A Generalized von Mises Criterion for Yield and Fracture

1980 ◽  
Vol 47 (2) ◽  
pp. 297-300 ◽  
Author(s):  
W. H. Yang
Keyword(s):  
Bauschinger Effect ◽  
Hydrostatic Stress ◽  
Fracture Criteria ◽  
Deformation History ◽  
Von Mises Criterion ◽  
Effect On Yield ◽  
Von Mises ◽  
New Criterion ◽  
Physical Phenomena ◽  
Special Case

Yield and fracture criteria for real materials are to a varying degree affected by a state of hydrostatic stress. Some materials, after certain deformation history, exhibit different yield point when the direction of the stress is reversed, a behavior known as the Bauschinger effect. These physical phenomena are not represented by the von Mises criterion. Based on a convexity theorem of matrices, a generalization of the von Mises criterion is presented. The new criterion satisfies the convexity requirement of plasticity theory and, with two scalar functions of deformation history α and β, produces a class of hardening behavior. The current values of α and β account for the effect of hydrostatic stress and an aspect of the Bauschinger effect on yield and fracture. The generalized criterion reduces to the form of the von Mises criterion as a special case.

The Proportional Anisotropic Elastic Invariants

1991 ◽  
Vol 58 (1) ◽  
pp. 50-57 ◽  
Author(s):  
A. M. Sadegh ◽  
S. C. Cowin
Keyword(s):  
Elastic Material ◽  
Hydrostatic Stress ◽  
Von Mises Stress ◽  
Stress And Strain ◽  
Fracture Criteria ◽  
Linear Elastic Material ◽  
Linear Elastic ◽  
Isotropic Elasticity ◽  
Anisotropic Elastic ◽  
Von Mises

There are two proportional invariants for a linear isotropic material, the hydrostatic invariant, and the deviatoric invariant. The former is proportional to the trace of the tensor and the latter is proportional to the trace of the square of the associated deviatoric tensor. The hydrostatic stress and strain and the von Mises stress and strain are directly related to the hydrostatic and deviatoric proportional invariants, respectively, for an isotropic, linear elastic material. For each anisotropic linear elastic material symmetry there are up to six proportional invariants. In this paper we illustrate the six proportional invariants of an orthotropic elastic material using the elastic constants for spruce as the numerical example. The proportional elastic invariants play a role in anisotropic linear elasticity similar to the roles played by the hydrostatic stress and strain and the von Mises stress and strain in isotropic elasticity. They are the unique parameters whose contours represent both the stress and the strain distributions. They also have potential for representing failure or fracture criteria.

scholarly journals Mathematical and numerical model for nonlinear viscoplasticity

2011 ◽  
Vol 369 (1947) ◽  
pp. 2864-2880 ◽  
Author(s):  
N. Favrie ◽  
S. Gavrilyuk
Keyword(s):  
Numerical Model ◽  
Specific Energy ◽  
Macroscopic Model ◽  
Material Behaviour ◽  
Plastic Deformations ◽  
Numerical Examples ◽  
Von Mises ◽  
Physical Phenomena ◽  
Deviatoric Part ◽  
Special Case

A macroscopic model describing elastic–plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatible with the von Mises yield criteria. In addition, Maxwell-type material behaviour is shown up: the deviatoric part of the stress tensor decays during plastic deformations. Numerical examples show the ability of this model to deal with real physical phenomena.

A note on the yielding of an accelerating, non-homogeneous disc of varying thickness and density with radial loading

1978 ◽  
Vol 13 (1) ◽  
pp. 59-63
Author(s):  
G V Gurushankar
Keyword(s):  
Uniform Density ◽  
Shear Stresses ◽  
Normal Stresses ◽  
Uniform Thickness ◽  
Varying Thickness ◽  
Von Mises Criterion ◽  
Yield Loci ◽  
Von Mises ◽  
Radial Loading ◽  
Special Case

The influences of non-homogeneity and density on the normal stresses and shear stresses developed due to the acceleration of a disc, of varying thickness, at any particular instant, are analysed. Yield loci, on the basis of von Mises' criterion, are found for discs of varying thickness and uniform thickness with a bore ratio ( a/ b) of 0.25 and also for linearly varying ( p = 1.0, q = 1.0) and nonlinearly varying ( p = 0.5, q = 0.5) density and homogeneity. A homogeneous, uniform density and uniform thickness disc forms a special case of the analysis.

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.

Proposal of the Local Failure Evaluation Method With Stress Parameters

2018 ◽  
Author(s):  
Takashi Sakaguchi ◽  
Mizuki Yoshida ◽  
Takuya Sato ◽  
Naoto Kasahara
Keyword(s):  
Fracture Surface ◽  
Evaluation Method ◽  
Hydrostatic Stress ◽  
Notch Root ◽  
Local Failure ◽  
Dominant Factor ◽  
Multiaxial Stress ◽  
Minimum Diameter ◽  
Nuclear Plants ◽  
New Criterion

The failure mode known as local failure could occur at structure discontinuities with multiaxial stress conditions. Experiments and analyses of notched bars, which generate multiaxial stress, were conducted. The experiments showed that the tensile strength of a notched bar was stronger than that of a smooth bar. The ratio of the maximum and minimum diameter has become the important factor of this notch strengthening. In addition, the initiation of failure was observed at the inner location from the notch root. According to the analysis results, the Mises-stress became the maximum at the notch root. On the other hand, hydrostatic stress became the maximum at the inner location from the notch root, and this location corresponded to the initiation of fracture. The maximum hydrostatic stress has good correlation with the notch strengthening ratio. These facts reveal that hydrostatic stress must be taken into account for strength evaluation as a dominant factor in addition to the Mises-stress. However, only Mises-stress is considered in the present structural design code of nuclear plants. From above results, the new criterion based on fracture surface, where the coordinate plane consists of hydrostatic stress and Mises-stress, was proposed for local failure. Furthermore, this fracture surface was extended to an isochronous fracture surface in a creep region based on isochronous stress-strain curves.

Fatigue Fracture Behavior of Steel Pipes With a Pre-Crack

2002 ◽  
Author(s):  
Jae-Kyoo Lim ◽  
Lichun Bian
Keyword(s):  
Fatigue Crack ◽  
Yield Criterion ◽  
Axial Loading ◽  
Potential Drop ◽  
Maximum Tensile Stress ◽  
Core Region ◽  
Fracture Criteria ◽  
Steel Pipes ◽  
Inclined Angle ◽  
Von Mises

The behaviour of fatigue crack propagation of mild steel pipes, each consisting of an inclined semi-elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the gowth of the fatigue crack was monitored using the AC potential drop technique. The Von Mises yield criterion was applied to define the core region, instead of assuming a core region with a constant distance r from the crack lip. The two commonly employed fracture criteria, i.e., the maximum tensile stress and the minimum strain energy density criteria, were modified by adopting Von Mises elasto-plastic boundary. The results obtained using the innproved fracture criteria are, in most cases, in better agreement with test results as compared with those obtained using the commonly employed fracture criteria.

Zircon Microstructures Record Deformation History of Shock- and Tectonically-generated Pseudotachylites: a Case Study from the Vredefort Impact Structure, South Africa

2019 ◽  
Vol 60 (12) ◽  
pp. 2529-2546 ◽  
Author(s):  
E Kovaleva ◽  
M S Huber ◽  
G Habler ◽  
D A Zamyatin
Keyword(s):  
Tectonic Deformation ◽  
Impact Structure ◽  
Deformation Bands ◽  
Deformation History ◽  
Meteorite Impacts ◽  
History Of ◽  
Tectonic Settings ◽  
New Criterion

Abstract High-strain rate deformation can cause in situ melting of rocks, resulting in the formation of dark, micro- to nanocrystalline pseudotachylite veins. On Earth, pseudotachylite veins form during meteorite impacts, large landslides, and earthquakes. Within the Vredefort impact structure, both impact-generated and (pre-impact) tectonically-generated pseudotachylite veins have been described, but are challenging to distinguish. Here, we demonstrate a genetic distinction between two pseudotachylite veins from Vredefort by studying their petrography, degree of recrystallization and deformation, cross-cutting relationships and the deformation microstructures in associated zircon. We conclude that Vein 1 is pre-impact and tectonically-generated, and Vein 2 is impact-generated. In agreement, zircon microstructures in Vein 1 contain planar deformation bands (PDBs), attributed to tectonic deformation, whereas zircon microstructures in Vein 2 reveal microtwin lamellae, indisputable evidence of shock metamorphism. Thus, deformation microstructures in zircon may provide a new criterion for distinguishing the genetic origin of pseudotachylite veins. Zircons that have been removed from their context (i.e., alluvial or detrital zircon, zircon from Lunar breccia) should be interpreted with caution in terms of their deformation history. For example, zircon with PDBs cannot reliably be used as a marker for shock deformation, because this feature has been shown to form in purely tectonic settings.

Plastic flow in extrusion and drawing through conical and wedge-shaped dies: Prediction of central bursting

2006 ◽  
Vol 220 (8) ◽  
pp. 1201-1210 ◽  
Author(s):  
S N Samy ◽  
Ch A R Saleh ◽  
A R Ragab
Keyword(s):  
Experimental Data ◽  
Plane Strain ◽  
Deformation Zone ◽  
Hydrostatic Stress ◽  
Plastic Instability ◽  
Instability Criterion ◽  
Fracture Criteria ◽  
Rigid Plastic ◽  
Stress Criterion ◽  
Plastic Materials

In this article, the plastic flowfields for extrusion and drawing - for rigid plastic materials forced through conical and wedge-shaped dies - are analysed on the basis of Shield's work. A modification to Shield's analysis is developed to account for the redundant deformation. Solutions for axisymmetric and plane strain flows are given. The total forces estimated for both drawing and extrusion operations are compared favourably with available experimental data. On the basis of the present modified Shield's analysis, expressions for the stresses within the die are then derived. These expressions are then employed to predict central bursting by applying two fracture criteria, namely: the hydrostatic stress criterion and the plastic instability criterion. The deformation zone geometry criterion has also been used for comparison. The predictions fairly agree with the experimental results.

Asymmetric two-dimensional jet efflux from a channel

1977 ◽  
Vol 80 (1) ◽  
pp. 1-15
Author(s):  
C. Samuel Martin
Keyword(s):  
Experimental Data ◽  
Analytical Approach ◽  
Two Dimensional ◽  
Asymmetric Case ◽  
Hodograph Plane ◽  
Single Jet ◽  
Von Mises ◽  
Two Jets ◽  
Direct Use ◽  
Special Case

Irrotational flow of two-dimensional jets from a channel is treated without direct use of a logarithmic hodograph plane. An analytical approach is introduced for solving the general problem of two jets issuing from a channel with three end plates. Numerical values of the contraction coefficient and the angle of jet deflexion are obtained for the special case where the two jets are located symmetrically and all the end plates are in line. Limiting cases of the resulting single-jet problem are the symmetric and asymmetric configurations solved by von Mises. Results for the asymmetric case improve upon the theoretical values reported by von Mises, and compare favourably with existing experimental data.

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