The cyclic stress-strain properties,hysteresis loop shape,and kinematic hardening of two high-strength bearing steels

Measurements of the shapes of the cyclic, stress-strain hysteresis loops obtained from AISI 1070 (HRC 60) and AISI 52100 (HRC 62) steels subjected to constant stress and constant plastic strain amplitude cycles in torsion are presented. The study examines plastic strain amplitudes in the range of 0.0002 ≤ Δε^p/2≤ 0.0015, which are similar to the strain amplitudes produced by rolling contact. The effects of a mean stress are also evaluated. The cyclic hardening of the two steels and other changes in the character of the loops during the cyclic life, 34 ≤N _f ≤ 2156, are defined. A three-parameter, bilinear, elastic-linear-kinematic-hardening-plastic (ELKP) model is shown to describe the multivalued cyclic stress-strain relations of these steels. The principal material properties of the model, in addition to the elastic modulus, the kinematic yield strength, and the plastic modulus, are evaluated. The ELKP properties define the material’s resistance to cyclic plasticity, the loop shape and area (plastic energy dissipation), the conventional cyclic stress-strain curve, the endurance limit, and the rolling contact shakedown pressure. The implications for rolling contact are discussed. Q. CHEN, formerly Visiting Scholar at Vanderbilt University     

Elastic-plastic analysis of hardened layers in rims subjected to repeated rolling contacts

This paper examines the effects of shallow, surface, and subsurface hardened layers on the response of rims to repeated, 2-dimensional (plane strain) rolling contacts. The rolling is simulated by translating a Hertzian pressure distribution across a finite element model of an elastic-plastic half-space. Four cases are examined: (1) a homogeneous rim, (2) and (3) rims with 0.2w-deep and 0.4w-deep (2w is the Hertzian contact width) hardened surface layers, and (4) a rim with a 0.4w-deep subsurface layer. The dimension 2w can be viewed as either the macrocontact width or the microasperity contact width. The calculations treat elastic-perfectly plastic, cycle and amplitude independent, Von Mises material behavior with the yield strength of the hardened layers twice the value of the surrounding material. The effects of pure rolling at a peak contact pressure-to-shear yield strength ratiop ₀/k = 5 are examined. The calculations describe the effects of the layers on the displacements of the rim surface, the extent of the plastic zone, the residual stresses, and incremental plastic strains. The results indicate that the response of the material at different depths is weakly coupled. Cyclic plasticity is eliminated in the hardened layers, but is not substantially altered in the adjacent material. The hardened layer must occupy a large part of the respective active plastic zones of the macrocontact and microasperity contact to prevent continuing cyclic plastic deformation in the two regions.     

Low-cycle fatigue of niobium

Commercially pure niobium (CPNb) and a niobium-1 pct zirconium (Nb-lZr) alloy were tested under low-cycle fatigue conditions at plastic strain amplitudes in the range of 0.02 pct ≤Δε_pl/2≤ 0.7 pct. At low temperatures, the cyclic deformation response of body-centered cubic (bcc) metals is strongly dependent on strain rate. Thus, it was necessary to test at slow (2 x 10_su-4 s^-1) and fast (2 x 10_-2 s^-1) strain rates in order to fully characterize the cyclic deformation at ambient temperature. Only cyclic hardening was observed for both metals under all testing conditions. As expected, higher cyclic stresses were recorded at the fast strain rate compared to the slow strain rate. The Nb-lZr alloy was always stronger than CPNb, although both metals had the same cyclic life at equal plastic strain amplitudes. Further, the strain rate had no effect on the cyclic life. At the fast strain rate, intergranular cracking occurred, and a microplastic plateau was observed in the cyclic stress-strain (CSS) curve for CPNb. At the slow strain rate, no definitely intergranular cracks were detected, and a microplastic plateau was not observed for CPNb. The results of these experiments are interpreted in terms of the influence of strain rate and solute content on the relative mobilities of edge and screw dislocations.     

The effect of strain rate and depressed temperature on the low cycle deformation behavior of alpha iron

The low cycle deformation saturation stress in Ferrovac-E a-iron was studied using diametral plastic strain (0.001 ≤ Δε_dp/2 ≤ 0.0135) as the control variable. Increasing strain rate (6 × 10^•5 s^•1 • 4 × 10^•3 s^•1) and decreasing temperature (295 to 173 K) increased the saturation stress levels. The cyclic work hardening coefficient decreased from 0.18 at 295 K to 0.10 at 173 K, which is consistent with previous studies of monotonie deformation. The temperature dependence of both the saturation stress and the strain rate sensitivity, as measured during cyclic deformation, were similar to that measured during monotonic tensile tests. The temperature dependence of the dislocation velocity indexm* was in good agreement with published values from high cycle fatigue and monotonie tensile tests. Thus the same deformation mechanisms are believed to occur in both monotonie and large plastic cyclic deformation (Δε_dp/2 ≥ 0.001) of a-iron.     

A strain energy-based approach to the low-cycle fatigue damage mechanism in a high-strength spring steel

Low-cycle fatigue tests were conducted using smooth, cylindrical specimens under a strain-controlled, fully reversed condition for a high-strength spring steel heat treated to different strength levels. The variation of the cyclic deformation substructure was observed with a transmission electron microscope (TEM). The results indicate that the average plastic strain energy dissipated per cycle (ΔW _ps ) is an important parameter upon which a consistent evaluation of the cyclic stress-strain, the strain-life, and the plastic strain energy-life relationships is made feasible. Furthermore, the total plastic strain energy dissipated prior to failure (W _f ), determined on the basis of ΔW _ps , is proven to be another important parameter, from the variation of which the extent of local damage accumulation can be evaluated. Confirmed by the results of TEM observations, a strain localization-induced damage mechanism is proposed and discussed.     

The relationship between microstructural and plastic instability in AI-4.0 Wt Pct Cu alloy

The investigation of the effect of plastic deformation on the stability of theθ′ precipitates in an aluminum-4.0 wt pct copper alloy was performed. The alloy was produced by directional solidification, with Ti added as a grain refiner. Hot compression tests were performed at 200 °C in the strain rate range of 10_-3 to 10_-5 s₁ and equivalent strain up to 0.7 on specimens that had been initially heat treated, also at 200 °C, in order to obtain a uniform distribution of theθ0′ precipitates within the matrix. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) of the plastically deformed specimens revealed a very heterogeneous distribution of strain. Also, the regions with localized strain contained randomly distributedθ precipitates of nearly equiaxed shape without any preferred orientation relationships to the matrix. Thus, the plastic deformation initiated the transformationθ′ →θ. The flow stress was reduced in the regions in which this transformation had occurred, which further accentuated the localization tendency of the strain. The combined process,θ′ →θ transformation/strain localization, thus developed in an avalanching way.     

Low-cycle fatigue behavior of INCONEL 718 superalloy with different concentrations of boron at room temperature

Symmetrical push-pull low-cycle fatigue (LCF) tests were performed on INCONEL 718 superalloy containing 12, 29, 60, and 100 ppm boron (B) at room temperature (RT). The results showed that all four of these alloys experienced a relatively short period of initial cyclic hardening, followed by a regime of softening to fracture at higher cyclic strain amplitudes (Δɛ _t /2≥0.8 pct). As the cyclic strain amplitude decreased to Δɛ _t /2≤0.6 pct, a continuous cyclic softening occurred without the initial cyclic hardening, and a nearly stable cyclic stress amplitude was observed at Δɛ _t /2=0.4 pct. At the same total cyclic strain amplitude, the cyclic saturation stress amplitude among the four alloys was highest in the alloy with 60 ppm B and lowest in the alloy with 29 ppm B. The fatigue lifetime of the alloy at RT was found to be enhanced by an increase in B concentration from 12 to 29 ppm. However, the improvement in fatigue lifetime was moderate when the B concentration exceeded 29 ppm B. A linear relationship between the fatigue life and cyclic total strain amplitude was observed, while a “two-slope” relationship between the fatigue life and cyclic plastic strain amplitude was observed with an inflection point at about Δɛ _p /2=0.40 pct. The fractographic analyses suggested that fatigue cracks initiated from specimen surfaces, and transgranular fracture, with well-developed fatigue striations, was the predominant fracture mode. The number of secondary cracks was higher in the alloys with 12 and 100 ppm B than in the alloys with 29 and 60 ppm B. Transmission electron microscopy (TEM) examination revealed that typical deformation microstructures consisted of a regularly spaced array of planar deformation bands on {111} slip planes in all four alloys. Plastic deformation was observed to be concentrated in localized regions in the fatigued alloy with 12 ppm B. In all of the alloys, γ″ precipitate particles were observed to be sheared, and continued cyclic deformation reduced their size. The observed cyclic deformation softening was associated with the reduction in the size of γ″ precipitate particles. The effect of B concentration on the cyclic deformation mechanism and fatigue lifetime of IN 718 was discussed.     

Low-Cycle fatigue of dispersion-strengthened copper

The cyclic deformation behavior of a dispersion-strengthened copper alloy, GlidCop Al-15, has been studied at plastic strain amplitudes in the range 0.1 pct ≤Δε _p/2 ≤ 0.8 pct. Compared to pure polycrystalline copper, the dispersion-strengthened material exhibits a relatively stable cyclic response as a consequence of the dislocation substructures inherited from prior processing and stabilized by the A1₂O₃ particles. These dislocation structures remain largely unaltered during the course of deformation; hence, they do not reveal any of the features classically associated with copper tested in fatigue. At low amplitudes, the fatigue lifetimes of the dispersion-strengthened copper and the base alloy are similar; however, the former is more susceptible to cracking at stress concentrations because of its substantially greater strength. This similarity in fatigue lifetimes is a consequence of the dispersal of both deformation and damage accumulation by the fine grain size and dislocation/particle interactions in the GlidCop alloy. The operation of these mechanisms is reflected in the fine surface slip markings and rough fracture surface features for this material. Formerly Graduate Research Assistant, University of California, Davis, CA     

The shape memory effect and superelasticity in two-phase polycrystalline α/β brasses

The shape memory effect (SME), superelasticity (SE), and cyclic deformation behavior of two-phase α/β brasses have been investigated at various temperatures, using tensile tests andin situ optical microscopic observations. The morphology and characteristics of the (thermoelastic) martensitic transformation and the mechanism of the SME are similar to those for single-phase β-brass, but the amount of irrecoverable strain is larger in the two-phase alloys due to plastic deformation of the α particles. After unloading and heating, the slipbands in the discrete a particles remain, whereas the martensite almost disappears; thus, the higher the volume fraction of α particles, the larger the amount of irrecoverable strain. The deformation behavior of alloy A at temperatures above the martensite start (M_s) temperature (with 26 pct α phase) is dominated by deformation of the α phase, so complete SE cannot be obtained after cyclic deformation, both at room temperature and at -40 °C. While in alloy B (containing 15 pct α phase), the deformation behavior is dominated by the formation of stress-induced martensite (SIM). The α particles are deformed before SIM formation on loading at room temperature, but on the contrary, SIM forms before the α particles are deformed on loading at -40 °C (>M_s). Complete SE can be obtained in alloy B after cyclic deformation at room temperature to a given strain but does not occur at -40 °C because the a particles are deformed along with the growth of pre-existing SIM under larger strain during cycling at this temperature.     

The quasi-static and cyclic fatigue fracture behavior of 2014 aluminum alloy metal-matrix composites

In this article, the quasi-static and cyclic fatigue fracture behavior of aluminum alloy 2014 discontinuously reinforced with fine particulates of aluminum oxide are presented and discussed. The discontinuous particulate-reinforced 2014 aluminum alloy was cyclically deformed under fully reversed, tension-compression loading over a range of strain amplitudes, well within the plastic domain of the engineering stress-strain curve, resulting in cyclic fatigue lives of less than 10⁴ cycles. The influence of both ambient and elevated temperatures on cyclic stress and cyclic stress-strain response is highlighted. The underlying mechanisms governing the fracture mode during quasi-static and cyclic fatigue are discussed and rationalized in light of the concurrent and mutually interactive influences of intrinsic composite microstructural features, deformation characteristics of the metal matrix and reinforcement particulate, cyclic strain amplitude and resultant fatigue life, and test temperature. This article is based on a presentation made in the Symposium “Mechanisms and Mechanics of Composites Facture” held October 11–15, 1998, at the TMS Fall Meeting in Rosemont, Illinois, under the auspices of the TMS-SMD/ASM-MSCTS Composite Materials Committee.     

The quasi-static and cyclic fatigue fracture behavior of 2014 aluminum alloy metal-matrix composites

In this article, the quasi-static and cyclic fatigue fracture behavior of aluminum alloy 2014 discontinuously reinforced with fine particulates of aluminum oxide are presented and discussed. The discontinuous particulate-reinforced 2014 aluminum alloy was cyclically deformed under fully reversed, tension-compression loading over a range of strain amplitudes, well within the plastic domain of the engineering stress-strain curve, resulting in cyclic fatigue lives of less than 10⁴ cycles. The influence of both ambient and elevated temperatures on cyclic stress and cyclic stress-strain response is highlighted. The underlying mechanisms governing the fracture mode during quasi-static and cyclic fatigue are discussed and rationalized in light of the concurrent and mutually interactive influences of intrinsic composite microstructural features, deformation characteristics of the metal matrix and reinforcement particulate, cyclic strain amplitude and resultant fatigue life, and test temperature. This article is based on a presentation made in the Symposium “Mechanisms and Mechanics of Composites Fracture” held October 11–15, 1998, at the TMS Fall Meeting in Rosemont, Illinois, under the auspices of the TMS-SMD/ASM-MSCTS Composite Materials Committee.     

Plastic straining effects on the microstructure of a Ti-rich NiTi shape memory alloy

A Ni-52 at. pct Ti shape memory alloy, cold drawn to 30 pct, was annealed at 1173 K for 1 hour, water quenched, and then subjected to differential scanning calorimetry (DSC). No evidence of the premartensitic R transformation was found during either the forward or the reverse transformation. Microstructurally, it was found that the alloy possessed a relatively large volume fraction (∼0.05) of coarse second-phase brittle particles. These precipitates acted as preferential sites for martensite plate nucleation and gave rise to a “starlike” morphology. The tensile and compressive properties of the alloy in the as-received condition were also investigated. The alloy exhibited relatively good ductility (fracture strain = 0.28), which was attributed to its inherent ability to relieve or delay the development of plastic instabilities through rapid strain hardening. In addition, X-ray diffraction (XRD) of deformed specimens indicated the presence of an extraintensity peak corresponding to the B2 phase (110)_B2 when the alloy was plastically deformed in compression. Accordingly, it is suggested that plastic deformation induces the reverse transformation to the B2 phase in highly stressed local regions. Transmission electron microscopy (TEM) of deformed martensite structures showed slip lines probably due to dislocation slip, as well as variant interpenetration. Besides, optical and scanning microscopy of regions adjacent to the fractured surfaces indicated that fine martensite plates and/or “apparent” new grains develop at regions of prior stress intensification (former crack-tip regions) during crack propagation.     

Rolling contact deformation,etching effects,and failure of high-strength bearing steel

This paper examines the connections between the continuing cyclic plastic deformation, the etching effects, and the fatigue life of a high-strength bearing steel under rolling contact. Etching effects, called the “dark etching regions” and the “white etching bands,” are observed after several million cycles. The inclinations of the white etching bands vary between 20 to 30 deg and 70 to 80 deg to the rolling direction, depending on the loading conditions and geometry of the rolling elements. The principal axes of stress and plastic strain rotate continuously as the rolling element translates over a fixed point below the running surface. At the same time, the cyclic plastic activity varies. A finite element model is used to calculate the inclinations and amounts of cyclic plastic strain as the roller translates over the running surface. The calculations are performed for both elastic linear kinematic-hardening plastic (ELKP) and elastic perfectlyplastic (EPP) material behaviors. Inclinations of concentrated plastic strain activity combined with low hydrostatic pressure are identified. There is a good correlation between the inclinations of the white etching bands and the inclinations of concentrated plastic activity calculated for the ELKP material behavior. No such correlation is obtained for the EPP behavior. Strain concentrations are intensified by the hydrostatic pressure dependence of the kinematic yield strength. While an equal amount of plastic strain activity occurs in the conjugate directions, no etching bands are observed at these inclinations. The reasons for this are not clear. The shakedown limit obtained for the two models is essentially the same. The fatigue lives under rolling contact are compared with the lives obtained in simple cyclic torsion experiments with the same cyclic plastic strain amplitudes. The rotation of the principal shear direction and the high hydrostatic pressure attending rolling contact may be responsible for the seven orders-of-magnitude longer contact lives.     

Plastic straining effects on the microstructure of a Ti-rich NiTi shape memory alloy

A Ni-52 at. pct Ti shape memory alloy, cold drawn to 30 pct, was annealed at 1173 K for 1 hour, water quenched, and then subjected to differential scanning calorimetry (DSC). No evidence of the premartensiticR transformation was found during either the forward or the reverse transformation. Microstructurally, it was found that the alloy possessed a relatively large volume fraction (∼0.05) of coarse second-phase brittle particles. These precipitates acted as preferential sites for martensite plate nucleation and gave rise to a “starlike” morphology. The tensile and compressive properties of the alloy in the as-received condition were also investigated. The alloy exhibited relatively good ductility (fracture strain=0.28), which was attributed to its inherent ability to relieve or delay the development of plastic instabilities through rapid strain hardening. In addition, X-ray diffraction (XRD) of deformed specimens indicated the presence of an extraintensity peak corresponding to the B2 phase (110)_B2 when the alloy was plastically deformed in compression. Accordingly, it is suggested that plastic deformation induces the reverse transformation to the B2 phase in highly stressed local regions. Transmission electron microscopy (TEM) of deformed martensite structures showed slip lines probably due to dislocation slip, as well as variant interpenetration. Besides, optical and scanning microscopy of regions adjacent to the fractured surfaces indicated that fine martensite plates and/or “apparent” new grains develop at regions of prior stress intensification (former crack-tip regions) during crack propagation.     

Model of Plastic Deformation of Powder Materials Taking Account of the Proportion of Contact Volume

A structural model is suggested that takes account of the contact nature of plastic deformation of a powder body. It is shown that in averaging local stresses and strain rates the volume of averaging can be presented as a combination of straight cylinders constructed at all contact areas of a particle and having a common nucleus formed by the intersection of cylindrical bodies. On the whole a plastically deformed powder body is an orientated contact-rod system composed of cylinders that are in contact by their bases and that experience uniform tension-compression deformation. The volume fraction of powder body contact volume determined using Bal'shin's and Zhdanovich's equations can be a quantitative measure of the volume fraction of plastically deformed material. The contact-rod model satisfies boundary conditions for the poured state of powder and it is good agreement with experimental data for isostatically compacted metal powders.     

An Evaluation of the summation of cyclic plastic strain damage in two high strength aluminum alloys

A damage equation based upon the integration of low cycle fatigue plastic strain ranges was verified experimentally for two high strength aluminum alloys 2024-T4 and 7075-T651. The damage equation which has been used extensively for many fatigue crack propagation theories assumes cyclic damage under increasing plastic strain ranges. In order to verify the damage equation, low cycle fatigue specimens were subjected to a fully reversed strain cycle in which the total strain-range was increased linearly by a constant amount Δ[Δε_d] per cycle. An excellent agreement was obtained between the predicted and observed fatigue lifetimes. The stress-strain response of these alloys was also measured. The experimental results showed that these two alloys cyclically harden substantially and that the single strain increment stress-strain curve is a fair lower bound approximation of the cyclic stress-strain curve.     

Mechanical behavior of Al−Li/SiC composites: Part II. Cyclic deformation

The deformation and failure mechanisms under cyclic deformation in an 8090 Al−Li alloy reinforced with 15 vol pct SiC particles were studied and compared to those of the unreinforced alloy. The materials were tested under fully reversed cyclic deformation in the peak-aged and naturally aged conditions to obtain the cyclic response and the cyclic stress-strain curve. The peak-aged materials remained stable or showed slight cyclic softening, and the deformation mechanisms were not modified by the presence of the ceramic reinforcements: dislocations were trapped by the S′ precipitates and the stable response was produced by the mobile dislocations shuttling between the precipitates to accommodate the plastic strain without further hardening. The naturally aged materials exhibited cyclic hardening until failure, which was attributed to the interactions among dislocations. Strain localization and slip-band formation were observed in the naturally aged alloy at high cyclic strain amplitudes, whereas the corresponding composite presented homogeneous deformation. Fracture was initiated by grain-boundary delamination in the unreinforced materials, while progressive reinforcement fracture under cyclic deformation was the main damage mechanism in the composites. The influence of these deformation and damage processes in low-cycle fatigue life is discussed.     

Mechanical behavior of Al-Li/SiC composites: Part II. Cyclic deformation

The deformation and failure mechanisms under cyclic deformation in an 8090 Al-Li alloy reinforced with 15 vol pct SiC particles were studied and compared to those of the unreinforced alloy. The materials were tested under fully reversed cyclic deformation in the peak-aged and naturally aged conditions to obtain the cyclic response and the cyclic stress-strain curve. The peak-aged materials remained stable or showed slight cyclic softening, and the deformation mechanisms were not modified by the presence of the ceramic reinforcements: dislocations were trapped by the S′ precipitates and the stable response was produced by the mobile dislocations shuttling between the precipitates to accommodate the plastic strain without further hardening. The naturally aged materials exhibited cyclic hardening until failure, which was attributed to the interactions among dislocations. Strain localization and slip-band formation were observed in the naturally aged alloy at high cyclic strain amplitudes, whereas the corresponding composite presented homogeneous deformation. Fracture was initiated by grain-boundary delamination in the unreinforced materials, while progressive reinforcement fracture under cyclic deformation was the main damage mechanism in the composites. The influence of these deformation and damage processes in low-cycle fatigue life is discussed.     

车轮轧制成形过程有限元分析

使用MSC.SuperForm对840火车轮轧制成形过程建立三维热力耦合有限元分析模型,研究分析了车轮立式轧制成形过程的金属变形规律.得出车轮轧制成形过程最大变形分布在辐板与轮辋连接处及轮辋外端靠近踏面处,轮辋外端变形明显大于轮辋内端变形,轮辋中心变形较难深透;车轮轧制中,辐板靠近轮辋端的金属周向流动明显,周向流动主要发生在轧制中后期;研究还得出车轮轧制过程各轧辊的受力及其变化情况,为制定车轮轧制工艺提供了参考.     

Local yielding attending fatigue crack growth

Fatigue crack growth rate measurements were performed at 100°C on an Fe-3Si steel in three thickness conditions and at different ΔK-levels. The test pieces were subsequently sectioned and etched to reveal the plastic deformation attending crack growth both on the surface and in the interior. Unlike preceding studies, the Fe-3Si steel displayed classical cyclic crack growth: well-defined fatigue striations with a spacing close to the per-cycle growth rate, and essentially the same growth rates that have been reported for low and medium strength steels. A highly strained region, approximately one-fifth the size of the monotonie plastic zone, is identified as the cyclic plastic zone. On this basis three regions with distinct cyclic strain histories that precede the crack are identified: a microstrain region wherein the material receives ∼10³ to 10⁴ strain cycles in the range 0 < Δε _P ≲ 10^-3; a cyclic plastic zone corresponding to ∼200 cycles in the range 10^-3 < Δ∈ _P ≲ 10^-1, and a COD-affected zone that receives ∼10 strain cycles in the range 10^-1 ≲ Δ∈ _P ≲ 1. It is suggested that the damage associated with the instabilities in the fatigue substructure to overstrain contribute to the growth mechanism.