Estimating Fatigue Due to Cyclic Multiaxial Stress

1987 ◽  
Vol 109 (1) ◽  
pp. 97-102 ◽  
Author(s):  
W. C. Orthwein
Keyword(s):  
Stress Tensor ◽  
Fatigue Resistance ◽  
Yield Criterion ◽  
Design Criterion ◽  
Multiaxial Stress ◽  
Cyclic Stresses ◽  
Energy Theory ◽  
Order Stress ◽  
Von Mises ◽  
Deviatoric Stress Tensor

A new expression similar to the Huber-von-Mises-Hencky criterion for multiaxial stresses, also known as the distortional energy theory, is derived from the second order stress invariants of the stress tensor, rather than from the deviatoric stress tensor, as in the derivation of the Huber-von Mises-Hencky criterion. It is proposed as a mutually constant design criterion for fatigue resistance under the action of multiaxial cyclic stresses which may be used with either the Gerber-yield criterion or the Goodman-yield (modified Goodman) criterion. As is shown in the following paragraphs, neither of these criteria may be used with the Huber-von Mises-Hencky criterion; it is suited only for the Soderberg criterion which does not involve the ultimate stress.

scholarly journals About Error Calculation in X-Ray Stress Measurement

2014 ◽  
Vol 996 ◽  
pp. 215-220
Author(s):  
Balder Ortner
Keyword(s):  
Stress Tensor ◽  
Stress Measurement ◽  
Von Mises Stress ◽  
Lattice Plane ◽  
Principal Stresses ◽  
X Ray ◽  
Special Cases ◽  
Standard Deviations ◽  
Von Mises ◽  
Deviatoric Stress Tensor

It is shown that the knowledge of standard deviations (Δσij) of the components of a stress tensor (σij) is not sufficient to calculate also standard deviations of quantities derived from the stress tensor, as principal stresses (σI, σII, σIII), von Mises stress, Tresca stress, and the components of the deviatoric stress tensor σ'ij. For such a calculation one needs all information about the measurement and the method for the calculation of σij. This information is: the accuracy of each measured lattice plane distance and the x-ray elastic factors Fij(φ,ψ,hkl) of each measured point. Equations are given for the calculation of the standard deviations of all the mentioned quantities. For special cases of measurement strategy the wanted calculations become easier. This is also given.

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.

Limit pressure for a spherical vessel with a circumferential slot at its junction with a radial cylindrical protruding branch

1987 ◽  
Vol 22 (4) ◽  
pp. 215-227 ◽  
Author(s):  
M Robinson ◽  
C S Lim ◽  
R Kitching
Keyword(s):  
Spherical Shell ◽  
Lower Bounds ◽  
Yield Criterion ◽  
Spherical Vessel ◽  
Non Linear Programming ◽  
Limit Pressure ◽  
Wide Range ◽  
Cylindrical Branch ◽  
Von Mises ◽  
Plastic Limit Pressure

One of the requirements of the two criteria method of safety assessment of a pressure vessel with a defect is an estimate of the plastic limit pressure. Here the defect is in a spherical shell close to its junction with a protruding radial cylindrical branch. The defect is assumed to be an axisymmetric circumferential slot of uniform depth on the outer surface of the shell. Lower bounds to the limit pressure are calculated for a wide range of geometries. The material is assumed to obey the von Mises yield criterion and a non-linear programming method is used to give optimum lower bounds. Data is supplied for spherical shell radius to thickness ratios from 25 to 100, nozzle radius to vessel radius ratios from 0 to 0.4, nozzle to vessel thickness ratios from 0.25 to 1.0 and ligament thickness to vessel thicknesses (ligament efficiencies) of 0 to 1. Slot widths vary from the significant to the infinitesimal, where it becomes a crack. Vessels of some proportions were shown to have their limit pressures reduced only a little by very low ligament efficiencies.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Overstraining of flush plain cross-bored cylinders

2004 ◽  
Vol 218 (2) ◽  
pp. 143-153 ◽  
Author(s):  
J M Kihiu ◽  
G O Rading ◽  
S M Mutuli
Keyword(s):  
Finite Element Method ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Condition ◽  
Solution Technique ◽  
Stress Distributions ◽  
Dimensional Finite Element ◽  
Von Mises ◽  
Three Dimensional Finite Element ◽  
Incremental Theory Of Plasticity

A three-dimensional finite element method computer program was developed to establish the elastic-plastic, residual and service stress distributions in thick-walled cylinders with flush and non-protruding plain cross bores under internal pressure. The displacement formulation and eight-noded brick isoparametric elements were used. The incremental theory of plasticity with a 5 per cent yield condition (an element is assumed to have yielded when the effective stress is within 5 per cent of the material yield stress) and von Mises yield criterion were assumed. The frontal solution technique was used. The incipient yield pressure and the pressure resulting in a 0.3 per cent overstrain ratio were established for various cylinder thickness ratios and cross bore-main bore radius ratios. For a thickness ratio of 2.25 and a cross bore-main bore radius ratio of 0.1, the stresses were determined for varying overstrain and an optimum overstrain ratio of 37 per cent was established. To find the accuracy of the results, the more stringent yield condition of 0.5 per cent was also considered. The benefits of autofrettage were presented and alternative autofrettage and yield condition procedures proposed.

Stress

2020 ◽  
pp. 9-28
Author(s):  
Adrian P. Sutton
Keyword(s):  
Shear Stress ◽  
Stress Tensor ◽  
Elastic Energy ◽  
Functional Derivative ◽  
Shear Stresses ◽  
Mechanical Equilibrium ◽  
Normal Stresses ◽  
Atomic Interactions ◽  
Insightful Analysis ◽  
Von Mises

The concept of stress is introduced in terms of interatomic forces acting through a plane, and in the Cauchy sense of a force per unit area on a plane in a continuum. Normal stresses and shear stresses are defined. Invariants of the stress tensor are derived and the von Mises shear stress is expressed in terms of them. The conditions for mechanical equilibrium in a continuum are derived, one of which leads to the stress tensor being symmetric. Stress is also shown to be the functional derivative of the elastic energy with respect to strain,which enables the stress tensor to be derived in models of interatomic forces. Adiabatic and isothermal stresses are distinguished thermodynamically and anharmonicity of atomic interactions is identified as the reason for their differences. Problems set 2 containsfour problems, one of which is based on Noll’s insightful analysis of stress and mechanical equilibrium.

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