Studies on Plastic Flow of Anisotropic Metals

1956 ◽  
Vol 23 (3) ◽  
pp. 444-450
Author(s):  
L. W. Hu
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Strain Hardening ◽  
Plane Strain ◽  
Plastic Flow ◽  
Plane Stress ◽  
Biaxial Tension ◽  
Plastic Behavior ◽  
Theory Of Plastic Flow ◽  
Walled Cylinder

Abstract This investigation deals with a study of the plastic behavior of anisotropic metals. By extending Hill’s theory of plastic flow of anisotropic metals, plastic stress-strain relations for anisotropic materials with strain hardening are developed. Applications of these relations are also made to plane-stress and plane-strain problems with anisotropy. The effect of anisotropy on the stress distribution and on the pressure to produce yielding in a thick-walled cylinder under internal pressure is discussed. The influence of anisotropy on the interpretation of conventional biaxial tension-tension and tension-torsion tests is also considered in this study.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

scholarly journals The theory of combined plastic and elastic deformation with particular reference to a thick tube under internal pressure

1947 ◽  
Vol 191 (1026) ◽  
pp. 278-303 ◽  
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Plastic Flow ◽  
Plastic Region ◽  
Strain Diagram ◽  
Combined Stresses ◽  
Usual Theory ◽  
Plastic Components ◽  
Longitudinal Extension ◽  
Elastic Strains

In certain problems of plastic flow, for example, a thick tube expanded by internal pressure, it is important to consider changes in the elastic strain of material which is flowing plastically in order to deduce the correct stress distribution and deformation. The usual plastic theory which neglects elastic strains in the plastic region may lead to considerable errors in certain cases. In this paper we review the theory of the deformation of a material under combined stresses which involves both elastic and plastic components of strain. The relationship between stress and strain is represented on a plane diagram, the reduced stress-strain diagram, which facilitates discrimination between the elastic and plastic components of strain and aids considerably the solution of certain problems. The diagram can also be used to express the relationships governing the dissipation of energy during plastic flow under combined stresses. The theory is applied to the deformation of a long thick tube under internal pressure with zero longitudinal extension. The solution is compared with that based on the usual theory which neglects elastic strains in the plastic region, revealing an error which reaches a maxi­mum of over 60% in the longitudinal stress distribution. The significance of the differences between the two solutions is discussed in detail.

Partially Plastic Thick-Walled Cylinder Theory

1952 ◽  
Vol 19 (2) ◽  
pp. 133-140
Author(s):  
M. C. Steele
Keyword(s):  
Internal Pressure ◽  
Experimental Evidence ◽  
Closed Form ◽  
Strain Hardening ◽  
Axial Stress ◽  
Quantitative Comparison ◽  
Stress Strain ◽  
Von Mises ◽  
Walled Cylinder

Abstract Previous theories for partially plastic thick-walled cylinders under internal pressure are reviewed. A quantitative comparison is given for (a) compressibility versus incompressibility of material, and (b) von Mises’ versus Tresca’s theory of failure. The former reveals that deflections at the outside and bore surfaces agree closely, although considerable percentage differences may be found in the axial stresses and strains. Large differences (except for the axial stress) are found in comparing the two theories of failure. Based on the comparison and available experimental evidence, a theory is presented in closed form to include the Hencky stress-strain relations, incompressibility, and Ludwik’s strain-hardening function.

Ductile Tearing Instability of a Center-Cracked Panel of an Elastic-Plastic Strain Hardening Material

1981 ◽  
Vol 103 (1) ◽  
pp. 46-54 ◽  
Author(s):  
Akram Zahoor ◽  
Paul C. Paris
Keyword(s):  
Plastic Strain ◽  
Strain Hardening ◽  
Plane Strain ◽  
Plane Stress ◽  
Hardening Material ◽  
Ductile Tearing ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Tearing Instability ◽  
Crack Stability

An analysis for crack instability in an elastic-plastic strain hardening material is presented which utilizes the J-integral and the tearing modulus parameter, T. A center-cracked panel of finite dimensions with Ramberg-Osgood material representation is analyzed for plane stress as well as plane strain. The analysis is applicable in the entire range of elastic-plastic loading from linear elastic to full yield. Crack instability is strongly influenced by the elastic compliance of the system, the conditions of plane stress or plane strain, and the hardening characteristics of the material. Numerical results indicate that if crack stability is ensured in a plane strain situation, then under the same circumstances a geometrically identical but plane stress panel will be stable.

Plastic Stress Concentration at a Circular Hole in an Infinite Sheet Subjected to Equal Biaxial Tension

1960 ◽  
Vol 27 (1) ◽  
pp. 59-64 ◽  
Author(s):  
Bernard Budiansky ◽  
O. L. Mangasarian
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Strain Hardening ◽  
Circular Hole ◽  
Applied Stress ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Deformation Theory ◽  
Biaxial Tension ◽  
Hardening Material

With the use of J2 deformation theory, the stress-concentration factor at a circular hole in an infinite sheet of strain-hardening material subjected to equal biaxial tension at infinity is found for a variety of representative materials. The analysis exploits a transformation which permits the calculation of the stress-concentration factor without determining the stress distribution in the sheet. Subsequent calculations reveal that, for a monotonically increasing applied stress, the stress history at all points in the sheet is nearly radial.

scholarly journals Strain Localization of Orthotropic Elasto–Plastic Cohesive–Frictional Materials: Analytical Results and Numerical Verification

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2040
Author(s):  
Sungchul Kim ◽  
Miguel Cervera ◽  
Jian-Ying Wu ◽  
Michele Chiumenti
Keyword(s):  
Plane Strain ◽  
Plastic Flow ◽  
Plane Stress ◽  
Strain Localization ◽  
Numerical Results ◽  
Flow Rule ◽  
Numerical Verification ◽  
Applied Loading ◽  
Analytical Results ◽  
Frictional Materials

Strain localization analysis for orthotropic-associated plasticity in cohesive–frictional materials is addressed in this work. Specifically, the localization condition is derived from Maxwell’s kinematics, the plastic flow rule and the boundedness of stress rates. The analysis is applicable to strong and regularized discontinuity settings. Expanding on previous works, the quadratic orthotropic Hoffman and Tsai–Wu models are investigated and compared to pressure insensitive and sensitive models such as von Mises, Hill and Drucker–Prager. Analytical localization angles are obtained in uniaxial tension and compression under plane stress and plane strain conditions. These are only dependent on the plastic potential adopted; ensuing, a geometrical interpretation in the stress space is offered. The analytical results are then validated by independent numerical simulations. The B-bar finite element is used to deal with the limiting incompressibility in the purely isochoric plastic flow. For a strip under vertical stretching in plane stress and plane strain as well as Prandtl’s problem of indentation by a flat rigid die in plane strain, numerical results are presented for both isotropic and orthotropic plasticity models with or without tilting angle between the material axes and the applied loading. The influence of frictional behavior is studied. In all the investigated cases, the numerical results provide compelling support to the analytical prognosis.

Model of Equal-Stressed Cylinder Based on the Mohr Failure Criterion

2014 ◽  
Vol 887-888 ◽  
pp. 869-872 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Anton S. Chepurnenko ◽  
Batyr M. Jazyev
Keyword(s):  
Stress State ◽  
Internal Pressure ◽  
Plane Strain ◽  
Plane Stress ◽  
Failure Criterion ◽  
Strain State ◽  
Elasticity Modulus ◽  
Plane Stress State ◽  
Analytical Dependence ◽  
Equivalent Stresses

In this article, an analytical dependence of distribution of elasticity modulus across the thickness of the cylinder loaded with internal pressure p, at which the equivalent stresses according the Mohr failure criterion are the same at all points. The problem is solved for the cases of plane strain state and plane stress state in the elastic formulation.

Analytical and finite element predictions of residual stresses in cold worked fastener holes

1995 ◽  
Vol 30 (4) ◽  
pp. 291-304 ◽  
Author(s):  
C Poussard ◽  
M J Pavier ◽  
D J Smith
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Residual Stresses ◽  
Aluminium Alloy ◽  
Strain Hardening ◽  
Plane Strain ◽  
Plane Stress ◽  
Analytical Models ◽  
Fe Model ◽  
Fe Simulations

Two-dimensional finite element (FE) studies, for plane stress, plane strain and axisymmetric conditions, were conducted to simulate 4 per cent cold working of a 6.35 mm diameter hole in a 6 mm thick plate of 2024 T 351 aluminium alloy. The simulations were used to assess the influence of strain hardening, the role of reversed yielding and through-thickness residual stress distributions. Experiments were also conducted to determine the tensile and compressive stress-strain response of the aluminium alloy, revealing a pronounced Bauschinger effect and non-linear strain hardening in compression. The FE simulations and results from several earlier analytical models were compared and substantial differnces found in the region of reversed yielding. Approximations used to model the compressive deformation behaviour of the material overestimate the compressive residual stresses at the hole edge. From the axisymmetric FE model a residual stress gradient through the plate thickness was found. The plane stress and plane strain assumptions used in the earlier analytical models did not satisfactorily approximate the three-dimensional residual stress fields obtained from the FE simulations.

Plastic Collapse Assessment of Thick Vessels Under Internal Pressure According to Various Hardening Rules

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
A. Chaaba
Keyword(s):  
Internal Pressure ◽  
Strain Hardening ◽  
Limit Analysis ◽  
Limit State ◽  
Plastic Behavior ◽  
Plastic Collapse ◽  
Perfectly Plastic ◽  
Von Mises ◽  
Hardening Rules ◽  
Collapse Assessment

This paper aims to deal with plastic collapse assessment for thick vessels under internal pressure, thick tubes in plane strain conditions, and thick spheres, taking into consideration various strain hardening effects and large deformation aspect. In the framework of von Mises’ criterion, strain hardening manifestation is described by various rules such as isotropic and/or kinematic laws. To predict plastic collapse, sequential limit analysis, which is based on the upper bound formulation, is used. The sequential limit analysis consists in solving sequentially the problem of the plastic collapse, step by step. In the first sequence, the plastic collapse of the vessel corresponds to the classical limit state of the rigid perfectly plastic behavior. At the end of each sequence, the yield stress and/or back-stresses are updated with or without geometry updating via displacement velocity and strain rates. The updating of all these quantities (geometry and strain hardening variables) is adopted to conduct the next sequence. As a result of this proposal, we get the limit pressure evolution, which could cause the plastic collapse of the device for different levels of hardening and also hardening variables such as back-stresses with respect to the geometry change.

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