Plastic Instability of Rate-Dependent Materials - A Theoretical Approach in Comparison to FE Analyses

In FE simulations of dynamic events, the accuracy of numerical results strongly depends on the quality of the material models and parameters used. Material characteristics identified in static tests are not suitable or are of limited suitability for the description of the deformation behaviour of components and structures under dynamic loading. On this account, it is neces-sary to determine material properties in dynamic tests and to provide reliable input data for numerical simulations, e.g. by means of rate-dependent material models or flow curves. This can be achieved, for instance, by carrying out tensile tests with different loading rates, which, – statically or dynamically – are characterised by a material dependent plastic instability and necking of the specimens. In certain applications, the evaluation of the tensile tests in the range between initial plastic deformation and uniform elongation is sufficient. However, for the consideration of large deformation problems, it is essential to evaluate and establish ma-terial properties for the plastic deformation behaviour beyond the uniform elongation. Comparisons of results from experimental studies and FE simulations of dynamic tensile tests with ductile materials show significant differences in terms of the necking strain as well as the post-critical deformation behaviour. In order to conduct research regarding the cause of determined disagreements, the present contribution displays a theoretical approach describ-ing the instability in rate-dependent elastoplastic materials in comparison to results of nu-merical analyses. It is well known that under dynamic conditions, in addition to the depend-ence on the strain, the strain rate and inertia, both thermal softening and damage evolution in the material affect real deformation processes. In contrast, analytical and numerical ap-proaches allow for a specific selection and separate evaluation of the aforementioned influ-encing factors. This paper focuses on the plastic instability of rate-dependent, ductile materi-als. For this purpose, an analytical instability criterion under isothermal conditions is derived and applied. In conclusion, the theoretical findings are compared to simulation results from numerical studies and differences are discussed.