Computational assessment of cracks under strain-gradient plasticity

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

Modeling damage and fracture within strain-gradient plasticity

Mode I and mode II stress intensity factors and dislocation density behaviour in 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.

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

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

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

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

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

Deformation processed metal–metal composites (DMMCs) are high-strength, high-electrical conductivity composites developed by severe plastic deformation of two ductile metal phases. The extraordinarily high strength of DMMCs is underestimated using the rule of mixture (or volumetric weighted average) of conventionally work-hardened metals. In this article, a dislocation-density-based, strain–gradient–plasticity model is proposed to relate the strain-gradient effect with the geometrically necessary dislocations emanating from the interface to better predict the strength of DMMCs. The model prediction was compared with the experimental findings of Cu–Nb, Cu–Ta, and Al–Ti DMMC systems to verify the applicability of the new model. The results show that this model predicts the strength of DMMCs better than the rule-of-mixture model. The strain-gradient effect, responsible for the exceptionally high strength of heavily cold worked DMMCs, is dominant at large deformation strain since its characteristic microstructure length is comparable with the intrinsic material length.

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.

Strain gradient plasticity has been the subject of extensive research in the past 40 years in order to model size effects in metal plasticity, on the one hand, and provide finite width shear bands in the simulation of localization phenomena, on the other hand. However, the use of the emerging models is still limited to academic applications and has not yet been adopted by industry practitioners. The present paper systematically reviews the pros and the cons of gradient plasticity at finite strains based on the gradient of scalar plastic variables, in particular the gradient of the cumulative plastic strain. It proposes benchmark tests addressing both size effect modeling and plastic strain localization simulation. It includes new analytical solutions for validation of FE implementation. It focuses on the micromorphic approach to gradient plasticity, as a convenient method for implementation in FE codes. New features of the analysis include the comparison of three distinct formulations of rate-independent gradient plasticity at finite deformations, based on the multiplicative decomposition of the deformation gradient and on quadratic potentials with respect to gradient terms. The performance of micromorphic and Lagrange-multiplier-based strain gradient plasticity models is evaluated for various monotonic and cyclic loading conditions including confined plasticity in simple glide and tension, bending and torsion at large deformations. Limitations are pointed out in the case of bending and torsion, which can be overcome for instance by the use of the gradient of equivalent plastic strain model.

The near-tip asymptotic field and full-field solution are obtained for a mode III crack in an elastic material with strain gradient effects. The asymptotic analysis shows that, even though the near-tip field is governed by a single parameter B (similar to the mode III stress intensity factor), the near-tip field is very different from the classical KIII field; stresses have r -3/2 singularity near the crack tip, and are significantly larger than the classical K III field within a zone of size l to the crack tip, where l is an intrinsic material length, depending on microstructures in the material. This high-order stress singularity, however, does not violate the boundness of strain energy around a crack tip. The parameter B of the near-tip asymptotic field has been determined for two anti-plane shear loadings: the remotely imposed classical K III field, and the arbitrary shear stress tractions on crack faces. The mode III full-field solution is obtained analytically for an elastic material with strain gradient effects subjected to remotely imposed classical K III field. It shows that the near-tip asymptotic field dominates within a zone of size 0.5 l to the crack tip, while strain gradient effects are clearly observed within 5l. It is also shown that the conventional way to evaluate the crack tip energy release rate would lead to an incorrect, infinite value. A new evaluation gives a finite crack tip energy release rate, and is identical to the J-integral.

Shakedown theorems are exact theories of classical plasticity for the direct computation of the load-carrying capacity under varying loads. Based on the classical Melan’s theorem, a numerical solution procedure for determining the shakedown load of elasto-perfectly plastic structure is presented firstly making use of the element free Galerkin (EFG) method. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration. The reduced-basis technique is adopted here to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. The self-equilibrium stress field is expressed by linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors can be generated by performing equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve nonlinear programming and determine the maximal load amplifier. The numerical results show that it is efficient and accurate to solve shakedown analysis problems by using the EFG method and nonlinear programming.

Hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are performed within the finite deformation theory to characterize the gradient-enhanced stress elevation and subsequent diffusion of hydrogen towards the crack tip. Results reveal that GNDs, absent in conventional plasticity predictions, play a fundamental role on hydrogen transport ahead of a crack. SGP estimations provide a good agreement with experimental measurements of crack tip deformation and high levels of lattice hydrogen concentration are predicted within microns to the crack tip. The important implications of the results in the understanding of hydrogen embrittlement mechanisms are thoroughly discussed.