Yield Point Drop Research Articles

Effects of Grain Size, Thickness and Tensile Direction on Yield Behavior of Pure Titanium Sheet

Yield phenomena during the tensile testing of pure titanium sheets of 0.2 mm and 0.4 mm in thickness were investigated in detail focusing on the effects of grain size (d), thickness (t), t/d ratio and tensile direction. With decreasing grain size, the yielding behavior changed from continuous yielding to one accompanied with yield point drop. Upper and lower yield stresses and 0.2%-proof stress followed the Hall–Petch relationship; however, coarse-grained specimens (d ≧ 20 µm) showed larger scatter in 0.2%-proof stress than the others. Consequently, the Hall–Petch coefficient (k) and friction stress (σ0) derived from 0.2%-proof stress are not accurate enough. The values of k and σ0 derived from various yield stresses and tensile directions were in the range of 250–600 MPa·µm0.5 and 30–180 MPa, respectively. Therefore, the validity of stress for yield stress was a concern, and the combination of the lower yield stress in the fine-grain range (d ≦ 20 µm) and 0.2%-proof stress excluding work-hardening in the coarse-grain range (d > 20 µm) was suggested to obtain reliable values of k and σ0, resulting in values of 370–460 MPa·µm0.5 and σ0 65–140 MPa, respectively. Moreover, it was revealed that k decreased and σ0 increased with the increasing angle of tensile direction to the rolling direction, regardless of thickness. The anisotropy of k is presumed to be affected by the grain boundary character rather than the Schmid factor, and neither rigidity nor the length of the Burgers vector are responsible. Meanwhile, the anisotropy of σ0 is verified to be affected by Schmid factors. Furthermore, it was clarified that the t/d ratio hardly affects upper and lower yield stresses (t/d > 14) nor 0.2%-proof stress (1.5 ≦ t/d ≦ 14).

Hot deformation behaviour of Ti alloys: A review on physical simulation and deformation mechanisms

Titanium and its alloys, owing to their properties like high strength, toughness, corrosion resistance and thermal stability, are employable in various engineering and medical applications. The properties of titanium alloys depend upon the processing routes and their final microstructure. Therefore, the present review paper compiles the deformation behaviour of various alloys during hot deformation using a physical simulation. Subsequently, the flow stresses are analysed and utilized to develop the processing maps and the constitutive equations that are advantageous for predicting deformation mechanisms during the hot deformation. Specific features reported in the flow stress curves include work hardening, flow softening and steady-state behaviour. In certain cases, the yield point drop and oscillatory behaviour or serrations are also observed. Softening and oscillatory behaviour is an indicator of either dynamic recrystallization or flow-instability, whereas yield discontinuity signifies locking and unlocking of dislocations. In the processing maps, high power dissipation efficiency, η, reveals safe processing conditions, and the η value higher than 40% demonstrates dynamic recrystallization or globularization in the deformed microstructure, whereas the instability domain expresses shear band, flow localization, void formation and wedge cracks in the deformed microstructure. Amongst all the constitutive equations, the Arrhenius-type hyperbolic sine equation is the most suitable for Ti alloys for calculating flow stress and predicting dominant deformation mechanism using activation energy Q and stress exponent n.

Crystal plasticity modeling and simulation considering the behavior of the dislocation source of ultrafine-grained metal

Ultrafine-grained metals (UFGMs) produced by warm- or cold-rolling under severe plastic deformation have attracted interest as high-strength structural materials. UFGMs with a grain size less than 1μm exhibits remarkable material and mechanical properties, and a computational model predicting these properties is desired in the field of materials science and engineering. In order to clarify the utility of UFGM numerically, it is important to investigate the size effects of metallic materials that depend on initial grain size. It is assumed that such unusual mechanical properties originate in grain size and the enormous volume fraction of the grain boundary. When grains are of the submicron order, dislocation loops are hardly generated from Frank–Read sources smaller than the grain size. Grain boundaries play an important role in dislocation dynamics. In this study, we develop a crystal plasticity model considering the effect of the grain boundary and dislocation source. In order to predict variation of critical resolved shear stress (CRSS) due to grain boundaries or dislocation sources, information on dislocation source and grain boundary is introduced into a hardening law of crystal plasticity. In addition, FE simulation for FCC polycrystal is used to analyze stress–strain responses such as increased yield stress and yield point drop, from the viewpoint of grain size and dislocation density. We thoroughly investigate the effect of dislocation behavior on the material properties of UFGMs.

A Triple-Scale Crystal Plasticity Simulation on Yield Behavior of Annealed FCC Fine-Grained Metals

In this study, the conventional Bailey-Hirsch’s relationship is extended in order to express the increase of critical resolved shear stress due to the lack of dislocation lines in a grain. This model is introduced into a triple-scale crystal plasticity model based on geometrically necessary crystal defects and the homogenization method. A FE simulation is carried out based on the proposed model for FCC polycrystals with different grain sizes. It is numerically predicted that yield behavior of fine-grained metals depends on the initial dislocation density and the initial grain size. Furthermore, yield point drop that is observed in annealed FCC fine-grained metal can be reproduced.

Segregation and wetting transition at dislocations

We investigate solute segregation and wetting transition at dislocations and the corresponding drag effect on dislocation glide using a continuum model developed previously for grain boundary and based on gradient thermodynamics. The dislocation core structure and stress field are described by the newly developed phase field model. This study differs from much previous work because it takes into account not only the long-range elastic interactions but the short-range chemical interactions between solute atoms and dislocation core as well as among solute atoms themselves. The latter leads to the prediction of a wetting transition at the dislocation core with respect to varying temperature, solute concentration, or dislocation velocity. The transition temperatures obtained during heating and cooling are different from each other, leading to a hysteresis loop in the solute concentration-temperature plot and the solute concentration-velocity plot. These predictions could provide new insights into the phenomena of sharp yield point drop and strain aging observed in metal alloys.

Slip in single crystals of niobium-molybdenum alloys deformed in compression

The slip geometry and morphology, and the hardening behaviour in compression of single crystals of Nb-Mo alloys with up to 50 at. % Mo has been investigated in the range 77–475°K; a few tensile experiments are also reported. Detailed results have been obtained for Nb-5 at. % Mo and Nb-16 at. % Mo. The orientation dependence of the operative slip plane [the ψ(χ) curve] is changed by temperature or alloying mainly for orientations in the left half of the stereographic triangle, i.e. near [001], and this behaviour cannot be fully explained by current theories. The change in the morphology of the slip bands with temperature and molybdenum content appears to depend largely on the stress level, and is interpreted in terms of the ability of screw dislocations to cross-slip. Some results indicate that the yield point drop is connected with the beginning of cross-slip. From measurements of work hardening rates, it is concluded that the effect of adding solute atoms is to increase the yield stress, increase θ I and decrease On. The increase in θ I is discussed in terms of our present knowledge of dislocation structure in deformed crystals.

Yield stress in niobium-nitrogen solid solutions

The yield point and associated parameters have been studied in electron-beam-refined niobium containing amounts of nitrogen ranging from 60 to 850 wt. p.p.m., tested at room temperature and strain rates from 1 × 10 −4 to 1.3 × 10 −1 sec −1. The upper and lower yield stresses and the lattice friction stress show three stages of solution hardening, whilst the yield point drop and the k y parameter show one stage only. A comparison of solution-hardening coefficients of the present niobium-nitrogen alloys with those for niobium-oxygen alloys 6 shows that nitrogen is twice as effective as oxygen as a solution hardener. The solution-hardening coefficients for the upper- and lower yield stresses and the lattice friction stress decrease, whilst those for the yield point drop and the k y parameter increase, with increasing strain rate. The yield point and associated parameters exhibit similar strain rate dependence to that observed in niobium-oxygen alloys 6. The dislocation velocity exponent ( m), as calculated from the strain-rate dependence of the upper and lower yield stresses using the equation log σ = log B + ( i m ) log ε ̇ , shows a relationship with nitrogen concentration ( C) of the form, m = m 0 + β C 1.3.

The effect of pressurization on the ductile-brittle transition temperature of polycrystalline chromium

The change in the ductile-brittle transition temperature of polycrystalline chromium produced by subjecting specimens to a hydrostatic pressure, P, in the range 5–31 kbars and then testing at atmospheric pressure was investigated. The transition temperature, T t , for the as-recrystallized material was ∼550°K and only treatments above 6 kbars resulted in a significant lowering of T t . For the pressure range 6–12 kbars the transition temperature was sensitively dependent on P; the 12 kbar treatment reduced T t to ∼290°K. For these pressurizations T t occurred at an approximately constant (critical) stress, at the upper yield point and brittle fracture, of 20 kg mm −2. Treatment of 31 kbars resulted in a further decrease in T T of only ∼20°K and the transition took place at a significantly higher stress. For all pressurizations there was a continuity, in the variation with temperature, between the values of the upper yield stress and the brittle fracture stress, which was identified with the crack nucleation stress. In some specimens fractured above T T non-propagating cracks were observed, demonstrating that then crack nucleation is easier than crack propagation. Treatments at 6 kbars and above resulted in decrease and eventual suppression of the yield point drop and lowering of the lower yield stress. A simple analysis indicates that the mobile dislocation density at the upper yield point is raised by an order of magnitude as the pressurization treatment is increased from 5 to 12 kbars.

Strain ageing effects and stress relaxation in iron during shock loading

The influence of prestraining and ageing upon the stress relaxation, which follows the elastic precursor wave during shock loading of iron, has been determined experimentally. Prestraining through the Lüders strain is observed to eliminate this stress relaxation under shock loading. Suitable time-temperature ageing treatments after prestraining cause a reappearance of the shock stress relaxation. Thus the influence of prestraining and ageing upon the stress relaxation in iron is qualitatively the same as the influence of these treatments upon the upper to lower yield point drop in conventional low strain rate tensile tests. Quantitative differences between the influence of strain ageing upon the shock stress relaxation and the conventional yield drop are observed. The return of the shock stress relaxation by ageing of prestrained iron (containing both nitrogen and carbon) appears to be governed by the diffusion of carbon while the return of the conventional yield drop appears to be governed by the diffusion of nitrogen. Further, for a given ageing temperature, the critical ageing time for the return of shock stress relaxation is from one to two orders of magnitude longer than the critical ageing time for return of the conventional yield drop. The relationship of these results to the current theories of dislocation behavior in iron containing small amounts of carbon and nitrogen is discussed.

A Method of Determining the Stress Effective during Lüders Band Propagation

IN materials which exhibit a well-defined yield-point drop followed by non-uniform yielding at a nearly constant stress, this stress is given by the Patch equation1 as: where σy is the lower yield stress, σi is the friction stress, ky is a term originally thought to be associated with an unlocking stress and 2d is the grain diameter. It is desirable to have an accurate value of the macroscopic stress, σy, in order that the slope of the lower yield stress vs. grain size curve, ky, be as meaningful as possible. In addition, the dependence on temperature of the lower yield stress is an important property in theoretical considerations. Difficulties may arise, however, in determining what value of the lower yield stress to use in such situations. This communication describes a method which can be used to determine, at least in an approximate manner, whether the magnitude of any corrections to the nominal yield stress is sufficiently large to warrant consideration.