Shear Localization in Metallic Materials at High Strain Rates

Multiple necking pattern in nonlinear elastic bars subjected to dynamic stretching: The role of defects and inertia

The critical neck spacing in ductile plates subjected to dynamic biaxial loading: On the interplay between loading path and inertia effects

At high strain rates, the fragmentation of expanding structures of ductile materials, in general, starts by the localization of plastic deformation in multiple necks. Two distinct mechanisms have been proposed to explain multiple necking and fragmentation process in ductile materials. One view is that the necking pattern is related to the distribution of material properties and defects. The second view is that it is due to the activation of specific instability modes of the structure. Following this, we investigate the emergence of necking patterns in porous ductile bars subjected to dynamic stretching at strain rates varying from 103 s-1 to 0.5×105 s-1 using finite-element calculations and linear stability analysis. In the calculations, the initial porosity (representative of the material defects) varies randomly along the bar. The computations revealed that, while the random distribution of initial porosity triggers the necking pattern, it barely affects the average neck spacing, especially, at higher strain rates. The average neck spacings obtained from the calculations are in close agreement with the predictions of the linear stability analysis. Our results also reveal that the necking pattern does not begin when the Considere condition is reached but is significantly delayed due to the stabilizing effect of inertia.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2017.0575

Random distributions of initial porosity trigger regular necking patterns at high strain rates.

An analytical model for necking strains in stretched plates under dynamic biaxial loading

An extension of the linear stability analysis for the prediction of multiple necking during dynamic extension of round bar

Extension of 1D linear stability analysis based on the Bridgman assumption. Applications to the dynamic stretching of a plate and expansion of a ring

The fragmentation of structures subject to dynamic conditions is a matter of interest for civil industries as well as for Defence institutions. Dynamic expansions of structures, such as cylinders or rings, have been performed to obtain crucial information on fragment distributions. Many authors have proposed to capture by FEA the experimental distribution of fragment size by introducing in the FE model a perturbation. Stability and bifurcation analyses have also been proposed to describe the evolution of the perturbation growth rate. In the proposed contribution, the multiple necking of a round bar in dynamic tensile loading is analysed by the FE method. A perturbation on the initial flow stress is introduced in the numerical model to trigger instabilities. The onset time and the dominant mode of necking have been characterized precisely and showed power law evolutions, with the loading velocities and moderately with the amplitudes and the cell sizes of the perturbations. In the second part of the paper, the development of linear stability analysis and the use of salient criteria in terms of the growth rate of perturbations enabled comparisons with the numerical results. A good correlation in terms of onset time of instabilities and of number of necks is shown.

S. El Mai

Papers

An extension of the linear stability analysis for the prediction of multiple necking during dynamic extension of round bar

Extension of 1D linear stability analysis based on the Bridgman assumption. Applications to the dynamic stretching of a plate and expansion of a ring

Towards the prediction of multiple necking during dynamic extension of round bar : linear stability approach versus finite element calculations