Unified Yield Criterion Research Articles

Elasto-Plastic Analysis of Soil around Tubular Pile Based on Triple Shear Unified Yield Criterion

The elasto-plastic analysis using the triple shear unified yield criterion and the cavity expansion theory is devoted to soil around the tubular pile. When the influence of the intermediate principal stress is considered, the driving effect of the tubular pile is studied. The relationship between plastic zone, the limit expansion pressure, the radial stresses and the parameterbis also obtained. The results show that the radius of plastic zone is decreased and the limit expansion pressure is increased, at the same radius, the radial stress is also increased, because of the effect of intermediate principal stress.

Elastoplastic Analysis of Surrounding Rocks of the Pressure Tunnel

According to the triple shear unified yield criterion, the mechanical behavior of the pressure tunnel was put forward. The calculation formulas of the radius of plastic zone were deduced with considerations of the effects of the intermediate principal stress. The results show that the intermediate principal stress effect parameter b has influences on the radius of plastic zone. With the increase of the intermediate principal stress effect parameter b, the radius of plastic zone decreases. The radius of plastic zone is increased, because of the increase of the porous hydraulic pressure.

Yield criteria of hexagonal symmetry in the π-plane

The theory of plasticity operates with different yield criteria of incompressible behavior for isotropic materials. Mostly known are the criteria of Tresca, Schmidt-Ishlinsky and von Mises. The first two criteria have a hexagonal symmetry, and the criterion of von Mises has a rotational symmetry in the π-plane. All these criteria do not distinguish between tension and compression (no strength differential effect), but numerous problems are treated in the engineering practice using these criteria. Within this paper, the yield criteria with hexagonal symmetry for isotropic incompressible materials are compared. For this purpose, their geometries in the π-plane will be presented in polar coordinates. The radii at the angles of 15◦ and 30◦ will be related to the radius at 0◦. Based on these two relations, well-known criteria will be shown in one diagram. The extreme shapes of the yield surfaces are restricted by two criteria: the unified yield criterion (UYC) and the multiplicative ansatz criterion (MAC). The examinations of the UYC and MAC depict a linear combination of these extreme yield surfaces. The resulting criterion with two parameters describes all possible convex forms of hexagonal symmetry. On the other hand, this criterion has one disadvantage: It is not possible to solve explicitly the equation for the equivalent stress. Other known criteria (Sokolovsky, Ishlinsky-Ivlev, Dodd-Naruse, Drucker) are depicted in the proposed diagram and compared with the above mentioned criteria. Further criteria are derived from the consideration of solids with orthogonal symmetry planes in the shear stress space. New criteria are introduced for practical applications. The constraints of convexity are established for them. The proposed consideration of the yield criteria simplifies the selection of a proper criterion. The extreme solutions for the analysis of construction parts can be found using these criteria.

Analysis of Axial Bearing Capacity of Concrete-Filled Steel Tube Hollow Columns

Based on the triple shear unified yield criterion, the mechanical behavior of the concrete-filled steel tube columns was analyzed. The calculation formulas of axial bearing capacity of the concrete-filled steel tube columns were deduced with considerations of the restriction effects of steel tube and the effects of the intermediate principal stressed. The results show that the intermediate principal stress effect parameter b has influences on the ultimate bearing capacity. With the increase of the intermediate principal stress effect parameter b, the ultimate bearing capacity of the concrete-filled steel tube columns increases too. The results show that formula deduced in the paper has good applicability and the solution has an important practical value.

Mechanics Behavior of Concrete-Filled Square Steel Tube Columns

This study presents a simplified analytical method for predicting the ultimate strength of compressed concrete filled square steel tube columns based on the triple shear unified yield criterion. Based on the triple shear unified yield criterion theory solutions of thick tube, the calculation formulas of axial bearing capacity of the concrete-filled square steel tube columns were deduced with considerations of the restriction effects of steel tube and the effects of the intermediate principal stressed. The results show that the intermediate principal stress effect parameter b has influences on the ultimate bearing capacity. The formulas in the paper have significance in exerting material potential and save material.

Study on the Ultimate Pullout Force of Prestressed Cable Based on Triple Shear Unified Yield Criterion

Based on the triple shear unified yield criterion and the ultimate equilibrium principle, the ultimate pullout force of prestressed cable is studied. The ultimate pullout force of prestressed cable is related to the rock type, the shapes of rapture surface, grouting pressures and compressive strength of rock, etc. The results show that the intermediate principal stress effect parameter b have influences on the ultimate pullout force of prestressed cable. With the increase of the intermediate principal stress effect parameter b, the ultimate pullout force of prestressed cable increases too. When the grouting pressure increases, the ultimate pullout force of prestressed cable increases also.

The Triple-Shear Unified Analytical Solution of Stress and Displacement of Softening Material Thick Walled Cylinder

Based on the further analysis to triple-shear unified yield criterion, the Lode parameter expression of the triple-shear unified yield criterion were given. This paper performs the analysis computation to softening material thick-walled cylinder under internal pressure based on triple-shear unified yield criterion. The analytical solution of stress and displacement is obtained. By using triple-shear unified yield criterion, more reasonable solution for different softening material can be derived.

Maximum Reduction in Thickness in a Single Sheet Forming Pass Based on Unified Strength Theory

Based on unified strength theory, the equation for estimating the maximum reduction in thickness in a single sheet forming pass is obtained. Included the contribution of both intermediate principal shear stress and varying tension-compression-ratio to material mechanical property, the equation developed by this paper can reasonably apply to a wide range of material. It can be proved that the equation for estimating the maximum reduction based on unified strength theory becomes that based on unified yield criterion, when material has equal strength in tension and compression, i.e., the tension-compression-ratio of material is equal to units; and, that the values of the maximum reduction obtained previously based on Mises, or Tresca criterion, are all just special cases of those based on unified yield criterion. In addition, the maximum reduction in thickness for sheet drawing and extrusion is equal to one another.

Unified Stresses Solution for Sheet Forming

Based on unified strength theory, the unified stresses solution for sheet forming is presented according to mechanical analysis developed, and accurate enough for much material due to the contributions of both intermediate principal shear stress and varying tension-compression-ratio included. Notably, by denoting a notation of h, the expressions presented to estimate stresses of billet for sheet forming can be apply to both drawing and extrusion. In addition, when material has identical strength in tension and compression, i.e., the tension-compression-ratio of the material is equal to unit, the stresses solution based on unified strength theory become that based on unified yield criterion. Accordingly, it can be proved that the stresses solution based on Mises criterion is just a special case of that based on unified yield criterion.

Stresses Unified Solution for Wire Forming Based on Unified Strength Theory

For known well the contributions of both tension-compression-ratio of material and intermediate principal shear stress to wire forming, the wire forming problem is developed based on unified strength theory. By denoting a notation of D, the unified stresses solution for wire forming is gained, which is suitable to both wire drawing and extrusion. In addition, when material has identical strength in tension and compression, the stresses solution based on unified strength theory become that based on unified yield criterion. Notably, it is proved that the stresses of wire forming are independent of the intermediate principal shear stress. Whether any yield criterion (e.g., Mises, Tresca or unified yield criterion) is adopted, for it is assumed that the tensile and compressive strength is equal to one another, the stresses solution is as same as that based on unified yield criterion, and is merely a special case of the unified stresses solution developed by this paper.

The Triple-Shear Unified Yield Criterion and its Applications

By taking account of the functions of shear stress couples acting on the dodecahedron element, a triple-shear unified yield criterion for materials is proposed to interpret a series of criteria, especially the commonly used criteria such as the Tresca’s yield criterion, the Von Mises’s yield criterion and the Mohr-Coulomb’s failure criterion through changing its contributive coefficient of the intermediate principal shear stress couples b and the tensile to compressive yield limit ratio α . In spite of that, problems of the limit inner pressures for thin and thick-wall cylinders are analyzed and the new unified solutions are deduced under the hypothesis of the perfectly elasto-plastic materials. The classical solutions based on the Tresca’s yied criterion, the Von Mises’s yield criterion and the Mohr-Coulomb’s failure yield criterion are only the special cases of the new unified solutions. Detailed analyses show that both the contributive coefficient of the intermediate principal shear stress couples b and the tensile to compressive yield limit ratio α have influences on the limit inner pressures for thin and thick-wall cylinders

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.

A unified criterion for yielding behavior of metallic glasses

The yield behavior of metallic glasses was studied. Three yield criteria, including von Mises yield criterion, Mohr-Coulomb yield criterion and the unified yield criterion were used to describe the yield phenomena of the metallic glasses. Two classes of the experimental data were chosen to draw the yield loci using the unified yield criterion. It is shown that the unified yield criterion can be used to describe the yield behavior of the metallic glasses no matter whether the metallic glasses show strength-different effect or non-strength-different effect. Almost all the widely accepted yield criteria are the subsets of the unified yield criterion if the intermediate principle stress and/or the intermediate principle shear stress are not considered at all.

Deduction of plastic work rate per unit volume for unified yield criterion and its application

A unified linear expression of plastic work rate per unit volume is deduced from the unified linear yield criterion and the associated flow rule. The expression is suitable for various linear yield loci in the error triangle between Tresca's and twin shear stress yield loci on the π-plane. It exhibits generalization in which the different value of criterion parameter b corresponds to a specific linear formula of plastic work rate per unit volume. Finally, with the unified linear expression of plastic work rate and upper-bound parallel velocity field the strip forging without bulge is successfully analyzed and an analytical result is also obtained. The comparison with traditional solutions shows that when b=1/(1+√3) the result is the same as the upper bound result by Mises' yield criterion, and it also is identical to that by slab method with m=1, σ 0=0.

An analytical solution for the large deflections of a slender sandwich beam with a metallic foam core under transverse loading by a flat punch

The large deflections of slender ultralight sandwich beams with a metallic foam core are studied under transverse loading by a flat punch, in which interaction of bending and stretching induced by large deflections is considered. Firstly, a unified yield criterion for metallic sandwich structures considering the effect of core strength is proposed, which is valid for metallic sandwich cross-sections with various core strengths and geometries. This can reduce to the yield criterion for a solid monolithic cross-section and the classical yield criterion for sandwich cross-sections with a weak core, respectively. Then, analytical solutions for the large deflections of fully clamped and simply supported metallic foam core sandwich beams are derived under transverse loading by a flat punch, respectively. Comparisons of the present solutions with experimental results are presented and good agreements are found. The effects of the core strength, the size of loading punch and the boundary conditions on the structural response of sandwich beams are discussed in detail. It is shown that the axial stretching induced by large deflections has significant effect on the load-carrying and energy absorption capacities of sandwich structures in the post-yield regime, and the load-carrying and plastic energy absorption capacities of metallic foam core sandwich beams may be underestimated as the core strength is neglected in analysis, especially for the sandwich beams with a strong core.

Analytical Solution for the Large Deflection of Fully Clamped Metallic Foam Sandwich Beam

A unified yield criterion is proposed in this paper, which is valid for the metallic sandwich sections with various core strength and geometrical dimensions and can reduce to the classical yield criteria for solid monolithic section and sandwich section with weak core, respectively. Then, the unified yield criterion is used to derive the analytical solution for the large deflection of fully clamped metallic sandwich beam subject to a transversely concentrated load, in which the interaction of bending and stretching is considered. Comparisons of the present solutions with experimental results are carried out and good agreements are found. It is seen that the axial stretching induced by large deflection has a significant effect on the deflection of sandwich structure in the post-yield regime, and the load carrying capacity of metallic foam core sandwich beam may be underestimated as the core strength is neglected in analysis.

Unified Yield Criterion for Masonry and Concrete in Multiaxial Stress States

In this paper, failure test results of brick masonry and concrete under biaxial stress state, and of concrete under triaxial stress state, are analyzed. In particular, in the biaxial compression stress state masonry is found to behave as an isotropic material. The pertinent failure interaction curve in terms of principal stress components can be expressed by an ellipse or a parabola. Because masonry can be conceived as a conglomerate material, as a concrete, formed by coarse aggregates (bricks) and cement paste (mortar joints), a generalized failure criterion in the form of an elliptical curve valid both for masonry and concrete in compression biaxial state is provided. In the case of the triaxial compression stress state, from an analysis performed on the test results available for concrete, a prediction of the hydrostatic compressive strength is derived, and a possible form of the limit surface in the principal stress space is hypothesized.

Dynamic plastic response of a circular plate based on unified strength theory

The study and design of structures under dynamic loads require a knowledge of the plastic response and deformation behavior under impact loading. The calculations of dynamic plastic response of structures are useful for the design and investigation of colliding vehicle, engine and various impacting structures. The unified solutions of dynamic plastic load-carrying capacities, moment fields and velocity fields of a simply supported circular plate are introduced. The strength is different in tension and compression and the effect on the yield criteria is taken into account by using the unified strength theory. Upper bound and lower bound plastic responses of the plate, under moderate partial uniformly distributed impulsive loading, are obtained. The static and kinematical admissibility of the dynamic plastic solutions are discussed. The unified solutions of the static plastic load-carrying capacities, moment fields and velocity fields of a simply supported circular plate are also obtained according to the dynamic solutions in this paper. The solutions are suitable for many materials with or without different strengths in tension and compression and the effect of intermediate principal stress. The solutions based on the Tresca, the von Mises, the Mohr–Coulomb theory, and the twin-shear strength theory, as well as the unified yield criterion, are all the special cases of the unified solutions. The influences of the coefficient of failure criteria, b, and tension-compression strength ratio, α, on the dynamic and static solutions, are investigated. It is shown that the effects of different strengths in tension and compression and yield criteria on the dynamic load-carrying capacity are greater than in the static plastic limit state.

Advances in strength theories for materials under complex stress state in the 20th Century

It is 100 years since the well-known Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including metallic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a brief discussion of the computational implementation of the strength theories and multi-axial fatigue.

Limit angular velocity of rotating disc with unified yield criterion

Plastic limit analysis of a rotating solid or annular disc with variable thickness is presented in terms of a unified yield criterion (UYC). Stress distributions of the discs in plastic limit state corresponding to different yield curves are deduced. Upper and lower bounds of the plastic limit solutions are derived by selecting a weighting coefficient in the unified yield criterion. Stress redistribution is solved when the stress field violates yield criterion locally. Limit angular velocity as well as the stress distributions with respect to three special criteria, namely the Tresca criterion, the Mises criterion (close form solution) and the Yu criterion are illustrated and compared. The influences of yield criterion as well as the thickness on plastic limit solution of a rotating disc are demonstrated and discussed.