Application of the Deformation Theory of Plasticity for Determining Elastoplastic Stress and Strain Concentration Factors

1976 ◽  
Vol 98 (4) ◽  
pp. 1152-1156 ◽  
Author(s):  
J. P. Eimermacher ◽  
I.-Chih Wang ◽  
M. L. Brown
Keyword(s):  
Deformation Theory ◽  
Analytical Data ◽  
Local Stress ◽  
Failure Criteria ◽  
Constitutive Law ◽  
Stress And Strain ◽  
Strain Concentration ◽  
Theory Of Plasticity ◽  
Concentration Factors ◽  
Von Mises

The deformation theory of plasticity is considered as a means for obtaining a solution to the problem of calculating stress and strain concentration factors at geometric discontinuities where the local stress state exceeds the yield strength of the material. Through the use of the Hencky-Nadai constitutive law and the Von Mises failure criteria, the elastoplastic element stiffness matrix is derived for a plane stress triangular plate element. An elastoplastic solution is arrived at by considering direct-iterative and finite element techniques. Verification of the analytical results is obtained by considering a numerical example and comparing the calculated results with published experimental and analytical data.

A method of successive approximation applied to an elastic-plastic deformation theory

1969 ◽  
Vol 4 (1) ◽  
pp. 40-44
Author(s):  
K V Wellner ◽  
I S Tuba
Keyword(s):  
Plastic Deformation ◽  
Circular Hole ◽  
Deformation Theory ◽  
Infinite Medium ◽  
Stress And Strain ◽  
Plane Shear ◽  
Strain Concentration ◽  
Elastic Plastic ◽  
Method Of Solution ◽  
Concentration Factors

Elastic-plastic stress and strain concentration factors are derived for a circular hole in an infinite medium under uniform anti-plane shear conditions. The suggested method of solution could be applied also to other problems of interest.

Plastic Deformation Theory Application in Finite Element Analysis

2012 ◽  
Vol 594-597 ◽  
pp. 2723-2726
Author(s):  
Wen Shan Lin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Element Analysis ◽  
Finite Element Program ◽  
Theory Of Plasticity ◽  
Element Program

In the present study, the constitutive law of the deformation theory of plasticity has been derived. And that develop the two-dimensional and three-dimensional finite element program. The results of finite element and analytic of plasticity are compared to verify the derived the constitutive law of the deformation theory and the FEM program. At plastic stage, the constitutive laws of the deformation theory can be expressed as the linear elastic constitutive laws. But, it must be modified by iteration of the secant modulus and the effective Poisson’s ratio. Make it easier to develop finite element program. Finite element solution and analytic solution of plasticity theory comparison show the answers are the same. It shows the derivation of the constitutive law of the deformation theory of plasticity and finite element analysis program is the accuracy.

Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory

2003 ◽  
Vol 125 (3) ◽  
pp. 260-265 ◽  
Author(s):  
C. L. Chow ◽  
M. Jie ◽  
S. J. Hu
Keyword(s):  
Strain Hardening ◽  
Deformation Theory ◽  
Yield Criterion ◽  
Strain Ratio ◽  
Yield Function ◽  
Forming Limit ◽  
Sheet Metals ◽  
Theory Of Plasticity ◽  
Von Mises Yield Criterion ◽  
Von Mises

This paper presents the development of a generalized method to predict forming limits of sheet metals. The vertex theory, which was developed by Sto¨ren and Rice (1975) and recently simplified by Zhu, Weinmann and Chandra (2001), is employed in the analysis to characterize the localized necking (or localized bifurcation) mechanism in elastoplastic materials. The plastic anisotropy of materials is considered. A generalized deformation theory of plasticity is proposed. The theory considers Hosford’s high-order yield criterion (1979), Hill’s quadratic yield criterion and the von Mises yield criterion. For the von Mises yield criterion, the generalized deformation theory reduces to the conventional deformation theory of plasticity, i.e., the J2-theory. Under proportional loading condition, the direction of localized band is known to vary with the loading path at the negative strain ratio region or the left hand side (LHS) of forming limit diagrams (FLDs). On the other hand, the localized band is assumed to be always perpendicular to the major strain at the positive strain ratio region or the right hand side (RHS) of FLDs. Analytical expressions for critical tangential modulus are derived for both LHS and RHS of FLDs. For a given strain hardening rule, the limit strains can be calculated and consequently the FLD is determined. Especially, when assuming power-law strain hardening, the limit strains can be explicitly given on both sides of FLD. Whatever form of a yield criterion is adopted, the LHS of the FLD always coincides with that given by Hill’s zero-extension criterion. However, at the RHS of FLD, the forming limit depends largely on the order of a chosen yield function. Typically, a higher order yield function leads to a lower limit strain. The theoretical result of this study is compared with those reported by earlier researchers for Al 2028 and Al 6111-T4 (Grafand Hosford, 1993; Chow et al., 1997).

scholarly journals Stress and Strain Concentration Factors in Orthotropic Composites with Hole under Uniaxial Tension

2018 ◽  
Vol 5 (1) ◽  
pp. 213-231
Author(s):  
Samit Ray-Chaudhuri ◽  
Komal Chawla
Keyword(s):  
Uniaxial Tension ◽  
Fiber Orientation ◽  
Composite Plates ◽  
Systematic Investigation ◽  
Stress And Strain ◽  
Governing Parameter ◽  
Strain Concentration ◽  
Wide Range ◽  
Orthotropic Composites ◽  
Concentration Factors

Abstract A systematic investigation is carried out on how different parameters influence stress and strain concentration factors (SCF and SNCF) in a composite plate with a hole under uniaxial tension. Flat and singly curved composite plates have been modelled in ANSYS 15.0. The governing parameter includes: (i) size, shape and eccentricity of hole, (ii) number of plies, (v) fiber orientation and (vi) plate curvature. It is observed that different parameters influence the SCF and SNCF with varying degrees. For example, SCF may be as high as 7.16 for a square shaped hole. Also, SCF and SNCF are found to be approximately same in most of the cases. Finally, simplified design formulas are developed for evaluation of SCF for a wide range of hole size, eccentricity and fiber orientation.

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