Showing papers on "von Mises yield criterion published in 1971"
TL;DR: In this paper, the effects of the stress states on the stability and the flow of rocks are investigated by using the ELASTIC AXIAL STRAIN from the total AXial STrain.
Abstract: A NEW TRIAXIAL COMPRESSION TECHNIQUE HAS MADE POSSIBLE THE STUDY ON GENERAL LAWS OF FRACTURE AND FLOW OF ROCKS UNDER GENERAL TRIAXIAL STRESS STATES, IN WHICH ALL THREE PRINCIPAL STRESSES ARE DIFFERENT. IN THIS PAPER, THE EFFECTS OF THE STRESS STATES ON FRACTURE AND YIELDING OF ROCKS ARE EXPERIMENTALLY STUDIED BY THIS METHOD. THE EXPERIMENTAL PROCEDURE IS DESCRIBED, AND THE EQUATIONS FOR STRESS STATES PRODUCING FRACTURE AND YIELDING ARE GIVEN AS MONOTONIC INCREASING FUNCTIONS OF THE THREE PRINCIPAL STRESSES. THE NEW FAILURE CRITERIA CORRESPONDING TO THE GENERALIZED VON MISES CRITERIA ARE INTERPRETED. THE DUCTILITY DEFINED AS THE PERMANENT STRAIN JUST BEFORE FRACTURE IS DETERMINED BY SUBTRACTING THE ELASTIC AXIAL STRAIN FROM THE TOTAL AXIAL STRAIN. FROM THE RESULTS ON THE EFFECT OF STRESS STATES, FRACTURE AND FLOW PROPERTIES OF THE EARTH'S UPPER MANTLE ARE DEDUCED. /AUTHOR/
506 citations
TL;DR: In this paper, a triaxial apparatus has been used to study failure of brittle rocks under a general three-strain system, in which all three principal stresses are different, and a new empirical failure criterion, which corresponds to the modified von Mises theory, has been proposed.
130 citations
TL;DR: In this article, the effect of pressure on the tensile deformation of amorphous polycarbonate and poly(ethylene terephthalate) and semi-crystalline polychlorotrifluoroethylene and polytetrafluorethylene was investigated up to 8 kb.
Abstract: The effect of pressure on the tensile deformation of amorphous polycarbonate and poly(ethylene terephthalate) and semi-crystalline polychlorotrifluoroethylene and polytetrafluoroethylene was investigated up to 8 kb. Tensile deformations of polycarbonate at atmospheric pressure at temperatures down to 116°K were also performed. The former three polymers showed increases of yield stress, yield strain and elastic modulus, and decreases of fracture strain. Polytetrafluoroethylene behaved in an analogous manner up to 4 kb, beyond which both the ‘yield’ stress and elastic modulus deviated systematically from the lower-pressure behaviour. This was found to correlate with changes of bulk modulus at a solid–solid phase transition near 5 kb. The pressure dependence of yield stress was fitted by modified von Mises and Mohr–Coulomb yield criteria. A material parameter describing this pressure dependence was obtained for these and other polymers and was found to correlate qualitatively with the strength-limit...
107 citations
TL;DR: In this article, various approximations to the yield surface for a thin shell made of material obeying the von Mises yield criterion have been examined and it is found that one proposed by Ilyushin is very close to the exact one in all cases and should prove useful for practical application.
101 citations
01 Dec 1971
TL;DR: In this paper, the yield expression for the initiation of slip in each 〈111〉 direction is a coupled quadratic function of all six stress components, and all four expressions reduce to the von Mises yield criterion when only principal stresses are applied along the cubic axes.
Abstract: Yielding under an arbitrary stress state and constrained deformation by polyslip were examined for bcc crystals deforming by 〈111〉 pencil glide,i.e., slip with equal ease on any plane containing a 〈111〉 slip direction. The pencil-glide equivalent of the generalized Schmid’s law was derived. The yield expression for the initiation of slip in each 〈111〉 direction is a coupled quadratic function of all six stress components, and all four expressions reduce to the von Mises yield criterion when only principal stresses are applied along the cubic axes. In order to accommodate an arbitrary imposed shape change by pencil glide, polyslip stress states were examined which simultaneously operate four or three 〈111〉 slip directions. A maximum-work procedure is proposed to choose that particular polyslip stress state required to enforce a given shape change.
35 citations
TL;DR: In this article, principal and slip-line methods of numerical analysis are presented for plane and axially symmetric deformations of rigid/plastic media obeying generalized Tresca/von Mises constitutive equations, and solutions for the particular problem of combined extension and expansion of a thick-walled circular cylinder under axial force and internal pressure are discussed.
Abstract: Some new principal- and slip-line methods of numerical analysis are presented for plane and axiallysymmetric deformations of rigid/plastic media. These methods are applicable to the solution of problems of incompressible isotropic, or incompressible anisotropic, or (special) compressible isotropic media obeying generalized Tresca/von Mises constitutive equations. The essential idea in the numerical methods considered is an artifice of the reduction of elliptic (and similar) problems of systems of partial differential equations to hyperbolic ones by means of a procedure based upon the initial estimation of one of the field quantities followed by iterations to determine all field quantities. Solutions for the particular problem of combined extension and expansion of a thick-walled circular cylinder under axial force and internal pressure are discussed.
17 citations
TL;DR: In this paper, the transient response of a uniformly expanding, impulsively loaded, long cylinder is obtained in terms of elementary functions for an elastic perfectly-plastic von Mises material.
Abstract: The transient response of a uniformly expanding, impulsively loaded, long cylinder is obtained in terms of elementary functions for an elastic perfectly-plastic von Mises material. The solution is obtained by utilizing a linearizing assumption on the plastic flow behavior. It is generally shown that differences in elastic-plastic response of (plane strain) long cylinders with various values of Poisson's ratio,v, are slight over a wide range ofv. However, differences in response between long cylinders and (plane stress) rings undergoing plasticity are quite significant.
10 citations
TL;DR: In this article, Griffiths and D.R. Owen showed that the stress maximum lies some way before the elastic-plastic interface, inside the plastic zone, and that the calculated stresses conflict with plastic slip-line field theory.
Abstract: Recent calculations by J.R. Griffiths and D.R.J. Owen (1971) on the growth of the elastic-plastic stresses for the plane strain bending of a V-notched bar reveal an interesting phenomenon : the stress maximum lies some way before the elastic-plastic interface, inside the plastic zone. Later calculations have confirmed this effect, for both work-hardening and perfectly-plastic von Mises and Tresca materials. At low applied loads the calculated stresses conflict with plastic slip-line field theory. This result is important, because it means that notch stresses before general yield cannot readily be deduced by etching up plastically-yielded zones. This paper explains the conflict analytically.
9 citations
TL;DR: In this article, partial analytical solutions are obtained for certain values of the power law exponent and the rigid-perfectly plastic von Mises material is considered as a special case, and boundary value problems obtained are readily solved numerically by reformulating them as initial value problems.
9 citations
TL;DR: In this article, the authors evaluated the creep design procedures for metal members subject to multiaxial-stress states and step changes in load and temperature, and found that the von Mises and Tresca flow criterion was the best flow criterion for free-cutting brass.
Abstract: Creep theories of metals are based often upon constitutive relations for constant-stress, constant-temperature creep data. For variable stress and temperature processes, a hardening rule is required. In addition, a flow criterion is required for multiaxial states of stress. In this paper, creep-design procedures are evaluated for metal members subject to multiaxial-stress states and step changes in load and temperature. Tension-test data for copper alloy 360 (fre-cutting brass) and SAE 1035 steel for constant stress levels at three elevated temperatures, are approximated by four different forms of creep relations. Timehardening and strain-hordening rules are employed with reasonable success to describe the experimental creep deformations of tension specimens subjected to step changes in load and temperature. In addition, experimental data for torsion members of solid cross section subjected to step changes in load and temperature are described by means of two creep relations and the strain-hardening rule and flow criteria of von Mises and Tresca. Accurate description of the experimental data for SAE 1035 steel is obtained with the von Mises criterion. However, for free-cutting brass, poor correlation between theory and experiment is obtained with both the von Mises and the Tresca flow criteria. Further study of the behavior of free-cutting brass is indicated.
6 citations
TL;DR: In this paper, a thin plate of exponentially varying thickness is loaded axisymmetrically and is minimized for volume satisfying two constraints: the material is homogeneous and isotropic, and minimum volume yields minimum weight.
Abstract: A thin plate of exponentially varying thickness is loaded axisymmetrically and is minimized for volume satisfying two constraints. In addition, the material is homogeneous and isotropic. Thus, minimum volume yields minimum weight. Only uniform load is considered. Such a combination of constraints may be required for pressure-sensitive devices and where clearances are tight. The state of stress in the plate remains everywehre elastic. A major contention of this paper is that volume minimization of thin plates should be considered in terms of certain classes of diametral shapes. Starting with the differential equation of equilibrium and von Mises' yield equation, the necessary mathematics is developed to effect the minimization process, and the resulting equations, containing infinite power series, are solved on the digital computer. A few representative design curves are plotted for wide ranges of values of the variables for the plate simply supported at the boundary. Sample calculations are given.
TL;DR: In this paper, an investigation was made on three machine-stiffened steel models to find the effect of ringstiffener size on the shell instability mode of failure and the increase in sizes of the stiffening rings showed only marginal increases in buckling pressures although the latter were well in excess of the predictions of the von Mises formula.
Abstract: An investigation was made on three machine-stiffened steel models to find the effect of ring-stiffener size on the shell instability mode of failure. The increase in sizes of the stiffening rings showed only marginal increases in buckling pressures although the latter were all well in excess of the predictions of the von Mises formula.
TL;DR: The von Mises yield criterion for sheet material under conditions of plane stress is given by where σ 1, σ 2 are the principal stresses in the plane of the sheet and σ y is the yield stress under uniaxial tension as discussed by the authors.
Abstract: The von Mises yield criterion for sheet material under conditions of plane stress is given by where σ 1 , σ 2 are the principal stresses in the plane of the sheet and σ y is the yield stress under uniaxial tension. If equation (1) is expressed in terms of elastic strains by virtue of the relations: where v=Poisson's ratio and E =Young's modulus, it is
found that when the term in ∊ 1 ∊ 2 vanishes and the criterion for the onset of yield simplifies to Now v * is very close to that of most materials of structural interest.
01 Oct 1971
TL;DR: In this paper, an effective incremental theory was developed for solving the problem of partially yielded, thick-walled cylinders made of strain-hardening materials subjected to any combination of internal pressure, external pressure, and end loading.
Abstract: : An effective incremental theory was developed for solving the problem of partially yielded, thick-walled cylinders made of strain-hardening materials subjected to any combination of internal pressure, external pressure, and end loading. The theory developed in the Research Directorate, U. S. Army Weapons Command, includes Prandtl-Reuss' incremental stress-strain laws, Von Mises' flow criterion, and the strain-hardening and compressibility properties of a material. Since the consideration of stress and strain history is involved in the analysis, the present theory is particularly suitable for predicting stress and strain distribution, and location of the elastic-plastic boundary of a thick-walled cylinder subjected to nonproportionate loading.