Study on Yield Function and Plastic Potential Under Non-Associated Flow for Accurate Earing Prediction in Cup Drawing

2015 ◽  
Vol 86 (8) ◽  
pp. 852-860 ◽  
Author(s):  
Mariana Paulino ◽  
Jeong Whan Yoon
Keyword(s):  
Yield Function ◽  
Plastic Potential ◽  
Cup Drawing

Effect of the Yield Stress and r-value Distribution on the Earing Profile of Cup Drawing with Yld2000-2d Yield Function

2010 ◽  
Author(s):  
Yanshan Lou ◽  
Gihyun Bae ◽  
Changsoo Lee ◽  
Hoon Huh ◽  
F. Barlat ◽  
...  
Keyword(s):  
Yield Stress ◽  
Yield Function ◽  
Value Distribution ◽  
R Value ◽  
Cup Drawing

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.

scholarly journals Prediction of Crashworthiness for Extruded Magnesium Materials

2015 ◽  
Vol 651-653 ◽  
pp. 1009-1014
Author(s):  
Dirk Steglich ◽  
X. Tian
Keyword(s):  
Deformation Behaviour ◽  
Compressive Loading ◽  
Yield Function ◽  
Loading Conditions ◽  
Compression Tests ◽  
Axial Deformation ◽  
Strain Anisotropy ◽  
Buckling Modes ◽  
Strength Differential ◽  
Plastic Potential

To assess the crashworthiness of simple wrought magnesium structures, the axial deformation behaviour of different square tubes produced from magnesium alloys AZ31 and ZE10 were numerically investigated under quasi-static compressive loading conditions. Finite-element simulations were conducted to predict and assess the plastic buckling and crush behaviour. The necessary data to determine parameters for the plastic potential were taken from compression tests conducted along different orientations. The yield function Hill48 was selected, despite its inability to capture the strength differential effect. The modelling approach pursued is justified by considering the mechanical loading conditions, the fabrication process of the profiles and its implication on strain anisotropy, balancing achievable accuracy and computational efforts. The simulation results revealed that the material work hardening rates evidenced in uniaxial compression tests influenced the buckling modes as well as the energy dissipation.

Convolute Cut-Edge Design with a New Anisotropic Yield Function for Earless Target Cup in a Circular Cup Drawing

2006 ◽  
Vol 505-507 ◽  
pp. 1297-1302
Author(s):  
Jeong Whan Yoon ◽  
Robert E. Dick ◽  
Frédéric Barlat
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Yield Function ◽  
Single Step ◽  
Anisotropic Model ◽  
Cut Edge ◽  
Anisotropic Yield Function ◽  
Blank Shape ◽  
Cup Drawing ◽  
Element Method

A convolute cut-edge design is performed using FEM (Finite Element Method) for a single step cup drawing operation in order to produce an earless cup profile. Mini-die drawing based on a circular blank shape is initially carried out in order to verify the earing prediction of the Yld2004 anisotropic model (Barlat et al. [1]) for a body stock material. Realistic cup geometry is then employed to design a non-circular convolute edge shape. An iterative procedure based on finite element method is initially used to design a convolute shape for an earless target cup height. A constant strain method is suggested to obtain a new convolute prediction for the next iteration from the current solution. It is proven that Yld2004 model is accurate to predict the anisotropy of the material.

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.

Advanced Anisotropic Damage Model Fully Coupled with Anisotropic Plasticity

2015 ◽  
Vol 784 ◽  
pp. 153-160 ◽  
Author(s):  
Houssem Badreddine ◽  
Khemais Saanouni
Keyword(s):  
Finite Strain ◽  
Plastic Anisotropy ◽  
Consistency Condition ◽  
Yield Function ◽  
Loading Path ◽  
Large Strains ◽  
Anisotropic Damage ◽  
Anisotropic Plasticity ◽  
Plastic Potential ◽  
Fully Coupled

In this work, a thermodynamically-consistent framework is used to formulate a non-associative finite strain anisotropic elastoplastic model fully coupled with anisotropic ductile damage. The finite strain assumption is considered using specific large strains kinematics based on multiplicative decomposition of the total transformation gradient and assuming a small elastic strains. The objectivity principle fulfillment is assumed using the well-known rotating frame formulation. The effective variables are defined to introduce the effect of the anisotropic damage on the other variables through the total energy equivalence assumption. The non-associative plasticity framework, for which equivalent stresses in yield function and in plastic potential are separately defined, allows better plastic anisotropy description. The evolution equations for overall dissipative phenomena are deduced from the generalized normality rule applied to the plastic potential while the consistency condition is still applied to the yield function. Applications are made to an RVE with generic material parameters by considering non-proportional loading paths. For each loading path the effect of the anisotropic plasticity on the damage evolution is studied in the context of finite strains.

Sign in / Sign up

Export Citation Format

Share Document