Annealed Polycrystalline Copper Research Articles

Influence of a Strong Low-Frequency Wave on the Propagation of Weak Ultrasonic Pulses in a Rod Resonator Made of Annealed Polycrystalline Copper

Influence of a Strong Low-Frequency Wave on the Propagation of Weak Ultrasonic Pulses in a Rod Resonator Made of Annealed Polycrystalline Copper

Influence of a strong low-frequency wave on the propagation of weak ultrasonic pulses in a rod resonator made of annealed polycrystalline copper

An experimental study of an influence of a strong low-frequency wave on the propagation of weak ultrasonic pulses in an acoustic resonator made of annealed polycrystalline copper has been carried out. The measurements were carried out with harmonic excitation of the resonator at its first four longitudinal modes in the range from 2 to 15 kHz, the frequency of ultrasonic pulses varied from 65 to 400 kHz. The analysis of the observed nonlinear effects was carried out within the framework of the polycrystal equation of state obtained on the basis of a modified string model of the Granato-Lucke dislocation. The values of the parameters of dissipative and reactive nonlinearity of dislocations in annealed copper are determined. Keywords: dislocation dissipative and reactive nonlinearity, polycrystalline copper, elastic waves.

Влияние сильной низкочастотной волны на распространение слабых ультразвуковых импульсов в стержневом резонаторе из отожженной поликристаллической меди

An experimental study of the effect of a strong low-frequency wave on the propagation of weak ultrasonic pulses in an acoustic resonator made of annealed polycrystalline copper has been carried out. The measurements were carried out with harmonic excitation of the resonator at its first four longitudinal modes in the range from 2 to 15 kHz, the frequency of ultrasonic pulses varied from 65 to 400 kHz. The analysis of the observed nonlinear effects was carried out within the framework of the polycrystal equation of state obtained on the basis of a modified string model of the Granato-Lucke dislocation. The values of the parameters of dissipative and reactive nonlinearity of dislocations in annealed copper are determined.

Эффекты амплитудно-зависимого внутреннего трения в низкочастотном стержневом резонаторе из отожженной поликристаллической меди

Experimental and theoretical studies of the effects of amplitude-dependent internal friction in a low-frequency rod resonator made of annealed polycrystalline copper are carried out. The results of measurements of nonlinear losses and the shift of resonant frequencies at the first three longitudinal modes of the resonator in the kilohertz frequency range from 2 to 11 kHz are presented. The analytical description of the observed effects is carried out in the framework of the rheological model and the equation of state of a microhomogeneous medium with saturation of hysteresis losses and relaxation of its visco-elastic defects. From the comparison of experimental and analytical results, the values of the effective parameters of the hysteresis nonlinearity of the annealed copper sample and their dependence on the frequency are determined.

The Wave Processes in the Media Having Inelastic Hysteresis with Saturation of The Nonlinear Loss

We study theoretically the nonlinear wave processes during excitation of a longitudinal harmonic wave in an unbounded medium and the rod resonator with inelastic hysteresis and saturation of the amplitude-dependent loss. The nonlinear-wave characteristics in such systems, namely, the amplitude-dependent loss, variation in the wave-propagation velocity, the resonant-frequency shift, and the higher-harmonic amplitudes are determined. The results of the theoretical and experimental studies of nonlinear effects in the rod resonator of annealed polycrystalline copper are compared. The effective parameters of the hysteretic nonlinearity of this metal are evaluated.

Effects of loading rate on development of pile-up during indentation creep of polycrystalline copper

Nanoindentation tests with loading rates spanning three orders of magnitude were carried out on annealed polycrystalline copper. In addition to the hardness increasing with loading rate, the formation and development of pile-up around the indentation sites were also found to be strongly rate-dependent. The development of pile-up with increased time at peak load was found to be sensitive to the prior loading rate, being much larger for tests at 50mN/s than at 0.05mN/s. The underlying mechanisms were investigated in terms of the kinetic aspects of the nucleation and interactions of dislocations, and can be well explained by the activation volume and the strain gradient plasticity theory.

Effect of deformation mode and grain size on Bauschinger behavior of annealed copper

The present investigation looks into the effect of forward deformation mode, monotonic and cyclic, but asymmetric, on the Bauschinger phenomenon of annealed polycrystalline copper in terms of different Bauschinger parameters for 2.5–18% unidirectional tensile strain. Apart from the amount of deformation, the Bauschinger phenomenon has also been looked into as a function of stress rate used for forward deformation and also the grain size. It is found that Bauschinger effect is less pronounced when the forward deformation is carried out through asymmetric cyclic loading as compared to monotonic loading. This difference in the Bauschinger effect is attributed to lower back stress developed during asymmetric cyclic loading as compared to monotonic deformation. In the present investigation very negligible influence of stress rate on Bauschinger effect has been observed. On the other hand, for both monotonic and asymmetric cyclic deformation it is observed that Bauschinger effect is more in case of fine grain size.

Nonlinear acoustic effects in a resonator with saturation of hysteretic loss

Nonlinear wave processes in an acoustic rod resonator with hysteretic nonlinearity under harmonic excitation are studied. The characteristics of longitudinal nonlinear modes of the resonator with hard and soft boundaries (amplitude-dependent loss, shifts of resonance frequencies, and amplitudes of the second and third harmonics) are determined. The comparison of the theoretical and experimental dependences of nonlinear acoustic effects in a resonator that is made of annealed polycrystalline copper is used to determine the parameters of the hysteretic nonlinearity.

Numerical investigation of indentation fatigue on polycrystalline copper

The dynamic indentation response of polycrystalline copper under cyclic fatigue loading is studied with a flat cylindrical indenter. First, a simple analytical model shows that in a purely elastic solid, the indentation depth responds with the same wavelength and frequency as the applied sinusoidal fatigue load. Next, a numerical simulation of an indentation fatigue test on an elastic-plastic solid (polycrystalline copper) is performed. Finite element analyses reveal that the mean indentation depth is controlled by both the mean of the indentation fatigue load and the load amplitude, while the amplitude of the indentation depth is independent of the mean load. Further investigations indicate that with an increased number of cycles, the increment of indentation depth reaches a constant rate. The steady state indentation depth rate is dependent not only on the amplitude of indentation fatigue load but also on the fatigue mean load, which is similar to strain accumulation during a conventional fatigue test. A parallel indentation experiment on annealed polycrystalline copper also confirms the effect of the fatigue mean load, indicating consistency with numerical results.

Study of the interaction between the indentation size effect and Hall–Petch effect with spherical indenters on annealed polycrystalline copper

Methods to obtain tensile stress–strain properties of materials from a practically non-destructive indentation test are of great industrial interest. Nanoindentation is a good candidate. However, to do this successfully, indentation size effects must be accounted for. An indentation size effect with spherical indenters has been shown for a range of fcc metals with relatively large grain size (Spary et al 2006 Phil. Mag. 86 5581–93); the increase in yield stress being proportional to the inverse cube root of indenter radius. Here, we investigate these differences further and present results for the indentation size effect with spherical indenters on Cu samples with a range of different grain sizes from 1 µm to single crystal. The important experimental control parameter, of the relative size of the indentation compared with the grain size, is also explored by using indenters of different radii on the different grain sized samples. When the grain size, d, is less than 6 times the radius of the projected contact area, a, a Hall–Petch-like behaviour is observed superimposed on the indentation size effect. For d > 6a the indentation size effect dominates. The two effects may be combined by addition in quadrature. This new parametric function is able to predict the indentation pressure in annealed copper given input values of indenter radius and grain size.

The Identation Size Effect and Hall-Petch Behaviour of Annealed Polycrystalline Copper

AbstractMethods to obtain tensile stress-strain properties of materials from a practically non-destructive indentation test are of great industrial interest. However, to do this successfully, indentation size effects must be accounted for. Many indentation size effects, such as strain gradient plasticity and micro-pillar experiments [1], show a size dependence proportional to the inverse square root of a length scale, in common with Hall-Petch behavior. Recently, however, the indentation size effect from small radius spherical indenters has been shown, for a range of fcc metals, not to follow a Hall-Petch-like relationship but to be proportional to the inverse cube root of indenter radius [2]. Here, we investigate these differences further and present results for the indentation size effect with spherical indenters on Cu samples that have been engineered to have different grain sizes. The important experimental control parameter of the relative size of the indentation compared to the grain size is also explored since the cross over from grains significantly smaller than the contact radius to grains significantly larger than the contact radius occurs at different length scales in each sample. A thorough understanding of the various length-scale effects in the different test methods (e.g. the indentation size effect and grain size effect in indentation), is essential if a relationship, robust enough for industrial application, is to be defined to obtain tensile properties from an essentially non-destructive indentation test.

Evolution of texture in electrodeposited Ni/Cu layered nanostructures

The objective of this research was to study the evolution of crystallographic texture in electrodeposited Ni/Cu laminated nanostructures. Thick films (14-40 µm) consisting of nickel and copper nanolayers (7-27 nm) were fabricated on annealed polycrystalline copper substrates using an electodeposition technique. The microstructure of the deposits was varied by changing the deposition time of each layer and the electrolyte temperature. X-ray diffraction, transmission electron microscopy and scanning electron microscopy were applied to characterize the deposits. Three microstructural behaviours were observed. The deposit with a very fine bilayer thickness (7 nm) was composed of coherent layers parallel to the substrate surface. This deposit replicated the cube orientation of the substrate and showed a strong ⟨100⟩ texture throughout the thickness of the deposit. An increase in the bilayer thickness (17 and 27 nm) caused a change in the texture from ⟨100⟩ on the substrate side to ⟨111⟩ on the solution side. This change in texture is suggested to be associated with a change in the deposition front orientation from {100} to {110} and the subsequent twinning of the cube-oriented crystals. A decrease in the electrolyte temperature inhibited faceting of the interface and hence no twinning was observed.

Strain Hardening around Spherical Indentations

Plastic strain distribution around spherical indentations in annealed polycrystalline copper has been determined by Vickers microhardness mapping of carefully prepared median plane sections through the indentations and comparing the microhardness values with those of small cylinders of the annealed copper which had been uniaxially compressed to different plastic natural strains (i.e. true strains, defined as ln(l0/l)) in the range of 0.01 to 0.97. The spherical indentations were of dimensionless sizes a/R in the range of 0.08 to 0.85, where a and R are the radii of contact and indenter, respectively. It is shown that the magnitude of the equivalent maximum plastic natural strain εmax increases nonlinearly with increasing a/R and reaches a value of 0.72 for an indentation of a/R = 0.85. The measured values of the εmax are considerably higher than the `representative' strain εr values predicted by the empirical formula εr = 0.2a/R. The implications of these findings have been discussed in relation to determining the uniaxial flow stress versus strain curve of a power-law hardening solid using the spherical indentation test.

Subsurface strain distribution around Vickers hardness indentations in annealed polycrystalline copper

Subsurface strain distribution around relatively large Vickers diamond indentations of a diagonal length of 2.003 mm in annealed copper has been determined by making a survey of Vickers hardness, using a low indenter load of 50 gf, of a sectioned plane which was normal to the specimen surface and an indentation edge and which was close to the median plane containing the indentation tip. The maximum strain hardening, corresponding to an estimated equivalent strain of between 0.25 and 0.36, occurs at the tip of indentation. It is shown that the measured strain distribution is distinctly different from the strain distribution that would occur if the displaced material were to flow out uniformly along radial directions. A discussion of the equivalent strain introduced within the sample by a Vickers indentation and the ratio of Vickers hardness to the uniaxial flow stress is also given. It is argued that the often-quoted value of 0.08 as the equivalent strain for a Vickers indentation may not be as unique as previously thought and may indeed be quite misleading. It is also shown that even for a metal, such as the annealed copper used in this work, the ratio of Vickers hardness to the prior flow stress may vary in the range from 2.8 to 11.5, depending upon the prior strain in the specimen.

Cyclic sofening in annealed polycrystalline copper: Polak, J., Obrtlik, K., Hajek, M. and Vasek, A. Mater. Sci. Eng. A 15 July 1992 A154, (2), L15–L18

Cyclic sofening in annealed polycrystalline copper: Polak, J., Obrtlik, K., Hajek, M. and Vasek, A. Mater. Sci. Eng. A 15 July 1992 A154, (2), L15–L18

On non-proportional infinitesimal plastic deformation after finite plastic prestraining and partial unloading

E xperimental data from combined tension-torsion loading of thin-walled tubes of annealed polycrystalline copper subjected to loading, partial unloading, and then loading in a different direction are presented. Special attention is focused on the direction of the plastic strain increment, experimental values of which are compared with predicted values from the Ziegler and Mroz kinematic hardening models, and endochronic theory. The back stress terms in the above mentioned three constitutive models are calculated using the entire deformation history of more than 10% strain in extension (or 15% in shear), followed by partial unloading, and then loading in torsion (or tension). Thus, the main objective of the study is to investigate the effect of finite deformation on subsequent infinitesimal deformation due to 180° and 90° changes in loading paths in the tension-torsion loading space. Among the three constitutive equations used for comparison, the Mroz model is shown to predict the direction of the plastic strain increment closest to the experimental results.

Large deformation in polycrystalline copper under combined tension-torsion, loading, unloading and reloading or reverse loading: A study of two incremental theories of plasticity

Experimental data from combined tension-torsion of thin walled tubes of annealed polycrystalline copper subjected to various non-proportionate loading, unloading and reverse loading paths are presented. The measurements are compared with predicted values from classical incremental theory of plasticity in terms of true stress and true strain and a recently developed incremental theory of plasticity by Bell in terms of nominal stress and nominal strain. These experimental data reveal that the plastic strain produced by the various proportionate and non-proportionate loading, unloading and reverse loading paths are in better agreement with Bell's incremental theory of plasticity as compared to classical incremental theory.

A study of two incremental theories of plasticity through large deformation in polycrystalline copper

Experimental data from combined tension-torsion of thin-walled annealed poly-crystalline copper tubes are compared with Prandtl-Reuss classical incremental theory and Bell's finite deformation incremental theory. In the experiment, the loads are prescribed and the loading paths include proportionate and nonproportionate tension and torsion. One of the main differences between the two theories is that the former is in terms of true stress and strain, whereas the latter is in nominal stress and nominal strain form. Also in one case, the equivalent stress and equivalent strain curves are approximated by a general power relation, whereas in the other case, the relation is parabolic. The results obtained in this investigation suggest that the finite deformation incremental theory in terms of nominal stress and nominal strain predicts the material behavior better than the classical incremental theory.

Sponge-like blisters on copper by H+-ion implantation at ambient temperatures

325 keV H+-ion implantation was done in annealed polycrystalline copper specimens in the fluence range 2.2-8.4*1018 ions cm-2 at ambient temperature. SEM examination of the surface topography showed the occurrence of blistering at 5.2*1018 ions cm-2. Blisters were observed to grow with increasing dose. At 8.4*1018 ions cm-2 severe sponginess localised only to blister skins, in contrast to the porous surface features developed on the whole implanted region by the high temperature (>or approximately=0.5 Tm) implantations, was observed. The present observations are explained in terms of the growth of bubbles contained within the blister skin at its ambient temperature.

High fluence hydrogen implantation in copper: Blistering and grain boundary movement

Abstract Annealed polycrystalline copper samples are implanted with 325 keV H+ -ions at ambient temperature for total fluences of 2.2–8.4 × 1018 ions/cm2, and are examined using SEM and optical microscope. The critical fluence for blistering is about 5.2 × 1018 ions/cm2. The observations reported are (i) preferential decoration of grain boundaries with elongated blisters which have a tendency of interconnecting each other, (ii) irradiation induced grain boundary movement, (iii) onset of blistering only on few grains and tendency of coalescence, at the critical dose, (iv) spongy blister skins, and (v) simultaneous occurrence of blister exfoliation from the top and from the periphery. The observation (i) is attributed to preferential nucleation of gas bubbles along the grain boundaries and their successive coalescence; (ii) and (iii) are assigned to partial channelling; (iv) is understood to be a consequence of the growth and the coalescence of the bubbles within the skin: and (v) is considered to be the be...