Bauschinger effect and residual phase stresses in two ductile-phase steels: Part I. The influence of phase stresses on the Bauschinger effect

The Bauschinger effect (BE) in dual-phase steels has been computationally simulated, and the influence of phase stresses, developed due to nonhomogeneous deformation during preloading, on the BE has been investigated. Isotropic-and anisotropic-hardening models were used in finite-element method calculation to produce the reverse flow stress-strain curves (compression) of dual-phase steels from the reverse stress-strain curves of single-phase materials. Aspects of the Bauschinger effect, including the rounding of the reverse flow curve, yielding at low reverse stresses, high initial work-hardening rates, and the absence of permanent softening,etc., were elucidated by the variation in phase stresses in the constituent phase.     

Bauschinger effect and multiaxial yield behavior of stress-reversed mild steel

Thin-walled cylindrical specimens subjected to torsional prestraining are stress-reversed along the Bauschinger curve. The Bauschinger effect (BE), yield behavior, and flow behavior of the stress-reversed mild steel were examined by using combined loadings of axial load, internal pressure, and torsion. The results indicate that the stress-reversed steel has the same yield stress at 0.2 pct offset strain in reloading tests of forward and reverse torsion, when the reverse strain is =0.77 pct. Furthermore, it is possible to cause the yield stresses in forward and reverse torsion to coincide in any offset strain. The yield locus of the stress-reversed steel is symmetric with respect to the tensile stress axis in a tension-torsion stress field. However, it has been found to be an anisotropy in the stress-reversed steel, and the magnitude of anisotropy is related to the offset strain. For example, there is a stronger anisotropy at 0.2 pct offset strain than at 2 pct offset strain, even though the BE is eliminated for the former. It is shown that the reduction in the BE by stress reversal is concerned with the relief of the long-range back-stress generated by prestraining. Besides, the roles of aging in the stress-aging process lie in the contributions to age hardening and development of directional back-stress.     

Phase transformations and control of residual stresses in thick spray-formed steel shells

Large, thick steel shells for tooling applications have been produced using a robot manipulated electric arc spraying technique with steady-state temperatures ranging from 170 °C to 450 °C. Critical to these experiments has been the use of a real-time feedback control system for surface temperature based on infrared thermal imaging. There was a reproducible trend in net residual shell distortion as a function of temperature with residual tensile stresses in the shell for temperatures ≤210 °C and ≥390 °C, and net compressive stresses at intermediate temperatures. In-situ linear displacement sensor experiments have been used to investigate the dynamic distortion of sprayed steel shells on steel substrates, over the same range of surface temperatures. Residual and in-situ distortion measurements confirmed two manufacturing temperatures at which stresses in the steel shells were either minimized or eliminated. A numerical model has been developed to relate shell quench and transformations stresses to the shell dynamic distortion behavior. It is proposed that tensile quench stresses are balanced by the time- and temperature-dependent expansive austenite-to-bainite phase transformation.     

The Bauschinger effect in precipitation strengthened aluminum alloys

The Bauschinger effect in precipitation strengthened Al-Cu-Mg, Al-Zn-Mg and Al-Cu polycrystals was measured as a function of applied strain. Alloys heat treated to contain easily shearable precipitates,i.e., GPB, GP and θ″ exhibited a small Bauschinger effect, on the order of that in pure aluminum. In contrast, alloys with nonshearable precipitates, S′, η and θ′ showed an anomolously large effect. A unique hysteresis loop shape, with a region of convex curvature between sharp inflection points, was observed in the nonshear-able precipitate alloys. The large Bauschinger effect and unusual hysteresis loop shape are due to internal elastic or back stresses exerted by the strong precipitates on the matrix. A nonlinear elastic hardening model is proposed in which the overall work harden-ing is partitioned into an elastic back stress component and a frictional dislocation forest hardening term. Plastic relaxation around the precipitates and inhomogeneous deformation in the polycrystal reduces the level of the internal stresses below that predicted theoretically by the Brown and Stobbs hardening theory.     

Effects of thermal residual stresses and fiber packing on deformation of metal-matrix composites

The combined effects of thermal residual stresses anmd fiber spatial distribution on the deformation of a 6061 aluminum alloy containing a fixed concentration unidirectional boron fibers have been analyzed using detailed finite element models. The geometrical structure includes perfectly periodic, uniformly spaced fiber arrangements in square and hexagonal cells, as well as different cells in which either 30 or 60 fibers are randomly placed in the ductile matrix. The model involves an elastic-plastic matrix, elastic fibers, and mechanically bonded interfaces. The results indicate that both fiber packing and thermal residual stresses can have a significant effect on the stress-strain characteristics of the composite. The thermal residual stresses cause pronounced matrix yielding which also influences the apparent overall stiffness of the composite during the initial stages of subsequent far-field loading along the axial and transverse direction. Furthermore, the thermal residual stresses apparently elevate the flow stress of the composite during transverse tension. Such effects can be traced back to the level of constraint imposed on the matrix by local fiber spacing. The implications of the present results to the processing of the composites are also briefly addressed.     

Control of residual stresses affecting fatigue life of pulsed current gas-metal-arc weld of high-strength aluminum alloy

The influence of pulse parameters on residual stresses of the gas-metal-arc (GMA) weld of a 10-mm-thick extruded section of high-strength Al-Zn-Mg alloy has been analyzed. The role of pulse parameters affecting the residual stresses of the weld joint has been studied by considering a summarized influence of pulse parameters defined by a dimensionless factor ϕ=[(I _b /I _p ) ft _b ]. The reason for the variation in residual stresses of the weld joint with a change in ϕ under different mean currents (I _m ) has been studied by correlating the extent of weld metal deposition and weld size with the ϕ. It is observed that the increase of ϕ reduces the longitudinal and transverse stresses of the weld joint. The nature of variation in residual stresses of the weld joint with ϕ shows an agreement to the trend of variation in its size with ϕ. In conformation of an earlier work, it is proposed that the use of a pulsed current gas-metal-arc welding (GMAW) at proper pulse parameters giving desired ϕ may produce a weld joint having comparatively lower residual stresses with improved fatigue life than that of the weld joint produced by conventional GMAW process through its influence on weld size.     

Influence of elastic inclusion morphology and matrix hardening behavior on bauschinger effect in metal matrix composites

Finite element modeling based on axisymmetrical cells was performed for relating the Bauschinger effect (BE) in metal matrix composites (MMCs) to the reinforcement volume fraction and shape, matrix hardening behavior, and plastic prestrain levels. It was found that elastic inclusions in MMCs introduce a significant BE, which is ascribed to the residual phase stresses in the component phases. The BE introduced by cylindrical inclusions is more significant than that of spherical ones and increases rapidly with increasing the aspect ratio of the cylindrical inclusion. The volume fraction of the elastic inclusion has a strong effect on BE. The hardening behavior of the matrix has a weak effect on BE. The BE increases with increasing plastic prestrain level.     

Sheet bending and determination off residual stresses by means of FEM

The simulation of metal forming processes with the finite element method (FEM) in the sense of a “numerical experiment” is gaining more and more importance. Bending of FeP04 (St1403), × 5 CrNi 189 and AIMgSi1 sheets in V- and U-shaped dies prove the quality of this type of calculation. Of particular interest here is the determination of punch forces, strains and stresses in the workpiece. The calculation of residual stresses is important for process optimisation. Comparisons between calculated and experimentally determined results indicate the calculation qualities. There are many possibilities of influencing the simulation quality of residual stress calculations. In particular, the material model has to be optimally selected. Two combined isotropic-kinematic hardening models (from Axelsson/Samuelsson and McNamara/Sharma) implemented in the FE program to take the Bauschinger effect into consideration point out the influence of material models on the calculated residual stresses.     

Comparison of three different techniques for measuring the residual stresses in an electron beam-welded plate of WASPALOY

The longitudinal, transverse, and through-thickness (short-transverse) residual stresses in an electron beam-welded plate of WASPALOY, a high-strength nickel-based superalloy, have been characterized using neutron diffraction, X-ray diffraction, and a hole-drilling method. Where possible, the results from the different techniques, and the associated uncertainties, have been compared. For the neutron measurements, the γ/γ′ {111} peak was used for the determination of lattice strains. The X-ray measurements were carried out using Fe K _α radiation, the sin² ψ technique, and the {311} γ/γ′ composite peak. The Matthar-Soete method was used for the incremental hole-drilling measurements. Unfortunately, due to texture effects, it was not possible to detect the residual stresses within the weld metal by the diffraction-based methods. For the estimation of residual stresses, plane-specific values of the Young’s modulus and Poisson’s ratio were determined from tensile testpieces using in situ neutron diffractometry. When these data are used, it is found that the neutron, X-ray, and hole-drilling residual stress data are mutually consistent, although the absolute certainties vary with the method employed. The results indicate that, next to the weld, the longitudinal residual stresses approach 1000 MPa and are typically far greater (up to 5 times) than those in the transverse and through-thickness directions. Measurements of the longitudinal strain with distance along the welding direction indicate that the stress state reaches a steady state over the central portion of the plate; for this reason, the majority of the diffraction measurements have been made in the plane perpendicular to the weld at the center of the plate. A simple analysis of the thermal cycles and the extent of plastic deformation induced in the specimen is presented. The plastic “upset zone” has a size which is at least 3 times greater than the cross-sectional area of the weld metal; this suggests that, for accurate analysis of weld-induced distortion, attention should be paid to the evolution of residual stresses in the heat-affected zone as well as the fusion zone.     

Residual stresses in silicon carbide particulate reinforced aluminum composites

In metal matrix composites (MMCs) residual stresses are unavoidable during cooling from high temperature in fabrication or heat treatment because of the difference in the thermal expansion coefficients between the matrix and the reinforcement. In particle reinforced MMC the residual stresses have been proved to be hydrostatic in this study by both experiments and mathematical analysis. A very slight surface effect on the measured stresses was predicted in the case Cu Kα radiation was used. The residual stresses were determined to be tensile in the Al matrix and compressive in the reinforcement. A reduction in residual stress magnitudes of both the matrix and reinforcement was observed after the sample was cooled into liquid nitrogen and heated back to room temperature, which is believed to be caused by plastic deformation of the matrix in low temperature treatment.     

Measurement and calculation of residual stresses after die forging

For die forgings, fabricated from steels Ck 45, 42 CrMo 4 and 38 MnSiV S 6 3, TTT and CCT diagrams were determined, and after different heat treatments, measurements of mechanical properties, fatigue strength and residual stresses were carried out. The diameter of the specimens after the forging process was 32 and 45mm. The residual stresses after quenching between ?450 and +160N/mm² could be reduced to about 60N/mm² by tempering up to 620°C. The fatigue strength in the range of 300N/mm² depends more on the strength than on the residual stresses. Calculations with the program Antras-Thepla correlate well with the measured microstructures and residual stresses. This shows that the materials and processing data used for the calculation are conform to real processes.     

Three-dimensional modelling of thermal residual stresses and mechanical behavior of cast SiC/A1 particulate composites

Thermal residual stresses developed during casting of SiC/aluminum particulate-reinforced composites were investigated as a function of cooling rate and volume fraction of particles using thermo-elastoplastic finite element analysis. The phase change of the matrix during solidification and the temperature-dependent material properties as the composite is cooled from the liquidus temperature to room temperature were taken into account in the model. Further, the effect of thermal residual stresses on the mechanical behavior of the composites was also studied. Based on the study, it was found that the matrix undergoes significant plastic deformation during cool down and has higher residual stress distribution as the cooling rate increases. The model which does not include the solidification of the matrix tends to overestimate the residual stresses in the matrix and underestimate the tensile modulus of elasticity of the composites. In addition, the presence of thermally induced residual stresses tends to decrease the apparent modulus of elasticity and increase the yield strength of the composites compared to those without residual stresses.     

Effect of boundary conditions and workpiece geometry on residual stresses and microstructure in quenching process

In this study, the internal and residual stress states in quenched C60 steel cylinders are analyzed both numerically and experimentally in order to investigate the effects of boundary conditions (such as quench severity and temperature of quench bath) and specimen geometry. Specimen geometry has been analyzed by introducing a hole in a cylinder and varying hole diameter and its eccentricity. In the numerical analysis, the finite element method is applied and both temperature gradients and phase transformations are considered. Experiments include microstructural examination and X-ray measurements of residual stresses of the first kind. It has been found that the value of the convective heat transfer coefficient is very critical to obtain simulation results close to real ones. For instance, when a constant value obtained as the mean of a temperature dependent distribution is used for this parameter, residual stresses are seriously underestimated (up to 40%). The temperature of the quench bath affects directly the convective heat transfer coefficient. The lower the bath temperature, the higher are the resulting residual stresses. Under the same quenching conditions, if the diameter of the hole is greater than a critical value, a transition occurs from the shallow hardening case to the through hardening case, i.e., the residual stress distribution is reversed. On the other hand, for a constant hole diameter, if the eccentricity ratio reaches a critial value, a complex residual stress state results, i.e., compressive/tensile stress transition regions along the circumference are observed.     

Residual stresses in ground steels

A new X-ray method for the evaluation of three dimensional (residual) stress states is demonstrated by studies of the effect of grinding on Armco iron and a medium carbon steel. Although the penetration depth of the Cr-radiation employed in this study is only 5 μm, there is evidence of residual stresses normal to the surface (normal and shear components). In the past it has been assumed that these stress components can be neglected. Shear stresses normal to the surface are small in Armco iron, but significant (± 60 MPa) in steel. From the sign of the shears, the direction of final grinding can be determined. Cooling decreases the tensile stresses parallel to the surface in steel; surprisingly, the opposite result is found in Armco iron.     

Hydrostatic stresses and their effect on the macroflow behavior and microfracture mechanism of two-phase alloys

The aspects of the hydrostatic pressure and tension stresses developed as a result of the interaction between hard and soft phases to maintain compatibility are represented for two-phase alloys with different microstructures. It has been theoretically proved that the stress triaxiality, defined as the ratio of the hydrostatic stress to the effective stress (Σ _H /Σ _e ), causes hardening or softening of the component phases. The average hydrostatic tension and pressure stresses in soft and hard phases developed during monotonic loading make the soft phase harden and hard phase soften. The extent of the hardening and softening increases with the strength ratio of the hard phase to soft phase and the size of the particles and decreasing the phase content. The hardening or softening effect of thein situ constituents has important influence on the flow stress of the composites and is one of the important reasons for deviation from the law of mixtures in prediction of the flow stress of composites based on that of the component phases in bulk. The stress triaxiality distributions in microstructure scale also provide an explicit physical picture of the microfracture mechanisms of the two-phase alloys.     

Phase composition and residual stresses in thermal barrier coatings

The phase composition and the residual stresses in multilayer thermal barrier coatings, which consist of an external ZrO₂–8Y₂O₃ ceramic layer, an intermediate gradient (metal ceramic) layer, and a transient metallic NiCrAlY sublayer, are studied. It is shown that an increase in the specific volume of the metallic sublayer as a result of the formation of thermal growing oxide Al₂O₃ generates high compressive stresses in this sublayer. The ceramic layer undergoes tensile stresses in this case. A method is proposed to estimate the stresses in gradient coatings from X-ray diffraction results.     

The bauschinger effect in a SiC/Al composite

An interesting mechanical property of SiC/Al composites is that the tensile yield stress is less than the compressive yield stress, even though the apparent modulus in tension is greater than that in compression. An investigation was undertaken to determine if the Bauschinger effect (BE) in a SiC/Al composite is asymmetrical. It was found that the BE is indeed asymmetrical in the case of the composite and the magnitude of the BE increases with total forward strain. These results can be explained in terms of the changes in “back stress” caused by the changes in the residual stress and the work hardening during forward strain.     

Residual stresses in high-velocity oxy-fuel metallic coatings

X-ray based residual stress measurements were made on type 316 stainless steel and Fe₃Al coatings that were high-velocity oxy-fuel (HVOF) sprayed onto low-carbon and stainless steel substrates. Nominal coating thicknesses varied from 250 to 1500 μm. The effect of HVOF spray particle velocity on residual stress and deposition efficiency was assessed by preparing coatings at three different torch chamber pressures. The effect of substrate thickness on residual stress was determined by spraying coatings onto thick (6.4 mm) and thin (1.4 mm) substrates. Residual stresses were compressive for both coating materials and increased in magnitude with spray velocity. For coatings applied to thick substrates, near-surface residual stresses were essentially constant with increasing coating thickness. Differences in thermal expansion coefficient between low-carbon and stainless steels led to a 180 MPa difference in residual stress for Fe₃Al coatings. Deposition efficiency for both materials is maximized at an intermediate (∼600 m/s) velocity. Considerations for X-ray measurement of residual stresses in HVOF coatings are also presented.     

The Bauschinger effect and cyclic hardening in copper

The Bauschinger Effect and cyclic hardening were studied during the first few cycles in copper single crystals of an “easy glide” orientation. Dislocation etch pitting was used to augment the mechanical measurements. It was found that significant rearrangements of the dislocation distribution occurred during stress reversal. Sharply defined kink bands which formed during forward straining broadened, and the overall dislocation distribution became more uniform during subsequent cyclic deformation. For cycling at constant strain amplitude, it was found that hardening above the prestress level occurred almost as rapidly as during unidirectional deformation. However, the absence of hardening during increments of Bauschinger strain yielded anomalously low hardening in terms of the cumulative strain. A cyclic hardening model is proposed in which the Bauschinger strains below the prestress level result from relaxation of internal stresses whereas “hardening strains” occur only above the prestress level. The non-symmetry, which causes higher Compressive stresses than tensile stresses during cycling at constant strain amplitude, is shown to result from larger Bauschinger strains below the prestress levelduring tensile half-cycles. Cell sizes and bundle spacings reported in the literature for cyclic tests have been correlated with the corresponding flow stresses and are consistent with predictions of the Long Range Stress Theory. Formerly Graduate Student, Carnegie-Mellon University, Pittsburgh, Pa. Formerly Associate Professor at Carnegie-Mellon University, This paper is based on a thesis submitted by R. C. DANIEL in partial fulfillment of the requirements of the degree of Doctor of Philosophy at Carnegie-Mellon University.     

Thermal residual stresses in functionally graded and layered 6061 Al/SiC materials

The thermal residual stresses that develop in spray atomized and codeposited functionally graded and layered 6061 Al/SiC metal-matrix composites (MMCs) during cooling from the codeposition temperature to ambient temperature were studied using thermo-elastoplastic finite element analysis. In an effort to investigate the effect of layered and graded structures on the residual stress distribution, the composites with homogeneous distribution of SiC particulates were also analyzed. The effect of SiC volume fraction in the SiC-rich layers and the effect of SiC-rich layer thickness on the residual stresses were investigated. Based on the present study, it was found that the residual stress distribution is very distinct for the aluminum and the SiC-rich layers in the layered materials. As the volume fraction of SiC increases in the SiC-rich layer, the magnitude of residual stresses also increases. The radial stress was found to be tensile in the aluminum layers and compressive in the SiC-rich layers. It was also found that, as the thickness of the SiC-rich layer increases, the magnitude of radial stress in the aluminum layers increases, and that in the SiC-rich layers decreases. In the graded material, the lower region of each layer exhibits tensile radial stress, and the upper region of each layer shows compressive radial stress in order to maintain continuity between layers during cooldown. In general, the layered and the graded materials have greater residual stresses and more complicated stress distribution, as compared with those in the composite materials with homogeneous distribution of SiC particulates.