Method and Verification for Material Calibration of the Chaboche Plasticity Model for Multiple Material Directions

The Chaboche model is a well-validated non-linear kinematic hardening material model. This material model, like many models, depends on a set of material constants that must be calibrated for it to match the experimental data. Due to the challenge of calibrating these constants, the Chaboche model is often disregarded. The challenge with calibrating the Chaboche constants is that the most reliable method for doing the calibration is a brute force approach, which tests thousands of combinations of constants. Different sampling techniques and optimization schemes can be used to select different combinations of these constants, but ultimately, they all rely on iteratively selecting values and running simulations for each selected set. In the experience of the authors, such brute force methods require roughly 2,500 combinations to be evaluated in order to have confidence that a reasonable solution is found. This process is not efficient. It is time-intensive and labor-intensive. It requires long simulation times, and it requires significant effort to develop the accompanying scripts and algorithms that are used to iterate through combinations of constants and to calculate agreement. A better, more automated method exists for calibrating the Chaboche material constants. In this paper, the authors describe a more efficient, automated method for calibrating Chaboche constants. The method is validated by using it to calibrate Chaboche constants for an IN792 single-crystal material and a CM247 directionally-solidified material. The calibration results using the automated approach were compared to calibration results obtained using a brute force approach. It was determined that the automated method achieves agreeable results that are equivalent to, or supersede, results obtained using the conventional brute force method. After validating the method for cases that only consider a single material orientation, the automated method was extended to multiple off-axis calibrations. The Chaboche model that is available in commercial software, such as ANSYS, will only accept a single set of Chaboche constants for a given temperature. There is no published method for calibrating Chaboche constants that considers multiple material orientations. Therefore, the approach outlined in this paper was extended to include multiple material orientations in a single calibration scheme. The authors concluded that the automated approach can be used to successfully, accurately, and efficiently calibrate multiple material directions. The approach is especially well-suited when off-axis calibration must be considered concomitantly with longitudinal calibration. Overall, the automated Chaboche calibration method yielded results that agreed well with experimental data. Thus, the method can be used with confidence to efficiently and accurately calibrate the Chaboche non-linear kinematic hardening material model.

The prediction of the cyclic mechanical behavior of stainless steel 304L at room temperature

Purpose The purpose of this paper is to highlight the performance of the Chaboche model in relation to the database identification, tests with imposed deformations were conducted at room temperature on 304L stainless steel specimens. Design/methodology/approach The first two tests were performed in tension-compression between ±0.005 and ±0.01; in the third test, each cycle is composed of the combination of a compression tensile cycle between ±0.01 followed by a torsion cycle between ±0.01723 (non-proportional path), and the last, uniaxial ratcheting test with a mean stress between 250 MPa and −150 MPa. Several identifications of a Chaboche-type model were then performed by considering databases composed of one or more of the cited tests. On the basis of these identifications, the simulations of a large number of ratchet tests in particular were carried out. Findings The results present the effect of the optimized parameters on the prediction of the behavior of materials which is reported in the graphs, Optimizations 1 and 2 of first and second tests and Optimization 4 of the third test giving a good prediction of the increasing/decreasing pre-deformation amplitude. Originality/value The quality of the model's predictions strongly depends on the richness of the database used for the identification of the parameters.

Full-Field Strain Measurement and Numerical Analysis of a Microalloyed Steel Subjected to Deformation with Strain Path Change

This study presents an effective technique for taking advantage of the full-field measurement method of Digital Image Correlation (DIC) for the assessment of the strain distribution during the metal forming process when the strain path change was performed. The applied methodology is based on the combination of a numerical simulation for the stress calculation and full-field surface strain measurement in a forward/reverse three-point bending test. In the numerical part, the Chaboche model and dislocation density-based model were selected and verified in terms of the prediction of a softening/hardening effect occurring during strain reversal. The Chaboche model parameters identification procedure, on the basis of a cyclic torsion test, combined with inverse analysis, was also described. The results of the study showed the advantages and disadvantages of both of the analyzed work hardening models. The obtained results were analyzed in the light of the deformation inhomogeneity and reorganization of the dislocation structure during the cyclic deformation test.

The application of Chaboche model in uniaxial ratcheting simulations

This article presents the application of Chaboche nonlinear kinematic hardening model in simulations of uniaxial ratcheting. First, the symmetrical strain-controlled cyclic tension/compression tests for PA6 aluminum samples were done. Using the experimental stress–strain curve, initial material hardening parameters were determined by the ABAQUS software. The experimental curve was compared with the numerical one. For better fitting of both curves, the optimization procedure based on the least-square method was applied. Using the determined hardening parameters, numerical simulations of the ratcheting were done by the finite element analysis software. Numerical results were then compared with the experimental data obtained in the stress-controlled cyclic loading test.

Investigation of Anisotropic Subsequent Yield Behavior for 45 Steel by the Distortional Yield Surface Constitutive Model

The subsequent anisotropic yield behavior of 45 steel was predicted by the distortional yield surface constitutive model, which can describe the anisotropic subsequent yield and the cross effect of metal associating with loading history. The yield characteristics and plastic hardening behaviors of the 45 steel were simulated under three preloading paths including pre-torsion, pre-tension, and pre-tension–torsion. Based on the comparison between the experimental yield stresses and the simulation by the classical Chaboche model, the proposed model can describe the remarkable anisotropic yield behavior related to the loading history, which can effectively describe the sharp point of yield surface in pre-loading direction and the smaller curvature near its opposite direction. It was successfully simulated by the constitutive model proposed that the subsequent distortional yield surface defined by small offset strain and the degradation process of the distortion feature defined by large offset strain.

Evaluation of Sensitivity and Calibration of the Chaboche Kinematic Hardening Model Parameters for Numerical Ratcheting Simulation

Ratcheting failure of materials and structures subjected to low cycle fatigue in the presence of significant mean stress is of great interest to researchers. In this experimental and numerical study, the response of 316L stainless steel samples was observed in symmetric strain control uniaxial test followed by post-stabilized monotonic test, uniaxial and biaxial ratcheting tests, in order to determine the Chaboche model parameters and to evaluate ratcheting prediction using finite element analysis. The critical elastic limit was initially obtained from incremental uniaxial cyclic tests. The Chaboche parameters were subsequently extracted from experimental hysteresis and post-stabilized monotonic stress plastic-strain curves using two optimization technics, namely, the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). The two optimization methods were compared for efficiency, in terms of time and accuracy. The PSO method presented higher efficient results and was subsequently used to derive the parameters from hysteresis and post-stabilized monotonic curves. Different values (by definition) of elastic limit were also used. The Finite Element commercial software ANSYS was utilized with the Chaboche model to predict the uniaxial and biaxial ratcheting behavior of 316L stainless steel pipe. The comparison between experimental and the numerical simulation demonstrates that adopting post-stabilized monotonic curve rather than hysteresis curve and with accurate elastic limit obtained from incremental loading test improves ratcheting prediction significantly.

Limited Versus Unlimited Strain Accumulation Due to Ratcheting Mechanisms

After distinguishing material ratcheting and structural ratcheting, different phenomena related to structural ratcheting are gathered. Ratcheting of elastic–plastic structures observed with stationary position of loads is distinguished from ratcheting with moving loads. Both categories are illustrated by examples. The effect of evolution laws for the internal variables describing kinematic hardening on the accumulation of strain due to a ratcheting mechanism, and whether the ratcheting mechanism ceases with the number of cycles so that the accumulated strains are limited, is discussed. Some conditions are shown, under which the Chaboche model can lead to shakedown. Scenarios where shakedown is guaranteed at every load level, or where it may or may not occur at a specific load level, or where it definitely cannot occur at any load level, are distinguished. Correspondingly, the usefulness of shakedown analyses, which are searching for maximum load factors assuring shakedown, or direct (or simplified) methods to obtain postshakedown quantities by avoiding incremental cyclic analyses is discussed.

Numerical prediction of the elastoplastic response of FG tubes using nonlinear kinematic hardening rule with power-law function model under thermomechanical loadings

PurposeThis study aims to explain the characterization of cyclic behavior of a tube made of functionally graded material (FGM) under different combinations of internal pressure and cyclic through-thickness temperature gradients.Design/methodology/approachThe normality rule, nonlinear kinematic hardening Chaboche model and Von Mises yield criterion were used to model the constitutive behavior of an FG tube in the incremental form. The material properties and hardening parameters of the Chaboche model vary according to the power-law function in the radial direction. The backward Euler integration scheme combined with return mapping algorithm which relies on the solution of a nonlinear equation performs the numerical procedure. The algorithm is implemented within the user subroutine UMAT in ABAQUS/standard.FindingsThe published works on FG components considering only the mechanical and physical properties as a function of spatial coordinate and nonlinear kinematic hardening parameters have not been considered to be changed continuously from one surface to another. Motivated by this, the present paper has deliberately been targeted to tackle this kind of problem to simulate the cyclic behavior of an FG tube as accurately as possible. In addition, to classify various behaviors the FG tube under cyclic thermomechanical loadings, Bree’s interaction diagram as an essential tool in designing of the FG pressure vessels in many engineering sectors is presented.Originality/valueProvides a detailed description of the FG parameters of Chaboche kinematic hardening parameters in the adopted constitutive equations. In this paper, the significant effects of internal pressure values, kinematic hardening models and also FG inhomogeneity index related to the hardening rule parameters on plastic deformation of the FG tube are illustrated. Finally, the various cyclic behaviors of the FG tube under different combinations of thermomechanical loading are fully explored.

Study on Damage Accumulation and Life Prediction with Loads below Fatigue Limit Based on a Modified Nonlinear Model

Most fatigue theories neglect the loads below fatigue limit in damage accumulation, which leads to inconsistency between the predicted and the actual fatigue lives. In this study, a novel damage model is proposed to take into account the loads below fatigue limit from two aspects: the strengthening effect and the cumulative damage. The strengthening effect is introduced by an exponential function and the cumulative damage is calculated by fuzzy method with membership functions (MFs). The proposed model is verified against the experimental data under variable amplitude loading conditions. It is found the modified model with Cauchy MF significantly reduces the relative error of predicted life from 35.18% (linear model) and 16.09% (original Chaboche model) to 8.38% (proposed model). As a case study, the proposed damage model is implemented to evaluate the service life of a compressor blade under variable amplitude loading spectrum containing small loads below the fatigue limit.