Showing papers in "Philosophical Magazine in 2002"
TL;DR: In this article, the authors introduce the concept of ideal hardness and strength, which relates the elastic properties of materials to the corresponding mechanical characteristics, the concepts that are less unambiguously determined and that depend on the conditions of measurements.
Abstract: Analysis of correlations between various physical properties of solids provides a formulation of simple criteria applicable to the search for new superhard materials. The prospects for the synthesis of new substances with the key elastic moduli, whose values approach or even exceed those of diamond are also discussed. We introduce the concept of ideal hardness and strength, which relates the elastic properties of materials to the corresponding mechanical characteristics, the concepts that are less unambiguously determined and that depend on the conditions of measurements. The control of material nanostructure makes it possible to approach the ideal hardness. The formulation of trends interrelating physical properties is expected to allow an essential guidance in the synthesis of new classes of superhard materials.
377 citations
TL;DR: In this article, a model based on the glide of single dislocations is developed to interpret the increasing strength of multilayered metals with decreasing layer thickness when the Hall-Petch model is no longer applicable.
Abstract: A breakdown from the dislocation-pile-up-based Hall-Petch model is typically observed in metallic multilayers when the layer thickness (one half of the bilayer period) is of the order of a few tens of nanometres. The multilayer strength, however, continues to increase with decreasing layer thickness to a few nanometres. A model based on the glide of single dislocations is developed to interpret the increasing strength of multilayered metals with decreasing layer thickness when the Hall-Petch model is no longer applicable. The model is built on the hypothesis that plastic flow is initially confined to one layer and occurs by the motion of single ‘hairpin’ dislocation loops that deposit misfit-type dislocations at the interface and transfer load to the other, elastically deforming layer. The composite yield occurs when slip is eventually transmitted across the interface, overcoming an additional resistance from the interface dislocation arrays. In a lower-bound estimate, the stress for the initial ...
276 citations
TL;DR: In this paper, the cyclic deformation behavior of ultrafine-grained (UFG) copper produced by equal-channel angular pressing was investigated and the parameters governing cyclic softening and cyclic grain coarsening were investigated.
Abstract: The cyclic deformation behaviour of ultrafine-grained (UFG) copper produced by equal-channel angular pressing was investigated. Special attention was paid to the parameters governing cyclic softening and cyclic grain coarsening. UFG copper shows significant cyclic softening for the tests performed at intermediate plastic strain amplitudes Δep1/2, that is in the range 2 × 10−4 ≤ Δepl/2 ≤ 1.0 × 10−3. Within this range, the cyclic softening as well as the intensity of grain coarsening increase with decreasing plastic strain amplitude. By contrast, under stress control, corresponding to a plastic strain amplitude range 2.4 × 10−5 ≤ Δepl/2 ≤ 1.2 × 10−4, cyclic softening as well as the intensity of grain coarsening decrease with decreasing plastic strain amplitude. Furthermore, cyclic softening and grain coarsening were also found to be enhanced by decreasing the deformation rate (and thus increasing the test time) and/or by increasing the temperature. These findings indicate that the responsible micro...
221 citations
TL;DR: In this article, the slip behavior in coherent and semicoherent metallic bilayer composites is examined by atomic simulation in the Cu/Ni and Cu/Ag systems and it is shown that the application of stresses needed for glide dislocations to cross the interface or to escape from the interface exacerbates the nonlinearities in the elastic response of the system.
Abstract: The slip behaviour in coherent and semicoherent metallic bilayer composites is examined by atomic simulation in the Cu/Ni and Cu/Ag systems. The coherent interface in Cu/Ni, although energetically unfavourable relative to the semicoherent interface in thick layers, reveals several interesting phenomena. Linear elastic predictions of lattice strains to achieve coherency (removing the 2.7% lattice mismatch) are found not to satisfy equilibrium. The cause is nonlinearity in the elastic response. The application of stresses needed for glide dislocations to cross the interface or to escape from the interface exacerbates the nonlinearities in the elastic response of the system. Koehler forces, arising from elastic mismatch, are in some cases observed to have the wrong sign relative to linear elastic predictions. Core structures of misfit dislocations in semicoherent interfaces are observed to be quite different in the cube-on-cube oriented Cu/Ni and Cu/Ag systems with interfaces parallel to (010). In t...
215 citations
TL;DR: In this paper, the structure of shear bands with voids was compared with that of undeformed regions of a metallic glass, and it was shown that the coalescence is thermo-dynamically possible.
Abstract: We have compared the structure of shear bands with that of undeformed regions of a metallic glass. Using quantitative high-resolution electron microscopy, we observed void-like defects, approximately 1 nm in diameter and at a concentration of one in 100nm3, which are generated as a result of plastic deformation in the shear bands. These defects may result from the coalescence of excess free volume upon cessation of the flow. By comparing the free energy of the shear band containing uniformly distributed free volume with that of the relaxed shear band with voids present, we show that the coalescence is thermo-dynamically possible.
196 citations
TL;DR: In this paper, the flow and fracture behavior of a Zr-Ti-Ni-Cu-Be bulk amorphous metal have been determined in tension and compression at room temperature with levels of superimposed hydrostatic pressure ranging from 0.1 to 700 MPa.
Abstract: The flow and fracture behaviour of a Zr-Ti-Ni-Cu-Be bulk amorphous metal have been determined in tension and compression at room temperature with levels of superimposed hydrostatic pressure ranging from 0.1 to 700 MPa. Metallographically polished cylindrical specimens tested in uniaxial tension and compression were utilized in the high pressure tests, while polished cylindrical torsion specimens were tested at 0.1 MPa (i.e. atmospheric pressure) in order to approach conditions of pure shear. All the tension and torsion tests, regardless of the level of superimposed pressure, exhibited linear elastic failure, as did the compression tests conducted with low levels (e.g. less than 450 MPa) of pressure. At the highest pressures (i.e. 450 MPa or higher), the compression tests exhibited elastic-perfectly plastic behaviour and an increase in the compressive elongation to fracture. The flow stress and fracture stress were not significantly affected by the superposition of pressure as failure occurred in ...
176 citations
TL;DR: In this article, a new high-temperature stage for small-scale mechanical property testing is described, which allows the determination of the load-penetration curve of a diamond tip in a temperature range extending from room temperature to 400°C.
Abstract: This paper describes a new high-temperature stage for small-scale mechanical property testing. This allows the determination of the load-penetration curve of a diamond tip in a temperature range extending from room temperature to 400°C. Both sample and indenter can be heated separately. Indentation curves show that very low thermal drift can be achieved. Nanoindentation results are presented for gold, soda—lime glass, fused silica and a polyimide and compared with existing microscale and bulk mechanical property data where available. Results from fused silica show that its mechanical properties exhibit a completely different temperature dependence from those of soda-lime glass, as expected since fused silica is an anomalous glass.
158 citations
TL;DR: In this paper, several relationships that relate features of indentation loading and unloading curves to the hardness, the elastic modulus and the work of conical indentation in elastic-plastic solids with various angles are investigated.
Abstract: Using dimensional analysis and finite-element calculations, several relationships that relate features of indentation loading and unloading curves to the hardness, the elastic modulus and the work of indentation are extended to conical indentation in elastic-plastic solids with various angles. These relationships provide new insights into indentation measurements. They may also be useful to the interpretation of results obtained from instrumented indentation experiments.
154 citations
TL;DR: In this article, a combination of molecular dynamics simulations and a line tension (LT) model was applied to identify the geometrical parameters that are relevant in the description of this process.
Abstract: We investigate the resistance on the glide of lattice dislocations between adjacent crystal grains due to the presence of a grain boundary (GB). Applying a combination of molecular dynamics (MD) simulations and a line tension (LT) model we identify the geometrical parameters that are relevant in the description of this process. In the MD simulations we observe slip transmission of dislocation loops nucleated from a crack tip near a series of pure tilt GBs in Ni. The results are rationalized in terms of a LT model for the activation of a Frank-Read source in the presence of a GB. It is found that the slip transmission resistance is a function of only three variables: firstly, the ratio of resolved stress on the incoming slip system to that on the outgoing slip system, secondly, the magnitude of any residual Burgers vector content left in the GB and, thirdly, the angle between the traces of the incoming and outgoing slip planes in the GB plane. Comparison with the MD simulations and experimental da...
126 citations
TL;DR: In this paper, the authors discuss the nucleation and growth of deformation twins, assuming that twinning occurs via the double-cross-slip mechanism first postulated by Pirouz for twinning in silicon.
Abstract: The nucleation and growth of deformation twins are discussed, assuming that twinning occurs via the double-cross-slip mechanism first postulated by Pirouz for twinning in silicon. The dislocation energetics in this model are described in detail. In all cases, dislocation dissociation occurs and gives rise to a stationary partial and a twinning partial; twin growth involves the twinning partial undergoing double cross-slip. We discuss three specific geometries: firstly, the dissociation of a perfect dislocation into three collinear partials of equal Burgers vectors, which describes basal twinning in sapphire and twinning in bcc metals; secondly, the dissociation of a perfect dislocation into two collinear partials with different Burgers vectors, which describes rhombohedral twinning in sapphire; thirdly, the dissociation of a perfect dislocation into two non-collinear Shockley partials, which is used to describe twinning in silicon. Finally, the double-cross-slip mechanism readily explains the for...
114 citations
TL;DR: In this paper, a solid mechanics analysis of the hydrogen solute interaction with material elastoplasticity demonstrates that localization of the deformation in the form of bands of intense shear can occur on the macroscale.
Abstract: In-situ deformation studies in a transmission electron microscope equipped with an environmental cell have shown that solute hydrogen increases the velocity of dislocations, decreases the stacking-fault energy, and increases the stability of edge character dislocations. Theoretical modelling has established that the hydrogen atmospheres formed at dislocations through the elastic interaction cause a change in the stress field of the dislocation-hydrogen complex in such a manner as to reduce the interaction energy between it and other elastic obstacles. Consequently, solute hydrogen increases the mobility of dislocations, which will be localized to regions of high hydrogen concentration. On the basis of this material softening on the microscale, a solid mechanics analysis of the hydrogen solute interaction with material elastoplasticity demonstrates that localization of the deformation in the form of bands of intense shear can occur on the macroscale. Thus, the present combined experimental and num...
TL;DR: Quasistatic microindentation hardness studies of specimens of high-purity polycrystals and single crystals of copper and aluminium have been made at room temperature using a Vickers diamond and a t...
Abstract: Quasistatic microindentation hardness studies of specimens of high-purity polycrystals and single crystals of copper and aluminium have been made at room temperature using a Vickers diamond and a t...
TL;DR: In this paper, the authors examined the time-dependent deformation and flow for an axisymmetric indenter (flat-ended, spherical or conical indenter) penetrating into a viscoelastic body.
Abstract: The time-dependent deformation and flow are examined for an axisymmetric indenter (flat-ended, spherical or conical indenter) penetrating into a viscoelastic body. The analytical solutions for elastic contact combined with the Boltzmann hereditary integral lead to the constitutive equations for linear viscoelastic indentation. Some numerical analyses for simple models of viscoelastic liquid and solid are conducted to gain further rheological insights into indentation viscoelasticity. Indentation techniques provide the most efficient microprobes and nanoprobes for examining the time-dependent viscoelastic deformation and flow; testing specimens with extremely small dimensions and thin films with no special preparation, as well as compressive loading makes the test easier at elevated temperatures and in hostile environments.
TL;DR: In this article, a new plastic flow mechanism observed by in-situ transmission electron microscopy deformation on Cu-Nb continuous multifilamentary nanostructured composites is presented.
Abstract: The fundamental mechanisms of the deformation of heavily deformed multiphase materials are not clearly understood despite the vast literature and the amount of data on this subject. This paper presents a new plastic flow mechanism observed by in-situ transmission electron microscopy deformation on Cu-Nb continuous multifilamentary nanostructured composites. The observed mechanism is interpreted in terms of dislocation loops nucleating in closely spaced parallel planes in the Cu channels. This behaviour explains many previous observations made on such composites such as the semicoherency of the interface and the 4° disorientation between the two phases. The modelling of the loop mechanism predicts the strength of the Cu-Nb nanocomposites. The very good agreement between the model and the experimental data suggests that the assumptions based on the in-situ observations are valid. The basic aspects of co-deformation of fcc-bcc nanostructured systems are reviewed in this new context.
TL;DR: In this paper, a finite-strain-continuum thermomechanical approach is applied to the problem of temperature-induced martensitic transformation in elastoplastic materials.
Abstract: A finite-strain-continuum thermomechanical approach is applied to the problem of temperature-induced martensitic transformation in elastoplastic materials. The key issue is to determine the transformation-induced stress and plastic strain fields and their effect on the thermodynamics and kinetics of transformation. The problems of appearance and growth of a temperature-induced rectangular martensitic unit in an austenitic matrix in both bulk and near-free-surface environments are formulated, solved and analysed. Very complex and heterogeneous stress-strain fields in the austenite and martensite phases and their non-monotonic time variation are predicted. Plastic shear strain at some points can reach 60∼ and, after an elastic growth stage, change sign and vary by 40∼. The interface velocity as a function of temperature and interface position is calculated. After the appearance of a martensitic particle, transformation work, which is the only variable part of the interface driving force, decreases ...
TL;DR: In this article, an equivalent continuum is defined for dynamically deforming atomistic particle systems treated with concepts of molecular dynamics, and the equivalence of the continuum to discrete atomic systems includes preservation of linear and angular momenta, conservation of internal, external and inertial work rates and conservation of mass.
Abstract: An equivalent continuum is defined for dynamically deforming atomistic particle systems treated with concepts of molecular dynamics. The discrete particle systems considered exhibit micropolar interatomic interactions which involve both central interatomic forces and interatomic moments. The equivalence of the continuum to discrete atomic systems includes, firstly, preservation of linear and angular momenta, secondly, conservation of internal, external and inertial work rates and, thirdly, conservation of mass. This equivalence is achieved through the definition of, firstly, continuum stress and couple stress fields that make the same contribution to motion and deformation as internal interatomic forces and couples, secondly, continuum fields of body force, body moment, surface traction and surface moment that make the same contribution to motion and deformation as external forces and moments on the atoms, thirdly, a continuum deformation field that is work conjugate to the continuum kinetic fiel...
TL;DR: In this article, the electronic structure and bonding of ideal hydroxyapatite and the substitution of Ca by Zn2+ were investigated and a self-consistent embedded-cluster density functional calculation was performed.
Abstract: First-principles self-consistent embedded-cluster density functional calculations were performed to investigate the electronic structure and bonding of ideal hydroxyapatite and the substitution of Ca by Zn2+. Atomistic simulations were carried out to obtain estimates of local geometry and lattice strain associated with fourfold, fivefold and sixfold Zn sites. Mulliken population analysis of density and bond distributions as well as electrostatic potential maps and approximate Zn K-edge absorption spectra were utilized to characterize this bone analogue material.
TL;DR: In this paper, equal-channel angular pressing (ECAP) was used to refine the grain sizes of pure Al and an Al 3 wt% Mg alloy containing minor additions of either Sc or Zr.
Abstract: Equal-channel angular pressing (ECAP) was used to refine the grain sizes of pure Al and an Al–3 wt% Mg alloy containing minor additions of either Sc or Zr. Following ECAP, the grain sizes were in the ultrafine submicrometre range. Diffusion couples were prepared from the fine-grained material produced by ECAP and from the coarse-grained material without ECAP and these couples were used to measure the interdiffusion coefficients for Mg in an Al lattice. The results show the interdiffusion coefficient is larger in the fine-grained material and the experimental data from this couple agree with predictions from molecular dynamic simulations using the embedded-atom method. An activation energy of about 87 kJ mol-1 is estimated for grain-boundary diffusion of Mg in Al where this value is consistent with the expectations from measurements of the activation energy for lattice diffusion of Mg in Al. There is no evidence for enhanced diffusion in the boundaries produced by ECAP due, it is suggested, to the rapid equilibration of these non-equilibrium boundaries at elevated temperatures.
TL;DR: In this article, the authors investigated the mechanism of intergranular-mode fracture in hydrogen-related failure of high-strength martensitic steels and revealed that the density of point defects increased owing to straining and was more noticeable in steels with a higher manganese content.
Abstract: The mechanism of intergranular-mode fracture in hydrogen-related failure of high-strength martensitic steels has been investigated. Pronounced degradation of tensile properties appeared with increasing manganese content in a slow-elongation-rate test under concurrent hydrogen charging. The fracture mode was intergranular with tear traces along martensite lath boundaries. The tear traces disappeared and the average surface roughness decreased with increasing manganese content. Thermal desorption analysis of hydrogen charged to deformed specimens has been conducted using hydrogen as a probe of defects. It was revealed that the density of point defects increased owing to straining and was more noticeable in steels with a higher manganese content. In common with transgranular-mode fracture, the primary function of hydrogen in intergranular-mode fracture is thought to be one of stabilizing and increasing the density of strain-induced vacancies that lead to the formation of microcracks or microvoids in...
TL;DR: In this paper, an electrically conductive VC tip has been used in conjunction with ex-situ transmission electron microscopy (TEM) and micro-Raman spectroscopy to examine the behaviour of silicon during nanoindentation testing.
Abstract: An electrically conductive VC tip has been used in conjunction with ex-situ transmission electron microscopy (TEM) and micro-Raman spectroscopy to examine the behaviour of silicon during nanoindentation testing. During loading, the contact resistance is low because of the presence of the metallic β-Sn phase of silicon. During unloading, the semimetallic BC8 phase and the rhombohedral R8 phase are formed, giving rise to an increase in the contact resistance. In large indentations there is a pronounced discontinuity in both the contact resistance-depth and load-depth curves during unloading. This signifies the formation of a phase with lower electrical resistance. TEM analysis suggests that this phase is amorphous silicon formed in the centre of large indentations. The position of the discontinuity on the load-depth curve is found to depend on the unloading rate, as would be expected for the generation of an amorphous phase. Micro-Raman analysis is largely in agreement with the TEM results, but the...
TL;DR: In this paper, atomistic simulation calculations based on energy minimization techniques have been used to predict the O positional parameter of a wide range of A2B2O7 pyrochlore oxides.
Abstract: Atomistic simulation calculations based on energy minimization techniques have been used to predict the O positional parameter of a wide range of A2B2O7 pyrochlore oxides. Cations studied range from Lu3+ to La3+ on the A site and Ti4+ to Pb4+ on the B site. In all cases the model included a specific predicted degree of disorder without which it was not possible to reproduce experimental values accurately. However, the extent of disorder invoked was dependent on the specific A and B cations involved, with Gd2Ti2O7 exhibiting the lowest and Gd2Pb2O7 the highest degree of disorder.
TL;DR: In this article, a procedure to obtain the elasto-plastic mechanical properties of strain-hardening materials from indentation tests, based on dimensional analysis and finite-element techniques, is proposed.
Abstract: A procedure to obtain the elasto-plastic mechanical properties of strain-hardening materials from indentation tests, based on dimensional analysis and finite-element techniques, is proposed. The method is applicable to homogeneous materials and to coatings deposited on substrates of known mechanical properties. The Young's modulus of the material is extracted from the initial slope of the unloading indentation curve and the yield strength and strain- hardening exponent are obtained from the maximum indentation load and the contact area after unloading. The method is used to obtain the properties of a high-alloy steel and Mo and AlSi coatings deposited on a steel substrate by plasma spraying. The sensitivity of the measurement to the depth of indentation is discussed.
TL;DR: In this article, it is argued that the correct Heidenreich-Shockley dislocation is obtained in the reaction of the primary dislocation with the faulted (Frank) dipole.
Abstract: Transmission electron microscopy observations of the dislocation substructure in Cu-8at.% Al single crystals deformed in tension have been carried out to elucidate the origin of the twinning dislocation which produces conjugate twinning in this alloy. It is argued that the ‘correct’ Heidenreich-Shockley dislocation is obtained in the reaction of the primary dislocation with the faulted (Frank) dipole. These interactions are expected to occur frequently during the deformation. Different configurations of the twinning sources are analysed with respect to the nucleation and the growth of the twin. Geometrical issues related to the pinning of the component dislocations at the nodes formed, the motion of the single twinning dislocation and the non-coherent twinning front and the passing barriers encountered during twin growth are analysed. It is shown that there are no geometrical and energetic obstacles to the development of a macroscopic twin by the pole mechanism from the source proposed here.
TL;DR: In this article, a three-dimensional finite-element analysis of a cone scratching and indenting elastic-perfectly plastic materials is presented, where the behavior of the scratched or indented material depends on the parameter X = (E/σ 0) cotθ, called the rheological factor.
Abstract: We have studied the distribution of plastic strain around normal indentation and scratches in elastic-perfectly plastic materials. A three-dimensional finite-element analysis of a cone scratching and indenting elastic-perfectly plastic materials is presented. The indenter is the axisymmetric equivalent cone of the Berkovich indenter, with semiapical angle θ = 70.3°. The plastic behaviour of the material is modelled with the yield stress σ0. No strain hardening and no sensitivity to the strain rate occur. The elasticity of the material is modelled with Young's modulus E, which varies from 2.79 to 2793 GPa. In fact, the behaviour of the scratched or indented material depends on the parameter X = (E/σ0) cotθ, called the rheological factor (X = 1, …, 1000). For small rheological factors, the deformation is mainly elastic; for high rheological factors, the deformation is essentially plastic, and in this case the behaviour of the material is close to the behaviour of a metal. The contact between the in...
TL;DR: In this article, it was shown that the twist misorientation across a large-angle boundary has a more profound effect on cleavage fracture resistance than the tilt misorientations does.
Abstract: Large-angle grain boundaries in steel offer an important resistance to the propagation of cleavage cracks that affects the fracture toughness and can modulate the ductile-to-brittle transition temperature of fracture downwards. This behaviour has been studied in bicrystals of Fe-3 wt% Si alloy in detail. It was noted that the twist misorientation across a large-angle boundary has a more profound effect on cleavage fracture resistance than the tilt misorientation does. Specific measurements of such resistance at −20°C over a random selection of large-angle grain boundaries in bicrystals and associated fractographic studies have led to quantitative models of this resistance. The study has also revealed a transition from pure cleavage to mixed cleavage at around 0°C for this alloy, above which the observed increment of fracture work could be associated with the sigmoidal plastic bending and rupture of ligaments left between separate primary cleavage strips in the adjoining grain.
TL;DR: In this article, the effect of grain size on void swelling has been investigated both experimentally and theoretically in pure copper irradiated with fission neutrons at 623 K to a dose level of about 0.3 displacement per atom.
Abstract: The effect of grain size on void swelling has its origin in the intrinsic property of grain boundaries as neutral and unsaturable sinks for both vacancies and self-interstitial atoms. The phenomenon had already been investigated in the 1970s and it was demonstrated that the grain-size-dependent void swelling measured under irradiation producing only Frenkel pairs could be satisfactorily explained in terms of the standard rate theory (SRT) and dislocation bias. Experimental results reported in the 1980s demonstrated, on the other hand, that the effect of grain boundaries on void swelling under cascade damage conditions was radically different and could not be explained in terms of the SRT. In an effort to understand the source of this significant difference, the effect of grain size on void swelling under cascade damage conditions has been investigated both experimentally and theoretically in pure copper irradiated with fission neutrons at 623 K to a dose level of about 0.3 displacement per atom. ...
TL;DR: In this article, cross-sections through nanoindentions in the (001) surface of sapphire, spinel and magnesia have been examined in the transmission electron microscope.
Abstract: Cross-sections through nanoindentions in the (001) surface of sapphire, spinel and magnesia have been examined in the transmission electron microscope. Electron-transparent sections were prepared using a focused ion beam microscope. All three recognized high-temperature slip systems were observed in sapphire, while spinel deformed in slip bands on the {111} planes. Evidence was obtained for slip on {110} planes in magnesia and the possibility that slip also occurs on {100} planes is discussed as an explanation of its high ratio of hardness to yield stress.
TL;DR: In this paper, a field-driven in-situ transmission electron microscopy (TEM) technique was developed to examine micromechanisms of field-induced cracking in ferroelectric ceramics.
Abstract: The field-driven in-situ transmission electron microscopy (TEM) technique was developed to examine micromechanisms of field-induced cracking in ferroelectric ceramics. The technique was constructed by combining a selectively deposited thin film electrode configuration with a modified hot stage to deliver a required electric voltage to a ferroelectric TEM specimen. Under cyclic electric fields, microcracks were found to initiate from pores at the triple junctions and propagate along the grain-boundary in a lead zirconate titanate (PZT) ceramic. Grain-boundary cavitation and coalescence of microcracks were directly observed for the first time during field-induced fracture of PZT at room temperature. The results suggest that dielectric breakdown of the grain-boundary phase was conducive to grain-boundary cavitation, and the crack growth followed the progressive accumulation of the cavity density with electric cycling.
TL;DR: In this article, the authors investigated the influence of the ratio of the elastic recovered depth h e to the maximum penetration depth h max on the deformation behavior of the material and its relationship with the material parameters [sgrave] y/E and n.
Abstract: The indentation of elastic-plastic strain-hardened material with a conical indenter was investigated using the finite-element method. The influence of the ratio of the elastic recovered depth h e to the maximum penetration depth h max on the deformation behaviour of the material and its relationship with the material parameters [sgrave] y/E and n were analysed. The finite-element results were compared with the results of Berkovich indentations on single-crystal aluminium, single-crystal tungsten, nickel, lead, fused silica and BK7 glass. It is found that h e/h max can be directly related to the elastic-plastic properties [sgrave] y/E and n of a material, which determine the deformation behaviour of materials. The pile-up and sinking-in behaviour of the material during indentation is controlled by both strain hardening and h e/h max. No pile-up occurs for materials with n > 0.3; for materials with n < 0.3, the critical value of h e/h ma? for pile-up and sinking-in is 0.12. The hardness of a materi...
TL;DR: In this article, a phenomenological approach based on a concept of the Kirkendall velocity construction is used to rationalize the movement of the inert markers upon diffusion-controlled growth of the β'-AuZn intermetallic phase.
Abstract: A Kirkendall-effect-mediated behaviour (migration) of fiducial markers originally situated at the contact surface of a diffusion couple can be complex in both temporal and spatial domains. A phenomenological approach based on a concept of the Kirkendall velocity construction is used to rationalize the movement of the inert markers upon diffusion-controlled growth of the β'-AuZn intermetallic phase. It is demonstrated (experimentally as well as theoretically) that the Kirkendall marker planes can be multiple, stable or unstable within the single-phase reaction product. A general criterion of the microstructural instability of the Kirkendall plane is introduced.