastic identification allows for characterization of the evolution of mechanical response across a range of strain rates in a single experiment. The experimentally identified viscoelastic parameters of the matrix can then be used to predict the behavior of the composite at high strain rates. This approach will also be validated experimentally using a single-stage gas-gun to characterize the high-rate viscoelastic response of PMMA.

The Laplace Virtual Fields Method for the direct extraction of viscoelastic properties of materials

“…An illustrative example using a onedimensional analytical model is given in Appendix D. In practice, this problem is well-known and one must define a time scale for which the viscoelastic behavior can be accurately observed. This time scale is impacted by two factors: the full-field measurement system framerate, and the temperature considered for the test since the time-temperature equivalence states that increasing or lowering the temperature of the sample is equivalent to respectively increase and decrease lower limit of the timescale [15,33].…”

“…The VFM can be applied to any kind of behaviour. It has been used to identify elastic [14], plastic [29], viscoplastic [30], anisotropic [31,32] and viscoelastic [15,33] material models, among others.…”

“…It was also used by Hoshino et al [16], where the minimisation was performed using a Newton-Raphson method. More recently, Matejunas et al [33] performed finite element simulations of an Image Based Intertial Impact test with a generalized Maxwell model. The authors addressed the ability of the non-linear VFM to identify a Prony series pair and defined a timescale of the test for which the parameter could be identified.…”

“…This is referred to as the linear VFM. For non-linear constitutive models, the identification relies on the minimisation of a cost function Φ, deduced from Equation ( 9) [15,[29][30][31][32][33]. It describes the normalized squared residuals between the internal virtual works and external virtual works as shown in Equation ( 10) (10) where X denotes the constitutive parameters set to be identified, N t the total number of load steps and t the actual time step.…”

Material Testing 2.0: A brief review

“…In a similar vein, the uniaxial relaxation behaviour of a nitrile rubber has been identified in reference [ 157 ] by a combination of high rate wave experiments and lower temperatures, with the VFM making use of acceleration as a load cell. A similar approach was used in reference [ 158 ] with an IBII test. The underpinning idea is that the heterogeneity of the strain rate field can give access to a range of relaxation times using a Prony series.…”