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.     

Crystallographic orientation dependence of nanoindentation hardness in austenitic phase of stainless steel

ABSTRACT

This paper presents the indentation hardness evolution in different in-plane directions of austenite grains whose {111} planes are parallel to the sample surface determined by nanoindentation tests and electron back scattering diffraction (EBSD) analysis. A scanning electron microscopy (SEM) image of the indentation surface around one of the indents indicated the activation of two sets of slip planes with respect to each of the three indenter surfaces for a Berkovich tip. The identification of the slip traces by EBSD data analysis is in accord with Schmid`s law. We therefore proposed a new approach for defining the orientation parameter to interpret the indentation hardness. The orientation parameter was shown to be the minimum value of the three maximum Schmid factors on the secondarily activated slip planes in three directions for a Berkovich tip. Indentation hardness increased with the decrease in the orientation parameter and was dependent on in-plane orientation.     

Transmission electron microscopy observations of low-load indents in GaAs

Nanoindentations have been made on (001) surfaces of GaAs single crystals at room temperature and the indents observed by transmission electron microscopy. The permanent deformation, generated by a Berkovitch indentor submitted to maximum loads ranging between 600 to 1700 muN, was analysed and interpreted as a function of the loading curves. The plastic zone size was measured as a function of the maximum load to determine the yield strength of GaAs at room temperature. Finally, the fine structure of the dislocations generated by the indenter has been analysed and this is compared with previously reported structures for higher indenting loads.     

Scaling relationships in indentation of power-law creep solids using self-similar indenters

We use dimensional analysis to derive scaling relationships for self-similar indenters indenting solids that exhibit power-law creep. We identify the parameter that represents the indentation strain rate. The scaling relationships are applied to several types of indentation creep experiment with constant displacement rate, constant loading rate or constant ratio of loading rate over load. The predictions compare favourably with experimental observations reported in the literature. Finally, a connection is found between creep and 'indentation-size effect' (i.e. changing hardness with indentation depth or load).     

Plasticity of GaAs(011) at room temperature under concentrated load

Indentations have been made on a (011) surface of GaAs single crystal at room temperature. The loading-unloading curves were compared with those obtained under the same experimental conditions on (001) surfaces. The indents formed were observed by transmission electron microscopy in plan view as well as in cross-sectional view in samples prepared by the focused-ion-beam technique. The gliding systems could be identified, providing a better understanding of the plastic flow under the indenter. The arrangements of dislocations generated by the indenter have been analysed and compared with results previously reported by Ning et al.     

An explanation of the indentation size effect in ceramics

Abstract

A quantitative model is proposed to explain the indentation size effect (ISE) often observed in the hardness response of hard brittle materials, namely that hardness is observed to increase with decreasing indentation size. The model is based on a mixed elastic/plastic materials deformation response whereby plastic deformation occurs in a discrete manner progressively to relieve stresses created by elastic flexure of the surface at the edges of the indentation. During unloading of the indenter, recovery of the elastic increment of deformation, which precedes each new band of plastic deformation, results in the indentation appearing smaller than expected, particularly as the indentation sizes decrease to approach the scale of the plastic deformation band spacing. The model fits observed experimental data well and analysis of hardness/size data in this way is shown to allow both a bulk hardness value and a characteristic deformation band scale to be calculated for a given sample.     

Dominant factors influencing the nanoindentation response of piezoelectric materials: a case study in relaxor ferroelectrics

The nanoindentation response of a piezoelectric material is, in general, influenced in a complex manner by its elastic, dielectric and piezoelectric properties. The present study is focused on obtaining a comprehensive understanding of the dominant material factors influencing the force–depth mechanical indentation response and the charge–depth electrical indentation response of piezoelectric materials. From a large number of three-dimensional finite element simulations of the indentation of simple and complex piezoelectric materials (such as PZT-5A and relaxor ferroelectrics), the following principal conclusions are obtained: (1) For indentations with both conducting and insulating indenters, the mechanical indentation stiffness is influenced more by the elastic properties, while the electrical indentation stiffness is influenced largely by the piezoelectric properties of the indented materials. (2) For longitudinal indentations using a conducting indenter, the elastic constants, C ₃₃ and C ₁₃, and piezoelectric constants, e₃₃ and e₁₅, are, respectively, the first and second most dominant material constants that influence the mechanical indentation stiffness and the electrical indentation stiffness. (3) For transverse indentations using a conducting indenter, the elastic constants, C ₁₁ and C ₁₂, are, respectively, the first and second most dominant material constants that influence the mechanical indentation stiffness. (4) In the indentation of relaxor ferroelectrics based on PMN-xPT and PZN-xPT, which exhibit a range of elastic, dielectric and piezoelectric properties, it is generally observed that materials with higher normal elastic and piezoelectric constants, i.e., C ₃₃ and e₃₃, respectively, exhibit higher mechanical and electrical indentation stiffnesses.     

On the dislocation mechanism of amorphization of Si by indentation

The formation of an amorphous phase underneath a Vickers indentation produced on a Si(001) surface at room temperature has been observed by cross-sectional transmission electron microscopy. Two types of location are observed for the amorphous phase. One is formed just underneath the image of the indentation and the other is parallel to the slip planes of Si. It is concluded that the latter type, at least, is formed as a result of activation of dislocations which is induced by an external shear stress combined with a hydrostatic pressure.     

Transmission electron microscopy of dislocations in SrTiO3

Dislocations have been introduced in SrTiO₃ by Vickers indentation at room temperature and analysed by transmission electron microscopy. The slip systems in SrTiO₃ were identified as ?110?-{110}. ?110? dislocations are dissociated into two partial dislocations. The stacking-fault energy γSF was determined to be 136 ± 15 mJm^-2.     

In situ characterization of the martensitic transformation temperature of NiTi shape memory alloys via instrumented microindentation

A novel, instrumented microindentation technique was successfully used to measure the temperature associated with the martensitic transformation leading to the recovery of plastic strain in a Nickel–Titanium (NiTi) shape memory alloy. Following a standard indentation cycle, the indenter was partially unloaded such that a good contact was maintained between indenter and specimen surface. The onset and finish temperature of the martensitic transformation, the associated volume contraction, and the amount of the recovered plastic deformation were determined by quantifying the indenter displacement as a function of temperature. These experiments were compared to conventional measurements of the transformation temperature by differential scanning calorimetry and compression testing.     

Mechanical hysteresis due to microplasticity in alumina with microcracks

Abstract

Stress-strain hysteresis in alumina with microcracks has been investigated by a loading–unloading test in the microstrain range around 10 ^?4 While there remains a permanent strain after the initial loading, steady-state cyclic loading results in a single closed hysteresis loop with a symmetrical shape. Such a stabilized hysteresis loop is responsible for internal friction and can be attributed to the microplasticity associated with a forerunning phenomenon of fracture.     

Plastic behaviour of an AlAs/GaAs superlattice with a short period

Nanoindentation has been used to investigate the plastic behaviour of an AlAs/GaAs superlattice with a short period. The sample was grown on a (001) surface of a GaAs single crystal by metal-organic vapour-phase epitaxy. The mechanical response of the superlattice to nanoindentation testing was compared with that of a (001) surface of bulk GaAs. The indents formed were observed by transmission electron microscopy. The plastic zone size associated with each indent was measured as a function of the maximum load. Finally the arrangement of the dislocations generated by the indenter has been analysed and compared with the arrangement observed in deformed bulk GaAs.     

A continuum model of deformation-twin dominant crack growth in fcc metals

A continuum model is proposed to address the effects of deformation twinning on ductile versus brittle fracture behaviour of low strain-hardening fcc metals after exhaustion of work hardening. Instead of discrete twin nucleation, a number of partial dislocations ahead of the tip exhibit themselves as twins at the final stage of failure. The crack-tip plasticity is amended for deformation twinning and the constitutive form for the flow strength of arrays of twins of the same sign is expressed as a second gradient of microrotation for their coupling. The twins not only shield the crack tip but also inhibit further dislocation emission to form a dislocation-free zone (DFZ) in the immediate vicinity of the tip. The stress fields induced by deformation twinning lead to fracture branching under Mode I loading. The model is borrowed from the conceptual model presented by Beltz et al. [Acta Mater. 44 3943 (1996)], based on the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the DFZ boundary. The DFZ size and the crack-tip shielding ratio are obtained, as well as the branching angle. The branching angle is noteworthy for low strain-hardening metals. A strong dependence of the toughness on intrinsic surface energy and hardening index is examined. The toughness reduction due to crack-tip constraints and in the ductile-to-brittle transition (DBT) temperature region is revisited and found to be in agreement with experimental observations and available predictions.     

A novel least-squares method to characterize in-vivo joint functional passive regional stiffness zones

ObjectiveTo present and evaluate a method to objectively quantify the functional regions of joint lumped passive stiffness.BackgroundJoint passive stiffness has an important clinical role in constraining the degrees of freedom at a given joint. Links between passive stiffness and injury, pathology and function may be better understood if joint passive stiffness can be accurately quantified. Thus, a technique was developed to objectively partition passive stiffness curves into 3 linear regions (low, transition and high stiffness).MethodsThe passive stiffness of the lumbar spine is presented as an example. Simulated data was used to determine the sensitivity of the method to Gaussian white noise in force measurements. An experimentally determined lumbar passive flexion curve was used to demonstrate the technique on human data. Breakpoint analysis was employed on the resulting moment-angle cures to partition the curve into low, transition and high stiffness zones.ResultsThe proposed method was successful at discriminating between the three stiffness zones and quantifying the passive stiffness within each zone. The algorithm had difficulty determining parameters in the low-stiffness zone in the presence of noise.ConclusionsThe proposed method can be used as an objective method to investigate passive stiffness. Breakpoint Analysis can identify the three functional linear zones of passive stiffness. The slopes of these linear regions are then used as a measure of passive stiffness, which have applications in clinical populations and research studies, to assess time varying responses, or changes in stiffness following an intervention.     

Nonparametric Calibration of Item-by-Attribute Matrix in Cognitive Diagnosis

A nonparametric technique based on the Hamming distance is proposed in this research by recognizing that once the attribute vector is known, or correctly estimated with high probability, one can determine the item-by-attribute vectors for new items undergoing calibration. We consider the setting where Q is known for a large item bank, and the q-vectors of additional items are estimated. The method is studied in simulation under a wide variety of conditions, and is illustrated with the Tatsuoka fraction subtraction data. A consistency theorem is developed giving conditions under which nonparametric Q calibration can be expected to work.     

Reversible plasticity under nanoindentation of atomically flat and stepped surfaces of fcc metals

Using atomistic simulation, the indentation of single-crystalline Cu is investigated for both an ideal and a stepped (111) surface. Both systems exhibit an intermediate regime of reversible plasticity, characterized by the formation of extended stacking faults, which heal entirely upon withdrawal of the indenter. This regime can be employed to clarify the role of pure stacking fault generation and cross-slip in plasticity. Its existence reveals that, on the atomistic scale, plastic deformation is characterized by material transport rather than by the nucleation of stacking faults. Finally, we establish a criterion–based on the total displacement of particles–to determine after which indentation depth plasticity is generated irreversibly in the material.     

Time-dependent adhesion of a polydimethylsiloxane (PDMS) elastomer film to a flat indenter tip characterized using a cohesive-zone law

The work of adhesion between a polydimethylsiloxane (PDMS) elastomer film and a flat diamond tip was measured by instrumented indentation. The results showed that the apparent work of adhesion between the tip and the PDMS film increases with increasing dwell time and retreating velocity; on the other hand, the indentation depth has no significant effect on adhesion. The indentation experiment was analysed with viscoelastic finite element simulations with rate-dependent cohesive elements, from which the time evolution of adhesion was quantitatively implemented into a rate-dependent cohesive-zone law.     

Local order description of an icosahedral Al–Cu–Fe quasicrystal

Abstract

A rapidly solidified Al₆₅Cu₂₀Fe₁₅ icosahedral alloy has been studied by extended X-ray absorption he structure above the Cu and Fe K absorption edges. The local order has been determined around Cu and Fe atoms and compared with results obtained previously in other icosahedral alloys