Bauschinger Effect Research Articles

Experimental research on mechanical, material, and metallurgical properties of Inconel 600: Application in elevated temperature environment

Experimental research on mechanical, material, and metallurgical properties of Inconel 600: Application in elevated temperature environment

The Influence of Reverse Yielding on the Plastic Conditioning of Interference Fits in Power Transmission Engineering

Interference fits are very common shaft–hub connections due to their low manufacturing costs and excellent technical properties. The Plastic Conditioning of this machine element is a new and not very well-known method. During the development of this method, it was discovered that Reverse Yielding occurs in certain applications and has a negative impact on the result. This paper examines the effects of Reverse Yielding on the technology of Plastic Conditioning of interference fits in Power Transmission Engineering. Based on the Shear Stress Hypothesis (SH), the Plane Stress State (PSS), and the ideal plastic behavior of materials, established stress–mechanical relationships are used to find the influencing parameters of Reverse Yielding on the technology of Plastic Conditioning and their limits. As a result, a new computational concept is developed that allows the user to maximize Plastic Conditioning while avoiding Reverse Yielding. Analytical calculation suggestions and diagrams for practical application are provided. Furthermore, the deviations in the obtained results, taking into account other material models such as the Von Mises Yield Criterion (VMYC) and material hardening, as well as the Bauschinger effect, are examined in comparison with our own numerical results from the development of Plastic Conditioning, and the resulting need for further research is defined. In addition, the method of Plastic Conditioning of interference fits is introduced and its basic principles are briefly explained.

Irreversible evolution of dislocation pile-ups during cyclic microcantilever bending

In single crystals, plastic deformations are predominantly governed by dislocation movement and interactions. The group of dislocations that creates strain gradients, known as geometrically necessary dislocations (GNDs), also deterministically contributes to strain hardening, micron-scale size effects, fatigue, and Bauschinger effect. During bending large strain gradients naturally emerge which makes this deformation mode exceptionally suitable to study the evolution of GNDs. Here we present bi-directional bending experiment of a Cu single crystalline microcantilever with in situ characterisation of the dislocation microstructure in terms of high-resolution electron backscatter diffraction (HR-EBSD). The experiments are complemented with dislocation density modelling to provide physical understanding of the collective dislocation phenomena. We find that dislocation pile-ups form around the neutral zone during initial bending, however, these do not dissolve upon reversed loading, rather they contribute to the development of a much more complex GND dominated microstructure. This irreversible process is analysed in detail in terms of the involved Burgers vectors and slip systems. We conclude that at this scale the most dominant role in the Bauschinger effect and corresponding strain hardening is played by short-range dislocation interactions. The in-depth understanding of these phenomena will aid the design of microscopic metallic components with increased performance and reliability.

Characterizing the mechanical deformation response of AHSS steels: A comparative study of cyclic plasticity models under monotonic and reversal loading

This study evaluates the performance of a user-defined combined hardening modeling method for advanced high-strength steels (AHSS) under monotonic and reversal loading conditions. The plastic behavior of TWIP980 and TRIP980 AHSS sheet metals is investigated using a cyclic plasticity modeling approach. The model incorporates an isotropic von Mises yield criterion and a single-term Chaboche nonlinear kinematic hardening rule. Monotonic and reversal loading stress-strain curves are predicted and compared with experimental results. The model accurately captured the Bauschinger effect for both materials, but it needs help to effectively model the permanent softening behavior observed in TWIP980 steel. Overall, the proposed modeling method agrees well with experimental results for monotonic loading and accurately represents the Bauschinger effect and transient behavior during reversal loading. However, better improvements are needed to capture the permanent softening behavior of TWIP980 steel.

The effect of varying stress intervals on fatigue of rock salt

The surrounding rock of underground energy storage salt caverns is subjected to periodic loading with stress intervals during actual operation. To study the fatigue behavior of rock salt with such stress intervals, one conventional fatigue test and three fatigue tests with multi-step varying stress intervals (MVSIs) were conducted. The results show that the circumferential deformation first decreases and eventually becomes similar to the axial deformation in fatigue tests with MVSIs, as the interval duration increases. Both the dissipated energy and the spacing between the loading and unloading curves of a single cycle first decreased, then remained constant, and finally increased sharply as the stress interval increased. When the stress intervals corresponded to the elastic phase of loading (between 20% and 40% of the uniaxial compressive strength), the rock salt was subjected to the minimum damage. Based on the Bauschinger effect and dislocation internal friction theory, the micromechanism of rock salt fatigue was further explained.

Explicit and Implicit Integration of Constitutive Equations of Chaboche Isotropic-Kinematic Hardening Material Model

The proper selection of the material model and its parameters in numerical simulations of the material response under loading is a very important task. In the cyclic load one should assume different phenomena, e.g. ratchetting effect, the mean stress relaxation, creep, etc. The Chaboche kinematic hardening model is mainly applied in order to capture the Bauschinger effect due to its good description of the material behaviour under the cyclic loading. The modified Chaboche isotropic-kinematic hardening model is considered in this paper in order to simulate the strain-controlled and stress-controlled uniaxial cyclic tension-compression test. The implicit and explicit integration procedures are tested here, showing advantages and disadvantages of both methods. It is shown that both approaches provide similar results. The implicit integration method of constitutive equations is unconditionally stable and thus less calculation steps are required in comparison to the explicit procedure. The implicit and explicit integration of the Chaboche model including isotropic and kinematic hardening are then implemented for the 3D case in commercial ABAQUS program in the form of the user material procedure. The correctness of results obtained for the user material model is verified by comparison to results for commercially implemented Chaboche model.

Investigation of the post-expansion collapse strength of solid expandable tubulars made of different steels

At present, there are different ideas about on the main factor influencing post-expansion collapse strength of solid expandable tubulars (SETs). In this study, three SETs with the same dimensions, which were made of 20 (Chinese grade), a twinning-induced plasticity (TWIP) and a transformation-induced plasticity (TRIP) steels, were expanded so the inner diameter increase by about 14%. The test results showed that the SETs made from high-strength steels (a TWIP and a TRIP) had poor resistance to collapsing after expansion. Through a combination of finite element method (FEM) simulations and experimental tests, the post-expansion collapse strength of three SETs were comparatively analyzed to find out the main influencing factor. After isolating the influences of geometric factors on the collapse strength, the influences of the Bauschinger effect and the residual stress on the collapse strength were studied. There was no correlation between the obvious degree of the Bauschinger effect of the three steels and the post-expansion collapse strength of the three SETs, which suggested that the Bauschinger effect was not the main factor influencing the post-expansion collapse strength. This is obviously different from the conclusion for SETs made from only one steel. The post-expansion collapse strength calculated by FEM simulations differed greatly from that of the actual measurement if the residual stress after expansion was ignored, though both were very close when the residual stress after expansion was considered. This clearly indicates that the residual stress after expansion has a significant effect on the post-expansion collapse strength and it is the main factor influencing the post-expansion collapse strength.

Deformation strengthening of uranium and dilute uranium alloys

The strength and ductility of uranium and dilute uranium alloys can be substantially improved by deformation strengthening. The yield strength of unalloyed uranium can be nearly doubled by rolling in the vicinity of 250 °C. The embrittling effect of hydrogen is also overcome, eliminating the need for vacuum outgassing to obtain good ductility. Significant differences in longitudinal versus transverse tensile properties result, in part, from texture introduced by unidirectional rolling. Warm rolling of U-2.3 %Nb results in both traditional strain hardening and a significant Bauschinger effect, resulting in differences between tensile and compressive yield strength. A similar combination of strain hardening and Bauschinger effect also occurs in deformation strengthened U-0.75 %Ti. Warm rolling of U-0.75 %Ti results in significantly better combinations of tensile yield strength and ductility than can be obtained by conventional age hardening. Warm rolling prior to aging also reduces the loss of ductility which typically accompanies conventional age hardening. An approach is developed in which the effects of prior deformation on tensile and compressive yield strengths are analyzed in terms of texture, long-range dislocation, and Bauschinger effects. The Bauschinger effect is shown to vary in sign with the type of deformation, thus providing opportunities to tailor tensile and compressive properties.

Numerical analysis of non-proportional biaxial reverse experiments with a two-surface anisotropic cyclic plasticity-damage approach

This paper deals with the numerical analysis of ductile damage and fracture behavior under non-proportional biaxial reverse loading conditions. A two-surface anisotropic cyclic elastic–plastic-damage continuum model is adequately presented, which takes into account the Bauschinger effect, the stress-differential effect, and the change of hardening rate after reverse loading. An efficient Euler explicit numerical integration algorithm, based on the inelastic (plastic or plastic-damage) predictor-elastic corrector approach, is utilized to analyze the stress and finite strain loading histories. Detailed discussions are provided on different numerical integration-related consistent tangent operators that achieve convergence within the global Newton–Raphson scheme. The proposed continuum model is implemented into the commercial software Ansys as a user-defined subroutine (UMAT). Furthermore, the novel non-proportional biaxial tensile reverse experiments are performed to validate the proposed continuum model. The associated numerical simulations investigate the stability and accuracy of the proposed algorithm and material model.

Mixed-mode crack growth analysis using a cyclic plasticity model

The effects of two singularity fields, namely, the HRR solution and modified form of the nonlinear kinematic hardening (NKH) solution, on the pure mode I and mixed mode I/II fatigue crack propagation were investigated. Experiments and computations were performed on compact tension shear (CTS) specimens of P2M steel, aluminium 7050, and Ti-6Al-4V with different monotonic and cyclic elastic–plastic properties. The analysis of the experimental data on the crack growth rate for all tested materials is given in terms of plastic stress intensity factors (SIFs) according to the HRR and NKH models. The elastic–plastic crack tip fields were obtained by FE computation as a function of the position along the curvilinear crack path for the monotonic condition and the first several cycles of fatigue deformation considering the Bauschinger effect. As a complement to the FE modelling, digital image correlation (DIC) measurements of the displacement and strain fields around the crack tip in the CTS specimens were performed. This study aimed to obtain more detailed information on the local cyclic strain ahead of the mixed mode crack tip by using DIC. From the sensitivity analysis, it was established that the DIC value depended significantly on the location along the crack direction of the pair of points selected before and behind the crack tip. In this study, acceleration or retardation of the crack growth rate in terms of the NKH plastic SIF with respect to the HRR model was observed because of the coupling effect of the mode mixity and cyclic plastic properties of the tested P2M steel, aluminium 7050, and Ti-6Al-4V.

Extra strengthening and Bauschinger effect in gradient high-entropy alloy: A molecular dynamics study

The gradient nano-grained (GNG) structures achieve a combination of high strength and ductility compared with homogeneous nano-grained structures. In order to study the mechanical behavior of GNG with extremely small grain size, the systematic tension, compression and cyclic deformation behavior of gradient and homogeneous nano-grained CoCrFeMnNi high-entropy alloy (G-HEA and H-HEA) are studied by the molecular dynamics (MD) simulation. The simulation results show that G-HEA and H-HEA have multiple plastic deformation mechanisms during uniaxial and cyclic loading, such as dislocation slip, deformation twinning, phase transformation from face-centered cubic (FCC) to hexagonal close-packed (HCP), and grain boundary plastic behavior. During uniaxial loading, the heterogeneous deformation makes the yield stress of G-HEA higher than that calculated by the rule of mixture (ROM), indicating an extra strengthening in GNG material. However, the extra strengthening of G-HEA is weakened with increased strain due to the dislocation without piled up in front of the grain boundary and relaxed heterogeneous deformation. During cyclic loading, the sessile dislocations promote the reverse movement of dislocations, resulting in the Bauschinger effect. However, the sessile dislocation density of G-HEA is close to that calculated by the ROM, resulting in the Bauschinger effect of G-HEA close to that calculated by the ROM. Therefore, as an alternative perspective, the MD simulation confirms that dislocation pinning in front of grain boundaries is an important source of extra strengthening for gradient structured materials as revealed by experiments. The results extend the understanding of the deformation mechanism of CoCrFeMnNi GNG HEA with extremely small grain size under tension, compression and cyclic loading.

Damage and fracture behavior under non-proportional biaxial reverse loading in ductile metals: Experiments and material modeling

This paper deals with a modified anisotropic stress-state-dependent plastic-damage continuum model incorporating combined hardening and softening rules to predict the plastic, damage, and fracture behavior of ductile metals under monotonic and reverse loading conditions. In the experimental part, a newly designed biaxially loaded cruciform flat HC-specimen of aluminum alloy EN AW 6082-T6 was subjected to biaxial non-proportional loading to generate a wide range of stress triaxialities during experiments. Thus, it is enabled to perform shear monotonic and reverse loading superimposed by various preloads without unloading processes. The experimental data reveal the Bauschinger effect, the strength-differential (SD) effect, and the change in the hardening ratio after shear reverse loading. This is captured by a Drucker–Prager-type yield criterion with an extended Voce isotropic hardening and modified Chaboche’s kinematic hardening rule. In addition, the damage surface is assumed to be translated in the direction of the rate of the damage strain. The numerically predicted global force–displacement curves and local strain fields are verified in terms of the digital image correlation (DIC) technique. Moreover, the scanning electron microscopy (SEM) is used to examine the fracture surfaces and to validate the proposed damage constitutive model.

Study on the burst pressure of support cylinder in expandable liner hanger based on matching between yield strength and fracture toughness

The expandable liner hanger (ELH) is one of the vital completion tools for ultra-deep oil and gas exploration and development. However, the burst pressure prediction of the support cylinder, which is the weak link of ELH, is extremely difficult due to unavoidable severe plastic deformation caused by expansion, which easily causes burst failure of the support cylinder under high temperature and high pressure with corrosive media, and poses a threat to wellbore integrity. Research shows that the classic models currently used to calculate the burst pressure of pipeline is mainly established based on yield design criterion and do not consider the effect of complex changes in mechanical properties caused by expansion and plastic deformation on burst pressure, especially the sharp decrease in fracture toughness so that they are not suitable for burst pressure prediction of support cylinder in the ELH. Hence, the strength-toughness (S-T) matching criterion used to consider both the burst failure due to the insufficient material strength and the environmental fracture failure due to the insufficient fracture toughness under internal pressure has been presented in this paper, by which the burst pressure model of support cylinder in ELH has been established with due consideration of the complex changes in geometric parameters (such as wall thickness, diameter-thickness ratio, uneven and ovality of wall thickness, manufacturing defects, etc.) and mechanical parameters (hardening exponent, fracture toughness, yield strength, tensile strength, compressive strength, yield-strength ratio, Bauschinger effect, etc.) caused by plastic deformation under different expansion rates by combining elastoplastic theory with fracture mechanics theory. The accuracy and reliability of this burst pressure model have been validated by full-scale burst test data of expansion pipe from the literature. The influences of expansion rate, diameter-thickness ratio, yield-strength ratio, Bauschinger effect, and fracture toughness on the burst pressure of the support cylinder have been obtained, by which the scientific method for improving the bursting pressure of the support cylinder has been formed. Research results could provide an important theoretical basis for predicting and optimizing burst pressure for the support cylinder in the ELH.

Finite element modeling of the JCO-E line pipe fabrication process; material properties and collapse pressure prediction

A numerical method for the simulation of the JCO-E pipe fabrication process is presented. The deformation and stresses induced by the manufacturing process, namely the edge crimping, the JCO forming, the LSAW welding, and the expansion (E) operation are calculated utilizing finite element simulation tools. This paper continues a recent work of the authors; it enhances the material model to account for the plate anisotropy, through the development of an in-house material subroutine, and simulates more accurately the welding process. Considering the fabrication parameters of the pipe mill, an X65 line pipe with 26-inch nominal diameter and 0.75-inch nominal thickness is simulated numerically with finite elements. The level of anisotropy is introduced in the model using stress–strain curves obtained from strip specimens, extracted from the steel plate. The predicted material properties of the JCO-E pipe are compared with test results from strip specimens extracted from the produced line pipe. Following the simulation of the fabrication process, and using the same finite element model, the analysis continues so that the mechanical response of the 26-inch-diameter pipe under external pressure is obtained, and its collapse pressure is calculated for different values of the applied expansion. The numerical results show that expansion reduces ovalization and residual stresses in the pipe, and there is an optimum range of expansion strain corresponding to maximum collapse pressure of the JCO-E pipe; beyond that range, the collapse pressure is reduced because of the Bauschinger effect.

Mechanical Characterization of Fatigue and Cyclic Plasticity of 304L Stainless Steel at Elevated Temperature

BackgroundThe mechanical characterization of the cyclic elastoplastic response of structural materials at elevated temperatures is crucial for understanding and predicting the fatigue life of components in nuclear reactors.ObjectiveIn this study, a comprehensive mechanical characterization of 304L stainless steel has been performed including metallography, tensile tests, fatigue tests, fatigue crack growth tests and cyclic stress-strain tests.MethodsIsothermal tests were conducted at both room temperature and 300 °C for both the rolling direction and the transverse direction of the hot rolled steel. Mechanical properties were extracted from the uniaxial experiments by fitting relevant material models to the data. The cyclic plasticity behavior has been modelled with a radial return-mapping algorithm that utilizes the Voce nonlinear isotropic hardening model in combination with the Armstrong-Frederick nonlinear kinematic hardening model. The plasticity models are available in commercial FE software and accurately capture the stabilized hysteresis loops, including a substantial Bauschinger effect.ResultsThe material exhibits near isotropic properties, but its mechanical performance is generally reduced at high temperatures. Specifically, in the rolling direction, the Young’s modulus is reduced by 16 % at 300 °C, the yield strength at 0.2 % plastic strain is lower by 23 %, and the ultimate tensile strength is lower by 30 % compared to room temperature. Fatigue life is also decreased, leading to an accelerated fatigue crack growth rate compared to room temperature. A von Mises radial return mapping algorithm proves to be effective in accurately modelling the cyclic plasticity of the material. The algorithm has also been used to establish a clear correlation between energy dissipation per cycle and cycles to failure, leading to the proposal of an energy-based fatigue life prediction model.ConclusionsThe material exhibits reduced mechanical performance at elevated temperatures, with decreased monotonic strength, compared to room temperature. Fatigue life is also compromised, resulting in accelerated fatigue crack growth. The material’s hardening behavior differs at room temperature and elevated temperature, with lower peak stress values observed at higher temperatures. The radial return mapping algorithm can be used to determine the dissipated energy per cycle which together with fatigue testing has been used to propose a low cycle fatigue life prediction model at both temperatures.

Simulation Research on Residual Stress of Swage Autofrettage-processed High-Pressure Cylinder

The vital component of the high-pressure pump is the high-pressure cylinder, which undergoes pulsating cyclic loads during operation. This exposure can lead to fatigue cracking and limit the pump’s overall performance. To address this issue, a swage autofrettage treatment method for the high-pressure cylinder is proposed based on the principles of autofrettage technology. The structure parameters of the mandrel are designed to optimize its role in the treatment process. Subsequently, a swage autofrettage simulation model is established, considering the Bauschinger effect to analyze the distribution of residual stress about the mandrel interference percentage. The results demonstrate that the swage autofrettage treatment improves the stress distribution in the high-pressure cylinder, causing the inner wall surface to undergo a circumferential residual compressive stress. Within a specific range, the Bauschinger effect becomes more significant as the mandrel interference percentage increases. This study provides insights for enhancing the durability and performance of high-pressure cylinders while adhering to mechanical engineering standards.

Experimental investigation on cyclic behaviour of wire arc additively manufactured carbon steel

AbstractWire arc additive manufacturing (WAAM) is a metal 3D printing technique that has attracted significant interest from the construction industry for its ability to efficiently and rapidly build large‐scale component. However, there is currently limited information on the cyclic performance of WAAM metal materials. To address this gap, an experimental investigation was conducted to study the cyclic behaviour of WAAM carbon steel. The investigation involved the testing of forty specimens with two nominal thicknesses and two surface finishes under ten cyclic loading protocols. Following this, the failure modes, cyclic performance, and elastic modulus degradation were analysed. The results indicate that WAAM carbon steel exhibits excellent ductility under cyclic loading. The phenomenon of Bauschinger effect, cyclic hardening and elastic modulus degradation were observed in the experiment. The cyclic performance of WAAM carbon steel was found to depend on strain amplitude and strain history.

Strain gradient plasticity with nonlinear evolutionary energetic higher order stresses

This paper explores the effect of evolutionary-type nonlinear energetic higher order stress inside the strain gradient plasticity framework that allows nonlinearity in dissipation. Based on the fundamental principles of thermodynamics, a multi-term Chaboche-type model has been formulated to describe the evolution of energetic moment stresses that depend on strain gradient and effective plastic strain. The derived evolutionary relation shows a coupling between energetic and dissipative length scales. The energetic part of the higher order stress, related to the GND formation, saturates as effective plastic strain increases during plastic flow. Higher order stress update equation and material tangent are derived using implicit time discretization. The proposed nonlinear energetic moment stress model confirms its applicability compared to experimentally observed responses. Our study demonstrates the importance of incorporating a nonlinear kinematic hardening rule to accurately represent the Bauschinger effect in samples with a thickness of less than 1μm. The cyclic bending experiment with a single slip sample shows that the nonlinear kinematic hardening rule can effectively capture nonlinearity in the experimental observation. Compressed shear layer simulation reveals that consideration of thickness-dependent relaxation coefficient accurately models the experimental observations. Thus, it makes further relevant consideration of a more advanced kinematic hardening rule through the proposed approach.

Magnetic evaluation of Bauschinger effect in marine engineering steels

In the present study, the association between the magnetic behavior of steels the Bauschinger effect was evaluated. For this reason, three different grades of steel were subjected to typical Bauschinger tests involving a single reversal from tension to compression loading, for the same amount of pre-strain. The reversal compression lasted until the opposite of the pre-strain's maximal stress was reached. As a nondestructive magnetic technique for determining the magnetic properties of the examined samples, magnetic Barkhausen noise was chosen. For the characterization of the Bauschinger effect, four indicators were used, in terms of strain, stress, and energy. Mechanical stresses alter material magnetization, but linking Bauschinger factor with magmatic noise parameters has not been widely studied. Comparing Bauschinger Effect parameter values and magnetic Barkhausen methods, results show consistency with ferromagnetic samples' mechanical behavior. As Bauschinger Effect becomes more forceful, disorder density and magnetic wall anchoring decrease. A new proposed parameter, the exponent ξ, is directly related to effect rate. The magnetic Barkhausen noise method and its peak position and full width half minimum parameters can be a promising complementary measure for evaluating BE contribution in cycle loading ferromagnetic steels. Finally, the applicability of the examined techniques for the non-destructive characterization of steel degradation was discussed.

Microstructural evolution and mechanical behaviors of the third–generation automobile QP980 steel under continuous tension and compression loads

As one of the representatives of the third–generation automobile steel, QP980 is a high–quality material for the improvement of automobile lightweight and crash safety. In this paper, tension and compression tests are conducted for the QP980 steel based on a self–designed testing platform. Microstructural evolution and mechanical behavior under monotonic and continuous tension/compression loads are investigated. The results show that the martensitic transformation in QP980 steel is more easily excited in the monotonic tension state than in the monotonic compression state. In the tension–compression–tension (T–C–T) and compression–tension–compression (C–T–C) modes, the Bauschinger effect of QP980 depends on the pre-strain amount and the pre–strain mode. The Bauschinger effect is stronger at a higher pre–strain. It is also stronger in T–C–T than in C–T–C because the transformation of retained austenite after T–C–T is greater than that after C–T–C. By analyzing the hardening and softening behaviors in the forward, reverse and reforward loading branches of T–C–T and C–T–C, the hardening ability during reverse and reforward loading branches is higher than that during forward loading. Permanent softening occurs between reverse loading and forward loading of T–C–T instead of C–T–C. The research result of this paper is favorable for understanding the relation between mechanical behavior and microstructural evolution of QP980 steel under the condition of complex loads, and promote its large–scale application.