High-temperature precipitation hardening of Y2O3 partially-stabilized ZrO2 (Y-PSZ) single crystals

Precipitation hardening in two-phase 4.5 m/o Y₂O₃ partially-stabilized ZrO₂ (Y-PSZ) single crystals has been studied at 1400°C, using crystals aged at 1600°C for various times up to 150 h. This aging allowed the formation and growth of low-solute tetragonal (t)-ZrO₂ precipitates in a high-solute cubic (c)-ZrO₂ solid solution matrix. These “colony” precipitates are internally twinned on {110}, and form fiber-like morphologies (fiber axis along 〈001〉) at the longest annealing times; the lamellar spacing within the colonies coarsens via conventional Ostwald ripening. Surprisingly, even large precipitates (> 1 μm long) are coherent. All crystals deformed by nucleation and propagation of Luders bands, leading to serrated flow. The yield stress increases linearly with lamellar spacing and reaches the very high value of 550 MPa (at 1400°C) for the 150 h sample. The particular dislocation-precipitate interactions leading to this exceptionally potent precipitation hardening are discussed.     

On the additivity of precipitation and solid solution hardening in under-and over-aged single crystals of (CuAu)-Co

The superposition of precipitation (τ_p) and solid solution (τ_s) hardening has been experimentally investigated for the system copper-gold-cobalt. The copper-rich copper-gold solid solution is precipitation hardened by cobalt-rich particles which have a lattice mismatch. Under- as well as over-aged single crystal specimens have been analyzed. It has been attempted to relate the total measured critical resolved shear stress τ_t to τ_p and τ_s by: τ_t^k = τ_p^k + τ_s^k. This is an ad hoc generalization of suggestions published with k = 1.0 and k = 2.0. τ_t and τ_s were measured as functions of the gold-concentration of the matrix, of the particle dispersion and of temperature (90–500 K). k is to be chosen such that τ_p derived with the aid of the above equation from τ_t and τ_s, varies with the particle dispersion as predicted theoretically. The result is: only for under-aged specimens containing no more than 3.2 at.% gold in the matrix, the above equation describes the experimental results satisfactorily, k equals 1.25. For higher gold-concentrations the above equation does not yield an acceptable representation of the data, k = 1.0 and k = 2.0 can be ruled out.     

Deformation of Nb-W single crystals: Athermal solid solution strengthening

The athermal component of the flow stress of single crystals of niobium and four substitutional solid solution strengthened Nb-W alloys (1, 3, 6, and 15 at. pct) has been measured. The magnitude of the athermal stress was obtained by the method utilizing the temperature dependence of the flow stress and by a stress relaxation method. The agreement between these two methods is good. Athermal strengthening is a linear function of concentration over most of the composition range. No current athermal hardening theory is completely consistent with the experimental results. Formerly with the Advanced Materials Research and Development Laboratory, Pratt and Whitney Aircraft, Middletown, Conn.,     

Latent hardening behavior of monocrystalline Al-Mg solid solution

The latent hardening behavior of dilute Al-Mg single crystal was investigated in this study. We performed the latent hardening tests on five systems, one in each of the five system groups. The latent hardening ratios (LHR) and the hardening rates were calculated. The LHR of systems that form attractive junctions is highest in this investigation. The LHRs of systems that form Lomer-Cottrell sessile locks, Hirth locks, or cross-slip systems are in the middle range. The coplanar system has the lowest LHR, which is in agreement with the theoretical prediction. An equation was developed that correlates the LHR with the dislocation densities at various prestrain values. The secondary deformation curve is predicted qualitatively in accordance with the interaction strength of the latent system with the primary system. Based on such a model, a prediction of the shapes of the secondary deformation curves in the strongest and weakest latent systems can be made.     

Latent hardening in cyclic deformation of copper single crystals

In order to explore latent hardening produced by cyclic deformation, single crystals of copper oriented for single slip were first cycled at strain amplitudes corresponding to those of the plateau in the cyclic stress-strain curve, and subsequently sectioned for compression testing. The specimens were cycled enough to form persistent slip bands, and orientations in the secondary test were chosen to excite selectively coplanar or non-coplanar slip systems. Coplanar systems were found to be similar in hardening to the primary system, but non-coplanar systems showed a latent hardening ratio of about 1.25. If the plastic shear strain amplitude of the initial cycling was greater than 2×10⁻³ (the threshold for producing secondary slip), then the hardening rate in the secondary test was high. If the cyclic strain amplitude was less than 2×10⁻³, the latent yield stress was high because of the frictional effect of the loop patches, but the hardening rate was found to be low.     

Earing in cup drawing face-centered cubic single crystals and polycrystals

A simple model of flange behavior during cup drawing was used to predict the earing profile of deep-drawn cups. The relationship between yield surface shape and earing tendency was established, with plane stress yielding corresponding to no hold-down pressure on the flange and plane strain corresponding to no thickening. Using the Schmid law, the earing model was applied to the case of a single crystal in cube position and compared to Tucker’s well-known results.^[6] For the plane strain case, good agreement was obtained with the experiment; but for plane stress, the predicted profile did not agree with the experimental one. Using the Taylor/ Bishop and Hill (TBH) theory^[8,9] and measured crystallite orientation distribution functions (CODF), the model was applied to the case of high-purity aluminum sheet with various cold-rolling reductions (35, 60, 80, and 90 pct). The major experimental trends were again correctly predicted by the plane strain case.     

Fatigue hardening of lif single crystals in push-pull cyclic deformation

The fatigue hardening response of LiF single crystals subjected to uniaxial cyclic deformation, at various strain amplitudes and strain-rates, has been related to the monotonic hardening rate. Cumulative strain in fatigue is obtained through Kocks' flow stress theory on a statistical distribution of obstacles. The difference between monotonie and cyclic deformation is in the relative rate of accumulation of short and long range internal stresses. In the case of LiF at room temperature, fatigue hardening is essentially due to the increase in short range stresses. LiF crystals which are susceptible to cleavage fracture, can withstand large tensile stresses in fatigue when compared to monotonie deformation. Activation volume analysis indicates that vacancy and jog concentrations determine the dislocation mobility and fatigue hardening of LiF single crystals. Microscopic examination reveals the existence of very fine slip bands. In the case of crystals subjected to large number of fatigue cycles, surface irregularities and dislocation banding is observed. Optical and electron microscopy suggests dynamic recovery in the crystal studied.     

Stress asymmetry of stoichiometric NiAl single crystals

The yield stress properties of stoichiometric NiAl single crystals were investigated in terms of crystal orientation, temperature and the deformation mode. The calculated critical resolved shear stress (CRSS) was a strong function of crystal orientation, temperature and the deformation mode whether tension or compression. The CRSS was, in a wide range of experimental conditions, higher in the sequence of {110}〈100〉, {100}〈100〉 and {hk0}〈100〉 slips. The CRSS in compression was higher particularly at low temperatures than the CRSS in tension. The tension-compression asymmetry on the CRSS was understood qualitativelys being due to the effect of the normal stress on the core structure of a 〈001〉 dislocation and a 〈111〉 dislocation. It was suggested that a compressive normal stress makes the core configuration more sessile, resulting in the increased stress effectively at low temperatures.     

Investigation of ZrO2/mullite solid solution by energy dispersive X-ray spectroscopy and electron diffraction

A mullite/15vol.% ZrO₂ composite was analyzed using the techniques of microdiffraction and energy dispersive X-ray spectroscopy (EDXS). The EDXS results indicate that there is a significantly high solid solubility of mullite in zirconia and zirconia in mullite; microdiffraction results suggest that ordering occurs in the ZrO₂ (ss) phase based on the presence of forbidden reflections for the P 2₁/c space group of monoclinic zirconia. The presence of a secondary phase at the grain boundaries, either amorphous or crystalline, has not been generally detected throughout the bulk. The results provide experimental evidence for the hypothesis of Moya and Osendi that the increased toughness and flexural strength of these composites are related to solid solution effects rather than to transformation or microcrack toughening mechanisms.     

Strain hardening of copper single crystals at high strains and dynamical recovery processes

Single crystals of copper lere deformed by rolling at room temperature in tlo orientations. Different stress-strain characteristics lere found. In hard orientation (Rolling Plane ∥ (11̄1), Rolling Direction ∥ [1̄45]) a period of rapid strain hardening is folloled by the constancy of the flol stress. In soft orientation (Rolling Plane ∥ (3̄2̄1), Rolling Direction ∥ [1̄45]) a tlo-stage process of the strain hardening las found but no plateau of stress las observed up to strains of the order of three. On the basis of strain rate change and temperature change experiments and structural observations (optical and electron microscopes) tlo different mechanisms of dynamical recovery lere identified. In particular, a nel dynamical recovery process (D.R.t-2) las found to be the result of activation of the formally inactive slip direction. The intensity of this process in hard-oriented crystals leads to localilation of strain into lell-defined shear bands resulting in a plateau on the σ-ϵ curve.     

The temperature independent plateau stress of solid solution crystals

A calculation of the plateau stress in solid solution crystals is presented assuming an arbitrarily oriented dislocation loop of lengthL, that moves under an applied stress. At high concentrations of solute atoms the dislocation segment does not interact with an individual solute atom but instead with all the solute atoms along the dislocation segment within a certain radius. The macroscopic flow stress is assumed to be determined by the maximum force that is encountered when a dislocation is moved over a distance equal to the distance between the position at zero stress and the critical position of an activated Frank-Read source. If the dislocation segment is assumed to be large compared to atomic distances, the interaction with groups of atoms will lead to an athermal process and therefore can explain the origin of the temperature independent flow stress in solid solution crystals. From this model the flow stress can be calculated with the help of statistical methods similar to those used in calculations of the movement of Bloch walls in magnetic materials. Besides the proper temperature dependence of the plateau stress the above model yields a dependence of the plateau stress upon the square root of the solute concentration, a result that is in good agreement with the measurements on silver, gold, and copperbased alloys. A linear relation between the solid solution hardening parameter dT/d√c and the strength of the solute atoms is obtained which is confirmed by the experimental results on copper-based alloys.     

Mechanisms of cyclic strain hardening in Ni3Al+B single crystals

The evolution of dislocation substructures and their correlation with strees response in Ni₃Al+B single crystals fatigued at room temperature has been studied. Fatigue was conducted at total-strain amplitudes of 0.05–0.2%. Cyclic strain hardening and a tension/compression flow stress asymmetry were observed. The magnitude of stress asymmetry was found to depend on the applied cyclic strain. A dislocation structure composed of jogged superdislocations and superdislocation dipoles was observed. The dislocation dipoles were mainly formed by nonconservative of jogged superdislocations. Dragging of jogs, interaction between dislocations, and impedance of dislocation motion by dislocation dipoles (point defect clusters) are considered to be the major contributors to cyclic strain hardening in Ni₃Al+B single crystals. The separation between superpartial dislocations of a paired superdislocation was found to fluctuate away from the equilibrium spacing during cyclic straining. The extent of the fluctuation became more pronounced as the applied cyclic strain increased. This phenomenon was intimately related to the cyclic-strain dependence of tension/compression flow stress asymmetry found in fatigued Ni₃Al+B single crystals.     

Latent hardening behavior of cyclically deformed Cu-16 at.%Al single crystals

The latent hardening behavior of cyclically deformed Cu-16 at.% Al alloy was investigated by measuring the flow stress and the hardening rate on secondary systems in monotonic compression. Latent hardening experiments of cyclic deformation in Cu-16 at.% Al are complicated by an ageing reaction that has time to develop during test interruptions needed to machine specimens, and produces bursts and yield points on reloading (except at the higher stresses). This problem was overcome to some degree, and the Latent Hardening Ratios (LHRs) for coplanar systems were found to be close to unity; also, the LHRs for intersecting systems were greater than 1, in accord with earlier results on wavy slip metals. The LHRs for these intersecting systems, however, were similar than those copper because of the large contribution of the friction stress due to alloying. The unit LHR in the coplanar systems can be explained if the multipoles inherited from cycling disintegrate upon reloading and the contribution of secondary dislocation walls to the hardening becomes significant. Generally, the mesh-length theory of hardening is found to explain the LHRs quite well. The LHR for the A3 system was found to be smaller than those of other intersecting systems in this alloy, consistent with an earlier result on pure copper. The lower value of the activation volume along with the observation of frequent double cross slip traces on the surface strongly suggest that cross slip is responsible for the lower LHR for the A3 latent system.     

Stress relaxation,internal stress,and work hardening in some Bcc metals and alloys

The stress-time relation during stress relaxation is interpreted in terms of a power relation between dislocation velocity and the effective stress. Such interpretation gives not only the velocity-stress exponent, but also the internal stress in the work-hardened state. The velocitystress exponents thus obtained agree with those obtained from etch pit dislocation velocity measurements. The variation of internal stress with strain shows that work hardening is largely due to the development of internal stresses. The temperature dependence of flow stress arises from the increase of effective stress with decreasing temperature, consistent with a thermally activated process for dislocation motion. Formerly Graduate Student, Columbia University, New York City, N. Y.