Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves

Hardening of polycrystalline copper subjected to tension-compression loading cycles in the plastic region is discussed with reference to changes in flow stress determined from equations describing dislocation glide. It is suggested that hardening is as a result of the accumulation of strain on a monotonic stress-strain curve. On initial loading, the behaviour is monotonic. On stress reversal, a characteristic cyclic stress-strain curve is followed until the stress reaches a value in reverse loading corresponding to the maximum attained during the preceding half cycle. Thereafter, the monotonic path is followed until strain reversal occurs at completion of the half cycle. Repetition of the process results in cyclic hardening. Steady state cyclic behaviour is reached when a stress associated with the monotonic stress-strain curve is reached which is equal to the stress associated with the cyclic stress-strain curve corresponding to the imposed strain amplitude.     

Influence of the localized initial plastic deformation on the effective thermomechanical response of metal-matrix composites

A generalized Eshelby model, allowing interaction among reinforcing particles under a Mori-Tanakalike scheme, is presented. Different inclusion aspect ratios are studied in the elastic and incipient elastoplastic regime for a model SiC-Al composite. The solution of the field equations is obtained via an explicit algorithm that yields the interaction field in terms of the stress and strain variables. The particles and fibers are taken as purely elastic, and the matrix is regarded as elastic-perfectly plastic. Coefficients of thermal expansion (CTE) are calculated both under the assumption of purely elastic response and at the onset of plastic localized deformation. The simulated stress-strain curves show the influence of interaction stresses on macroscopic yield stress for different inclusion aspect ratios, with no consideration of matrix hardening. The model allows a good simulation of the thermomechanical behavior of composite materials and contributes to the understanding of the elastoplastic transition in stress-strain curves. It can also simply explain some of the most distinctive features of the mechanical behavior of composites. The model presents the possibility of controlling many input variables and geometries and simultaneously considering three-dimensional deformation of interacting inclusion-reinforced materials with low computational effort. Comparisons to experimental CTE and residual stresses are provided.     

The influence of residual stress on the yielding of metal matrix composites

A systematic numerical study of the effect of residual stresses on the yielding behavior of composites comprised of elastic particles well bonded to a ductile matrix is carried out. The calculations are made within the framework of continuum plasticity theory using cell models. An investigation is made into the roles volume fraction, particle shape, and hardening play in this interaction. A slight transient softening of the composite in both tension and compression is found, but the limit stress of the composite is unaffected by the residual stress. Thus the limit stress-strain response is symmetric in tension and compression for strains greater than a few times the matrix yield strain. A qualitative connection is made between the transient reduction in stiffness and the extent to which there was prior plastic deformation in the matrix due to residual stresses.     

冷变形对Inconel 690合金力学行为与组织的影响

 本文研究了Inconel 690合金在冷轧变形过程中的组织演变和形变强化规律。结果表明,在15%和20%之间存在一个临界应变εL,小于临界变形量时,加工硬化能力随着变形量的增加递减,真应力-真应变曲线可用Ludwigson模型描述,位错运动主要是单系滑移,加工硬化主要来自位错的长程应力场。临界应变到40%变形量之间,加工硬化能力随着变形量的增加又增强,真应力-真应变曲线也可用Hollomon方程描述,位错运动出现了多滑移和交滑移,加工硬化主要是位错滑移和林位错交割的短程交互作用。     

Shock-loading response of 6061- T6 aluminum metal-matrix composites

The purpose of this research was to systematically study the influence of peak-shock pressure and second-phase reinforcement on the structure/property response of shock-loaded 6061-T6 Al-alumina composites. The reload stress-strain response of monolithic 6061-T6 Al, used as a baseline for comparison, showed no increased shock hardening compared to the unshocked material deformed to an equivalent strain. The reload stress-strain response of the shock-loaded 6061-T6 Al-alumina composites exhibited a lower reload yield strength than the flow stress of the starting composites. The degree of strength loss was found to increase with increasing shock pressure. Wavespeed measurements of shock-prestrained specimens showed no degradation compared to unshocked specimens, indicating that particle cracking had not occurred under shock. This result was supported by optical metallography, which did not reveal cracked particles or particle decohesion in the shock-prestrained samples. The reload stress-strain response of the shock-prestrained composites, after resolutionizing and T6 reaging, showed that the composites recovered their full as-received preshock stress-strain responses. This result supports the finding that degradation in reload strength was attributable to matrix microstructural changes resulting from the shock. Transmission electron microscopy (TEM) examination of the shock-loaded microstructures revealed that the matrix regions adjacent to the particle/matrix interface had undergone significant recovery and partial recrystallization resulting from the shock. This type of near-interface substructure is in stark contrast to the heavily dislocated near-interface dislocation substructure of the as-received composites. The loss of dislocation density(i.e., strain hardening) in the near-interface matrix region, resulting from the shock, highlights the importance of the thermally introduced dislocation substructure changes in establishing the strength of metal-matrix composites (MMCs). This article is based on a presentation made in the symposium “Dynamic Behavior of Materials,” presented at the 1994 Fall Meeting of TMS/ASM in Rosemont, Illinois, October 3-5, 1994, under the auspices of the TMS-SMD Mechanical Metallurgy Committee and the ASM-MSD Flow and Fracture Committee.     

The deformation behaviour of single crystals of the CuCrSiO2 system—I. Yield and pre-yield behaviour

The yield behaviour and pre-yield behaviour of Cu-0,4% Cr and CuCrSiO₂ single crystals have been studied as a function of aging time for this age hardening system. The stress at the onset of gross plasticity in CuCr is comparable with the stress required for the Orowan process. The dislocation configurations at yield have been examined and found to be determined by the cross-slipping of screw segments.The stress for gross plasticity in CuCrSiO₂ crystals is shown to be controlled by the Cr precipitates and not by the SiO₂ particles which have an immeasureable effect. However, the SiO₂ particles modify both the pre-yield behaviour and the dislocation structures observed in the crystal after small strains.     

Particle reinforcement of ductile matrices against plastic flow and creep

A theoretical investigation is made of the role of non-deforming particles in reinforcing ductile matrix materials against plastic flow and creep. The study is carried out within the framework of continuum plasticity theory using cell models to implement most of the calculations. Systematic results are given for the influence of particle volume fraction and shape on the overall behavior of composites with uniformly distributed, aligned reinforcement. The stress-strain behavior of the matrix material is characterized by elastic-perfectly plastic behavior or by power-law hardening behavior of the Ramberg-Osgood type. A relatively simple connection is noted between the asymptotic reference stress for the composite with the power-law hardening matrix and the limit flow stress of the corresponding composite with the elastic-perfectly plastic matrix. The asymptotic reference stress for the composite with the power-law matrix is applicable to steady-state creep. A limited study is reported on the overall limit flow stress for composites with randomly orientated disc-like or needle-like particles when the particles are arranged in a packet-like morphology.     

Primary creep of TiN dispersion hardened 20%Cr-25%Ni stainless steel at 160 MPa and 1123 K—II. Annealing behaviour

The annealing response of specimens of TiN dispersion hardened 20%Cr-25%Ni stainless steel after primary creep to a range of strains at 160 MPa, 1123 K is described (the microstructural development during primary creep has been reported elsewhere). It is shown that there is a driving force not only for reduction of the density, but also for an increase in perfection of the creep-induced matrix dislocation network. Moreover, it is shown that there is a driving force for the recovery of the dislocation tangles which develop at TiN particles during deformation. The details of the way in which the network characteristics change in annealing as a function of prior creep strain are fully consistent with the development during primary creep of an internal stress distribution. The latter is modelled as arising due to the presence of the dislocation tangles, which themselves occur as a result of stress relaxation associated with Orowan bypass at TiN particles. In the presence of such an internal stress during deformation, load removal produces a negative effective applied stress in the matrix, which dominates the network behaviour. It is concluded that the model of primary creep response described earlier is realistic, and emphasised that the observed strain/time variation during deformation depends on the mutually interdependent behaviour of all the components of the dislocation substructure.     

Effect of temperature and strain rate on the compressive flow of aluminum composites containing submicron alumina particles

Uniaxial compression tests were conducted on aluminum composites containing 34 and 37 vol pct submicron alumina particles, to study the effect of temperature and strain rate on their flow stress. For temperatures between 25 °C and 600 °C and strain rates between 10⁻³ and 1 s⁻¹, the flow stress of the composites is significantly higher than that of unreinforced aluminum tested under similar conditions. This can be attributed to direct strengthening of the composites due to load sharing between the particles and the matrix, and an enhanced in-situ matrix flow stress resulting from a particle-induced increase in dislocation density. The composites, however, exhibit the same stress dependence on temperature and strain rate as unreinforced aluminum, indicating a common hardening mechanism, i.e., forest dislocation interactions. The forest hardening present under the explored testing conditions masks the effects of direct dispersion strengthening operative at lower deformation rates in these materials.     

Computational modeling of metal matrix composite materials—II. Isothermal stress-strain behavior

The mechanical behavior of particulate reinforced metal matrix composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically using the computational micromechanics approach. In this, the second in a series of four articles, the isothermal overall stress-strain behavior and its relation to microstructural deformation is examined in detail. The macroscopic strengthening effect of the reinforcement is quantified in terms of a hardness increment. As seen in the first article for microscale deformation, inhomogeneous and localized stress patterns develop in the microstructures. These are predominantly controlled by the positions of the reinforcing particles. Within the particles stress levels are high, indicating a load transfer from matrix to reinforcement. The higher straining that develops in the matrix grains, relative to the unreinforced polycrystal, causes matrix hardness advancement. Hydrostatic stress levels in the composite are enhanced by constraints on plastic flow imposed by the particles. Constrained plastic flow and matrix hardness advancement are seen as major composite strengthening mechanisms. The latter is sensitive to the strain hardening nature in the matrix alloy. To assess the effects of constraint more fully, simulations using external confining loads were performed. Both strengthening mechanisms depend strongly on reinforcement volume fraction and morphology. In addition, texture development and grain interaction influence the overall composite behavior. Failure mechanisms can be inferred from the microscale deformation and stress patterns. Intense strain localization and development of high stresses within particles and in the matrix close to the particle vertices indicate possible sites for fracture.     

The structure and properties of some heavily cold worked aluminum alloys

Several particle containing aluminum alloys have been heavily cold worked by wire drawing and torsion, and their stress-strain behaviour monitored. The shape of the resulting stress-strain curve is shown to be independent of the mode of deformation and consists of an initial region of high work hardening rate which gradually decreases to a reasonably constant work hardening region at large strains. This terminal work hardening rate increases with increasing solute, which inhibits dynamic recovery mechanisms.Two of the alloys containing higher volume fractions of particles exhibit work softening in addition to work hardening. The results are discussed in terms of some of the current work hardening models.     

Plasticity of continuous fiber-reinforced metals

Continuous parallel alumina fiber-reinforced metals produced by pressure infiltration are tested in tension/compression along the fiber axis with a goal of measuring the influence exerted by long fibers on the flow stress of their matrix. In this configuration, the equistrain rule of mixtures, modified to take into account stresses due to differential lateral contraction, can be used to back-calculate the matrix flow stress from that of the composite. This method provides the least physically ambiguous measurement of matrix flow stress in the composite; however, experimental uncertainty can be high. This uncertainty is evaluated in detail for the present experiments, in which matrix in situ stress-strain curves are measured for cast 3M NEXTEL 610 and DUPONT FIBER FP reinforced pure and alloyed aluminum- and copper-based matrices of varying propensity for recovery and cross-slip. Within experimental uncertainty, data show no enhanced matrix work-hardening rates such as those those that have been measured with tungsten fiber-reinforced copper. It is found that the fibers alter the matrix plastic flow behavior by increasing the flow-stress amplitude of the matrix, and by rendering initial yield in compression more progressive than in initial tension. Essentially, all observed features of matrix/fiber interaction can be rationalized as attributable to dislocation emission in the matrix caused by thermal mismatch strains within the material during composite cooldown from processing temperatures.     

Fatigue deformation-induced response in a superduplex stainless steel

The cyclic deformation behavior of SAF 2507 superduplex stainless steel (SDSS) was studied under constant plastic-strain amplitudes. The cyclic hardening/softening curves show initial hardening, followed by softening and, finally, saturation behavior. Two regimes can be differentiated in the cyclic stress-strain curve (CSSC) of SDSS. The transition point at which the cyclic strain-hardening rate changes is identified to be ɛ _p/2=7 × 10⁻³. Transmission electron microscopy (TEM) results on dislocation structures suggested that there is a close relationship between the CSSC, hardening/softening curves, and the dislocation substructure evolution. In the low-plastic-strain-amplitude regime of the CSSC, the dislocation activity in the austenite grains is found to be higher than that in the ferrite grains. At higher plastic strain amplitudes, low-energy dislocation structures are found in the ferrite grains, while clusters and bundles of dislocations can be observed in the austenite grains. Strain localization due to formation of these structures resulted in a decrease in the cyclic strain-hardening rate within the high-plastic-strain-amplitude regime. Dislocation substructure evolution is also used to explain the shape of the hardening/softening curve.     

Hardening behavior in fatigue

Cyclic hardening behavior has been reviewed (1) in relation to cumulative strain, in which the hardening rate is small compared to that in monotonic deformation but can be related to it under certain conditions, and (2) in relation to the cyclic stress-strain curve, in which it is extremely large because dislocation densities become large in saturation. It is shown that single crystals of both wavy and planar slip character have plateaus in their cyclic stress-strain curves and that the localized strain is similar, although the dislocation structures associated with the regions of persistent slip are different. Strain avalanches are shown to be widely prevalent in cyclic deformation, and their interpretation yields valuable insight about dislocation behavior. Cyclic hardening in polycrystals of both pure metals and alloys is also reviewed. The cyclic stress-strain curves depend strongly on history, microstructure, and test conditions, and the flow stress can be explained by the Schmid factor, Sachs factor, or Taylor factor-depending on those conditions. This paper is based on a presentation made at the symposium “50th Anniversary of the Introduction of Dislocations” held at the fall meeting of the TMS-AIME in Detroit, Michigan in October 1984 under the TMS-AIME Mechanical Metallurgy and Physical Metallurgy Committees.     

A Combined Precipitation,Yield Strength,and Work Hardening Model for Al-Mg-Si Alloys

In the present article, a new two-internal-variable model for the work hardening behavior of commercial Al-Mg-Si alloys at room temperature is presented, which is linked to the previously developed precipitation and yield strength models for the same class of alloys. As a starting point, the total dislocation density is taken equal to the sum of the statistically stored and the geometrically necessary dislocations, using the latter parameters as the independent internal variables of the system. Classic dislocation theory is then used to capture the overall stress-strain response. In a calibrated form, the work hardening model relies solely on outputs from the precipitation model and thus exhibits a high degree of predictive power. In addition to the solute content, which determines the rate of dynamic recovery, the two other microstructure parameters that control the work hardening behavior are the geometric slip distance and the corresponding volume fraction of nonshearable Orowan particles in the base material. Both parameters are extracted from the predicted particle size distribution. The applicability of the combined model is illustrated by means of novel process diagrams, which show the interplay between the different variables that contribute to work hardening in commercial Al-Mg-Si alloys.     

Reversibility in the work hardening of spheroidised steels

Estimates of the contributions made by directional and non-directional components of work hardening, to the flow strengths of two spheroidised steels in monotonic and reversed axisymmetric deformation, have been based on measurements in X-ray diffraction, indentation hardness and shapechange tests. The results show that, in monotonic deformation of a 1.1% carbon steel, the directional component of internal stress made the dominant contribution to work hardening with applied strains up to ~ 0.02 and it accounted for about half the hardening increment with ~ 0.05 strain. In reversed deformation, the directional mean stress was fully reversed at the reverse strains required to give near-parallelism between the “forward” and “reverse” stress-strain curves. Thus the directional component of internal stress had little direct influence on the magnitude of permanent softening observed in Bauschinger tests. To a close approximation, permanent softening was a measure of the extent to which non-directional hardening was wiped out in reversed deformation. Comparison with the behaviour of a low-carbon steel showed that the extent of this reversibility in work hardening increased with an increasing volume fraction of non-deforming particles. Some implications of these findings are discussed.     

A dislocation model for the plastic relaxation of the transformation strain energy of a misfitting spherical particle

A dislocation approach is developed to explain the dependency of the plastic zone size on precipitate size and misfit for a spherical misfitting particle. The dislocation model is predicated upon the punching and mutual interaction of dislocation prismatic loops and is used to explain the presence of both prismatic loops and dense tangles of dislocations surrounding the precipitate. The plastic zone is modeled as a series of concentric dislocation loop shells which can climb and glide in such a way as to minimize the energy of the system; the extent of climb and glide being limited by the critical resolved shear stress of the matrix phase. It is found that plastic zone size is a strong function of particle size. As particle size increases, the ratio of plastic zone radius to particle radius increases. For large particles, plastic zone radii approach the predictions of earlier work in which the three dimensional elasto-plastic problem for a misfitting sphere was solved exactly using the Prandtl-Reuss equations and von Mises yield criterion.     

Micromechanics effects in creep of metal-matrix composites

The creep of metal-matrix composites is analyzed by finite element techniques. An axisymmetric unit-cell model with spherical reinforcing particles is used. Parameters appropriate to TiC particles in a precipitation-hardened (2219) Al matrix are chosen. The effects of matrix plasticity and residual stresses on the creep of the composite are calculated. We confirm (1) that the steady-state rate is independent of the particle elastic moduli and the matrix elastic and plastic properties, (2) that the ratio of composite to matrix steady-state rates depends only on the volume fraction and geometry of the reinforcing phase, and (3) that this ratio can be determined from a calculation of the stress-strain relation for the geometrically identical composite (same phase volume and geometry) with rigid particles in the appropriate power-law hardening matrix. The values of steady-state creep are compared to experimental ones (Krajewskiet al.). Continuum mechanics predictions give a larger reduction of the composite creep relative to the unreinforced material than measured, suggesting that the effective creep rate of the matrix is larger than in unreinforced precipitation-hardened Al due to changes in microstructure, dislocation density, or creep mechanism. Changes in matrix creep properties are also suggested by the comparison of calculated and measured creep strain rates in the primary creep regime, where significantly different time dependencies are found. It is found that creep calculations performed for a timeindependent matrix creep law can be transformed to obtain the creep for a time-dependent creep law. This article is based on a presentation made in the symposium entitled “Creep and Fatigue in Metal Matrix Composites” at the 1994 TMS/ASM Spring meeting, held February 28–March 3, 1994, in San Francisco, California, under the auspices of the joint TMS-SMD/ASM-MSD Composite Materials Committee.     

Precipitate effects on the mechanical behavior of aluminum copper alloys: Part I. Experiments

This article focuses on understanding the mechanical behavior of precipitation-hardened alloys by studying single and polycrystalline deformation behavior with various heat treatments. Aluminumcopper alloys are the focus in this work and their changing stress-strain behavior is demonstrated resulting from the different hardening mechanisms brought about by the various precipitates. Extensive transmission electron microscopy investigations facilitated the interpretation of the stress-strain behavior and the work hardening characteristics. The use of both single and polycrystals proved valuable in understanding the role of anisotropy due to crystal orientation vs precipitate-induced anisotropy. The experiments show that precipitation-induced anisotropy could offset the crystal orientation anisotropy depending on the orientation. This is clearly demonstrated with similar [111] and [123] behaviors under 190 °C and 260 °C aging temperatures. Experiments on pure aluminum crystals are also provided for comparison and understanding the crystal anisotropy in the absence of precipitates. Part I of this article will focus on experiments, and part II will describe the modeling of the effect of different metastable phases in the matrix acting as barriers to dislocation motion.