Experimental study of the origin of strain-rate sensitivity in a common Pb-Sn alloy

The origin of strain-rate sensitivity existing in the room-temperature plastic distortion of a 60 pet Pb-40 pet Sn alloy is examined experimentally using simple tension loadings. It is found that the response of this material to both constant stress and constant strain-rate loadings is accurately described by a single uniaxial constitutive relation which is independent of the instantaneous level of straining rate and dependent explicitly only on stress, strain and lapse-time variables. The rate sensitivity exhibited by this alloy during room-temperature quasistatic tensile deformations is thus concluded to be explainable directly in terms of a combination of the competing effects of strain hardening and time-dependent thermal softening without the necessity of introducing explicit strain-rate mechanisms of any kind.     

Tensile strain-rate sensitivity of

The tensile strain-rate sensitivity of continuous-tungsten-fiber reinforced niobium composites (W/Nb), fabricated by an arc-spray process, was studied in the 1300 to 1600 K temperature range. The tensile properties of the fiber and matrix components, as well as of the composites, were measured and compared to rule of mixtures (ROM) predictions. The deviation from the ROM was found to depend upon the chemistry of the tungsten alloy fibers, with positive deviations for thoria-dispersed W wire (ST300) reinforced Nb composite(i.e., stronger composite strength than the ROM) and negative or zero deviations for lamp-grade W wire (218) reinforced Nb composite. In addition, it was found that the composites tested at higher crosshead speeds exhibited a strain-rate sensitivity greater than that of the free fibers tested at the same crosshead speeds, even though the composite tensile strength is determined mainly by the fiber component.     

Operant strain-rate sensitivity during tensile necking

Precisely machined tensile specimens of aluminum-killed steel sheet were used to measure the continuous strain-rate sensitivity,m _c, in a series of isothermal tests at different crosshead speeds.m _cwas found to be independent of strain and strain rate, in contrast with the “jump” test instantaneous strain sensitivity, m_i, which was found to vary strongly with strain rate. A series of matched tensile specimens was also photogridded and deformed at three rates and terminated at four elongations. The strain distributions obtained from these tests were compared with Finite Element Modeling (FEM)—calculated ones based on several strain-rate sensitivity formulations. Comparison of calculations with experiments revealed that the opérant rate sensitivity during tensile localization,m _t, was intermediate betweenm _candm _iat each rate and elongation. Once the effective rate sensitivity was established, detailed predictions of strain distributions and failure elongations agreed very well with experiment. A qualitative model of strain-based stress transients was proposed for both strain-rate and strain-state path changes. Formerly Staff Research Scientist, General Motors Research Laboratories. Formerly Senior Staff Scientist, General Motors Research Laboratories.     

Vacancy versus pipe diffusion mechanisms for subgrain growth in OFHC copper

Oxygen free high conductivity (OFHC) copper wires have been annealed in a temperature range of 443–473 K. The subgrain size (D) in these wires have been observed to follow a parabolic growth law (D² = d² + K · t) with respect to annealing time (t) at a given temperature, where d is the subgrain size in the cold worked condition and K is a temperature dependent constant. It has been found that K decreases as the amount of prior cold work increases while it increases as the annealing temperature increases. The temperature dependence of K has been analysed in terms of both vacancy and pipe diffusion mechanisms. The pipe diffusion mechanism dominates the subgrain growth process at lower recovery temperatures while the conventional vacancy mechanism prevails at higher recovery temperatures.     

Effect of strain rate on tensile behaviour of cryo-rolled ultrafine grained OFHC copper

The effect of strain rate on tensile behaviour of cryo-rolled ultrafine grained OFHC Cu was investigated in the strain rate range 10⁻⁵-10⁻²s⁻¹ in the present study. A significant increase in yield and ultimate tensile strength but a reduction in uniform elongation was observed in cryo-rolled Cu as compared to microcrystalline Cu. However, surprisingly a significant uniform elongation was observed at all strain rates, unlike in UFG Cu processed by other synthesis methods.     

The problem of the negative strain-rate sensitivity of metals under the portevin-lechatelier deformation conditions

Experimental data are used to show that the ‘negative’ strain rate sensitivity of metals, under conditions producing ‘jerky flow’, is only an apparent value. Taking into account the mode of propagation of slip-bands, a simple model of the phenomenon is postulated. Also discussed are the most important features of non-uniform deformation in Cu-base and Al-base alloys.     

The development of strain-rate gradients

The development of nonuniformities in tensile deformation and its dependence on material parameters and external conditions have been reanalyzed. It is found that the major influence of strain rate on neck growth is usually through its effect on the rate of strain hardening, rather than on the flow stress itself. In addition, the curvature of the stress-strain curve plays an important role: its usual sign is responsible for the unavoidability of eventual unbounded neck growth. The new analysis uses the state-parameter formulation of constitutive laws, avoiding the integrated strain as a variable. The result is a second-order differential equation describing the development, at each cross section, of the relative gradients of cross-sectional area and of strain rate. Numerical solutions are presented for small strains, analytical ones for slow neck growth. The application of a strain-rate criterion for catastrophic growth leads to a quantitative formula for the maximum tensile ductility, which is in agreement with observations, and provides guidelines for material development.     

Solid solution softening and strain-rate sensitivity of Fe-Re and Fe-Mo alloys

The resolved shear stress and strain-rate sensitivity of Fe-Mo and Fe-Re alloys, well within the solid solution range, were measured versus temperature and compared with previous results for Fe-Ti alloys. The strain-rate sensitivity-temperature curves shifted systematically to lower temperatures as solute was added. The resolved shear stress was divided into two parts, a dynamic part which is a function of strain-rate and a static part which is not. The strain-rate sensitivity data were inverted to give the dynamic part of the flow stress and this was subtracted from the resolved shear stress to give the static part of the flow stress. Significant solid solution softening occurred in the dynamic part of the flow stress at 166 and 196 K. This is due to intrinsic effects and not to scavenging of im-purities. The static part of the flow stress is made up of two parts, a peaking effect super-imposed on normal solid solution hardening.     

Work hardening and rate sensitivity material coefficients for OFHC Cu and 99.99% A1

Large strain tensile tests were carried out on OFHC Cu and 99.9% A1 with the aim of determining the first and second order work hardening and rate sensitivity coefficients. The tests were performed at room temperature and 473 K and at constant true strain rate in the range 5 x 10^-4 to 10⁻¹s⁻¹. The use of a diameter transducer to measure and control the rate of reduction of the neck diameter of the tensile specimens is described. In this way, the strain rate at the minimum cross-section was held constant well beyond the point of maximum load. A second diameter sensor for use at 473 K is also described. In order to determine the coefficients for Cu at 698 K, constant strain rate compression tests were performed. The detailed dependence of the material coefficients on stress, strain rate and temperature is characterized. It is shown that the values of the rate sensitivity of the work hardening rate B_σ beyond the maximum load are less than one, but are not negligible. As a result, the rate sensitivity] at constant work hardening rate N is not the material coefficient that controls the growth of strain rate gradients at large strains. It is also shown that the actual value of the coefficient B_σ is substantially higher than the one obtained from the single state parameter approach.     

On the origin of cube texture in copper

A crystallographic etch in which 111 planes are exposed in copper has been used to determined the orientation of the neighbouring substructures sorrounding cube oriented microbands in heavily cold rolled copper. These, after characterisation into orientation groups, were compared with the neighbourhoods of undeveloped cube oriented microbands in lightly annealed material in which almost all well developed recrystallised grains were of cube orientation. By inspection of the two sets of orientation neighbourhoods it is demonstrated that only cube microbands sorrounded by material with a φ° <111> orientation relationship provide cube nuclei. Thus the cube texture arises from competition between nuclei in a variety of orientation environments, the successful nuclei having environments into which they initially grow characterised by a φ° <111> relationship. The process is best described as micro-growth selection, in which the local texture determines the viability and competitive advantage of nuclei, while the global deformation texture (i.e. that determined by traditional diffraction methods) is that which is consumed by those nuclei, with the possibility of further growth selection as recrystallisation proceeds.     

The effects of combined strain-path and strain-rate changes in aluminum

The effect of changes in both the direction of tensile stress and the strain rate upon the plastic behavior and microstructure of aluminum has been investigated. The reduction in strain-hardening rate following a strain-path change was influenced by the strain rate prior to and after the change; higher strain rates in the first stage and lower rates in the second stage decreased the initial transient hardening rate. The introduction of a large path change significantly reduced the effect of strain-rate changes on the strain-hardening rate observed in testing without changing the tensile axis. Evidence of cell wall disruption following a path change was found, and this mechanism combined with effects of cell wall orientation can qualitatively explain the removal of the rate sensitivity of hardening rate because the usual recovery events in cell walls no longer have a dominant influence on flow stress development.     

Recrystallisation mechanisms and the origin of cube texture in copper

Microstructures and textures have been examined in various samples of copper after cold rolling and annealing treatments. Deformation substructures may differ considerably according to material and processing variables. This is most evident lhen considering the density of shear bands present after high strains. During annealing, the mechanism of recrystallisation is strongly dependent on the prior deformation structure. Clear evidence is presented for the nucleation of cube-oriented grains lithin transition bands. It is argued that these grains are favoured because of the special geometry of the bands and because the cube-oriented deformation structure is capable of rapid recovery. This latter effect is a result of the peculiar dislocation populations activated during rolling. Shear banding greatly leakens the subseluent cube recrystallisation texture. On annealing, nel recrystallised grains lith lidely scattered orientations are created lithin shear bands. Furthermore, it seems likely that shear bands can destroy the very favourable sites in lhich the cube nuclei develop.     

Flow localization in OFHC Cu and 99.99% Al

The work hardening and rate sensitivity coefficients determined in an earlier investigation are used to integrate numerically the evolutionary constitutive relation proposed by Kocks et al. under conditions where the acceleration remains constant during testing. The numerical predictions are compared with flow curves obtained from constant acceleration tests and the agreement found is excellent. These experiments were performed with the aid of a diametral transducer attached at the minimum cross-section of the tensile samples which monitored and controlled the rate of reduction of the sample diameter. The material coefficients are also employed for the numerical integration of the first and second order differential equations describing flow localization. Tensile tests were carried out on Cu and Al samples at room temperature and on Al specimens at 473 K in which the flow localization process was followed by photographic means. The strain measurements obtained are reproduced more closely when the combined “first” and “second order” material coefficients rather than only the ‘first order’ coefficients are used. This is largely because of the nonnegligible value of B_σ, the rate sensitivity of the work hardening rate. In the case of the Al, the onset of flow localization is retarded by 0.15–0.2 strain beyond the UTS because of the magnitude of B_σ.