Exact solutions of near crack line fields for mode I crack under plane stress condition in an elastic-perfectly plastic solid

1996 ◽  
Vol 17 (4) ◽  
pp. 351-358 ◽  
Author(s):  
Yi Zhijian ◽  
Wang Shijie
Keyword(s):  
Exact Solutions ◽  
Plane Stress ◽  
Stress Condition ◽  
Mode I ◽  
Mode I Crack ◽  
Plane Stress Condition ◽  
Crack Line ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

A Complete Perfectly Plastic Solution for the Mode I Crack Problem Under Plane Stress Loading Conditions

2006 ◽  
Vol 74 (3) ◽  
pp. 586-589 ◽  
Author(s):  
David J. Unger
Keyword(s):  
Stress Field ◽  
Plane Stress ◽  
Plastic Material ◽  
Crack Problem ◽  
Yield Condition ◽  
Internal Crack ◽  
Mode I ◽  
Mode I Crack ◽  
Loading Conditions ◽  
Perfectly Plastic

A continuous stress field for the mode I crack problem for a perfectly plastic material under plane stress loading conditions has been obtained recently. Here, a kinematically admissible velocity field is introduced, which is compatible with the continuous stress field obtained earlier. By associating these two fields together, it is shown that they constitute a complete solution for the uncontained plastic flow problem around a finite length internal crack, having a positive rate of plastic work. The yield condition employed is an alternative criterion first proposed by Richard von Mises in order to approximate the plane stress Huber-Mises yield condition, which is elliptical in shape, to one that is composed of two intersecting parabolas in the principal stress plane.

A Plane Stress Perfectly Plastic Mode I Crack Solution With Continuous Stress Field

2005 ◽  
Vol 72 (1) ◽  
pp. 62-67 ◽  
Author(s):  
David J. Unger
Keyword(s):  
Plane Stress ◽  
Plastic Material ◽  
Crack Problem ◽  
Yield Condition ◽  
Admissible Solution ◽  
Mode I ◽  
Mode I Crack ◽  
Perfectly Plastic ◽  
Compressive Stresses ◽  
Von Mises

A statically admissible solution for a perfectly plastic material in plane stress is presented for the mode I crack problem. The yield condition employed is an alternative type first proposed by von Mises in order to approximate his original yield condition for plane stress while eliminating most of the elliptic region as pertaining to partial differential equations. This yield condition is composed of two intersecting parabolas rather than a single ellipse in the principal stress space. The attributes of this particular solution of the mode I problem over that previously obtained are that it contains neither stress discontinuities nor compressive stresses anywhere in the field.

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.

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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