Elastic interaction stresses: parti. the influence of bicrystal size on stresses in [213] Iso-Axial 70-30 alpha-brass bicrystals

The shear and normal strains which are created around the circumference of a [213] 70-30 alpha brass single crystal were determined. Bicrystal orientations were then selected which would maximize incompatibility parallel to and normal to the bicrystal boundary. Finite element method (FEM) analysis was carried out to determine the distribution of resolved shear stress for a given elastic strain on each of the 12 possible slip systems, and the slip systems with the highest total resolved shear stress were determined. From these data the volume fraction of the bicrystal in which an enhanced grain boundary resolved shear stress zone existed was ascertained. The greatest enhancement of resolved shear stress at the grain boundary, σ_gb, occurred for shear incompatibility parallel to the bicrystal boundary. Similarly, largest volume fractions of enhanced grain boundary resolved shear stress zones,V _gb, were found for this incompatibility. The effects of changes in bicrystal size normal and parallel to the grain boundary on both σ_gb andV _gb were ascertained. Both σ_gb andV _gb pass through a maximum as dimensions normal and parallel to the boundary were changed. Values of σ_gb at the surface were found to be both higher and lower than σ_gi, at the interior depending on which bicrystal component is considered.V _gb at the interior was found to be much larger thanV _gb at the surface. Application of these results to polycrystalline yielding is discussed.     

The Friction Stress of the Hall–Petch Relationship of Pure Mg and Solid Solutions of Al,Zn, and Gd

Temperature and solute concentration effects on the friction stress, σ_o, of cast (texture-free) polycrystals of pure Mg, and of Mg-Al, -Zn and -Gd binary solid solutions are discussed using phenomenological arguments. The temperature effects on the pure metal suggest that σ_o relates to the ratio between the CRSS of prism and basal slip, against early suggestions that it should only relate to the CRSS for basal slip. Solid solution softening upon prism slip accounts for the minima in σ_o at ~ 0.5 at. pct in Mg-Zn and Mg-Gd alloys. In the concentrated alloys, solute-specific hardening effects upon slip and twinning lead to diverging behaviors: in Mg-Al and Mg-Zn, σ_o remains below that of pure Mg. Strong short-range order by Gd leads to a steep monotonic increase, and to a value larger in compression than in tension due to the activation of {10-11} twinning at high concentrations. The negative σ_o of the dilute Mg-Zn alloys is an artifact created by the tension/compression asymmetry stemming from the polar character of {10-12} twinning.     

Vickers indentations in glass—II. Comparison of finite element analysis and experiments

This paper presents a comparison of a three-dimensional finite element numerical analysis of Vickers indentation with an experimentally observed indentation load—depth (P—h) relation on soda-lime glass. Several mechanical properties, such as yielding stress, strain hardening and elastic modulus, are then estimated from the analysis of the experimental P—h curve. This paper also compares the experimentally-measured residual stress field around a Vickers indentation at the surface of glass with an FEM numerical calculation. The FEM calculation uses Mises elastoplasticity to describe the residual stress state at the unloading. The comparison shows a very good agreement between the numerical calculation and the experimental results for the P—h relation, the Mises stress and the hydrostatic stress. The results further confirm that the residual stress field close to the indentation is a non-equal bi-axial stress field, which is not circular in shape but reflects the shape of the indentation impression. The formation of radial cracks also causes significant modification of the stress field. The FEM analysis shows that the P—h relation can provide much useful information on mechanical properties using the analysis developed here.     

Numerical and Experimental Study on Residual Stress in Gray Cast Iron Stress Lattice Shape Casting

The prediction of residual stress in a stress lattice shape casting (stress lattice) has been conducted and discussed by some researchers via the Finite Element Method (FEM). However, most of the previous studies used the first-order tetrahedral element, which has poor analysis accuracy in problems including bending. The use of the first-order tetrahedral element makes the verification of these studies uncertain because the bending deformation essentially occurs in the stress lattice casting. This study first shows that the thermal stress analysis for the stress lattice should use the element that can represent the bending deformation in principle for bending of the thin parts. Second, the simulated residual stress was compared with the measured value. The thermal stress analysis successfully predicted the residual stress of the stress lattice casting with and 11 pct difference. In addition to the prediction of the residual stress, it is important from the viewpoint of the productivity of castings to reveal the effect of the shake-out temperature on the residual stress. However, in the previous studies, conclusions concerning the effect of the shake-out temperature on the residual stress were not consistent (i.e., the one study said the higher shake-out temperature decreased the residual stress, and another study said a higher shake-out temperature increased the residual stress). Therefore, the current study first discusses the reason for the inconsistent conclusions in the previous studies. Second, stress lattice castings were cast and shaken out at various shake-out temperatures. Then, the current study validated the effect of the shake-out temperature on the residual stress. Consequently, the experimental results supported the conclusion of Kasch and Mikelonis that the shake-out at higher temperature contributed to the increase of the residual stress in the casting.     

Tensile stress relaxation behaviour of Ni-based superalloy single crystals between 973 and 1273 K

A series of tensile stress relaxation experiments was conducted on flat specimen of superalloy CMSX-2, oriented with 〈100〉 axis, exploring several temperatures and various initial plastic strains for a fixed temperature. The stress relaxation curves can be described through a hyperbolic type law with a non zero asymptotic stress σ_∞, which proved to be proportional to the initially applied stress σ₀ for a given temperature. Between 973 K (700°C) and 1173 K (900°C), which is the temperature range where the yield stress of the alloy reaches its maximum, the ratio σ_t8/σ₀ decreases rapidly from from 0.8 to 0.35, and keeps this value up to 1273 K (1000°C). Several kinds of defects have been observed by Transmission Electron Microscopy in the deformed specimens. Some of these defects are similar to those detectable after creep tests and some others are described here for the first time. The microstructural observations and the numerical results of the relaxation experiments are discussed with reference to previous works on the same kind of alloys and to a recent theoretical model proposed by McLean [Acta metall. 33, 545 (1985)].     

Analysis of the Deformation Behavior in Tension and Tension-Creep of Ti-3Al-2.5V (wt pct) at 296 K and 728 K (23 °C and 455 °C) Using In Situ SEM Experiments

The deformation behavior of a Ti-3Al-2.5V (wt pct) near-α alloy was investigated during in situ deformation inside a scanning electron microscopy (SEM). Two plates with distinct textures were examined. Tensile experiments were performed at 296 K and 728 K (455 °C) (~0.4T _m), while a tensile-creep experiment was performed at 728 K (455 °C) and 180 MPa (σ/σ _ys = 0.72). The active deformation systems were identified in the α phase using electron backscattered diffraction based slip-trace analysis and SEM images of the surface. Prismatic slip deformation was the dominant slip mode observed for all the experiments in both plates, which was supported by a critical resolved shear stress (CRSS) ratio analysis. However, due to the texture of plate 1, which strongly favored the activation of prismatic slip, the percentages of prismatic slip activity for specimens from plate 1 tested at 296 K and 728 K (23 °C and 455 °C) were higher than the specimens from plate 2 under the same testing conditions. T1 twinning was an active deformation mode at both 296 K and 728 K (23 °C and 455 °C), but the extent of twinning activity decreased with increased temperature. T1 twinning was more frequently observed in specimens from plate 2, which exhibited a higher fraction of twinning systems favoring activation at both 296 K and 728 K (23 °C and 455 °C). The tension-creep experiment revealed less slip and more grain boundary sliding than in the higher strain rate tensile experiments. Using a previously demonstrated bootstrapping statistical analysis methodology, the relative CRSS ratios of prismatic, pyramidal 〈a〉, pyramidal 〈c+a〉, and T1 twinning deformation systems compared with basal slip were calculated and discussed in light of similar measurements made on CP Ti and Ti-5Al-2.5Sn (wt pct).     

The effect of residual stresses on the debonding of coatings—II. An experimental study of a thermally sprayed system

Specimens have been produced by plasma spraying of boron carbide coatings about 1 mm in thickness on to titanium alloy substrates about 3 mm thick. The residual stress distributions in these specimens have been calculated using a numerical process model and also estimated from observed changes in curvature on debonding. Good agreement was observed between the two methods, with both suggesting the average substrate stress to be about + 20 MPa and the average coating stress to be about −60 MPa. In both constituents, there was a significant positive gradient of stress level through the thickness. These specimens were loaded in four point bending until cracks propagated along the interface between substrate and coating. From the load/displacement plots obtained during this testing, and taking account of the effect of relaxation of the residual stresses during debonding, the critical strain energy release rates of the interfaces, G_ic, were estimated to be ∼ 0.2–0.5 kJ m⁻². Substantial errors would have resulted from neglect of the presence of the residual stresses. Also of significance is the effect of the residual stresses on the mode mixity of interfacial loading, as characterised by the phase angle, ψ, since G_ic has been often observed to vary with ψ. The value of ψ for the four point bend test in the absence of residual stress is about 47°, whereas for the specimens tested here it was estimated to cover the complete range from 90° (pure shear) to 0° (pure opening) as the applied load was increased. The quoted values of G_ic were obtained in a regime where ψ ∼ 30°.     

The internal stress in titanium deformed at low temperatures (T<0.33TM)

The internal stressσ _i at 300 K produced by deforming commercial Ti-50A titanium (0.5 at. pct O _eq ) wire of 2 and 22μm grain size to 1 pet strain at temperatures of 78 to 650K was investigated employing the back-extrapolation and decrementai unloading techniques. Concurrent observations of the amount of twinning and the dislocation structure were made by transmission electron microscopy,σ _i by the decrementai unloading method was higher, and was inferred to have a stronger temperature dependence, than that by back-extrapola tion, the difference inσ _i being relatively independent of grain size.σ _i by both methods was found to be relatively independent of the deformation temperature and neither twinning nor dynamic strain aging was found to have a noticeable influence on its value. Since no pro nounced changes in dislocation structure or slip mode were observed for the present material as a function of deformation temperature, the difference inσ _i obtained here between the decremental unloading and the back-extrapolation methods could not be correlated with such changes as was possible by Williamset al. for titanium sheet material of higher in terstitial solute content.     

Tensile Work Hardening Behavior of Thin-Section Plate and Thick-Section Tubeplate Forging of 9Cr-1Mo Steel in the Framework of One-Internal-Variable Kocks–Mecking Approach

Comparative tensile flow and work hardening behavior of normalized and tempered plate and quenched and tempered tubeplate forgings of 9Cr-1Mo steel have been examined in the framework of one-internal-variable Kocks–Mecking approach at temperatures ranging from 300 K to 873 K (27 °C to 600 °C). Detailed analysis in terms of the variations of instantaneous work hardening rate, θ (θ = dσ/dε _p = dσ _p/dε _p, where σ is the true stress, σ _p is the plastic flow stress component, and ε _p is the true plastic strain) with σ and σ _p indicated two-stage work hardening behavior, and three distinct temperature regimes in the variations of work hardening parameters, θ ? σ and θ ? σ _p, with temperature. The influence of initial microstructures associated with different product forms of the steel is reflected in the systematic variations in work hardening parameters at temperatures ranging from 300 K to 873 K (27 °C to 600 °C). Tubeplate forging exhibited improved work hardening characteristics in terms of higher plastic component of flow stress because of microstructural softening than that of the plate material in the steel.     

The application of fractography to demonstrate the presence of crack tip residual stresses during programmed fatigue crack propagation in mild steel

Constant amplitude and programmed loading fatigue crack propagation tests were carried out on a low carbon steel in three point bending. The Palmgren-Miner summation(&#x03A3; _Nⁿ) was found to be consistent and always slightly greater than unity irrespective of the load program. It is suggested that this effect is caused by crack tip compressive stresses opposing propagation. Fracture surface observations using a scanning electron microscope showed changes in fracture mode immediately after a load drop from which it was possible to make estimates of the levels of residual stress present.     

The application of fractography to demonstrate the presence of crack tip residual stresses during programmed fatigue crack propagation in mild steel

Constant amplitude and programmed loading fatigue crack propagation tests were carried out on a low carbon steel in three point bending. The Palmgren-Miner summation(&#x03A3; _N ⁿ ) was found to be consistent and always slightly greater than unity irrespective of the load program. It is suggested that this effect is caused by crack tip compressive stresses opposing propagation. Fracture surface observations using a scanning electron microscope showed changes in fracture mode immediately after a load drop from which it was possible to make estimates of the levels of residual stress present.      

Mechanics of the push-out process from in situ measurement of the stress distribution along embedded sapphire fibers

The basic mechanics of the fiber push-out process are studied by measuring the stress distributions along c-axis sapphire fibers in γ-TiAl matrices. The stress measurements were made in situ during fiber push-out tests using a piezo-spectroscopy method. By focussing an optical microprobe into a sapphire fiber, the frequency shift distribution of the characteristics R lines of Cr³⁺, and hence the stress distribution along the fiber were determined at each increment of applied load. By comparing the measured stress distributions with ones calculated using finite element method, key mechanical parameters including residual stress before composite slicing, debond length at each load, debond energy and the frictional stress along the interface in both debonding and sliding phases were determined. Two coating systems (Mo/Al₂O₃ and CVD-C/Al₂O₃) were studied. The results also show that while the debond energies differ by an order of magnitude, the frictional stresses are very similar in magnitude, suggesting that the interface morphology is of greater importance than the nature of the coating.     

The effect of extrinsic grain boundary dislocations on the grain size strengthening in polycrystals

The grain size dependence of flow stress at room temperature in the regime of small strains (0–2%) has been examined in as-annealed and 2% pre-strained and subsequently annealed specimens of 316L stainless steel. Grain sizes in the range of 3.4–22.4 μm were considered. The stress-strain curves exhibit linear hardening characteristic beyond 0.2% plastic strain. The analysis of the Hall-Petch parameters show a linear increase in σ₀(ϵ) and a linear decrease in K(ϵ) with strain in the as-annealed specimens. The increase in σ₀(ϵ) has been associated with both, the work-hardening processes in the grain interior and the long range stress field of extrinsic grain boundary dislocations (EGBDs). The EGBDs also act as sites of stress concentration thereby making it easier to generate dislocations in the vicinity of grain boundaries. Therefore, K(ϵ) which is function of the stress required to generate dislocations decreases with increasing strain. The observed drop in flow stress as a result of annealing of pre-stained specimens at 800°C has been related with the annihilation of dislocations at and in the vicinity of grain boundaries. Annealing at 550°C (this temperature is sufficient for the delocalization of the cores of EGBDs) does not have any significant effect on the density of dislocation at and in the vicinity of grain boundaries. Therefore, no significant change in the flow stress was obsereved.     

Experimental Study on Bond Behavior between Concrete and FRP Reinforcement

Bonding between fiber-reinforced polymer (FRP) sheets and concrete supports is essential in shear and flexural applications for transfer of stress between concrete structure and reinforcement. This paper aims at better understanding FRP–concrete bond behavior and at assessing some of the common formulations for effective bond length and bond–slip models (τ-s) by means of an extensive experimental program on 39 concrete specimens strengthened with various types and amounts of FRP strips and covering a wide range of FRP axial rigidities, subjected to both double-shear and bending tests. Effective bond length, maximum bond/shear stress, slip when bond stress peaks, and slip when bond stress falls to zero, were all experimentally measured. The influence of FRP stiffness on effective bond length and bond–slip behavior was observed. New expressions for (1) effective bond length; (2) maximum shear/bond stress; (3) slip at peak value of bond stress; and (4) slip at ultimate, taking into account the influence of FRP stiffness, are proposed.     

The role of elastic interaction stresses on the onset of plastic flow for oriented two ductile phase structures

Elastic interactions at the Widmanstättenα-β titanium alloy interfaces that arise due to compatibility requirements have been calculated for various orientations of the interface with respect to the stress axis. It is shown that maximum interactions are found when the stress axis lies in or close to the interface and 40 deg inclined to the [0001]_α. The interaction stresses could be of the order of 30 to 35 pct of the resolved shear stress on the basal slip systems.β aids the elastic deformation ofα much more strongly on the basal slip systems than on either prism or pyramidal slip systems. The significance of these interaction stresses on the initiation of plastic flow is considered and it is shown that a good qualitative agreement has been obtained between these calculations and an earlier investigation by Wojcik and Koss.²⁴ The effect of the interface phase on the elastic interaction stresses has been considered and a possible role of interface stresses on elevated temperature creep ofα-β alloys has been suggested.