Saturation Stress Research Articles

Mechanical behaviour and the evolution of the dislocation structure of copper polycrystal deformed under fatigue–tension and tension–fatigue sequential strain paths

Two sequences of tension–fatigue and fatigue–tension tests were performed on copper polycrystal sheet, with a mean grain size of 32 μm. For the angle between the two successive loading directions, two typical values (0 and 45°) have been chosen. The effect of strain path change on subsequent initial work hardening rate and saturation stress in tension–fatigue, as well as the effect of strain path change on subsequent yield and flow behaviour in fatigue–tension have been investigated. The strain rate for the tension tests was 5×10 −3 s −1, while the fatigue tests were performed under constant plastic strain amplitude control with different values of amplitudes ( ε pl=6×10 −4, 1.5×10 −3, 3×10 −3). Slip morphology and dislocation microstructure were observed by optical and transmission electron microscopy (TEM) after mechanical tests. Under these conditions, in the case of fatigue–tension, it was found that fatigues prestraining influences the subsequent yield and flow behaviour in tension. However, the subsequent mechanical behaviour of samples seems only to be affected by the magnitude of strain path change (namely, the angle between the two successive loading directions), and not by the value of the plastic strain amplitude of the preceding fatigue tests. In the case of tension–fatigue, the strain amount of preloading in tension obviously affects the initial cyclic hardening rate, while it has almost no effect on the saturation stress of subsequent fatigue tests, irrespective of the value of the angle between the two successive loading directions. The occurrence of microbands in the saturation fatigue dislocation structures of samples prestrained in tension implies that fatigue is a more effective loading mode than tension, in causing intense glide on the activated slip systems. The correlation between mechanical properties and microstructural observations is discussed.

On the mechanical properties of the advanced martensitic steel EUROFER 97

In an effort to better understand the plasticity of tempered martensitic steels, uniaxial tension and compression tests were carried out. The temperature dependence of both the yield stress and the post-yield stress behavior were compared, and it was shown that a good correspondence exists between tensile and compressive behavior. The strain-hardening of EUROFER 97 steel was examined in terms of dislocation mechanics. A simple strain-hardening law was established within the framework of a model accounting for dislocation storage and annihilation. Moreover, an analytical constitutive equation was derived which describes the overall post-yield curve. While the equation predicts the flow stress should reach a saturation stress with strain, this could not be verified by the mechanical tests due to deformation instabilities such as necking in tension or side-slip buckling in compression. Additional tests will have to be devised and applied to investigate these predictions.

Fatigue testing and the evolution of the defect microstructure in Si single crystalsby transmission electron microscopy

We performed fatigue testing of single-crystalline silicon in a temperature andstrain rate domain where lattice friction is still effective: 800–900°C and (1.5–6) ×10−4 s−1. Tension–compression loading was applied under plastic strain amplitudecontrol. For plastic strain amplitudes ranging from 6 × 10−4 to 10−2, cyclicstress–strain curves exhibit two different stages of hardening and pass through amaximum before saturation is reached. At variance from what is observed inmetals, the saturation and maximum stresses are decreased when the strainamplitude per cycle is increased. Microscopical observations suggest that strainlocalization takes place near the maximum cyclic stress and beyond. Several typesof dislocation arrangement have been revealed by transmission electronmicroscopy observations. Before mechanical saturation, edge dislocation dipolessit mainly in thick rectilinear walls. When observed perpendicularly, these wallsform either linear or corrugated arrangements. Once the maximum stress isreached, it seems that part of the microstructure ceases to participate in theimposed deformation while other regions concentrate it. In the former case, thedislocation structure anneals and a loop structure is created from thedipolar walls. In the latter case, active dislocation walls condense in muchthinner walls, similarly to what is observed in the persistent slip bands inface-centred cubic metals, but deformation bands in Si are much wider.

The influence of thermal annealing on residual stresses and mechanical properties of arc-evaporated TiC xN 1−x[formula omitted] thin films

We report the stress relaxation behavior of arc-evaporated TiC x N 1− x thin films during isothermal annealing between 350 and 900°C. Films with x= 0, 0.15, and 0.45, each having an initial compressive intrinsic stress σ int = −5.4 GPa, were deposited by varying the substrate bias V s and the gas composition. Annealing above the deposition temperature leads to a steep decrease in the magnitude of σ int to a saturation stress value, which is a function of the annealing temperature. The corresponding apparent activation energies for stress relaxation are E a =2.4 , 2.9, and 3.1 eV, for x= 0, 0.15, and 0.45, respectively. TiC 0.45N 0.55 films with a lower initial stress σ int = −3 GPa, obtained using a high substrate bias, show a higher activation energy E a =4.2 eV. In all the films, stress relaxation is accompanied by a decrease in defect density indicated by the decreased width of X-ray diffraction peaks and decreased strain contrast in transmission electron micrographs. Correlation of these results with film hardness and microstructure measurements indicates that the stress relaxation is a result of point-defect annihilation taking place both during short-lived metal-ion surface collision cascades during deposition, and during post-deposition annealing by thermally activated processes. The difference in E a for the films of the same composition deposited at different V s suggests the existence of different types of point-defect configurations and recombination mechanisms.

High-temperature tensile tests and activation volume measurement of free-standing submicron Al films

Tensile tests on free-standing, 200-nm-thick Al films were conducted between room temperature and 200 °C. Applied strain rates were in the range 1×10−8–2×10−6/s. At a temperature of 200 °C a saturation of the flow stress was observed. The strain required to achieve steady-state saturation is of the order of 2×10−3, which is much smaller than for bulk Al. From the observed strain rate sensitivity of the saturation stress we calculate an activation volume Ωact=60b3, which is small compared to the value of 700b3 observed in bulk Al (b is the magnitude of Burgers vector).

Mechanical behaviour and dislocation arrangements of cyclically deformed silicon single crystals

Abstract The mechanical behaviour of single-crystal Si tested in fatigue was investigated under plastic strain amplitude control conditions, at a plastic shear strain rate of 3 × 10−4 s−1 in the temperature range 825–900°C, where the lattice frictional forces are still effective, for plastic strain amplitudes ranging from 6 × 10−4 to 5 × 10−3. Cyclic stress-strain curves exhibit two different stages of hardening and pass through a marked maximum before saturation is reached. The saturation stress is decreased when the strain amplitude per cycle is increased. Scanning electron microscopy observations suggest that strain localization takes place near the maximum stress and beyond. Transmission electron microscopy reveals a variety of dislocation arrangements, the most typical of which are, firstly, regularly spaced elongated braids of edge dipoles, secondly, thicker stripes with dense shells and whose cores contain apparently self-organized secondary dislocations and, thirdly, long rows of prismatic loops. ...

Application of Barkhausen noise to biaxial residual stress measurements in welded steel tubes

The relationship between Barkhausen noise and biaxial stress was studied in mild steel specimens in as received and annealed conditions. In the as received condition the saturation stress of the Barkhausen noise was higher but the stress sensitivity was lower than in the annealed condition. In the as received condition the Barkhausen noise response was different in the rolling and transverse directions. In the annealed condition no difference was observed. The stress sensitivity was found to be independent of stress perpendicular to the magnetising direction in the annealed condition. In the as received condition the stress sensitivity depended on the perpendicular stress. The biaxially calibrated Barkhausen noise method was applied to residual stress measurements of welded steel tubes. The results were compared with X-ray diffraction and hole drilling results. In the axial direction of the tube all methods produced consistent results. In the hoop direction of the tube Barkhausen noise and X-ray diffraction provided similar results. They were different from those obtained with the hole drilling method.

A dipole model for the cross-slip of screw dislocations in fcc metals

Abstract An attempt is made to reconcile observations and theories of cross-slip with recent models of cyclic plasticity and the fatigue endurance limit of crystals. According to this view, the stress required to separate two screw dislocations of opposite signs, which are just on the point of mutual annihilation by cross-slip, controls both the stress τIII at the end of linear (stage II) hardening and the saturation stress [sgrave]sat in the cyclic stress-strain curve. It is shown, in confirmation of conclusions by many earlier researchers, that direct annihilation of the dislocations cannot account for the temperature dependence of the stress, although it might account for observations on silver and copper at liquid-helium temperature. Based on the work of Hirsch, a model of stress-aided migration of jogs is proposed, which seems able to account for the observations if the activation energy for the migration is about 0.1 eV in copper, nickel and aluminium. A by-product of the model is a possible reinter...

A dipole model for the cross-slip of screw dislocations in fee metals

Abstract An attempt is made to reconcile observations and theories of cross-slip with recent models of cyclic plasticity and the fatigue endurance limit of crystals. According to this view, the stress required to separate two screw dislocations of opposite signs, which are just on the point of mutual annihilation by cross-slip, controls both the stress τIII at the end of linear (stage II) hardening and the saturation stress [sgrave]sat in the cyclic stress-strain curve. It is shown, in confirmation of conclusions by many earlier researchers, that direct annihilation of the dislocations cannot account for the temperature dependence of the stress, although it might account for observations on silver and copper at liquid-helium temperature. Based on the work of Hirsch, a model of stress-aided migration of jogs is proposed, which seems able to account for the observations if the activation energy for the migration is about 0.1 eV in copper, nickel and aluminium. A by-product of the model is a possible reinterpretation of the Bordoni peaks in the damping of face-centred metals in terms of jog migration.

Saturation of yield stress and embrittlement in fine lamellar TiAl alloy

It has been proposed by Sun that the yield stress of lamellar materials is increased by refinement of lamellar spacing but there is an upper limit to the increase. This paper aims at the examination of this prediction by experimental results of a fully lamellar Ti–39 mol% Al alloy tested at room temperature and at 950 K. The lamellar spacing is varied from 20 to 590 nm, while keeping the same grain size of 90 μm. The Hall–Petch relation holds between the lamellar spacing and the yield stress of the alloy. However, the yield stress saturates at a level of 1 GPa, which is achieved below a critical lamellar spacing of about 100 nm. These results support the prediction by Sun. The Hall–Petch slope, the critical lamellar spacing and the saturation stress level can be explained consistently by a pile-up model of dislocations at lamellar boundaries. Contrary to the beneficial effect on the yield stress, the lamellar refinement deteriorates ductility of the lamellar material.

An analysis of the effect of hydrostatic pressure on the tensile deformation of aluminum-matrix composites

The effect of superposed hydrostatic pressure on the tensile deformation of particle-reinforced Al-matrix composites was analyzed using a self-consistent approximation. The composite was represented in terms of an interpenetrating network of randomly distributed spheres, which stand for the intact and damaged regions in the composite. Each sphere contained an intact or broken ceramic particle at the center, and the model assumed that the fraction of damaged spheres increased during deformation. The load partitioning between intact and damaged regions in the composite as well as the stress redistribution due to damage was computed through a self-consistent scheme. It was shown that the tensile stresses in the ceramic particles, and thus the fraction of broken particles, were reduced as the hydrostatic pressure increased. This led to a moderate improvement in the composite flow stress but more significant gains were achieved in the strain at the onset of plastic instability. Both magnitudes increased with the hydrostatic pressure until a saturation stress was reached. Particle fracture was completely inhibited at this point, and higher pressures did not have any influence on the composite behavior, which was equivalent to that of the undamaged phase in the absence of hydrostatic pressure. Using reasonable values for the matrix and reinforcement properties, the model predictions for the composite strength and strain at the onset of plastic instability were in good agreement with the experimental data in the literature for high strength Al alloys reinforced with SiC and Al 2O 3 particles.

Effects of solidification structure and aging condition on cyclic stress–strain response in Al–7% Si–0.4% Mg cast alloys

Stress–strain response under cyclic loading at fixed plastic strain amplitude condition was examined for age-hardenable Al–7% Si–0.4% Mg (A356) cast alloys. The specimens examined include the cast alloys with ordinary dendrite structure and semi-liquid die-cast alloys with fine effective grain structure. Al–0.5% Mg–0.4% Si (6063) alloy was also tested for comparison. Special attention was paid to the effect of solidification structure and aging condition on cyclic hardening behavior. Cyclic hardening behavior was sensitive to the solidification structure. The refined grain size, DAS and unmodified acicular eutectic Si particles increased stress levels of cyclic hardening curves. Drastic change in cyclic hardening behavior was obtained by changing aging condition. After the initial rapid hardening, the stress amplitude kept increasing steadily until fracture in as-quenched and under-aged materials containing shearable GP zone. In contrast, for over-aged (and peak-aged materials), which were hardened by non-shearable β′-precipitates, the initial hardening occurred more rapidly and the stress amplitude reached the saturation stress in a quite early stage of the fatigue life. The attained stress level was almost constant until fracture. Essentially the same aging condition dependence was obtained for the 6063 alloy with no dendrite structure and eutectic Si particles. This indicated that nature of strengthening precipitates controlled the cycle hardening behavior of the present cast alloys.

Soft iron-based magnetic materials for alternating and direct current applications

The key events in the development of amorphous alloys are briefly summarized within the context of applying them as soft magnetic alloys. Some of their pertinent magnetic properties, such as saturation magnetization, losses, exciting current, permeability and stress sensitivity are reviewed and compared with conventional alloys. New results on iron-rich alloys will be presented. We have recently discovered that increasing the diameter of the toroid prepared from narrow tapes produces a remarkable improvement in the magnetic properties attributable to the decreasing contribution of stress induced ordering. The losses become significantly less than the best results reported for the Permalloys and are much less than 1/10 the losses of Fe−3.2% Si.

Stress saturation in a nickel-base superalloy, under different aging treatments

The effect of γ′-precipitates on the saturation stress, extrapolated from stage III of work hardening (WH), has been studied in the superalloy Inconel X-750 on two situations, the solution heat treated, and peakaged-overaged samples. The WH was analysed by means of diagrams θ=d σ/d ε versus σ, and Θ d=d σ d/d ε versus σ d, where σ is the flow stress and σ d is the dislocation related stress component of σ, obtained by the application of a superposition rule. The results indicate that, for the overaged alloy, the storage of dislocation loops leads to a high initial WH rate; but during stage III a strong dynamic recovery reduces the effect of the precipitates on the saturation stress. The influence of the superposition rules, used in the data analysis for the interpretation of the saturation stress in terms of the dislocation density, was also discussed.

Effects of lamellar spacing on mechanical properties of fully lamellar Ti–39.4mol%Al alloy

Effects of lamellar spacing on mechanical properties of a fully lamellar TiAl alloy were investigated at room temperature and at 950K by compression tests. Lamellar spacing was varied from 20 to 590 nm, keeping the same grain size of 90 μm. The Hall–Petch relation holds between lamellar spacing and yield stress of the alloy. However, the yield stress saturates at a value of about 1 GPa below a critical lamellar spacing of about 100 nm. The Hall–Petch slope, critical lamellar spacing and saturation stress can be explained consistently by the pile-up model of dislocations at lamellar interfaces. Contrary to the beneficial effect on yield stress, the refinement of lamellar spacing deteriorates ductility of the alloy probably due to the suppression of the hard deformation modes.

Substructural recovery in a cold worked Ti-modified austenitic stainless steel during high temperature low cycle fatigue

Total axial strain controlled fatigue tests have been conducted in air at 823 and 923 K to ascertain the influence of cold work on LCF behaviour of a 15Cr–15Ni, Ti modified austenitic stainless steel, designated as Alloy D9. The LCF behaviour of the 20% cold worked alloy was compared with that of solution annealed alloy. A symmetrical triangular waveform at a constant strain rate of 3×10 −3 s −1 was employed for all the tests performed over the strain amplitude in the range of ±0.25 to ±1.00%. The cyclic stress response varied as a complex function of microstructure, temperature and strain amplitude. The cyclic stress response of solution-annealed alloy was generally characterized by initial hardening to the maximum stress followed by a regime of nearly stable peak stresses. The degree of initial hardening was higher at 823 K due to dynamic strain ageing effects. The cold worked alloy displayed a gradual softening prior to the attainment of saturation stress response stage. The plastic strain fatigue resistance of the cold worked alloy was inferior compared to that in solution-annealed condition at both 823 and 923 K. At low strain amplitudes, the cold worked alloy exhibited better total strain fatigue resistance at 923 K. The observed variations in fatigue life and cyclic stress response behaviour have been explained on the basis of crack initiation, development of substructure, precipitation behaviour and evolving changes in plastic strain during cycling.

Dislocation structures and cyclic behaviour of [011] and [formula omitted]-oriented nickel single crystals

[011] and [ 1 ̄ 11] -oriented nickel single crystals were cycled at room temperature with constant plastic strain amplitudes ( ε pa) ranging from 1×10 −4 to 1×10 −2. The paper describes the cyclic stress–strain curves (CSSC), the surface features and the saturated dislocation structures for both crystals orientations. The CSSC of the [011]-crystals shows a very pronounced plateau in the range of 1×10 −4 to 5×10 −3 in which the saturation stress amounts to 123 MPa. The occurrence of persistent deformation bands is the most typical feature of the surfaces of cycled [011]-crystals. A deformation band is characterised by a stack of densely distributed and strongly localised slip markings which belong to a certain slip system. The dislocation structures of [011]-crystals are typically grouped in structure bands which consist of short ladder-like substructures (short persistent slip bands), wall-like dislocation configurations and patch dislocation patterns in the plateau region. At ε pa≥5×10 −3 elliptical cells exist in the entire crystal. The CSSC of [ 1 ̄ 11] -crystals shows apparently no plateau. The surfaces of cycled [ 1 ̄ 11] -crystals are typically covered by two sets of slip traces crossing one another. Deformation bands with the characteristics of conventional kink bands were also found but as a minor case. The dislocation structures of [ 1 ̄ 11] -crystals consist of long “condensed” wall-like dislocation configurations with the longest extension lying perpendicular to the tensile axis. The observed structure types fall in line with those found in corresponding oriented grains of cycled nickel polycrystals.

Cyclic deformation and strain burst behavior of Cu–7at.%Al and Cu–16at.%Al single crystals with different orientations

[ 1 ̄ 12] Cu–7at.%Al single crystals as well as [ 1 ̄ 23], [ 1 ̄ 17] and [023] Cu–16at.%Al single crystals were cyclically deformed under constant plastic strain control at room temperature. The cyclic hardening curve of [ 1 ̄ 12] Cu–7at.%Al single crystal can be divided into three stages, namely initial non-hardening stage, rapid hardening stage and saturation stage. The cyclic stress–strain (CSS) curve exhibited a plateau region in the range of γ pl, from 1.1×10 −3 to 4.5×10 −3. The saturation stress of the plateau is about 27 MPa. The occurrence of strain burst depends on the applied plastic strain amplitude γ pl. No strain burst was detected when γ pl, was below 4.4×10 −4 or above 1.1×10 −3. The cyclic deformation and strain burst behavior of [ 1 ̄ 23], [ 1 ̄ 17] and [023] Cu–16at.%Al single crystals are different from that of [ 1 ̄ 12] Cu–7at.%Al single crystal. The cyclic deformation of all three differently oriented Cu–16%Al single crystals is unstable with the frequent occurrence of irregular strain bursts. The specimens cyclically hardened at a very low rate and saturation was not attained at high strain amplitudes. The experimental results indicate that the crystallographic orientation has almost no effect on the cyclic deformation and strain burst behavior of Cu–16at.%Al single crystals. The evolution of slip bands during cyclic deformation in both Cu–7at.%Al and Cu–16at.%Al single crystals is similar to the development of Lüders band. The percolation of slip bands along the gauge length is generally accompanied by strain bursts. The above experimental results were explained in terms of the variation of slip mode with Al content in the alloys and the corresponding strain localization during cycling.

Cyclic plastic deformation behaviour of Ni single crystals oriented for single slip as a function of hydrogen content

Ni single crystals oriented for single slip, exhibit well defined cyclic stress-strain curves at room temperature, corresponding, partly to the formation of persistent slip bands in a given plastic strain range. The aim of the paper is to study the influence of hydrogen on the cyclic plastic behaviour of such crystals. Tests on pre-charged specimens show a decrease of the saturation stress, in comparison with pure nickel samples. Such effects are discussed in terms of hydrogen-dislocation interactions, and reduced cross slip ability in presence of hydrogen.

Cyclic deformation behavior of single crystal NiTi

Single crystals of NiTi (with 50.8 at.% Ni) were subjected to cyclic loading conditions at room temperature which is above the M s (martensite start) temperature of −30°C. The single crystals exhibited remarkable cyclic hardening under zero to compression strain control experiments. The stress range under strain control increased by as much as a factor of 3 in compression. The increase in stress range is primarily due to the increasing strain hardening modulus. In the tension case, loop shape changes occurred but the increase in stress range is rather small. The fatigue cycling was undertaken with a strain range of 3% which is far below the theoretical transformation strains levels exceeding 6%. The maximum stress levels reached in the experiments are below those that cause martensite slip. Therefore, the stress–strain response is governed by transformation from the austenite to the martensitic phases and the dislocation structure evolution in the austenite domains. Two single crystal orientations [148] and [112] were examined during the experiments with single and double CVP (correspondent variant pair) formations respectively. The strain hardening in compression cases is rather substantial with the stress range in the double CVP case surpassing the single CVP case. Two heat treatments were selected to produce coherent and incoherent precipitates in the microstructure respectively. The influence of the coherent precipitates on the stress–strain response is significant as they lower the transformation stress from austenite to martensite, and at the same time, they raise the flow stress of the austenite and martensite domains leading to higher saturation stresses in fatigue.