Elastic-plastic Transition Research Articles

Energy accumulation and dissipation in metals as a result of structural-scaling transitions in a mesodefect ensemble

The localization of plastic deformation and its wave-like propagation are well-known and experimentally studied phenomena. Modern experiments carried out with highly sensitive infrared cameras have allowed us to investigate in detail energy accumulation and dissipation in the material which accompany the above process. It is found that plastic deformation occurs together with great energy accumulation in the material. The energy accumulation rate peaks on the initial stage of plastic deformation and vanishes at developed plastic flow. At the moment of elastic-plastic transition dissipative waves induced by plastic deformation localization can be generated and propagate in some metals. The given paper puts forward a theoretical model of energy accumulation and dissipation in metals under plastic deformation. The model is based on a statistical description of evolution of an ensemble of typical mesodefects (microshears). The derived constitutive equations adequately describe certain experimentally observed peculiarities of energy dissipation in metals.

Dislocation Nucleation and Source Activation during Nanoindentation Yield Points

The onset of plasticity during nanoindentation of a tungsten single crystal was examined as a function of pre-existing dislocation density. Vickers indentations were used to generate a spatially varying dislocation density, and nanoindentation was then carried out at regions of high and low dislocation densities. Even with dislocation densities as high as 1.8 × 1013 m−2, a sharp elastic-plastic transition was observed during some indentations. At lower dislocation densities, 3.5 × 109 m−2, the shear stress at the elastic plastic transition increased and approached the theoretical shear stress of the crystal. A first-order model that predicts the load required for the onset of plasticity during nanoindentation from the activation of a dislocation source within a critical volume of material, rather than homogeneous dislocation nucleation, is developed. The model correlates well with experimentally measured loads at the onset of plasticity for dislocation densities of 1012 m−2 and higher for these nanoindentation conditions.

In situ electrochemical nanoindentation: A technique for local examination of hydrogen embrittlement

Nanoindentation combined with AFM (NI-AFM) has been used to study the effect of electrochemically in situ charged hydrogen on the deformation of small volumes of nickel and copper single crystals. Hydrogen reduces the unstable elastic plastic transition load (pop-in) in nickel, but does not have any effect on copper. It has been shown that the activation energy for the onset of plasticity (dislocation nucleation) is reduced by dissolved hydrogen. This is because hydrogen reduces shear modulus and stacking fault energy in nickel, whereby the former results in hydrogen-enhanced decohesion (HEDE) and the latter in the hydrogen-enhanced plasticity (HELP) mechanism.

Nanoindentation-induced elastic–plastic transition and size effect in α-Al2O3(0001)

The mechanical properties of α-Al2O3(0001) have been investigated using the technique of nanoindentation with a Berkovich indenter. Coupled with the Hertzian contact theory, a theoretical shear strength of 28 ± 2 GPa was determined from the onset of pop-in events on load–displacement curves during loading, and the intrinsic hardness 30 ± 3 GPa was obtained by analysis of the so-called indentation size effect, based on the concept of geometrically necessary dislocations. The predicted values of the shear strength, hardness and elastic modulus are in good agreement with available experimental data. The importance of experimentally calibrating the area function over the contact depth range prior to nanoindentation tests is emphasized.

Correlations between parameters of acoustic-emission signals and corrosion damage in aluminum alloys

Results of the studies of correlations between different parameters of acoustic-emission signals and the degree of corrosion damage of an aluminum alloy exposed to two different active media are presented. The critical values of the acoustic-emission count rate and the total acoustic-emission signal that correspond to the elastic-plastic transition and subsequent active creation of microcracks are obtained for Д16M. The limiting values of the known Ivanov-Bykov criterion, which characterizes the moment when corrosion cracking starts in Д16M, are calculated. The acoustic-emission technique may be used for nondestructive testing of corrosion damage on inner surfaces of piping in poorly accessible structures.

The nano- and mesoscopic cooperative collective mechanisms of inhomogenous elastic-plastic transitions in polycrystalline TiNi shape memory alloys

The cooperative collective effects of strain-induced martensitic variant accommodation in nano- and micrograined polycrystalline TiNi shape memory alloys were discovered to form macroscopic strain-induced shearing bands—the Lüders-like deformation bands. We use the in situ electron backscattered diffraction technique and the single surface trace analysis method to unambiguously elucidate the formation and propagation of shearing bands derived from the chain effect of intergrain selective martensite habit plane variants. The macroscopic characteristics of shearing bands can be well interpreted by mesoscale crystallographic features using phenomenological crystallographic theory and Schmid’s law with a strong correlation to texture. It was also discovered that the nonlinear elastic feature in the stress-strain curve prior to the stress-strain plateau correlates to lattice/grain rotations other than martensitic variant reorientation.

Modelisation of plastic deformation of nanocrystalline solids-IA-166

Emphasis is put on the importance of analyzing properly the elastic–plastic transition in order to describe the mechanical properties of nanograined polycrystals. Specific constraints resulting from the imposed small-length scale, and of the shape of the specimens are discussed. The need for new paradigms adapted to this specific situation is discussed.

Nanoindentation studies on Ti–Zr–Ni bulk quasicrystalline intermetallics

Polycrystalline Ti40Zr40Ni20 bulk quasicrystals are used for microindentation and nanoindentation studies. The microindentation test gives the Meyer's hardness as 6.22 ± 0.16 GPa, but it does not exhibit any indentation size effect (ISE) nor any cracking, even at a higher 200g load. From nanoindentation tests, the reduced Young's modulus (E r) was found to vary from 115 to 124 GPa. Assuming suitable elastic constants of the indenter, the average Young's modulus (E) was determined to be 127 ± 6 GPa. Nanohardness appears to vary from 8.5 to 11.2 GPa over a wide range of load, indicating an indentation size effect at a nanoscale. The discontinuities in the plot (known as pop-ins or strain bursts) of P–h data, obtained from nanoindentation tests, are observed frequently and these are correlated with shear bands, which are observed under atomic force microscopy (AFM). The first pop-ins, observed in the load range 50–100 µN, led to the estimation of maximum shear stress as ∼8 GPa, close to the theoretical shear strength (∼E/25), and estimation of the energy as 0.67 eV/atom, which is required for elastic–plastic transition of this type of material. Thus, the pop-ins has been attributed to elastic–plastic transition during nanoindentation tests.

Formation of surface roughness on nanocrystalline aluminium samples under straining by molecular dynamics studies

The surface roughening of nanocrystalline aluminium samples was investigated by molecular dynamics simulations. Attention was focused on the fact that roughness increases with the grain size and the strain. The elastic–plastic transition was found at around 3.5% strain and a reverse Hall–Petch effect was observed under straining conditions. Then, different strain distributions in grains and grain boundaries at the sample surface were highlighted, yielding to the formation of local roughness. Finally, a linear relationship between the magnitude of roughness and the out-of-plane strain component was found.

Thermo elastic-plastic transition in a thin rotating disc with inclusion

Stresses for the elastic-plastic transition and fully plastic state have been derived for a thin rotating disc with shaft at different temperatures and results have been discussed and depicted graphically. It has been observed that the rotating disc with inclusion and made of compressible material requires lesser angular speed to yield at the internal surface and higher percentage increase in angular speed to become fully plastic as compare to disc made of incompressible material. With the introduction of thermal effect the rotating disc with inclusion required lesser angular speed to yield at the internal surface. Rotating disc made of compressible material with inclusion requires higher percentage increase in angular speed to become fully-plastic as compare to disc made of incompressible material. Thermal effect also increases the values of radial and circumferential stresses at the internal surface for fully-plastic state. .

Overstress Model with Tangential-Viscoplastic Strain Rate by Incorporation of Overstress Tensor

The elastoplastic stress is first defined as the stress which evolves as the actual strain rate is induced in an imaginary quasi-static process of elastoplastic deformation, while internal variables evolve with the viscoplastic strain rate calculated by the viscoplastic constitutive equation. Further, the novel variable “overstress tensor” reaching the current stress from the elastoplastic stress is defined. Then, the overstress model is extended so as to describe also the tangential viscoplastic strain rate induced by the overstress tensor component tangential to the yield surface. Furthermore, the viscoplastic strain rate due to the change of stress inside the yield surface is incorporated by adopting the concept of the subloading surface which falls within the framework of the unconventional elastoplasticity describing the smooth elastic-plastic transition fulfilling the smoothness and continuity conditions.

Mapping of the Initial Volume at the Onset of Plasticity in Nanoindentation

AbstractUnderstanding the finite volume throughout which plastic deformation begins is necessary to understand the mechanics of small-scale deformation. In indentation using spherical indenters, conventional yield criteria predict that yield starts at a point on the axis and at a depth of half the contact radius. However, Jayaweera et al (Proc. Roy. Soc. 2003)[4] concluded that yield occurs over a finite volume at least 100 nm thick. Semiconductor superlattice structures, in which the stress and thickness of individual layers can be varied and in which known internal stresses can be incorporated, open up new possibilities for investigation that cannot be achieved by varying external stresses on a homogenous specimen. We have designed samples with bands of highly strained InGaAs superlattice, which are essentially bands of low yield-stress material devoid of other metallurgical artifacts. These bands are placed at different depths in a series of samples. Spherical indenters with a range of radii were used to determine the elastic-plastic transition. The stress field from different sized indenters interacts with the low yield-stress material at different depths below the surface to map out the size of the initial yield volume.

Generation of Plastic Strain due to Constant Cyclic Loading Under Macroscopically Elastic Condition

In order to describe cyclic plasticity phenomena the plastic stretching within a yield surface has to be considered. Subloading surface model categorized in the unconventional plasticity models and describing a smooth elastic-plastic transition would be applicable to non-proportional loading process including cyclic loading behavior of materials with a smooth yield surface. In this study the model is extended for materials exhibiting a purely elastic response under a particular state of stress state, named an elastic boundary surface, whilst they also exhibit a smooth elastic-plastic transition. A damage evolution is also described by incorporating a damage function for the conventional model. The applicability of the model to the cyclic plasticity phenomena observed for the cyclic stresses below the yield stress is verified through the comparison with the experimental data.

Low-Temperature in Situ Large Strain Plasticity of Ceramic SiC Nanowires and Its Atomic-Scale Mechanism

Large strain plasticity is phenomenologically defined as the ability of a material to exhibit an exceptionally large deformation rate during mechanical deformation. It is a property that is well established for metals and alloys but is rarely observed for ceramic materials especially at low temperature ( approximately 300 K). With the reduction in dimensionality, however, unusual mechanical properties are shown by ceramic nanomaterials. In this Letter, we demonstrated unusually large strain plasticity of ceramic SiC nanowires (NWs) at temperatures close to room temperature that was directly observed in situ by a novel high-resolution transmission electron microscopy technique. The continuous plasticity of the SiC NWs is accompanied by a process of increased dislocation density at an early stage, followed by an obvious lattice distortion, and finally reaches an entire structure amorphization at the most strained region of the NW. These unusual phenomena for the SiC NWs are fundamentally important for understanding the nanoscale fracture and strain-induced band structure variation for high-temperature semiconductors. Our result may also provide useful information for further studying of nanoscale elastic-plastic and brittle-ductile transitions of ceramic materials with superplasticity.

The strain energy and shape evolution of hydrides precipitated at free surfaces of metals

The volume changes, which are associated with hydride formation involve large strain energy. In the present work, Finite Element calculations of the strain energy of hydrides formed at the free surface of a metal matrix is done as function of several variables: the shape of the hydride precipitate, the elastic anisotropy of the crystals with cubic symmetry, the elastic heterogeneity, elastic–plastic transition and the effect of an oxide layer on the surface. The effect of these variables on the kinematics of the elastic strains and on the distribution of the energy between the matrix and hydrides are used to interpret the results and to deduce the preferred shapes, those having the lowest energy. The elastic energy of half-spherical hydrides at the surface is found to be minimal in most of the elastic and elastic–plastic systems considered (due to different reasons). A plate-shaped hydride with broad face parallel to the free surface may become preferred in an elastic matrix if the hydride is significantly softer than the matrix, or its broad face is parallel to a soft crystallographic plane. The existence of a thick oxide layer over the free surface increases the total energy of the system and moderates the dependence of the energy on the shape. As the hydride grows, the preference of the spherical shape is enhanced. For the case of a plastic matrix covered with an oxide layer, the preferred growth shape changes from a sphere to an elongated precipitate perpendicular to the free surface.

Elastic–plastic transition during nanoindentation in bulk GaN crystal

Mechanical properties of a defect-free bulk GaN single crystal has been studied by nanoindentation in the C (0001) surface. Our experiments provide consistent evaluations of Young's modulus ( E = 320 GPa) measured with both Berkovich and spherical indenters. Additionally, Berkovich hardness ( H = 17 GPa) and true hardness ( H t = 25 GPa) were determined. Pop-in events are confirmed to indicate the elastic–plastic transition of the material, and give also consistent yield (maximum) shear stress, τ max = 19 GPa, for both the indenters. To achieve these precise analyses, the effective curvature of the indenter was determined by the Hertz analysis of the contact between the indenter and a diamond crystal, in addition to the Oliver–Pharr method with a standard fused quartz.

In situ electrochemical nanoindentation of a nickel (111) single crystal: hydrogen effect on pop-in behaviour

Abstract The hydrogen effect on dislocation nucleation in Ni single crystals with (111) surface orientation has been examined with the aid of a specifically designed nanoindentation set-up for in situ electrochemical experiments. The effect of the electrochemical potential on the indent load–displacement curve, especially the unstable elastic-plastic transition (pop-in), was studied in detail. The experiments allowed the exclusion of the surface from hydrogen effects. The observations showed a pop-in load drop from an average value of 250 to 100N due to in situ hydrogen charging, which is reproducibly observed within sequential hydrogen charging and discharging. Clear evidence is provided that hydrogen atoms facilitate homogeneous dislocation nucleation.

Investigation of Residual Stress by the Indentation Method with the Flat Cylindrical Indenter

Experiments and numerical simulations have been carried out to study residual stress of copper specimens by the identation method with a flat cylindrical indenter. Copper specimens were annealed at different temperatures for 35 min to obtain different residual stress levels. The experiments carried out on these specimens demonstrated the influence of residual stress on indentation behavior. The influence of annealing temperature on the elastic-plastic transition region is quite obvious. A method has been presented to determine material properties, such as elastic modulus and Poisson ratio. This method can also be applied to determine residual stress with the assumption of knowing the yield stress in advance. The advantage of this method is that it can avoid calculating the contact area. In the finite element modeling (FEM), residual stresses on copper specimens are simulated by preapplying stresses. The influence of residual stress on the indentation load-depth curves has been studied by FEM. There is good agreement between experimental and FEM numerical results. A numerical method has also been presented to determine residual stress. In addition, Mises stress and plastic distribution ahead of the indenter have also been studied to help us further understand the influence of residual stress.

Electrochemical nanoindentation: A new approach to probe hydrogen/deformation interaction

The effect of hydrogen on dislocation nucleation is examined on Ni single crystals with (1 1 1) surface orientation with a specifically designed nanoindentation setup for in situ electrochemical experiments. This is the first time that hydrogen/deformation interaction has been studied in situ on a nanoscale under realistic conditions. The effect of the electrochemical potential on the indent load–displacement curve, especially the unstable elastic plastic transition (pop-in) is studied in detail. Clear evidence is provided that hydrogen atoms facilitate homogenous dislocation nucleation.

Influence of mechanical properties on the nanoscratch behaviour of hard nanocomposite TiN/Si3N4 coatings on Si

A dual ion beam system has been used to produce hard nanocomposite TiN/Si3N4 coatings on silicon substrate. Mechanical properties have been determined by nanoindentation and tribological properties have been measured by nanoscratch testing. Nanoindentation showed that harder nanocomposites exhibited higher ratios of hardness to modulus (H/E). The dependence of the resistance to plastic deformation (H3/E2) on hardness was approximately linear. The H/E value influenced the nanoscratch behaviour. Coatings with higher H/E showed higher critical loads for elastic–plastic transition and also the total coating failure occurring in front of the probe. However, coatings with higher H/E also exhibited an unloading failure, occurring behind the probe at much lower load than the loading failure. Optimizing this stress-related unloading failure could be more important for tribological applications.