A method of elastic-plastic plane stress and strain analysis

1966 ◽  
Vol 1 (2) ◽  
pp. 115-120 ◽  
Author(s):  
I. S. Tuba
Keyword(s):  
Boundary Value Problems ◽  
Plane Stress ◽  
Stress Function ◽  
Biharmonic Equation ◽  
Strain Analysis ◽  
Plane Boundary ◽  
Stress And Strain ◽  
Plastic Strains ◽  
Elastic Plastic ◽  
Governing Relation

Plane boundary value problems are formulated in terms of an elastic-plastic stress function and the plastic strains. The governing relation is a non-homogeneous biharmonic equation. It is applicable to the total or deformation theories and to the incremental theories. Sample problems illustrate the practicality of the method.

Elastic-Plastic Stress and Strain Analysis of a Hole-Edge Crack under Biaxial Load

2013 ◽  
Vol 321-324 ◽  
pp. 218-221 ◽  
Author(s):  
Zhong Xian Wang ◽  
Wei Xu ◽  
Rui Liu
Keyword(s):  
Stress Concentration ◽  
Crack Growth ◽  
Circular Hole ◽  
Structural Damage ◽  
Strain Analysis ◽  
Plastic Zone Size ◽  
Stress And Strain ◽  
Elastic Plastic ◽  
Biaxial Load ◽  
Plastic Stress

In this study, the effects of biaxial load on the elastic-plastic stress concentration factor and the plastic zone size of the circular hole are investigated, and the elastic-plastic stress and strain fields of the crack emanating from the circular hole are calculated in the process of crack growth. The elastic-plastic stress concentration factors for various biaxial load ratios are obtained. In order to provide a reference for structural damage monitoring, the variation characteristic of strain at crack front ligament are analyzed in the process of the crack growth.

Experimental Solution of Elastic-Plastic Plane-Stress Problems

1962 ◽  
Vol 29 (4) ◽  
pp. 735-743 ◽  
Author(s):  
P. S. Theocaris
Keyword(s):  
Plane Stress ◽  
Yield Condition ◽  
Strain Curve ◽  
Loading Path ◽  
Flow Rule ◽  
Stress And Strain ◽  
Stress Strain ◽  
Plane State ◽  
Elastic Plastic ◽  
Principal Strains

The paper presents an experimental method for the solution of the plane state of stress of an elastic-plastic, isotropic solid that obeys the Mises yield condition and the associated flow rule. The stress-strain law is an incremental type law, determined by the Prandtl-Reuss stress-strain relations. The method consists in determining the difference of principal strains in the plane of stress by using birefringent coatings cemented on the surface of the tested solid. A determination of relative retardation using polarized light at normal incidence, complemented by a determination in two oblique incidences at 45 deg along with the tracing of isoclinics, procures enough data for obtaining the principal strains all over the field. The calculation of the elastic and plastic components of strains is obtained in a step-by-step process of loading. It is assumed that during each step the Cartesian components of stress and strain remain constant. The stress increments and the stresses can be found thereafter by using the Prandtl-Reuss stress-strain relations and used for the evaluation of the components of strains and their increments in the next step. The method can be used with any material having any arbitrary stress-strain curve, provided that convenient formulas are established relating the stress and strain components and their increments at each point of the loading path. The method is applied to an example of contained plastic flow in a notched tensile bar of an elastic, perfectly plastic material under conditions of plane stress.

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