Showing papers on "von Mises yield criterion published in 2012"

A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some representative cell

Abstract: Gurson (1977) 's famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al., 1993 , Gologanu et al., 1994 , Gologanu et al., 1997 to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellipsoidal cavities, through approximate homogenization of some representative elementary porous cell. As a first step, we perform in the present Part I a limit-analysis of such a cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confocal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008) , satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.

Evaluation of residual stress in ferromagnetic steels based on residual magnetic field measurements

Abstract: The paper presents a residual stress evaluation method using the gradients of the residual magnetic field (RMF) components. Distributions of the RMF components were measured on the surface of samples with a various degree of plastic strain. The finite element method was used to model residual stress in samples. The impact of residual stress on changes in the residual magnetic field was shown. A very good qualitative correlation was found between places with residual stress and areas with increased values of the gradients of the RMF components. An algorithm was developed and verified for steel T/P24 to make a quantitative evaluation of residual equivalent (von Mises) stress based on the gradients of tangential component dH T , Y /dx and field gradient dH / dx . Directions of further research were formulated, which included the validation of the method and which took into consideration the factors affecting its accuracy. The developed algorithm can be a significant complement to the Metal Magnetic Memory (MMM) method.

Atomistic mechanisms of cyclic hardening in metallic glass

Abstract: Molecular dynamics with an embedded-atom method potential is used to simulate the nanoindentation of Cu63.5Zr36.5 metallic glasses. In particular, the effects of cyclic loading within the nominal elastic range on the overall strength and plasticity of metallic glass are studied. The simulated results are in line with the characteristics of experimentally observed hardening effects. In addition, analysis based on local von Mises strain suggests that the hardening is induced by confined microplasticity and stiffening in regions of the originally preferred yielding path, requiring a higher applied load to trigger a secondary one.

A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

Abstract: The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the she...

TSV Stress-Aware Full-Chip Mechanical Reliability Analysis and Optimization for 3-D IC

Abstract: In this paper, we propose an efficient and accurate full-chip thermomechanical stress and reliability analysis tool and design optimization methodology to alleviate mechanical reliability issues in 3-D integrated circuits (ICs). First, we analyze detailed thermomechanical stress induced by through-silicon vias in conjunction with various associated structures such as landing pad and dielectric liner. Then, we explore and validate the linear superposition principle of stress tensors and demonstrate the accuracy of this method against detailed finite element analysis simulations. Next, we apply this linear superposition method to full-chip stress simulation and a reliability metric named the von Mises yield criterion. Finally, we propose a design optimization methodology to mitigate the mechanical reliability problems in 3-D ICs. Our numerical experimental results demonstrate the effectiveness of the proposed methodology.

Energy-based yield criterion for PMMA from large-scale molecular dynamics simulations

Abstract: We use molecular dynamics (MD) with the DREIDING force field to characterize the ultimate mechanical response of amorphous poly(methyl methacrylate). We characterize how volumetric and deviatoric strains contribute to yield for a wide range of loading conditions from pure deviatoric, volume-conserving cases to isotropic volume expansion. We propose and apply an energy-based yield criterion to define yield consistently for all cases. Our results show that permanent deformation occurs when either the deviatoric or volumetric strains reach critical values, except in a narrow region around the transformation between deviatoric- and volumetric-dominated yield where the two strain invariants interact. In contrast, the pressure-modified von Mises criterion is only applicable to shear-dominated loading conditions. These results provide insight into the physics of yield in amorphous polymers and provide quantitative information and guidance for physics-based yield criteria for polymer-matrix composite materials.

Second-order cone programming with warm start for elastoplastic analysis with von Mises yield criterion

Abstract: The incremental problem for quasistatic elastoplastic analysis with the von Mises yield criterion is discussed within the framework of the second-order cone programming (SOCP). We show that the associated flow rule under the von Mises yield criterion with the linear isotropic/kinematic hardening is equivalently rewritten as a second-order cone complementarity problem. The minimization problems of the potential energy and the complementary energy for incremental analysis are then formulated as the primal-dual pair of SOCP problems, which can be solved with a primal-dual interior-point method. To enhance numerical performance of tracing an equilibrium path, we propose a warm-start strategy for a primal-dual interior-point method based on the primal-dual penalty method. In this warm-start strategy, we solve a penalized SOCP problem to find the equilibrium solution at the current loading step. An advanced initial point for solving this penalized SOCP problem is defined by using information of the solution at the previous loading step.

C-Stationarity for Optimal Control of Static Plasticity with Linear Kinematic Hardening

Abstract: An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. Existence and uniqueness of the plastic multiplier is rigorously proved, which allows for the reformulation of the forward system using a complementarity condition. In order to derive necessary optimality conditions, a family of regularized optimal control problems is analyzed, wherein the static plasticity problems are replaced by their viscoplastic approximations. By passing to the limit in the optimality conditions for the regularized problems, necessary optimality conditions of C-stationarity type are obtained.

Elasto-Plastic Stresses in a Functionally Graded Rotating Disk

Abstract: A numerical method based on the extension of the variable material property method was developed to obtain the elasto-plastic stress field in a functionally graded (FG) rotating disk. The method was applied to estimate the stress field in a metal–ceramic functionally graded solid disk. To establish the validity of the proposed method, results were compared with finite element results. Unlike uniform rotating disks, where yielding starts from the disk center, plasticity in FG disks can originate at any point. The effect of different metal–ceramic grading patterns as well as the relative elastic moduli and densities of the ceramic and metallic constituents on the developed stresses were studied. Reinforcement of a metal disk with ceramic particles, in both elastic and plastic regimes, can significantly influence the mechanical response of the disk such as the stress distribution and the critical angular velocities corresponding to the onset of plasticity in the disk and plastic disk. Disks with increasing ceramic content from inner to outer radius showed a more uniform von Mises stress distribution for a fixed value of total ceramic content. In contrast, disks with decreasing ceramic content from inner to outer radius had the lowest outer edge displacement for a fixed value of total ceramic content.

Planar Power Module With Low Thermal Impedance and Low Thermomechanical Stress

Abstract: In recent years, there has been growing demand to increase the power density in power modules. Therefore, the thermal management of power modules has become more and more critical. In this paper, we show that conventional single-sided power module with wire-bond connection cannot achieve both good steady-state and transient thermal performance under high heat transfer coefficient conditions. The plate-bonded power module has been proposed to resolve this issue. However, the thick copper plate embedded in the power module induces large thermomechanical stress during temperature cycling, leading to poor reliability. To reduce the thermomechanical stress without significantly compromising the thermal performance, a trenched copper plate power module is designed and presented. A parametric study shows that the maximum von Mises stress and plastic strain in the solder layer can be reduced by 18.7%, and 67.8%, respectively, if the single piece of copper plate is replaced by a 3 × 3 trenched copper plate.

Shakedown analysis with multidimensional loading spaces

Abstract: A numerical method for the computation of shakedown loads of structures subjected to varying thermal and mechanical loading is proposed for the case of multidimensional loading spaces. The shakedown loading factors are determined based on the lower bound direct method using the von Mises yield criterion. The resulting nonlinear convex optimization problem is solved by use of the interior-point method. Although the underlying theory allows for the consideration of arbitrary numbers of loadings in principle, until now applications have been restricted to special cases, where either one or two loads vary independently. In this article, former formulations of the optimization problem are generalized for the case of arbitrary numbers of loadings. The method is implemented into an interior-point algorithm specially designed for this method. For illustration, numerical results are presented for a three-dimensional loading space applied to a square plate with a central circular hole.

Steady motion of Bingham liquid plugs in two-dimensional channels

Abstract: We study numerically the steady creeping motion of Bingham liquid plugs in two-dimensional channels as a model of mucus behaviour during airway reopening in pulmonary airways. In addition to flow analysis related to propagation of the plug, the stress distribution on the wall is studied for better understanding of potential airway epithelial cell injury mechanisms. The yield stress behaviour of the fluid was implemented through a regularized constitutive equation. The capillary number, , and the Bingham number, , which is the ratio of the yield stress to a characteristic viscous stress, varied over the ranges 0.025–0.1 and 0–1.5, respectively. For the range of parameters studied, it was found that, while the yield stress reduces the magnitude of the shearing along the wall, it can magnify the amplitude of the wall shear stress gradient significantly, and also it can elevate the magnitude of the wall shear stress and wall pressure gradient up to 30 % and 15 %, respectively. Therefore, the motion of mucus plugs can be more damaging to the airway epithelial cells due to the yield stress properties of mucus. The yield stress also modifies the profile of the plug where the amplitude of the capillary waves at the leading meniscus decreases with increase in . Other findings are that: the thickness of the static film increases with increasing ; the driving pressure difference increases linearly with ; and increasing extends any wall stagnation point beneath the leading meniscus to an unyielded line segment beneath the leading meniscus. With an increase in , the unyielded areas appear and grow in the adjacent wall film as well as the core region of the plug between the two menisci. The plug length, , mostly modifies the topology of the yield surfaces. It was found that the unyielded area in the core region between the two menisci grows as the plug length decreases. The very short Bingham plug behaves like a solid lamella. In all computed liquid plugs moving steadily, the von Mises stress attains its maximum value near the interface of the leading meniscus in the transition region. For Bingham plugs moving very slowly, , the driving pressure is non-zero.

Finite element analysis and experimental investigation on deformation mechanism of non-axisymmetric tube spinning

Abstract: This paper developed 3D elastoplastic finite element analysis (FEA) models to investigate non-axisymmetric tubes neck spinning The three-roller mandreless neck spinning process was simulated by commercial FEA software, MSC Marc The distribution of the transient von Mises stresses in the contact zone between the roller and the blank, and the equivalent plastic strains after spinning were obtained The locations and causes of fractures were analyzed The thickness distribution of the spun workpiece was investigated numerically and experimentally It shows that during 3D non-axisymmetric tubes spinning, diametral elongation and fractures mostly occur at the opening end of workpiece, which considered as the primary location of defects Fractures may also occur easily at the initial spinning area, which may be considered a secondary location of defects The distributions of equivalent stresses and strains are non-uniform during both offset and oblique 3D non-axisymmetric tubes spinning The maximum stress and strain values occur at the location where the biggest offset or inclination is induced, while the minimum values occur at the opposite location of 180° away from the maximum values For the oblique tube, however, the strain distribution changes gradually along the axial direction, which is different from that of the offset tube Thinning occurs during forward path spinning and thickening occurs during backward path spinning Therefore, for multipath neck spinning processes, forward and backward paths should be applied alternately to avoid excessive thinning or thickening of workpiece