Effect of Yield Surface Curvature on Necking and Failure in Porous Plastic Solids

1986 ◽  
Vol 53 (3) ◽  
pp. 491-499 ◽  
Author(s):  
R. Becker ◽  
A. Needleman
Keyword(s):  
Plane Strain ◽  
Volume Fraction ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Ductile Failure ◽  
Isotropic Hardening ◽  
Void Coalescence ◽  
Potential Surfaces ◽  
Plane Strain Tension ◽  
Path Dependent

The effect of material path dependent hardening on neck development and the onset of ductile failure is analyzed numerically. The calculations are carried out using an elastic-viscoplastic constitutive relation that has isotropic hardening and kinematic hardening behaviors as limiting cases and that accounts for the weakening due to the growth of micro-voids. Final material failure is incorporated into the constitutive model by the dependence of the plastic potential on void volume fraction. Results are obtained for both axisymmetric and plane strain tension. Failure is found to initiate by void coalescence at the neck center in axisymmetric tension and within a shear band in plane strain tension. The increased curvature of flow potential surfaces associated with the kinematic hardening solid leads to somewhat more rapid diffuse neck development than occurs for the isotropic hardening solid. However, a much greater difference between the predictions of the two constitutive models is found for the onset of ductile failure.

scholarly journals Prediction of Strain Path Changing Effect on Forming Limits of AA 6111-T4 Based on A Shear Ductile Fracture Criterion

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 546
Author(s):  
Silin Luo ◽  
Gang Yang ◽  
Yanshan Lou ◽  
Yongqian Xu
Keyword(s):  
Ductile Fracture ◽  
Uniaxial Tension ◽  
Plane Strain ◽  
Strain Path ◽  
Fracture Criterion ◽  
Kinematic Hardening ◽  
Isotropic Hardening ◽  
Ductile Fracture Criterion ◽  
Plane Strain Tension ◽  
Strain Paths

Strain path changing is a phenomenon in the stamping of complex panels or multiple-step stamping processes. In this study, the influence of the strain path changing effect was investigated and assessed for an aluminum alloy of 6111-T4 with a shear ductile fracture criterion. Plastic deformation of the alloy was modeled by an anisotropic Drucker yield function with the assumption of normal anisotropy. Then the shear ductile fracture criterion was calibrated by the fracture strains at uniaxial tension, plane strain tension and equibiaxial tension under proportional loading conditions. The calibrated fracture criterion was utilized to predict forming limit curves (FLCs) of the alloy stretched under bilinear strain paths. The analyzed bilinear strain paths included biaxial tension after uniaxial tension, plane strain tension and equibiaxial tension. The predicted FLCs of bilinear strain paths were compared with experimental results. The comparison showed that the shear ductile fracture criterion could reasonably describe the effect of strain path changing on FLCs, but its accuracy was poor for some bilinear paths, such as uniaxial tension followed by equibiaxial tension and equibiaxial tension followed by plane strain tension. Kinematic hardening is suggested to substitute the isotropic hardening assumption for better prediction of FLCs with strain path changing effect.

scholarly journals Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1166
Author(s):  
Stanislav Strashnov ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Plane Strain ◽  
Kinematic Hardening ◽  
Tensile Force ◽  
Plastic Region ◽  
Equivalent Plastic Strain ◽  
Isotropic Hardening ◽  
Finite Plane ◽  
Present Solution ◽  
Bending Under Tension ◽  
Elastic Unloading

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

Plane-Strain Tension Tests on Aluminum Alloy Sheet

1995 ◽  
Vol 117 (2) ◽  
pp. 168-171 ◽  
Author(s):  
Fadi Taha ◽  
Alejandro Graf ◽  
William Hosford
Keyword(s):  
Aluminum Alloy ◽  
Plane Strain ◽  
Yield Criterion ◽  
Alloy Sheet ◽  
Isotropic Hardening ◽  
Aluminum Alloy Sheet ◽  
Strain Measurements ◽  
Plane Strain Tension ◽  
Tension Tests ◽  
High Exponent

A simple way of making plane-strain tension tests on sheet specimens has been developed. This method was used to test sheets of aluminum alloy 2008 T4 and the results were analyzed in terms of a high exponent yield criterion and isotropic hardening. Experimentally measured forces agreed with those calculated from strain measurements using uniaxial tension test curves.

Constitutive Modeling of Creep and Damage Behaviors of the Non-Mises Type for a Class of Polycrystalline Metals

2002 ◽  
Vol 11 (3) ◽  
pp. 223-245 ◽  
Author(s):  
M. Kawai
Keyword(s):  
Hydrostatic Stress ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Irreversible Thermodynamics ◽  
Polycrystalline Materials ◽  
Isotropic Hardening ◽  
Stress Deviator ◽  
Third Invariant ◽  
Scaling Parameters ◽  
Von Mises

Phenomenological constitutive models to describe the creep and damage behaviors that deviate from the von Mises type for a class of polycrystalline materials are developed. Theoretical and empirical approaches are taken to the formulation. The effective stresses that govern the rates of creep and damage are scaled to describe any deviation from the response of the von Mises type. A general form of scaling parameter is proposed which can consider the hydrostatic stress and/or the third invariant of the stress deviator. A kinematic hardening model is first formulated on the basis of irreversible thermodynamics using the scaling parameters for creep and damage. Then, two kinds of empirical basis models are presented for cases of kinematic hardening and isotropic hardening, respectively. The proposed models can describe the primary, secondary and tertiary creep behaviors and distinguish between the creep and damage behaviors under different modes of loading. To illustrate the features of the proposed models, numerical simulations of the unequal creep behaviors under tension, compression, and torsion are carried out and compared with experimental results.

scholarly journals On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

2021 ◽  
Author(s):  
Cyprian Suchocki
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Small Strain ◽  
Cyclic Plasticity ◽  
Isotropic Hardening ◽  
Mapping Algorithm ◽  
Hardening Rule ◽  
Return Mapping ◽  
Cyclic Plasticity Model

AbstractIn this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Use of Plane-Strain Tension and Shear Tests to Evaluate Yield Surfaces for AA1050 Aluminium Sheet

2014 ◽  
Vol 794-796 ◽  
pp. 596-601
Author(s):  
Kai Zhang ◽  
Bjørn Holmedal ◽  
Odd Sture Hopperstad ◽  
Stéphane Dumoulin
Keyword(s):  
Experimental Data ◽  
Plane Strain ◽  
Yield Function ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Shear Tests ◽  
Anisotropic Plasticity ◽  
Type Iii ◽  
Plane Strain Tension ◽  
Force Displacement

Plane-strain tension and shear tests were carried out for a fully annealed AA1050 sheet. The tests were simulated numerically with a commercial finite element method (FEM) code using an anisotropic plasticity model including the Yld2004-18p yield function, the associated flow rule and isotropic hardening. The advanced yield function was calibrated by three different methods: using uniaxial tension data combined with FC-Taylor model predictions of the equibiaxial yield stress and r-value, using 201 virtual yield points in stress space, and using a combination of experimental data and virtual yield points (i.e., a hybrid method). The virtual stress points at yielding were provided by the recently proposed Alamel model with the so-called Type III relaxation (Alamel Type III model). FEM simulations of the tests were then made with parameters of Yld2004-18p identified by these three methods. Predicted force-displacement curves were compared to the experimental data, and the accuracy of the parameter identification methods for Yld2004-18p was evaluated based on these comparisons.

Comparison of Different Constitutive Models in Sheet Metal Forming

2013 ◽  
Vol 554-557 ◽  
pp. 1203-1216 ◽  
Author(s):  
Meriç Uçan ◽  
Haluk Darendeliler
Keyword(s):  
Constitutive Model ◽  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Kinematic Hardening ◽  
Piecewise Linear ◽  
Constitutive Models ◽  
Isotropic Hardening ◽  
Anisotropic Plasticity ◽  
Elastic Plastic

The effects of different constitutive models in sheet metal forming are investigated by considering the cylindrical and square cup drawing and V-bending processes. Numerical analyses are performed by employing eight different constitutive models. These are elastic plastic constitutive model with isotropic hardening, elastic plastic constitutive model with kinematic hardening, elastic plastic constitutive model with combined hardening, power law isotropic plasticity, piecewise linear isotropic plasticity, three-parameter Barlat, anisotropic plasticity and transversely anisotropic elastic plastic models. The simulations are performed for three different materials, St12 steel, Al-5182 aluminum and stainless steel 409 Ni, by using a commercial finite element code. A number of experiments are carried out and the experimental and analytical results are utilized to evaluate the results of simulations.

scholarly journals Evaluation of constitutive models for textured aluminium alloys using plane-strain tension and shear tests

2011 ◽  
Vol 4 (2) ◽  
pp. 227-241 ◽  
Author(s):  
Dasharatha Achani ◽  
Odd-Geir Lademo ◽  
Olaf Engler ◽  
Odd Sture Hopperstad
Keyword(s):  
Plane Strain ◽  
Aluminium Alloys ◽  
Constitutive Models ◽  
Shear Tests ◽  
Plane Strain Tension

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

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