scholarly journals The roles of yield function and plastic potential under non-associated flow rule for formability prediction with perturbation approach

2020 ◽  
Vol 967 ◽  
pp. 012027
Author(s):  
Q Hu ◽  
J W Yoon
Keyword(s):  
Yield Function ◽  
Flow Rule ◽  
Perturbation Approach ◽  
Plastic Potential ◽  
Formability Prediction ◽  
Associated Flow Rule

scholarly journals An Evolutionary Yield Function Model Based on Plastic Work and Non-Associated Flow Rule

Metals ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 611 ◽  
Author(s):  
Taejoon Park ◽  
Fadi Abu-Farha ◽  
Farhang Pourboghrat
Keyword(s):  
Yield Stress ◽  
Stress Function ◽  
Biaxial Tension ◽  
Yield Function ◽  
Plastic Work ◽  
Constitutive Law ◽  
Flow Rule ◽  
Tension Tests ◽  
Plastic Potential ◽  
Associated Flow Rule

A constitutive law was developed based on the evolutionary yield function to account for the evolution of anisotropy induced by the plastic deformation. For the effective description of anisotropy, the yield stress function and plastic potential were separately defined based on the non-associated flow rule. In particular, for the description of the equivalent status, the accumulated plastic work was employed as an alternative to the accumulated plastic strain. Numerical formulations based on the plastic work were also derived in case the hardening rule, as well as the evolution of the plastic potential and yield stress function, were defined in terms of the plastic work. The developed constitutive law was characterized using the mechanical properties of the multi-phase BAO QP980 steel and niobium sheets at room temperature. From the uniaxial tension tests and the balanced biaxial tension test, separate sets of anisotropic coefficients for each of the plastic potential and yield stress functions were obtained as a function of the plastic work. By comparing with non-evolving yield functions, the importance of the developed constitutive law to properly describe the evolution of the plastic potential and yield function were validated.

scholarly journals A Framework for Versatile Shape of Yield Surfaces for Structured Aniso-tropic Soft Soils

2016 ◽  
Author(s):  
Nallathamby Sivasithamparam ◽  
Jorge Castro
Keyword(s):  
Yield Surface ◽  
Earth Pressure ◽  
Type Model ◽  
Flow Rule ◽  
Lateral Movement ◽  
Plastic Potential ◽  
Yield Surfaces ◽  
Anisotropic Clays ◽  
Associated Flow Rule ◽  
Cam Clay

A framework based on logarithmic contractancy is proposed to produce versatile shapes of yield surfaces for structured anisotropic clays. The recently proposed constitutive model (E-SCLAY1S) is an extension of existing model called S-CLAY1S, which is a Cam Clay type model that accounts for anisotropy and structure. A new parameter called contractancy parameter is introduced to control the shape of the yield surface as well as the plastic potential (as an associated flow rule is applied). This new parameter can be used to fit the coefficient of earth pressure at rest, the undrained shear strength or the stiffness under shearing stress paths predicted by the model. The model predicts the uniqueness of the critical state line and its slope is independent of the contractancy parameter. The effect of the shape of the yield surface was investigated on computed results of a benchmark embankment constructed on Bothkennar (Scotland) clay by employing the E-SCLAY1S model as a user-defined soil model into the PLAXIS finite element code. The results demonstrate that the contribution of the shape of yield surface (logarithmic contractancy parameter) have a relatively large effect on lateral movement of subsoil beneath the toe of the embankment compared to the settlement of subsoil at the centre of the embankment.

A Comparative Study on the Formability Prediction of Steel Sheets by Anisotropic Models Based on Associated Flow Rule and Non-Associated Flow Rule

2015 ◽  
Vol 651-653 ◽  
pp. 150-155 ◽  
Author(s):  
Jun He Lian ◽  
Deok Chan Ahn ◽  
Dong Chul Chae ◽  
Sebastian Münstermann ◽  
Wolfgang Bleck
Keyword(s):  
Comparative Study ◽  
Transverse Direction ◽  
Steel Sheet ◽  
Rolling Direction ◽  
Tensile Tests ◽  
Biaxial Stress ◽  
Flow Rule ◽  
Anisotropic Models ◽  
Formability Prediction ◽  
Associated Flow Rule

A comparative study on the formability prediction of a ferritic steel sheet by anisotropic models based on associated flow rule and non-associated rule is carried out. The uniaxial tensile tests along seven directions of the sheet from rolling direction to transverse direction with an interval of 15° are performed for the anisotropic yield stress and r-value. For the biaxial stress state, both bulge test and punch test are performed. The BBC2003 based on the associated flow rule is employed and its anisotropic parameters are calibrated to the yield stresses and r-values from the tensile tests along rolling direction, transverse direction and diagonal direction and the biaxial test. The non-associated quadratic Hill48 model is also calibrated to the same set of experimental data. Similar level of the predicative capability on the yield and plastic deformation directionality by the associated and non-associated based models is observed. With the common basis on the anisotropic plasticity characteristics, they are combined with the Marciniak–Kuczynski (MK) model to predict the formability of the steel sheet and distinct difference in the prediction is observed between the two models.

scholarly journals Application of an Evolving Non-Associative Anisotropic-Asymmetric Plasticity Model for a Rare-Earth Magnesium Alloy

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1013 ◽  
Author(s):  
Armin Abedini ◽  
Cliff Butcher ◽  
Michael Worswick
Keyword(s):  
Plastic Deformation ◽  
Rare Earth ◽  
Magnesium Alloy ◽  
Constitutive Model ◽  
Magnesium Alloys ◽  
Yield Function ◽  
Flow Rule ◽  
Proportional Loading ◽  
Plastic Potential ◽  
Stress States

Magnesium sheet metal alloys have a hexagonal close packed (hcp) crystal structure that leads to severe evolving anisotropy and tension-compression asymmetry as a result of the activation of different deformation mechanisms (slip and twinning) that are extremely challenging to model numerically. The low density of magnesium alloys and their high specific strength relative to steel and aluminum alloys make them promising candidates for automotive light-weighting but standard phenomenological plasticity models cannot adequately capture the complex plastic response of these materials. In this study, the constitutive plastic behavior of a rare-earth magnesium alloy sheet, ZEK100 (O-temper), was considered at room temperature, under quasi-static conditions. The CPB06 yield criterion for hcp materials was employed along with a non-associative flow rule in which the yield function and plastic potential were calibrated for a range of plastic deformation levels to account for evolving anisotropy under proportional loading. The non-associative flow rule has not previously been applied to magnesium alloys which require the use of flexible constitutive models to capture the severe anisotropy and its evolution with plastic deformation. The non-associative flow rule can provide the required flexibility by decoupling the yield function and plastic potential. For the associative flow rule, such flexibility can only be achieved by multiple linear transformations of the stress tensor resulting in expensive models for calibration and simulations. The constitutive model was implemented as a user material subroutine (UMAT) within the commercial finite element software, LS-DYNA, for general 3-D stress states along with an interpolation technique to consider the evolution of anisotropy based upon the plastic work. To evaluate the accuracy of the implemented model, predictions of a single-element model were compared with the experimental results in terms of flow stresses and plastic flow directions under various proportional loading conditions and along different test directions. Finally, to assess the predictive capabilities of the model, full-scale simulations of coupon-level formability experiments were performed and compared with experimental results in terms of far-field load-displacement and local strain paths. Using these experiments, the constitutive model was evaluated across the full range of representative stress states for sheet metal forming operations. It was shown that the predictions of the model were in very good agreement with experimental data.

Prediction of Central Bursting in Drawing and Extrusion of Metals

2004 ◽  
Vol 127 (3) ◽  
pp. 698-702 ◽  
Author(s):  
A. R. Ragab ◽  
S. N. Samy ◽  
Ch. A. R. Saleh
Keyword(s):  
Volume Fraction ◽  
Yield Function ◽  
Void Volume Fraction ◽  
Void Volume ◽  
Process Conditions ◽  
Flow Rule ◽  
Mean Stress ◽  
Band Formation ◽  
Void Shape ◽  
Associated Flow Rule

In this work central bursting in drawing and extrusion of metals is investigated. The analysis is based on a modified stress distribution within the die zone due to Shield (Shield, R. T., 1955, J. Mech. Phys. Solids, 3, pp. 246–258) together with Gurson–Tvergaard’s yield function (Tvergaard, V., 1981, Int. J. Fract., 17, pp. 389–407) and its associated flow rule for voided solids. The effects of hardening and evolution of void shape on void growth are considered. Various fracture criteria are employed to predict the process conditions at which central bursting occurs. The first criterion is due to Avitzur (Avitzur, B., 1968, ASME J. Eng. Ind., 90, pp. 79–91 and Avitzur, B., and Choi, J. C., 1986, ASME J. Eng. Ind., 108, pp. 317–321), the second and simplest criterion is based on vanishing mean stress while a suggested third criterion depends on the current value of the void volume fraction. Two other criteria which are basically due to Thomason’s internal necking condition (Thomason, P. F., 1990, Ductile Fracture of Metals, Pergamon, Oxford) as well as McClintock’s shear band formation criterion are applied (McClintock, F. A., Kaplan, S. M., and Berg, C. S., 1966, Int. J. Fract. Mech., 2, p. 614, and McClintock, F. A., 1968, in Ductility, ASM, Metals, Park, OH). The critical process conditions are predicted and compared with the available experimental data. Comparison showed that predictions based on the vanishing mean stress and the current void volume fraction criteria are closer to experiments than those based on Thomason’s internal necking and McClintock criteria.

scholarly journals Simulation of the micro Single Point Incremental forming process of very thin sheets

2021 ◽  
Author(s):  
Stéphanie Thuillet ◽  
Pierre-Yves Manach ◽  
Fabrice Richard ◽  
Sébastien Thibaud
Keyword(s):  
Incremental Forming ◽  
Single Point ◽  
Small Diameter ◽  
Flow Rule ◽  
Single Point Incremental Forming ◽  
Shear Tests ◽  
Forming Process ◽  
Punch Force ◽  
Plastic Potential ◽  
Associated Flow Rule

The purpose of this paper is to simulate a complex forming process with parameters identified from tensile and shear tests. An elastic-plastic model is retained which combines a Hill’s 1948 anisotropic criterion and plastic potential using a non-associated flow rule. Firstly, a mechanical characterization is made with homogenous tests like tensile and shear tests [1]. On the other hand a process of micro Single Point Incremental forming is simulated [2]. It consists in deforming a clamped blank using a hemispherical punch which has a small diameter compared to the blank dimensions. From a small-size sheet of 0.2 mm thick, a square-based pyramid is obtained incrementally, with a define height path and advanced speed, by a tool instrumented to measure the forming force, which deforms locally the material. It is shown that the non-associated flow plasticity model leads to a good agreement between experimental and numerical results for the evolution of the punch force during the process.

Application of Associated and Non-Associated Flow Metal Plasticity for F.S.S Sheet

2021 ◽  
Vol 406 ◽  
pp. 473-480
Author(s):  
Oualid Chahaoui ◽  
Houssem Soltani ◽  
Nadjoua Matougui
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Mechanical Anisotropy ◽  
Flow Rule ◽  
Plastic Behavior ◽  
Sheet Plane ◽  
Yield Criteria ◽  
Plastic Potential ◽  
Associated Flow Rule

In the last decade, several phenomenological yield criteria for anisotropic material has been proposed to improve the modeling predictions about sheet metal-forming processes. In regard to this engineering application, two proprieties of models have been used. If the yield function and the plastic potential are not same (not equal), the normality rule is non associative flow rule (NAFR), otherwise, when the stresses yield has been completely coupled to the anisotropic strain rate ratio (plastic potential), is called the associated flow rule (AFR). The non-associated flow rule is largely adopted to predict a plastic behavior for metal forming, accurately about à strong mechanical anisotropy presents in sheet metal forming processes. However, various studies described the limits of the AFR concept in dealing with highly anisotropic materials. In this study, the quadratic Hill1948 yield criteria is considered to predict mechanical behavior under AFR and NAFR approach. Experiment and modeling predictions behaviour of normalized anisotropic coefficient r (θ) and σ (θ) evolved with θ in sheet plane. and the equibiaxial yield stress σb was assumed σb=1 but the rb-values was computed from Yld96 [15].

scholarly journals Plastic Dissipation of the Fractional Plasticity using Modified Cam-Clay Yielding Function

2020 ◽  
Vol 36 (3) ◽  
pp. N1-N7
Author(s):  
P. Tai ◽  
Y. Sun
Keyword(s):  
Flow Rule ◽  
State Dependent ◽  
Plastic Dissipation ◽  
Modified Cam Clay ◽  
Plastic Potential ◽  
Classical Plasticity ◽  
Material State ◽  
Associated Flow Rule ◽  
Fractional Plasticity ◽  
Cam Clay

ABSTRACTSoils usually exhibit state-dependent frictional behaviour that undergoes plastic volumetric deformation. To correctly capture such response under the framework of classical plasticity, a non-associated flow rule using additional plastic potential is inevitably needed. Recently, a novel fractional plasticity (FP) without using plastic potential has been developed, and successfully applied in modelling the state-dependent nonassociated behaviour of soils. However, the energy dissipation characteristics of FP has not been probed in depth. This note examines the plastic dissipation behaviour of FP, when modelling the constitutive behaviour of soils. It is found that the plastic dissipation of FP increases continuously with the shear strain. However, the rate of plastic dissipation depends on the initial material state in relation to the critical state line.

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