Bauschinger Effect Research Articles

A Transition State Theory-Based Continuum Plasticity Model Accounting for the Local Stress Fluctuation

Based on the transition state theory, a continuum plasticity theory is developed for metallic materials. Moreover, the nature of local stress fluctuation within a material point is considered by incorporating the probability distribution of the stresses. The model is applied to investigate the mechanical behaviors of 316 L stainless steel under various loading cases. The simulated results closely match the results obtained by the polycrystal plasticity model and experiments. The mechanical behaviors associated with strain rate sensitivity, temperature dependence, stress relaxation, and strain creep are correctly captured by the model. Furthermore, the proposed model successfully characterizes the Bauschinger effect, which is challenging to capture with a conventional continuum model without additional assumptions. The proposed model could be further employed in the design, manufacturing, and service of engineering components.

Orientation-dependent yield and Bauschinger effects in two-dimensional Yukawa solids

Langevin dynamics simulations of two-dimensional (2D) Yukawa solids are performed to investigate the orientation-dependent yield and Bauschinger effects in solid 2D dusty plasmas. The yield stress of 2D Yukawa solids under different conditions is determined from the corresponding stress-strain response curve, defect fraction, and deviation from the affine displacement. It is discovered that both the shear modulus and yield stress are orientation dependent, exhibiting the significant anisotropic behaviors. It is found that the dependence of the calculated atomic elastic constant on the lattice orientation completely agrees with those of the shear modulus and yield stress. It is also found that, for different initial lattice orientations, the Yukawa solid exhibits the significant regular or reverse Bauschinger effects, or even non-Bauschinger effect. Published by the American Physical Society 2024

Strain path dependent dynamic recrystallization and its resulted material flow and microstructure evolution of a titanium alloy

Changing strain path is an effective method to optimize the hot working process and improve microstructure and mechanical performance of titanium alloys. In this work, dynamic recrystallization (DRX) and its resulted material flow and microstructural behaviors in monotonic torsion (MT) and forward-reverse torsion (FRT) were comparatively explored by experimental and crystal plastic finite element simulation methods. The results indicate that both MT and FRT can induce discontinuous DRX (DDRX) and continuous DRX (CDRX). However, compared to MT where CDRX always prevails, FRT makes DDRX more important since it inhibits CDRX by recovering the lattice rotation during the reversal stage. Moreover, in FRT, the driving force and the grain boundary content for DDRX nucleation and bulging are relatively low at a small total strain. And the recovery of lattice rotation in FRT can also suppress CDRX. Therefore, DRX kinetics is obviously delayed at a smaller strain. As strain increases, both the stored energy for DDRX and the long-range misorientation gradient for CDRX are gradually greater, thus improve DRX kinetics. With these effects by DRX, although FRT exhibits a lower grain refinement degree at a smaller total strain compared to MT, it can make grain refinement degree rapidly rise and even close to that in MT at a greater strain. Also, FRT can obviously weaken the deformation texture by inducing extensive DDRX grains and recovering the lattice rotation of retained grains. In addition, the texture formed in forward stage and DRX delaying can result in a decrease in yield strength and softening rate in reversal stage, respectively, i.e., exhibiting remarkable Bauschinger effect, especially at a higher forward strain. These results can provide a basic guidance for designing the hot working process of titanium alloys to obtaining more refined microstructure and excellent properties of the components.

Interpretation of the stress dip test as a means of characterizing backstress: Experiments and backstress-aided crystal plasticity modeling of polycrystalline tantalum

Backstresses, associated with certain dislocation arrangements and their inter-dislocation long-range stresses, are known to contribute significantly to deformation response of metals, including kinematic hardening, the Bauschinger effect (BE) and the Hall-Petch effect. Various methods have been employed to quantify these backstresses at the macro-scale. One of these approaches, which has received relatively little attention, is the stress dip test. The strain rate observed during a load dip and hold, after previous plastic deformation, can be positive or negative, depending upon the level at which the load is held, and the relative magnitudes of competing friction and backstresses. The most direct interpretation of previously reported tests indicates a surprisingly high level of backstress in common materials, and which is generally also higher than the value extracted from an unload-reload test. In this paper, stress dip tests are performed on pure polycrystalline tantalum, along with unload-reload tests. A plateau is seen in the strain rate observed during the stress dip test, which has not been previously reported. If the backstress is interpreted to correspond with the stress level associated with the middle point of the plateau, in line with the friction/backstress model of the unload-reload test, the resulting backstress obtained from both tests are very similar. A novel crystal plasticity model, incorporating backstress, reversible dislocations and non-Schmid effects, is used to help justify this new approach. The model predicts the observed plateau in strain rate, and provides a slip-level interpretation of the macroscopically observed backstress. The slip-level backstress (when considered as a fraction of the stress prior to the dip) is reasonably similar to the values interpreted from the dip test experiment. The ∼23% lower value in the simulation may be due to the lack of certain aspects of the actual physics in the model.

Direct application of elasto-visco-plastic self-consistent crystal plasticity model to U-draw bending and springback of dual-phase high strength steel

The incremental elasto-visco-plastic self-consistent polycrystal model (ΔEVPSC) was utilized to describe the constitutive behavior of dual-phase 980 (DP980) steel. A simple baseline modeling approach was chosen: the hardening behavior of each constituent phase in the DP980 steel was described by a simple Voce hardening law without explicitly considering the back stress; and it was assumed that using the same single crystal elastic modulus for ferrite and martensite is sufficiently representative. The adequacy of this baseline modeling approach was evaluated by comparing various mechanical experimental data with model predictions in terms of the stress vs. strain curves obtained from uniaxial tension, tension-compression, and loading-unloading-loading (LUL) tests. Additionally, the evolution of experimental lattice strain data reported in literature was used to validate the phase-specific Voce hardening parameters. Despite its minimalistic modeling description, the baseline ΔEVPSC model successfully captured key features: 1) the Bauschinger effect, 2) the decrease in chord modulus, and 3) the non-linearity in the stress vs. strain curves resulting from the LUL test. All three mentioned characteristics are crucial for accurate prediction of springback in sheet metals. The ΔEVPSC model, interfaced with a finite element solver (Abaqus/standard) as the user material subroutine, was employed to simulate the Numisheet93 benchmark problem. The strip of DP980 was first U-drawn followed by springback. The model-predicted springback profile aligned well with the experimental results only when stress relaxation was properly considered, resulting in improved predictive accuracy compared to predictions based on a distortional plasticity model.

Uniaxial material model with softening for simulating the cyclic behavior of steel tubes in concrete‐filled steel tube beam‐columns

AbstractThis paper presents a new uniaxial constitutive material formulation with softening for simulating the inelastic behavior of steel rectangular tubes in concrete‐filled steel tube (CFST) members. The primary behavioral characteristics of the steel tube in CFST members are isolated and pronounced through a carefully designed experimental campaign with CFST specimens subjected to uniaxial strain‐based loading protocols. The model is expressed in an effective stress–strain domain, where the effective uniaxial strain is defined as the uniaxial displacement within a dissipative zone over a predefined length. In the pre‐peak state, the proposed model can effectively capture the combined kinematic/isotropic hardening and Bauschinger effect—characteristic of mild structural steels—within the framework of rate‐independent plasticity. In the post‐peak state, the proposed model traces strength deterioration due to outward local buckling, which is a characteristic nonlinear geometric instability in CFST members due to the presence of the filled concrete in the steel tube. The proposed constitutive formulation incorporates a softening branch that exponentially decays to trace the stabilization of the outward buckling wave within the buckling region in successive inelastic loading cycles. Cyclic deterioration of the effective stress is explicitly considered via an energy‐based rule. The proposed model is calibrated to a CFST dataset. Regression equations are proposed for predicting the input model parameters. These equations cover a wide range of geometric parameters and structural steel materials in CFST members. Comparisons with prior tests on actual CFST beam‐columns under planar symmetric cyclic loading suggest that conventional 2‐dimensional displacement‐based beam‐column elements can predict the full‐range of the hysteretic behavior of the CFST members with the proposed constitutive formulation including cases where the post‐peak response of CFST members exhibits negative stiffness.

Crystal-plasticity modelling of the yield surfaces and anelasticity in the elastoplastic transition of metals

The paper presents a full-field crystal-plasticity computational investigation of 10με small-strain-offset yield surfaces with pointed vertexes that are seen in the elastoplastic transition of pre-strained polycrystal metals. It is concluded that the shape of these yield surfaces obtained with a full-field spectral solver compares reasonably well with calculated ones by a simple aggregate Taylor model. The influence of material strength, work hardening, and texture are discussed. An assessment is made of the origin of anelasticity and Bauschinger effects at small strains, considering two mechanisms. Firstly, there is a built-in composite effect in crystal elastoplastic simulations due to the mixture of elastically and plastically loaded grains. Secondly, kinematic hardening of reverse slip systems will contribute to the Bauschinger effect. Based on analyses of the computed selected cases and comparison to previously published measurements, it is concluded that both mechanisms are important.

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%.

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.

Monotonic tensile and cyclic deformation of a Ni-based single crystal superalloy with anisotropic microstructural rafting patterns at high temperature: Experiment and constitutive modelling

Monotonic tensile and cyclic deformation behaviours are investigated under different microstructural rafting states of a SC Ni-based superalloy, with emphasis on the influences of the rafting extent, type and loading orientation. The deformed microstructures and the dislocation configurations are characterized to give a micro-based understanding on the varying of deformation behaviours due to rafting. It is found that the decreases in the initial yield point and cyclic stress amplitude are only related to the rafting extent. Nevertheless, the rafting type (namely, the plate-like and needle-like morphology) has an undeniable contribution to the shape of hysteresis loops, where the plate-like rafting morphology results in more significant Bauschinger effect than needle-like rafting morphology. The variation of monotonic and cyclic deformation induced by rafting shares affinity with the alteration of internal stress and the movement of dislocations. Afterwards, a microstructure-sensitive constitutive model with two-phase flow rules has been developed. The effect of rafting on the monotonic and cyclic stress-strain responses is captured by introduce a series of microscopic mechanisms and a micromechanics-based back stress model that considers the morphology and size of the γ'/γ two-phase structures. The developed model is used to simulate the macroscopic stress-strain responses of the SC Ni-based superalloy under different rafting states. Model predictions are in good agreement with tests, capturing the reduction of cyclic stress amplitudes and the change in hysteresis loops. Finally, the impacts of the two-phase flow rules and the micromechanics-based back stress on the simulation capability have been discussed.

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.

Evaluation of Rotation Capacity and Bauschinger Effect Coefficient of I-Shaped Beams Considering Loading Protocol Influences

Recent catastrophic earthquake events have reinforced the necessity of evaluating the seismic performance of buildings. Notably, the buildings can go into the plastic phase during a striking earthquake disaster. Under this condition, the current design codes assume seismic response reduction by virtue of the energy dissipation capacity of the structural members. In the strong-column–weak-beam design, which involves I-shaped beams and boxed columns, the mechanism is defined as a standard design scheme to prevent the building from collapsing. Therefore, energy dissipation relies highly on the I-shaped beam performance. However, the I-shaped beam performance can differ depending on the loading history experienced, whereas this effect is untouched in the prevailing evaluation equation. Hence, this study first performs cyclic loading tests of 11 specimens using different loading protocols. The experimental results clarify the fluctuation in the structural performance of I-shaped beams depending on the applied loading hysteresis, proving the necessity of considering the stress history for proper assessment. Furthermore, the database of experimental results is constructed based on the previous experimental studies. Ultimately, the novel evaluation equation is proposed to reflect the influences of the loading protocol. This equation is demonstrated to effectively assess the member performance retrieved from the experiment of 65 specimens, comprising 11 specimens from this investigation and 54 specimens from the database. The width–thickness ratio, shear span-to-depth ratio, and loading protocols are utilized as the evaluation parameters. Moreover, the prediction equation of the Bauschinger effect coefficient is newly established to convert the energy dissipation capacity under monotonically applied force into hysteretic energy dissipation under the cyclic forces.

Modeling Bauschinger effect through the reversibility of dislocation slip in an Al–Cu–Li alloy

Al–Cu–Li alloys are promising lightweight materials for extensive applications in aerospace. As aerospace components often experience strain path changes during service, understanding the resulting Bauschinger effect is crucial for optimizing the fatigue resistance and performance of these alloys. This study investigates the role of T1 precipitates in the Bauschinger effect in AA2099. The presence of shearable T1 precipitates has been found to significantly influence the Bauschinger effect by reducing the strengthening effect of T1 precipitates during reverse straining. An analytical expression for slip reversibility has been derived to quantify this phenomenon, and a microstructure-based constitutive model has been developed to accurately predict the Bauschinger effect in AA2099.

Dynamic strength differential and Bauschinger effects in an extruded AZ80 magnesium alloy

Quasi-static and high-rate tension and compression properties of an extruded AZ80 Mg alloy rod were investigated at loading rates of 0.001 and 500 s−1. Acquired stress – strain results show that tension and compression plastic deformations of AZ80 rod are asymmetric, and such strength differential effect is dependent of strain rate and loading orientation. Strength differential effect is weakened at 500 s−1 when the sample was loaded along the extrusion direction. Crystal plasticity simulations on the basis of the visco-plastic self-consistent method were performed. Numerical results indicate that the rate and orientation dependency of strength differential effect in AZ80 alloy is related to {101‾2} extension twinning. High-rate tests for pretension, unloading and reverse compression were realized to investigate the dynamic Bauschinger effect. Experimental results show that Bauschinger effect of AZ80 alloy is anisotropic and sensitive to the strain rate. A Bauschinger effect parameter considering strength differential effect was proposed, and it was found that the Bauchinger effect in the extrusion direction is reduced significantly at 500 s−1.

Ductile damage and fracture characterizations in bi-cyclic biaxial experiments

This paper discusses novel extremely low-cycle bi-cyclic biaxial reverse experiments with large strains. Various tests with tension–compression–tension (TCT) shear cyclic loads, superimposed by either non-reverse or reverse cyclic loading patterns, are newly designed to investigate the plastic, damage, and fracture behavior. These experiments fill the gaps in carrying out complex reverse loading by utilizing 4mm thick biaxially loaded cruciform specimens. The deformed specimens in different loading stages are examined metallographically with micrographs to elucidate the influence of loading histories on the occurrence and evolution of micro-defects. In addition, scanning electron microscopy (SEM) is also used to analyze the fractured surfaces and verify the anisotropic damage mechanism. An advanced anisotropic cyclic plastic-damage continuum model is utilized to characterize the material behavior, including the Bauschinger effect, the stress-differential effect and the non-hardening effect after shear reverse loading as well as stress-state-induced damage mechanisms. Due to the utilization of the digital image correlation (DIC) technique, the numerical results can be compared with the experimental ones in both load–displacement curves and strain fields, respectively. The elastic strain triaxiality and strain Lode parameter are introduced, providing a novel perspective for analyzing the cyclic loading experiments.

Bauschinger effect in an aluminium alloy designed for laser powder bed fusion

Aluminium alloys designed for additive manufacturing often exhibit heterogeneous microstructures. A bimodal grain size distribution is observed with submicron equiaxed grains at the bottom of the melt pool and coarser columnar grains in the melt pool interior. Microstructural heterogeneities also develop at the intragranular scale (a large proportion of intermetallics with differences in size and morphology) down to the atomic scale (solid solution variations and nanoprecipitation) depending on the region of interest. Using uniaxial tensile-compression tests, we evaluate the Bauschinger effect in a new Al-4Mn-3Ni-2Cu-1Zr alloy designed for additive manufacturing. The strong Bauschinger effect is attributed to short-range and long-range back-stresses caused respectively by a high density of interfaces (grain boundaries and intermetallic/matrix interfaces), and strain partitioning between different regions of the microstructure showing different mechanical behaviour. We conclude that the impact of the back-stress should be systematically considered when investigating the mechanical response of this new class of alloys.

On the role of higher-order condition of strain gradient plasticity in the cyclic torsion of thin metallic wires: Experiments and modeling

Cyclic torsion tests are performed on micron-scale copper wires with and without surface passivation to study the role of the higher-order condition in the plastic behavior of thin wires under non-proportional loading. A typical strengthening size effect is observed in the symmetric cycles. More obvious strength enhancement exists in the torsional response of passivated copper wires. An unusual Bauschinger effect is found during the loading-unloading cycles, which is more pronounced in passivated wires. The finite element implementation based on Gudmundson's strain gradient plasticity theory is developed for wire torsion to characterize the observed size-dependent phenomena. The higher-order boundary conditions are introduced to simulate the passivated surface. The predicted radial distributions of plastic strain, stress components, and geometrically necessary dislocation density for the passivated and unpassivated wires are given and compared. This work provides a reasonable basis for understanding the role of higher-order conditions of strain gradient plasticity.

Opposite Bauschinger Effects on Wear of High-Entropy Alloy AlCoCrFeNix (x = 0 to 2) Under Sliding Wear and Machining Conditions

Opposite Bauschinger Effects on Wear of High-Entropy Alloy AlCoCrFeNix (x = 0 to 2) Under Sliding Wear and Machining Conditions

A Full-Field Crystal Plasticity Study on the Bauschinger Effect Caused by Non-Shearable Particles and Voids in Aluminium Single Crystals

In the present work, the goal is to use two-scale simulations to be incorporated into the full-field open software DAMASK version 2.0.3 crystal plasticity framework, in relation to the Bauschinger effect caused by the composite effect of the presence of second-phase particles with surrounding deformation zones. The idea is to achieve this by including a back stress of the critical resolved shear stress in a single-phase simulation, as an alternative to explicitly resolving the second-phase particles in the system. The back stress model is calibrated to the volume-averaged behaviour of detailed crystal plasticity simulations with the presence of hard, non-shearable spherical particles or voids. A simplified particle-scale model with a periodic box containing only one of the spherical particles in the crystal is considered. Applying periodic boundary conditions corresponds to a uniform regular distribution of particles or voids in the crystal. This serves as an idealised approximation of a particle distribution with the given mean size and particle volume fraction. The Bauschinger effect is investigated by simulating tensile–compression tests with 5% and 10% volume fractions of particles and with 1%, 2%, and 5% pre-strain. It is observed that an increasing volume fraction increases the Bauschinger effect, both for the cases with particles and with voids. However, increasing the pre-strain only increases the Bauschinger effect for the case with particles and not for the case with voids. The model with back stress of the critical resolved shear stress, but without the detailed particle simulation, can be fitted to provide reasonably close results for the volume-averaged response of the detailed simulations.

Molecular Dynamics Simulation of Bauschinger Effect in Cu Nanowire with Different Crystallographic Orientation

In this study, the Bauschringer Effect (BE) resulting from tension-compression deformation applied to nanowires obtained by placing Cu atoms in , and highly symmetric crystallographic directions was investigated using the Molecular Dynamics (MD) simulation method. The forces between atoms were determined from the gradient of the Embedded Atom Method (EAM) potential function, which includes many-body interactions. It was determined that there is an asymmetry between the stress-strain curves obtained as a result of the tension and compression deformation process applied to the model system. From this asymmetry, it was determined that the yield stress obtained in the drawing process for nanowire with crystallographic orientation was greater than the yield strain obtained as a result of the compression process. In contrast, the opposite was found for nanowires with crystallographic orientation and . In addition, after the yield strain value is exceeded as a result of the drawing process applied to the model nanowire system, compression deformation process was applied at different pre-strain values. The existence of the Bauschinger Effect (BE), which is expressed as the yield strength value as a result of forward loading corresponding to the tension operation, is smaller than the yield value obtained as a result of the compression process in which the loading is removed, was determined. To clarify the effect of BE on Cu nanowires with different crystallographic orientations, Bauschinger Stress parameter (BSP) and Bauschinger Parameter (BP) values were calculated.