Modeling damage and fracture within strain-gradient plasticity

The effective threshold for fatigue crack propagation: a plastic size effect?

A study of particle size effect and interface fracture in aluminum alloy composite via an extended conventional theory of mechanism-based strain-gradient plasticity

The indentation size effect in the spherical indentation of iridium: A study via the conventional theory of mechanism-based strain gradient plasticity

Recent micro- and nano-indentation experiments have shown strong indentation size effects at the micron and sub-micron scales. Classical plasticity theories cannot explain the indentation size effect because their constitutive models possess no intrinsic material lengths. The Mechanism-based Strain-Gradient (MSG) plasticity theory and its simplified version, the Conventional theory of Mechanism-based Strain-Gradient plasticity (CMSG), have been established from the Taylor dislocation model and have successfully explained the indentation size effect. This paper provides a review of these theories and their applications to study the indentation of face- and body-centred-cubic metals and thin films on hard or soft substrates.

Micromechanical modeling of damage evolution and fracture behavior in particle reinforced metal matrix composites based on the conventional theory of mechanism-based strain gradient plasticity

In a remarkable series of experiments, Elssner et al. (1994) and Korn et al. (2002) observed cleavage cracking along a bimaterial interface between Nb and sapphire. The stress required for cleavage cracking is around the theoretical strength of the material. Classical plasticity models fall short to reach such a high stress level. We use the conventional theory of mechanism-based strain gradient plasticity (Huang et al., 2004) to investigate the stress field around the tip of an interface crack between Nb and sapphire. The tensile stress at a distance of 0.1 µm to the interface crack tip reaches 13.3σY ,w hereσY is the yield stress of Nb. This stress is nearly 4 times of that predicted by classical plasticity theory (3.6σY ) at the same distance to the crack tip, and is high enough to trigger cleavage cracking in materials and interfaces. This is consistent with Elssner et al.'s (1994) and Korn et al.'s (2002) experimental observations.

With introducing the strain gradient into plasticity theory, the crack field singularity at the crack tip changes. Characterization of the crack in strain-gradient dependent materials has not found a common consensus. In the present work the crack tip field is systematically investigated within the frame of the strain-gradient plasticity using the element-free Galerkin method. Under both small scale yielding and finite yielding conditions the crack field in strain-gradient plasticity consists of three zones: The elastic K-field, the known plastic HRR-field dominated by the known energy release rate, \({\mathcal G}\), and the hyper-singular stress field which cannot be characterized by the known fracture mechanics parameters. Effects of the finite strains have been considered for both small scale yielding and finite cracked specimens. The computational results show that the finite strains do not change the characterization of the crack tip fields under the strain-gradient plasticity. In all investigated cases the hyper-singular zone is small (\({r < \mathcal G/\sigma_0}\)) and well contained by the HRR zone under the \({\mathcal G}\) dominance condition. The hyper-singular zone is in the size of \({r/(\mathcal G/\sigma_0)}\) and may grow with the material length, but decrease with applied load. The known elastic-plastic fracture mechanics parameter, \({\mathcal G}\), can be directly applied to characterize the crack under strain-gradient plasticity, within the intrinsic material length much smaller than the overall component size, l < 0.1%L0. In this case the strain-gradient term in the gradient plasticity will not affect description of cracks.

Taylor-based nonlocal theory of plasticity: numerical studies of the micro-indentation experiments and crack tip fields

Mode I and mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity

Bauschinger and size effects in thin-film plasticity

Mixed mode near-tip fields for cracks in materials with strain-gradient effects

A simple model for size effects in constrained shear

Establishment of damage estimation rules for brittle fracture after cyclic plastic prestrain in steel

Plane strain elastic-plastic analyses were performed on a variety of 2-D planar cracked geometries and loading conditions, based on a small strain formulation and de-formation theory plasticity (termed finite boundary (FB) analysis hereafter). For the majority of the cases analyzed, the crack-tip fields in the mechanistically significant region around the crack tip agreed well with those of the corresponding modified boundary layer (MBL) solutions for load levels up to large scale yielding. The crack-tip fields in the MBL solutions were normalized using the elastic-plastic J values and the elastically-scaled T-stress values of the corresponding FB specimens. However, good agreement could be obtained with (J, T) only up to moderate scale yielding for a center-cracked tension (CCT) geometry. At large scale yielding, the MBL solution based on the elastically-scaled T-stress could not capture the effects of crack tip stress and strain redistribution in the CCT. An alternative method was proposed to calculate the T-stress using weight functions and the elastic-plastic remote stress field of the CCT (termed effective T-stress). Incorporating the effective T-stress into the MBL solutions, good agreement in both stress and strain fields was obtained between the MBL solution and the FB CCT solution at load levels up to general yielding. To demonstrate the limits of two-parameter characterizations in accurately describing elastic-plastic cracktip fields, a three-point-bend specimen was analyzed for load levels up to large plasticity. It is shown that although Q-values could be operationally defined at large plasticity, in general, no complete, consistent, two-parameter description was forthcoming to accurately describe the crack-tip stress and strain fields beyond certain limits. The inherent limits of two-parameter characterization of elastic-plastic crack tip fields should be recognized, analogous to those of one-parameter (J) characterization. A locus of two-parameter (J, T) characterization limits is proposed based on the crack-tip stress fields of the geometry and loading configurations analyzed. The J-T based two-parameter approach is shown to greatly extend the validity domain of fracture mechanics analysis for specimens with negative T-stress.

A systematical study of size effects and mechanical behaviors for the nanocrystalline (nc) metals is performed. The grain boundary fracture process is considered and described by the mixed-mode interface cohesive model. The grain material is characterized by the conventional theory of strain gradient plasticity. In the present investigation, the effects of five important parameters on the overall mechanical behavior are studied systematically, which include the grain size, critical separation strength, energy release rate of interface separation, mixity of separation strength, as well as the mixity of separation energy release rate. A finite element method (FEM) covering the above characteristics within the grain and on the grain boundary is developed. The present results show that the overall strength and ductility of the nc metals strongly depend on the grain boundary features described by the mixed-mode cohesive interface model, and there is a competition of deformation of grain boundary with that of grain interior.