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.

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].

Stress update algorithm for non-associated flow metal plasticity

2012 ◽  
Vol 3 (2) ◽  
pp. 106-110
Author(s):  
Mohsen Safaei ◽  
Wim De Waele
Keyword(s):  
Plastic Strain ◽  
Yield Stress ◽  
Kinematic Hardening ◽  
Quadratic Function ◽  
Yield Function ◽  
Plastic Strain Rate ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Strain Rate Tensor ◽  
Incremental Change

. In this paper we present the continuum plasticity model based on non-Associated Flow Rule (nonAFR) for Hill’s48 quadratic yield function. In case of non-AFR, Hill’s quadratic function used as plasticpotential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate.In addition, the yield function uses direction dependent yield stress data. Therefore more accuratepredictions are expected in terms of both yield stress and strain ratios at different orientations. Weimplemented a modified version of the non-associative flow rule originally developed by Stoughton [1] intothe commercial finite element code ABAQUS by means of a user material subroutine UMAT. The mainalgorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumesproportional loading cases and therefore only isotropic hardening effect is considered. In our model theincremental change of plastic strain rate tensor is not equal to the incremental change of the compliancefactor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finiteelement simulations with experimentally determined values for deep drawing steel DC06. A criticalcomparison is made between numerical results obtained from AFR and non-AFR based models.

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