Tresca Yield Criterion Research Articles

Theoretical and experimental study on axial compression concrete-filled tubes with different confinements

In order to investigate the mechanical properties of concrete-filled tube columns with a wider range of confinement factors under axial compression, 14 specimens, including plain concrete columns and concrete-filled PVC, plexiglass and steel tube columns are subjected to axial compression. The axial load-displacement curves and damage process of the columns are analyzed, and the results indicate that the ultimate axial compressive strength of the concrete-filled tubes increases as the confinement factor ascends. The stiffness and deformation capacity of columns with lower hoop restraint increase as the confinement factor ascends. The axial load-displacement curve of concrete-filled steel tube (CFST) columns with higher confinement factors can be divided into five stages, and the secondary strengthening effect of CFST columns is discovered and explained. The nominal Poisson's ratio of the steel tube under triaxial stress is derived by the elastic property and the geometric parameters of the concrete and tube. The local initial yield of the steel tube is discovered based on the plastic yield theory, which precedes the entire yield of the CFST columns. Theoretical formulas of the ultimate bearing capacity for the CFST columns based on the four yield criteria are presented and the present results are compared with the values calculated by the typical codes and the experimental results. The value calculated by Tresca yield criterion is more conservative and safer, so it is an appropriate reference for the lower limit design of axial compressive capacity of CFST columns.

Nonlinear deflection analysis of helical spring in elastic–perfect plastic material: Application to the plastic extension of piano wire spring

A mechanics-of-materials theory of the nonlinear deflection of helical spring within and beyond the elasticity limit was developed. The theory examined the nonlinearity due to the combined stresses of the torsion and bending of spring element by assuming the elastic–perfect plastic material obeying Tresca yield criterion. Free rotation of spring around the spring axis was taken into account. It was shown in experiment that the stress–strain curve of a piano wire was close to elastic–perfect plastic one. The outcome of the theory was compared with the experimental result of nonlinear load–deflection curves in plastically extended helical spring made of the piano wire.

Ultimate bearing capacity of strip and circular foundations using power type yield criterion using the method of stress characteristics

For determining the bearing capacity of foundations, the existing investigations have been mainly performed by using a linear yield criterion in shear stress (τ)-normal stress (σn) domain, for instance, the Mohr-Coulomb (MC) and Tresca yield criteria. However, the yield criteria for most granular soils are generally nonlinear with continuously increasing friction angle at decreasing stress level. In the present research, the method of stress characteristics has been employed to compute the ultimate bearing capacity of circular and strip foundations considering a power type (PT) nonlinear yield criterion which depends on three material parameters rather than two in the MC yield criterion. Rigorous solutions have been generated for both rough and smooth footing bases and the results have been expressed in terms of the variation of the bearing capacity factor Nσ with the changes in different material parameters and the overburden pressure. The slip line patterns and the variation of the vertical normal pressure below the footing base have also been examined. Further, the effectiveness of the PT nonlinear yield criterion in determining the bearing capacity of foundations has been discussed. The solutions obtained have been found to compare well with different computational and experimental results reported in literature.

Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels

An analytical solution is presented to analyze the thermoelastoplastic response of a rotating thick-walled cylindrical pressure vessel made of functionally graded material (FGM). The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening material behaviour. The uncoupled theory of thermoelasticity is used, and the plane strain condition is assumed. The material properties except for Poisson's ratio, are assumed to vary nonlinearly in the radial direction. Elastic, partially plastic, fully plastic, and residual stress states are investigated. The heat conduction equation for the one-dimensional problem in cylindrical coordinates is used to obtain temperature distribution in the vessel. It is assumed that‏ the inner surface is exposed to an airstream and that the outer surface is exposed to a uniform heat flux. Tresca's yield criterion and its associated flow rule are used to formulate six different plastic regions for a linearly hardening‏ condition. All these stages are studied in detail. It is shown that the thermoelastoplastic stress response of a rotating FGM pressure vessel is affected significantly by the nonhomogeneity of the material and temperature gradient. The results are validated with those of other researchers for appropriate values of the system parameters and excellent agreement is observed.

Design of a disk-mandrel assembly for achieving rotational autofrettage in the disk

Rotational autofrettage is a recently proposed method to induce beneficial residual stresses in axisymmetric hollow cylindrical bodies. The feasibility of the process has been studied for both disks and cylinders used in many engineering applications. The earlier analyses of rotational autofrettage of disks are based on certain assumptions. One of the crucial assumptions is the free rotation of the disk. However, the free rotation of the disk is practically difficult. In practice, it is feasible to rotate the disk by shrink-fitting it over a solid cylindrical mandrel. In view of this, a design of a disk-mandrel assembly for achieving rotational autofrettage in disks is proposed in this article. The main aim of the design is to obtain appropriate values of the disk-mandrel interference and the rotational speed of the assembly to prevent the loss of contact of the disk with the mandrel during rotation. The critical speeds corresponding to the yield onset, contact separation and the full plastic deformation of the disk are obtained as a function of shrink interference. The safe operating design parameters can be decided by plotting the critical speeds with varying interference values. A detailed stress analysis during elastic-plastic loading of the assembly followed by the analysis of residual stresses in the assembly after unloading is presented. The analysis is based on the plane stress assumption, Tresca yield criterion and elastic unloading. The analysis is validated with a finite element method model in ABAQUS. The proposed design is illustrated through the numerical example of an ASTM A723 disk-mandrel assembly to achieve rotational autofrettage in the disk. With a small overstrain level of 17.5% in the disk, a large magnitude of compressive residual stress, viz., 0.52 times the yield stress, is induced.

Analytical method for determining the elastoplastic interface of a circular hole subjected to biaxial tension-compression loads

Based on the Tresca yield criterion, an analytical method is proposed to determine the elastoplastic interface around a circular hole in an infinite plate subjected to biaxial tension-compression loads at infinity. Comparing with the plastic region formed under the action of biaxial tension-tension or biaxial compression- compression loads, the characteristic of the plastic regions is that they cannot completely surround the hole and there may be two or four nonintersecting plastic regions around the hole. In both cases, the conformal mapping is employed to map the elastic region in the physical plane onto the outer region of a unit circle in the image plane, which transforms this kind of plane elastoplastic problem into a problem of mapping. According to the stress continuity conditions on the elastoplastic interface and the stress boundary conditions on the elastic part of the circular hole, a set of nonlinear equations containing the mapping function coefficients is established. The problem can be further transformed into an optimization problem determined by the differential-evolution algorithm. The correctness of the presented method is verified by numerical method. The influence of loads and material constant on the size and shape of the plastic regions is discussed in detail.

Analysis of Deformation Characteristics of Fully Grouted Rock Bolts Under Pull-and-Shear Loading

A new analytical approach able to predict the mechanical behavior of fully grouted rock bolts subjected to pull-and-shear load is been proposed. The elastic theory of a semi-infinite length beam and approximate differential equation of the deflection curve (elastic and elastoplastic) are employed to analyze the lateral behavior of a bolt under surrounding rock pressures. Bolt axial behavior is based on a realistic tri-linear bond-slip model with residual bond strength at the grout–bolt interface. According to the Tresca yield criterion, important failure parameters such as shear displacement, tangent direction, tensile displacement, and tensile force can be determined via the analytical approach while the shear force and other basic parameters are provided. Results of the proposed analytical approach for 0°, 20°, 40°, 60°, and 90° displacing angles correlate well with experimental test results. Parametric analysis of both the rock and bolt mechanical behavior are also carried out using this new analytical approach.

Mathematical modeling of rotating disk states

We consider the problem of a rapidly rotating disk in the elastic-plastic state. The piecewise linear plasticity condition in general form is chosen. It is believed that all plastic curves have the common point of intersection which corresponds to uniaxial tension. For external parameters, we obtain the conditions that determine the probability of inception of plastic zones. It is shown that plastic zones could incept in the center of the disk and/or on the boundary of it. The problem in the plastic zone is statically determinate. The case when the plastic zone occupies some central part (core) of the disk, where one regime of plastic condition is fulfilled, is considered. In order to estimate the stress state inside the elastic zone of the disk, equivalent stress which is equal to the chosen plasticity function is defined. In order to define the relationship between plastic deformations and stresses, the piecewise linear plastic potential being equal to the plasticity function is chosen. The plastic incompressible body is considered. The associated flow rule can be integrated so that the problem of getting displacements turns into quasistatic one. The problem of determining displacements in the plastic region leads to a first-order differential equation with respect to the radial component of the displacement vector. Therefore the continuity condition for displacements at the elastic-plastic boundary and the assumption that the displacements in the center of the disk are equal to zero leads to an overdetermined problem. So, only the continuity condition for displacements at the elasto-plastic boundary is accepted. It is assumed that plastic deformations at the elastic-plastic boundary are equal to zero. It is shown that displacements at the center of the disk are equal to zero automatically for all piecewise linear conditions of plasticity apart from the Tresca yield criterion. For the Schmidt–Ishlinskii yield criterion, all deformations at the center of the disk attain finite values. Meanwhile, for other piecewise linear conditions, plastic deformations at the center of the disk attain infinitely large values. This explains the discontinuity of displacements at the center of the disk for the Tresca yield criterion. The calculation results are presented as graphs of stresses, displacements, and deformations.

Mechanical behavior of a titanium alloy scaffold mimicking trabecular structure

BackgroundAdditively manufactured porous metallic structures have recently received great attention for bone implant applications. The morphological characteristics and mechanical behavior of 3D printed titanium alloy trabecular structure will affect the effects of artificial prosthesis replacement. However, the mechanical behavior of titanium alloy trabecular structure at present clinical usage still is lack of in-depth study from design to manufacture as well as from structure to mechanical function.MethodsA unit cell of titanium alloy was designed to mimick trabecular structure. The controlled microarchitecture refers to a repeating array of unit-cells, composed of titanium alloy, which make up the scaffold structure. Five kinds of unit cell mimicking trabecular structure with different pore sizes and porosity were obtained by modifying the strut sizes of the cell and scaling the cell as a whole. The titanium alloy trabecular structure was fabricated by 3D printing based on Electron Beam Melting (EBM). The paper characterized the difference between the designs and fabrication of trabecular structures, as well as mechanical properties and the progressive collapse behavior and failure mechanism of the scaffold.ResultsThe actual porosities of the EBM-produced bone trabeculae are lower than the designed, and the load capacity of a bearing is related to the porosity of the structure. The larger the porosity of the structure, the smaller the stiffness and the worse the load capacity is. The fracture interface of the trabecular structure under compression is at an angle of 45o with respect to the compressive axis direction, which conforms to Tresca yield criterion. The trabeculae-mimicked unit cell is anisotropy. Under quasi-static loading, loading speed has no effect on mechanical performance of bone trabecular specimens. There is no difference of the mechanical performance at various orientations and sites in metallic workspace. The elastic modulus of the scaffold decreases by 96%–93% and strength reduction 96%–91%, compared with titanium alloy dense metals structure. The apparent elastic modulus of the unit-cell-repeated scaffold is 0.39–0.618 GPa, which is close to that of natural bone and stress shielding can be reduced.ConclusionWe have systematically studied the structural design, fabrication and mechanical behavior of a 3D printed titanium alloy scaffold mimicking trabecula bone. This study will be benefit of the application of prostheses with proper structures and functions.

Analytical modelling of a tunnel accounting for elastoplastic unloading and reloading with reverse yielding and plastic flow

Abstract Applying a high internal pressure inside an underground cavity can increase the extent or intensity of the Excavation Damaged Zone (EDZ). This issue arises in many situations: the geological disposal of radioactive waste where different swelling materials can be encountered (engineered barriers, …), in-situ pressuremeter tests, gas storage projects, etc. This paper presents an analytical approach of the elastoplastic behaviour of a tunnel subjected to a simplified 2-stage loading under the assumption of small strains. In stage-1 (unloading), its excavation is represented in a classical way by cancelling the fictitious internal pressure initially applied to the wall of the future tunnel. In stage-2 (reloading), the internal pressure is increased up to relatively high values. The mechanical behaviour considered is elastic-perfectly-plastic, obeying Tresca's yield criterion and its associated flow rule. In both stages, the elastic phase preceding yielding is considered. During stage-2, the reversed direction of the stress path compared to stage-1 induces reverse yielding, reversing the direction of plastic strain rates. A fully analytical solution is presented, where all field quantities can be assessed by entirely explicit equations. Notably, the critical values of the internal pressure for which yielding resumes, then further extends, are presented.

Study on the Expansion Force of TWIP Steel Expandable Tubular in Solid Expandable Tubular Technology

Abstract This paper focuses on the expansion process of twinning-induced plasticity (TWIP) steel tubular undergoing the large circumferential plastic deformation in expandable tubular technology. The expansion process was performed by propagating a mandrel through the tubular mechanically. This paper aimed at developing the mathematical models to predict the expansion force required for the radial expansion of the TWIP steel tubular using the rigid-perfectly plastic model and the linear hardening rigid plastic model, respectively. The volume incompressible condition together with the Tresca yield criterion was used to describe the plastic behavior of the tubular material in the expansion process. Besides, the finite element analysis of the expansion process was developed using the commercial software abaqus to validate the theoretical results and determine the scope of application of the derived expansion force formula. Further to this, the effect of the process parameters, such as the expansion ratio, friction coefficient and the cone angle, on the expansion force was investigated. It was found that the expansion force difference of two models have similar variation trend. The accuracy and applicability of the expansion force formula using the linear hardening rigid plastic model improve as the expansion ratio increases and the expansion cone angle decreases.

Mathematical modeling of creep and viscoplastic flow of a cylindrical layer material

Within the framework of a mathematical model of large elastoplastic deformations, taking into account viscous properties of materials, a boundary value problem of creep and viscoplastic flow of a material in the gap between two rigid coaxial cylindrical surfaces under rectilinear motion of the inner surface is considered. Irreversible deformations accumulate from the beginning of the deformation process and are initially associated with the creep process of the material, which is described using the Norton creep power law. With a subsequent increase in the speed of movement of the inner cylinder at some time point, the stress state will reach the yield surface and a viscoplastic flow will begin in the material. As a plastic potential, we use the Tresca yield criterion, generalized in the case of taking into account the viscous properties of the material. The viscoelastic deformation, the emergence and development of the viscoplastic flow under uniformly accelerated motion of the inner surface, the flow under constant speed, and the flow inhibition under equal slow motion of the surface to a full stop are considered. Stresses, reversible and irreversible deformations, displacements are calculated, stress relaxation after the complete stop of the cylinder is investigated.

Position design of the casing shoe of an abandoned horizontal salt cavern to be used for gas storage

ABSTRACT China’s salt mines have a typical bedded structure, composed of many interlayers and salt rock layers. If the conventional vertical single cavern leaching technology is used, the shape control of the caverns is difficult. Horizontal salt cavern gas storage (HSCGS) can be built in thicker pure salt sections. The internal pressure, casing shoe position and the range of plastic, dilatation, and failure zones are significant factors to be considered in the design. The yield behavior of rock salt can be described by the Tresca yield criterion. The second invariant of the plastic strain was used as the hardening parameter to analyze the hardening behavior. The dilatancy boundary is defined to determine the dilatation zone. Based on the Mohr-Coulomb criterion, a failure criterion of rock salt is established. The constitutive model was modified and the state parameters were self-defined in FLAC3D. Thus a Yield-Dilatancy-Failure (YDF) model is established. Based on the YDF model, the rock surrounding a HSCGS is divided into four zones: elastic, plastic, dilatation and failure zone. The casing shoe position should be outside the dilatation zones. When the dilatation zone of the HSCGS in the middle part is prevented from developing. The minimum pressure (9 MPa) is determined that prevents the formation of a dilatation zone around the middle part of the HSCGS. The research results can provide a reference for determining pressure and casing shoe position of an HSCGS.

Quasi-static analysis and multi-objective optimization for tape spring hinge

Mechanical attributes of interest are always mutually exclusive in the design process of tape spring hinge. Here we present a complete optimization framework consisting of computational mechanics, optimization design, engineering application, and experimental research to compromise mechanical attributes such that an optimal solution set can be obtained to provide design strategies for engineering practices. Tape spring hinge in folding and unfolding processes with large non-linearity is firstly simulated using quasi-static analysis technique. During the quasi-static process, the ratio of kinetic energy to strain energy is observed to determine mass scaling parameters that measure the precision of analysis. Based on the parameters analyzed, moment-rotation responses of tape spring hinge in quasi-static folding and unfolding processes are investigated and experimentally verified. Yield theory derived from the combination of thin shell theory and Tresca yield criterion is introduced to control the yield of the hinge during folding and deploying processes. In addition, tape spring hinge is released transiently when in spatial conditions; thus the fundamental frequency is calculated and selected herein to be a measurement of stiffness that is maximized to avoid the vibration. Then a multi-objective optimization model is established using the derived yield theory control equation and critical moment as optimization constraints, with the fundamental frequency and strain energy as objectives. The non-dominated sorting genetic algorithm is used to solve the optimization model, and then feasible solution distribution and Pareto frontier are obtained. These results are compared and discussed with two additional single-objective optimizations. Ultimately we achieve the optimal design for tape spring hinge, which is verified well with numerical simulation.

Determination of bearing capacity factor Nc for circular piles in clays by using lower bound finite element analysis

ABSTRACT The aim of this present paper is to provide lower bound bearing capacity factor Nc for axially loaded circular piles in clays by using two-dimensional finite elements and the three-dimensional non-linear Tresca yield criterion. The clay layer is assumed to be completely saturated and subjected to undrained loading. The edge discontinuities of the Tresca surface was smoothened by providing a C 2 rounded surface at the vicinity of the sharp corners of the regular hexagon lying on the octahedral plane. No inherent assumption of hoop stress was considered in the present analysis. The clay has been considered to be heterogeneous where the cohesion increases linearly with depth. The study is useful in providing the methodology for simulating the axisymmetric structures and providing the design chart for the bearing capacity factors for circular piles in clays whose cohesion increases linearly with depth.

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.

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.

Implementation of the Tresca yield criterion in finite element analysis of burst capacity of pipelines

The Tresca and von Mises criteria are two classic yield criteria for metals. While the von Mises criterion has been widely implemented in commercial finite element analysis (FEA) software package, the Tresca yield criterion in the context of the associated-plastic flow rule is not available in any well-known FEA packages such as ABAQUS and ANSYS. In this study, the Tresca yield criterion as well as the associated plastic flow and hardening rules are implemented in a user-defined material model (UMAT) in commercial FEA package ABAQUS based on the return-mapping technique. The consistent tangent operator for the Tresca criterion is also implemented in the UMAT model to facilitate the computation of the tangent stiffness matrix during the Newton-Raphson iteration for solving the nonlinear global equilibrium equations in the plastic domain. The constitutive integration algorithm for the Tresca UMAT is written in the principal stress space, which markedly simplifies the implementation. The implemented Tresca UMAT model is validated by theoretical solution and full-scale burst tests of both pristine and defected pipes. Furthermore, based on the Tresca-based and von Mises-based FEA predictions, a new formula is proposed to accurately predict burst pressure of thin-walled corroded pipes.

Theoretical analysis of the influence of drilling compaction on compressional wave velocity in hydrate‐bearing sediments

AbstractBorehole wall would be disturbed during sampling when drilling into gas hydrate‐bearing sediments, thereby changing the reservoir physical characteristics obtained by well logging. It would cause significant errors using such logging data to estimate the reservoir parameters such as hydrate saturation and mechanical properties. In this paper, the theoretical method of combination cavity expansion theory with the time‐average equation to predict the compressional velocity (Vp) of hydrate‐bearing sediment after drilling disturbance were proposed based on the hypothesis that the compaction of hydrate‐bearing sediments only causes the porosity change in sediments. The theoretical derivation process of calculation the porosity change caused by drilling compaction based on both Tresca's yield criteria and Mohr–Coulomb yield criteria were presented in detail. And the influence of drilling compaction on Vp were discussed by theory method developed in this paper and experimental method. Both theory‐based results and experimental results show that the Vp difference caused by drilling compaction is considerable. Drilling compaction would cause the increase in Vp, and the increment increase with the increase of bit weight, and samples with low hydrate concentrations would be more sensitive to bit weight variations. The proposed method is feasible to simplify the influences of complex processes involved in the disturbance of hydrate‐bearing sediments during drilling.

Analysis of Residual Stress in the Rotational Autofrettage of Thick-Walled Disks

Autofrettage is a means of generating compressive residual stresses at the inner side of a thick-walled cylinder or hollow disk by causing nonhomogeneous plastic deformation of the material at the inner side. The presence of residual compressive stresses at the inner region of the cylinder/disk enhance the pressure withstanding capacity, fatigue life and the resistance to stress corrosion cracking of the component. Despite the hydraulic and swage autofrettage are the widely practiced processes in industries, there are certain disadvantages associated with these processes. In view of this, in the recent years, researchers have proposed new methods of achieving autofrettage. Rotational autofrettage is such a recently proposed autofrettage method for achieving the beneficial compressive residual stresses in the cylinders. In the present work, the rotational autofrettage is studied for a thick-walled hollow circular disk. A theoretical analysis of the residual stresses produced in the disk after unloading are obtained assuming plane stress condition, Tresca yield criterion and its associated flow rule. The analysis takes into account the effect of strain hardening during plastic deformation. Further, the effect of residual stresses in the typical SS304 and aluminum disk is studied by subjecting them into three different types of loads viz., internal pressure, radial temperature difference, and rotational speed individually. A three-dimensional (3D) finite element method (FEM) validation of the theoretical stresses during rotational autofrettage of a disk is also presented.