Non-existence of separable crack tip field in mechanism-based strain gradient plasticity

Shi, Miao; Huang, Y.; Gao, Huajian; Hwang, Kwang‐il

doi:10.1016/s0020-7683(99)00217-6

Cited by 53 publications

(48 citation statements)

References 35 publications

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“…It is also observed that the absolute value of the slope at each point on the curve for MSGplasticity exceeds or equals to 1=2, suggesting the crack tip field in MSG plasticity is not only more singular than the HRR field, but also more singular than the elastic K field. This high stress singularity results from the dominance of geometrically necessary dislocations around the crack tip in MSG plasticity (Shi et al, 2001). Fig.…”

Section: Fracture Analysis Of a Stationary Mode-i Crackmentioning

confidence: 98%

“…It agrees well with McElhaney et alÕs (1998)Õs micro-indentation experiments of bulk copper (see Huang et al, 2000b) and Saha et alÕs (2001) indentation experiments of aluminum thin film on a glass substrate, with Fleck et alÕs (1994) micro-torsion and Stolken and EvansÕ (1998) micro-bend experiments (see Gao et al, 1999a), and with LloydÕs (1994) metal-matrix composite (see Xue et al, 2002a). It has also been successfully applied to study a few important problems at the micron and submicron scales, including microelectro-mechanical systems (Xue et al, 2002b), plastic flow localization (Hao et al, 2000;Shi et al, 2000b), and fracture (Shi et al, 2000a;Jiang et al, 2001). However, the present MSG plasticity theory is a deformation theory which has not accounted for elastic unloading nor for non-proportional deformation as in crack propagation.…”

Section: Introductionmentioning

confidence: 99%

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The flow theory of mechanism-based strain gradient plasticity

Qiu

Huang

Wei

et al. 2003

Mechanics of Materials

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The flow theory of mechanism-based strain gradient (MSG) plasticity is established in this paper following the same multiscale, hierarchical framework for the deformation theory of MSG plasticity in order to connect with the Taylor model in dislocation mechanics. We have used the flow theory of MSG plasticity to study micro-indentation hardness experiments. The difference between deformation and flow theories is vanishingly small, and both agree well with experimental hardness data. We have also used the flow theory of MSG plasticity to investigate stress fields around a stationary mode-I crack tip as well as around a steady state, quasi-statically growing crack tip. At a distance to crack tip much larger than dislocation spacings such that continuum plasticity still applies, the stress level around a stationary crack tip in MSG plasticity is significantly higher than that in classical plasticity. The same conclusion is also established for a steady state, quasi-statically growing crack tip, though only the flow theory can be used because of unloading during crack propagation. This significant stress increase due to strain gradient effect provides a means to explain the experimentally observed cleavage fracture in ductile materials

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Section: Fracture Analysis Of a Stationary Mode-i Crackmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

The flow theory of mechanism-based strain gradient plasticity

Qiu

Huang

Wei

et al. 2003

Mechanics of Materials

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show abstract

“…These boundary layers are due to the additional boundary conditions introduced in the higher-order theory of MSG. Furthermore, Shi et al 44 showed that the thickness of boundary layers is on the order of L 2 /l, and is typically around 10 nm for metallic materials, where L is the average dislocation spacing and l is the intrinsic material length in Eq. (8).…”

Section: The Constitutive Model In Cmsgmentioning

confidence: 99%

Indenter tip radius effect on the Nix–Gao relation in micro- and nanoindentation hardness experiments

et al. 2004

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Nix and Gao established an important relation between microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range), but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). We have developed a unified computational model for both micro-and nanoindentation in an effort to understand the breakdown of the Nix-Gao relation at indentation depths approaching the nanometer scale. The unified computational model for indentation accounts for various indenter shapes, including a sharp, conical indenter, a spherical indenter, and a conical indenter with a spherical tip. It is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The unified computational model for indentation indeed shows that the Nix-Gao relation holds in microindentation with a sharp indenter, but it does not hold in nanoindentation due to the indenter tip radius effect.

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“…This lower order scheme is adopted in the present work to characterize gradient effects from a mechanism-based approach, as it does not suffer convergence problems when addressing numerically demanding problems, such as crack tip deformation under large strains, unlike its higher order counterpart (see [68,69]). In MSG plasticity the differences between the higher order and the lower order versions are restricted to a very thin boundary layer (≈ 10 nm) [14,70].…”

Section: Cmsg Plasticitymentioning

confidence: 99%

Strain Gradient Plasticity-Based Modeling of Damage and Fracture

Martínez‐Pañeda¹

2018

Springer Theses

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Non-existence of separable crack tip field in mechanism-based strain gradient plasticity

Cited by 53 publications

References 35 publications

The flow theory of mechanism-based strain gradient plasticity

The flow theory of mechanism-based strain gradient plasticity

Indenter tip radius effect on the Nix–Gao relation in micro- and nanoindentation hardness experiments

Strain Gradient Plasticity-Based Modeling of Damage and Fracture

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