Abstract
A model of a shear band as a zero-thickness nonlinear interface is proposed and tested using finite element simulations. An imperfection approach is used in this model where a shear band, that is assumed to lie in a ductile matrix material (obeying von Mises plasticity with linear hardening), is present from the beginning of loading and is considered to be a zone in which yielding occurs before the rest of the matrix. This approach is contrasted with a perturbative approach, developed for a J2-deformation theory material, in which the shear band is modelled to emerge at a certain stage of a uniform deformation. Both approaches concur in showing that the shear bands (differently from cracks) propagate rectilinearly under shear loading and that a strong stress concentration should be expected to be present at the tip of the shear band, two key features in the understanding of failure mechanisms of ductile materials.
Highlights
When a ductile material is brought to an extreme strain state through a uniform loading process, the deformation may start to localize into thin and planar bands, often arranged in regular lattice patterns
After localization, unloading typically1 occurs in the material outside the bands, while strain quickly evolves inside, possibly leading to final fracture or to a progressive accumulation of deformation bands
It follows from the above discussion that as strain localization represents a prelude to failure of ductile materials, its mechanical understanding paves the way to the innovative use of materials in extreme mechanical conditions
Summary
When a ductile material is brought to an extreme strain state through a uniform loading process, the deformation may start to localize into thin and planar bands, often arranged in regular lattice patterns. Research initiated with pioneering works by Hill (1962), Nadai (1950), Mandel (1962), Prager (1954), Rice (1977), Thomas (1961), and developed – from theoretical point of view – into two principal directions, namely, the dissection of the specific constitutive features responsible for strain localization in different materials (for instance, as related to the microstructure, Danas and Ponte Castaneda, 2012; Bacigalupo and Gambarotta, 2013; Tvergaard, 2014) and the struggle for the overcoming of difficulties connected with numerical approaches [reviews have been given by Needleman and Tvergaard (1983) and Petryk (1997)] These problems are still not exhausted, surprisingly, the most important questions have only marginally been approached and are still awaiting explanation. These are as follows: (i) Why are shear bands a preferred mode of failure for ductile materials? (ii) Why do shear bands propagate rectilinearly under mode II, while cracks do not? (iii) How does a shear band interact with a crack or with a rigid inclusion? (iv) Does a stress concentration exist at a shear band tip? (v) How does a shear band behave under dynamic conditions?
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