Table 2 - uploaded by George Z. Voyiadjis
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Performance of the proposed kinematic hardening rule is examined using several examples of cyclic plasticity phenomena observed in experiments. Results obtained and compared with experimental observations on various loading histories are presented. With the memory effects added to the model, impressive results are obtained without using an anisotro...
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... elasto-plastic stiffness tensor, D, as represented by the corresponding equation in Table 1, uses the plastic modulus in which the proximity parameter corresponds to the quantities at the jth step, i.e. c5 u). Other quantities are discretized and updated as represented by equations in Table 2. ...
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... For a safe design of critical components submitted to fatigue loadings, constitutive models that can describe reasonably well the stress-strain responses under proportional and non-proportional cyclic paths are required. To address this need, many efforts have been made in developing improved constitutive models [1][2][3][4][5][6][7][8]. Type 304 stainless steel (304 SS) is known as a material which shows a significant additional cyclic hardening under non-proportional loading. ...
This work is devoted to a survey of the multi-mechanism (MM) models proposed in literature during the last two decades. This MM approach is a possible alternative to the wide-spread Chaboche’s model when modeling complex material behavior. Here, the description of the cyclic behavior under complex loading histories is in the focus. The capabilities of two recent versions of the MM models are demonstrated through the simulation of cyclic proportional and non-proportional loading paths under stress or the combination of stress–strain control. The reliability of the two MM models is investigated through the study of the mechanical behavior of a 304 stainless steel (304 SS) at room temperature. Beside the assessment of the stress–strain overall behavior, the local contribution of stress and strains at each mechanism level is discussed.
... Voyiadjis and Kattan (1991) showed that Tseng and Lee (1983) evolution expression for the backstress is a special case of eqns (12) and (14) such that``that``a'' and``and``b'' acquire speci®c values. Voyiadjis and Sivakumar (1991 Sivakumar ( , 1994) used the evolution eqns (12) and (14) such that when the yield surface is away from the bounding surface, the unit tensor # is predominantly along the direction while as it drifts closer to the bounding surface, # acquires the direction of the evolution law of the backstress as given by Tseng and Lee (1983). This is in order to ensure nesting of the yield surface and the bounding surface. ...
The hardening behavior of metals to non-proportional loading and ratchetting effects is investigated here using the proposed model presented by Voyiadjis and Basuroychowdhury (1998). The backstress evolution equations are modified here in order to account for non-proportionality of loading. The same general form of the kinematic hardening formulation defined previously by Voyiadjis and Basuroychowdhury (1998) is used here. The material constant, β(i), is now expressed in a functional form, β̄(i), to account for the variation in the loading direction. Numerical results are obtained using the proposed model for a series of plastic strain controlled cyclic tests due to multiaxial cyclic tests performed at room temperature on thin-walled tubural specimens of Type 316 stainless steel. The results are compared with the experimental values obtained by Tanaka, et al. (1985). The drift correction due to the finite increments of stress or strain is corrected using an efficient approach that corrects the backstress only. The model is also tested for cyclic creep which occurs due to a non-zero mean stress. The cyclic creep occurs initially and saturates reaching a stable cycle.The modified proposed kinematic hardening rule and the associated bounding surface are used in conjunction with a robust plasticity model for metals. The hardening dependence on the plastic strain path is also investigated in this work.
In this study, a modified distortional hardening model is proposed based on the homogeneous yield-function based anisotropic hardening (HAH). An improvement is made to capture differential permanent softening (DPS) under strain-path changes in sheet metals, whereas the other anisotropic hardening features such as the Bauschinger effect, transient behavior, and cross hardening phenomenon are retained as they are in the original HAH model.
The modified HAH (M-HAH) model is implemented in a commercial finite element software using the user-defined material subroutine, and validated well by reproducing the flow stress behaviors after differently programmed strain-path changes for dual-phase steel, extra deep drawing quality steel, and ferritic stainless steel. Additionally, the M-HAH can simulate the DPS in two-step tension tests, which cannot be accurately modeled by the original HAH. Finally, the V-bending springback tests with pre-tensioned specimens are evaluated with different modeling schemes including the classical isotropic hardening, kinematic hardening and distortional hardening models.
A robust kinematic hardening rule is proposed which appropriately blends the deviatoric stress rate rule and the Tseng-Lee rule in order to satisfy both the experimental observations made by Phillips et al. and the nesting of the yield surface to the limit surface. Performance of the proposed rule is examined using several examples cyclic plasticity observed in experiments. An additional surface called the memory surface is introduced in order to accommodate for anisotropy of the yield model. An efficient method of correcting the drift of yield surface is proposed. The direct relation of the kinematic hardening of the limit to that of the yield surface ensures nesting.
A cyclic plasticity model is proposed here to predict the behavior of directionally reinforced metal matrix composites. A six parameter general anisotropic yield criterion is proposed and used here. This anisotropic plasticity model uses a non-associative flow rule, a kinematic hardening rule of Phillips type and the usage of a modified form of the bounding surface to model cyclic behavior. Also a new form for evaluating the plastic modulus for anisotropic materials is proposed here. The experimental data of Dvorak et. al. (1988) and Nigam et. al. (1993) have been used in the evaluation of the various parameters, and for comparison of results.
C. Lexcellent (Président), Professeur Université de Franche-Comté, Besançon
A. Abdul-Latif (Rapporteur), Professeur Université Paris 8, IUT de Tremblay-En-France
Y. Rémond (Rapporteur), Professeur Université Louis Pasteur, Strasbourg
C. Cunat (Examinateur) Professeur, E.N.S.E.M., Nancy (Directeur de thèse)
M. Haboussi (Examinateur) Maître de Conférence, I.N.P.L., Nancy
Y. Meimon (Examinateur) Directeur de Recherche, I.F.P, Rueil-Malmaison
Classical constitutive models of cyclic plasticity are very poor in predicting the progressive deformation of ratchetting, though ratchetting is an important factor in the design of structural components. Recent works done in the last decade, however, have enabled us to simulate the strain accumulation due to ratchetting with reasonable accuracy. In the present paper, first, the state of the art in constitutive modeling for ratchetting is described by criticizing the classical models and by reviewing the recent modifications introduced for ratchetting. Then, the application of recent and calssical models to ratcheting problems such as the thermal ratchetting induced by moving temperature distribution is discussed to show the effectiveness of recent models in simulating ratchetting.
Experimental results of monotonic uniaxial tensile tests at different strain rates and the reversed strain cycling test showed the characteristics of rate-dependence and cyclic hardening of Z2CND18.12N austenitic stainless steel at room temperature, respectively. Based on the Ohno–Wang kinematic hardening rule, a visco-plastic constitutive model incorporated with isotropic hardening was developed to describe the uniaxial ratcheting behavior of Z2CND18.12N steel under various stress-controlled loading conditions. Predicted results of the developed model agreed better with experimental results when the ratcheting strain level became higher, but the developed model overestimated the ratcheting deformation in other cases. A modified model was proposed to improve the prediction accuracy. In the modified model, the parameter mi of the Ohno–Wang kinematic hardening rule was developed to evolve with the accumulated plastic strain. Simulation results of the modified model proved much better agreement with experiments.
In finite element calculation of plastic mechanics, isotropic hardening model, kinematic hardening model and mixed hardening model have their advantages and disadvantages as well as applicability area. In this paper, by use of the tensor analysis method and mixed hardening theory in plastic mechanics, the constitutive relation of 3-D mixed hardening problem is derived in detail based on the plane mixed hardening. Numerical results show that, the proposed 3-D mixed hardening constitutive relation agrees well with the test results in existing references, and can be used in the 3-D elastic-plastic finite element analysis.
A two-complementary-trio material model for cyclic plasticity is proposed in this paper. In this formulation we consider a contact surface to confine the motion of contact stress. While the on-off switching criteria of plasticity are derived from the first complementary trio, the switching criteria of Kinematic hardening rules are derived according to the second complementary trio. In terms of the new concept of contact stress and contact surface, it becomes easier to derive the governing rule of back stress during the contact of yield surface and bounding surface. The validity of the new model is confirmed by comparing the computational results with the experimental data for materials of SAE 4340 and RHA under uniaxial cyclic tests and biaxial cyclic tests. Even though the material constants used in the new model are parsimonious (with only 12), it is immediately recognized that the cyclic response curves described by the new model are in good agreement with the experimental data.
