Strain-Hardening Solutions to Plate Problems

1959 ◽  
Vol 26 (2) ◽  
pp. 276-284
Author(s):  
Nicholas Perrone ◽  
P. G. Hodge
Keyword(s):  
Strain Hardening ◽  
Plane Stress ◽  
Kinematic Model ◽  
Circular Plates ◽  
Flow Laws

Abstract Two sets of strain-hardening flow laws based on an analogy with a kinematic model are derived for circular plates made of an initially Tresca material. The two sets of flow laws, called complete and direct hardening, differ in the point at which the plane-stress assumption is introduced. The complete-hardening flow laws are more consistent since the plane-stress assumption is made at the latest possible stage in their derivation. Complete and direct-hardening solutions are obtained to each of three different plate problems. The results indicate that the direct-hardening solutions give a fair approximation to the complete-hardening ones.

Axisymmetric Plane Stress Problems in Anisotropic Plasticity

1969 ◽  
Vol 36 (1) ◽  
pp. 7-14 ◽  
Author(s):  
Wei Hsuin Yang
Keyword(s):  
Stress Concentration ◽  
Strain Hardening ◽  
Plane Stress ◽  
Analytic Solutions ◽  
Anisotropic Plasticity ◽  
Stress Plane ◽  
Method Of Solution ◽  
Degree Of Anisotropy ◽  
Concentration Factors ◽  
Stress Concentration Factors

Based on an established theory of anisotropic plasticity, a class of axisymmetric plane stress problems is solved for sheet metals which harden according to a power law and are isotropic in their plane. A new method of solution, the stress plane method, is used. The analytic solutions for the problems considered are obtained in the stress plane. The stress-concentration factors introduced by a hole or a rigid inclusion at the center of an infinite sheet are obtained for arbitrary degree of anisotropy and strain-hardening characteristics. The influence of anisotropy and strain-hardening on the deep-drawing problem is also studied. The results show that the type of anisotropy and strain-hardening assumed always influences the stress concentration and drawability in a favorable way.

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.

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.

On Plane Stress Solution of an Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (3) ◽  
pp. 407-410
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Stress ◽  
Yield Surface ◽  
Complete Solution ◽  
Yield Function ◽  
The State ◽  
Perfectly Plastic ◽  
State Of Stress ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic ◽  
Flow Laws

Abstract With the use of Tresca’s yield function and its associated flow laws, the complete solution is obtained for an isotropic elastic, perfectly plastic wedge (with an included angle β < π/2) subjected to a uniform traction in the state of plane stress. Unlike its corresponding plane strain solution, the state of stress in a portion of the plastic domain of the wedge is at a corner of Tresca’s yield hexagon where, in general, the normal to the yield surface is not defined uniquely.

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.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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