Elastic‐Plastic Transition in Copper Crystals as Determined by an Etch‐Pit Technique
01 Oct 1961-Journal of Applied Physics (American Institute of PhysicsAIP)-Vol. 32, Iss: 10, pp 1815-1820
TL;DR: In this paper, the authors used pure bending moment (Pfister's moment) to stress a set of coarse-grained copper (99.999%) crystals with a dislocation density of 50/mm2 and found that the resolved stress necessary to move grown-in dislocations was about 4 g/mm 2.
Abstract: Copper (99.999%) crystals with a dislocation density of 50/mm2 have been prepared. These crystals were stressed by applying a pure bending moment, and they were etched with a dislocation etch either before and after or while the stress was applied. The motion of dislocations was determined by observing the size and nature of the dislocation etch pits. The resolved stress necessary to move grown‐in dislocations was about 4 g/mm2. Examples of dislocation motion under stress, then return motion when the stress was removed, and of multiple motion under stress were observed. Multiplication of dislocations occurred at a resolved stress of about 18 g/mm2. The observed phenomena are discussed in terms of simple dislocation theory.
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TL;DR: In this paper, the authors discuss and review connections between classical micro-plasticity and intermittent flow across all length scales, with the aim of highlighting the value of miniaturized testing as a means to unravel this very early regime of bulk plasticity.
115 citations
TL;DR: In this article, the third-order elastic constants of copper were determined at 295, 77, and 4.2 K from measurements of the change in the velocity of sound accompanying the application of a uniaxial stress.
Abstract: The six third-order elastic constants of copper were determined at 295, 77, and 4.2\ifmmode^\circ\else\textdegree\fi{}K from measurements of the change in the velocity of sound accompanying the application of a uniaxial stress. Irradiation with neutrons or $\ensuremath{\gamma}$ rays as well as dilute alloy additions was used in an attempt to pin the dislocations so that their effects could be eliminated. It was found that dislocation still contributed to the measurements even though the experimental data were linear and reproducible and showed no changes in ultrasonic attenuation with stress. The ultimate criterion for determining when the dislocation effects had been eliminated was the comparison of the pressure derivatives of the second-order elastic constants calculated from the uniaxial stress measurements with the pressure derivatives obtained by direct measurement. Only the neutron-irradiated sample passed this test, and all the results presented were obtained on this sample. At room temperature the third-order elastic constants agree with those obtained by Hiki and Granato. At 4.2\ifmmode^\circ\else\textdegree\fi{}K, the results are ${C}_{111}=\ensuremath{-}20\ifmmode\pm\else\textpm\fi{}2$, ${C}_{112}=\ensuremath{-}12\ifmmode\pm\else\textpm\fi{}1.5$, ${C}_{123}=\ensuremath{-}5\ifmmode\pm\else\textpm\fi{}1.5$, ${C}_{144}=\ensuremath{-}1.3\ifmmode\pm\else\textpm\fi{}0.2$, ${C}_{166}=\ensuremath{-}7.1\ifmmode\pm\else\textpm\fi{}0.25$, and ${C}_{456}=+0.25\ifmmode\pm\else\textpm\fi{}0.08{10}^{12}$ dyn/${\mathrm{cm}}^{2}$. It should be noted that these results do not satisfy the Cauchy relations ${C}_{112}={C}_{166}$ and ${C}_{123}={C}_{144}={C}_{456}$. A value of the Gr\"uneisen $\ensuremath{\gamma}$ in the limit of low temperatures was calculated and found to be within the experimental error of the value obtained from thermal-expansion measurements.
83 citations
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TL;DR: In this paper, the authors discuss and review connections between classical micro-plasticity and intermittent flow across all length scales, with the aim of highlighting the value of miniaturized testing as a means to unravel this very early regime of bulk plasticity.
Abstract: Prior to macroscopic yielding, most materials undergo a regime of plastic activity that cannot be resolved in conventional bulk deformation experiments. In this pre-yield, or micro-plastic regime, it is the initial three dimensional defect network that is probed and the intermittently evolving microstructure admits small increments in plastic strain. By reducing the sample size, this intermittent activity becomes increasingly apparent and can be routinely observed through small-scale mechanical testing. In some cases, the intermittent activity was shown to exhibit aspects of scale-free behavior, prompting a paradigm shift away from traditional microstructure-dependent unit mechanisms that may be associated with a well defined length and stress scale. In this article, we discuss and review connections between classical micro-plasticity and intermittent flow across all length scales, with the aim of highlighting the value of miniaturized testing as a means to unravel this very early regime of bulk plasticity.
82 citations
Cites background from "Elastic‐Plastic Transition in Coppe..."
...5]. Interestingly, this pre-yield micro-plastic activity does not change the yield strength noticeably and 4 it is also said to not alter the internal length scales of the pre-existing microstructure [16, 17, 18]. Being less direct and more difficult to verify than a definition based on deviations from elasticity, this microstructural definition relies on knowing, and being able to trace the properties of a p...
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...ues for the so -called micro-yield stresses obtained from high resolution (~nm) extensometry, etch-pit studies, or x-ray topography on bulk single crystals are ~2 MPa (Mo, W, Fe, [19]), ~1-4 MPa (Cu, [16, 20]), ~0.2-0.5 MPa (Zn, [21, 22]), ~ 0.5 MPa (Be, [23]), and ~1.5 MPa (Cu, [24]), ~2 MPa 5 (Al, [25]), ~2-30 MPa (Fe, [19, 25, 26]) was found for polycrystals. These values are thus distinctly lower than...
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TL;DR: In this article, the dislocation density and arrangement in the crystals were determined before, during, and after the deformations using an etch pit technique, and the yield stress was determined by the stress necessary to break the gliding dislocations through impurity atom barriers.
Abstract: 99.999% copper crystals were deformed in tension using an Instron tensile tester, and the dislocation density and arrangement in the crystals were determined before, during, and after the deformations using an etch pit technique. For crystals of low initial dislocation density, it was found that a large amount of dislocation multiplication occurred prior to yielding. Experimental relationships of dislocation density versus applied stress and versus shear strain were determined. It was found that the yield stress was not related to the initial dislocation density or arrangement. The yield stress was postulated to be determined by the stress necessary to break the gliding dislocations through impurity atom barriers in the crystal.
79 citations
TL;DR: The characteristic motion of dislocations in copper single crystals of low dislocation density has been studied by etch pitting, especially near yield stress Dislocations are presumed to be locked at each position in as-annealed crystals as mentioned in this paper.
Abstract: The characteristic motion of dislocations in copper single crystals of low dislocation density has been studied by etch pitting, especially near yield stress Dislocations are presumed to be locked at each position in as-annealed crystals The motion of dislocations due to the application of stress is composed of three processes: (1) unlocking from the as-annealed position, (2) moving at a high speed, eg 400 cm/sec at a stress of 22 g/mm 2 , and (3) stopping at a certain final position depending on the stress level below yield stress It is considered tentatively that the locking is due to discrete pinning by impurity atoms, and the main obstacles to the dislocation motion are thought to be other locked dislocations From quantitative studies of each process a possible mechanism of yielding of copper crystals is suggested
74 citations
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1,275 citations
TL;DR: In this article, the equilibrium shape of a dislocation segment between two pinning points in the same glide plane is calculated using an energy per unit length, which is a function only of the angle between the Burgers vector and the tangent to the dislocation.
Abstract: The equilibrium shape of a dislocation segment between two pinning points in the same glide plane is calculated. The assumption is made that the dependence of the dislocation self-energy on the geometry of the dislocation line can be expressed by using an energy per unit length, $E$, which is a function only of the angle, $\ensuremath{\theta}$, between the Burgers vector and the tangent to the dislocation. Only glide of the dislocation, not climb, is considered. The results obtained are compared with those for elastically isotropic crystals. It is found that the character of the dislocation shape is altered considerably if $E+\frac{{d}^{2}E}{d{\ensuremath{\theta}}^{2}}$ can be negative. It is suggested that the change in sign of this quantity is associated with diffusionless phase changes.
257 citations
TL;DR: A modification of an etch discovered by Lovell and Wernick has been shown to be a reliable means of revealing dislocations as etch pits on (111) faces of copper crystals as mentioned in this paper.
Abstract: A modification of an etch discovered by Lovell and Wernick has been shown to be a reliable means of revealing dislocations as etch pits on (111) faces of copper crystals. The etch has been employed to study dislocation distributions in as‐grown, annealed, and deformed crystals.A high‐temperature anneal is found to lower the dislocation density of melt‐grown crystals. A ``double‐etch'' technique is employed to observe the motion of dislocations, and to show that the dislocations initially present in these crystals are mobile at low stresses. Subboundaries are numerous in these crystals and are found capable of hindering dislocation movement. Observations of the dislocation structure of crystals deformed in bending and in tension are reported, including the appearance of ``glide polygonization'' after room‐temperature deformation.
119 citations
TL;DR: In this paper, a possible mechanism for the development of pits at dislocations in copper by etching in solution is presented, and experiments are described which may substantiate this mechanism.
Abstract: A possible mechanism for the development of etch pits at dislocations in copper by etching in solution is presented, and experiments are described which may substantiate this mechanism. Etchants which will develop pits at clean dislocations on the (111), (100), and (110) faces of copper are described. These etchants are capable of distinguishing between clean dislocations and dislocations with a ``Cottrell atmosphere'' in 99.999% copper. Clean edge and screw dislocations can also be differentiated with these etchants. Some observations concerning the relation of facet structure, developed by etching, to the dislocation structure of the crystal are reported.
115 citations