Saturation Stress Research Articles

Dislocation arrangements in cyclically deformed Au single crystal

Cyclic deformation was carried out on [ 2 ¯ 2 7 ] Au single crystal at plastic resolved strain amplitudes of 1.11 × 10 −3 and 2.22 × 10 −3 with a cyclic saturation stress of 23.4 MPa. Persistent slip bands (PSBs) were also found in the cyclically saturated specimens. In comparison with the fatigue-induced dislocation arrangements of other fcc metals, such as Cu, Ni and Ag, two basic criteria for determining whether the ladder-like PSBs form or not were proposed. Besides PSBs, the vein, wall and labyrinth structure also appeared in cyclically deformed [ 2 ¯ 2 7 ] Au single crystals. Experimental results show that cyclic deformation behaviors of Au single crystals are very similar to those of Cu, Ni and Ag single crystals, which will become the important and fundamental basis to determine the cyclic deformation mechanism of fcc single crystal.

Cyclic deformation and fatigue damage behaviors of oriented Ag single crystal

The cyclic deformation and fatigue damage behaviors of oriented Ag single crystal were investigated in terms of cyclic stress–strain (CSS) curves, surface slip morphologies and dislocation configurations. A clear plateau region appears in the CSS curve of the Ag single crystal over a strain range of with average saturation shear stress amplitude of ∼26.6 MPa. Corresponding ladder-like persistent slip bands (PSBs) also appear in the Ag single crystal. Compared with other Cu and Ag single crystals with single or double-slip orientations, the saturation resolved shear stresses of the critical double-slip-oriented single crystals, no matter whether for Cu or Ag, are significantly higher than that of the single-slip-oriented ones. Combining the two-phase model with the hindering effect of sessile jogs on screw dislocation movement, a three-phase model is proposed to rationalize the increase of saturation stress. In addition, the surface slip morphologies of the Ag single crystal were characterized by the interactions between the primary and secondary SBs. According to the difference in their slippage, their interactions can be divided into three types, which could simultaneously appear in different local areas of the same crystal. The current experimental results extend the fundamental understanding of the intrinsic fatigue damage behaviors of fcc metal crystals.

Effect of heat treatment on the strain hardening behaviour of an Al–Zn–Mg alloy

Abstract The strain hardening of the Al-5.2Zn-1.2Mg alloy AA7030 in different conditions has been investigated. The dislocation related strengthening was described by the Voce equation and the quantitative effects of different superposition laws have been studied. All tempers, except the over-aged, suffer from plastic instability before the geometric Considère condition is reached. This was attributed primarily to the occurrence of shear failure due to dynamic strain ageing effects. For plastic strain levels below approximately 8 %, preceding the plastic instability, the results show that the saturation stress in the under and peak-aged tempers is independent of heat treatment, whereas the kinetics of structure formation differs. Using a linear superposition law in the under and peak aged tempers has negligible effects, whereas the use of Pythagorean addition for the over-aged temper significantly decreases the goodness-of-fit, although not to unacceptable levels. Furthermore, the naturally aged temper shows strong influence of dynamic precipitation.

Shrinkage/swelling of compacted clayey loose and dense soils

This Note presents an experimental study performed on expansive compacted loose and dense samples using osmotic oedometers. Several successive wetting and drying cycles were applied in a suction range between 0 and 8 MPa under different values of constant net vertical stress (15, 30, and 60 kPa). During the suction cycles, the dense samples showed cumulative swelling strains, while the loose samples showed volumetric shrinkage accumulation. At the end of the suction cycles, the volumetric strains converged to an equilibrium stage that indicated elastic behavior of the swelling soil for any further hydraulic variations. At this stage, the compression curves for the studied soil at the different imposed suctions (0, 2, and 8 MPa) converged towards the saturated state curve for the high applied vertical stresses. We defined this pressure as the saturation stress ( P sat ) . The compression curves provided sufficient data to examine the soil mechanical behavior at the equilibrium stage. To cite this article: H. Nowamooz, F. Masrouri, C. R. Mecanique 337 (2009).

Cyclic deformation and fatigue cracking behaviors of Cu–28wt%Ag binary alloy

The cyclic deformation and fatigue cracking behaviors of coarse-grained Cu–28wt%Ag binary alloy were investigated under axial plastic strain amplitudes ranging from 10−4 to 7.5 × 10−4. It was found that the cyclic stress of the Cu–Ag alloy increased rapidly in the initial tens of cycles and became saturation with further cyclic deformation. The cyclic saturation stress increased with increasing the plastic strain amplitude. The interfaces are classified into two categories based on the orientations of the eutectic and the dendrites, i.e. type I and type II interfaces. The surface damage morphologies show that fatigue cracks normally nucleated either along the type I interfaces or along the slip bands (SBs), while no cracking occurred along the type II interface. Fatigue striations with different spacings appeared on the fracture surface, and secondary cracks along the striations were also observed. Based on the experimental results, the cyclic deformation and fatigue cracking behavior of the Cu–Ag binary alloy were discussed in detail.

The assessment of the ambient-temperature mechanical properties of ultra-fine-grained Ag with nano-twins using microshear tests

The mechanical properties of ultra-fine-grained (UFG) 150 μm silver interlayers prepared by planar magnetron sputtering were studied using microshear torsion tests. The interlayers have very high ductility in pure shear, comparable to conventional grain sizes, and show a mechanical steady-state. The Hall–Petch behavior at 1.25 μm is consistent with other earlier work. The hardening rates (dσ/de) are substantially higher in the UFG Ag. The saturation stress and strain-rate sensitivity at this stress are identical to coarse-grained silver.

Plane-Strain Compression of a Three Layer Strip Containing Viscoplastic Material with Saturation Stress

The plane strain compression of a long symmetric strip consisted of a three layer material between rigid, parallel, rough plates is under consideration. Two possible geometrical configurations of the layers are examined (a) a viscoplastic material is situated between two layers consisting of a rigid/perfectly plastic material, (b) a rigid/perfectly plastic material lies between two viscoplastic layers. It is assumed throughout the paper that the viscoplastic law is bounded in that sense that it reaches its critical value (saturation stress) as the strain rate tends to infinity. Exploiting closed form solutions obtained, qualitative differences between them and the known from literature solutions for three layer material structure with classic viscoplastic material are discussed. Asymptotic behaviour of solutions in the vicinity of maximum friction surfaces is analysed for any configuration.

Density-dependent hydromechanical behaviour of a compacted expansive soil

To further our knowledge of the coupling between the hydraulic and mechanical behaviours of the swelling soils, this paper presents an experimental study on a bentonite/silt mixture using an osmotic odometer. A loading/unloading cycle was applied to samples with different initial dry densities (1.27, 1.48, and 1.55 Mg m − 3 ) at different constant suctions (0, 2, and 8 MPa). We noted that the initial state of the soils after compaction significantly influenced the values of the apparent preconsolidation stress p 0( s), the virgin compression index λ( s), and the elastic compression index κ. These experimental results provided a sufficient database to interpret the mechanical behaviour of the swelling soil and define three yielding surfaces: – the suction limit between micro- and macrostructure ( s m/M) and the suction limit between nano- and microstructure ( s n/m), which depend completely on the soil fabrics and the diameter separating the nano-, micro-, and macrostructure, – the Loading Collapse (LC) curve, representing the preconsolidation stress variation as a function of suction, – the Saturation Curve (SC), representing the variation of the saturation stress ( P sat) as a function of suction. In general, we can state that the increase of compaction pressure unified the LC and SC surfaces and decreased the ( s m/M) value without modifying the ( s n/m) value.

The Avrami kinetics of dynamic recrystallization

Twenty-six flow curves determined under dynamic recrystallization (DRX) conditions on 11 different steels were analyzed. The double-differentiation method was used to define the critical strain ε c for initiation of DRX. The “athermal” hardening parameter h and the dynamic recovery parameter r were evaluated from the work-hardening behavior prior to ε c. The saturation stresses σ sat pertaining to the unrecrystallized regions as well as the associated work-hardening curves, σ recov, were derived in this way. The net softening attributable to DRX was then defined as the difference between the σ recov and experimental curves. Avrami plots were prepared from all 26 sets of data. The time exponents were all in the neighborhood of 3.0; however, the strain rate and temperature dependences differed considerably from their static values. The dependence of the time of half-softening, t 50, on strain rate and temperature is used to predict the DRX curves expected under industrial conditions.

High strain rate compression behavior for Sn–37Pb eutectic alloy, lead-free Sn–1Ag–0.5Cu and Sn–3Ag–0.5Cu alloys

This paper emphasized on studying the high strain-rate compression behavior of the unleaded Sn–3Ag–0.5Cu (SAC305), Sn–1Ag–0.5Cu (SAC105) solders and the traditional Sn–37Pb eutectic solder. The split Hopkinson pressure bar (SHPB) apparatus was used to conduct high strain rate tests in order to characterize the associated high rate mechanical response of these alloys. Specimens were tested at strain rates ranging from 380 to 3030 s −1 to obtain the dynamic stress–strain relationship for the Sn–37Pb, SAC305 and SAC105 alloys. The tested soft and ductile samples experienced a large amount of elastoplastic deformation due to impact test. In the high strain rate range studied, limited strain rate hardening effect was observed for SAC305, SAC105 and Sn–37Pb alloys studied. The strain rate sensitivity parameter ( m) related to the power law creep equation was also calculated for the present solder materials at specific strain values. In addition, the saturation stresses for the leaded and lead-free solders at the strain rate range studied are also reported.

Tensile and fatigue fracture of nanometric alumina reinforced copper with bimodal grain size distribution

Alumina dispersion-strengthened copper was produced by an internal oxidation process and hot powder extrusion method. The microstructure of the composite consisted of fine-grained region with an average grain size of 1.1 ± 0.1 μm, coarse-grained region with an average grain size of 5.6 ± 0.1 μm, nanometric alumina particles (γ-type) with an average diameter of 30 nm, and coarse alumina particles (350 nm) at the boundaries of the large grains. The tensile and fatigue fracture of the composite was studied in the extruded condition and after 11% cold working. The low cycle fatigue behavior was examined in strain control mode ( ɛ = 0.5%) under fully reverse tension-compression cycle at 1 Hz up to 1000 cycles. High cycle fatigue was conducted using rotate-bending test up to 10 7 cycles. To reveal the role of alumina particles and the bimodal grain size structure, the tensile and fatigue fracture of extruded copper with normal grain structure was examined. It is shown that: (1) the strength and hardness of the nanocomposite are about three folders of the magnitude of the unreinforced copper; (2) fatigue strength of the nanocomposite at 10 7 cycles is about 40% higher than that of the copper; (3) both extruded copper and the nanocomposite exhibit cyclic hardening during the early stages of low cycle fatigue test which eventually approaches to a saturation stress; (4) dimple-type fracture is realized on the fracture surface of the tensile tests where dimple size decreases in the presence of the alumina particles; (5) the fatigue fracture mechanism is locally ductile deformation, microscopic void formation and coalescence.

Cyclic Deformation Behavior and Fatigue Crack Propagation of Low Carbon Steel Prestrained in Tension

The tests were performed on low carbon steel plate. In the tension fatigue tests, two angle values (ϕ = 0° and ϕ = 45°, ϕ is the angle between the loading and the rolling direction) have been chosen. The influence of strain path change on the subsequent initial work softening rate and the saturation stress has been investigated. Dislocation microstructure was observed by transmission electron microscopy. It was found that the strain amount of preloading in tension has obviously affected the cyclic softening phenomenon and the initial cyclic softening rate. It was observed that the reloading axial stress for ϕ = 45° case increased more than that of ϕ = 0° case, due to the anisotropism of Q235. In the fatigue crack propagation tests, the experimental results show that with increasing the pretension deformation degree, the fatigue crack growth rate increases, especially at the near threshold section.

Simulating the effect of capillary flux on the soil water balance in a stochastic ecohydrological framework

Groundwater uptake can play a major role in the survival of vegetation in semiarid areas, but this has not yet been included in an earlier developed ecohydrological stochastic framework. In this paper we provide a piecewise linear equation which includes capillary fluxes from shallow groundwater in the loss function of the ecohydrological stochastic model. The results indicate that this model is able to simulate the capillary fluxes, and the model also reflects the impact of the fluxes on the soil moisture balance. In addition, the results are analytically tractable and allow calculation of the probability density functions of soil water saturation and water stress for different groundwater depths below the root zone.

Elastic Model for Partially Saturated Granular Materials

This paper presents the development of an elastic model for partially saturated granular materials based on micromechanical factor consideration. A granular material is considered as an assembly of particles. The stress-strain relationship for an assembly can be determined by integrating the behavior at all interparticle contacts and by using a static hypothesis, which relates the average stress of the granular assembly to a mean field of particle contact forces. As for the nonsaturated state, capillary forces at grain contacts are added to the contact forces created by an external load. These are then calculated as a function of the degree of saturation, depending on the grain size distribution and on the void ratio of the granular assembly. Hypothesizing a Hertz-Mindlin law for the grain contacts leads to an elastic nonlinear behavior of the particulate material. The prediction of the stress-strain model is compared to experimental results obtained from several different granular materials in dry, partially saturated and fully saturated states. The numerical predictions demonstrate that the model is capable of taking into account the influence of key parameters, such as degree of saturation, void ratio, and mean stress.

Modelling of work-hardening behaviour for laser welded magnesium alloy

Abstract To investigate the reliability of the laser welding process for the magnesium alloy ZE41A-T5, eight butt joints were welded using the same processing parameters. These joints were tensile tested in the as-welded and aged conditions and the tensile data were analyzed from work-hardening characteristics. The flow curves cannot entirely be satisfactorily described by the Kocks–Mecking model; however, the model is still applicable to the high strain zone of the flow curves where work-hardening rate decreases linearly with flow stress. The reproducibility of the initial work-hardening rate and saturation stress is statistically analyzed. The initial work-hardening rates for the base castings and welded joints vary from approximately 4000 to 7000 MPa, i. e. 1/4 to 1/3 of the base material shear modulus. The as-welded joints have slightly higher initial work-hardening rates than the base castings. Artificial aging produces lower initial work-hardening rates compared with the base material. The saturation stress ranges approximately from 260 to 320 MPa, i. e. about 2 % of the shear modulus. The saturation stress for the welded joints is lower than that for the base material. Compared with the as-weld joints, aging decreases initial work-hardening rate but slightly increases saturation stress. Both initial work-hardening rate and saturation stress become more scattered after aging.

Cyclic stress–strain behavior of conventional grain and ultrafine grain nickel under biaxial straining

Results are presented on the effects of biaxial straining on the cyclic stress–strain response of ultrafine grain nickel (grain size ≈ 260 nm) and conventional grain nickel (grain size ≈ 50 μm) over a range of effective plastic strain amplitudes from 1 × 10−4 to 1 × 10−3. Grain refinement causes an increase in saturation stress. For conventional grain nickel, non-proportional straining causes higher saturation stress than proportional straining; but the ultrafine grain material exhibits the opposite behavior.

Evaluation of the creep–fatigue damage mechanism of Type 316L and Type 316LN stainless steel

Low-cycle fatigue tests with continuous cycling and creep–fatigue tests with 10 min hold times at tensile maximum strain were conducted at 600 °C in air for Type 316L and Type 316LN stainless steels containing nitrogen contents of 0.04% and 0.10%. The creep–fatigue life was less than the fatigue life for both alloys. The fatigue and creep–fatigue life and saturation stress were increased with the addition of nitrogen. The fracture mode was transgranular for fatigue and intergranular for creep-fatigue regardless of the nitrogen content. The dislocation structure was cellular for Type 316L and planar for Type 316LN after fatigue and creep-fatigue tests. Carbides were precipitated at grain boundaries after creep-fatigue tests and nitrogen decreased the precipitation. Creep–fatigue life was well predicted by a model based on cavity nucleation and growth at grain boundaries. The increase of creep–fatigue life with the addition of nitrogen was due to the decrease of precipitation and stress relaxation by the change in dislocation structure.

Flow of viscoplastic materials through converging channels

AbstractMany classical rigid perfectly/plastic solutions cannot be extended to more complicated rigid plastic materials, such as rigid plastic hardening materials and rigid viscoplastic materials. The present paper reveals sources of this difficulty in the case of flow of rigid viscoplastic material through infinite converging rough wedge‐shaped and axisymmetric channels. Two types of viscoplastic models without strain hardening are considered, with and with no saturation stress. The maximum friction law is adopted at the friction surface. Qualitative features of the solutions are compared to those occurring in compression of a rigid plastic layer between rough, parallel plates. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Hot-Carrier-Induced Degradation under Current Saturation Bias in p-Channel Low-Temperature Polycrystalline Silicon Thin-Film Transistors

A two-dimensional (2-D) physical model of p-channel polycrystalline silicon (poly-Si) thin-film transistor (TFT) was proposed to analyze hot-carrier degradation based on a 2-D device and process simulator. It is found that, for current saturation bias, the maximum 2-D lateral electric field is located in the deep drain region under the gate. It can be predicted from the 2-D device simulation and experimental results that hot-electron trapping at both upper and bottom interfaces can contribute to hot-carrier degradation under current saturation stress. The degradation will first occur in a high-field region in the p+ drain region, and, with the increase in stress time, the electron-trapped region expands mainly toward the channel. For high-|Vd| bias, a decrease in impact ionization due to the presence of the trapped charges will reduce the drain current, resulting in the reduction in kink current. In low-|Vd| bias, the current flow after the long-time stress is located at the upper and bottom interfaces near the drain junction due to trapped electrons and the trapped charges at both interfaces will result in the enhancement of the Vg–Id characteristics.

Constitutive relationships for 22MnB5 boron steel deformed isothermally at high temperatures

The strain, strain rate and temperature dependency of a boron steel, which was isothermally deformed under uniaxial compression tests, has been investigated at temperatures between 600 and 900°C, and at strain rates of 0.1, 1.0 and 10.0 s −1. Two constitutive models were used to correlate the plastic behavior: the Voce constitutive relation in combination with the kinetic model proposed by Kocks and the phenomenological model proposed by Molinari–Ravichandran. The Kocks model has been introduced in the Voce formulation to describe the temperature and the strain rate dependency of the saturation stress and of the yield stress. The Molinari–Ravichandran model is based on a single internal variable that can be viewed as being related to a characteristic length scale of the microstructure that develops during deformation. It has been shown that the plastic behavior of the boron steel can be well described using these two models.