Tresca Criterion Research Articles

A universal fracture criterion for high-strength materials

Recently developed advanced high-strength materials like metallic glasses, nanocrystalline metallic materials, and advanced ceramics usually fracture in a catastrophic brittle manner, which makes it quite essential to find a reasonable fracture criterion to predict their brittle failure behaviors. Based on the analysis of substantial experimental observations of fracture behaviors of metallic glasses and other high-strength materials, here we developed a new fracture criterion and proved it effective in predicting the critical fracture conditions under complex stress states. The new criterion is not only a unified one which unifies the three classical failure criteria, i.e., the maximum normal stress criterion, the Tresca criterion and the Mohr-Coulomb criterion, but also a universal criterion which has the ability to describe the fracture mechanisms of a variety of different high-strength materials under various external loading conditions.

AZ31マグネシウム合金押出し材の常温における降伏曲面に関する実験的研究

The yield surface and the deformation mechanism of the extruded AZ31 magnesium alloy rod at room temperature were studied. The uniaxial tensile, compressive and pure shear tests with the simultaneous observation of the microstructure were carried out for specimens sampled along different directions in an extruded rod. In the plane-stress condition within the plane perpendicular to extrusion, the yield surface almost fits the Tresca's criterion for isotropic materials, because of the activation of the basal slip or {10-12} twinning, regardless of the loading direction. The deformation mechanism with higher critical resolved shear stress than those of basal slip or {10-12} twinning is driven by the tensile loading parallel to extrusion, due to the texture with the direction of its c-axis perpendicular to tensile direction. Therefore the tensile yield stress for this direction increase more than compression or shear, and the twinning pattern at the yield for tensile loading does not appear.

OS0403 AZ31マグネシウム合金押出し材の常温における降伏曲面に関する実験的研究

The yield surface and the deformation mechanism of the extruded AZ31 magnesium alloy rod at room temperature were studied. The uniaxial tensile, compressive and pure shear tests with the simultaneous observation of the microstructure were carried out for specimens sampled along different directions in an extruded rod. In the plane-stress condition within the plane perpendicular to extrusion, the yield surface almost fits the Tresca's criterion for isotropic materials, because of the activation of the basal slip or {1012} twinning, regardless of the loading direction. The deformation mechanism with higher critical resolved shear stress than those of basal slip or {1012} twinning is driven by the tensile loading parallel to extrusion, due to the texture with the direction of its c-axis perpendicular to tensile direction. Therefore the tensile yield stress for this direction increase more than compression or shear, and the twinning pattern at the yield for tensile loading does not appear.

Review on Yielding and Hardening Behavior of Sheet Metal

Yield criterion, work-hardening law and constitutive model is the theoretical foundation for the investigation of the plastic forming of sheet metals. With more and more new materials and new technology emerged, the temperature and the strain rate effect on plastic forming process can not be ignored, the existing theory of plasticity has been unable to meet the need of research and application. Researches on criteria since 1864's Tresca criterion will be reviewed. Also three kinds of hardening mode such as isotropic hardening mode, kinematic hardening mode and mixed hardening mode, and Bauschinger effect, which has great influence on hardening modes, will be elaborated. Yield hardening research considering temperature and strain rate are also discussed. Since experimental method has great importance on yield hardening research, it will be introduced on one part. It is pointed that the yield hardening research considering temperature and strain rate, experimental method, application of new criterion and hardening model in finite element analysis(FEA) will be hotspot of research.

AN ANALYTICAL SOLUTION FOR OPTIMUM DESIGN OF SHRINK-FIT MULTI-LAYER COMPOUND CYLINDERS

In this paper, employing an analytical method, optimum design of multi-layer compound cylinders is investigated. To this end, considering Tresca criterion, maximum shear stress in each layer is minimized. Analytical relations for optimum values of a layer dimension, residual pressures and radial interferences are derived. A technique for shrink-fitting of layers is also proposed and relationships for radial interferences, residual pressures and required temperature differences during the shrink-fitting process are derived. Three different examples are presented to show the effectiveness of the proposed method. It is shown that increasing the number of layers makes shear stress distribution near to uniform. As a result, with specified maximum shear stress and inner radius, the weight of compound cylinder is decreased when the number of layers is increased. Moreover, compound cylinders with more layers have lower maximum shear stress for a specified weight. It is also concluded that if the ratio of outer to inner radii be larger, increasing the number of layers is more effective.

Diffusion-induced stresses of electrode nanomaterials in lithium-ion battery: The effects of surface stress

Nanomaterials offer large reaction surfaces making for high-rate lithium-ion transfer and fewer constraints to avoid fracture. Nevertheless, surface effect arises inevitably due to so high surface-to-volume ratio. Accordingly, the fundamental framework of surface stress is involved to study diffusion-induced stresses within electrode nanoparticles in this work. As simple one-dimension models, solid and hollow nanowire electrode particles are investigated. The results show that surface tensile stress produces compressive stresses through the electrode materials, especially reducing maximum tensile stress, which may become a resistance to brittle fracture. Owing to high special surface area, it is demonstrated that diffusion-induced stresses for hollow materials are largely reduced compared to solid electrode materials. The influences of surface modulus on diffusion-induced stresses are much stronger under generalized plane strain condition in comparison with plane strain condition. Analysis based on the Tresca criterion indicates that shear failure may occur at the inner surface with decreasing radius.

Evaluation of vertical and horizontal bearing capacities of bucket foundations in clay

The present paper presents the results of three-dimensional finite element analyses of bucket foundations in normally consolidated uniform clay under undrained conditions. The stress–strain response of clay was simulated using the Tresca criterion. The bearing capacities were calculated and found to be largely dependent on the aspect ratio of the bucket foundation. Based on the results of the analyses, new equations were proposed for calculating vertical and horizontal bearing capacities. In the proposed equations, the vertical capacity consisted of an end-bearing resistance and a skin friction resistance, whereas the horizontal capacity consisted of a normal resistance, a radial shear resistance, and a base shear resistance. Comparison of the numerical results showed that the proposed equations properly predicted the capacities of the bucket foundations in uniform or non-uniform clays.

STUDY OF STRESS AND STRAIN RATES IN A ROTATING CYLINDER SUBJECTED TO INTERNAL AND EXTERNAL PRESSURE

The creep behavior of a thick walled hollow circular cylinder, made of aluminum silicon carbide particulate composite material has been investigated in the present study and creep behavior in this case is assumed to follow Sherby's constitutive model. The stress and strain rate distributions of cylinder rotating about its own axis, have been obtained using von Mises and Tresca yield criteria. The effect of pressure on the stresses and strain rates in the cylinder has been investigated and it is observed that with the increase of the internal pressure in the cylinder the strain rate increases. The introduction of external pressure along with the internal pressure causes the strain rates to decrease. It is also observed that the values of effective stress and strain rate obtained using Tresca criterion are higher than those obtained using Mises criterion. Thus it is suggested to use Tresca criterion for the analysis while designing the cylinder.

Fine Stress Analysis and Strength Prediction of Joints in Axial Shear

A fine analysis model for joints in axial shear is given on the base of observation of experiment. Failure of the pin connecting adherends is due to combined deformation of pressure-shear. Both critical region of the pin and the stress state in critical rejoin are evaluated. Ultimate load Fu of the joint in axial shear is evaluated with strength criteria. The following conclusions are obtained. (1) Fu is related to ratio of adherend thickness t to length L. Fu increases with t when t/L is less than 0.1 and hold as a constant when t/L is greater than 0.2; (2) Fu can well be predicted by bi-shear theory or maximum tension strain criterion, but not by Tresca and Mises criteria; (3) Although traditional approximate calculation method of connections is widely used, related experiment must be done for obtaining ultimate shearing stress. Thus, the fine analysis method presented in this paper is useful for stress analysis and strength evaluation of connections.

TORSIONAL DEFORMATION AND FATIGUE BEHAVIOUR OF 6061 ALUMINIUM ALLOY

Torsional deformation and fatigue behaviour of both solid and thin-walled tubular specimens were made from as-received and heat treated 6061 aluminium alloy were studied. 6061 aluminium alloy have been widely used as a candidate material in automobile, aerospace, aircraft and structural application because of their superior mechanical properties such as high strength to weight ratio, good ductility and others. The differences in cyclic deformation and fatigue behaviours between round and solid specimens where a stress gradient exist, and thin-walled tubular specimens where a uniform stress state is commonly assumed, are also discussed. Von Mises and Tresca criteria has been used to predict the monotonic and cyclic deformation curve and compared to the torsional data obtained from the experiment. The S-N curve was used to present and evaluate the fatigue life of the specimens. Through fractographic analysis, failure criteria of fracture surfaces were observed and discussed.

Tresca criterion for plasticity and viscoplasticity: Application to localization in biaxial loading conditions

It has been proved that plastic instabilities in biaxial stretching conditions were better reproduced by using a Tresca yield surface rather than a Von Mises one. The simulation of the phenomenon in an expanding TA6V4 (Ti-6Al-4V alloy) shell experiment is performed using the Tresca criterion and both elasto-plastic and viscoplastic constitutive models: in this aim, Tresca flow surfaces had to be defined in viscoplasticity. The two models exhibit localization but, whereas the elastoplastic case develops shear banding in times in agreement with the onset of instabilities in the experiment, the viscoplastic case develops diffuse necking at later times. On the contrary, the viscoplastic simulation exhibits patterns the size of which seems in better agreement with the experimental ones.

Assessment of a smart concept for d15 shear piezoceramic direct torsion actuation

An experimentally proved smart concept for piezoceramic direct torsion actuation is here numerically assessed with regards to the bonding and segmentation influence on its behavior and performance. The TRESCA and deflection criteria analysis indicates that the actuator sandwiching with composites contributes to its integrity enhancement, but in the cost of its performance reduction. It is also found that modeling the core inter-rows and composites inter-layers bonding is more influential than that of the core rows segmentation. The conducted open-circuit modal analysis confirms that the inter-rows adhesive softens the actuator, while the inter-layers one stiffens it. Besides, the conducted adhesive parametric analysis indicates that, as expected, the most influential bonding parameters are its thickness and shear modulus.

Application of GM Yield Criterion in Plastic Zone of ModeⅠCrack and Burst Pressure for Pipeline

Based on GM yield criterion, the analytical solutions for shape and size of mode I crack tip plastic zone and the burst pressure for X70 pipeline steel are derived. Comparing the solutions with those based on Mises and Trasca criteria shows that under plain strain condition the area of plastic zone on GM is between Tresca and Mises solutions, and very close to Mises one. Among the areas Tresca’s is the largest and Mises is the smallest and all three zones are dumbbell shaped. However, for pipeline burst pressure based on Tresca criterion is the smallest and that on Twin shear stress criterion (TSS) is the largest, those on GM and Mises are also very close to each other and lie between Tresca and TSS results.

Deformation and fracture behavior of corrosion-resistant, potentially biocompatible, Ti40Zr10Cu38Pd12 bulk metallic glass

Metallic glass rods (2.5mm in diameter) with composition Ti40Zr10Cu38Pd12 exhibit considerably high compressive yield stress (1.9GPa), hardness above 7GPa, total engineering strain around 2.7% and Young's modulus of 100GPa. The fracture angle in this alloy is around 42° (i.e., lower than 45°), which evidences that yielding is influenced by normal stresses acting on the shear plane. Finite-element simulations of nanoindentation curves confirm that the Mohr–Coulomb yield criterion, rather than the conventional Tresca criterion, governs the deformation behavior of this material. The compressive yield stress and plasticity of the investigated alloy correlate with its glass transition temperature and the ratio between the shear and bulk elastic moduli, respectively. The Young's modulus of Ti40Zr10Cu38Pd12 is also relatively low. In addition, Ti40Zr10Cu38Pd12 exhibits good corrosion resistance in simulated body fluid (Hank's solution). From all these interesting properties this alloy may be a good candidate to be used as biomaterial.

Evaluation of burst pressure prediction models for line pipes

Accurate prediction of burst pressure plays a central role in engineering design and integrity assessment of oil and gas pipelines. Theoretical and empirical solutions for such prediction are evaluated in this paper relative to a burst pressure database comprising more than 100 tests covering a variety of pipeline steel grades and pipe sizes. Solutions considered include three based on plasticity theory for the end-capped, thin-walled, defect-free line pipe subjected to internal pressure in terms of the Tresca, von Mises, and ZL (or Zhu-Leis) criteria, one based on a cylindrical instability stress (CIS) concept, and a large group of analytical and empirical models previously evaluated by Law and Bowie (International Journal of Pressure Vessels and Piping, 84, 2007: 487–492). It is found that these models can be categorized into either a Tresca-family or a von Mises-family of solutions, except for those due to Margetson and Zhu-Leis models. The viability of predictions is measured via statistical analyses in terms of a mean error and its standard deviation. Consistent with an independent parallel evaluation using another large database, the Zhu-Leis solution is found best for predicting burst pressure, including consideration of strain hardening effects, while the Tresca strength solutions including Barlow, Maximum shear stress, Turner, and the ASME boiler code provide reasonably good predictions for the class of line-pipe steels with intermediate strain hardening response.

Limit Analysis of Defect-Free Pipe Elbow under Internal Pressure with MY Criterion

With MY (mean yield) criterion, the limit load of defect-free pipe elbow under inner pressure is analyzed, and an analytical solution is first obtained. The solution shows that the limit load is a function of wall thicknesst, average radiusr, yield strength as well as curvature radiusR0. The limit load increases with the increase of the curvature radiusR0and will get the same value with the burst pressure of straight pipe ifR0→∞. The limit load calculated by the solution is compared with those based on Tresca, Mises, as well as TSS yield criteria. It is also concluded that Tresca criterion predicts a lower bound to the limit load, while TSS criterion predicts an upper bound one. However, the limit load based on the MY criterion lies just between the TSS and Tresca solutions, most notably, the MY criterion almost has the same prediction precision with Mises solution.

Plastic collapse analysis of thin-walled pipes based on unified yield criterion

Based on a unified yield criterion (UYC), the plastic collapse analysis of thin-walled pipes is conducted in the framework of finite strain. A unified analytical solution for the burst pressure of end-capped defect-free pipes is derived, which is fit for various kinds of non-SD (strength differential) materials. A series of solutions can be deduced from this unified solution, and those solutions of burst pressure on the basis of Tresca, von Mises, ASSY, and TS criteria are special cases of it. By comparing with existing test result, it is found that the present unified solution is very convenient and effective for the prediction of burst pressure.

Assessment of a smart concept for d15 shear piezoceramic direct torsion actuation

An experimentally proved smart concept for piezoceramic direct torsion actuation is here numerically assessed with regards to the bonding and segmentation influence on its behavior and performance. The TRESCA and deflection criteria analysis indicates that the actuator sandwiching with composites contributes to its integrity enhancement, but in the cost of its performance reduction. It is also found that modeling the core inter-rows and composites inter-layers bonding is more influential than that of the core rows segmentation. The conducted open-circuit modal analysis confirms that the inter-rows adhesive softens the actuator, while the inter-layers one stiffens it. Besides, the conducted adhesive parametric analysis indicates that, as expected, the most influential bonding parameters are its thickness and shear modulus.

A local viewpoint for evaluating the influence of stress triaxiality and Lode angle on ductile failure and hardening

All damage and failure models, describing either the evolution of microvoids, the development of shear bands or local rupture, rely on the knowledge of the hardening function at large plastic strains which, then, becomes an essential prerequisite for any failure prediction. The phenomenon of ductile failure is analyzed here by focusing on its relationship with the variables for the stress--strain characterization, and by discussing the influence of plastic strain, stress triaxiality and Lode angle parameters on both the above aspects of materials behavior. Failure predictions are presented for different metals and different combinations of load-specimen geometry, according to three theories (the Tresca criteria and two models by Wierzbicki et al.) and to a procedure previously developed for the stress--strain characterization in the post-necking range. Experimental tests are performed by pulling tensile specimens and notched flat samples up to failure, then finite elements simulations are used to calculate the required failure-related variables within the volume of failing specimens; the results of the failure calculations are compared each other and with experimental data, and a discussion about the peculiarities of the methods used for predicting failure is also provided.

Fatigue life estimation in welded joints under multiaxial loadings

Welded joints are frequently locations for cracks initiation and propagation that may cause fatigue failure of engineering structures. Biaxial or triaxial stress-strain states are present in the vicinity of welded joints, due to local geometrical constraints, welding processes and/or multiaxial external loadings. Fatigue life evaluation of welded joints under multiaxial 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 unsafe if these conventional hypotheses are used. A criterion initially proposed by the authors for smooth and notched structural components has been extended to the fatigue assessment of welded joints. In more detail, fatigue life of welded joints under multiaxial stress states can be evaluated by considering a nonlinear combination of the shear stress amplitude (acting on the critical plane) and the amplitude and the mean value of the normal stress (acting on the critical plane). In the present paper, fatigue lifetimes predicted through the proposed criterion are compared with experimental fatigue life data available in the literature, related to fatigue biaxial tests.