Tresca Criterion Research Articles

On strength criteria of fillet welds

A comparison between two widely used strength criteria (ISO and Eurocode 3) for welding design is carried out in this paper. Limit analysis theorems are applied for analysis of collapse load of a fillet weld using von Mises yield criterion, generalizing a previous methodology in which Tresca criterion was used. Using von Mises criterion, lower bounds of collapse load can be found by solving a quartic equation, thus avoiding the numerical sweep needed with Tresca criterion. The results of limit analysis fit much better with those of Eurocode 3 criterion, and this criterion also reasonably fits experimental results for side-fillets, but experimental results on end-fillets agree with ISO criterion and not with Eurocode 3 criterion and limit analysis. A numerical finite element analysis shows that this apparent contradiction is originated by the influence of overlapping between the welded plates, which gives rises to the transmission of part of the internal moment through contact forces between plates and not through the throat. The results support the use of Eurocode 3 criterion instead of ISO, and this is confirmed by the analysis of a varied set of welded layouts using the former in a general numerical method developed previously, which gives results that show a very reasonable agreement with experimental results found in the bibliography.

Yield criterions of metal plasticity in diffierent stress states

Five types of tensile tests were conducted to study the yield behavior of 2A12-T4 aluminum alloy. Parallel finite element models were built for each test and solved with ABAQUS with diffierent yield criterions. The result shows that any of the four criterions: von Mises yield criterion, Tresca criterion, Twin-Shear criterion and von Mises criterion with hydrostatic pressure correction, overestimates the yield strengths of the specimens. Rather than hydrostatic pressure, Lode stress parameter is the key factor that affiects the diffierences between experimental and simulation results. Based on this concept, a new yield model with Lode dependence modified from von Mises criterion is postulated. Although one more parameter needs to be confirmed, the simulation results of this yield model are better than those of other criterions.

CALCULATION OF THE ULTIMATE BEARING CAPACITY OF SOIL SLOPE BASED ON THE UNIFIED STRENGTH THEORY

At present, the failure criteria used in calculating the ultimate bearing capacity of soil slope are the Tresca and Mohr-Coulomb criteria. But the results are conservative and the potential strength of soil mass cannot be utilized sufficiently because these two criteria do not take into account the effect of the intermediate principal stress. In this paper the unified strength theory was used to analyze the ultimate bearing capacity of soil slope. The formula for calculating the ultimate bearing capacity of soil slope using the unified strength theory was established. At the end, a case history was analyzed and it indicated that the result of the unified strength theory is larger than that of the Mohr-Coulomb criterion. This indicates that calculation of ultimate bearing capacity of soil slope with the unified strength theory can sufficiently exploit the strength of material. Therefore, the calculation of ultimate bearing capacity of the soil slope based on the unified strength theory will be of great significance in future applications.

A two-parameter expression for failure surfaces

The Mohr–Coulomb, Tresca and Von Mises criteria are classical failure criteria, widely accepted and used for various materials. To take into account the influence of intermediate principal stress on the strength of soil, Bishop, Lade–Duncan and Matsuoka proposed criteria in terms of three principal stresses or three stress invariants. This note describes an expression with two parameters for modeling the shape of the failure surface in the octahedral plane. By studying the roles of these two parameters and comparing the new criterion with the aforementioned criteria, the advantage and flexibility of the proposed function is explored. Application of the function is demonstrated by fitting the new surface to experimental data for various soils.

Multiaxial fatigue life estimation in welded joints using the critical plane approach

Many engineering structures experience multiaxial fatigue states of stress–strain in the vicinity of welded joints. Fatigue assessment of welded joints under proportional (in-phase) cyclic loading can be performed by using conventional hypotheses (e.g., see the von Mises criterion or the Tresca criterion) on the basis of local approaches. On the contrary, the fatigue life predictions of welded joints under non-proportional (out-of-phase) cyclic loading are generally poor if these conventional hypotheses are used. In the present paper, the critical plane-based multiaxial fatigue criterion proposed by Carpinteri and Spagnoli for smooth and notched structural components is extended to the fatigue assessment of welded joints under in- and out-of-phase loadings. The applicability of this criterion, expressed in terms of nominal stresses, to the fatigue life prediction of welded specimens is investigated by using experimental data available in the literature.

Plastic Anisotropy of A2024BE-T6 and O Aluminum Alloys

Multiaxial stress tests were carried out on thin-walled cylindrical specimens of the A2024BE-T6 alloy aged at 120°C for 1 hr and the A2024BE-O alloy fully annealed at 495°C for 1hr. The shear strength of these alloys is much lower than the tensile one, and the equi-strain surfaces in the tension-torsion stress field lie within Tresca's criterion. Planar anisotropy was determined from two types of multiaxial stress tests by means of the combined loading of axial load, internal pressure and torsion, referred to as “off-axis tension test” and “off-axis torsion test”. The degree of anisotropy is expressed by using two different measures : one is the proof stress and the other is the angle deviation between the directions of the principal stress (or principal shear stress) and principal strain increment (or principal shear strain increment). The A2024BE-T6 alloy exhibits more severe anisotropy than the A2024BE-O alloy and both alloys reveal more severe anisotropy in off-axis tension test than in off-axis torsion test. The plastic deformation behavior can be analyzed precisely by the constitutive equation derived from the anisotropic yield function, hardening law and associated flow rule.

Seismic Bearing Capacity of a Circular Footing on a Heterogeneous Cohesive Soil

ABSTRACT This study concerns the determination of the seismic bearing capacity of a circular footing resting on a purely cohesive heterogeneous soil layer. The problem is treated using the kinematic approach of the Yield Design theory. The soil strength is modelled by the Tresca criterion with C0 the cohesion at the soil surface and G the vertical cohesion gradient. The loading process of the system is described by four loading parameters: an inclined force (N: vertical component, V: horizontal component), a moment (M) acting at the center of the footing and horizontal uniform inertial forces (Fh) acting in the soil volume during the seismic excitation. Two cases are considered for the soil: a soil with an infinite tensile strength and a soil with zero tensile strength. The soil-footing interface is considered purely cohesive with zero tensile strength. The study presents optimal upper bounds for the ultimate combinations of the dimensionless loading parameters (N, V, M, Fh) by the examination of a series of three-dimensional virtual kinematic mechanisms of failure. The results are presented in the form of surfaces in the space of the parameters (N, V, M) for a range of values of Fh.

Study of tube flaring forming limit in the tube flaring process

The aim of the current paper is to develop analytical theories for industry to predict the relations between the punch stroke, flaring ratio, tube thickness, and flaring forming limit in the tube flaring process. The volume incompressible condition, Levy-Mises equation, and explicit die profile description are combined to derive the analytical expressions relating the flaring ratio to the punch stroke and velocity in the tube flaring process. Then, according to the stress equilibrium state of a small tube element, the relation of the tube-end thickness ratio to the flaring ratio is developed on the basis of Tresca's criterion. Combining these two analytical theories and the fractured thickness at the tube end, the flaring forming limit can be determined. An elastoplastic finite element method based on the updated Lagrangian formulation is also developed to verify the analytical theories. A flaring experiment, using a 30° semi-cone angle to describe the conical die, is conducted to validate the analytical theories and simulated results. It is found that relations such as tube thickness ratio to flaring ratio, and punch stroke ratio to flaring ratio, show good agreement between analytical theories, finite element prediction, and experiment.

Unified solutions to mixed mode crack tip under small scale yielding

Based on Yu Maohang's unified strength theory, the unified analytical solutions to the shapes and sizes of I , II mixed mode crack tip plastic zone under small scale yielding are derived. Then a set of loci for crack tip plastic zone under different material parameters: The ratio of tensile strength to compressive strength a, poisson's ratio v and material constant b are obtained. Furthermore the influences of the material parameters to the shapes and sizes of crack tip plastic zone are discussed essentially. Amongst them the a parameter effects much more than other parameters, it causes discontinuity in crack's up and down surface as a#l, meanwhile upper bound and lower bound of the loci for the plastic zone are corresponded to parameters using b=0 and b=1. The new solutions are compared with the former solutions to the problem by using Tresca criterion and Von Mises criterion, the former solutions are only the special cases or linear proximity to this problem. The new solutions have unification in the strength theory and universality for the different materials.

Unified Solutions to the Limit Load of Thick-Walled Vessels

Unified solutions to the elastoplastic limit load of thick-walled cylindrical and spherical vessels under internal pressure are obtained in terms of the unified strength theory (UST) and the unified slip-line field theory (USLFT). The UST and the USLFT include or approximate an existing strength criterion or slip-line field theory by adopting a parameter b, which varies from 0 to 1. The theories can be used on pressure-sensitive materials, which have the strength difference (SD) effect. The solutions, based on the Tresca criterion, the von Mises criterion, the Mohr–Coulomb criterion, and the twin shear strength criterion, are special cases of the present unified solutions. The results based on the Mohr–Coulomb criterion (b=0) give the lower bound of the plastic limit load, while those according to the twin shear strength criterion (b=1) are the upper bound. The solution of the von Mises criterion is approximated by the linear function of the UST with a specific parameter (b≈0.5). Plastic limit solutions with respect to different yield criteria are illustrated and compared. The influences of the yield criterion as well as the ratio of the tensile strength to the compressive strength on the plastic limit loads are discussed.

Semidefinite optimization models for limit and shakedown analysis problems involving matrix spreads

Limit and shakedown analysis problems of Computational Mechanics lead to convex optimization problems, characterized by linear objective functions, linear equality constraints and constraints expressing the restrictions imposed by the material strength. It is shown that two important strength criteria, the Mohr–Coulomb and the Tresca criterion, can be represented as systems of semidefinite constraints, leading this way to semidefinite programming problems.

Estimation of the plastic zone by finite element method under mixed mode (I and II) loading

Material fracture by opening (mode I) is not lonely responsible for fracture propagation. Many industrial examples show the presence of mode II and mixed mode I+II. The present work consists in the elaboration of a code to estimate the size of the plastic zone at the crack tip under mode I, mode II and mixed mode I+II loading. The computations are made according to Von Mises and Tresca criteria. The results obtained are compared to those measured by experiments.

Calculation of a Safety Margin for Hydrogenerator Thrust Bearings

During the design or refurbishment of a thrust bearing a question that occurs frequently is, “How safe is this bearing?” Factors of safety are widely used in engineering design, and some applications require compliance with safety factors that are specifically stated in codes of practice. Most manufacturers have limits on the maximum allowable bearing temperature. These can be useful as a guide but offer no graded answer as to how much safer (or less safe) a bearing is made by applying a particular design decision. A numerical factor of safety would give a quantitative measure of the safety of a bearing and would be useful in judging whether a proposed design change is worthwhile in terms of improved safety. Experience has shown that failure of a babbitt bearing often develops from a local yielding (and subsequent flow) at a discrete point on the surface. This develops into rippling and folding of the material and escalates rapidly to a bearing “wipe.” This article describes the application of the Tresca and von Mises criteria of yielding to give a numerical factor of safety against plastic flow of the babbitt. The method uses data for the yield point of the babbitt as a function of temperature and assumes that the material on the bearing surface is constrained in both lateral coordinate directions. In practice, any data on the failure of hydrothrust bearings are invariably regarded as proprietary by manufacturers and there is apparently no published work available that can be used to correlate the model. However, the method developed in this paper is quite general and applicable to any fully hydrodynamic bearing loaded to the yield point of the surfaces. Results for large babbitt-faced journal bearings that were deliberately taken to failure are used for a correlation. Reasonable agreement is shown between predicted and actual failure. The calculation of a factor of safety can be a useful tool for evaluating initial designs or modifications during refurbishment. Some factors concerning the assessment of an acceptable minimum film thickness are also discussed. Presented at the STLE Annual Meeting in Toronto, Ontario, Canada May 17-20, 2004 Manuscript approved June 1, 2005 Review led by Itzhak Green

Shakedown analysis of thick-walled cylinders subjected to internal pressure with the unified strength criterion

Most previous studies on shakedown of thick-walled cylinders were based on the assumption that the compressive and tensile strengths of the materials were identical. In this paper the shakedown of an internally pressurized cylinder made of a material with a strength-difference and intermediate principal stress effects is dealt with by using a unified strength criterion which consists of a family of convex piecewise linear strength criteria. Through an elasto-plastic analysis the solutions for the loading stresses, residual stresses, elastic limit, plastic limit and shakedown limit of the cylinder are derived. It is shown that the present solutions include the classical plasticity solutions as special cases and have the ability to account for the strength-difference and intermediate principal stress effects. Finally, the influence of the two effects on the shakedown limit of the cylinder is investigated. The results show that the shakedown limit depends on the two effects and is underestimated if these effects are neglected as in the classical plasticity solution based on the Tresca criterion.

Stress distributions in elastic-plastic rotating disks with elliptical thickness profiles using Tresca and von Mises criteria

Analytical and numerical solutions for the elastic-plastic stress distribution in rotating variable thickness solid and annular disks are obtained under plane stress assumption. The thickness of the disk is assumed to vary radially in elliptic form which represents a wide range of continuously variable nonlinear cross-sectional profiles. Tresca's yield criterion and its associated flow rule are used to obtain analytical solutions for a linear hardening material. A computational model is developed to obtain solutions using the von Mises yield criterion, deformation theory of plasticity and a Swift-type hardening law. Both linear and nonlinear hardening materials are considered in solutions obtained by using von Mises criterion. The stresses, displacement and plastic strains are calculated for solid and annular disks rotating at different speeds and the results are presented in graphical forms.

Unified Tensile Fracture Criterion

We find that the classical failure criteria, i.e., maximum normal stress criterion, Tresca criterion, Mohr-Coulomb criterion, and von Mises criterion, cannot satisfactorily explain the tensile fracture behavior of the bulk metallic glass (BMG) materials. For a better description, we propose an ellipse criterion as a new failure criterion to unify the four classical criteria above and apply it to exemplarily describe the tensile fracture behavior of BMGs as well as a variety of other materials. It is suggested that each of the classical failure criteria can be unified by the present ellipse criterion depending on the difference of the ratio alpha=tau(0)/sigma(0).

The Effect of D/T on the Load Interaction Behavior of a Plain Pipe

The objective of the study is to determine the effect of diameter/thickness (D/T) ratio on the interaction of axial force, bending moment, torsion and internal pressure in plain pipes. The Tresca and von Mises criteria are used to determine the first yield behavior of pipes when subjected to combined loads. The results show that for certain load combinations, the load interaction behavior is affected by D/T ratio and some load interaction relations change with a load dominance. The general trend is an increase in effective stress as D/T is increased. Most design codes show slightly conservative pipe design.

Fatigue and fracture behavior of bulk metallic glass

Tensile, compressive, cyclic tension-tension, and cyclic compression-compression tests at room temperature were systematically applied to a Zr52.5CU17.9Al10Ni14.6Ti5 bulk metallic glass for comprehensive understanding of its damage and fracture mechanisms. Under tensile loading, the metallic glass only displays elastic deformation followed by brittle shear fracture. Under compressive loading, after elastic deformadon, obvious plasticity (0.5 to 0.8 pct) can be observed before the final shear fracture. The fracture strength under compression is slightly higher than that under tension. The shear fracture under compression and tension does not occur along the maximum shear stress plane. This indicates that the fracture behavior of the metallic glass does not follow the Tresca criterion. The fracture surfaces show remarkably different features, i.e., a uniform vein structure (compressive fracture) and round cores coexisting with the radiating veins (tensile fracture). Under cyclic tension-tension loading, fatigue cracks are first initiated along localized shear bands on the specimen surface, then propagated along a plane basically perpendicular to the stress axis. A surface damage layer exists under cyclic compression-compression loading. However, the final failure also exhibits a pure shear fracture feature as under uniaxial compression. The cyclic compression-compression fatigue life of the metallic glass is about a factor of 10 higher than the cyclic tension-tension fatigue life at the same stress ratio. Based on these results, the damage and fracture mechanisms of the metallic glass induced by uniaxial and cyclic loading are elucidated.

Tresca and von Mises yield criteria: a view from strain space

In this paper, we present a study of Tresca and von Mises criteria in strain space. The plastic strains that can meet these criteria are found analytically for the Tresca criterion and numerically for the von Mises criterion. Such information will be useful for determining the relationship between yield criterion and the lattice structure of a material.

The Effect of Fabrication Processes on the Governing Mechanical Failure Criteria for Alloy 22, Ti-Grade 2/7, and Ti-Grade 5/24 Alloys

AbstractThe effect of fabrication processes on the governing mechanical failure criteria for Alloy 22, Ti-Grade 2/7, and Ti-Grade 5/24 has been evaluated through the development of material specific failure assessment diagrams (FAD). The Barsom and Rolfe Charpy V-Notch (CVN) energy to KICempirical relationship was shown to be conservative when compared to experimental KJC data for Alloy 600 and 690, which indicates that the KIC derivation is most likely conservative for Alloy 22 as well. In contrast, the CVN to KICH2 relationship was found to be non-conservative for Ti-Grade 2/7 and Ti-Grade 5/24. The derived KIC value for Alloy 22 was then used to construct a K-based FAD, which indicated that the governing mechanical failure theory was the Tresca criterion for plastic collapse. Both the derived KIC and experimental KQ values were used in the development of the Ti-Grade 2/7 and Ti-Grade 5/24 FADs. The Ti-Grade 2/7 FAD indicated that the governing mechanical failure theory is also plastic collapse while the Ti-Grade 5/24 FADsuggested mixed mode failure processes where neither linear-elastic fracture mechanics (LEFM) nor Tresca can accurately predict.