On thermodynamic yield criteria

Summary It is shown that a thermodynamic yield criterion, previously proposed by the author for a specific model of viscoplasticity, may be derived from the Clausius-Planck inequality for a very general model of plasticity, rate-dependent or rate-independent, provided only that a flow rule (as defined in the paper) exists. Special cases of the yield criterion thus derived include the Schmid law and the von Mises criterion. Moreover, under appropriate assumptions the thermodynamic yield stress may be identified with the Frank-Read source activation stress.

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Thermodynamische Fließkriterien

Zusammenfassung Es wird gezeigt, daß ein thermodynamisches Fließkriterium, das vom Autor in früheren Veröffentlichungen für ein besonderes viskoplastisches Modell vorgeschlagen wurde, aus der Clausius-Planck-Ungleichung für ein sehr allgemeines Modell der Plastizität hergeleitet werden kann, sei es geschwindigkeitsabhängig oder-unabhängig, wobei es nur eine Fließregel, wie es in dieser Arbeit definiert wird, geben darf. Spezielle Fälle dieses solcherart hergeleiteten Fließkriteriums beinhalten das Gesetz von Schmid und die von-Mises-Bedingung. Darüber hinaus wird unter geeigneten Annahmen die thermodynamische Fließspannung identisch mit der für die Aktivierung der Frank-Read-Quelle notwendige Spannung.

     

Approximate yield criteria for anisotropic porous ductile sheet metals

An approximate macroscopic yield criterion for anisotropic porous sheet metals is developed under plane stress conditions in this paper. The metal matrices are assumed to be rigid perfectly plastic and incompressible. The Hill quadratic and non-quadratic anisotropic yield criteria are used to describe the matrix normal anisotropy and planar isotropy. The voids in sheet metals are assumed in the form of through-thickness holes. Under axisymmetric loading, a closed-form upper bound macroscopic yield criterion is derived as a function of the anisotropy parameter R, defined as the ratio of the transverse plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial loading conditions. The plane stress upper bound solutions for different in-plane strain ratios can be fitted well by the closed-form macroscopic yield criterion.     

Statistical criteria of yield for various mechanisms of shear formation

Statistical criteria of the start of macroyield for various mechanisms of shear formation, including the correlation coefficient of tangential microstresses, which makes it possible to take into consideration the mutual influence of the single crystalline grains, are formulated for a model of a polycrystalline material, a microinhomogeneous medium possessing local anisotropy of mechanical properties and consisting of grains with a cubic type of crystalline lattice. Known criteria of strength are compared and it is shown that they are particular cases of the proposed statistical criteria for certain values of this correlation coefficient.Translated from Problemy Prochnosti, No. 3, pp. 46–52, March, 1990.     

On yield criteria in plasticity coupled with damage

The coupling of elasto-plasticity and damage is still the subject of many papers, namely in the construction of evolution laws for internal parameters. In this paper we propose to partly overcome some difficulties by using the only basic fact that a plastic-damaged body is made up of two physical constituents, namely the matrix material and the micro-defects. The elasto-plastic matrix material is the resisting skeleton connecting the elements of the body and the micro-defects bring their own contributions to reversible and irreversible strains. Naturally strong couplings exist between the stress states of the body and the matrix material. These considerations will lead to generalisations and new formulations of the so-called equivalence principles and a new equivalence principle will be proposed. Finally, concerning the irreversible strains due to both plasticity of the matrix and growing of micro-defects, we will prove that yield conditions must be used simultaneously on the body as well as on the matrix, leading to some non-smooth resultant yield-damage surface. The modified Gurson model for porous material is then analysed in order to illustrate this last point. In this paper, large strains are considered, but time-dependant plasticity and thermal effects are excluded.     

Evaluation of yield criteria for forming simulations based on residual stress measurement

Process induced anisotropy in sheet metal is accounted for in analytical modeling by anisotropic yield criteria. The suitability of a yield criterion for predicting sheet metal forming process is generally validated by way of its ability to predict surface strains. However, the sensitivity of surface strains to yield criteria is dependent upon strain modes, with plane strain mode exhibiting higher sensitivity. To eliminate dependency on strain modes, stresses are used to evaluate yield criteria, since forming stresses are less sensitive to strain modes. In the study, the residual stresses remaining in a hemispherical cup formed in plain strain mode is predicted using Hill48 and Barlat89 criteria. The residual stresses are experimentally characterized by using X-Ray diffraction method. Suitable yield criterion for forming simulation is validated based on the correlation of theoretical predictions with experimental residual stress values.     

On yield criteria and incipient plastic motion of soils

Summary The general tensorially linear relation between the stress and the strain rate tensors is studied in order to specify the independent material functions describing the kinematics and the bearing capacity of isotropic soils. It is found that the plastic dilatation remains indeterminate at linear yield loci. A general tensorially linear form of the flow law is obtained and its relation to the associated flow law is indicated.

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Zusammenfassung Die allgemeine lineare Tensorbeziehung zwischen Spannung und Verzerrungsgeschwindigkeit wird untersucht, um die unabhängigen Materialfunktionen, die die Kinematik und die Tragfähigkeit isotroper Böden beschreiben, zu spezifizieren. Es ergibt sich, daß die plastische Volumsdilatation auf linearen Fließflächen unbestimmt bleibt. Eine allgemeine lineare Tensorbeziehung des Fließgesetzes wird hergeleitet; seine Beziehung zum zugeordneten Fließgesetz wird aufgezeigt.

     

On distortion of tensor and yield criteria of granular materials

The distortion of tensor defined by use of normals on the tensor ellipsoid and the mean distortion are introduced. It is explained that the distortion represents the unit shear strain for the finite strain tensor, and the shear-normal stress ratio for the stress tensor. The spatial mobilized plane which plays a very important role in the mechanics of granular materials is regarded as a plane on which the distortion of stress tensor coincides with its mean distortion, and the yield criteria of granular materials are considered applying the concept of the distortion of stress tensor.     

Comparison of different yield criteria in various deep drawn cups

The aim of the study is to evaluate the performance of three recent yield criteria namely; BBC2008-8p, Yld2003-8p, Hu2003 through the simulation of the hemispherical, cylindrical and square cup drawing processes by comparing the results with the ones obtained by using the von Mises criterion for the isotropic, kinematic and combined hardening and the Hill’48 criterion. For this purpose, two different sheet materials, SS304 stainless steel and DKP6112 steel, and various punch travels were used in the simulations and experimental phases of this study. The BBC2008-8p, Yld2003-8p and Hu2003 models were implemented to the ABAQUS software through the user material subroutine VUMAT. The thickness strain distributions obtained from the simulations were compared with the experimental results to analyze the validity of the three aforementioned criteria. Compared with the other models, the material behavior in deep drawing cases of this study is better predicted with more recent models, namely BBC2008-8p, Yld2003-8p and Hu2003, which include anisotropy parameters found from uniaxial and biaxial tension tests.     

Macroscopic yield criteria for ductile materials containing spheroidal voids: An Eshelby-like velocity fields approach

Making use of limit analysis theory, we derive a new expression of the macroscopic yield function for a rigid ideal-plastic von Mises matrix containing spheroidal cavities (oblate or prolate). Key in the development of the new criterion is the consideration of Eshelby-like velocity fields which are built by taking advantage of the solution of the equivalent inclusion problem in which the eigenstrains rate are unknown for the plasticity problem. These heterogeneous trial velocity fields contain non-axisymmetric components which prove to be original in the context of limit analysis of hollow spheroid. After carefully computing the macroscopic plastic dissipation and implementing a minimization procedure required by the use of the Eshelby-like velocity fields, we derive, for the porous medium, a two-field estimate of the anisotropic yield criterion whose closed-form expression is provided. This estimate is compared to existing criteria based on limit analysis theory. Interestingly, in contrast to these criteria, the new results predict a significant effect of shear loadings in the particular case of ductile materials weakened by penny-shaped cracks.     

Assessment on the performance of distinct stress integration algorithms for complex non-quadratic anisotropic yield criteria

In this work, three distinct return mapping algorithms are presented and analyzed in detail: (i) a semi-explicit algorithm that accounts for the sub-incrementation technique, which reduces to (ii) a fully-explicit algorithm and, finally, (iii) a semi-implicit algorithm,. In order to describe the complex anisotropic behaviour of some metals, such as aluminium alloys, two non-quadratic anisotropic yield criteria were implemented: the Yld91 and Yld2004-18p. The performance of the developed algorithms is inferred in a series of sheet metal forming benchmarks and the quality of the results is assessed when compared to experimental results presented in the literature. The numerical simulations show that the semi-implicit algorithm is quite efficient with the von Mises yield criterion. However, when anisotropy is taken into account, the algorithm requires several iterations to return the stresses to the yield surface, particularly when the stresses are located at corner regions of that surface. The semi-explicit algorithm proved to be the most robust and efficient algorithm with anisotropic yield criteria. The good agreement between the experimental data and the obtained numerical results demonstrate the high efficiency of the presented algorithms and the ability of the anisotropic criteria to predict the material’s complex anisotropic behaviour.     

A comparative study of the yield criteria applicable to replicated foams

In this article, first some published evidence for yielding of aluminum and polymeric replicated foams and a numerical study on regular porous structures are revisited in which a kind of twist in the shape of yield surface along the hydrostatic axis was reported. Next, motivated by this observation, some existing appropriate yield functions and a new extended generalized failure criterion capable of capturing this effect are presented. Finally, using the experimentally measured yield clouds of aluminum replicated foams from the literature, the efficiency, inherent features, and limitations of these criteria are thoroughly assessed, compared, and discussed.     

The plastic deformation of oriented polypropylene: tensile and compressive yield criteria

Polypropylene, oriented by hot-drawing, has been deformed in tension and compression, at various angles to the initial draw direction. The behaviour in tension is described well by a three-part criterion of the type applied in previous work to fibre-composites [8, 9]. The Hill-von Mises treatment of the plasticity of an anisotropic metal, which has been previously extended successfully to polymers [1], can be applied to describe the tensile yield stresses but is unsatisfactory in its prediction of the form of the strain in polypropylene. In compression, the variation of the yield stress with the angle of the stress axis is much less than in tension, and the modes of deformation are different from those operating in tension at the same angle. In particular, compressing at right angles to the molecules produces shear in a direction normal to the molecules (transverse shear). The critical stress for transverse shear in compression is approximately the same as the critical stress for shear parallel to the molecules in tension.     

Polymeric antimicrobial N-halamine epoxides

A new N-halamine copolymer has been prepared, characterized, and evaluated for antimicrobial efficacy, stability toward hydrolyses, and stability toward UVA degradation when covalently bound to cellulose fibers. A copolymer of 3-chloro-2-hydroxypropylmethacrylate and glycidyl methacrylate was coated onto cotton, and, after curing, was treated with an aqueous solution containing the potassium salt of 5,5-dimethylhydantoin to form a coating which became antimicrobial upon exposure to househod bleach (sodium hypochlorite). The coating inactivated S. aureus and E. coli O157:H7 within minutes of contact time and was quite stable toward washing and UVA photodegradation.     

Pyramidal nanostructures of zinc oxide

Zinc oxide (ZnO) nanostructures have been prepared by pulsed laser deposition of the oxide onto Si(100) substrate at 600 degrees C. An examination of the morphology using atomic force microscopy and scanning electron microscopy reveals well formed pyramidal structures consistent with the growth habit of ZnO. A domain matched epitaxy across the interface makes the ZnO pyramids orient along the axes of Si(100) surface. The pyramidal nanostructures signify an intermediate state in the growth of hexagonal nanorods of ZnO. The hardness of the nanostructures as well as their response to oxygen gas have been investigated using nanoindentation and conducting probe methods respectively. ZnO nanostructures are much harder than their bulk. The hardness of ZnO pyramids obtained by nanoindentation is 70 +/- 10 GPa which is about one order more that of bulk ZnO. Besides, the nanostructures exhibit high sensitivity towards oxygen. A 70% increase in the resistance of ZnO nanostructures is observed when exposed to oxygen atmosphere.     

屈服准则对不锈钢弯管变形预测精度影响

通过XRD衍射及不同方向单向拉伸试验验证,经过多道次拉拔生产出的304奥氏体不锈钢管材存在有明显的各向异性现象.采用Mises各向同性、Hill1948和Barlat1991各向异性屈服准则对不锈钢弯管过程进行有限元模拟,分析弯曲后管材内外侧壁厚分布、弯曲角度及管坯截面椭圆度的变化规律,通过模拟与实验结果对比发现,当实验数据较少时,采用Hill1948各向异性屈服准则,能够很好预测304奥氏体不锈钢管材弯曲成形过程,而Barlat1991各向异性屈服准则中的一些参数经过近似后,对成形行为的预测精度明显降低.     

Effect of different yield criteria on prediction of wrinkling initiation of interstitial-free galvanized steel sheet

Thin interstitial-free (IF) galvanized steel sheets have great usage in auto industry due to their high formability and corrosion resistance. However presence of wrinkle waves in deep drawn parts of thin IF steel sheets is a common challenging issue. Achieving a reliable method to predict the wrinkling onset enables the manufacturers to avoid wrinkling by modification of forming parameters. In the present study, sidewall wrinkling of an IF-galvanized steel sheet was both analytically and experimentally examined during a conical cup wrinkling test. Using an energy method approach together with a newly developed deflection function, Hosford and Hill-1948 yield criteria were employed to predict the critical values of stress and cup height at the onset of wrinkling. According to the obtained results, applying Hill-1948 yield criterion resulted in prediction of wrinkling onset closer to the experimental value than Hosford yield criterion. It was also found that the newly presented deflection function has a great suitability for prediction of the real status of wrinkling phenomenon.