Mises Yield Criterion Research Articles

Size-dependent yield function for single crystals with a consideration of defect effects

In this work, a size-dependent yield function for a single crystal is developed by considering defect effects, including dislocation pile-up, dislocation starvation, and source exhaustion, especially for micro-pillars. It is found that the proposed yield function compares well with the experimental data, and the proposed model is the extension of a single-arm source model to describe the yielding behavior under a more complicated loading case, not only the uniaxial compression test. Our quantitative conclusions suggest that the stacking-fault energy (SFE), the crystallographic orientation, and the slip system are significant factors for the shape of the yield surface: the slip system determines the number of the edges of the yield surface; the crystallographic orientation controls the angles between the adjacent edges but does not change the number of the edges; the low SFE can make sharp corners rounded and contract the shape of the yield surface, or even curve the edge of the yield surface. Moreover, we investigate the explicit relationship among the stacking-fault energy, the dislocation pile-up effect inside the sample, and the shape of the yield surface: materials with a low stacking-fault energy exhibit pronounced dislocation pile-up effects, and their yield surfaces tend to display rounded vertices, corresponding to the v. Mises yield criterion for the single-crystal sample with a {1 1 1} slip system for example; those with a high stacking-fault energy show typical Tresca criterion-type yield surfaces displaying sharp vertices for the single-crystal sample with a {1 1 1} slip system for example. We also show that this yield function can describe the size-dependent yield surface by considering the stochastic length of the dislocation source and the dislocation pile-up length in single-crystalline micro-pillars.

Modelling the cyclic elasto-viscoplastic behaviour of polymers

The mechanical behaviour of polymeric materials presents some peculiarities, especially regarding the evolution of their hardening under stresses above the proportional limit. For many types of polymers (Epoxy, Polyamides, Polyvinylidene, etc.) the elastic properties are not rate-dependent, and the behaviour is elasto-viscoplastic. Also, in the case of load-unload tensile tests, preliminary studies show that the kinematic hardening of this kind of material can be much more significant than the isotropic hardening, and a negative plastic strain rate may occur even with a positive stress. Thereby, nonlinear phenomena may occur during tractive load-unload cyclic tests executed above the proportionality limit, leading to dissipation of mechanical energy. The present paper aims at the development of a general elasto-viscoplastic model for polymers, able to describe the progressive accumulation of plastic deformation for an arbitrary loading history. This model considers dissipative phenomena by the coupled effect of the internal variables with nonlinear hardening equations. Since a volume variation can be observed during plastic deformation, a modified von Mises yield criterion that accounts for the influence of the hydrostatic pressure is proposed. All parameters arisen from theory can be identified experimentally from tensile tests with different strain rates and load-unload tensile tests. The model adequacy was tested for particular types of Polyvinylidene fluoride (PVDF) and of Polyamide (PA 12), which are materials commonly used as an internal pressure sheath in offshore flexible pipes in the Brazilian pre-salt basin. One-dimensional numerical simulations were performed aiming to compare the numerical results with the experimental ones, showing a very good agreement.

Prediction of insertion torque and stiffness of a dental implant in bovine trabecular bone using explicit micro-finite element analysis

The assessment of dental implant performance is dominated by the concept of mechanical stability. Primary stability is defined as the capacity of a bone-implant structure to bear loads without occurrence of excessive damage and loosening. In order to achieve the highest primary stability, dental implants are inserted into bone using a press-fit procedure. Pre- and postoperative evaluation of primary stability using implantation torque and resonance frequency analysis are valid approaches but do not allow the systematic comparison of different protocols in similar situations. The aim of this research is to develop and validate an explicit, micro-finite element (μFE) methodology to study the effect of different amounts of initial press-fit on implantation torque and initial stiffness of a dental implant. Ten bovine trabecular bone samples were prepared that cover a wide range of bone volume fraction. A dental implant was inserted using two implantation protocols named soft (small initial drilled hole) and dense (increased initial drilled hole). The implantation torque was measured and the stiffness was calculated using an infinitesimal off-axis loading. Finite element simulations of the implant insertion and subsequent loading were performed on micro-computed tomography (μCT) reconstructions of the samples using an explicit solver. Bone was defined as an elasto-plastic material with von Mises yield criteria and hardening. Element deletion was triggered by a threshold in cumulated plastic strains. A sensitivity analysis was performed on friction, hardening and fracture strain to provide a better insight into the effects of these parameters on the results. The implantation torque required for the soft protocol was higher compared to the dense approach in both experiment and simulation due to the higher amount of bone compaction in the first approach. Interestingly, stiffness did not show a significant dependency on the drilling protocol in both experiment and simulation. In conclusion, the explicit microFE methodology developed in this study was able to capture the outcome of two drilling protocols in terms of torque and stiffness and represents a powerful tool to explore the effect of different parameters on primary stability of dental implants.

Efficiency of the Tresca yield criterion in modeling of annular plates with rigid constraint

• Tresca and Mises yield criteria are compared based on the mathematical modeling . • For loads up to critical (low-to-medium), the Tresca yield criterion is indicated. • For strain and failure analyses, the Mises yield criterion is preferred. • Decohesive carrying capacity does not depend neither on geometry nor on Poisson ratio . • Results can be used in commercial numerical codes for various engineering applications. Correct prediction of the load carrying capacity and initiation of failure of compound annular plates (with or without inner solid disk) embedded into a rigid container are crucial for achieving their optimal structural design and reliable service conditions. In this paper an analytical study devoted to mathematically and physically rigorous stress/strain analysis of such structures has been performed. The decohesive carrying capacity criterion based on the radial strains is applied and discussed. The material of the plate is considered to be elastic/perfectly-plastic, and the inner insert is modeled as purely elastic. Two principle engineering criteria for material yielding, namely, the Tresca and the Mises, are employed, discussed and compared. The range of validity of each criterion is analyzed, and the choice of the suitable criterion for particular engineering applications is suggested. The advantages of the Tresca yield criterion both in mathematical modeling and engineering design are outlined.

Study Explores Mechanisms of Surface Damage on Coiled Tubing

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 194254, “Study on Mechanism of Coiled Tubing Surface Damage in Injector Heads,” by Zhihong Zhou, Guofeng Zhang, Fayong Yuan, Tang Wang, Yunwei Gao, and Weijia Wang, Jianghan Shale Gas Development Technical Service Company, prepared for the 2019 SPE/ICoTA Well Intervention Conference and Exhibition, The Woodlands, Texas, USA, 26–27 March. The paper has not been peer reviewed. Although several kinds of mechanical damage cause coiled tubing (CT) failure, longitudinal plowing marks (LPMs) account for a large portion of such damage. Understanding the mechanisms of LPM damage on CT surfaces will help reduce the occurrence of this type of damage. In this paper, the authors study the stress status of CT string held by gripper blocks, the axial force distribution of gripper blocks, and the longitudinal resonance of CT strings in vertical wells. Introduction The overwhelming majority (greater than 80%) of CT failures have been classified into four categories: corrosion, mechanical damage, string-manufacturing issues, and human error. Of these, failures caused by mechanical damage constitute almost 30% of all CT failures. Further study of these types of mechanical damage reached the following two important conclusions: LPMs, which are injector-related, account for 46% of mechanical damage observed on CT strings from 2006 to 2017. Recent periods that have seen dramatic increases in mechanical damage coincide with plug milling and higher-grade-CT operations. The authors propose that the pressure in the CT string plays a role in mechanical damage. Contact Status Between CT and Gripper Blocks The gripper blocks carried by chains are used to hold CT strings in place. The gripper blocks are divided into single-pitch and two-pitch categories. The engagements between the CT string and the gripper blocks are sometimes suboptimal. The contact area between the gripper and CT string is only at the end-point of the arc, and the contact stress is much higher there than at the point at which the gripper blocks grip the original CT string. According to the von Mises yield criterion, if the von Mises stress is larger than the yield stress at any point, the material at that point will yield and plastic strain will be produced. Distribution of Gripper-Block Lifting Forces in the Injector Commonly, several pairs of gripper blocks engage the CT string to provide the friction forces needed for deployment and retrieval of the tubing into and out of the wellbore. How the axial loads of these pairs of gripper blocks are distributed is essential to safe operation and avoidance of CT damage. To obtain the axial load distribution of all pairs of gripper blocks, a mechanical model is created by the authors and discussed in the complete paper.

Burst pressure models for thin-walled pipe elbows

This paper is focused on the development of burst pressure models for thin-walled pipe elbows subjected to internal pressure. Three analytical burst pressure models are derived based on the Tresca, Mises, and ASSY yield criteria, respectively. A modified Goodall model is further proposed with markedly improved accuracy in burst pressure predictions compared with the original Goodall model. The proposed models are validated using full-scale burst tests of pipe elbows reported in the literature and parametric finite element analyses carried out in the present study. The accuracy of the proposed models is also compared with that of analytical burst pressure models reported in the literature.

Two-Dimensional Plastic Flow of a Flange when Deep Drawing a Thin-Walled Polygonal Prism

Two-dimensional plastic flow of a flange when deep drawing a thin-walled polygonal prism with a flat bottom of round blank provided with Mises yield criterion based on the theory of plane stress condition according to Sokolovskii is simulated. The slip lines, the stress condition, the hodograph of displacement velocities, and the dissipative function of plastic flow are calculated. The limit parameters of deep drawing are defined by the maximum tensile stress at the mold contour and by zones with negative dissipative function, which depends on the radius of rounding of mold angles and the prism height.

СТЕКЛОФИБРОБЕТОН В ТОНКОСТЕННЫХ КОНСТРУКЦИЯХ

Fibrous composites are progressive materials for buildings and structures. Structures based on them are characterized by high technical and economic characteristics. Glass fiber concrete is effective for thin-walled structures. Various principles of structural mechanics applied to fiber composites are pro-posed for solving design problems. The optimal configuration of the covering is determined by the sta-tionarity of its potential energy for given values of the calculated resistances of the material compo-nents. This formulation of the problem leads to a global minimum of the covering volume. In particu-lar, an axisymmetrically loaded spherical cover is considered; the optimal thickness is determined from the condition of equal resistance by the von Mises yield criterion. Types of elements for precast glass-fiber concrete of various spans are recommended. In addition, the shallow tunnels are consid-ered; they are a prevalent object of transport communications. The rationality of using the thin-walled spatial systems consisting of rectangular plates is established. The isoperimetric problem is solved for a given volume of material based on the generalized Lagrangian principles. The thickness of the rec-tangular plates of the spatial system of the tunnel is taken as a variable parameter.

A peridynamic plastic model based on von Mises criteria with isotropic, kinematic and mixed hardenings under cyclic loading

In this study, an elastoplastic model based on ordinary state-based peridynamic theory is presented. The von Mises yield criteria is used to describe plastic yielding and the equivalent plastic stretch is utilized as internal variable for the general form of isotropic hardening, the modified form of kinematic hardening and the mixed of isotropic and kinematic hardening. Like classical approach to plasticity, a plastic flow rule is proposed based on the yield function. The proposed plastic model is described in the thermodynamic framework and it is shown that the proposed plastic flow and hardening of the peridynamic model are satisfied the requirements of the second law of thermodynamics. The proposed plastic model is rate-independent and the quasi-static analysis is considered. A numerical approach is proposed for the elastoplastic model and Newton Raphson algorithm is used to solve the nonlinear peridynamic equations. The numerical validation of proposed peridynamic models are done by comparing the results of 2-D peridynamic models under cyclic loading with the results of finite element methods based on the classical local continuum mechanic assumptions. The numerical results show that the proposed PD elastoplastic model can predict plastic yielding and linear/nonlinear hardening of materials beyond initial yield stress accurately. Moreover, it is observed that the presented method it is capable of modeling the kinematic hardening and Bauschinger effect in cyclic loading too.

Finite element modelling of biologic system in orthopedic trauma

Surgical treatment of the proximal femur fractures is a challenge due to the lack of a unified treatment strategy. Among these, of particular importance is the analysis of the processes occurring in bone tissue during the healing of fractures under dynamic conditions, especially the analysis of mechanical stresses. The finite element method is an effective method of mathematical modelling of complex objects and a description of the stress-strain states of these objects. With the aim of improving the results of fracture treatment of the proximal femur and pelvic bones, a mathematical simulation was performed using the finite element method on the intertrochanteric fracture of the femur fixed by a dynamic hip screw and a pelvic fracture fixed by submersible osteosynthesis under various conditions. The calculation parameters are based on the literature data and the optimal accuracy of the ratio specified and the calculation time of the "bone–implant" software system. The models were constructed by taking into account the various properties of cortical and spongy bone as well as the implant. A virtual weight of 80 kg was applied to the models. The estimation of the displacement of the bone–implant system was done along with the prediction of stresses according to the von Mises yield criterion. Thus, the results of mathematical modelling with the use of finite element method allows prediction of the movement of bone fragments in the broken skeleton segment and to choose the correct method of osteosynthesis of the fragments and to evaluate its consequences. The application of methods of mathematical modelling expands the possibilities of scientific and personified approach to surgical treatment of diseases of the musculoskeletal system.

Influence of Porosity on the Mechanical Behavior during Uniaxial Compressive Testing on Voronoi-Based Open-Cell Aluminium Foam.

We have studied an application of the Voronoi tessellation method in the modeling of open-cell aluminium foam under uniaxial compressive loading. The Voronoi code was merged with computer-aided design (CAD) for converting the polyhedral model into an irregular open-cell cellular structure to create porous samples for compression testing simulations. Numerical simulations of the uniaxial compression uniformly over the upper surface of the sample in the z-axis direction at a constant 20 N load was realised. Samples with three different porosities (30%, 60% and 80%) were studied. A nonlinear elasto-plastic material model with perfect plasticity, without hardening, based on the von Mises yield criterion was applied below 10% strain. Corresponding stress–strain curves were observed and the influence of porosity on deformation mechanism was discussed. Samples with higher porosity exhibited significantly higher normal stress under the same load, and increased stress plateaus. An increase of porosity produced an increase of both compressive and tensile stresses and struts exhibited complex stress fields. Voronoi-based modeling was in accordance with experimental results in the literature in the case of the quasi-static condition and linear elastic region (below 1% strain). Further study is necessary to enable the simulation of real dynamic behaviour under all deformation regimes by using the Voronoi tessellation method.

A finite–strain elastoplasticity material model for ETFE membrane structures

This work presents a numerical model for the simulation of the behavior of membrane structures fabricated using ethylene tetrafluoroethylene (ETFE) materials. The elastoplastic material model with von Mises yield criteria is considered in the numerical analysis. Small strain and large strain formulation were adopted for comparison. The model simulates material tests, uniaxial and biaxial, and a burst test, for which experimental measurements are available. The use of von Mises yield criteria is suggested for ETFE foils. The results obtained with the numerical analysis with large strains are in accordance with the experimental results. On the other hand, the results of the numerical analysis with small strains are valid only in the first few steps of the analysis. These results reinforce the importance of considering a material model with large strains to model this type of material.

Characterization of adhesive yield criteria usingmixed-mode loading

While structural adhesives are used widely, relatively little is known regarding their plastic behavior. Few studies exist, for instance, to experimentally validate yield criteria for adhesives. The following considered adhesive joints under biaxial stress using an Arcan fixture. Adhesive strain was measured from the relative displacement of the adherends using digital image correlation. Two adhesive systems showed better correlation with a von Mises yield criterion in comparison to the commonly used Drucker-Prager criterion. The results were applied to a single lap shear joint, with mixed mode stress in the gauge section, which again showed better agreement with von Mises. The Drucker-Prager criterion, for instance, overestimated the yield stress by up to 11% while von Mises was within 2%.

A numerical elastic–plastic contact model for a half-space with inhomogeneous inclusions and cracks

The elastic–plastic contact problem plays an important role in predicting the mechanical properties of materials. In this paper, a semi-analytic solution is developed to investigate the plastic behaviors of a half-space with inhomogeneous inclusions and cracks under contact loading. In this solution, the plastic zones are determined based on the stress field equations and the von Mises yield criterion. The contact area and surface pressure distribution are obtained by solving a set of governing equations via a modified conjugate gradient method. The inhomogeneous inclusions are modeled as homogeneous inclusions with the initial eigenstrains plus unknown equivalent eigenstrains according to the Eshelby’s equivalent inclusion method. The cracks are treated as a collection of distributions of unknown dislocation densities according to the distributed dislocation technique. The case studies of a cylinder loaded against a half-space with inhomogeneous inclusions and vertical or horizontal cracks are conducted to explore the effects of the Young’s moduli and positions of the inhomogeneous inclusions on the plastic behavior of materials.

Confinement effectiveness of circular concrete-filled steel tubular columns under axial compression

In this paper, a large database of 491 test results of circular concrete-filled steel tube (CFT) columns under axial compression was collected from the available literature. The collected results were employed to investigate the effects of loading conditions, diameter-to-thickness ratio, concrete type and compressive strength on the load-carrying capacity of CFT columns, from which models for the hoop stress of steel tubes are obtained through nonlinear regression analyses. Based on the von Mises yield criterion together with the proposed hoop stress models, a model for predicting the load-carrying capacity of CFT columns was developed. The performances of the proposed model and the existing models were evaluated using the database. Due to the rationality of the model development process, the proposed model offers a more reasonable and accurate prediction of load-carrying capacity for CFT columns under various loading conditions.

An explicit micro-FE approach to investigate the post-yield behaviour of trabecular bone under large deformations.

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.

Distributed plasticity model for analysis of steel structures subjected to fire using the direct stiffness method

This article develops a temperature-dependent distributed plasticity model in a direct stiffness method (DSM) based formulation for coupled nonlinear thermo-mechanical analysis of steel space frames. The developed framework considers geometric and material nonlinearities, and performs coupled thermo-mechanical analysis by a two-level spatial discretization strategy. An isotropic hardening plasticity in combination with the von Mises yield criterion is considered, where the temperature-dependent yield function is derived from the stress-strain relations of Eurocode 3. The effects permanent plastic strains, large deformations and temperature-dependent material properties are directly incorporated in to the force deformation relations derived in a DSM based setting. Such a DSM based framework in conjunction with the distributed plasticity model facilitates higher computational efficiency. To ensure full coupling between mechanical and thermal solvers, thermodynamically consistent plastic heating term is added to the energy balance of the system. Also, connection flexibility is accounted for by developing a zero-length spring element integrated with 1-D beam-column elements. Five numerical examples are presented to demonstrate the efficacy of the developed framework. Within the numerical investigation, the importance of plastic heating coupling in the context of macro modelling based structural fire analysis of steel structures is quantified and the results indicate that such a coupling can be ignored in such macro scale structural fire computations.

Nanocrystallization in single-crystal copper under laser shock compression: A molecular dynamics study

Molecular dynamics simulations are performed to investigate nanocrystallization of <100>-oriented monocrystal copper subjected to ultrafast laser shock compression. The differences between laser shock compression and direct mechanical shock compression are first studied. To reveal the intrinsic mechanism of nanocrystallization, the evolution of dislocations and the formation of sub-grain boundaries are presented and analyzed in detail. The nucleation of dislocations is analyzed using Schmid's law and the von Mises yield criterion. Dislocation evolution and the corresponding reactions are presented. To better understand the evolution of dislocations, typical thermophysical quantities, including stress and strain, are discussed in detail. The formation of dislocation cells, walls and entanglements due to interactions between dislocations is investigated, and the mechanism of the interactions is analyzed.

The yield normal stress

Normal stresses in complex fluids lead to new flow phenomena because they can be comparable to, or even larger than, the shear stress. In addition, they are of paramount importance for formulating and testing constitutive equations for predicting nonviscometric flow behavior. Very little attention has thus far been paid to the normal stresses of yield stress fluids, which are difficult to measure. We report the first systematic study of the first and second normal stress differences in both continuous and slow oscillatory shear of three model nonthixotropic yield stress fluids, with N1 > 0 and N2 < 0. We show that both normal stress differences are quadratic functions of the shear stress both above and below the shear yield stress, leading to the existence of a yield normal stress. However, the contribution of the normal stresses to the von Mises yield criterion for these materials is small.

A 3D full layer-wise method for yield achievement in Functionally Graded Sandwich Plates with general boundary conditions

The onset of yielding in Functionally Graded Sandwich Plates (FGSP) with ceramic core and Functionally Graded (FG) face sheets is presented in this paper. Full layer-wise theory which has been proved to be accurate and computationally efficient is developed for static analysis of these plates. The volume fraction of the ceramic phase is assumed to vary via a power-law function in the thickness direction of FG face sheets. TTO model which indicates the initials of the names of the authors who firstly introduced it as well as Rule of Mixture (ROM) are employed to determine the material properties variation through the FGSPs. The results associated with central deflection, and stress distribution through these structures were found to be significantly influenced by the utilized material models. After obtaining the stress fields, Von Mises yield criterion is implemented to find the first node(s) at which the yielding of FGSPs initiates. According to the final results, depending on the type of boundary conditions and core to face sheet thickness ratio, the yielding commencement could occur at the enriched metal or enriched ceramic surfaces. Power-law exponent however found to have no influence on the area at which yielding initiation occurs. Nevertheless, decreasing this parameter results in FGSPs with higher strength and postpones the yielding initiation of these structures. A comparison study is also presented which demonstrates how FGSPs are capable of undergoing bending loads, before yielding, up to twice as large as conventional Functionally Graded Plates (FGPs) while having the same weight and material constituents.