Hydrostatic stress-dependent perfectly-plastic stress fields at a stationary plane-stress crack-tip

1992 ◽  
Vol 13 (8) ◽  
pp. 767-770
Author(s):  
Lin Bai-song
Keyword(s):  
Plane Stress ◽  
Hydrostatic Stress ◽  
Crack Tip ◽  
Stress Fields ◽  
Perfectly Plastic ◽  
Stress Dependent ◽  
Plastic Stress

scholarly journals The stress field near the tip of a plane stress crack in a gel consisting of chemical and physical cross-links

2019 ◽  
Vol 475 (2227) ◽  
pp. 20180863 ◽  
Author(s):  
Jingyi Guo ◽  
Chung-Yuen Hui ◽  
Mincong Liu ◽  
Alan T. Zehnder
Keyword(s):  
Plane Stress ◽  
Crack Opening ◽  
Three Dimensional ◽  
Crack Tip ◽  
Stress Fields ◽  
Asymptotic Results ◽  
Constant Stretch ◽  
Cross Links ◽  
Theoretical Results ◽  
Gel Network

We study the time-dependent asymptotic stress fields near the tip of a mode I plane stress crack in a hydrogel. The analysis is based on a three-dimensional continuum model which describes the viscoelastic behaviour of a hydrogel gel with permanent and transient cross-links. The viscoelasticity results from the breaking and healing of the transient cross-links in the gel network. We show that the crack tip fields satisfy a local correspondence principle—that is, the spatial singularities of these fields are identical to a hyperelastic cracked body with the same but undamaged networks. Asymptotic results compare very well with finite-element simulations on a single-edge crack specimen loaded under constant stretch rate. We also compare the theoretical results (crack opening profile and crack tip strain field) with experiments and find excellent agreement.

scholarly journals Strain-Softening Analyses of a Circular Bore under the Influence of Axial Stress

2021 ◽  
Vol 11 (17) ◽  
pp. 7937
Author(s):  
Xuechao Dong ◽  
Mingwei Guo ◽  
Shuilin Wang
Keyword(s):  
Rock Mass ◽  
Plane Stress ◽  
Strain Softening ◽  
Hydrostatic Stress ◽  
Axial Stress ◽  
Perfectly Plastic ◽  
Out Of Plane ◽  
Softening Process ◽  
Elastic Perfectly Plastic ◽  
Proper Consideration

Strain-softening analyses were performed around a circular bore in a Mohr–Coulomb rock mass subjected to a hydrostatic stress field in cross section and out-of-plane stress along the axis of the bore. Numerical procedures that simplify the strain-softening process in a step manner were employed, and on the basis of the theoretical solutions of the elastic–brittle–plastic(EBP) medium, the strain-softening results of the displacements, stresses and the plastic zones around the circular bore were obtained. The numerical solution was validated based on the fact that the strain-softening process became EBP when the softening slope was very steep and elastic-perfectly plastic(EP) when the softening slope was near zero. The results illustrated that the stresses and displacements in the rock mass surrounding the bore was affected by axial stress and that a proper consideration of out-of-plane stress is necessary. Moreover, the presented results can be used for the verification of numerical codes.

Asymptotic Crack-Tip Fields for Perfectly Plastic Solids Under Plane-Stress and Mixed-Mode Loading Conditions

1990 ◽  
Vol 57 (3) ◽  
pp. 635-638 ◽  
Author(s):  
P. Dong ◽  
J. Pan
Keyword(s):  
Plane Stress ◽  
Mixed Mode ◽  
Crack Tip ◽  
Mode I ◽  
Mode Ii ◽  
Crack Tip Field ◽  
Crack Tip Fields ◽  
Perfectly Plastic ◽  
Mixed Mode Crack ◽  
Small Constant

In this paper, we first discuss some of the properties of the crack-tip sectors for perfectly plastic materials under plane-stress conditions. Then starting with the plane-stress mixed-mode crack-tip fields suggested by Shih (1973), we assemble these sectors in a slightly different manner from those in Shih (1973). The missing governing equations needed to completely specify the crack-tip fields for both near mode I and near mode II mixed-mode loadings are derived. The mode I crack-tip field, as the limit of the near mode I cases, differs from Hutchinson’s solution (1968) by the appearance of a small constant stress sector ahead of the crack tip. In addition, the relevance of the solutions of the near mode II cases to some interesting features of the mixed-mode crack-tip fields, as suggested by Budiansky and Rice (1973), is also discussed.

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