The exact solutions of von mises yielding criterion for ideally plastic body under uniform pressure in case of plane strain

1982 ◽  
Vol 3 (4) ◽  
pp. 573-579
Author(s):  
Fan Ja-shen
Keyword(s):  
Exact Solutions ◽  
Plane Strain ◽  
Uniform Pressure ◽  
Plastic Body ◽  
Von Mises

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.

Behavior of Lode Dependent Plasticity at Plane Strain Condition and its Implication to Ductile Fracture

2016 ◽  
Vol 258 ◽  
pp. 213-216 ◽  
Author(s):  
František Šebek ◽  
Jindrich Petruška ◽  
Petr Kubík
Keyword(s):  
Ductile Fracture ◽  
Plane Strain ◽  
Uniaxial Stress ◽  
Complex Materials ◽  
Fracture Criteria ◽  
Dependent Plasticity ◽  
Ductile Fracture Criteria ◽  
Stress States ◽  
Aluminum Alloy 2024 ◽  
Von Mises

Variety of metals are complex materials exhibiting various behavior under different loading. Many metallic materials exhibit Tresca-like behavior rather than von Mises. It means different behavior in tension under plane strain and uniaxial stress conditions. This might be described by Lode dependent plasticity which should result in better prediction in force or torque responses of material tests. Good agreement between computation and experiment is also very important when calibrating the ductile fracture criteria. Several tests under plane strain and uniaxial stress states were carried out on aluminum alloy 2024-T351 where the Lode dependency was significant. The Lode dependent plasticity was implemented along with von Mises and Tresca-like yield criteria, which resulted in improvement of force–displacement responses of plane strain tests simulations. But it also caused significant change in the stress state of tensile flat and grooved plates which wrongly approached uniaxial tension condition. This inconvenience prevents plane strain experiments from using for calibration of ductile fracture criteria under these circumstances.

Exact Analysis of Dynamic Sliding Indentation at any Constant Speed on an Orthotropic or Transversely Isotropic Half-Space

2002 ◽  
Vol 69 (3) ◽  
pp. 340-345 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Space ◽  
Contact Zone ◽  
Transversely Isotropic ◽  
Exact Formula ◽  
Constant Speed ◽  
Displacement Fields ◽  
Rigid Indentor

A plane-strain study of steady sliding by a smooth rigid indentor at any constant speed on a class of orthotropic or transversely isotropic half-spaces is performed. Exact solutions for the full displacement fields are constructed, and applied to the case of the generic parabolic indentor. The closed-form results obtained confirm previous observations that physically acceptable solutions arise for sliding speeds below the Rayleigh speed, for a single critical transonic speed, and for all supersonic speeds. Continuity of contact zone traction is lost for the latter two cases. Calculations for five representative materials indicate that contact zone width achieves minimum values at high, but not critical, subsonic sliding speeds. A key feature of the analysis is the factorization that gives, despite anisotropy, solution expressions that are rather simple in form. In particular, a compact function of the Rayleigh-type emerges that leads to a simple exact formula for the Rayleigh speed itself.

A fretting finite element investigation of a plane-strain cylindrical contact of Inconel 617/Incoloy 800H at room and high temperatures

2018 ◽  
Vol 233 (4) ◽  
pp. 553-569 ◽  
Author(s):  
Huaidong Yang ◽  
Itzhak Green
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Room Temperature ◽  
Tangential Force ◽  
Alloy 800H ◽  
Incoloy 800H ◽  
Inconel 617 ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Two Bodies

This work presents a finite element study of a 2D plane strain fretting model of a half-cylinder in contact with a flat block under oscillatory tangential loading. The two bodies are deformable and are set to Inconel 617 and Incoloy 800H at room temperature (20 ℃) and 800 ℃. However, because the results are normalized, they can characterize a range of contact scales (micro to macro). Different coefficients of friction are used at the interface. This work finds that the edges of the contacting areas experience large von Mises stresses along with significant residual plastic strains, while pileup could also appear when the coefficients of friction are sufficiently large. In addition, junction growth is investigated, showing that the direction of the growth is in the same direction of the tangential force that the weaker material (Incoloy alloy 800H) experiences. The fretting loop (caused by the tangential force during the fretting motion) for the initial few cycles of loading is generated, and it compares well with the reported experimental results. The different extents of damage at room temperature and 800 ℃ are also compared.

Magnetic Fields Generated by a Mechanical Singularity in a Magnetized Elastic Half Plane

1989 ◽  
Vol 56 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Chau-Shioung Yeh
Keyword(s):  
Fourier Transform ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Plane ◽  
Elastic Solids ◽  
Soft Ferromagnetic ◽  
Single Force ◽  
The Fourier Transform

The induced magnetic fields generated by a line mechanical singularity in a magnetized elastic half plane are investigated in this paper. One version of linear theory for soft ferromagnetic elastic solids which has been developed by Pao and Yeh (1973) is adopted to analyze the plane strain problem undertaken. By applying the Fourier transform technique, the exact solutions for the generated magnetic inductions due to various mechanical singularities such as a single force, a dipole, and single couple are obtained in a closed form. The distributions of the generated inductions on the surface are shown with figures.

Dynamic Shear Band Development in Plane Strain

1989 ◽  
Vol 56 (1) ◽  
pp. 1-9 ◽  
Author(s):  
A. Needleman
Keyword(s):  
Shear Band ◽  
Plane Strain ◽  
Local Maximum ◽  
Loading Conditions ◽  
Strain Development ◽  
Initial Direction ◽  
Von Mises ◽  
Dynamic Loading Conditions ◽  
Viscoplastic Solid ◽  
Internal Inhomogeneity

Plane strain compression of a rectangular block is used as a model problem to investigate the dynamics of shear band development from an internal inhomogeneity. The material is characterized as a von Mises elastic-viscoplastic solid, with a hardness function that exhibits a local maximum. Regardless of whether the material is hardening or softening, plastic strain development involves the evolution of fingerlike contours emanating from the inhomogeneity at 45 deg to the compression axis. Once a given strain contour crosses the specimen, it fans out about its initial direction of propagation. For a softening solid, this fanning out ceases for some strain level greater than the strain at the hardness maximum and further straining takes place in an ever narrowing band. Many of the qualitative features of shear band development under dynamic loading conditions are the same as under quasistatic loading conditions, but a significant retardation of shear band development due to inertial effects is found.

Estimation of the Stresses in Rotational Autofrettage of Thick-Walled Pressure Vessels Using von Mises Yield Criterion

2021 ◽  
Author(s):  
S. M. Kamal ◽  
Faruque Aziz
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Stress Distributions ◽  
Von Mises Yield Criterion ◽  
Potential Methods ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Theoretical Analyses

Abstract Rotational autofrettage is one of the recently proposed potential methods for eliminating the in-service yielding of thick-walled cylindrical pressure vessels. A few researchers have studied the feasibility of the process theoretically, and asserted certain advantages over the practicing hydraulic and swage autofrettage processes. In the literature, all theoretical analyses on the rotational autofrettage are based on the Tresca yield criterion and its associated flow rule, along with the assumption of different plane end conditions (plane strain and generalized plane strain). In this paper, an analysis of the rotational autofrettage of cylindrical vessel is attempted incorporating von Mises yield criterion. The plane strain condition is used for the analysis. A numerical shooting method is used to solve the governing differential equations providing the elastic-plastic stress distributions in the cylinder during loading. The present procedure is numerically experimented for a typical AH36 pressure vessel. It is found that the achievable level of the maximum stress pressure of the rotationally autofrettaged vessel is 74.46% higher than that of its non-autofrettaged counterpart for an overstrain level of 46.7%.

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