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.

Analytical Solutions of Crack Tip Plasticity Zone Shape for a Semi-Infinite Crack

2003 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Analytical Solutions ◽  
Yield Criterion ◽  
Plasticity Zone ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Classical Plasticity ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.

Closed-Form Solutions for the Mode ii Crack tip Plastic Zone Shape

2003 ◽  
Vol 122 (3/4) ◽  
pp. L137-L142 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plastic Zone ◽  
Closed Form ◽  
Crack Tip ◽  
Mode Ii ◽  
Closed Form Solutions ◽  
Mode Ii Crack

scholarly journals The yield condition strongly influences the formation of Dugdale plastic strips ahead of crack tips under tensile plane stress loading conditions

2012 ◽  
Vol 21 (1-2) ◽  
pp. 37-39
Author(s):  
David J. Unger
Keyword(s):  
Plane Stress ◽  
Plastic Material ◽  
Yield Condition ◽  
Loading Conditions ◽  
Element Analysis ◽  
Plastic Strip ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

AbstractA finite element analysis indicates a good correlation between the Dugdale plastic strip model and a linear elastic/perfectly plastic material under plane stress loading conditions for a flow theory of plasticity based on the Tresca yield condition. A similar analysis under the von Mises yield condition reveals no plastic strip formation.

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.

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.

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.

A Finite Element Study of Stable Crack Growth Under Plane Stress Conditions: Part I—Elastic-Perfectly Plastic Solids

1987 ◽  
Vol 54 (4) ◽  
pp. 838-845 ◽  
Author(s):  
R. Narasimhan ◽  
A. J. Rosakis ◽  
J. F. Hall
Keyword(s):  
Finite Element ◽  
Plastic Zone ◽  
Crack Growth ◽  
Plane Stress ◽  
Stable Crack Growth ◽  
Small Scale ◽  
Finite Element Study ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Element Study

A detailed finite element study of stable crack growth in elastic-perfectly plastic solids obeying an incremental plasticity theory and the Huber-Von Mises yield criterion is performed under plane stress, small-scale yielding conditions. A nodal release procedure is used to simulate crack extension under continuously increasing external load. It is found that the asymptotic angular extent of the active plastic zone surrounding the moving crack tip is from θ = 0 deg to about θ = 45 deg. Clear evidence of an elastic unloading region following the active plastic zone is found, but no secondary (plastic) reloading is numerically observed. The near-tip angular stress distribution inside the active plastic zone is in good agreement with the variation inside a centered fan, as predicted by a preliminary asymptotic analysis by Rice. It is also observed that the stress components within the plastic zone have a strong radial variation. The nature of the near-tip profile is studied in detail.

The analytical solution of a growing steady-state mode III crack in an elastic perfectly plastic solid through an electrical analogy

1989 ◽  
Vol 425 (1869) ◽  
pp. 291-327 ◽  
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Plastic Zone ◽  
Crack Tip ◽  
Mode Iii ◽  
Steady State Mode ◽  
Screw Dislocations ◽  
Mode Iii Crack ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

An approximate analytical solution is found of a quasi-static growing steady-state mode III crack in an elastic perfectly plastic solid. The analysis makes use of a close analogy between the mode III crack problem and the problem of the thin electrical conducting plate that is embedded in a medium of finite conductivity through which electrical current flows. Plastic strain is calculated from the motion of nonredundant infinitesimal screw dislocations. Screw dislocations are Eshelby’s analogue of lines of electrical charge. Calculation of the dislocation crack tip shielding can be used to check the analysis. The plastic zone is a combined Dean & Hutchinson (DH) type unfocused fan plastic zone and a Chitaley & McClintock (CM) type focused fan plastic zone. The asymptotic solution at the crack tip is the CM one. The plastic zone found differs significantly in size and shape from the DH and the CM plastic zones. Novel features in the analysis are the use of a (dislocation density required) stress gradient boundary condition and the introduction of a shifting centre cylindrical coordinate system.

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