Mode I and mixed mode crack-tip fields in strain gradient plasticity

Abstract

To cite this version:Stergios Goutianos.Mode I and mixed mode crack-tip fields in strain gradient plasticity.International Journal of Non-Linear Mechanics, Elsevier, 2011, 46 (9) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractStrain gradients develop near the crack-tip of Mode I or mixed-mode cracks.A finite strain version of the phenomenological strain gradient plasticity theory of Fleck-Hutchinson (2001) is used here to quantify the effect of the material length scales on the crack-tip stress field for a sharp stationary crack under Mode I and mixed-mode loading. It is found that for material length scales much smaller than the scale of the deformation gradients, the predictions converge to conventional elastic-plastic solutions. For length scales sufficiently large, the predictions converge to elastic solutions. Thus, the range of length scales over which a strain gradient plasticity model is necessary is identified. The role of each of the three material length scales, incorporated in the multiple length scale theory, in altering the near-tip stress field is systematically studied in order to quantify their effect.

Scale-Dependent Crack Modeling for Investigation the Effect of Geometrically Necessary Dislocations in Micro/Nano Grain Size of Copper

“…First, considering only the homogeneous hardening part related to l = 0 which they are labeled "modified classic" and second, with considering both the homogeneous and the nonhomogeneous hardening part which they are marked "non-H modified classic". In spite of [17], where the length scale was systematically varied, here it is intended to use and implement realistic parameters related to the length scale from the constitutive equation. As demonstrated in [17], the plastic flow resistance is proliferated because of large plastic strain gradients in the crack-tip region.…”

“…In spite of [17], where the length scale was systematically varied, here it is intended to use and implement realistic parameters related to the length scale from the constitutive equation. As demonstrated in [17], the plastic flow resistance is proliferated because of large plastic strain gradients in the crack-tip region. This brings about lower the amount of plastic deformation in this region for materials at small scales.…”

“…To investigate near crack-tip behavior, Fig. 7 shows the effective plastic strain for the model in Eq.1 for the grain size of 20µm, and the power-law hardening model from [17]. It is apprehended that the earlier saturation state for stress is occurred in the stress-strain curve of nanocrystalline solids in Eq.1 rather than mentioned power-law model.…”

“…Therefore, the resistance at crack-tip in nanocrystalline material model prevent evolution of plastic strain to neighbouring areas. It is worth mentioning that in the research of [17], higher strain concentration at the crack-tip for power-law model was obtained when higher constants of length scale is employed.…”

“…Researchers usually used the elastic-power law plastic hardening for investigation size effects with the role of material length scale in crack-tip models ( [7,10,12,17]). The most widely used theories for numerical studies of crack-tip stresses based on the strain gradient plasticity are the higher order theories of Fleck and Hutchinson in [18,19] and lower order theory of Gao and colleagues in [20,21].…”