Showing papers on "von Mises yield criterion published in 2003"

Ultimate Strength and Failure Mechanism of Resistance Spot Weld Subjected to Tensile, Shear, or Combined Tensile/Shear Loads

Abstract: Strength tests were performed to reveal the failure mechanisms of spot weld in lap-shear and cross tension test samples. It is shown the while the lap-shear (cross tension) sample is subjected to shear (normal) load at the structural level the failure mechanism at the spot weld is tensile (shear) mode at the materials level. Based on the observed failure mechanism, stress distribution is assumed and related to the far field load for the lapshear and cross tension test samples. It appears that the failure load of the cross tension sample is 74 percent of the lap-shear sample based on the classical von Mises failure theory. The theoretical model is further extended to the mixed normal/shear loading condition. Data from strength tests as well as finite element numerical method are used to validate the model. Finally, the utility of the model in accessing the failure strength of spot welds is discussed. @DOI: 10.1115/1.1555648#

Elasto-plastic stresses in thick walled cylinders

Abstract: In the optimal design of a modern gun barrel, there are two main objectives to be achieved: increasing its strength-weight ratio and extending its fatigue life. This can be carried out by generating a residual stress field in the barrel wall, a process known as autofrettage. It is often necessary to machine the autofrettaged cylinder to its final configuration, an operation that will remove some of the desired residual stresses. In order to achieve a residual stress distribution which is as close as possible to the practical one, the following assumptions have been made in the present research on barrel analysis: A von Mises yield criterion, isotropic strain hardening in the plastic region in conjunction with the Prandtl-Reuss theory, pressure release taking into consideration the Bauschinger effect and plane stress conditions. The stresses are calculated incrementally by using the finite difference method, whereby the cylinder wall is divided into N-rings at a distance Δr apart. Machining is simulated by removing rings from both sides of the cylindrical surfaces bringing the cylinder to its final shape. After a theoretical development of the procedure and writing a suitable computer program, calculations were performed and a good correlation with the experimental results was found. The numerical results were also compared with other analytical and experimental solutions and a very good correlation in shape and magnitude has been obtained.

Influence of the Yield-to-Tensile Strength Ratio on the Failure Assessment of Corroded Pipelines

Abstract: It is well known that both the yield strength and the tensile strength of a material have significant effect on the failure behavior of pipelines. Thus it can be anticipated that the yield-to-tensile strength (Y/T) is closely related to the strain hardening behavior of the material, and it also influences the failure behavior. This paper theoretically explores the influence of T/Y (the inverse of Y/T) ratio on the failure pressure of pipelines with or without corrosion defects. Based on the instability of deformation and finite strain theory, a plastic collapse criterion for close-ended pipes without corrosion defects is developed first. The constitutive behavior of line pipes is characterized by a power-law strain hardening relation, while the plastic deformation obeys the Mises yield criterion and the associated deformation theory of plasticity. An approximate relationship between the T/Y ratio and the strain hardening exponent n is obtained, and a closed-form solution to the limit pressure of pipe based on T/Y is derived. This plastic instability model is extended to predict the failure pressure of pipelines with corrosion defects, and validated by the PCRI experimental database. The results show that (a) the T/Y ratio is simply proportional to the strain hardening exponent n, which is almost independent of the yield strain and affected by the definition of the yield stress; (b) the failure pressure predicted by the present plastic instability model increases as the T/Y ratio decreases; and (c) as T/Y → 1, the present solution approaches to that predicted by the Mises strength criterion based on the nominal hoop and axial stresses.Copyright © 2003 by ASME

Three-dimensional finite element stress analysis of a cuneiform-geometry implant.

Abstract: PURPOSE The biomechanical behavior of an osseointegrated dental implant plays an important role in its functional longevity inside the bone. Studies of this aspect of dental implants by the finite element method are ongoing. In the present study, a cuneiform-geometry implant was considered with a 3-dimensional model that had a mesh that was finer than in the models commonly found in the literature. MATERIALS AND METHODS A mechanical model of an edentulous mandible was generated from computerized tomography, with the implant placed in the left first premolar region. A 100-N axial load was applied at the implant abutment, and the mandibular boundary conditions were modeled considering the real geometry of its muscle supporting system. The cortical and trabecular bone was assumed to be homogeneous, isotropic, and linearly elastic. RESULTS The stress analysis provided results that were used to plot global and detailed graphics of normal maximum (S1), minimum (S3), and von Mises stress fields. The results obtained were analyzed and compared qualitatively with the literature. DISCUSSION Quantitative comparisons were not performed because of basic differences between the model adopted here and those used by other authors. The stress distribution pattern for the studied geometry was similar to those found in the current literature, but insignificant apical stress concentration occurred. The stress concentration occurred at the neck of the implant, ie, in the cortical bone, which was similar to results for other implant shapes reported in the literature. CONCLUSION The studied geometry showed a smooth stress pattern, with stress concentrated in the cervical region. The values, however, were within the range of values found in the cortical layer far from the implant, caused by the muscular action. No significant stress concentration was found in the apical area.

Abfraction: 3D analysis by means of the finite element method.

Abstract: Objective: Tooth deflections under functional loads are considered to be the etiologic factor of noncarious cervical lesions. There are several studies on the materials used to restore these lesions; however, there are few discussing this phenomenon's etiology from a biomechanic point of view. This study was undertaken to evaluate tooth behavior when forces were applied from different directions. Method and materials: A 3D finite element model of a maxillary central incisor was designed. A distributed force of 1.5 N was applied on the palatal side of the crown in five stages, with varying directions progressing from tipping to intrusion. Two separate approaches (displacement and stress) were considered to evaluate the cervical area from a stress perspective. Results: The displacement approach resulted in a curved path when compared to a straight line connecting the apical and incisal areas. The maximum deflections were in the cementoenamel junction area. The same area was shown to undergo the maximum of von Mises stress and stress intensity. Patterns of the von Mises stress when evaluated in a mesiodistal direction were in complete agreement with the shape of the cervical lesions (except for the application of the intrusive force, which rules out its effect in producing such lesions). Conclusion: Force applications, except for intrusive force, can produce increases in the von Mises stress and tooth deflections that can answer the question of the etiology of noncarious cervical lesions. The highest amounts of deflection and von Mises stress were produced by the 45-degree force application.

Residual stress determination in cold drawn steel wire by FEM simulation and X-ray diffraction

Abstract: This paper presents a study on residual stress in cold drawn wire of low carbon steel by means of finite-element method (FEM) simulation and X-ray diffraction. A thick wire with a diameter of 17.9 mm drawn from an annealed wire with a diameter of 20.1 mm was investigated. First, FEM simulations were performed based on a suitable model describing the boundary conditions and the exact material behavior. Due to the initial texture in the original material, the anisotropy of the material plastic behavior was taken into account on the basis of the texture measurement of the wire. Instead of the isotropic von Mises yield criterion, a texture-based anisotropic yield locus was incorporated into the model to simulate the wire drawing process and calculate residual stresses. Next, X-ray diffraction measurements were carried out at the surface of the wire to obtain the distribution of the lattice spacing versus sin 2 ψ , from which the macroscopic residual stresses at the wire surface were calculated. The comparison between the results from the simulations and the measurements shows that a good agreement has been reached.

Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure

Abstract: In this work, we present a finite element model capable of describing both the plastic deformation which accumulates during the hardening phase as the precursor to failure and the failure process leading to softening phenomena induced by shear slip lines. This is achieved by activating subsequently hardening and softening mechanisms with the localization condition which separates them. The chosen model problem of von Mises plasticity is addressed in detail, along with particular combination of mixed and enhanced finite element approximations which are selected to control the locking phenomena and guarantee mesh-invariant computation of plastic dissipation. Several numerical simulations are presented in order to illustrate the ability of the presented model to predict the final orientation of the shear slip lines for the case of non-proportional loading.

Theoretical modelling of the effect of plasticity on reverse transformation in superelastic shape memory alloys

Abstract: Stimulated by recent experimental results on superelastic NiTi shape memory alloy, a theoretical study is carried out to quantify the effect of plasticity on stress-induced martensite transformation, using a constitutive model that combines phase transformation and plasticity. A constraint equation is introduced to quantify the phenomenon of the stabilisation of plasticity on stress-induced martensite. The stabilised martensite volume fraction is determined by the equivalent plastic strain. The transformation constitutive model is adopted from a generalised plastic model with Drucker–Prager type phase transformation functions, which are pressure sensitive, while the plasticity is described by the von Mises isotropic hardening model. The martensite volume fraction is chosen as the internal variable to represent the transformation state and it is determined by the consistency transformation condition. An approach to calibrate model parameters from uniaxial tensile tests is explored, as well as the issue of elastic mismatch between austenite and martensite is discussed. Based on the proposed constitutive model, the influence of hydrostatic stress on transformation is examined. As an example of application, this new constitutive model is employed to numerically study the transformation field and the plastic deformation field near a crack tip.

Numerical simulation of stress evolution during electromigration in IC interconnect lines

Abstract: A finite element simulation of stress evolution in thin metal film during electromigration is reported in this paper. The electromigration process is modeled by a coupled diffusion- mechanical partial differential equations (PDEs). The PDEs are implemented with a plane strain formulation and numerically solved with the finite element (FE) method. The evolutions of hydrostatic stress, each component of the deviatoric stress tensor, and Von Mises' stress were simulated for several cases with different line lengths and current densities. Two types of displacement boundary conditions are considered. The simulation results are compared with Korhonen's analytical model and Black and Blech's experimentalesults.

Kinematic hardening in large strain plasticity

Abstract: A finite strain hyper elasto-plastic constitutive model capable to describe non-linear kinematic hardening as well as nonlinear isotropic hardening is presented. In addition to the intermediate configuration and in order to model kinematic hardening, an additional configuration is introduced - the center configuration; both configurations are chosen to be isoclinic. The yield condition is formulated in terms of the Mandel stress and a back-stress with a structure similar to the Mandel stress. It is shown that the non-dissipative part of the plastic velocity gradient not governed by the thermodynamical framework and the corresponding quantity associated with the kinematic hardening influence the material behaviour to a large extent when kinematic hardening is present. However, for isotropic elasticity and isotropic hardening plasticity it is shown that the non-dissipative quantities have no influence upon the stress-strain relation. As an example, kinematic hardening von Mises plasticity is considered, which fulfils the plastic incompressibility condition and is independent of the hydrostatic pressure. To evaluate the response and to examine the influence of the non-dissipative quantities, simple shear is considered; no stress oscillations occur. (Less)

Interior point optimization and limit analysis: an application

Abstract: The well-known problem of the height limit of a Tresca or von Mises vertical slope of height h, subjected to the action of gravity stems naturally from Limit Analysis theory under the plane strain condition. Although the exact solution to this problem remains unknown, this paper aims to give new precise bounds using both the static and kinematic approaches and an Interior Point optimizer code. The constituent material is a homogeneous isotropic soil of weight per unit volume γ. It obeys the Tresca or von Mises criterion characterized by C cohesion. We show that the loading parameter to be optimized, γh/C, is found to be between 3.767 and 3.782, and finally, using a recent result of Lyamin and Sloan (Int. J. Numer. Meth. Engng. 2002; 55: 573), between 3.772 and 3.782. The proposed methods, combined with an Interior Point optimization code, prove that linearizing the problem remains efficient, and both rigorous and global: this point is the main objective of the present paper. Copyright © 2003 John Wiley & Sons, Ltd.

Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory

Abstract: This paper presents the development of a generalized method to predict forming limits of sheet metals. The vertex theory which was developed by Storen and Rice (1975) and recently simplified by Zhu, Weinmann and Chandra (2001), is employed in the analysis to characterize the localized necking (or localized bifurcation) mechanism in elastoplastic materials. The plastic anisotropy of materials is considered. A generalized deformation theory of plasticity is proposed. The theory considers Hosford's high-order yield criterion (1979), Hill's quadratic yield criterion and the von Mises yield criterion. For the von Mises yield criterion, the generalized deformation theory reduces to the conventional deformation theory of plasticity, i.e., the J 2 -theory. Under proportional loading condition, the direction of localized band is known to vary with the loading path at the negative strain ratio region or the left hand side (LHS) of forming limit diagrams (FLDs). On the other hand, the localized band is assumed to be always perpendicular to the major strain at the positive strain ratio region or the right hand side (RHS) of FLDs. Analytical expressions for critical tangential modulus are derived for both LHS and RHS of FLDs. For a given strain hardening rule, the limit strains can be calculated and consequently the FLD is determined. Especially, when assuming power-law strain hardening, the limit strains can be explicitly given on both sides of FLD. Whatever form of a yield criterion is adopted, the LHS of the FLD always coincides with that given by Hill's zero-extension criterion. However, at the RHS of FLD, the forming limit depends largely on the order of a chosen yield function. Typically, a higher order yield function leads to a lower limit strain. The theoretical result of this study is compared with those reported by earlier researchers for Al 2028 and Al 6111-T4 (Grafand Hosford, 1993; Chow et al., 1997).

Effect of Residual Stress in Surface Layer on Contact Deformation of Elastic-Plastic Layered Media

Abstract: The effect of residual stress in the surface layer on the deformation of elastic-plastic layered media due to indentation and sliding contact loading and unloading was analyzed with the finite element method. A three-dimensional finite element model of a rigid sphere interacting with a deformable layered medium was developed, and its accuracy was evaluated by contrasting finite element results with analytical solutions for the surface stresses of an elastic homogeneous half-space subjected to normal and friction surface traction. Deformation of the layered medium is interpreted in terms of the dependence of the von Mises equivalent stress, first principal stress, and equivalent plastic strain on the magnitudes of residual stress and coefficient of friction. The effect of residual stress on the propensity for yielding and cracking in the layered medium is discussed in the context of results for the maximum Mises and tensile stresses and the evolution of plasticity in the subsurface. It is shown that the optimum residual stress in the surface layer depends on the type of contact loading (indentation or sliding), coefficient of friction, and dominant deformation mode in the layer (i.e., plastic deformation or cracking).

Comparison of models for finite plasticity: A numerical study

Abstract: We introduce a general framework for the numerical approximation of finite multiplicative plasticity. The method is based on a fully implicit discretization in time which results in an iteratively evaluated stress response; the arising nonlinear problem is then solved by a Newton method where the linear subproblems are solved with a parallel multigrid method. The procedure is applied to models with different elastic free energy functionals and a plastic flow rule of von Mises type. In addition these models are compared to a recently derived frame indifferent approximation of finite multiplicative plasticity valid for small elastic strains which leads to linear balance equations. Rate independent and rate dependent realizations of the former models are considered. We demonstrate by various 3D simulations that the choice of the elastic free energy is not essential (for material parameters representative for metals) and that the new model gives the same response quantitatively and qualitatively as the standard models.

A study on the stress and nonuniformity of the wafer surface for the chemical-mechanical polishing process

Abstract: In this paper, a two-dimensional axisymmetric quasic-static model for the chemical-mechanical polishing process (CMP) was established. Based on the principle of minimum total potential energy, a finite element model for CMP was thus established. In this model, the four-layer structures including the wafer carrier, the carrier film, the wafer and the pad are involved. The von Mises stress distributions on the wafer surface were analysed, and the effects of characteristics of the pad and the carrier film and the load of the carrier on the von Mises stress and nonuniformity on the wafer surface were investigated. The findings indicate that the profile of the von Mises stress distributions correlates with the removal rate profile. The elastic modulus and thickness of pad and carrier load would significantly affect the von Mises stress and nonuniformity, but those of the film did not affect very much.

Elasto-plastic load transfer in bulk metallic glass composites containing ductile particles

Abstract: In-situ diffraction experiments were performed with high-energy synchrotron X-rays to measure strains in crystalline reinforcing particles (5 and 10 vol. pct W or 5 vol. pct Ta) of bulk metallic glass composites. As the composites were subjected to multiple uniaxial tensile load/unload cycles up to applied stresses of 1650 MPa, load transfer from the matrix to the stiffer particles was observed. At low applied loads, where the particles are elastic, agreement with Eshelby elastic predictions for stress partitioning between matrix and particles is found, indicating good bonding between the phases. At high applied loads, departure from the elastic stress partitioning is observed when the particles reach the von Mises yield criterion, as expected when plasticity occurs in the particles. Multiple mechanical excursions in the particle plastic region lead to strain hardening in the particles, as well as evolution in the residual strain state of the unloaded composite.

Limit analysis of ductile composites based on homogenization theory

Abstract: A numerical method is presented in this paper for determining the load–bearing capacities of ductile composites such as metal matrix composites based on homogenization theory and the kinematic limit theorem. A representative volume element is chosen to reflect the microstructure of a periodic composite. By directly introducing the von Mises yield criterion into the kinematic limit theorem, a nonlinear optimization formulation can be obtained to calculate the ultimate strength of a ductile composite. The finite–element modelling of the kinematic limit analysis is formulated as a nonlinear mathematical programming problem with equality–constraint conditions, which can be solved by a direct iterative algorithm. An interface failure model based on the microscopic fluctuation displacements is proposed to account for the effects of interfaces on the failure of composites. The present method can effectively reveal the effects of the microstructure on the macroscopic properties and micromechanical failure mechanisms of composites. Finally, some numerical examples illustrate the validity of the present method.

The effect of proximity of a rail end in elastic-plastic contact between a wheel and a rail

Abstract: This paper investigates the effects of a free rail end on the contact stress distribution near the rail end by employing elastic-plastic finite element methods. The contact elements were used to simulate the interaction between a wheel and a rail. A plane strain model was used in this study. Variations in contact stress fields at various contact points near the rail end were compared. The availability of the Hertz contact theory in the region near the rail end was also investigated. The numerical results indicated that the contact stress distributions around the rail end are sensitive to the contact distance. The location of the maximum von Mises stress was shifted to the contact surface as the contact point moves close to the rail end. Results also show that the plastic zone size and the von Mises stress are increased gradually and extend to the rail end as the contact point moves near the rail end. A higher stress, larger deflection and serious plastic deformation occurring at the rail end may l...