Viscoplastic parameter estimation by high strain-rate experiments and inverse modelling – Speckle measurements and high-speed photography

Abstract

A methodology based on inverse modelling for estimating viscoplastic material parameters at high strain-rate conditions is presented. The methodology is demonstrated for a mild steel exposed for compression loading in a split Hopkinson pressure bar arrangement. By using dog-bone shaped specimens nonhomogeneous states of deformation are obtained throughout the entire deformation process. The resulting nonhomogeneous deformation of the specimens is evaluated using digital speckle photography (DSP) to give in-plane point-wise displacement and strain fields. The photographs are captured with a high-speed camera of image converter type, which acquire time resolved images during the impact loading. The experiments are simulated using finite element analysis (FEA), where the material model suggested by Johnson-Cook for high-strain rate conditions are utilised. Experimental and FE-calculated field information are compared in order to estimate the viscoplastic parameter in the Johnson-Cook material model. The estimation is performed by minimising least-square functions that contain the differences in displacements and strains, respectively. The quality of the estimated parameters is studied from statistical point of view.

Full-Field Strain Measurement and Identification of Composites Moduli at High Strain Rate with the Virtual Fields Method

“…In the first one, Kajberg and Wikman tried to identify visco-plastic parameters of a mild steel submitted to a compression loading through a SHPB set up [5]. They used a dog-bone shaped sample in order to get inhomogeneous strains from 2D image correlation measurements.…”

Beyond Hopkinson's bar

“…Such measurements have also been used to have better insights into strain localization in uniaxial tests [17,18]. More rarely, the full-field data have been used to identify a model using a uniform stress approach [17] or finite-element (FE) model updating [19][20][21]. It is to be noted that large strains (metals in plastic deformation or polymers) are usually measured, which is in the favourable end of the DIC usage range.…”

Exploration of Saint-Venant’s Principle in Inertial High Strain Rate Testing of Materials

“…A more recent study [18] combined impact force and strain at the centre of the specimen to construct the cost function but again, inertial effects were neglected and force measurements relied on specific hypotheses. Finally, strain maps have been used in FEMU on a SHPB test [19] but again, the force needed to be measured with a Hopkinson bar. It should also be noted that all these studies were looking at rather large plastic strains where inertial effects were not a problem anymore.…”

“…The main benefit from this is that iterative solving of finite element models is avoided, resulting in much faster computations. This is even more critical at high strain rates where a single finite element model may already take several to several tens of minutes to run and this will have to be done many times to evaluate the cost function until convergence, leading to several hours of computations until convergence (2.5 to 3h in [19] for one parameter only, private communication from the corresponding author, J. Kajberg).…”