Back Stress Evolution Research Articles

Development of Inelastic Constitutive Equations for Ni-Based Superalloy IN 738 LC. 2nd Report, Unified Constitutive Model Considering Nonisotropic Evolution of Back Stress.

Development of Inelastic Constitutive Equations for Ni-Based Superalloy IN 738 LC. 2nd Report, Unified Constitutive Model Considering Nonisotropic Evolution of Back Stress.

On rafting in a single crystal nickel-base superalloy after high and low temperature creep

A microstructure-sensitive crystal plasticity constitutive framework is proposed for simulating the tensile, cyclic, and creep response of single crystal Ni-based superalloys. In this framework, a non-Schmid model is used to account for the orientation- and temperature-dependent yield anisotropy. A model for the evolution of the slip system-level backstress is developed to simulate the cyclic response. The model accounts for the effect of microstructural features like precipitate volume fraction and size, and matrix channel width, on the associated hardening mechanisms. A physical model for creep deformation has also been developed that accounts for dislocation climb normal to the slip plane and the microstructure evolution due to rafting and isotropic coarsening of the precipitates. Application of the model is demonstrated by predicting the orientation- and temperature-dependent thermo-mechanical deformation of two single crystal superalloys, CMSX-4 and PWA-1484. The model is calibrated to the experimental tensile, cyclic and creep response for these alloys. Finally, the model is qualitatively validated by predicting the creep-fatigue interactions for different loading orientations and a range of thermo-mechanical conditions for CMSX-4 and PWA-1484.

A multiaxial cyclic plasticity model for non-proportional loading cases

Abstract 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, β (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.

Nonlinear kinematic hardening rule parameters— direct determination from completely reversed proportional cycling

A methodology for the determination of parameters for superposed, uncoupled, A-F type nonlinear kinematic hardening rules is presented for reversed cyclic plasticity or viscoplasticity. The important aspects of the procedure are presented for general reversed proportional cycling and then special cases of axial-torsional and uniaxial loadings are considered along with several experimental examples. The approach yields a quantitative estimate of the saturation state of stress for these types of models, directly from experimental responses to reversed proportional cycling. Iterations are not required to obtain parameter estimates, except for the numerical solution to a set of nonlinear algebraic equations when more than two A-F type rules are superposed to model backstress evolution.

From Micro- to Macro-Plasticity: The Scale Invariance Approach

An account of recent contributions to the theory of plasticity advanced by the author and his co-workers is provided with emphasis on deformation-induced anisotropy and texture formation. For the description of these effects, the so-called scale invariance approach is adopted which allows information and constitutive relations pertaining to single slip to be cast in the form of macroscopic constitutive equations. Various phenomenological plasticity models are derived this way with the extra dividend of deducing explicit expressions for the phenomenological coefficients. The method is particularly suited for large deformation anisotropic plasticity, as it reveals the inherent coupling between the evolution of back stress and the plastic spin. Extended models of macroscopic plastic behavior accounting for vertex and texture phenomena can also be obtained by slightly generalizing the kinematics and kinetics of the microscopic configuration to include rate, non-Schmid, secondary slip and grain orientation effects.

Continuum slip foundations of elasto-viscoplasticity

A continuum slip theory for dislocation glide is employed to derive macroscopic, phenomenological models for incompressible viscoplasticity. The microstructural origins of kinematic/isotropic hardening and rate-dependence are examined within the framework of the continuum slip theory of Rice and the single slip scale invariance theory of Aifantis for dislocation glide. In the process, the limitations on primitive assumptions for existing forms of state variable viscoplasticity become apparent. A form for rate-dependent evolution of backstress is derived which supports recent phenomenological approaches. Extensions to finite strain and compressible viscoplasticity are discussed.

Anisotropic hardening model and its application to cyclic loading

The experimental study of evolution rules of two state variables: back stress α ij and yield stress R is first discussed. It is shown that back stress evolution is affected by the maximal prestress and asymptotic value of yield stress depends on strain amplitude. The constitutive model is presented and its prediction for cyclic loading program is compared with experimental data.

Phenomenological evolution equations for the backstress and spin tensors

A formulation of a constitutive model involving a new kinematic hardening rule is presented in the Eulerian reference system. The corotational stress and backstress rates involving spin tensors are discussed and incorporated in the evolution equations. The backstress evolution model is compared with other models and is found to be decomposable into a model that consists of two backstresses whose evolution is independent of each other.

A dislocation based analysis of continuum mechanical and microscopic local stresses during cyclic deformation of copper

A relationship between continuum mechanical internal stress variables, kinetic back stress, isotropic drag stress, and microscopic local stresses in the dislocation cell interior and cell walls, is developed based upon Mughrabi's composite model of deformation of heterogeneous microstructure during cyclic deformation in cell forming metals. The experimental data on the evolution of kinematic back stress and isotropic drag stress during cyclic deformation of Cu along with TEM measurements of cell diameter and cell width are utilized to determine the evolution of mobile and immobile dislocation densities in the cell interior and cell walls, respectively, as a function of the number of cycles. The range of values obtained is in agreement with the available experimental data.

Bauschinger effect and dislocation structure in stainless steel during cyclic deformation: Xia, Y., Wang, Z. and Du, X. Acta Metall. Sin. (China) Aug. 1988 24, (4), A221–A227 (in Chinese)

This paper presents a constitutive model that has a high capability of describing the deformation behavior of large-strain cyclic plasticity and also the stress–strain responses at small-scale re-yielding after large prestrain. A new equation of backstress evolution is proposed for an accurate simulation of the transient Bauschinger effect. Furthermore, an original idea of a non-isotropic-hardening surface defined in the stress space is presented for the description of the workhardening stagnation appearing under reverse deformation, as well as the strain-range and mean-strain dependencies of cyclic hardening characteristics. The validity of this model is confirmed by comparing the cyclic stress–strain responses calculated by the model with the experimental observations on some steel sheets and an aluminum sheet.

Creep, fatigue and creep-fatigue crack growth rates in parent and simulated HAZ type 321 stainless steel: Gladwin, D.N., Miller, D.A., Neate, G.J. and Priest, R.H.Fatigue Fract. Eng. Mater. Struct. 1988, 11, (5), 355–370

Cyclic behavior of a nickel-based GH4169 superalloy under fully-reversed and asymmetric creep-fatigue tests with strain-controlled is investigated at 650℃. Significant tension–compression asymmetry and continuous cyclic softening are observed for all loading waveforms. The material exhibits mean stress relaxation under asymmetric loading and fully-reversed loading with valley strain dwells. Moreover, stress relaxation behavior during the dwell period is almost independent of the number of cycles. In order to identify the deformation mechanism, the evolutions of mean value and amplitude of the internal stress (back stress and effective stress) based on the partition of hysteresis loops are analyzed. Results show that both the cyclic softening and mean stress relaxation are primarily dominated by the evolution of back stress and secondarily affected by that of effective stress. Such findings lay a solid foundation for further investigations of reasonable cyclic deformation description and accurate life prediction in GH4169 alloy under creep-fatigue loadings.