Hardening Law

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Kwansoo Chung - One of the best experts on this subject based on the ideXlab platform.

  • Hardening Law for evolution of yield surface
    2018
    Co-Authors: Kwansoo Chung, Myounggyu Lee
    Abstract:

    Inthe past few decades, a few experimentations have been conducted to better understand the evolution of the yield surface during plastic deformation.

  • inverse characterization method for mechanical properties of strain strain rate temperature temperature history dependent steel sheets and its application for hot press forming
    Metals and Materials International, 2015
    Co-Authors: Hyunki Kim, Dongun Kim, Kanghwan Ahn, Donghoon Yoo, Hyunsung Son, Gyosung Kim, Kwansoo Chung
    Abstract:

    In order to measure the flow curves of steel sheets at high temperatures, which are dependent on strain and strain rate as well as temperature and temperature history, a tensile test machine and specimens were newly developed in this work. Besides, an indirect method to characterize mechanical properties at high temperatures was developed by combining experiments and its numerical analysis, in which temperature history were also accounted for. Ultimately, a modified Johnson-Cook type Hardening Law, accounting for the dependence of Hardening behavior with deterioration on strain rate as well as temperature, was successfully developed covering both pre- and post-ultimate tensile strength ranges for a hot press forming steel sheet. The calibrated Hardening Law obtained based on the inverse characterization method was then applied and validated for hot press forming of a 2-D mini-bumper as for distributions of temperature history, thickness and hardness considering the continuous cooling transformation diagram. The results showed reasonably good agreement with experiments

  • consistency condition of isotropic kinematic Hardening of anisotropic yield functions with full isotropic Hardening under monotonously proportional loading
    International Journal of Plasticity, 2013
    Co-Authors: Kwansoo Chung, Taejoon Park
    Abstract:

    For the combined type isotropic–kinematic Hardening Law to account for the Bauschinger, transient and permanent softening behaviors observed in reverse loading, formulations have been initially developed for isotropic yield functions, mainly based on the von Mises criterion, and then later extended for anisotropic yield functions. Among the efforts to introduce anisotropic yield functions to the combined type Hardening formulation, however, some inconsistency has been encountered in manipulating the kinematic Hardening Law, especially for the nonlinear type Law, even though their von Mises yield function versions have been consistent. Therefore, theoretical clarification and clearance of such inconsistency were attempted in this work by imposing the following consistency condition: the combined type Hardening Law is expected to behave the same as the full isotropic Hardening for monotonously proportional loading, regardless of anisotropic yield functions which are coupled with the combined type Hardening Law. An example to account for the anisotropic Hardening of an anisotropic yield function utilizing the combined type Hardening Law, but for which the consistency condition was partially released, was also demonstrated.

  • non associated flow rule with symmetric stiffness modulus for isotropic kinematic Hardening and its application for earing in circular cup drawing
    International Journal of Solids and Structures, 2012
    Co-Authors: Taejoon Park, Kwansoo Chung
    Abstract:

    Abstract Under a standard derivation, the stiffness modulus for the non-associated flow rule is asymmetric since its plastic potential (for the plastic strain increment under the normality rule) differs from the plastic yield stress function (to define the elastic range). A new formulation was developed in this work, which leads to the symmetric stiffness modulus for the non-associated flow rule, under the framework of the combined isotropic-kinematic Hardening Law for generalization purposes. As for its application, the non-quadratic Yld2000-2d ( Barlat et al., 2003 ) function (and Hill’s (1948) function for comparison) was utilized to validate the formulation for earing in circular cup drawing of AA2090-T3 and AA5042 sheets, which successfully represented 6 and 8 ears, respectively.

  • formability evaluation of friction stir welded 6111 t4 sheet with respect to joining material direction
    International Journal of Mechanical Sciences, 2010
    Co-Authors: Dae Yong Kim, Chongmin Kim, Wonoh Lee, Junehyung Kim, Kwansoo Chung
    Abstract:

    Abstract In order to evaluate the formability of friction stir welded (FSW) automotive TWB (tailor-welded blank) sheets with respect to base material direction, the aluminum alloy 6111-T4 sheet was joined with three different types of combination: RD||RD, TD||RD, TD||TD (Here, RD and TD mean the rolling direction and transverse direction, respectively). Formability performance was experimentally and numerically studied in three applications including the simple tension tests, hemisphere dome stretching and cylindrical cup drawing tests. For numerical simulations, the non-quadratic orthogonal anisotropic yield function, Yld2004-18p and the isotropic Hardening Law were implemented into the material constitutive model. As for the failure criterion, the forming limit diagram (FLD) was utilized to determine the failure strain.

Frederic Barlat - One of the best experts on this subject based on the ideXlab platform.

  • anisotropic strain Hardening behavior in simple shear for cube textured aluminum alloy sheets
    International Journal of Plasticity, 2005
    Co-Authors: Jeong Whan Yoon, Frederic Barlat, J Gracio, E F Rauch
    Abstract:

    Abstract Finite element (FE) simulations of the simple shear test were conducted for 1050-O and 6022-T4 aluminum alloy sheet samples. Simulations were conducted with two different constitutive equations to account for plastic anisotropy: Either a recently proposed anisotropic yield function combined with an isotropic strain Hardening Law or a crystal plasticity model. The FE computed shear stress–shear strain curves were compared to the experimental curves measured for the two materials in previous works. Both phenomenological and polycrystal approaches led to results consistent with the experiments. These comparisons lead to a discussion concerning the assessment of anisotropic Hardening in the simple shear test.

  • anisotropic strain Hardening behavior in simple shear for cube textured aluminum alloy sheets
    International Journal of Plasticity, 2005
    Co-Authors: Jeong Whan Yoon, Frederic Barlat, J Gracio, E F Rauch
    Abstract:

    Abstract Finite element (FE) simulations of the simple shear test were conducted for 1050-O and 6022-T4 aluminum alloy sheet samples. Simulations were conducted with two different constitutive equations to account for plastic anisotropy: Either a recently proposed anisotropic yield function combined with an isotropic strain Hardening Law or a crystal plasticity model. The FE computed shear stress–shear strain curves were compared to the experimental curves measured for the two materials in previous works. Both phenomenological and polycrystal approaches led to results consistent with the experiments. These comparisons lead to a discussion concerning the assessment of anisotropic Hardening in the simple shear test.

  • spring back evaluation of automotive sheets based on isotropic kinematic Hardening Laws and non quadratic anisotropic yield functions part i theory and formulation
    International Journal of Plasticity, 2005
    Co-Authors: Kwansoo Chung, Michael L Wenner, Frederic Barlat
    Abstract:

    Abstract In order to improve the prediction capability of spring-back in automotive sheet forming processes, the modified Chaboche type combined isotropic-kinematic Hardening Law was formulated based on the modified equivalent plastic work principle to account for the Bauschinger effect and transient behavior. As for the yield stress function, the non-quadratic anisotropic yield potential, Yld2000-2d, was utilized under the plane stress condition. Besides the theoretical aspect of the constitutive Law including the general plastic work principle for monotonously proportional loading, the method to determine Hardening parameters as well as numerical formulations to update stresses were developed based on the incremental deformation theory and the consistency requirement as summarized in Part I, while the characterization of material properties and verifications with experiments are discussed in Part II and III, respectively.

Jeong Whan Yoon - One of the best experts on this subject based on the ideXlab platform.

  • anisotropic strain Hardening behavior in simple shear for cube textured aluminum alloy sheets
    International Journal of Plasticity, 2005
    Co-Authors: Jeong Whan Yoon, Frederic Barlat, J Gracio, E F Rauch
    Abstract:

    Abstract Finite element (FE) simulations of the simple shear test were conducted for 1050-O and 6022-T4 aluminum alloy sheet samples. Simulations were conducted with two different constitutive equations to account for plastic anisotropy: Either a recently proposed anisotropic yield function combined with an isotropic strain Hardening Law or a crystal plasticity model. The FE computed shear stress–shear strain curves were compared to the experimental curves measured for the two materials in previous works. Both phenomenological and polycrystal approaches led to results consistent with the experiments. These comparisons lead to a discussion concerning the assessment of anisotropic Hardening in the simple shear test.

  • anisotropic strain Hardening behavior in simple shear for cube textured aluminum alloy sheets
    International Journal of Plasticity, 2005
    Co-Authors: Jeong Whan Yoon, Frederic Barlat, J Gracio, E F Rauch
    Abstract:

    Abstract Finite element (FE) simulations of the simple shear test were conducted for 1050-O and 6022-T4 aluminum alloy sheet samples. Simulations were conducted with two different constitutive equations to account for plastic anisotropy: Either a recently proposed anisotropic yield function combined with an isotropic strain Hardening Law or a crystal plasticity model. The FE computed shear stress–shear strain curves were compared to the experimental curves measured for the two materials in previous works. Both phenomenological and polycrystal approaches led to results consistent with the experiments. These comparisons lead to a discussion concerning the assessment of anisotropic Hardening in the simple shear test.

  • incorporation of sheet forming effects in crash simulations using ideal forming theory and hybrid membrane and shell method
    Journal of Manufacturing Science and Engineering-transactions of The Asme, 2005
    Co-Authors: Hansun Ryou, Kwansoo Chung, Jeong Whan Yoon, Jae Ryoun Youn, Tae Jin Kang
    Abstract:

    In order to achieve reliable but cost-effective crash simulations of stamped parts, sheet-forming process effects were incorporated in simulations using the ideal forming theory mixed with the three-dimensional hybrid membrane and shell method, while the subsequent crash simulations were carried out using a dynamic explicit finite element code. Example solutions performed for forming and crash simulations of I- and S-shaped rails verified that the proposed approach is cost effective without sacrificing accuracy. The method required a significantly small amount of additional computation time, less than 3% for the specific examples, to incorporate sheet-forming effects into crash simulations. As for the constitutive equation, the combined isotropic-kinematic Hardening Law and the nonquadratic anisotropic yield stress potential as well as its conjugate strain-rate potential were used to describe the anisotropy of AA6111-T4 aluminum alloy sheets.

  • incorporation of sheet forming effects in crash simulations using ideal forming theory and hybrid membrane and shell
    2005
    Co-Authors: Hansun Ryou, Kwansoo Chung, Jeong Whan Yoon, Jae Ryoun Youn, Chungsouk Han, Tae Jin Kang
    Abstract:

    forming process effects were incorporated in simulations using the ideal forming theory mixed with the three-dimensional hybrid membrane and shell method, while the subsequent crash simulations were carried out using a dynamic explicit finite element code. Example solutions performed for forming and crash simulations of I- and S-shaped rails verified that the proposed approach is cost effective without sacrificing accuracy. The method required a significantly small amount of additional computation time, less than 3% for the specific examples, to incorporate sheet-forming effects into crash simulations. As for the constitutive equation, the combined isotropic-kinematic Hardening Law and the nonquadratic anisotropic yield stress potential as well as its conjugate strain-rate potential were used to describe the anisotropy of AA6111-T4 aluminum alloy sheets. @DOI: 10.1115/1.1830050#

  • crash simulations considering sheet forming effects based on ideal forming theory and hybrid membrane shell method
    MATERIALS PROCESSING AND DESIGN: Modeling Simulation and Applications - NUMIFORM 2004 - Proceedings of the 8th International Conference on Numerical M, 2004
    Co-Authors: Hansun Ryou, Jeong Whan Yoon, Kwansoo Chung, Farhang Pourboghrat
    Abstract:

    In order to achieve reliable but cost‐effective crash simulations of stamped parts, sheet forming process effects were incorporated in simulations using the ideal forming theory mixed with the 3D hybrid membrane/shell method, while the subsequent crash simulations were carried out using a dynamic explicit finite element code. Example solutions performed for forming and crash simulations of I‐ and S‐shaped rails verified that the proposed approach is cost‐effective without sacrificing accuracy. The method required a significantly small amount of additional computation time, less than 3% for the specific examples, to incorporate sheet forming effects to crash simulations. As for the constitutive equation, the combined isotropic‐kinematic Hardening Law and the non‐quadratic anisotropic yield stress potential as well as its conjugate strain‐rate potential were used to describe the anisotropy of AA6111‐T4 aluminum alloy sheets.

Myounggyu Lee - One of the best experts on this subject based on the ideXlab platform.

  • return mapping with a line search method for integrating stress of the distortional Hardening Law with differential softening
    Computers & Structures, 2021
    Co-Authors: Jinwoo Lee, Hyuk Jong Bong, Myounggyu Lee
    Abstract:

    Abstract A stress-update algorithm for the recently proposed distortional anisotropic Hardening Law is developed based on the Newton–Raphson (N–R) algorithm and line search method. The investigated yield function enables the modeling of complex path-dependent flow stress evolutions, particularly the Bauschinger effect, latent Hardening/softening, and differential permanent softening. Computationally, the continuous distortion of the yield function under strain-path changes leads to numerical instability, which is overcome by a newly reformulated step-size control method in the line search algorithm. The developed algorithms were implemented in ABAQUS using the closest-point projection method and validated for extra-deep drawing quality and DP780 steel sheets in terms of numerical accuracy and stability under reverse- and cross-loading path changes. The results show that the return-mapping algorithm significantly improves the accuracy and speed of convergence when the proposed line search method is incorporated. In contrast, the conventional N–R based algorithm fails to obtain converged stresses under abrupt loading path changes owing to the sharp corners introduced by the distorted yield surface.

  • Hardening Law for evolution of yield surface
    2018
    Co-Authors: Kwansoo Chung, Myounggyu Lee
    Abstract:

    Inthe past few decades, a few experimentations have been conducted to better understand the evolution of the yield surface during plastic deformation.

  • anisotropic asymmetric yield criterion and anisotropic Hardening Law for composite materials theory and formulations
    Fibers and Polymers, 2006
    Co-Authors: Ji Hoon Kim, Kwansoo Chung, Jae Ryoun Youn, Myounggyu Lee, Tae Jin Kang
    Abstract:

    In this paper, elasto-plastic constitutive equations for highly anisotropic and asymmetric materials are developed and their numerical implementation is presented. Some engineering materials such as fiber reinforced composites show different material behavior in the different material directions (anisotropy) as well as in tension and compression (asymmetry). Although these materials have mostly been analyzed using the anisotropic elastic constitutive equations, the necessity of consideration of plastic properties has been frequently reported in the previous works. In order to include both the anisotropic and asymmetric properties of composite materials, the Drucker-Prager yield criterion is modified by adding anisotropic parameters and initial components of translation. The implementation procedure for the developed theory and algorithms is presented based on the implicit finite element scheme. The measured data from the previous work are used to validate the present constitutive equations.

  • spring back evaluation of automotive sheets based on isotropic kinematic Hardening Laws and non quadratic anisotropic yield functions part ii characterization of material properties
    International Journal of Plasticity, 2005
    Co-Authors: Myounggyu Lee, Chongmin Kim, Michael L Wenner, Dae Yong Kim, R H Wagoner, Kwansoo Chung
    Abstract:

    In order to improve the prediction capability of spring-back in the computational analysis of automotive sheet forming processes, the modified Chaboche type combined isotropic-kinematic Hardening Law was formulated to account for the Bauschinger and transient behavior in Part I. As for the yield stress function, the non-quadratic anisotropic yield potential, Yld2000-2d, was utilized under the plane stress condition. Experimental procedures to obtain the material parameters of the combined Hardening Law and the yield potential are presented here in Part II for three automotive sheets: AA5754-O, AA6111-T4 and DP-Steel. The modified Chaboche model was confirmed to well represent the measured Hardening behavior including the Bauschinger and transient behavior. While the theoretical and numerical formulations of the constitutive Law are discussed in Part I, experimental verifications for spring-back of formed parts are further discussed in Part III.

  • spring back evaluation of automotive sheets based on isotropic kinematic Hardening Laws and non quadratic anisotropic yield functions part iii applications
    International Journal of Plasticity, 2005
    Co-Authors: Myounggyu Lee, Michael L Wenner, Chongmin Kim, Dae Yong Kim, Kwansoo Chung
    Abstract:

    Abstract In order to improve the prediction capability of spring-back in the computational analysis of automotive sheet forming processes, the modified Chaboche type combined isotropic–kinematic Hardening Law was formulated to account for the Bauschinger and transient behavior in Part I. As for the yield stress function, the non-quadratic anisotropic yield potential, Yld2000-2d, was utilized under the plane stress condition. Experimental procedures to obtain the material parameters of the combined Hardening Law and the yield potential were presented in Part II for three automotive sheets. For verification purposes, comparisons of simulations and experiments were performed here for the unconstrained cylindrical bending, the 2-D draw bending and the modified industrial part (the double-S rail). For all three applications, simulations showed good agreements with experiments. Simplified one-dimensional plane strain analytical and numerical methods were also developed here to better understand the spring-back in forming processes.

Charbel Moussa - One of the best experts on this subject based on the ideXlab platform.

  • identification of the Hardening Law of materials with spherical indentation using the average representative strain for several penetration depths
    Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2014
    Co-Authors: Charbel Moussa, Xavier Hernot, Olivier Bartier, Guillaume Delattre, Gerard Mauvoisin
    Abstract:

    Abstract The identification of plastic properties with spherical indentation has been the subject of many studies in the last decades. In the present work, a new method for the determination of the Hardening Law of materials using the load–displacement curve of a spherical indentation test is proposed. This method is based on the use of an average representative strain. The advantage of the proposed average representative strain is that it is strictly obtained from the material in response to the indentation test. By using various values of penetration depth, the proposed method gives the range of strain for which the Hardening Law is precisely identified and allows determining a confidence domain that takes into account experimental imprecision and material heterogeneity. The influence of penetration depth and the error formula on the identified Hollomon Hardening Law are discussed in the present study. The present study clarifies many problems that were observed in previous studies such as the uniqueness of solution and the sensitivity of the indentation test to the plastic parameters of the Hollomon Hardening Law.

  • evaluation of the tensile properties of a material through spherical indentation definition of an average representative strain and a confidence domain
    Journal of Materials Science, 2014
    Co-Authors: Charbel Moussa, Xavier Hernot, Olivier Bartier, Guillaume Delattre, Gerard Mauvoisin
    Abstract:

    In the present article, a new method for the determination of the Hardening Law using the load displacement curve, F–h, of a spherical indentation test is developed. This method is based on the study of the error between an experimental indentation curve and a number of finite elements simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytic equation. Except for the fact that the identified Hardening Law is a Hollomon type, no assumption was made for the proposed identification method. A new representative strain of the spherical indentation, called “average representative strain,” e aR was defined in the proposed article. In the bottom of the valley, all the stress–strain curves that intersect at a point of abscissa e aR lead to very similar indentation curves. Thus, the average representative strain indicates the part of the Hardening Law that is the better identified from spherical indentation test. The results show that a unique material parameter set (yield stress σ y, strain Hardening exponent n) is identified when using a single spherical indentation curve. However, for the experimental cases, the experimental imprecision and the material heterogeneity lead to different indentation curves, which makes the uniqueness of solution impossible. Therefore, the identified solution is not a single curve but a domain that is called “solution domain” in the yield stress–work Hardening exponent diagram, and “confidence domain” in the stress–strain diagram. The confidence domain gives clear answers to the question of uniqueness of the solution and on the sensitivity of the indentation test to the identified Hardening Laws parameters.

  • local evaluation of the Hardening Law of a material through spherical indentation definition of an average representative strain and a confidence domain
    2013
    Co-Authors: Charbel Moussa, Xavier Hernot, Olivier Bartier, Gerard Mauvoisin, Guillaume Delattre
    Abstract:

    The indentation test is widely used for the determination of the stress-strain curve of materials. One of the advantages of this technique is that it is local and can be applied to materials in some conditions for which the classic tensile test cannot be done. One of the disadvantages of the indentation test is that the field of strain in the deformed sample is not homogenous which makes it difficult to identify the Hardening Law of the material from an indentation curve. The application of the concept of the representative strain can significantly simplify the analysis of the indentation response and has often been used in the stress-strain curve determination from the indentation test. In the present work, a new method based on the definition of an "average representative strain", eaR, is developed for the determination of the Hardening Law using the load displacement curve, F-h, of a spherical indentation test. This method consists to calculate the error between an experimental indentation curve and a number of FE simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytical equation. In the bottom of the valley, all the stress-strain curves that intersect at a point of abscissa eaR lead to very similar indentation curves. Thus, the average representative strain indicates the part of the Hardening Law that is identified with the highest precision for a given penetration depth. Hence, considering multiple penetration depths, several values of eaR are determined. The Hardening Law is precisely constructed using these values of eaR and their corresponding values of stresses, σaR . This way, no assumption on the mathematical form of the Hardening Law of the studied material is made. Since the indentation test is local, material heterogeneity lead to different indentation curves for the same material and under the same conditions. The proposed method leads to the determination of a "confidence domain" that takes into account the experimental imprecision and the material heterogeneity using several indentation curves. The results obtained for a 20MnB5 steel alloy show that the identified Hardening Law (and confidence domain) is in agreement with the tensile test curve