Showing papers on "von Mises yield criterion published in 1993"
TL;DR: In this paper, a gspeneral expression for the yield surface of polycrystalline materials is developed, which can describe both isotropic and anisotropic materials.
Abstract: A gspeneral Expression for the yield surface of polycrystalline materials is developed. The proposed yield surface can describe both isotropic and anisotropic materials. The isotropic surface can be reduced to either the Tresca or von Mises surface if appropriate, or can be used to capture the yield behavior of materials (e.g. aluminum) which do not fall into either category. Anisotropy can be described by introducing a set of irreducible tensorial state variables. The introduced linear transformation is capable of describing different anisotropic states, including the most general anisotropy (triclinic) as opposed to existing criteria which describe only orthotropic materials. Also, it can successfully describe the variation of the plastic strain ratio (R-ratio), where polycrystalline plasticity models usually fail. A method for obtaining the material constants using only uniaxial test data is described and utilized for the special case of orthotropic anisotropy. Finally, the use of tensorial state variables together with the introduced mathematical formulation make the proposed yield function a very convenient tool for numerical implementation in finite element analysis.
622 citations
TL;DR: In this paper, the authors studied the effect of the aspect ratio of the reinforcement, particle distribution and grouping behavior-clustering on the nonuniform stress distribution in the material and found that the triaxial stress state around a particle or inside a particle cluster may change the von Mises stress and result in plastic deformation features, such as strain localization.
Abstract: Finite element calculations were carried out to study the stress distribution in particulate SiC-reinforced Al metal-matrix composites (MMCs) subjected to external load. The results showed that, in addition to the effect of the aspect ratio of the reinforcement, particle distribution and grouping behavior-clustering, resulting from the casting process in the present materials, also contribute considerably to the nonuniform stress distribution in the material. The triaxial stress state around a particle or inside a particle cluster may change the von Mises stress and result in plastic deformation features, such as strain localization. Furthermore, the relative orientation of the particle distribution to the external load was found to be important to the stress distribution. As the applied stress increases, the state of triaxial stress inside a cluster appears to promote the early particle cracking, interface debonding, and void formation in the ductile matrix. Experimental observations of slip band distribution and other features in compression tests are consistent with the calculated results.
103 citations
TL;DR: In this article, the authors investigated the influence of the non-linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator, and showed that it is not generally recommendable to propose large load steps.
Abstract: One possibility of formulating the tinite element method is founded on the principle of virtual displacement, in which we want to include a rate-independent elastoplastic constitutive model based on the assumption of a yield surface. The constitutive equations result from the assumptions of small deformations, Hooke's law for the elastic domain, the normality rule for the evolution of plastic strains, the von Mises yield condition and a special kind of kinematic hardening due to Armstrong and Frederick,1 in which linear kinematic hardening is generalized with a saturation term. We show that it is not generally recommendable to propose large load steps. To this end, we investigate the influences of the non-linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator. The main topics of this paper are: (1) development of a problem-optimized backward Euler method with regard to the kinematic hardening model, (2) study of the influence of the saturation term on the numerical accuracy through isoerror maps and (3) computation of the consistent elastoplastic tangent operator.
76 citations
TL;DR: In this article, the authors derived a relation between the Hugoniot elastic limit (HEL) of brittle materials and their compressive strength (Yc) based on Griffith's yield criterion.
Abstract: We derive a new relation between the Hugoniot elastic limit (HEL) of brittle materials and their compressive strength (Yc). This relation is based on Griffith’s yield criterion [Proceedings of the 1st Conference on Applied Mechanics, Delft, Holland (1924), p. 55] for brittle behavior in contrast with the traditional relation, which is based on the criteria of Tresca or von Mises. Our newly derived relation results in a larger ratio between the HEL and Yc, in agreement with all the experimental observations on polycrystalline ceramics.
71 citations
TL;DR: In this paper, the influence of the von Mises and Tresca equivalent offset strains on the subsequent yield surfaces is studied. But this was not the case when large von-Mises offset strains were used, and the corresponding subsequent yield surface passed through the Von Mises loading surface.
66 citations
TL;DR: In this paper, the effect of fiber and interfacial layer morphologies on thermal fields in metal matrix composites (MMCs) was examined. But the authors focused on the thermal properties of the SCS6 silicon carbide fiber and the use of multiple compliant layers at the fiber/matrix interface.
58 citations
TL;DR: In this article, the development of elastic and plastic constitutive relations as functions of relative density for partially consolidated aluminum powder was described, and the yield surface is asymmetric with respect to hydrostatic tension and compression.
Abstract: This article describes the development of elastic and plastic constitutive relations as functions of relative density for partially consolidated —100 mesh aluminum powder. First, measurements of yield stress as a function of stress state and relative density are described. Measurements of the plastic strain increments associated with yielding in unconstrained compression tests and elastic properties, both as functions of relative density, are also described. The experimental results are combined with the associated flow rule to show that the yield surface is asymmetric with respect to hydrostatic tension and compression. Second, it is shown that the yield stress results can be represented by a two-part (capped Drucker-Prager) yield surface. The consoli-dation yield surface moves along the hydrostatic stress axis during densification, while the shear yield surface approaches the Mises yield surface. For the Al powder used in the present inves-tigation, superposition of shear stress on a hydrostatic stress state aids the densification process. However, the hydrostatic stress requirement was found to be reduced by only about 20 pct for relative densities below 0. 98.
47 citations
TL;DR: The aim of this study was to validate the FE model for prefailure and failure modelling, by comparing the computational results with the laboratory observations and failure results, and it is made that validation of FE calculations is essential.
45 citations
TL;DR: In this article, a unified approach for exact integration of the constitutive equations in elastoplasticity is presented, assuming the total strain-rate direction to be constant, including all previous exact integration procedures as special cases and some new closed-form solutions for combined kinematic and isotropic hardening.
Abstract: A unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity, assuming the total strain-rate direction to be constant. This unified approach includes all previous exact integration procedures as special cases and, in addition, some new closed-form solutions are derived for combined kinematic and isotropic hardening. Special emphasis is laid on combined kinematic and isotropic hardening for von Mises' material and on isotropic hardening for Mohr-Coulomb and Tresca materials.
43 citations
TL;DR: In this paper, a model based on probability theory is proposed to determine the orientation of the tectonic stress field from fault slip and earthquake focal mechanism data on the assumption that slip and shear stress direction on the fault plane coincide, and measured slip direction and fault plane orientation are random variables following the von Mises and the Fisher distribution, respectively.
Abstract: A model based on probability theory is proposed to determine the orientation of the tectonic stress field from fault slip and earthquake focal mechanism data On the assumptions that (1) slip and shear stress direction on the fault plane coincide, and (2) measured slip direction and fault plane orientation are random variables following the von Mises and the Fisher distribution, respectively, the effects of measurement errors in both variables on stress field inversion are considered The distribution of shear stress direction on the fault plane can also be approximately modeled by the von Mises distribution, with the concentration parameter varying from infinity to zero according to the orientation of the fault plane, the direction of the principal stress axes, and the stress shape parameter Measurement errors in both slip direction and fault plane orientation give rise to misfit angles between the predicted shear stress and the measured slip direction even if the tectonic stress field is uniform A new inversion method is proposed that takes both measurement errors simultaneously into account This method makes it possible to evaluate statistically the extent and significance of the deviations of the stress field from uniformity, ie, the likelihood that a given fault population originates from a constant tectonic stress state For sufficiently large sample size, misfit angles should belong to a von Mises family if the stress field is uniform A significant deviation from a von Mises distribution implies that the tectonic stress field is not uniform A few examples of application of the new inversion method are presented, together with a comparison with the results obtained from different methods and an assessment of the uncertainties in the inverted stress field
38 citations
TL;DR: In this paper, a micromechanical composite model is used in the sense that the matrix and fiber local con- stitutive damage relations are treated separately and then linked to the overall response through a certain homogenization procedure.
Abstract: Damage is incorporated along with plastic deformation in this model for the analysis of fiber-reinforced metal matrix composite materials. In the formulation, a micromechanical composite model is used in the sense that the matrix and fiber local con- stitutive damage relations are treated separately and then linked to the overall response through a certain homogenization procedure. In this process, two local damage tensors M and M are introduced where M accounts for the damage in the ductile matrix such as nucleation and growth of voids, while the tensor M reflects the damage in the fibers such as fiber fracture. The problems of debonding and delamination can be conveniently represented by either M or Mor a combination of both depending on the extent of complexity that is desired of the final constitutive model. A von Mises type yield criterion with an associated flow rule is first assumed for the undamaged matrix material. It is shown that the resulting overall yield function for the damaged composite is of the anisotropic type, while the derived overall flow rule is nonassociative due to the presence of damage. In addition, an overall kinematic hardening rule is obtained for the damaged composite system that is a combination of a generalized Ziegler-Prager rule and a Phillips-type rule. Finally, an elasto-plastic stiffness tensor is
TL;DR: In this paper, it was shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function from a generalized Pareto distribution.
Abstract: It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function $F$ from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if $F$ is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an iid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true.
TL;DR: In this article, the Von Mises criterion was used to obtain an elastic mechanical pressure from a transverse compression test of a thin walled porous tube, and a permeability test was evaluated to evaluate the hydraulic limiting pressure beyond which flux decline becomes irreversible and compaction occurs.
TL;DR: In this paper, the effect of the twisting moment on the reduction of the plastic-moment capacity of an inclined yield line under axial force was considered. And lower bound solutions based on the Tresca yield criterion and the von Mises yield criterion were derived to determine the reduced PLM capacity.
Abstract: Existing formulae for the reduced plastic-moment capacity of an inclined yield line under axial force are reviewed. Lower-bound solutions, which are based on the Tresca yield criterion and the von Mises yield criterion, are derived to determine the reduced plastic-moment capacity of an inclined yield line under axial force. The effect of the twisting moment on the reduction of the plastic-moment capacity is considered.
TL;DR: In this paper, the yield surface equations for three-dimensional frames subjected to combined actions of an axial force, shear forces, bending moments, warping moment, and a torque are derived based on two different approaches: (i) continuum-based description in terms of stress components and (ii) stress resultants.
TL;DR: In this article, an exact elasto-plastic analytical solution for a large-strained internal-pressurized, closed-end, elastic linear-hardening material is derived based on the notion of finite strains, the deformation theory of Hencky and the yield criterion of von Mises.
TL;DR: A detailed description of the computer implementation of a generalized midpoint algorithm for integration of constitutive relations for von Mises' hardening material is presented.
TL;DR: In a probabilistic approach to failure, use of the Driicker-Prager equivalent stress appeared to be superior, because the average failure load of notched beams was predicted with an error smaller than 8%.
Abstract: In clinical situations, the mechanical performances of dental structures--for example, composite restorations--depend on many factors. Most of them have a probabilistic character. Because composites are brittle materials, their strength should also be considered as a probabilistic quantity. For successful prediction of mechanical failure of structures consisting of these materials, a probabilistic approach is indispensable, and a suitable definition of equivalent stress must be introduced. An equivalent stress facilitates the transfer of strength data of laboratory specimens to situations where the stress state is much more complicated. The tensile and compressive strengths of composites differ considerably. Of two equivalent stress definitions that potentially describe this experimental fact (the Drucker-Prager and the Modified von Mises equivalent stress), the predictive capacity was investigated for a microfine composite. In a probabilistic approach to failure, use of the Drucker-Prager equivalent stress appeared to be superior, because the average failure load of notched beams was predicted with an error smaller than 8%.
TL;DR: In this paper, a new theory is proposed that assumes a nonuniform distribution of slips depending on the orientation of an infinite number of possible slip planes at each point in the plate.
TL;DR: In this paper, the authors extended the Dugdale model to cases combining modes I, II and III, based on the von Mises yield criterion, and provided an a posteriori estimate for plasticity effects, based only on the stress intensity factors from the elasticity solution.
Abstract: A model attributed to Dugdale provides a correction for plasticity effects at crack tips in Mode I, under the assumption of small-scale yielding. Similar models have been proposed for Modes II and III, the former fairly recently. In the present study, the Dugdale model is extended to cases combining Modes I, II and III, based on the von Mises yield criterion. The combined model provides an a posteriori estimate for plasticity effects, based only on the stress intensity factors from the elasticity solution. It also provides an estimate for the crack-opening displacement and theJ-integral value. In the limit of small loads, the corresponding elastic results are recovered.
TL;DR: This paper argued that Mises's method of justifying laissez faire has more in common with the natural rights approach of Herbert Spencer and Auberon Herbert than the utilitarianism of Bentham and Mill.
Abstract: L udwig von Mises was one of this century's most principled and uncompromising defenders of laissez faire. He was also an outspoken advocate of utilitarianism and the doctrine of social expediency, and a critic of any kind of objective ethics such as natural law or natural rights. This raises the obvious question as to how successful Mises was in turning the sow's ear of social expediency into the silk purse of laissez faire. Murray N. Rothbard's answer is that Mises was not successful-that no one, not even Mises, could accomplish such a feat (1982, pp. 205-13). Henry Hazlitt (1964) and Leland Yeager (1992), on the other hand, have argued that utilitarianism really is not the sow's ear that its critics have made it out to be-or a t least not the brand of utilitarianism that they attribute to Mises: indirect utilitarianism. Furthermore, they argue that only utilitarianism, properly understood , can provide a moral foundation for laissez faire. While I agree with Rothbard that utilitarianism, whether direct or indirect, cannot provide a principled defense of laissez faire, I shall argue that Mises's method of justifying laissez faire has more in common with the natural rights approach of Herbert Spencer and Auberon Herbert than the utilitarianism of Bentham and Mill. It should be stressed that I am not disputing the easily documented fact that Mises proclaimed himself to be a utilitarian, and was highly critical, even scornful of natural law and natural rights doctrines (Rothbard 1980). One can dredge up quote aRer quote where Mises defends utilitarianism and social expediency and attacks natural law and natural rights theories. On the other hand, one cannot ignore Mises's \"apparent use of natural law-type constructs, in spite of his explicit rejection of natural law\" (Tucker and Rockwell 1991, p. 48).
TL;DR: In this article, the authors define a class of simple plasticity models, for which an incremental potential energy can be constructed This potential has, in general, multiple stationary points, which correspond to equilibrium solutions when the material shows softening characteristics Explicit expressions of the incremental energy are derived for von Mises plasticity with linear isotropic hardening within the context of a standard dissipative material using the Hill criterion for static stability.
Abstract: Using the fully implicit rule for temporal integration, one may define a class of simple plasticity models, for which an incremental potential energy can be constructed This potential has, in general, multiple stationary points, which correspond to equilibrium solutions when the material shows softening characteristics Explicit expressions of the incremental potential energy are derived for von Mises plasticity with linear isotropic hardening within the context of a standard dissipative material Using the Hill criterion for static stability, we show that stable incremental solutions are also (local) minimum points of the incremental potential energy for this particular material Finite element results for this (simple) plasticity model are presented, which show that the stable solution also exhibits strong localization of plastic deformation
TL;DR: In this article, a closed-form genera1 asymptotic solution for singular centered fan sectors is given as a function of p, which is a pressure sensitivity parameter introduced in the yield condition.
TL;DR: In this paper, the authors used an elasto-plastic finite-element method to predict the joint strength of single-lap adhesive joints with an increase of tensile shear load.
Abstract: Stress distributions in single-lap adhesive joints are analyzed using an elasto plastic finite-element method in order to predict joint strength. With an increase of tensile shear load, adherends tend to be yielded and the interface then starts to peel. The peel process and the yielded regions of the adherends are examined with an increase of the tensile shear load. The effects of rigidity and yield stress of adherends and so on are clarified on the peel process. It is seen that the peel stress increases with a decrease of adherend rigidity. In addition, the joint strength is estimated taking the peel produced at the inter face, by the von Mises's criterion. Experiments concerning joint strength were performed. The numerical results are in fairly good agreement with the experimental ones concerning joint strength. It is shown that joint strength increases as the adherend rigidity increases.
TL;DR: In this paper, a mixed variational formulation and computational procedure for the shape optimization problem of linear elastic solids in possible contact with a rigid foundation is proposed, subject to a constraint on its volume and bound constraints on the design.
Abstract: This paper is concerned with the development of a mixed variational formulation and computational procedure for the shape optimization problem of linear elastic solids in possible contact with a rigid foundation. The objective is to minimize the maximum value of the von Mises equivalent stress in a body (non-differentiable objective function), subject to a constraint on its volume and bound constraints on the design. For design purposes, the contact boundary is considered fixed.
TL;DR: In this article, stress analysis using the theory of plasticity and von Mises yield criterion predicts a resultant compressive stress state surrounding a ballised hole, which is a function of the radius of the elastic-plastic boundary.
TL;DR: In this paper, an optimal design procedure for circular and annular plates taking the post-yield behaviour of structures into account was developed, and the problem posed was transformed into a non-linear boundary value problem which was solved numerically.
Abstract: An optimal design procedure is developed for circular and annular plates taking the post-yield behaviour of structures into account. Employing the variational methods of optimal control theory, the problem posed is transformed into a non-linear boundary value problem which is solved numerically.
01 May 1993
TL;DR: In this article, the authors measured the Rockwell C hardness (Rc) as a function of position on the three steel rings cut from tubes with different amounts of autofrettage.
Abstract: : The Rockwell C hardness (Rc) was measured as a function of position on the three steel rings cut from tubes with different amounts of autofrettage. These rings had different residual stress profiles through the wall that were measured using an ultrasonic technique. An experimental correlation between residual stress and Rc was obtained. In order to model the effects of residual stress on the measured hardness, the Tresca (linear) and the von Mises-Hencky (power) yield criteria were utilized within a model given by Shaw, Hoshi, and Henry that depicts the stress state within a spherical indenter. The von Mises- Hencky method was more successful in matching the data.... Hardness, Residual stress, Yielding criteria, Autofrettage, Ultrasonics
Journal Article•
TL;DR: In this paper, a method for aiding the design of rectangular rubber seals is suggested, using pure shear homogeneous deformation tests performed on Silicone Dow 888, which showed a rearrangement of molecules at 27.5% nominal displacement.
Abstract: A method for aiding the design of rectangular rubber seals is suggested. Rectangular cross sections are evaluated using plane strain, nonlinear, incompressible, hyperelastic (Mooney-Rivlin) finite element formulation of the software ABAQUS. On the basis of pure shear laboratory tests, a method for determining the limiting stress is suggested. Pure shear homogeneous deformation tests performed on Silicone Dow 888 showed a rearrangement of molecules at 27.5% nominal displacement. Even though rubber materials generally do not have a yield point, this point appeared as a monotonic yield point and was used as a design benchmark by comparing it with the equivalent Von Mises stress obtained using the finite element method.
TL;DR: In this paper, an anisotropic yield function of the sixth degree was proposed by combining Drucker's yield function with Hill's quadratic yield function, which is able to include the effects of the third deviatoric stress invariant and initial anisotropy.
Abstract: By means of combining Drucker's yield function with Hill's quadratic yield function, an anisotropic yield function of the sixth degree is proposed. It is able to include the effects of the third deviatoric stress invariant and initial anisotropy. Experiments are carried out on fully annealed 1,050 aluminum tubes under multiaxial stress states. By applying proportional loadings of axial load, internal pressure and torsion to the specimens, the change in yield stress with a rotation of the principal stress axes and the difference between the directions of the principal stress and principal strain increment are examined. The yield surface in the tension-internal pressure stress field reveals orthotropic anisotropy. The yield surface in the tension-torsion stress field lies outside von Mises' yield surface. Such behavioral characteristics can be expressed precisely by the proposed yield function. In addition, it is experimentally verified that the normality rule is obeyed in strain behavior.