The Flow Stress of Ultra-High-Purity Molybdenum Single Crystals

Abstract

The paper investigates the dependence of the flow stress σ of ultra‐high‐purity molybdenum single crystals on temperature T, strain rate, and crystallographic orientation of the crystal axis. The cyclic‐deformation technique developed by Mughrabi and Ackermann allowed a complete set of flow‐stress data (covering the temperature range 125 to 460 K at 15 different shear strain rates, varying from 5.9 × 10—7 to 1.7 × 10—3 s—1) to be obtained on one and the same specimen. The two crystals investigated, with Schmid factors μ{110} = 0.50 and μ{112} = 0.43, or μ{110} = 0.40 and μ{110} = 0.43, respectively, had residual resistivity ratios exceeding 2.5 × 105, the main impurity being W. The data are in excellent agreement with the theory of flow‐stress control by kink‐pair formation and kink migration. It is shown that for both orientations the elementary glide steps of the a0 〈111〉/2 screw dislocations controlling the flow stress occur on {112} planes. The formation energy of a pair of isolated kinks on a {112} plane is 1.27 eV, in perfect agreement with the activation energy of the so‐called γ‐relaxation as determined by internal‐friction measurements. The apparent kink mass and the kink diffusivity could be determined, too. The present results leave no doubt that the “hump” observed in the σ–T relationship of high‐purity b.c.c. metals is due neither to a change in the glide mechanism nor to a special form of the Peierls potential but is a natural consequence of the dependence of the kink‐pair formation enthalpy on the resolved shear stress.

Peierls potential of screw dislocations in bcc transition metals: Predictions from density functional theory

“…Assuming the term inside the square root is not material dependent, we have a scaling relationship between the kink formation energy and the pre-logarithmic energy factor. Since the kink formation energy has been extracted from experiments [47][48][49][50][51] , we can test this scaling relationship directly. To do this we use the kink energies reported in 51 for Ta, Fe, Nb, Mo and W; and we compute the pre-logarithmic energy factors from the elastic constants in 32 and multiply them by the lattice constants a o from 52 .…”

“…This in turn dictates the temperature and strain rate dependent flow stresses at low temperatures 3,46 . In experiments [47][48][49][50][51] , the flow stress is typically fit using stress-strain rate relationships derived from kink-pair theory assuming that the Peierls potential follows the Eshelby potential; which is very close to the sinusoidal profile that our results support. The second result is that the Peierls potential height scales with the dislocation pre-logarithmic energy factor, which we can further check against experimental measurements of the kink formation energy of an isolated kink.…”

Multiscale modeling of plastic deformation of molybdenum and tungsten. III. Effects of temperature and plastic strain rate

“…However, since for ! " = 0 the activation enthalpy is equal to 2H k , the energy of a kink can be estimated with high precision from experimental data of the temperature dependence of the flow stress at low stresses [44,45] and/or from studies of internal friction [46]. Values of 2H k determined in this way for Mo and W are presented in Table 2.…”

“…! ) obtained for Mo and W from experiments in [44] and [45], respectively, are given in Table 2. Table 2: Energy of two isolated kinks deduced from experiments in [44] and [45], the shear modulus µ entering the expression for the line tension, temperature T k at which the thermal component of the yield stress in tension vanishes and corresponding values of ln Finally, it should be noted that several slip systems may operate concurrently when deforming a single crystal and thus the total plastic strain is…”

“…The temperature dependence of the yield stress in molybdenum single crystals loaded in tension was measured in [44,48,49] for three different orientations of the tensile axis and we compare here our calculations with measurements for the loading along the [149] axis, when χ = 0. In these experiments the plastic strain rate is !…”