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1

Yield surface characterization for lightweight alloy sheets via an improved combined shear–tension experimental method

Zheng L. H., Wang Z. J., Wan M., Meng Bao

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 2

art. no. e96, 1--17

EN

Combined shear and tension (CST) tests are important experimental methods for characterizing yield surfaces for metal sheets, which is vital to ensure the effectiveness of the constitutive models employed in finite element simulation. However, the existing CST experimental method with a reduced thickness specimen, designed for advanced high strength steel sheets, is not suitable for accurately characterizing yield surfaces for lightweight alloy sheets, such as aluminum alloy sheets. In this paper, an improved experimental method employing CST loading along with an appropriate full-thickness specimen is proposed to address the problem. To establish the proposed experimental method, an appropriate full-thickness specimen is presented through finite element method and combined with a newly developed biaxial testing machine. To verify the effectiveness and feasibility of the improved experimental method, virtual simulations and real experiments on the proposed full-thickness specimen obtained from 6K21-T4 aluminum sheets under different CST loading cases are conducted. Research results show that the yield surfaces of the aluminum alloy sheets between simple shear and plane strain (SSPS) can be described accurately by employing the improved experimental method. In addition, according to the experimental results, the prediction capability of the Yld2000 and Hill48 yield criteria is studied. It is found that the commonly used Yld2000 yield criterion cannot accurately predict the yield behavior of the aluminum alloy sheets under shear-dominant loading.

2

Closed system of coupling effects in generalized thermo-elastoplasticity

Śloderbach Z.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 2

461--483

EN

In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such materials as rocks, soils, concretes and in some metalic materials. In this paper not only the usual postulate of existence of a dissipation qupotential (the Gyarmati postulate) is used to derive the velocity equation. The plastic flow constitutive equations have the character of non-associated flow laws even when the Gyarmati postulate is assumed. In general formulation, the plastic strain rate tensor is normal to the surface of the generalized function of plastic flow defined in the the space of internal thermodynamic forces Π but is not normal to the yield surface. However, in general formulation and after the use the Gyarmati postulate, the direction of the sum of the plastic strain rate tensor and the coupled elastic strain rate tensor is normal to the yield surface.

3

Description of the Yield State of Bioplastics on Examples of Starch-Based Plastics and PLA/PBAT Blends

Fras T., Nishida M., Rusinek A., Pęcherski R. B., Fukuda N.

Engineering Transactions

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2014

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Vol. 62, iss. 4

329–-354

EN

The present work concerns the description of the yield state of biodegradable materials. As examples, biodegradable polymers are chosen – cornpole CRP-M2, starch fatty acid ester, and PLA/PBAT, poly(lactic acid) (PLA) blended with poly(butylene adipate/terephthalate) (PBAT) [1, 2]. These biodegradable, plant-derived bioplastics are a promising alternative to petroleum-based plastics. To describe the onset of plasticity in the bioplastics under discussion, Burzyński ’s hypothesis of material effort has been applied [3, 4]. The applied criteria account for the strength differential effect and for the shear correction resulting from the difference between experimental and theoretical values obtained as a result of the Huber-Mises approach [5, 6]. In general, these properties of yield state are characteristic for polymers. The description of yield state for bioplastics is an issue that has hardly been investigated, which illustrates the novel nature of this paper where this topic is discussed.

4

Elasto-plastic model of unsaturated soil

Fedczuk P.

AGH Journal of Mining and Geoengineering

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2012

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Vol. 36, no. 2

137-144

EN

The paper presents the concept of an elasto-plastic model for partially saturated soil. Elastic properties are described by the classical elastic rule, taking into consideration the effective stresses. Plastic properties are defined by extension of the critical state theory which also takes the suction effect into consideration. The behaviour of soil is described by the extended incremental elasto-plastic constitutive relation (in form "effective stress - strain and suction" relationship). The model operates the equation of the Wheeler and Sivakumar's plastic surface. The generalized hardening rule (for the changing value of suction) connects the increment of the plastic part of the void ratio with stress and suction levels.

PL

W pracy prezentuje się koncepcję sprężysto-plastycznego modelu częściowo nawodnionego gruntu. Sprężyste własności gruntu opisuje klasyczne równanie sprężystości, uwzględniającego efektywne naprężenia. Plastyczne własności definiuje rozwinięta teoria stanu krytycznego uwzględniająca efekt ssania. Zachowanie gruntu opisuje rozszerzone przyrostowe prawo sprężysto-plastyczności (w formie zależności "efektywne naprężenie - odkształcenie i ssanie"). Model operuje zmodyfikowanym równaniem powierzchni plastyczności Wheelera i Sivakumara. Uogólnione prawo wzmocnienia (dla zmiennej wartości ssania) wiąże przyrost plastycznej części wskaźnika porowatości z poziomem efektywnego naprężenia i ssania.

5

Yield criterion accounting for the influence of the third invariant of stress tensor deviator. Part II. Analysis of convexity condition of the yield surface

Szeptyński P.

Engineering Transactions

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2011

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Vol. 59, iss. 4

283-283

EN

General form of yield condition for isotropic and homogeneous bodies is considered in the paper. In the space of principal stresses, the limit condition is graphically represented by a proper regular surface which is assumed here to be at least of C 2 class. Due to Drucker’s Postulate, the yield surface should be convex. General form of convexity condition of the considered surface is derived using methods of differential geometry. Parametrization of the yield surface is given, the first and the second derivatives of the position vector with respect to the chosen parameters are calculated, what enables determination of the tangent and unit normal vectors at given point, and also determination of the first and the second fundamental form of the considered surface. Finally the Gaussian and mean curvatures, which are given by the coefficients of the first and the second fundamental form as the invariants of the shape operator, are found. Convexity condition of the considered surface expressed in general in terms of the mean and Gaussian curvatures, is formulated for any form of functions determining thecharacter of the surface.

6

A graphical approach to yield and boundary surfaces of selected hypoplastic constitutive equations

Sikora Z., Cieśla P.

Archives of Civil Engineering

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2011

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Vol. 57, nr 2

139-151

EN

The article describes how to identify the boundary and yield surface for hypoplastic constitutive equations proposed by Wu, Gudehus and Bauer. It is shown how to identify and plot the surfaces for any equation in this class. Calculation errors are analyzed characteristic for applied set of numerical formulas. In the paper there are computer links to the source code prepared in the MATLAB system, based on instructions in the article. A sample consitutive domains are shown, plotted using the attached computer program.

PL

W artykule przedstawiono sposób wyznaczania powierzchni płynięcia oraz powierzchni granicznej dla przykładowych równań konstytutywnych w ramach teorii hypoplastyczności zaproponowanych przez Wu, Gudehus'a oraz Bauer'a. Pokazano jak wyznaczać i wykreślać obie powierzchnie dynamicznie dla dowolnych równań tej klasy. Przeanalizowano błędy obliczeniowe charakterystyczne dla użytych formuł numerycznych. W pracy podano linki do komputerowych kodów źródłowych przygotowanych w komercyjnym systemie MATLAB, stosujących instrukcje przedstawione w niniejszym artykule. Przedstawiono przykładowe dziedziny równań konstytutywnych narysowanych przy pomocy załączonego programu komputerowego.

7

Applications of the Burzyński hypothesis of material effort for isotropic solids

Frąś T., Pęcherski R. B.

Mechanics and Control

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2010

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Vol. 29, no. 2

45-50

EN

The paper contains a short presentation of main idea of energy-based hypothesis of material effort proposed by Burzyński with discussion of the resulting failure criteria. Some examples illustrating applications of these criteria are discussed and visualizations of limit surfaces in the space of principal stresses are presented.

PL

Praca zawiera krótką prezentację głównej idei energetycznej hipotezy wytężenia zaproponowanej przez Burzyńskiego wraz z dyskusją wynikających z niej kryteriów wytrzymałości. Przedstawiono kilka przykładów zastosowań tych kryteriów wraz z wizualizacją granicznych powierzchni w przestrzeni naprężeń głównych.

8

Applications of Burzyński failure criteria. Part I. isotropic materials with asymmetry of elastic range

Frąś K., Kowalewski Z. L., Pęcherski R. B., Rusinek A.

Engineering Transactions

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2010

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Vol. 58, iss. 1/2

31-63

EN

The main idea of energy-based hypothesis of material effort proposed by Burzyński is briefly presented and the resulting failure criteria are discussed. Sonic examples, based on the own studies, which depict applications of these criteria are discussed and visualizations of limit surfaces in the spacce of principal stresses are presented.

9

Material responses to the laboratory simulation of complex cyclic loadings

Szymczak T., Kowalewski Z. L., Rutecka A.

Journal of KONES

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2008

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Vol. 15, No. 3

509-516

EN

The paper presents investigations identifying an influence of complex cyclic loading controlled by the strain signals on the selected mechanical properties of the 2024 aluminium alloy. Investigations of proportional and non-proportional loading paths in the form of square and circle were carried out at room temperature using thin-walled tubular specimens enabling realisation of complex stress states due to acting of axial force and twisting moment. The hardening effect of the material due to cyclic loading was observed on the basis of: stress responses into the strain controlled loading programme; hysteresis loop variations and amounts of stress amplitude. In the case of the non-proportional cyclic loading an additional hardening effect was identified. Second-order effects, which allow better understanding of the influence of proportional and non-proportional loading paths on mechanical behaviour of engineering materials, were identified. In the case of the circular loading path a delay of the maximum stress signals with respect to strain ones is demonstrated. For the square loading path a softening effect was observed. It is reflected by the rapid stress drop on this direction, which is perpendicular to that where the stress level begins to turn back. The yield surface approach is also applied in order to assess the mechanical properties variations due to cyclic loading of the material.

10

Experimental method of defining biaxial fatigue properties of elastic-plastic construction materials. Part 2 - Experimental research

Cichański A., Sempruch J.

Journal of Theoretical and Applied Mechanics

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2005

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Vol. 43 nr 1

65--80

EN

The paper is concerned with the authors' own method of defining biaxial fatigue properties of elastic-plastic construction materials, for which a theoretical basis was formulated before (Cichański and Sempruch, 2005). In the present paper, results of experimental investigations (divided into preliminary and main research) appropriate for the proposed method are described. In the preliminary research phase, an experimental verification of major assumptions and numerical verification of conditions on preparation of test specimens were carried out. During the main research phase, model parameters of plastic and fatigue properties were described and the evaluation of the proposed model (Cichański and Sempruch, 2005) was done.

PL

Niniejsza praca jest zorientowana na własną metodę wyznaczania dwuosiowych własności zmęczeniowych sprężysto-plastycznych materiałów konstrukcyjnych, dla której podstawy teoretyczne zostały sformułowane wcześniej (Cichański i Sempruch, 2005). W prezentowanej pracy przedstawiono wyniki badań doświadczalnych właściwych dla zaprezentowanej metody, podzielonych na badania wstępne i główne. Na etapie badań wstępnych wykonano doświadczalną weryfikację najważniejszych założeń metody oraz numeryczną weryfikację warunków przygotowania próbek do badań. Na etapie badań zasadniczych wyznaczono modelowe parametry opisu własności plastycznych i zmęczeniowych oraz dokonano oceny modelu zaproponowanego w Cichański i Sempruch (2005).

11

Experimental method of defining biaxial fatigue properties of elastic-plastic construction materials. Part 1 - model formulation

Cichański A., Sempruch J.

Journal of Theoretical and Applied Mechanics

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2005

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Vol. 43 nr 1

51--64

EN

The paper presents formulation of a method of biaxial fatigue testing in conditions of cyclic uniaxial loads with the use of specimens made of a material characterised by controlled mechanical properties. The origin for the paper was a successful attempt to adapt the plastic potential for describing biaxial fatigue strength made by Troost and El.-Magd (1974) in relation to the "stress anisotropy" effect, pointed out by him. On the basis of the carried-out reasoning, a model formulation of the allowable stress amplitude was introduced, which is a formalised record of the relations between the fatigue stress amplitudes and the yield stresses. The article suggests an experimental method of defining the appointed model parameters, which is a development of Szczepiński's method (Szczepiński, 1963).

PL

W artykule przedstawiono sformułowanie metody badania dwuosiowego zmęczenia w warunkach cyklicznych obciążeń jednoosiowych z wykorzystaniem próbek wykonanych z materiału o kontrolowanych własnościach mechanicznych. Jako genezę pracy wskazano udaną próbę adaptacji potencjału plastycznego do opisu dwuosiowego zmęczenia wykonaną przez Troosta (Troost i El.-Magd, 1974) w odniesieniu do wskazanego przez niego efektu "anizotropii naprężeniowej". Na podstawie przeprowadzonego rozumowania wyprowadzono modelowe ujęcie dopuszczalnej amplitudy naprężeń będące sformalizowanym zapisem zależności amplitudy naprężeń zmęczeniowych od naprężeń uplastyczniających. W pracy zaproponowano doświadczalną metodę wyznaczania parametrów wskazanego modelu, będącą rozwinięciem metody Sczepińskiego (Szczepiński, 1963).

12

An engineering methodology taking into account the effect of local damage on the global behavior of surface cracked shell structures

Chiesa M., Ostby E., Skallerud B., Thaulow Ch.

International Journal of Applied Mechanics and Engineering

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2002

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Vol. 7, no 1

267-291

EN

The line spring finite element is a versatile numerical tool for performing engineering fracture mechanics analysis of surface cracked shells. An accurate yield surface of plane strain single-cracked (SEC) specimens having shallow, as well as deep, cracks is presented here. The meaning of the J-integral when crack growth occurs is discussed. The J-integral is regarded as a sort of accumulated measure of the global deformation in the ligament. The complete Gurson is used in order to support our observations. Furthermore a crack propagation law relating a local criterion for crack growth to the global deformation field is outlined. A methodology to link micro-mechanically based crack growth simulations with line spring analysis is proposed by suggesting an alternative way to calculate the J-integral from the line spring framework. Some details of the numerical implementation of the backward Euler integration scheme at the integration point of the line spring element in order to account for plasticity are presented here for a bilinear material model. An efficient numerical procedure, based on a proposed crack growth law, is also presented in order to account for ductile crack propagation. A numerical case is considered in order to show that the proposed procedure is suited to the purpose.