Showing papers on "von Mises yield criterion published in 1997"

Yield criteria for amorphous glassy polymers

Abstract: Three amorphous polymers, polymethyl methacrylate, polystyrene and polycarbonate were tested in uniaxial tension, uniaxial compression, plane strain compression and simple shear, over a range of temperatures. In each test, the yield point was precisely determined via residual strain measurements after unloading. With the yield stresses determined for these four different stress states, two pressure dependent shear yield criteria, i.e, the modified Von Mises and the modified Tresca criteria, were checked and compared. It is shown that (i) in each case (material, temperature, initial ageing state), the yield locus is satisfactorily described by either one or the other of the two criteria, and (ii) each criterion can be associated with a specific deformation mode (either homogeneous or localized in shear bands). As for the temperature dependence of the yield stress sensitivity to the hydrostatic pressure, it appears to be related to the glass transition temperature (Tg) and more precisely to the α and β relaxations. Finally, the pressure dependence of the yield stress can be possibly explained as being due to two effects: (i) the influence of pressure on molecular motions leading to yielding and (ii) the influence of pressure on the microstructural state.

Influence of a Hard Surface Layer on the Limit of Elastic Contact—Part I: Analysis Using a Real Surface Model

Abstract: A numerical simulation technique for calculating the pressure distribution and the deformed geometry of an elastic half space which has a hard surface layer in contact with a rigid indenter with a rough surface is presented. In order to reduce the computing time, the Conjugate Gradient Method ( CGM ) is applied to solve a set of linear equations for unknown pressures. In each iteration of the CGM, the Fast Fourier Transform (FFT) is used for the task of multiplying a direction vector by an influence coefficient matrix. An FFT-based scheme for evaluating subsurface stresses in the layer and the substrate is also presented. As an example, the pressure distribution and the deformed geometry of a steel surface coated with a TiN layer in contact with a rigid rough indenter are calculated. The subsurface stresses are also compared with von Mises yield criterion to investigate the deformation mode at the asperity contacts. The results show that the limit of elastic contact is highly dependent on the layer thickness and the surface roughness.

Von Mises Stress in Chemical‐Mechanical Polishing Processes

Abstract: In this paper we (i) describe a model for the stress distribution across a wafer during chemical-mechanical polishing, which is solved using I-DEAS (a commercial software package) and (ii) summarize the predicted effects of carrier film and pad compressibility on polishing nonuniformity. Results indicate that (i) the Von Mises stress correlates with polishing nonuniformity, while the normal stress does not correlate with the nonuniformity and (ii) CMP uniformity improves with decreasing polishing pad and carrier film compressibility.

On large deformations of thin elasto-plastic shells: Implementation of a finite rotation model for quadrilateral shell element

Abstract: A large-deformation model for thin shells composed of elasto-plastic material is presented in this work, Formulation of the shell model, equivalent to the two-dimensional Cosserat continuum, is developed from the three-dimensional continuum by employing standard assumptions on the distribution of the displacement held in the shell body, A model for thin shells is obtained by an approximation of terms describing the shell geometry. Finite rotations of the director field are described by a rotation vector formulation. An elasto-plastic constitutive model is developed based on the von Mises yield criterion and isotropic hardening. In this work, attention is restricted to problems where strains remain small allowing for all aspects of material identification and associated computational treatment, developed for small-strain elastoplastic models, to be transferred easily to the present elasto-plastic thin-shell model. A finite element formulation is based on the four-noded isoparametric element. A particular attention is devoted to the consistent linearization of the shell kinematics and elasto-plastic material model, in order to achieve quadratic rate of asymptotic convergence typical for the Newton-Raphson-based solution procedures. To illustrate the main objective of the present approach-namely the simulation of failures of thin elastoplastic shells typically associated with buckling-type instabilities and/or bending-dominated shell problems resulting in formation of plastic hinges-several numerical examples are presented, Numerical results are compared with the available experimental results and representative numerical simulations.

A generalized model for the yield behavior of epoxy networks in multiaxial stress states

Abstract: Several yield criteria for glassy polymers are reviewed, and their limitations in predicting the effects of stress state, strain rate, test temperature, and molecular architecture are noted. These criteria are then generalized, so that a working model can be developed for predicting the yield response of glassy networks subjected to a multiaxial state of stress. To form the model, we summarize the phenomenological yield and fracture response of amine cured epoxies. In stress states ranging from uniaxial compression to biaxial tension, the yield response of these glassy networks follows a modified von Mises criterion (T y oct = T yo oct ), when tested at a constant temperature and octahedral shear strain rate, y oct . Furthermore, changes in y oct and molecular weight between crosslinks, M C , affect T yo oct only, and μ remains unchanged. This was shown to be true for a broad range ofM C (380 to 1790 g/mol). Additional results are included to illustrate the effects of temperature and strain rate on yield response. These results show that the yield behavior of epoxy resins is best described by a thermally activated process, similar to an Eyring type process. Finally, we extend the model to include intrinsic properties of the resin (e.g., M C , O, and T g ) and compare the model's predictions with experimental results.

Deformation and yield of epoxy networks in constrained states of stress

Abstract: A series of epoxy networks were made with molecular weights between crosslinks, Mc, ranging from 380 to 1790 g mol-1. Resins were cast into thin walled hollow cylinders and tested in stress states ranging from uniaxial compression to biaxial tension. These tests elucidated the effects of stress state, strain rate, and Mc on the yield and fracture response of epoxy networks. Throughout the study, the strain rate along the octahedral shear plane, γoct, was maintained constant independent of stress state, for each failure envelope. The hollow cylinder tests showed that the yield behaviour of epoxy networks can be described by a modified von Mises criterion, τocty=τocty0−μσm where τoctg is the octahedral shear stress at yield, τocty0 is the octahedral shear stress at yield in pure shear, μ is the coefficient of internal friction and Vm is the hydrostatic tensile stress imposed on the sample. Furthermore, these tests showed that changes in γoct and Mc only affect τocty0, while μ remains constant. Standard tensile and compression tests were run to confirm the hollow cylinder result and to test the effect of temperature on the yield and brittle response. Tensile tests showed that changes in Mc only affect the glass transition temperature, Tg, of the materials, and the glassy modulus remained independent of Mc. With regard to the yield strength, changes in Mc cause a shift in the Tg of the materials, and the yield strengths of all the materials collapse together at a constant temperature relative to Tg. Finally, yielding of these epoxies was shown to follow an Eyring type flow model over the range of temperatures and strain rates tested.

MML mixture modelling of multi-state, Poisson, von Mises circular and Gaussian distributions

Abstract: Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also consistent and efficient. We provide a brief overview of MML inductive inference (Wallace and Boulton (1968) , Wallace and Freeman (1987)) , and how it has both an information-theoretic and a Bayesian interpretation. We then outline how MML is used for statistical parameter estimation, and how the MML mixture modelling program, Snob (Wallace and Boulton (1968), Wallace (1986) , Wallace and Dowe(1994)) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with selection of the number of components. The message length is (to within a constant) the logarithm of the posterior probability of the theory. So, the MML theory can also be regarded as the theory with the highest posterior probability. Snob currently assumes that variables are uncorrelated, and permits multi-variate data from Gaussian, discrete multi-state, Poisson and von Mises circular distributions.

Shear and tensile thermomechanical behavior of near equiatomic NiTi alloy

Abstract: The industrial development of devices using the intriguing properties of shape memory alloys involves accurate prediction of their thermomechanical behavior. This may be achieved using Computer Aided Design together with Finite Element programs. Reliable constitutive laws are needed for the execution of such programs. Several tensorial constitutive laws have been proposed to model the unusual thermomechanical properties of shape memory alloys. However, for all these tensorial models, it is necessary to make assumptions which cannot be verified when only tensile property data are available. The purpose of this paper is to present a new set of experimental mechanical data, including tensile and simple shear tests performed on sheet samples of near equiatomic NiTi alloy. Both mechanical behaviors are compared for a large temperature range (from below Mf to above Af). It is shown that the von Mises assumptions usually made in the establishment of tensorial constitutive equations are not always valid. Other yield locus forms are proposed to model the typical tension and simple shear thermomechanical behavior of shape memory alloys.

Semi-Analytical Modeling of Crack Initiation Dominant Contact Fatigue Life for Roller Bearings

Abstract: The fatigue test of a needle roller bearing suggests that the dominant failure mechanism is subsurface crack initiation and propagation. Therefore, a new semi-analytical contact fatigue model is derived from a micromechanics based crack initiation model. The analysis indicates that in the life calculation the selection of the critical stress, such as the maximum orthogonal shear stress, maximum shear stress, octahedral shear stress, or von Mises equivalent stress, becomes arbitrary under the nonfrictional Hertzian line contact condition. The fatigue life of roller bearings under the pure rolling condition can be predicted by simply knowing the Hertzian contact pressure and the contact width, which avoids complicated calculation of the subsurface stresses. The film thickness, roughness, and the material hardness effects on contact fatigue are also included in the new model. The comparisons with different models and the experimental data indicate that the new model makes similar life predictions as the loannides-Harris model, but the new model is much simpler to use. The Lundberg-Palmgren model does not fit with the experiment data.

Nonlinear Analysis of RC Members Using Plasticity with Multiple Failure Criteria

Abstract: Concrete plasticity models for the analysis of reinforced-concrete (RC) members in plane stress are studied. The proposed plasticity model for reinforced concrete provides a unified approach combining plasticity theory and damage models. It addresses strength enhancement under multiaxial compression, and tensile cracking damage. The model uses multiple failure criteria for compressive crushing and tensile cracking. For tensile cracking behavior, rotating-crack and fixed-crack plasticity models are compared. As crushing failure criterion, the Drucker-Prager and von Mises models are used for comparison. The proposed model uses new and existing damage models for tension softening, tension stiffening, and compression softening due to tensile cracking. Finite-element analyses using the plasticity model are compared with existing experimental results. To verify the proposed crushing and cracking plasticity models, the experiments have load capacities governed either by compressive crushing of concrete or by yielding of reinforcing steel. The advantages and disadvantages of rotating-crack and fixed-crack plasticity models are discussed.

A Yield Criterion for Porous Ductile Media at High Strain Rate

Abstract: An approximate yield criterion for porous ductile media at high strain rate is developed adopting energy principles. A new concept that the macroscopic stresses are composed of two parts, representing dynamic and quasi-static components, is proposed. It is found that the dynamic part of the macroscopic stresses controls the movement of the dynamic yield surface in stress space, while the quasi-static part determines the shape of the dynamic yield surface. The matrix material is idealized as rigid-perfectly plastic and obeying the von Mises yield. An approximate velocity field for the matrix is employed to derive the dynamic yield function. Numerical results show that the dynamic yield function is dependent not only on the rate of deformation but also on the distribution of initial micro-damage, which are different from that of the quasi-static condition. It is indicated that inertial effects play a very important role in the dynamic behavior of the yield function. However, it is also shown that when the rate of deformation is low (≤10 3 /sec), inertial effects become vanishingly small, and the dynamic yield function in this case reduces to the Gurson model.

Biaxial Testing of 2219-T87 Aluminum Alloy Using Cruciform Specimens

Abstract: A cruciform biaxial test specimen was designed and seven biaxial tensile tests were conducted on 2219-T87 aluminum alloy. An elastic-plastic finite element analysis was used to simulate each tests and predict the yield stresses. The elastic-plastic finite analysis accurately simulated the measured load-strain behavior for each test. The yield stresses predicted by the finite element analyses indicated that the yield behavior of the 2219-T87 aluminum alloy agrees with the von Mises yield criterion.

Rayleigh–Taylor stability criteria for elastic-plastic solid plates and shells

Abstract: The Rayleigh–Taylor (R-T) instability theory is usually applied to the acceleration of one fluid by a lower density one, but also becomes applicable to a solid accelerated by a fluid at very high pressure. Approximate analytic R-T stability criteria are derived for both finite and infinitesimal perturbations of the driven surface of an incompressible solid plate of a given thickness, shear modulus, and von Mises yield stress uniformly accelerated by a massless fluid. The Prandtl-Reuss equations of elastic-plastic flow are assumed for the solid. A single degree of freedom, amplitude q, is assumed for the spatial dependence of the perturbation, which is approximated to be that of the semi-infinite half-plane ideal fluid linear R-T eigenfunction. The temporal dependence of q, however, is determined self-consistently from global energy balance, following a previously published model. The (significant) effect of the unperturbed solid’s stress tensor is included and related to the converging/diverging geometrie...

Viscoplasticity with dynamic yield surface coupled to damage

Abstract: A formulation of viscoplasticity theory, with kinetic coupling to damage, is presented. The main purpose is to describe rate-dependent material behavior and failure processes, including creep-rupture (for constant load) and creep-fatigue (for cyclic load). The Duvaut-Lions' formulation of viscoplasticity is adopted with quite general hardening of the quasistatic yield surface. The formulation is thermodynamically consistent, i.e. the dissipation inequality is satisfied. Like in the classical viscoplasticity formulations, the rate-independent response is activated at a very small loading rate. In addition, an (unconventional) dynamic yield surface is introduced, and this is approached asymptotically at infinite loading rate. Explicit constitutive relations are established for a quasistatic yield surface of von Mises type with nonlinear hardening. The resulting model is assessed for a variety of loading situations.

Numerical simulation of yield loci for PST crystals of TiAl

Abstract: The yield strength of polysynthetically twinned (PST) crystals of TiAl depends on the orientation angle between the lamellar boundaries and the load axis. It is the aim of this work to model this anisotropic behaviour. A micromechanical model is employed which considers the lamellar microstructure and the deformation mechanisms such as ordinary slip and deformation twinning in γ -TiAl. Since the calculated and measured yield strength data show good agreement in the case of uniaxial loading, there is a real motivation to study numerically the behaviour of a PST crystal under biaxial loading. Yield points are calculated for various proportional stress paths defined by the ratio of the principal stresses σ 1 / σ 2 in relation to the orientations of the load axes towards the lamellae. These predicted yield loci are compared with the von Mises and the Hill yield criteria.

An iterative approach to mechanical properties of MMCs at the onset of plastic deformation

Abstract: The current work presents a generalized Eshelby model allowing interaction among reinforcing particles under a Mori-Tanaka like scheme. Different aspect ratios and geometries are studied in the elastic and incipient elasto-plastic regime for a model SiC Al composite. The fibers are taken as purely elastic and the matrix is regarded elastic perfectly plastic responding to a Von Mises yield criterion. The phenomenon of plastic localization in the vicinities of the inclusions is carefully described for different reinforcement volume fractions and thermo-mechanical loading. Equivalent stress, hydrostatic pressure and elastic and plastic strains are depicted as contour levels around a representative inclusion. Effective coefficients of thermal expansion of composites are calculated both under purely elastic composite response and at the onset of plastic localized deformation. The influence of plastic strain over those effective coefficients is shown to be detectable. The simulated stress-strain curves show the influence of interaction stresses over macroscopic yield stress by isolating this phenomenon from matrix hardening. Accumulated elastic energies and plastic work are calculated to show the different nature of purely thermal and mechanical loads.