Hardening Model Research Articles

Nanocarbon architecture-dependent strengthening and deformation in Al matrix composites

The extraordinary strength of inner graphene walls in carbon nanotube (CNT) is barely exerted due to the weak inner-wall shear resistance, which extremely limits its load-bearing capability. To overcome such deficiency, nanocarbon architecture engineering from CNT to graphene nanoribbon (GNR) was performed via longitudinal unzipping of multi-walled CNT, which was utilized to reinforce pure Al. Results show that the activation volume of composites at macroyielding point, evaluated by stress relaxation experiments, monotonically decreases from CNT/Al to GNR/Al, which results in the continuous increase of critical resolved shear stress (CRSS) called for dislocation nucleation/cross-slip at the grain boundaries. Shear-lag model and numerical simulations demonstrate the increased load-transfer effect from CNT/Al to GNR/Al. Meanwhile, the isotropic and kinematic hardening in nanocarbon/Al composites were investigated both by loading-unloading-reloading tests and strain hardening model on basis of dislocation behavior, wherein the effective stress was determined as being larger than back stress in the composites. Detailed analysis further indicates that the nanocarbon architecture from CNT to GNR increases the back stress strengthening due to the enhanced dislocation accumulation at nanocarbon/Al interface. Moreover, as CNT was unfolded to GNR, the failure mode of reinforcements in the composites gradually changed from pull-out to breakage.

Welding Distortions Analysis Considering the Hardening Model, Deposition Processes, and Dissimilar Mechanical Behavior of the Base and Filler Metal

Welding Distortions Analysis Considering the Hardening Model, Deposition Processes, and Dissimilar Mechanical Behavior of the Base and Filler Metal

Modeling and Crystal Plasticity Analysis of Strain Hardening in Metallic Materials under the Influence of Microstructure

Modeling and Crystal Plasticity Analysis of Strain Hardening in Metallic Materials under the Influence of Microstructure

Elastoplastic Mechanical Properties and Kinematic Hardening Model of 35CrNi3MoVR.

The existing tensile-compression elastoplastic models are not suitable for varies of materials. An accurate constitutive model of the elastoplastic mechanical properties more suitable for 35CrNi3MoVR was produced by optimizing the existing fitting equations based on uniaxial tensile-compression tests, which are able to describe the elastoplastic stress-strain relation and Bauschinger effect varying with the maximum tensile plastic strain. A UMAT subroutine of the constitutive model in ABAQUS was proposed and conducted for FEM calculation. Hydraulic autofrettage tests were carried out under different pressures on thick-walled 35CrNi3MoVR tubes, and the results were compared with those of FEM calculations to further validate the accuracy of the fitting model. The results show that the constructed power function kinematic hardening model can effectively describe the elastoplastic mechanical properties of 35CrNi3MoVR and can be applied to the autofrettage calculation of this material. The comparison among the calculation results of different models proved that the model proposed in this research has better performance compared to other existing models. Taking the Mises stress at the inner surface of the thick-walled tubes as the evaluation criterion, the error of the power function kinematic hardening model reaches less than 3%, decreasing the error by at least 50%.

Application of Dimension Extending Technique to Unified Hardening Model

This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so that the constitutive integration of the plasticity can be reduced to an initial value problem of differential–complementarity equations, which is solved using the Gauss–Seidel algorithm-based Projection–Correction for the mixed complementarity problem. The Gauss–Seidel based Projection–Correction algorithm does not require the calculation of the Jacobean matrix of the potential function, making it relatively easy to implement in programming. The unified hardening model is proposed based on the modified Cam–Clay model and the sub-loading surface model, and the elastic properties are pressure-dependent. Two processing methods, backward Euler integration and exact elastic property, are used for the variable elasticity properties. The constitutive integration of the increased dimensional unified hardening model is reduced to a special mixed complementarity problem and solved by the proposed algorithm, which does not need to calculate the Jacobean matrix of the potential function, and greatly simplifies the derivation process. Several numerical examples are given to verify the feasibility of the incremental constitutive integration in the unified hardening model, including the single integral point and the boundary value problems. The research results have expanded the scope of use of the Gauss–Seidel based Projection–Correction algorithm.

A probabilistic coupled hardening model of double irradiation defects in iron

Irradiation hardening effect is of significance to the design and life extension of nuclear materials. Although various types of defects coexist under in-pile condition, most irradiation hardening models like the dispersed barrier hardening (DBH) model ignore their strength difference and treat them as a single defect type. In this work, the barrier strengths in presence of combined 〈111〉 and 〈100〉 loops in bcc iron are investigated using discrete dislocation dynamics simulations. Considering the coupling effect, the non-periodic distributed effect is preliminarily analyzed. A probabilistic model accounting for their coupled hardening effect is established based on dislocation depinning mechanism from simulation results, which can be also integrated into the modified DBH model using an effective barrier strength factor. The model presents good agreements with experimental results of iron alloy, and exhibits potential applicability in predicting the coupling effects of other defect types, including the dislocation loops and voids.

Effects of kinematic hardening of mucus polymers in an airway closure model

The formation of a liquid plug inside a human airway, known as airway closure, is computationally studied by considering the elastoviscoplastic (EVP) properties of the pulmonary mucus covering the airway walls for a range of liquid film thicknesses and Laplace numbers. The airway is modeled as a rigid tube lined with a single layer of an EVP liquid. The Saramito–Herschel–Bulkley (Saramito-HB) model is coupled with an Isotropic Kinematic Hardening model (Saramito-HB-IKH) to allow energy dissipation at low strain rates. The rheological model is fitted to the experimental data under healthy and cystic fibrosis (CF) conditions. Yielded/unyielded regions and stresses on the airway wall are examined throughout the closure process. Yielding is found to begin near the closure in the Saramito-HB model, whereas it occurs noticeably earlier in the Saramito-HB-IKH model. The kinematic hardening is seen to have a notable effect on the closure time, especially for the CF case, with the effect being more pronounced at low Laplace numbers and initial film thicknesses. Finally, standalone effects of rheological properties on wall stresses are examined considering their physiological values as baseline.

User friendly FE Formulation for anisotropic distortional hardening model based on non-associated flow plasticity and its application to springback prediction

Based on non-associated flow plasticity, a newly developed anisotropic distortional hardening model developed by Hu and Yoon [15] is implemented in finite element analysis in a user-friendly manner. The derivatives of complex hardening models are calculated using the Finite Difference Method (FDM), which is much more convenient than using the analytical derivatives. To further improve the accuracy of the proposed method, the step size analysis in FDM is performed by analyzing the derivative formation. To evaluate the accuracy and computational efficiency of a proposed step size for FDM, single element simulations are performed under different loading paths. It has been found that the maximum absolute error of the flow curves between the simulation and the theoretical result is less than 0.3%. The U-bending tests for DP600 and TRIP1180 are used to verify the ability of the distortional hardening model for springback prediction. The simulation result of the strain hardening model is in good agreement with the experiment. The computational efficiency is also increased by 24% due to the improved convergence rate.

Modeling of distortional hardening including plane strain tension and pure shear for a TWIP steel

This paper focuses on calibrating and modeling of distortional hardening behaviours in twinning induced plasticity steels. True stress-strain curves for uniaxial tension, plane strain tension, and pure shear specimens are inversely identified from corresponding load-displacement curves. The study reveals that accurately predicting the hardening behaviours of TWIP980 steel under plane strain tension and pure shear stress states is challenging with an isotropic hardening model, and a negative hydrostatic effect for TWIP980 is observed through shear testing. A novel distortional hardening model is proposed to simultaneously accommodate the three stress states on the contours of plastic work. Coefficients of the distortional hardening model are calibrated at discrete levels of plastic work and then interpolated to describe the distortion of the initial yield surface. The model is then expanded to consider the true stress-strain curves under uniaxial tension along 0, 45 and 90-degree directions, as well as under the plane strain tension along the 0-degree direction simultaneously. This expansion explicitly incorporates the three true stress-strain curves under uniaxial tension, with the curve of plane strain tension captured by an evolutionary exponent related to plastic work. The developed distortional hardening models demonstrate reasonable reproduction of load-displacement curves for TWIP980 steel under uniaxial tension, plane strain tension, and pure shear stress states.

Residual Stress Analysis of Re-autofrettage of a Swage-Autofrettaged Tube by Computer Modeling Incorporating Accurate Material Representation

Autofrettage processes allow engineers to reduce the thickness of thick-walled cylinders or components in high-pressure applications without sacrificing strength, life, or safety. However, during the autofrettage process, residual stresses will be generated due to plastic deformation. The complex tube material behavior is dominated by the Bauschinger effect. A better understanding and accurate prediction of the residual stress field is critical, which will enable better piping design strategies to minimize deformation and stresses under operating conditions. This study aims to predict and analyze residual stresses resulting from hydraulic re-autofrettage of a swage-autofrettaged thick-walled cylinder by computer modeling. A case study was performed on a thick-walled cylinder of A723 alloy with a radial interference of 2.5%. In order to investigate the effect of the chosen material constitutive representation, results based on the true material constitutive model were compared with the simplified prevalent material model of bi-linear kinematic strain hardening. Computer implementation for the true material was via a user-developed subroutine that incorporates the complex Bauschinger effect. The results indicate that an accurate material constitutive representation is crucial for better and more accurate prediction and understanding of residual stresses induced by autofrettage processes. Computer modeling based on the true material constitutive representation will likely prove to be a powerful tool for the design of autofrettage processes in general and thick-walled cylinders in particular.

Atomistic investigation of the interaction between an edge dislocation and 1/2 interstitial dislocation loops in irradiated tungsten

By impeding dislocation motion, the irradiation-induced dislocation loops cause irradiation hardening and further embrittlement of plasma-facing tungsten in fusion reactors, leading to its performance degradation. But fundamental questions regarding the mechanisms remain to be clarified and predictive model for loop hardening remains to be built. In this paper, interactions between gliding edge dislocations and interstitial dislocation loops (with Burger vector bL = ½<111>) are studied using atomistic simulations. The influences of bL orientations, dislocation-loop intersection positions, loop sizes, and loading conditions (temperature and strain rate) on the interactions are systematically calculated and analyzed. Results show a large variety of interaction mechanisms, depending mainly on the relative orientations of bL to dislocation slip plane, while slightly affected by loading conditions. Although loops with bL parallel to the plane can be easily swept away by gliding dislocations, loops with bL inclined to dislocation slip plane can strongly pin the gliding dislocation by forming a sessile 〈100〉 segment, which would bend the dislocation line into a screw dipole. Thus, high stress is required for the dislocation line to break away from the inclined loops by cross-slip of each individual arm of the screw dipole coupled with glide of the 〈100〉 segment. On the other hand, increasing temperature and/or decreasing strain rate hardly change the above mechanisms, but monotonically reduce the obstruction by these loops. Simplifying the complex motion of the edge dislocation pinned by the inclined loops as a thermally-activated process of a 1/2[111] edge dislocation overcoming barriers, a hardening model for the inclined loops is proposed. This model well describes the dependence of loop strength on loop sizes, temperatures and strain rates. The model is then applied to predict irradiation hardening at experimental strain rates, and it shows reasonable agreement with experimental results.

Investigation of the influence of plane strain constrained anisotropic plastic flow on the localized necking prediction

PurposeThe purpose of this manuscript is to investigate the influence of the satisfying of plane strain conditions on the prediction of the localized necking and to evaluate this effect by the different hardening models.Design/methodology/approachHigh-order anisotropic Drucker yield function, two types of hardening models, namely Hollomon power and Voce saturated, and the modified maximum force criterion (MMFC) are employed to predict the forming limit strains of AA3104-H19 alloy. Two identification methods, namely conventional and plane strain constrained, are applied and forming limit diagrams of the material are predicted by the incorporation of the anisotropic Drucker criterion and the hardening models into the MMFC for both calibration methods.FindingsThe enhancement in the prediction accuracy of the forming limits provided by the implementation of the plane strain constrained method is strongly dependent upon the selected hardening model type in the MMFC. About 18% improvement in the prediction of the biaxial limit strains is provided via Hollomon power law hardening, whereas the opposite result is occurred in case that the Voce saturated hardening law is used, and the predictions match with the experimental data only in the plane strain point and its surroundings.Originality/valueThe plane strain constrained identification method precisely predicts the location of the plane strain point on the yield locus and also any yield stress or anisotropy coefficient in the plane strain state is not required during the calibration, therefore the method can reduce the number of the required experiments for the constitutive characterization, and it will be attractive for both academy and industry. Additionally, the improvement in the prediction of the biaxial forming limits can be provided by applying of this method along with the appropriate hardening law.

Calculating the grain size effect during strain hardening through a probabilistic analysis of the mean slip distance in polycrystals

Grain refinement is an important mechanism to produce stronger alloys. Strain hardening is an essential phenomenon in metal forming processes. The interaction between grain size and strain hardening is evident: a decrease in grain size (dg)causes an increase in ultimate tensile strength but a decrease in uniform elongation. The Kocks-Mecking (KM) model for strain hardening is based on the relationship between shear strain and the path length for dislocation slip. It provides good general estimates for stress-strain curves, and empirical modifications have been made to include dg. Here, the empirical approach is substituted by theoretical probability calculations, accounting for the fact that the grain size imposes a bound on the mean slip distance, while strain compatibility defines a relationship between grain boundary-dislocation interaction and bulk storage and annihilation. The resulting differential only uses the two parameters inherent to KM. Fitting to published tensile curves for Al, Cu, and Ni produces excellent results. The fitting parameters allow to predict the tensile strength as a function of dgto good approximation, for dg>1μm. Below this limit, fundamental changes in dislocation statistics impose the activation of grain boundary dislocation sources and may induce dislocation density gradients, which seem to determine the flow stress in the sub-μm range.

Characterisation and modelling of anisotropic hardening behaviour of cubic and hexagonal close packed polycrystalline metals

ABSTRACT In this study, anisotropic non-proportional hardening behaviour of the sheet metals with different crystalline structures is investigated. The investigated materials particularly exhibit the Bauschinger effect and complex transient hardening behaviour during loading path change. Furthermore, the finite element simulations are carried out to evaluate the performance of the distortional and multi-surface-kinematic hardening models in flow stress prediction under loading path change. Both models can well reproduce the measured anisotropic hardening, but the distortional hardening concept shows better predictive capability for flow stresses. The improved accuracy of the flow stress prediction with the distortional hardening model compared to the kinematic hardening is attributed to its flexibility in distortion of the yield surface following microstructure deviator independent on the initial yield surface. In contrast, the initial size of the yield surface in the kinematic hardening significantly affects the determination of the re-yielding stress at load reversal.

Experimental analysis and modeling of mixed hardening of Steel Matrix Composites under monotonic and reverse simple shear loading: Application to SPIF process

This study explores the distinctive characteristics of Steel Matrix Composites (SMCs) reinforced with TiB2, concentrating on their hardening behavior during simple shear tests. The analysis considers an elastoplastic model with Isotropic and Mixed hardening. Emphasizing the necessity of kinematic hardening, experimental characterizations using EBSD and XRD highlight effects of matrix grain size and reinforcement impact on mechanical properties. Validation of the numerical model through Stress-Strain curves reveals a strong correlation, particularly with the mixed hardening model under reverse shear loading. Comprehending SMC strain hardening is crucial for optimizing parameters and numerically designing forming processes, enhancing manufacturing efficiency.

A numerical model simulating cyclic behavior of high-strength steel

High-strength steel (HSS) can effectively and economically design structural members that withstand large forces induced by extreme events such as earthquakes. To evaluate the seismic performance of HSS members and structures using nonlinear finite element (FE) analyses, using an accurate material model is important, which can simulate the inelastic cyclic behavior of the HSS. The peculiar material behavior of HSS needs to be considered in the model. This study used a combined hardening model to construct the material model. The configuration of the model and the constituent model parameter values are determined to precisely simulate the low-cycle fatigue (LCF) behavior of HSS. An efficient particle swarm optimization (PSO) algorithm is used to determine parameter values with LCF test data of 54 individual HSS coupons. In additions, to conveniently determine the model parameter values with only monotonic tensile test data instead of conducting expensive LCT tests, empirical equations are proposed. It is shown that the LCF curves of HSS can be accurately simulated using the constructed material model with the proposed equations.

Plastic behavior and shakedown limit of defected pressurized pipe under cyclic bending moment

Pipelines subjected to thermal or mechanical loads may fail due to plastic strain accumulation which leads to ratcheting. In this research, cyclic plastic behavior and shakedown limit are investigated experimentally and numerically for a defected pressurized pipe under cyclic bending moment. In the numerical model, the combined isotropic/kinematic hardening model based on the Chaboche model is adopted to represent the cyclic plastic flow of the material. The hardening parameters are determined experimentally and used in the finite element (FE) model. A four-point bending test rig is manufactured to test a pressurized API 5L steel pipe under cyclic bending. An elliptical defect is created by machining to depict corrosion pits in pipes. The plastic strains are measured experimentally and the results are used to tune the parameters of the FE model. The shakedown limit of the defected pipe is determined numerically by tracking the critical points behavior and the results are verified experimentally. Furthermore, the plastic work dissipated energy (PWD) is estimated within the defective structure to study the behavior of the pipe. By running this compatible model, it is found that the yield and the shakedown limits are lowered by mean values of 55% and 25% respectively due to the presence of metal loss defect occupying almost half of the pipe thickness.

Low-Cycle Fatigue Behavior and the Combined Cyclic Hardening Material Model of Plate-Shaped Zn-22Al Alloy for Seismic Dampers.

This study investigates the potential of the plate-shaped Zn-22 wt.% Al (Zn-22Al) alloy as an innovative energy dissipation material for seismic damping devices, since plate-shaped material is more suitable to fabricate large-scale devices for building structures. The research begins with the synthesis of Zn-22Al alloy, given its unavailability in the commercial market. Monotonic tensile tests and low-cycle fatigue tests are performed to analyze material properties and fatigue performance of plate-shaped specimens. Monotonic tensile curves and cyclic stress-strain curves, along with SEM micrographs for microstructure and fracture surface analysis, are acquired. The combined cyclic hardening material model is calibrated to facilitate finite element analysis. Experimental results reveal exceptional ductility in Zn-22Al alloy, achieving a fracture strain of 200.37% (1.11 fracture strain). Fatigue life ranges from 1126 to 189 cycles with increasing strain amplitude (±0.8% to ±2.5%), surpassing mild steel by at least 6 times. The cyclic strain-life relationships align well with the Basquin-Coffin-Manson relationship. The combined kinematic/isotropic hardening model in ABAQUS accurately predicts the hysteretic behavior of the material, showcasing the promising potential of Zn-22Al alloy for seismic damping applications.

Comparison of homogeneous anisotropic hardening models in the case of the direct redrawing of a DP600 steel

The use of DP600, an advanced high strength steel, has gained significant attention in automotive industry, especially for complex structures that require multi-step forming operations, leading to non-linear strain path changes. From a numerical modelling perspective, the use of advanced constitutive equations has enabled a precise representation of a large range of behaviors, encompassing reverse and orthogonal strain path changes. Within this context, this study is dedicated to the numerical simulation of a two-step deep drawing process based on distortional plasticity. Two models developed within the Homogeneous Anisotropic Hardening (HAH) framework are considered. This study presents a comparison of the model predictions, calibrated over the same experimental database, in terms of their ability to predict the strain path changes and mechanical behavior of the material during the forming process. Several outputs like the punch load evolution and the strain field are compared with experimental data.

Crystal plasticity finite element method investigation of normal tensile deformation anisotropy in rolled pure titanium sheet

Industrial pure titanium with hexagonal close-packed (HCP) crystal structure has a high degree of anisotropy at room temperature. On the mesoscopic scale, this is due to the rolling texture presented by its crystal orientation. Tensile tests were performed on smooth specimens with five angles in the first quadrant at room temperature, and the central deformation region and fracture region were characterized using EBSD and SEM, respectively. The modified Salem anisotropic hardening model is incorporated into the crystal plasticity finite element method (CPFEM) framework in the form of incremental hardening to describe the initial strength and hardening increment evolution of each deformation system of pure titanium. Both slip dislocation and twinning mechanisms are considered in the CPFEM simulation. Three models with different meshing strategies are used to simulate the tensile conditions to capture the evolution of macro and micro variables of pure titanium sheet. The results show that there are anisotropy in stress-strain, system activity, cumulative shear strain, crystal orientation, twin volume fraction, stress triaxiality and Lode parameter. The purpose of this paper is to explore the anisotropy of macro-meso variables in different directions before damage occurs, so as to provide reference for the subsequent construction of related damage models.