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.

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.

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.

Approximate Elastic-Plastic Analysis of Intersecting Equal Diameter Cylindrical Shells

1981 ◽  
Vol 103 (1) ◽  
pp. 111-115
Author(s):  
D. P. Updike
Keyword(s):  
Plastic Material ◽  
Cylindrical Shells ◽  
Yield Condition ◽  
Pressure Vessels ◽  
Ductile Materials ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Analysis ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Design of connections of pipes and pressure vessels on the basis of a calculated maximum elastic stress often proves to be too conservative in the case of ductile materials. Elastic-plastic analysis by the finite element method proves to be too costly. This paper presents an alternative method which reduces the calculations to those of a rotationally symmetric shell subjected to axisymmetric loading. Using this approach approximate elastic-plastic deformations on the meridian passing through the crotch of a tee branch connection of cylindrical shells of equal diameter and thickness are determined. The method is limited to cases of the normal intersection of very thin shells of identical diameter, thickness, and material and to internal pressure loading. Numerical results for the intersection of two shells of R/t equal to 100 are given for an elastic-perfectly plastic material satisfying the von Mises yield condition.

Transient and Residual Thermal Stresses in an Elastic-Plastic Cylinder

1960 ◽  
Vol 27 (3) ◽  
pp. 481-488 ◽  
Author(s):  
H. G. Landau ◽  
E. E. Zwicky
Keyword(s):  
Thermal Stresses ◽  
Plastic Material ◽  
Numerical Procedure ◽  
Yield Condition ◽  
Transient Temperature ◽  
Temperature Dependent ◽  
Perfectly Plastic ◽  
Plastic Cylinder ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Equations are given for the stress rates in solid cylinders subject to transient temperature distributions, based on the assumption of an elastic, perfectly plastic material obeying a von Mises temperature-dependent yield condition. A numerical procedure for integrating the equations is developed and applied to a temperature distribution approximating a phase transformation and to a quenched cylinder. The effect of various factors on the residual stresses is noted.

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.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

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