Bauschinger Effect Factor Research Articles

Constitutive modeling of high strength steels; application to the analytically strengthening of thick-walled tubes using the rotational autofrettage

This paper focuses on high-strength and hardness steels which are used as an upgraded material in the construction of high-pressure vessels. Their mechanical behavior shows that these steels have perfectly plastic or linear hardening behavior with slight slopes during their loading phase. In contrast, their reversed loading behavior is nonlinear and quite easily affected by the prior plastic strain, in a way that the Bauschinger effect factor, trend, and nonlinearity degree of the reversed loading plastic part are strongly dependent on the prior plastic strain level. At first, a constitutive model was proposed to capture the test data of the nonlinear part of the stress-strain curve and the Bauschinger effect factors, as a function of prior plastic strain. Furthermore, this model should be proposed so that its application in solving boundary value problems such as thick-walled tubes leads to a closed-form analytical solution. To this end, the proposed model was adjusted to find a closed-form analytical solution for the analysis of thick-walled tubes under rotational autofrettage. In the following, the optimum autofrettage level for strengthening a thick-walled tube made of high-strength steel is obtained for proposed and other simplified constitutive models. By comparing the results, it was concluded that consideration of the dependency of mechanical behavior of this material on the prior plastic strain makes significant changes on the equivalent stresses.

The Effects of the Material's Exact Yield Point and Its Plastic Properties on the Safe Maximum Pressure of Gun Barrels

The design of a gun barrel aims at maximizing its firing power, determined by its safe maximum pressure (SMP)—the maximal allowed firing pressure—which is considerably enhanced by inducing a favorable residual stress field through the barrel's wall commonly by the autofrettage process. Presently, there are two distinct processes: hydrostatic and swage autofrettage. In both processes, the barrel's material is fully or partially plastically deformed. Recently, a 3D computer code has been developed, which finally enables a realistic simulation of both swage and hydraulic autofrettage processes, using the experimentally measured stress–strain curve and incorporating the Bauschinger effect. This code enables a detailed analysis of all the factors relating to the final SMP of a barrel and can be used to establish the optimal process for any gun-barrel design. A major outcome of this analysis was the fact that the SMP of an autofrettaged barrel is dictated by the detailed plastic characteristics on the barrel's material. The main five plastic parameters of the material that have been identified are: the exact (zero offset) value of the yield stress, the universal plastic curve in both tension and compression, the Bauschinger effect factor (BEF) curve, and the elastic–plastic transition range (EPTR). A detailed comparison between three similar barrel materials points to the fact that the major parameter determining the barrel's SMP is the yield stress of the material and that the best way to determine it is by the newly developed “zero offset” method. All other four parameters are found to have a greater influence on the SMP of a hydraulically autofrettaged barrel than on a swaged one. The simplicity of determining the zero offset yield stress will enable its use in any common elastic and elastoplastic problem instead of the present 0.1% or 0.2% yield stress methods.

Influence of the Movement of the Neutral Axis on the Relation Between the Critical Current and Strain in Bending Bi2223/Ag Composite Tapes

For the Bi2223/Ag composite tape, on the existence of thermally residual stress, the neutral axis usually shifts away from the center of the cross section due to the Bauschinger effect of Ag and Ag alloy under the bending deformation. The movement of the neutral axis causes the redistribution of the stress and strain in the tape and further affects its critical current. In this paper, based on our modified model with the damage stress of the Bi2223 superconducting filaments, the movement of the neutral axis, the influence of the movement on the relation of the critical current versus the bending strain, and the distribution of the stress and strain on the cross section have been studied. The calculated results show that, the relation of the normalized critical current I c/I c0 versus the bending strain with taking account of the movement of the neutral axis is closer to the experimental data than without that, the neutral axis moves always to the compressive side of the tape, and the movement increases with the bending radius R decreasing (i.e., the bending deformation increasing). Furthermore, in the different cases of the Bauschinger effect factor (BEF), the elastic modulus and volume fraction of the superconducting filaments, the movement of the neutral axis, the normalized critical current I c/I c0 with the bending radius R, and the distributions of the stress on the cross section have been comprehensively investigated.

The Investigation of Modelling Material Behavior in Autofrettaged Tubes Made from Aluminium Alloys

Normal 0 false false false EN-US X-NONE AR-SA The ratio of compression yield strength to the initial tensile yield strength is called Bauschinger effect factor, BEF. A nonlinear strain hardening mathematical model is proposed for 7075 aluminium alloy (A7075). Uniaxial tension-compression experimental data are used to figure out a suitable model to study the BEF. Hence, uniaxial tension-compression tests on some specimens having 12.5 mm and 6 mm diameters were carried out by an Instron servohydraulic machine and were compared. In this paper several factors including Young’s modulus, the amount of offsets to determine yield point and BEF were studied. Besides, BEF in the aluminium tubes made from alloys of A5083 and A7075 were compared. This model will be employed to predict residual stress and fatigue life in autofrettaged tubes.

Plastic Deformation Influence on Material Properties of Autofrettaged Tubes Used in Diesel Engines Injection System

According to the DIN2391 standard, the DIN1.0406 steel is used to manufacture high-pressure injection tubes of diesel engines. The parts are autofrettaged during the manufacturing process to increase operating pressure and fatigue life. The autofrettage process is affected by loading–unloading cycle. In Bauschinger effect (BE) phenomenon, plastic deformation causes a loss in unloading yield strength. The ratio of unloading yield strength to the loading yield strength is called Bauschinger effect factor, BEF. In this paper, plastic deformation influence on the loading and unloading behaviors of DIN1.0406 steel is studied considering the BE. Uniaxial tension–compression experimental data are used to figure out a suitable model to study the BE. To carry out these experiments, a servohydraulic Instron machine is used. The sample tubes having inside diameter of 2.4 mm and outside diameter of 6 mm were made based on the standard ASTM E8M-97a. The tests were carried out using the total strain of 4.31%. Another important purpose of this paper is to investigate the effect of the amount of plastic strain on loading–unloading Young's modulus. Finally, the behavior of DIN1.0406 steel is compared with the steels such as DIN1.6959, HY 180, and PH 13-8Mo used in tubes.

Study on Metals Behavior Subjected to Cyclic Loading Based on Bauschinger Effect of Reversible Fine Machining Sequence

Reversible cutting method is a new research thesis proposed to shorten processing route, decrease tool number and handling time, increase machining efficiency. Based on nonlinear hardening during reverse loading and the change of the Bauschinger effect factor with plastic strain, reverse loading released strain energy of elastic responses of machined underlayer. The chip formation model of reversible finish cutting was established. The difference between the advance and return stroke was analyzed in crystal slipping and elongating, residual stress, micro-hardness of machined surface. Experimental research indicted that the results of micro-hardness of reversible fine machining technique are smaller than that of general fine machining, the circumferential residual stress at the finished surface is compressive, the surface roughness of machined surface are smaller than that of general fine machining. The kinematic hardening models of the advance and return stroke finishing cutting based on Bauschinger effect is presented.

A Study on Hydraulic Autofrettage of Thick-Walled Cylinders Incorporating Bauschinger Effect

Pressure vessels which are subjected to cyclic external or internal high pressure are used in many fields of industry and need to be sure of reliability and safety. To ensure of reliability and safety, thick-walled cylinder, such as a cannon or nuclear reactor, is autofrettaged to induce advantageous residual stresses. The compressive residual stress which was introduced by autofrettage process acts to offset the tensile residual stress induced by internal pressure. It increases operating pressure and restrains crack initiation and crack propagation. As the autofrettage level increases, the magnitude of compressive residual stress at the bore also increases. However, the Bauschinger effect reduces the compressive residual stresses with prior tensile plastic strain, and decreases the beneficial autofrettage effect. There are some differences between theoretical solution considering elastic-perfectly material behavior and real autofrettage process results. The purpose of the present paper is to predict the accurate residual stress of SNCM 8 high strength steel using the Kendall model which was adopted by ASME Code. The tensile and uniaxial Bauschinger effect tests of SNCM 8 were performed to evaluate Bauschinger effect factor(BEF), thereafter this constant was used in calculating the residual stress. The residual stress distribution which is considering the Bauschinger effect was profiled using Kendall model, and the results were compared with the analytical and Finite Element analysis. The results were found that residual stress incorporating the Bauschinger effect at bore was smaller than ideal calculation. These results should be considered in designing pressure vessels.

Residual Stress in an Autofrettaged Tube Taking Bauschinger Effect as a Function of the Prior Plastic Strain

Autofrettage is a practical method for increasing the elastic carrying capacity and the fatigue life of thick-walled cylinders such as cannon and high-pressure tubular reactor. Many analytical and numerical solutions for determining the residual stress distribution in an autofrettaged tube have been reported. It is still difficult to model the Bauchinger effect, which is dependent on the prior plasticity in an analytical solution. The reduced Young’s modulus during unloading affects residual stress distribution. However, until now this effect has not been considered in any analytical model. In this paper, an autofrettage analytical solution considering Young’s modulus and the reverse yield stress dependent on the prior plasticity, based on the actual tensile-compressive curve of the material and the von Mises yield criterion, has been proposed. New model incorporates the Bauschinger effect factor and the unloading modulus variation as a function of prior plastic strain, and hence of the radius. Thereafter it assumes a fixed nonlinear unloading profile. The comparison of predicted residual stress distribution by the present solution with that of fixed unloading curve model, and test results shows that the present solution gives accurate prediction of residual stress distribution of an autofrettaged tube. This analytical procedure for the cylinder permits an excellent representation of various pressure vessel steels.

Analysis of Reversible Fine Machining Sequence Effect on Surface Integrity

Reversible cutting method is a new research thesis proposed to shorten processing route, decrease tool number and handling time, increase machining efficiency. The aim of the presented work was to analysis the effects of reversible fine machining sequence on surface integrity in machined layer. Nonlinear hardening during reverse loading and the change of the Bauschinger effect factor with plastic strain were properly taken into account. In experiments, the residual stresses have been measured using the X-ray diffraction technique (at the surface of the workpiece and in depth). Moreover, micro-hardness and surface roughness of machined surface are presented. Experimental data for the range of cutting parameters tested showed that the reversible fine machining produce the tensile residual stresses at the surface, which are critical in the performance of the machined components. The experimental results of micro-hardness of reversible fine machining technique are smaller than that of general fine machining show that decreased plastic deformation of the surface layer and work-hardening. Surface roughness of machined surface with reversible finishing is discussed. Research results indicted that it can be adopted such planning which rough machining during advance stroke and fine machining or semi-finishing during return stroke in machining process. In this way, it has such advantages that increase machining efficiency and machining accuracy, decrease bending deformation.

The Influence of the Bauschinger Effect on the Yield Stress, Young’s Modulus, and Poisson’s Ratio of a Gun Barrel Steel

The Bauschinger effect (BE) was originally defined as the phenomenon whereby plastic deformation causes a loss of yield strength restraining in the opposite direction. The Bauschinger effect factor (BEF), defined as the ratio of the yield stress on reverse loading to the initial yield stress, is a measure of the magnitude of the BE. The aim of the present work is to quantitatively evaluate the influence of plastic deformation on other material properties such as Young’s modulus and Poisson’s ratio for gun barrel steel, thus extending the definition of the Bauschinger effect. In order to investigate the change in this material’s properties resulting from plastic deformation, several uniaxial tension and compression tests were performed. The yield stress and Young’s modulus were found to be strongly affected by plastic strain, while Poisson’s ratio was not affected at all. An additional result of these tests is an exact zero offset yield point definition enabling a simple evaluation of the BEF. A simple, triphase test sufficient to characterize the entire elastoplastic behavior is suggested. The obtained experimental information is readily useful for autofrettage residual stress field calculations.

THE BAUSCHINGER AND HARDENING EFFECT ON RESIDUAL STRESSES IN THICK-WALLED CYLINDERS OF SUS 304

A thick-walled cylinder of strain hardening material with closed ends, which is assumed to obey Von-Mises yield criterion is considered. An elastoplastic and residual stress analysis of thick-walled cylinders is performed with the incremental theory of plasticity. Critical pressures of direct and reverse yielding are investigated using the Von-Mises yield criterion as well as the Bauschinger effect factor (BEF). The material selected is SUS 304 stainless steel. The material's loading and unloading properties including the (BEF) are obtained experimentally and represented mathematically as a continuous function of effective plastic strain. The material model and the BEF have been incorporated in an analytical-numerical model so as to predict the cylinders plastic and residual stresses as well as the critical pressures of direct and reverse yielding. The analytical-numerical model for the prediction of critical inner pressure, plastic stress distributions and the subsequent residual stresses of thick-walled cylinders is validated by using experimental results. Residual stresses with and without the BEF are obtained and the corresponding results are compared. In the case study of a specific cylinder (Radii ratio of β=2), it has been concluded that residual stresses subsequent to a 45% overstrained condition are at the onset of reverse yielding when the BEF is considered.

Experimental Data, Numerical Fit and Fatigue Life Calculations Relating to the Bauschinger Effect in High Strength Armament Steels

The uniaxial Bauschinger effect has been evaluated in several high strength steels being considered for armament application. The steels investigated include ASTM A723 (1130 and 1330 MPa), PH 13-8 Mo stainless steel (1380 MPa), PH 13-8 Mo super tough stainless steel (1355 MPa), and HY 180 (1180MPa). Tests were conducted at plastic strains up to 3.5%. Results of testing show a progressive decrease in Bauschinger effect up to plastic strains of approximately 1% (for all materials investigated), after which there is little further decrease in the Bauschinger effect. Several key features were discovered during testing. First, all of the materials tested exhibited a changing modulus, where the elastic modulus on unloading after tensile plastic straining is consistently lower than that observed in the original loading of the specimens. The amount of modulus reduction is dependent upon the material tested, and larger reductions are observed with increasing amounts of tensile plastic strain. Prior work by Milligan reported Bauschinger effect factor β for a modified 4340 steel (old vintage A723 steel), which compares well with the present work. However, his results failed to mention any observations about a modulus reduction. The second observation was the expected strength reduction where a reduced compressive strength is observed as a result of prior tensile plastic straining. Numerical curve fits used to calculate residual stresses, which take into account both the modulus reduction and strength reduction are presented for all materials. Fatigue life calculations, utilizing the numerical curve fits, show good agreement with full size A723 laboratory fatigue test results.

The overstrain of Thick-Walled cylinders considering the bauschinger effect factor (BEF)

An independent kinematic hardening material model in which the reverse yielding point is defined by the Bauschinger effect factor (BEF), has been defined for stainless steel SUS 304. The material model and the BEF are obtained experimentally and represented mathematically as continuous functions of effective plastic strain. The material model has been incorporated in a non-linear stress analysis for the prediction of reverse yielding in thick-walled cylinders during the autofrettage process of these vessels. Residual stress distributions of the independent kinematic hardening material model at the onset of reverse yielding are compared with residual stresses of an isotropic hardening model showing the significant effect of the BEF on reverse yielding predictions. Critical pressures of direct and reverse yielding are obtained for the most commonly used cylinders and a range of permissible internal pressures for an efficient autofrettaged process is recommended.

An Axisymmetric Method of Elastic-Plastic Analysis Capable of Predicting Residual Stress Field

Linear elastic solution of an axisymmetric boundary value problem is used as a basis to generate its inelastic solution. This method treats the material parameters as field variables. Their distribution is obtained as a part of solution in an iterative manner. Two schemes of updating material parameters are discussed and compared. A procedure for calculation of residual stress field is presented. Application of the method to autofrettage is presented. Residual stress calculation based on actual material curve, isotropic and kinematic hardening models, and variable Bauschinger effect factor (BEF) is carried out. It is concluded that consideration of dependency of BEF on plastic strain makes significant changes to residual hoop stress near the bore for low-level autofrettage. However, this dependency is insignificant for high-level autofrettage. Results obtained here are shown to be in good agreement with experimental and finite element results.

Different solutions for stress and strain fields in autofrettaged thick-walled cylinders

In the first part of the paper we will present an analytical solution to the plastic stress and strain distribution induced by a single over-pressure cycle in a cylindrical vessel. The solution is valid for materials which, during the loading phase, can be described by a linear hardening law as well as by the modified Ramberg-Osgood law. We will clarify the conditions for which the stress field expressions can be simplified, thus facilitating a parametric analysis of their increase with respect to the values one would obtain when considering an ideal elastic-perfectly plastic behaviour of the material. In the second part of the paper, residual stress fields will be numerically evaluated, taking into account, during the unloading phase, both the variability of the stress flow and the Bauschinger effect factor as a function of pre-strains.

Solving the elastoplastic unloading problems of an axisymmetric body with actual material hardening models by BEM

This paper presents a boundary element formulation and numerical implementation of the elastoplastic unloading problem of an axisymmetric body with an actual material hardening model in which the reverse yield stress does not lie between the kinematic hardening yield stress and the isotropic hardening yield stress of present plastic theory. Three elastoplastic unloading stress-strain models of high strength low alloy steel with both strain hardening and Bauschinger effect factor are discussed. The modified Aitken method is used for the unloading iteration process. Comparison of the results of this paper with the data of FEM and experiment is given finally.

On the unloading solution by viscoplastic BEM of axisymmetric pressure vessels with three material hardening models

This paper presents a viscoplastic boundary element formulation and numerical implementation of the nonlinear unloading problem of axisymmetric pressure vessels with new material hardening models for which the reverse yield stress does not lie between the kinematic hardening yield stress and the isotopic hardening yield stress of present nonlinear theory. Three nonlinear unloading stress-strain models of high strength low alloy steel with both the strain hardening and Bauschinger effect factor are discussed. The modified Aitken method is used for the unloading iteration process. Comparisons of this paper's results with the data of FEM and experiment are given.

Residual stresses analysis for actual material model of autofrettaged tube by non-linear boundary element method

This paper presents a material model with expressions for the Bauschinger effect and hardening factors based on experiments. The material model considers both the Bauschinger and hardening effects during loading and unloading. The residual stresses are analysed by the 2D non-linear unloading boundary element method, and the new results for the relationships of residual stresses with the Bauschinger effect factor f and the strain hardening factor m′ are discussed.

Prediction of Residual Stresses in an Autofrettaged Thick–Walled Cylinder

ABSTRACTMost of the earlier results for residual stresses are based on the assumption of elastic unloading. In this paper, the prediction of residual stresses for the case of reverse yielding including the combined Bauschinger and hardening effect will be reported for an autofrettaged thick-walled cylinder. The Bauschinger effect factor is varying as a function of overstrain. The strain-hardening effect is considered with different parameters used for loading and unloading process. The new results indicate that the influence of the combined Bauschinger and hardening effect on residual stress distribution is significant.

Bauschinger effect in API X60 linepipe steels

As part of a programme to evaluate changes in mechanical properties occurring during U-O-E pipe forming, laboratory tests were carried out to assess the Bauschinger effect in 12·7mm thick, controlled-rolled Nb–V API X60 steels. Assuming a stress-strain relationship of the form σ = Coεna for the initial strain cycle, empirical relationships are established between C1 and n1 of the reverse cycle, with prestrain. A Bauschinger-effect factor is defined for linepipe steels, and a method is developed to calculate this factor using Co, no, and prestrain values. The Bauschinger effect was found to increase with increasing prestrain up to ∼ 0·03, and it was more prominent when the reverse-flow stress was measured at small offsets (0·005) in the transient region than at high strains, which tend to eliminate the effect. In the context of pipe testing, the Bauschinger effect resulting from the cold flattening-tensile testing operation is practically unaffected by the preceding strain cycle.