Bauschinger Effect Research Articles

Grain size effect on cyclic deformation behavior and springback prediction of Ni-based superalloy foil

In order to clarify the influence of grain size on cyclic deformation response of superalloy sheets and springback behavior, cyclic loading–unloading and shearing tests were performed on the superalloy foils with 0.2 mm in thickness and diverse grain sizes. The results show that, the decline ratio of elastic modulus is weakened with increasing grain size, and the Bauschinger effect becomes evident with decreasing grain size. Meanwhile, U-bending test results determine that the springback is diminished with increasing grain size. The Chaboche, Anisotropic Nonlinear Kinematic (ANK) and Yoshida-Uemori (Y-U) models were utilized to fit the shear stress–strain curves of specimens. It is found that Y-U model is sufficient of predicting the springback. However, the prediction accuracy is degraded with increasing grain size.

Experimental characterization and crystal plasticity modeling of dual-phase steels subjected to strain path reversals

This paper is concerned with monotonic and load reversal deformation of four dual-phase (DP) 590, 780, 980, 1180 and one martensitic (MS) 1700 steel sheets. While the monotonic data are presented for all steels, the load reversal data are provided for DP 590, DP 780, and DP 1180. Particularities pertaining to the reversal deformation including the decreasing hardening rate during forward tension, a linear and then a non-linear unloading, followed by the Bauschinger effect, and a shift in the hardening rate during continuous straining were quantified and discussed as a function of loading history. Moreover, parameters such as the reloading stress differential, reloading softening stress, ratcheting strain, and unloading deviation stress were determined and discussed as a function of martensite fraction. The data were interpreted and predicted using an elasto-plastic self-consistent (EPSC) crystal plasticity model incorporating anisotropic elasticity, a dislocation density based hardening law, and a slip system backstress law. The model parameters associated with the slip strengths of ferrite and martensite and backstress were established. This work demonstrated the ability of crystal plasticity modeling to account for the co-dependent nature of crystallographic slip in ferrite and martensite and the sources of hardening caused by history-dependent dislocation density evolution and backstress to predict not only monotonic but also hysteresis in plastic response during the forward-reversal cycles. The combination of comprehensive experimental data and modeling results allowed us to infer that the tradeoff between the magnitude of backstress per phase and the volume fraction of ferrite versus martensite per steel governs the unloading and subsequent yielding per steel, while the dissolution of dislocations facilitates capturing the hardening rates during load reversal deformation.

Experimental characterization and crystal plasticity modeling for predicting load reversals in AA6016-T4 and AA7021-T79

The detailed contribution of microstructural-level phenomena, such as dislocation structure development and annihilation, as well as inter-granular and intra-granular backstress fields, to reverse loading behavior in metal alloys remains an area of active research and debate. The ability to predict unloading nonlinearities, the Bauschinger effect (BE), and changes in hardening rates during reverse loading is necessary for accurate modeling of deformation and springback in forming operations that involve strain path changes. This paper applies a recently developed elasto-plastic self-consistent (EPSC) crystal plasticity model to predict and interpret reverse loading in two commercially sensitive aluminum alloys (AA): 6016-T4 and 7021-T79. Model calibration and verification was enabled by an extensive experimental campaign of cyclic loading applied to the two alloys. The experimental data included hardening rates during monotonic tension, linear followed by non-linear unloading, the BE, and hardening rate changes during reverse loading that induce permanent softening. By considering anisotropic elasticity, dislocation density-based hardening, intra-granular slip system-level backstress fields, and inter-granular stress fields, the model predicted and quantified the contribution of different micro-scale phenomena to the observed behavior. The ability of the model to capture contrasting characteristics of the two alloys, particularly the distinct permanent softening and reloading yield stresses, demonstrated its ability to account for the co-dependent nature of crystallographic glide and the sources of hardening originating from the deformation history-dependent dislocation density evolution and backstress fields. Comparison of the experimental and modeling results revealed that the unloading behavior is primarily driven by backstress, the BE is governed by backstress and inter-granular stresses, and the hardening rates upon load reversals are controlled primarily by the strain-path sensitive evolution of dislocation density.

Influence of neighbouring tube expansion on the residual stress of tubesheet with single-row holes

Abstract 1 The expansion joint is a commonly used method of connection tube and tubesheet in the pressure vessel industry. This paper established the rationality of the numerical simulation method by comparing with the analytical model. On this basis, the effect of neighbouring tube expansion on the residual stress of tubesheet with single-row holes was investigated, as well as the effect of the cyclic joint temperature changes on the tubesheet stress amplitude. Finally, preliminary work was conducted to determine the fatigue life of pressure vessels considering expansion factors. The results indicated that as the model was extended from one hole to 10 holes, the maximum and average stresses of each hole increased gradually and stabilized at a limit value when the model reached 10 holes, and the maximum and average stress in the expanded cases were approximately 13% and 10% higher than those in the unexpanded case, respectively. Residual stress results will lead to the change of stress distribution and the increase of stress amplitude, and then affect the fatigue life of the pressure vessel equipment. •Multilinear kinematic hardening model are used to exhibits the Bauschinger effect. •Numerical simulation method is validated by the analytical model. •Expansion process has a great influence on the stress level of the tube holes. •Residual stress leads to a significant change of tubesheet stress distribution. •Residual stress increases the stress amplitude and affects fatigue life.

Experimental and numerical investigation on the Bauschinger effect during cold forming of TC4 ELI alloy

Experimental and numerical investigation on the Bauschinger effect during cold forming of TC4 ELI alloy

The Effect of Compression on the Void Coalescence under Strong Dynamic Loading

The void coalescence under strong dynamic loading is a significant spallation process for ductile metals. Since the spallation is basically dominated by tension waves, most void coalescence studies have focused on the tension effect. However, it is known that in spallation, the material initially undergoes a strong compression wave, and then an irreversible deformation is produced by the compression wave inside the material. Therefore, in this paper, the effect of compression on the void coalescence is investigated using the molecular dynamics (MD) simulation. It was found that as the compressive strain increases, the yield strength decreases first and then increases. The results showed that due to the Bauschinger effect (BE), the yield strength decreases by 19.43% from 5.66 GPa without compressive loading to 4.56 GPa when the compressive strain is −7.5%, after which the yield strength increases. The voids do not coalesce when the compressive strain is −8%. In addition, it was found that during the compressive phase, the void surfaces would generate dislocations, which could obstruct the void coalescence in the tensile phase. Furthermore, under compressive loading, the temperature effect on the void coalescence was studied, and it was found that lower temperatures could suppress the void coalescence.

Anisotropic damage constitutive model of AA5754 aluminum alloy considering warm forming history

A multipath two-stage loading test for AA5754 aluminum alloy is carried out. In the first loading stage, the tensile tests of big samples were conducted with different preforming conditions. Then small samples were cut off from the pre-strained big samples. In the second loading stage, the mechanical properties of small samples were measured, and the influence of preforming factors such as prestrain value, temperature, strain rate and stress state on the mechanical properties of the sheets has been studied. With increasing prestrain, the yield stress of the sheet increases and the failure strain decreases linearly. The higher the preforming temperature is, the lower the yield strength of the sheet is under the same prestrain, and the greater the hardening index and failure strain. Moreover, the mechanical properties of the sheet are not sensitive to the forming strain rate and stress state. In addition, a transient softening effect appeared during the two-stage loading test. A damage constitutive model considering the history of warm forming is established by VUMAT subroutine of ABAQUS commercial software. The parameters of the constitutive model are determined by the two-stage loading experimental data and a genetic algorithm. This model can describe the transient softening and Bauschinger effect of AA5754 aluminum alloy after preforming at different temperatures. Good agreement is also observed between the stress-strain responses of AA5754 aluminum alloy after warm preforming and the predictions of the model.

Twins and grain boundaries-dominated the reverse Bauschinger effect and tension-compression asymmetry

The failure modes and mechanisms of single and polycrystalline aluminum under different stress states are very different. Therefore, molecular dynamics methods were used to study the tension-compression asymmetry and Bauschinger effect of single and polycrystalline aluminum under different loads. We found both single and polycrystalline aluminum exhibit work hardening under tensile and compressive loads. The difference in this hardening phenomenon is manifested in that the characteristics of single and polycrystalline aluminum are brittle fracture and ductile fracture, respectively. Furthermore, we found that the tension-compression asymmetry of polycrystalline aluminum is more obvious than that of single crystal aluminum, and it manifested as a reverse tension-compression asymmetry. The Bauschinger effect is caused by the defects introduced by preloading, and the asymmetry of the Bauschinger effect is caused by different microscopic defects. Dislocations introduced by the pre-stretching of single crystal aluminum degrade its performance under reverse loading. Polycrystalline aluminum has more twinned regions under compressive load, which hinder the movement of dislocations and grain boundaries during reverse stretching, showing the reverse Bauschinger effect. This study has important theoretical guiding significance for a comprehensive and in-depth understanding of the mechanical properties and microstructural evolution mechanism of single and polycrystalline aluminum.

Eulerian constitutive equations for the coupled influences of anisotropic yielding, the Bauschinger effect and the strength-differential effect for plane stress

Recently, an Eulerian formulation based on evolving microstructural vectors was used (Lee and Rubin, 2020) to model anisotropic inelastic deformation rate in sheet metals. In contrast to Lagrangian formulations, the Eulerian formulation is insensitive to arbitrariness of reference and intermediate configurations. Here, additional constitutive equations are introduced to model asymmetric inelastic behaviors, such as the Bauchinger effect, permanent softening and the strength-differential effect within the context of the Eulerian formulation. The resulting model is calibrated to produce good agreement with several material data sets. In addition, example data sets are used to demonstrate advantages of the new model, especially for severe anisotropic response and large deformations.

Phase transformation and plastic behavior of QP steel sheets: Transformation kinetics-informed modeling and forming limit prediction

A previous study on quenching and partitioning (QP) steel showed that the transformation-induced plasticity (TRIP) effect strongly depends on the stress triaxiality and Lode angle parameters during the plastic deformation. However, only the impact of stress states on the linear hardening response (first-order effect) was investigated, assuming its yield and plastic flow evolution (second-order effect) follow isotropic behavior for both tension and compression. The high-order effects of phase transformation on plasticity are still elusive and difficult to incorporate owing to the inconsistent usage of the equivalent strain in kinetics law and constitutive modeling. In this study, the hardening law, considering martensitic transformation, was utilized in conjunction with a strength differential (SD) effect-induced asymmetric yield function based on the proposed work-conjugate framework. The contradiction where the previous model correlates the martensitic transformation law based on the von Mises strain and the mechanical responses based on the normalized plastic work-per-unit material (or the work-conjugate equivalent strain) was eliminated. This elimination imposed the phase transformation influence into size evolution of the yield surface for QP980 because the effective stress directly correlated with the martensitic transformation using the work-conjugate equivalent strain. One can use any yield function in conjunction with this work-conjugate framework to correlate the martensitic transformation and its impact on the mechanical behavior for both first- and second-order effects. Thus, the yield surface of QP980 steel was stably normalized through asymmetric function under different plastic strains and deformation modes. The SD effect of QP980 steel has proven to be anisotropic and the martensitic transformation has negligible impact on the shape evolution of its yield surface. The pressure-dependent phenomenon in the plastic flow behavior of the employed QP steel suggested that its volume change during the plastic deformation can be neglected. The correlation between the microstructure volume fraction, evolving yield surface, and the stress–strain response under nonlinear loadings (Bauschinger effect) was predicted accurately. The forming limit imperfection analysis served as a typical application, where the phase transformation was further correlated with the localized necking phenomenon. The framework to understand the impact of microstructure evolution in QP steel sheets on its final forming limits was provided, suggesting that an optimized strain path design will greatly enhance the accumulated plastic limit before the localized necking.

Bauschinger Effect, Masing Principle and Hencky Theorem for Bending Moment at Repeated Alternating-Sign Bending of Steel Sheet

In the production of the large-diameter thick-walled steel pipes (with a diameter of 1020-1420 mm and with a wall thickness of up to 32-48 mm from the high-strength steels of the strength class K50-K65) under the SMS Meer technology for the main gas-and-oil pipelines, the steel sheet is bent several times sequentially during the technological transitions from one press to another. At the elastoplastic alternating-sign bends of the sheet, the yield strength of the bending moment of the sheet changes from one bend to another, which causes great difficulties for the metallurgical technologists when they calculate the curvature of the tube’s wall and the final diameter of the pipe. To solve this problem, we propose the new analytical method for calculating the bending moment and curvature of a steel sheet under the low-cycle alternating-sign bending.

A molecular dynamics study on the cyclic plastic deformation mechanism of Al–Mg alloys

The deformation mechanism and hardening law of single-crystal and polycrystalline Al–Mg alloy materials during the cyclic loading deformation process of different paths are studied herein according to the principle of molecular dynamics. An analysis of the single-crystal simulation results indicates that the Bauschinger effect decreases with the increase of strain. The cyclic loading leads to dislocation locking and other obstacles, which, in turn, lead to hardening of the material. After that, the force generated by the accumulated strain moves the dislocation obstacle and causes the material to soften. Based on the Voronoi polygon method, polycrystalline models with different grain sizes are established, and the plastic deformation mechanism of these models under cyclic loading is analyzed. The results show that the critical grain size of the direct and inverse Hall–Petch relationship exists in the Al–Mg alloy. When the grain size is below this value, grain rotation and grain boundary sliding become the main deformation mechanisms of the small polycrystalline grains. Dislocation blockage remains an important factor in the hardening of polycrystalline materials, while the aggregation of solute atoms at the grain boundaries is another contributing factor.

Dislocation pile-up polarization model for mechanical properties of polycrystalline metals based on grain boundary resistance variability

A novel dislocation mechanism to interpret the Bauschinger effect in polycrystalline metals is proposed namely dislocation pile-up polarization. We show that the variability of GB resistance to dislocation transmission, an inherent characteristic in polycrystalline metals, can break the symmetry of double dislocation pile-ups during plastic deformation, resulting in the polarization of dislocation pile-ups. This polarization mechanism strengthens the material in forward loading but softens it in reverse loading, thus being a source of back stress, which is verified by the dislocation dynamic simulations. Further, an analytical model based on the polarization mechanism is proposed and coupled with the crystal plasticity constitutive framework to analyze the stress–strain behavior of materials during loading and reverse loading. It is found that the Bauschinger effect and the strain-dependent Hall–Petch effect naturally appear as the intrinsic properties of polycrystalline metals in this theoretical framework, and the associated microstructural sensitivity is well captured. Our theoretical studies demonstrate the key role of GB resistance variability in regulating mechanical properties of polycrystalline metals and shed light on the physical mechanism of the Bauschinger effect. Moreover, this study indicates that the back stress hardening can be enhanced by the polarization mechanism, which might reveal new routes for design of high-performance metallic materials.

Significant Bauschinger effect and back stress strengthening in an ultrafine grained pure aluminum fabricated by severe plastic deformation process

Bauschinger test in uniaxial tension-compression mode was carried out for the first time on the pure Al specimens having homogeneous ultra-fine grained (UFG) microstructures fabricated by equal-channel angular pressing (ECAP) and subsequent annealing processes. Significant Bauschinger stress (transient softening), Bauschinger energy parameter and their strong dependences on the tensile plastic pre-strain at the very early stage of the tensile deformation were measured in the UFG specimens, in sharp contrast to their coarse-grained (CG) counterpart. The grain size dependence of the Bauschinger effect in pure Al was qualitatively discussed in terms of the back stress arising from the formation of dislocation pile-up against the grain boundary during plastic deformation.

Anisotropic distortional hardening based on deviatoric stress invariants under non-associated flow rule

An anisotropic distortional hardening (ADH) model is developed under non-associated flow rule by evolving the analytical asymmetric Yoon2014 yield criterion (Hu and Yoon, 2021). The deviatoric stress invariants in the proposed hardening model are analytically expressed. Then, the evolving equations are imposed to describe Bauschinger effect and transient behavior. The anisotropic parameters in yield function can be directly expressed with the four hardening curves along 0°, 45°, 90° and equi-biaxial directions under the proportional loadings. Most importantly, nonlinear strain paths are incorporated in the model. Permanent softening & strengthen, work-hardening stagnation & overshooting behaviors during strain path changes have also been taken into account in the proposed model. The corresponding parameters for these characteristics are relatively independent, although optimization is required for the parameter identifications. The effectiveness and accuracy of the proposed ADH model have been compared with the kinematic hardening models for SPCC material. The constitutive description for 780R AHSS from the proposed model has also been compared with the YU model (Yoshida et al., 2015) under tension-compression along RD, DD and TD. The accuracy of the proposed model under complex strain paths has also been verified by comparing with the results predicted from the eHAH model (Barlat et al., 2013) for EDDQ and DP780. In addition, a plastic potential function is developed based on the form of the proposed model for non-associated flow rule. The accuracy has been verified by applying it to 780R AHSS, EDDQ and DP780.

A mechanism of strain hardening and Bauschinger effect: shear-history-dependent microstructure of elasto-plastic suspensions.

Dispersing solid hard particles in an elasto-plastic material leads to important shear-history dependence of the behavior, namely strain hardening and Bauschinger effect. Strain hardening is observed as the progressive strengthening of a material during its plastic deformation and is usually associated with ductility, a property often sought after in composite materials to postpone fractures and failure. In addition, anisotropic mechanical properties are developed, the material resistance being larger in the direction of the imposed flow, which is referred to as the Bauschinger effect. We show that this is related here to shear-history-dependent particle-pair distribution functions. Roughness and interparticle contacts likely play a major role, as replacing hard particles by non-deformable bubbles modifies the suspension microstructure and suppresses strain hardening. Beyond suspensions, our study provides new insight in the understanding and control of strain hardening and Bauschinger effect in composite materials.

Simulation of the Premium Threaded Connections Deformation under Cyclic Loading by Considering the Bauschinger Effect

Simulation of the Premium Threaded Connections Deformation under Cyclic Loading by Considering the Bauschinger Effect

Prediction of Spring Properties of the V–Bending Terminal Made from Copper Alloy Sheet with FE Simulation Considering Bauschinger Effect

Prediction of Spring Properties of the V–Bending Terminal Made from Copper Alloy Sheet with FE Simulation Considering Bauschinger Effect

Distinguishing process - impact of down milling and up milling in machining aluminium thin wall

The study aims to understand the deformation mechanics that occurs during down and up milling of aluminium thin wall fabrication. With cutting forces as inputs, material properties were defined by the Coffin-Manson relation and the Smith-Watson-Topper model. Hysteresis was found in the process of machining aluminium thin walls. Furthermore, the pattern of cutter loads differentiated the up and down milling through hysteresis. The finite element method was followed using ANSYS v14.5 software in the fatigue workbench to analyse the aspect. Down milling introduced both deflection and deformation. Conversely, up milling did not exhibit deflection. However, the Bauschinger effect and distinct fracture surfaces were diagnosed during up milling. By exploring the nature of hysteresis and fracture surfaces, the selection of down and up milling was made.

Attenuation of the Bauschinger effect and enhancement of tension-compression asymmetry in single crystal aluminum by temperature.

Temperature has a great influence on the mechanical properties of nano-materials. The molecular dynamics method was used to study the effect of temperature on the tension–compression asymmetry and Bauschinger effect of nano single crystal aluminum (NSCA). The strain-hardening behavior of NSCA in the tensile plastic stage is significantly enhanced when the temperature is higher than 400 K. The plastic deformation mechanism of tensile loading shifts from slip blocking of dislocations in grains to dislocation nucleation. The degradation of the mechanical properties of NSCA under compressive loading increases gradually with the increase of temperature. Dislocation emission is limited under compressive loading. Nonetheless, plastic deformation may still be regulated by dislocation slip during severe plastic deformation stages and at elevated temperatures. Temperature enhancement can effectively promote the movement of pre-dislocations and eliminate residual stresses. A new microscopic insight into the temperature attenuated Bauschinger effect is provided. This study provides important theoretical guidance for a comprehensive and in-depth understanding of the high-temperature mechanical properties and microstructure evolution mechanism of NSCA.