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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

Experimental and numerical investigation on plasticity and fracture behaviors of aluminum alloy 6061-T6 extrusions

Zhu Peihua, Zhang Qilin, Xu Hongjun, Ouyang Yuanwen

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 3

13--30

EN

Aluminum alloy 6061-T6 (AA 6061-T6) extrusions have been widely applied in large-span reticulated shells. However, researches on behaviors of the aluminum alloy under large deformation and fracture by means of meso-mechanics are still insufficient. This paper focuses on the plastic and fracture behaviors of AA 6061-T6 extrusions over a wide range of stress states. Experiments on smooth and notched round bars, grooved plates and shear plates are conducted. It is observed that the yield stress decreases as the notch or groove radius decreases. The yield stress under plane strain or pure shear is lower than that under axisymmetric tension. In addition, true stress–true strain data obtained from tensile coupon tests overestimate the hardening behavior at large deformation. To fully describe these experimental observations, a new plastic model considering the pressure dependence, Lode angle effect, and hardening with post-necking correction is proposed. Regarding the ductile fracture, modified Mohr–Coulomb fracture model with damage-induced softening is adopted to predict crack initiation and propagation under different stress states. The material models of plasticity and fracture are numerically implemented into FE code ABAQUS/explicit by the material subroutine VUMAT. It is found that both the overall nominal stress–strain curves and fracture patterns for all specimens are well predicted by the material models. For practical engineering design, recommended reduced values of shear strength and high-triaxiality tensile strength of AA 6061-T6 extrusions are given.

3

Badania plastyczności stopu AlZn5,5MgCu dla warunków przeróbki plastycznej na gorąco

Kułakowska A., Laber K., Dyja H.

Obróbka Plastyczna Metali

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2018

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T. 29, nr 3

213--228

PL

Najbardziej wiarygodnym sposobem wyznaczenia zdolności danego materiału do odkształcenia plastycznego bez naruszenia spójności jest określenie tzw. kryterium plastyczności. Kolejnym parametrem charakteryzującym podatność danego materiału do kształtowania plastycznego jest naprężenie uplastyczniające, zależne od odkształcenia, prędkości odkształcenia, temperatury oraz historii przebiegu odkształcenia. Istotny wpływ na plastyczność ma również stan mikrostruktury badanego materiału. W celu jego określenia w zależności od zmieniających się parametrów obróbki cieplno-plastycznej należy wykonać badania dylatometryczne, które umożliwiają wyznaczenie temperatury charakterystycznej badanego materiału oraz pozwalają na ujawnienie procesów zachodzących w jego strukturze podczas kolejnych etapów obróbki cieplno-plastycznej. Zakres przedstawionych w pracy badań obejmował określenie kryterium plastyczności stopu aluminium AlZn5,5MgCu w stanie T6 oraz po wyżarzaniu. Badania te przeprowadzono w statycznej próbie rozciągania w podwyższonej temperaturze, przy zastoso-waniu maszyny wytrzymałościowej Zwick Z/100. W pracy wyznaczono również tem-peraturę rozpuszczania się i wydzielania w badanym materiale związków międzymetalicznych, z wykorzystaniem dylatometru DIL805A/D.Ponadto określono zmiany wartości naprężenia uplastyczniającego badanego materiału w zależności od parametrów odkształcenia oraz opracowano model matematyczny zmian własności reologicznych badanego stopu. Badania krzywych plastycznego płynięcia przeprowadzono w próbie skręcania z zastosowaniem plastometru skrętnego STD 812. Przeprowadzone w ramach pracy badania stanowiły podstawę doboru optymalnych parametrów procesu walcowania badanego stopu w trójwalcowej walcarce skośnej. Na podstawie otrzymanych wyników stwierdzono istotny wpływ parametrów odkształcenia na wartość naprężenia uplastyczniającego badanego stopu aluminium. Stosując operację wyżarzania wsadu z badanego stopu aluminium AlZn5,5MgCu dostarczonego w stanie T6, można poprawić jego właściwości plastyczne, co umożliwia stosowanie większych odkształceń jednostkowych w procesie walcowania. Stwierdzono, że właściwą temperaturą walcowania analizowanego stopu w trójwalcowej walcarce skośnej będzie temperatura powyżej 200°C.

EN

The most reliable method of establishing the ability of a given material to deform plastically, while not losing its integrity, is by determining its so-called yield criterion. Another parameter that describes the susceptibility of a given material to being plastically formed is the yields stress, which is dependent on the strain, strain rate, temperature and the history of deformation. The ductility is also significantly influenced by the microstructural state of the material under examination. In order to determine it as dependent on the varying parameters of thermo-mechanical treatment, it is necessary to perform dilatometric tests to determine the characteristic temperatures of the examined material and to reveal processes occurring within its structure during successive thermo-mechanical treatment stages. The scope of the investigation covered in this study encompassed exa-minations to determine the yield criterion for the AlZn5.5MgCu aluminium alloy in condition T6 and after annealing. These examinations were carried out in static tensile tests at elevated temperature using a Zwick Z/100 testing machine.The temperatures of dissolution and precipitation of intermetallic compounds in the examined material were also determined using a DIL805A/D dilatometer.In addition, the variations in the magnitude of the yield stress of the examined material were determined as dependent on the deformation parameters, and a mathematical model of the rheological properties of the examined alloy was developed. The examination of the plastic flow curves was performed in a torsion test using an STD 812 torsion plastometer. The investigation carried out within the study provided a basis for the selection of the optimal parameters of the process of rolling the examined alloy on a three-high reeling mill. From the obtained results, a significant effect of the deformation parameters on the magnitude of the yield stress of the investigated aluminium alloy has been found. Using the operation of anne-aling the charge of the examined AlZn5.5MgCu aluminium alloy supplied in state T6, its plastic properties can be improved, which will enable larger unit deformation to be used in the rolling process. It has been found that the appropriate temperature of rolling the examined alloy on a three-high reeling mill will be a temperature above 200°C.

4

Propozycja nowego kryterium plastyczności dla blach ortotropowych z uwzględnieniem asymetrii zakresu sprężystego

Szeptyński P., Pęcherski R. B.

Rudy i Metale Nieżelazne

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2012

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R. 57, nr 4

243-250

PL

W artykule przedstawiono propozycję nowego kryterium plastyczności dla blach ortotropowych wykazujących różnicę wytrzymałości przy rozciąganiu i ściskaniu. Nowe kryterium bazuje na energetycznym warunku stanu granicznego dla materiałów anizotropowych zaproponowanym przez Rychlewskiego [2] i łączy się z wprowadzoną przez Burzyńskiego [3] koncepcją zależnych od charakteru stanu naprężenia funkcji określających udział poszczególnych składników rozkładu głównego gęstości energii sprężystej w całkowitej mierze wytężenia materiału. Podano specyfikację kryterium dla wszystkich płaskich symetrii sprężystych. Zaprezentowano ogólną metodę pozyskiwania danych niezbędnych do wyznaczenia parametrów kryterium na podstawie wyników prostych prób wytrzymałościowych - rozciągania, ściskania i ścinania. Wskazano na szczególne konsekwencje w opisie deformacji plastycznej blach w przypadku przyjęcia prawa płynięcia plastycznego stowarzyszonego z zaprezentowanym warunkiem plastyczności.

EN

A new proposition of a yield criterion for orthotropic metal sheets exhibiting the strength-differential effect is presented in the paper. New criterion is based on the energetic limit condition for anisotropic bodies proposed by Rychlewski [2]. It is extended by introduction of a concept of stress state dependent functions defining the contribution of each component of the main elastic energy density decomposition to the total measure of material effort - the concept which was first introduced by Burzyński [3]. Criterion specification for all plane elastic symmetries is given. General method of acquiring the data which are necessary for determination of the criterion parameters basing on simple strength tests - tension, compression, shearing - is presented. Specific properties of the plastic deformation description in case of taking the flow-rule associated with the presented yield criterion are indicated.

5

Yield criterion accounting for the third invariant of stress tensor deviator. Part I. Proposition of the yield criterion based on the concept of influence functions

Nowak M., Ostrowska-Maciejewska J., Pęcherski R. B., Szeptyński P.

Engineering Transactions

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2011

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Vol. 59, iss. 4

273-281

EN

A proposition of an energy-based hypothesis of material effort for isotropic materials ex-hibiting strength-differential (SD) e?ect, pressure-sensitivity and Lode angle dependence is discussed. It is a special case of a general hypothesis proposed by the authors in [11] for anisotropic bodies, based on Burzyński’s concept of influence functions [2] and Rychlewski’s concept of elastic energy decomposition [16]. General condition of the convexity of the yield surface is introduced, and its derivation is given in the second part of the paper. Limit condition is specified for Inconel 718 alloy, referring to the experimental results published by Iyer and Lissenden [7].

6

Hedge's instability mechanics for the prediction of forming limit in sheet metal forming

Hedge G.S., Nataraj J.R., Sridhar R.

Archives of Computational Materials Science and Surface Engineering

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2009

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Vol. 1, nr 3

155-160

EN

Purpose: The purpose of the paper is to investigate the Hegde's instability mechanics for the prediction of forming limit in sheet metal forming. Design/methodology/approach: Hegde's Instability Mechanics (HIM) paves way for explaining the effects of diffuse instability and localization due to necking in sheet metal forming. For different ranges of stress ratios, the ratio of strain differentials has been computed and hence the forming limits are predicted. Findings: Basing the formulation of HIM on the von Misess yield criterion and applying the interface theory (briefed in appendix) the state-of-the-art purpose is deemed to be well served and demonstrated. Interface theory to explain in simple terms, gives the optimal decision variables in an 'n' dimensional hyper-space. The concept of HIM is demonstrated on isotropic and anisotropic materials. The anisotropic materials show better stability than isotropic materials in sheet metal forming. However the geometric instability is analyzed with the assumptions that the thickness stresses are negligible and biaxial state of stress persists in sheet metal forming. Practical implications: The observations are based on the theoretical findings for which the experimental validation exists in the reviewed references. Originality/value: To the sincere knowledge of authors, is both different and unique of its kind in sheet forming mechanics needing horizontal exploration by potential researchers.

7

An energy-based yield criterion for solids of cubic elasticity and orthotropic limit state

Kowalczyk K., Ostrowska-Maciejewska J., Pęcherski R. B.

Archives of Mechanics

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2003

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Vol. 55, nr 5-6

431-448

EN

The aim of the paper is to formulate a particular case of the J. Rychlewski yield condition for anisotropic linear elastic solids with Hooke's law and the limit tensor representing elastic range in the Mises yield condition under the assumption that different symmetry of elasticity tensors and the limit tensor appears. The elasticity tensor C is assumed to have cubic symmetry. The yield condition is based on the concept of stored elastic energy density, the theory of proper elastic states and energy orthogonal stress states developed by J. Rychlewski [1-3]. Three possible specifications of energy-based yield condition for cubic crystals are considered: the criterion based on the total distortion energy, the criterion based on the energy accumulated in the three proper states pertinent to cubic symmetry and the energy based criterion for cubic symmetry in elastic range and orthotropic symmetry in the limit state. Physical motivation, comparison with available experimental results and possible applications in mechanics of anisotropic solids as well as in nanomechanics are discussed.

8

Yield criterion of the softwood under conditions of variable humidity

Kowal M., Mielniczuk J.

Engineering Transactions

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2001

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Vol.49, iss.4

529-535

EN

Wood is a porous material. In a dry state the unit volume of wood consists of water-free volume of the wood substance, the so-called wood skeleton, and of the air-filled pores. The variable humidity produces the internal forces within the loaded wood bulk loading to destruction in the form of loosening wood fibers, cracks and twists. In the paper the yield criterion or the transition of the softwood into the plastic state is discussed. The outset of yielding is examined in accordance with the Hill criterion for anisotropy with various ratios of humidity. The case of plane stress with the orthotropic structure is used as an example for which the material constants are identified, resulting in a special form of the yield criterion.