Asymptotic Fields of a Perfectly-Plastic, Plane-Stress Mode II Growing Crack

1986 ◽  
Vol 53 (4) ◽  
pp. 831-833 ◽  
Author(s):  
P. Ponte Castan˜eda
Keyword(s):  
Plane Stress ◽  
Velocity Fields ◽  
Mode I ◽  
Mode Ii ◽  
Perfectly Plastic ◽  
Stress Mode ◽  
Mode Ii Crack ◽  
Growing Crack ◽  
Elastic Perfectly Plastic ◽  
Elastic Unloading

The asymptotic near-tip stress and velocity fields are presented for a plane-stress Mode II crack propagating quasi-statically in an elastic-perfectly plastic Mises solid. The solution is found to have fully continuous stress and velocity fields, and a configuration similar to that of the anti-plane strain problem: a singular centered fan plastic sector ahead of the crack, followed by an elastic unloading sector and a constant stress plastic sector extending to the crack flank. The impossibility of a plane-stress Mode I crack solution having these properties is also discussed.

Dislocation-based approximate solution of the plastic zone of the mode II crack in an elastic perfectly plastic solid

1991 ◽  
Vol 435 (1893) ◽  
pp. 43-68 ◽  
Keyword(s):  
Approximate Solution ◽  
Dislocation Density ◽  
Companion Paper ◽  
Mode Ii ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Mode Ii Crack ◽  
Density Vector ◽  
Elastic Perfectly Plastic ◽  
Dislocation Crack

A dislocation-based (approximate) solution is found for the stress-strain field of the plastic zone (in small-scale yielding) of the stationary mode II crack in an elastic perfectly plastic and incompressible solid. General dislocation equations applicable for plane strain elastic-plastic conditions are presented and used to solve the problem. These equations have broader application than to the particular problem of the paper. The solution is obtained with use of dislocation crack tip shielding and the dislocation crack extension force. Derived dislocation boundary conditions which play an important role in the analysis are B t = 0 at an elastic–plastic boundary and, at elastic–plastic, plastic–plastic and crack plane boundaries, the jump condition [(1 – v )/2 G ) {∂σ tt /∂ x n } jump = { t· B } jump + ∂ B n /∂ x t , where G is the shear modulus, σ tt is the non-traction stress, v is Poisson’s ratio. B is the (area) dislocation density vector. B is the surface dislocation density vector and t and n are the tangential and normal directions to a boundary. The strain compatibility equation is [ G /(1 – v )] (∇ x B ) z = ∇ 2 ½(σ nn + σ tt ). The near tip strain and stress contours of fan sectors are given by the equation r = r c h(θ) , where r c is a constant and the azimuthal function h(θ) is given by the equation h'" + 9 h' = ( p 0 – 2 θ ) ( h" + h ), where p 0 is a constant and a prime denotes ∂/∂ θ . The (approximate) elastic region stress field solution is presented in the companion paper to this one. A mode I crack solution, similar in its structure to the mode II crack solution, also is presented in the paper. This latter solution is shown in the companion paper to be flawed.

FEM solutions for plane stress mode-I and mode-II cracks in strain gradient plasticity

2000 ◽  
Vol 43 (9) ◽  
pp. 969-979
Author(s):  
Xinming Qiu ◽  
Tianfu Guo ◽  
Kezhi Huang ◽  
Kehchih Hwang
Keyword(s):  
Plane Stress ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Mode I ◽  
Mode Ii ◽  
Gradient Plasticity ◽  
Stress Mode

Elastic region solution of the mode II crack in an elastic perfectly plastic solid

1991 ◽  
Vol 435 (1893) ◽  
pp. 69-84 ◽  
Keyword(s):  
Stress Field ◽  
Plastic Zone ◽  
Elastic Region ◽  
Mode Ii ◽  
Stationary Mode ◽  
Crack Plane ◽  
Field Solution ◽  
Perfectly Plastic ◽  
Mode Ii Crack ◽  
Elastic Perfectly Plastic

The approximate stress field solution is found of the elastic region which surrounds the plastic zone of the stationary mode II crack in an elastic perfectly plastic and incompressible solid. The plastic zone solutions are given in a companion paper. The elastic region region stress field solution depends upon a determination of the crack plane (surface) dislocation distribution. Equations are derived to give this distribution. The elastic region stress field is found from an integration of the stress fields of all the dislocations present in the plastic zones and on the crack plane. A failed solution for the mode I crack also is considered in this paper.

Errata - Elastic region solution of the mode II crack in an elastic perfectly plastic solid

1992 ◽  
Vol 436 (1898) ◽  
pp. 664-664
Keyword(s):  
Elastic Region ◽  
Mode Ii ◽  
Perfectly Plastic ◽  
Mode Ii Crack ◽  
Elastic Perfectly Plastic

Page 78, equation (3.6 b ) for G * I = cos½θ 2 +½sinθ 2 sin½θ 2 read G * I = cos θ 2 cos θ 2 cos½θ 2 + ½sinθ 2 sin½θ 2 .

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.

Analytical Solutions for Crack Tip Plastic Zone Shape Using the Von Mises and Tresca Yield Criteria: Effects of Crack Mode and Stress Condition

2004 ◽  
Vol 20 (3) ◽  
pp. 199-210 ◽  
Author(s):  
P. H. Jing ◽  
T. Khraishi
Keyword(s):  
Plastic Zone ◽  
Plane Stress ◽  
Stress Condition ◽  
Crack Tip ◽  
Mode Ii ◽  
Yield Criteria ◽  
Closed Form Solutions ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

AbstractAnalytical closed-form solutions for the crack tip plastic zone shape have been derived for a semi-infinite crack in an isotropic elastic-perfectly plastic solid under both plane stress and plane strain conditions. Two yield criteria have been applied: the Von Mises and Tresca yield criteria. The solutions have been developed for crack modes I and III (mode II has been published previously). The results, which favorably compare to a limited number of existing experimental and analytical findings, indicate that the Tresca zone is larger in size than the Von Mises zone. Moreover, an interesting observation is that both zones are generally much larger than the ones predicted by classical Irwin and Dugdale-Barenblatt solutions.

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