Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity

Abstract

Mode I steady-state crack growth is analysed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by a generalization of JZ flow theory which accounts for the influence of the gradients of plastic strains on hardening. The constitutive model involves one new parameter, a material length 1, specifying the scale of nonuniform deformation at which hardening elevation owing to strain gradients becomes important. Gradients of plastic strain at a sharp crack tip result in a substantial increase in tractions ahead of the tip. This has important consequences for crack growth in materials that fail by decohesion or cleavage at the atomic scale. The new constitutive law is used in conjunction with a model which represents the fracture process by an embedded traction-separation relation applied on the plane ahead of the crack tip. The ratio of the macroscopic work of fracture to the work of the fracture process is calculated as a function of the parameters characterizing the fracture process and the solid, with particular emphasis on the role of 1. 0 1997 Elsevier Science Ltd

Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

“…In the present section, we intend to describe the nanoindentation size effect of the hierarchical structure by using the trans-scale mechanics theory considering both strain gradient effect and the surface/interface effect. The used strain gradient plasticity theory is Wei-Hutchinson's version [39,40], which can be used in a wide variety of materials, and is not limited to the cases of the typical metal materials like other versions which were built up specifically based on the dislocation concepts.…”

“…(2), the adopted constitutive equations of the strain gradient theory are Wei-Hutchinson's version expressed in the component form as follows [39,40]:…”

Discrete dislocation plasticity and crack tip fields in single crystals

“…Aifantis (1984), Fleck et al (1994), Fleck and Hutchinson (1997), Gao et al (1999), Acharya and Bassani (2000), Gurtin (2000). An isotropic non-local plasticity theory that associates this strength increase with geometrically necessary dislocations does raise stress levels in the vicinity of a crack tip (Wei and Hutchinson, 1997). A similar analysis for crack tip ÿelds in a crystalline solid permits a direct comparison with the discrete dislocation predictions for the stress elevation and allows non-local e ects on the emergence of kink bands to be explored.…”

Strain gradient theory based on a new framework of non-local model

“…It is established that the stress level estimated by the couple strain theory of strain gradient plasticity near a model I crack tip is essentially the same as that in classical plasticity. Wei and Hutchinson [47] used SG theory to investigate the crack tip field. The numerical results have clearly shown that stretch gradients indeed remarkably elevate the stress level around a steadily propagating crack tip.…”

“…Fleck and Hutchinson [7] and Fleck et al [21] developed a phenomenological theory of strain gradient plasticity and a material length scale was introduced for dimensional grounds. From these theoretical developments and consequent attempts at explaining experimental findings of indentation [18,19,23] and fracture [24,25], it has been found necessary to introduce two length parameters [8]. One length, l R , refers to rotational gradients.…”