Transverse properties of a Ti-6-4 matrix/SiC fibre-reinforced composite under monotonic and cyclic loading

The transverse response of a Ti-6-4/SM1140+ fibre-reinforced composite to both monotonic and cyclic loading has been investigated. Five distinct regions were found in the monotonic stress versus strain curve: (I) elastic deformation of the composite, (II) failure of the fibre/matrix interfaces, (III) elastic deformation of the remaining matrix ligaments, (IV) yielding of the matrix ligaments, and (V) gross plastic deformation, which ultimately leads to specimen failure. The stresses at which interface debonding, matrix yield and final failure occurred rose with increased displacement rate. Stressing to levels above the interface failure stress caused significant damage and limited (0.025%) plastic deformation. A non-linear stress-strain response was observed on unloading/reloading, because the presence within the specimen of constrained holes (containing debonded fibres) resulted in non-homogeneous elastic straining of the matrix. The transverse low-cycle fatigue lives of Ti-6-4/SM1140+composite specimens were strongly dependent on maximum stress for values up to the interfacial failure stress, but less so for maximum stresses greater than 260–265 MPa, where full fibre/matrix debonding had occurred. Fatigue life was also dependent on the uniformity of fibre spacings within the composite.     

1000 to 1300 K slow plastic compression properties of Al-deficient NiAl

Nickel aluminides containing 37, 38.5 and 40 at % Al have been fabricated by XD^tm synthesis and hot pressing. Such materials were compression tested in air under constant velocity conditions between 1000 and 1300 K. Examination of the microstructures of hot pressed and compression tested aluminides indicated that the structure consisted of two phases, and NiAl, for essentially all conditions, where was usually found on the NiAl grain boundaries. The stress-strain behaviour of all three intermetallics was similar where flow at a nominally constant stress occurred after about two plastic per cent deformation. Furthermore the 1000 to 1300 K flow stress-strain rate properties are nearly identical for these materials, and they are much lower than those for XD^tm processed Ni-50Al [1]. The overall deformation of the two phase nickel aluminides appears to be controlled by dislocation climb in NiAl rather than processes in .     

A cyclic multiaxial model for concrete

A rate-independent plasticity constitutive model is proposed, for the stress-strain and strength behavior of plain concrete, under complex multiaxial stress-paths, including stress reversals. The only material parameters required by the model are the uniaxial cylinder strength f _cand the strain at the peak of the monotonic stress-strain curve, ₀ . The model is based on a bounding surface in stress space, which is the outermost surface that can be reached by the stress point. When the size of the bounding surface decreases with increasing maximum compressive principal strain _max on the material, strength degradation during cyclic loading as well as the falling post-failure branch of the stress-strain curves, can be modeled. The distance from the current stress point to the bounding surface, determines the values of the main parameters of the inelastic stress-strain relations, i.e. of the plastic shear modulus H ^P, and the shear-compaction/dilatancy factor Strains are almost completely inelastic from the beginning of deformation. The inelastic portion of the incremental strain is computed by superposition of 1) the deviatoric strain increment, which occurs in the direction of the deviatoric stress and is proportional to the octahedral shear stress increment and inversely proportional to the plastic shear modulus 2) the volumetric strain increment, which consists of a portion which is proportional to the hydrostatic stress increment, and another which equals the product of the octahedral shear strain increment and the shear compaction/dilatancy factor Stress reversals are defined separately for the hydrostatic and the deviatoric component of the stress tensor, and the parameters of the inelastic stress-strain relations are given as different functions of the stress and strain history, for virgin loading, unloading, reloading, or for the post-failure falling branch.The incremental stress-strain law is set in the form of incremental compliance and rigidity matrices, and implemented into a nonlinear dynamic finite element code.     

Influence of the martensitic transformation on the deformation behaviour of an AISI 316 stainless steel at low temperatures

The deformation behaviour of an AISI 316 stainless steel under uniaxial tension was examined at 25, – 70 and – 196° C. The flow curves exhibited peculiar shapes and the work hardening rates were found to increase with strain beyond certain values of plastic strain. X-ray diffraction analyses showed that the transformation to-martensite commenced at these values of plastic strain and thereafter the volume fraction of increased steadily with strain. On the other hand, the amount of the-martensite was found to increase with plastic strain initially, reach a maximum and then decrease gradually. The contribution of the-phase to the flow stress of the alloy was found to be directly proportional to the volume fraction of. It is shown that the analysis of the flow curves provides a simple method of detecting the onset of the strain-induced martensitic transformation as well as estimating the amount of this martensite during further deformation.     

Superplastic deformation of strongly textured Ti-6 Al-4 V

Stress and strain anisotropy of a strongly textured Ti-6 Al-4 V alloy bar during superplastic deformation at 880 and 928° C has been investigated. After 0.9 superplastic strain at 928° C the deformation tended to become isotropic. The anisotropic superplastic deformation was found to be dependent upon the aligned microstructure and not influenced by the original -phase crystallographic texture. The room-temperature anisotropy before and after superplastic plastic deformation was controlled by the original -phase texture, which was still present even after 1.48 strain (344% elongation) at 928° C.     

Low-cycle biaxial fatigue of a polycrystalline magnesium-lithium alloy

We analyze the life duration of a magnesium-lithium alloy subjected to biaxial low-cycle fatigue under out-of-phase combined tension-compression and torsion. It was discovered that the life duration depends on the angle of the phase shift between the two perpendicular cyclic loads. The maximum life duration is attained in the case where the phase shift is absent, i.e., =0. It was also shown that deformation always remains plastic if exceeds a critical angle _c, i.e., no unloading of the specimen may occur. Fatigue properties are studied using the von Mises equivalent stresses and strains. We also present data on the evolution of the density of deformation twinning. It is assumed that the decrease in life duration is explained by permanent changes in the direction of loading in the presence of a phase shift, which inhibits the process of stabilization of plastic deformation in the constituent grains of polycrystals.Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 1, pp. 19–30, January – February, 1995.     

Fracture behaviour of Cu-Zn-Co and Cu-Zn-Ni alloys during superplastic deformation

Cavitation and fracture behaviour in two commercial /gb brasses, one modified with 2wt% Co (Cu-Zn-Co) and the other with 2wt% Cr (Cu-Zn-Cr), have been investigated in Region II of superplastic flow. These alloying elements form cobalt-rich (0.3 m average diameter) and chromium-rich (5 m average diameter) precipitate particles which are distributed uniformly in the matrix and which play an important role in cavitation and inhibiting grain growth during deformation. Void size distributions, volume fraction of voids and the number of voids per unit area have been measured as a function of strain in Region II and the results show a very marked difference in the degree of cavitation in Cu-Zn-Co and Cu-Zn-Cr alloys. Experiments show that the deformation is quasi-uniform with little or no necking in the specimens of Cu-Zn-Co alloy in Region II, and the final fracture occurred by the growth and interlinkage of internal voids. On the other hand, in the specimens of Cu-Zn-Cr alloy a sharp or localized neck developed early in the deformation in Region II and the specimen pulled down to a fine point leading to failure by necking. The importance of diffusion or slip accommodation of grain boundary sliding in void formation during superplastic flow is discussed and a criterion for failure is suggested.     

Crystal plasticity-based finite element analysis of deformation and fracture of polycrystalline lamellar γ-Tial + α2-Ti3al alloys

Deformation behavior of fully-lamellar polycrystalline -TiAl + ₂-Ti₃Al alloys has been analyzed using a finite element method. A three-dimensional rate-dependent, finite-strain, crystal-plasticity based materials constitutive model is used to represent the deformation behavior of the bulk material. The constitutive behavior of -TiAl/-TiAl lamellar interfaces and lamellae-colony boundaries, on the other hand, are modeled using a cohesive-zone formulation. The interface/boundary potentials used in this formulation are determined through the use of atomistic simulations of the interface/boundary decohesion. The constitutive relations for both the -TiAl + ₂-Ti₃Al bulk material and the lamellar interfaces and colony boundaries are implemented in the commercial finite element program Abaqus/Standard within which the material state is integrated using an Euler-backward implicit formulation. The results obtained show that plastic flow localizes into deformation bands even at an overall strain level of only 0.5% and that incompatibilities in plastic flow between the adjacent colonies can give rise to high levels of the hydrostatic stress and, in turn, to intercolony fracture. Furthermore, it is found that when lamellar interfaces are admitted into colonies, fracture is delayed and the materials fail in a more gradual manner.     

Equal-channel angular pressing of an Al-6061 metal matrix composite

An Al-6061 metal matrix composite, reinforced with 10 vol % Al₂O₃ particulates, was subjected to equal-channel angular (ECA) pressing at room temperature to a total strain of 5. It is shown that the intense plastic straining introduced by ECA pressing reduces the grain size from 35 m to 1 m and this leads to an increase in the microhardness measured at room temperature. Inspection revealed some limit cracking of the larger Al₂O₃ particulates as a consequence of the ECA pressing. Tensile testing after ECA pressing gave a maximum ductility of 235% at a temperature of 853 K when testing at strain rates from 10^–4 to 10^–3 s^–1. It is suggested that high strain rate superplasticity is not achieved in this material after ECA pressing due to the presence of relatively large Al₂O₃ particulates.     

Semi-automated image analysis of the true tensile drawing behaviour of polymers to large strains

An image analysis system has been developed using commercially available hardware with custom software to investigate the deformation behaviour of solid polymers in uniaxial tension. This technique provides a rapid, semi-automated non-contacting method for determining true process stress-strain-strain-rate behaviour for both homogeneous and inhomogeneous deformation. The relative displacements of printed transverse grid lines are determined from images captured during a standard monotonic tensile test, providing local measures of strain. The examination of a time series of images allows the generation of true strain-rate data, and concurrent monitoring of the total draw force from the load cell allows the generation of true stress data at those times when the images are captured. Therefore, it is possible to produce a series of process uniaxial true stress-strain curves for individual elements of material within the gauge length of the specimen. Synthetic elastomers drawn at ambient temperature have been found to display relatively homogeneous deformation, resulting in a simple process axial stress-strain curve for the single-speed test, whereas in the case of inhomogeneous deformation (necking) exhibited by polypropylene, it is verified that each element of material experiences a slightly different deformation process. This spatially variant deformation is related to the original location of the particular element with respect to the point of neck initiation.     

Activation energies for superplastic tensile and compressive flow in microduplex α/ß copper alloys

Logarithmic stress against strain rate curves have been determined at various temperatures for a superplastic commercial/ nickel-silver alloy strained in tension, and a laboratory prepared microduplex alloy of nominally similar composition strained in compression. The shapes of the curves were found to be affected by grain growth at high temperatures and strain softening at low temperatures. After taking these factors into account, it was apparent that with decreasing strain rate in both alloys a change in deformation mechanism occurred giving rise to a Region I of low strain-rate sensitivity. By confining activation energy (Q) measurements to temperatures at which steady-state deformation occurred, it was found thatQ for Region II was very similar to that measured for grain boundary diffusion in the phase of a nickel-silver alloy of similar composition, whileQ for Region I was substantially higher than that for lattice diffusion. Values of strain-rate sensitivity andQ were found to be similar for each direction of applied stress.     

The crack tip strain field of AISI 4340 Part II Experimental measurements

Crack tip strain maps have been measured for AISI 4340 high strength steel. No significant creep was observed. The measured values of CTOD were greater than expected from the HRR model. Crack tip branching was observed in every experiment. The direction of crack branching was in the same direction as a major ridge#x201D; of _yy strain, which in turn was in the same direction as predicted by the HRR model. Furthermore, the measured magnitudes of the _yy strain in this same direction were in general greater than the values predicted by the HRR model. This indicates more plasticity in the crack tip region than expected from the HRR model. This greater plasticity could be related to the larger than expected CTOD values. The following discrepancies between the measured strain fields for AISI 4340 and the HRR predictions are noteworthy: (1) The crack branching. (2) Values of CTOD significantly higher than predicted by HRR. (3) The major ridge of _yy strain an angle of about 60° with the direction of overall propagation of the fatigue precrack, in which the measured magnitudes of the _yy strain were greater than the values predicted by the HRR model. (4) Asymmetric shape of the plastic zone as measured by the _yy strain. (5) Values of shear strain _xy significantly higher than predicted by the HRR model.     

Cyclic deformation behavior of a low carbon steel in the temperature range between room temperature and 850 K

Stress-controlled uniaxial push-pull fatigue tests were carried out with cylindrical specimens of low carbon steel with a carbon content of 0.1 percent. Resistent heated grips provided testing temperatures up to 550°C. During all fatigue tests the time-dependent strain was measured. The strain at zero load, the plastic strain amplitude plotted against the number of cycles is known as the cyclic deformation curve. At room temperature, this curve depends on the applied stress amplitude. The shape of the cyclic deformation curve at the same stress amplitude is strongly temperature-dependent. In the temperature region of blue brittleness the endurance shows a maximum connected with a very low plastic strain amplitude. Also the cyclic stress strain curves have a different appearance within varied temperature ranges.The observation of the dislocation structure of the specimen's interior after fatigue damage by means of the transmission electron microscopy showed different pictures within different temperature regions. For instance, besides other structures at other temperatures, dislocation channeling was found, connected with a cyclic softening process which is evident from the cyclic deformation curve. The dislocation structures of specimens fatigued at various conditions differ from clouds to cells, channels, walls, and blocks.

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Résumé Des essais de fatigue traction compression uniaxiale en contrainte contrôlée ont été éffectués sur des éprouvettes cylindriques d'acier à bas C, le carbone étant de 0,1%. Grâce à des mordaches résistant à la température, on a pû réaliser des essais jusque 550°C. Durant tous les essais de fatigue, on a mesuré la dilatation en fonction du temps.La déformation à charge nulle ou amplitude de déformation plastique portée en diagramme en fonction du nombre de cycles est connu comme la courbe de déformation cyclique. A la température ambiante, cette courbe dépend de l'amplitude des contraintes appliquées. La forme de la courbe de déformation cyclique à même amplitude de contrainte dépend directement de la température. Dans la région de température correspondant à la fragilité au bléu, l'endurance fait état d'un maximum en relation avec une très faible amplitude de déformation plastique. On constate également que les courbes de contrainte et de déformation cyclique ont une forme différente suivant la gamme de températures.L'observation de la structure de dislocation à l'intérieur d'un échantillon soumis à dommage de fatigue montre, en utilisant une microscopie électronique par transmission différents aspects suivant les zones de températures différentes atteintes. Ainsi, parmi diverses structures correspondant à d'autres températures, on a constaté des alignements de dislocations en connexion avec un processus d'adoucissement cyclique qui apparait clairement à partir des courbes de déformation cyclique. Les structures des dislocations des éprouvettes soumisses à fatigue sous diverses conditions prennent la forme de nuages, de cellules dalignements de parois et de blocs.

     

A Local Approach to Brittle Fracture Analysis and Its Physical Interpretation

The paper presents a review of studies dedicated to the development of a local approach to brittle fracture in metals and alloys. To work out a statistical criterion of local fracture in a metal in the vicinity of a stress concentrator is shown to be the key task of the local approach. The author substantiates a possibility of describing the process of brittle (quasibrittle) fracture in metals ahead of the notch on the basis of primary principles, i.e., on the basis of the analysis of the processes of formation and catastrophic growth of crack nuclei. The physical effects have been established, which must be allowed for in the development of the local fracture criterion. The author considers the main factors that govern the size of the process zone. This parameter has been found to depend on the value of the relative gradient of the local plastic strain intensity. The appropriateness of using the Weibull distribution to describe quasibrittle fracture of metals is analyzed. It is demonstrated that the Weibull parameters are not material's constants as postulated in the conventional variant of the local approach. Their values depend on the local plastic strain and the metal stress state in the vicinity of the stress concentrator.     

Effect of swaging on the 1000‡C compressive slow plastic flow characteristics of the directionally solidified eutectic alloy γ/γ'′-α

Swaging between 750 and 1050 C has been investigated as a means to introduce work into the directionally solidified eutectic alloy /gg- (Ni-32.3 wt % Mo-6.3 wt % Al) and increase the elevated temperature creep strength. The 1000 C slow plastic compressive flow stress-strain rate properties in air of as-grown, annealed, and worked nominally 10 and 25% materials have been determined. Swaging did not improve the slow plastic behaviour. In fact large reductions tended to degrade the strength and produced a change in the deformation mechanism from uniform flow to one involving intense slip band formation. Comparison of 1000 C tensile and compressive strength-strain rate data reveals that deformation is independent of the stress state.     

Electronic specific heat of La2−xSrxCu1−yMyO4(M=Ga,Zn): Impurity effects on a D-wave superconductor

The electronic specific heat C_el was studied in Ga- and Zn-doped La_2–xSr_xCuO₄ (0.16x0.22) at T10K. Partial substitution of Ga or Zn for Cu suppresses T_c and revives the T-linear electronic specific heat, T, markedly. The (y)/n vs T_c/T_c0 relation for Zn-doped samples with x0.2 is in good agreement with the theoretical one for resonant impurity scattering in a d-wave superconductor, while those for Ga-doped samples and for Zn-doped samples with x 0.2 deviate slightly from the theoretical curve. The deviation will be discussed in relation to changes in the magnetic properties of 3d electrons.     

Tensile properties and inhomogeneous deformation of ferrite-martensite dual-phase steels

The tensile properties and inhomogeneous deformation of coarse ferrite-martensite dual-phase steels containing 17–50% martensite were analysed. The stress of dual-phase steels at equal strain increased with increasing volume fraction of martensite, f, but the rate of increase was reduced after f=0.3. The strain hardening rate was dependent on f at small strains ( 0.03), however, it became independent of f at larger strains. It was found that the deformation of the dual-phase steels divided into three different stages when f was less than about 0.3. The concurrent in situ stress-strain states of ferrite, martensite and their composite, and the stress ratios and strain ratios between ferrite and martensite were evaluated by means of a new stress and strain partition theory. The martensite phase deformed plastically after the uniform strain for f < 0.25, while it was plastic before the uniform strain for f > 0.25. The theoretical analyses for inhomogeneous deformation implied that the volume-fraction dependence of the stress and the characteristics of the strain-hardening rate were influenced by the plastic deformation of martensite. Further, the in situ stress-strain curves of ferrite and martensite and the internal stresses at respective phases were calculated from the partitioned stresses and strains.     

Stress corrosion cracking mechanisms in ductile FCC materials

Recent results on the SCC behaviour of ductile fcc materials are reviewed. Critical experiments are presented to test the corrosion enhanced plasticity model proposed some years ago by one of the present authors to describe the SCC of austenitic stainless steels in Cl^- solutions. Slow strain rate tests on 110 and 100 316L alloy single crystals clearly confirm that the macroscopically brittle fracture is in fact achieved by microcracking on {111} microfacets in zig-zag. Moreover the corrosion deformation interactions on which the model is based are quantitatively analysed through softening effects observed in cyclic plastic deformation in the corrosive solution. The conditions for hydrogen entry in the material are described, which leads to the notion of critical surface defects for hydrogen effects. New developments of the model are then discussed and a numerical simulation of the corrosion deformation interactions is presented.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.     

A fractographic study of hydrogen-assisted cracking and liquid-metal embrittlement in nickel

Metallographic and fractographic studies of crack growth in nickel polycrystals and single crystals in a number of environments are described. Brittle intercrystalline and transcrystalline cleavage-like fractures were observed for specimens tested in liquid mercury, liquid lithium, liquid sodium, gaseous hydrogen, and for hydrogen-charged specimens tested in air. Brittle fractures were associated with considerable slip, and dimples/tear ridges were observed on fracture surfaces, suggesting that crack growth occurred by localized plastic flow. There were remarkable similarities between adsorption-induced liquid-metal embrittlement and hydrogen-assisted cracking which, along with other observations, suggested that adsorbed hydrogen at crack tips was responsible for hydrogen-assisted cracking. It is concluded that adsorbed atoms weaken interatomic bonds at crack tips thereby facilitating the nucleation of dislocations and promoting crack growth by localized plastic flow.     

Plane stress deformation zones at crack tips in polycarbonate

The plastic deformation produced crack tips in polycarbonate (PC) films stretched in tension, has been characterized by optical and transmission electron microscopy. An extensive and diffuse region of deformation is formed in unannealed specimens. Within this zone the ratio (v _f) of local film thickness to the (undeformed) thickness far away from the crack varies gradually both along and across the zone. The minimum ratio of 0.5 occurs at the crack tip. In contrast to this behaviour, films annealed for a short time just below the glass transition temperature T _g showed a highly localized response, the plastic strain being confined to a well-defined flame shaped deformation zone (DZ) ahead of the crack. Within most of this DZ, v _f is constant at 0.7, rising to 1 over a distance of 10 m at the zone tip, and falling to 0.5 over a distance of 4 m around the crack tip. Bi-refringence measurements show that a high degree of molecular orientation occurs within the zone. These experiments support the idea that an increase in the localization of the plastic strain response upon annealing below T _g is responsible for the embrittlement of PC by such heat treatment.