Showing papers on "von Mises yield criterion published in 2016"

Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening

Abstract: This study presents the ordinary state-based peridynamic constitutive relations for plastic deformation based on von Mises yield criteria with isotropic hardening. The peridynamic force density–stretch relations concerning elastic deformation are augmented with increments of force density and stretch for plastic deformation. The expressions for the yield function and the rule of incremental plastic stretch are derived in terms of the horizon, force density, shear modulus, and hardening parameter of the material. The yield surface is constructed based on the relationship between the effective stress and equivalent plastic stretch. The validity of peridynamic predictions is established by considering benchmark solutions concerning a plate under tension, a plate with a hole and a crack also under tension.

Assessment of crack tip plastic zone size and shape and its influence on crack tip shielding

Abstract: This paper presents a novel methodology for the experimental quantification of the crack tip plastic zone during fatigue crack growth. It is based on the application of yielding criteria to estimate the area and shape of the crack tip plastic zone using both the von Mises and Tresca yield criteria. The technique employs strain maps calculated from displacement fields obtained by digital image correlation. Stress maps were subsequently found by applying these yield criteria. Fatigue cracks were grown in compact tension specimens made from commercially pure titanium at R ratios of 0.1 and 0.6, and the ability was explored of three different analytical elastic crack tip displacement models [Westergaard, Williams and Christopher–James–Patterson (CJP)], to predict shape and size of the crack tip plastic zone. This analysis indicated that the CJP model provided the most accurate prediction of the experimentally obtained plastic zone size and shape.

Thermo-Elasto-Plastic Analysis of Thick-Walled Spherical Pressure Vessels Made of Functionally Graded Materials

Abstract: An exact closed-form analytical solution is presented to solve the thermo-elasto-plastic problem of thick-walled spherical vessels made of functionally graded materials (FGMs). Assuming that the inner surface is exposed to a uniform heat flux, and that the outer surface is exposed to an airstream. The heat conduction equation for the one-dimensional problem in spherical coordinates is used to obtain temperature distribution in the sphere. Material properties are graded in the thickness direction according to a power law distribution, whereas the Poisson’s ratio is kept constant. The Poisson’s ratio due to slight variations in engineering materials is assumed constant. The plastic model is based on von Mises yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. For various values of inhomogeneity constant, the so-obtained solution is then used to study the distribution of limit heat flux, displacement and stresses versus the radial direction. Moreover, t...

Three-dimensional evaluation of different prosthesis retention systems using finite element analysis and the Von Mises stress test.

Abstract: Background The aim of this paper is to underline the prosthodontics components features of two different overdenture retention systems on dental implants. The use of titanium, dental implants for replacing missing teeth is today considered to be a predictable procedure giving the patients esthetic and function for long time. Methods Finite element analysis (FEA) and tests based on the Von Mises criterion have been applied in order to evaluate the stress distribution over two different prosthodontics retention systems. Two models with the ball attachment and with the Locator® systems have been created and put on simulated chewing stresses. Results The two systems were subjected to axial and oblique forces and both guaranteed good results over simulated masticatory cycle. However, the Locator system seemed to better respond to the overall load distributions. Conclusions Clinicians should choose the better prosthetic solution for the ridge they want to restore. Both retention systems offer long-term success if applied following the manufacture guide limitations and suggestions.

Phase-field slip-line theory of plasticity

Abstract: A variational approach to determine the deformation of an ideally plastic substance is proposed by solving a sequence of energy minimization problems under proper conditions to account for the irreversible character of plasticity. The flow is driven by the local transformation of elastic strain energy into plastic work on slip surfaces, once that a certain energetic barrier for slip activation has been overcome. The distinction of the elastic strain energy into spherical and deviatoric parts is used to incorporate in the model the idea of von Mises plasticity and isochoric plastic strain. This is a “phase field model” because the matching condition at the slip interfaces is substituted by the evolution of an auxiliary phase field that, similar to a damage field, is unitary on the elastic phase and null on the yielded phase. The slip lines diffuse in bands, whose width depends upon a material length-scale parameter. Numerical experiments on representative problems in plane strain give solutions with noteworthy similarities with the results from classical slip-line field theory, but the proposed model is much richer because, accounting for elastic deformations, it can describe the formation of slip bands at the local level, which can nucleate, propagate, widen and diffuse by varying the boundary conditions. In particular, the solution for a long pipe under internal pressure is very different from the one obtainable from the classical macroscopic theory of plasticity. For this case, the location of the plastic bands may be an insight to explain the premature failures that are sometimes encountered during the manufacturing process. This practical example enhances the importance of this new theory based on the mathematical sciences.

On the existence of a unique class of yield and failure criteria comprising Tresca, von Mises, Drucker–Prager, Mohr–Coulomb, Galileo–Rankine, Matsuoka–Nakai and Lade–Duncan

Abstract: In this paper, it is mathematically demonstrated that classical yield and failure criteria such as Tresca, von Mises, Drucker–Prager, Mohr–Coulomb, Matsuoka–Nakai and Lade–Duncan are all defined by the same equation. This can be seen as one of the three solutions of a cubic equation of the principal stresses and suggests that all such criteria belong to a more general class of non-convex formulations which also comprises a recent generalization of the Galileo–Rankine criterion. The derived equation is always convex and can also provide a smooth approximation of continuity of at least class C 2 of the original Tresca and Mohr–Coulomb criteria. It is therefore free from all the limitations which restrain the use of some of them in numerical analyses. The mathematical structure of the presented equation is based on a separate definition of the meridional and deviatoric sections of the graphical representation of the criteria. This enables the use of an efficient implicit integration algorithm which results in a very short machine runtime even when demanding boundary value problems are analysed.

A Numerical Investigation of the Thermal Stresses of a Planar Solid Oxide Fuel Cell

Abstract: A typical operating temperature of a solid oxide fuel cell (SOFC) is quite high above 750 °C and affects the thermomechanical behavior of the cell. Thermal stresses may cause microstructural instability and sub-critical cracking. Therefore, a joint analysis by the computational fluid dynamics (CFD) and computational structural mechanics based on the finite element method (FEM) was carried out to analyze thermal stresses in a planar SOFC and to predict potential failure locations in the cell. A full numerical model was based on the coupling of thermo-fluid model with the thermo-mechanical model. Based on a temperature distribution from the thermo-fluid model, stress distribution including the von Mises stress, shear stress as well as the operating principal stress were derived in the thermo-mechanical model. The FEM calculations were performed under different working conditions of the planar SOFC. The highest total stress was noticed at the lower operating voltage of 0.3 V, while the lowest total stress was determined at the voltage of 0.7 V. The obtained stress distributions allowed a better understanding of details of internal processes occurring within the SOFC and provided helpful guidance in the optimization of a new SOFC design.

Multiaxial fatigue modeling for Nitinol shape memory alloys under in-phase loading.

Abstract: The realistic loading condition for many components is multiaxial arising from multidirectional loading or geometry complexities. In this study, some multiaxial stress-based classical and critical plane fatigue models are briefly reviewed and their application for martensitic Nitinol under torsion and in-phase axial-torsion loading is evaluated. These models include von Mises equivalent stress, Tresca, Findley, McDiarmid, and a proposed stress-based Fatemi-Socie-type model. As the fatigue cracks appear to be on the maximum shear plane for the martensitic Nitinol, all the models examined here consider the shear stress as the primary damage parameter. Among all the models considered in this study, the proposed Fatemi-Socie-type model provides a better prediction for fatigue lives when compared to torsion and in-phase multiaxial fatigue experimental data from literature. Analyses indicate that critical plane approaches are more appropriate for multiaxial fatigue prediction of Nitinol alloys, at least in martensitic phase. Finally, recommendations are made to calibrate more reliable multiaxial fatigue models for Nitinol.

The self-similarity theory of high pressure torsion.

Abstract: By analyzing the problem of high pressure torsion (HPT) in the rigid plastic formulation, we show that the power hardening law of plastically deformed materials leads to self-similarity of HPT, admitting a simple mathematical description of the process. The analysis shows that the main parameters of HPT are proportional to β q , with β being the angle of the anvil rotation. The meaning of the parameter q is: q = 0 for velocity and strain rate, q = 1 for shear strain and von Mises strain, q = n for stress, pressure and torque (n is the exponent of a power hardening law). We conclude that if the hardening law is a power law in a rotation interval β, self-similar regimes can emerge in HPT if the friction with the lateral wall of the die is not too high. In these intervals a simple mathematical description can be applied based on self-similarity. Outside these ranges, the plasticity problem still has to be solved for each value of β. The results obtained have important practical implications for the proper design and analysis of HPT experiments.

An incremental numerical method for calculation of residual stresses and strains in cold-formed steel members

Abstract: The residual stresses and strains in cold-formed steel members are a result of the manufacturing process. It has been shown that the variation of residual stresses through the thickness of cold-formed steel members is not linear. In this study a numerical algorithm is developed to calculate the through-thickness variation of residual stresses and strains. The algorithm calculates the stresses and strains by viewing the manufacturing process as a combination of elasto-plastic bending and springback in a wide plate under plane strain conditions. In order to calculate the plastic deformations, the Prandtl-Reuss flow rule associated with von Mises yield criterion is used. With regard to satisfying the boundary conditions on the surface, the bisection method is used to find the location of the neutral axis. The results obtained via the proposed algorithm are verified with the available closed formed solutions, finite element analysis results and experimental measurements. A parametric study is performed to evaluate the effect of the coil radius and cross-sectional and material properties on the residual stresses and strains. It is shown that, while in the corner regions the most important parameter is the corner radius, it is the coil radius and yield stress that play a significant role in the variation of residual stresses and strains in the flat regions.

Stress sensitivity analysis and optimization of automobile body frame consisting of rectangular tubes

Abstract: At conceptual design stage, beam element is extensively used to create the frame structure of automobile body, which can not only archive the accurate stiffness but also reduce much computational cost. However, the stress definition of beam element is very complex so that the stress sensitivity and optimization are difficult to analytically derive and numerically program. This paper presents an solution to this problem and an application in the lightweight optimization design of automobile frame. Firstly, maximal Von Mises stress of rectangular tube is calculated by using the superposition of stress, which is together induced by the axial force, bending moments, torsional moment and shear force. Secondly, the sensitivity of Von Mises Stress with respect to size design variables: breadth, height and thickness are derived, respectively. Thirdly, an optimal criterion is constructed by Lagrangian multiplier method to solve the frame optimization with stress constraints. Lastly, numerical example of car frame proves that the proposed method can guarantee the stress of each beam element almost fully reaches at the yielding stress.

Phase field modeling of damage in glassy polymers

Abstract: Failure mechanisms in amorphous polymers are usually separated into two types, shear yielding and crazing due to the differences in the yield surface. Experiments show that the yield surface follows a pressure modified von Mises relation for shear yielding but this relation does not hold during crazing failure. In the past different yield conditions were used to represent each type of failure. Here, we show that the same damage model can be used to study failure under shear yielding and crazing conditions. The simulations show that different yield surfaces are obtained for craze and shear yielding if the microstructure is included explicitly in the simulations. In particular the breakdown of the pressure modified von Mises relation during crazing can be related to the presence of voids and other defects in the sample.