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.     

Equivalent and effective strains during severe plastic deformation (SPD)

ABSTRACT

This paper considers the characteristics of severe plastic deformation (SPD) to estimate its efficacy and to compare different processing techniques. In contrast to effective strains by von Mises and Hencky, the rotation component of the strain rate is included in the analysis as a mode of deformation, which ranges from simple shear to pure shear. Distortions of material elements during a uniform plane plastic flow are calculated using a kinematic approach. For the fixed deformation mode, the current state is defined by the accumulated shears that are identical to the von Mises effective shear strains. In specific cases of pure shear and simple shear, the accumulated shears match the specific distortions of round or square elements prescribed by Hencky or von Mises approach, respectively. The mode of deformation is important to the structural effects of SPD. In general, two separated characteristics, accumulated shear and the coefficient of deformation mode, are necessary to describe strains during SPD.     

Negative incremental bulk modulus in foams

Negative incremental stiffness is known to occur in structures such as post-buckled flexible tubes and single-cell models. A single foam cell under uniaxial loading buckles and exhibits a non-monotonic S-shaped deformation curve, which is indicative of negative incremental stiffness. Negative stiffness is not observed in bulk materials. For example, individual foam cells display negative stiffness but foams tested in uniaxial compression exhibit a plateau in the stress–strain curve because the buckled cells localize in bands. This behaviour is consistent with the continuum view in which strong ellipticity and, hence, a positive shear modulus G and positive C ₁₁ modulus are required for stability, even for a constrained object. It is hypothesized that a solid with negative bulk modulus can be stabilized by control of the surface displacement. Experimentally, foams were hydrostatically compressed by controlled injections of small volumes of water into a plastic chamber, causing volumetric deformation. A negative incremental bulk modulus was observed in a foam with 0.4-mm cell size beyond about 20% volumetric strain. A foam with large cells, 2.5–4?mm in size, was anisotropic and did not exhibit the cell buckling required for negative modulus.     

Strain localization in nickel single crystals cyclically deformed at 77 K

Nickel monocrystals oriented for single slip have been cyclically deformed at 77 K at plastic strain amplitude between 5 x 10^-4 and 1 x 10^-2 up to saturation of the stress amplitude. After unloading from maximum compression, the slip markings on the surface of the specimens were removed and the deformation continued for one half cycle in tension. As previously observed for room-temperature deformation, the plastic strain was found to be localized in narrow slip bands (SBs). Using atomic force microscopy at a given imposed strain amplitude, a wide spectrum of local plastic strains was found. The averaged resolved shear strain of the SBs was found to be independent of the imposed plastic strain amplitude and turned out to be a factor of three larger than the upper plateau strain limit of the cyclic stress-strain curve.     

Dislocation density evolution upon plastic deformation of Al-Pd-Mn single quasicrystals

Dislocation density studies have been performed on icosahedral Al-Pd-Mn single quasicrystals after plastic deformation and after subsequent heat treatment. The deformation tests were carried out at a constant strain rate of 10- 5 s-1 at temperatures between 695 and 820 C. The heat treatments were performed at 730 C, corresponding to one of the deformation temperatures. The development of the dislocation density during heat treatment and that during plastic deformation are compared. The experimental data are interpreted using a kinetic equation, which describes the evolution of the dislocation density during deformation. Numerical values for the dislocation multiplication constant and the annihilation rate for icosahedral Al-Pd-Mn are presented.     

Critical length scales for the deformation of amorphous metals containing nanocrystals

Shear localization is studied in simulated amorphous systems containing individual nanocrystalline inclusions. Systematic variation of the inclusion diameter and the shear band thickness reveals a crossover in length scales that separates distinct plastic flow mechanisms in and around the nanocrystalline inclusion. When considered relative to the shear band thickness, small inclusions deform via heterogeneous, interface-dominated mechanisms, while large inclusions yield via the homogeneous nucleation of dislocations in the nanocrystal interior; nanocrystals roughly twice as large as the shear band width are required for the strongest interaction.     

A phase-field model for deformation twinning

We propose a phase-field model for modeling microstructure evolution during deformation twinning. The order parameters are proportional to the shear strains defined in terms of twin plane orientations and twinning directions. Using a face-centered cubic Al as an example, the deformation energy as a function of shear strain is obtained using first-principle calculations. The gradient energy coefficients are fitted to the twin boundary energies along the twinning planes and to the dislocation core energies along the directions that are perpendicular to the twinning planes. The elastic strain energy of a twinned structure is included using the Khachaturyan's elastic theory. We simulated the twinning process and microstructure evolution under a number of fixed deformations and predicted the twinning plane orientations and microstructures.     

Onset of plasticity in a Σ = 5 GaAs compliant structure

Compliant structures have been fabricated in which a thin GaAs layer (thickness between 10 and 20nm) was bonded on top of a GaAs substrate with a large twist angle (about 37). This twist angle value was chosen so that the energy of the boundary (coincident boundary of type =5 (001)) was minimized. The structure of the interface was characterized and the onset of plasticity in such a compliant substructure was investigated using nanoindentation that allowed the low-load deformation regime to be observed. The results are compared with those obtained under the same conditions on a GaAs bulk substrate alone. No plastic zone was observed by transmission electron microscopy in the compliant structure under loads below 0.25mN while, under the same loads, plastic deformation was observed in the bulk substrate. For higher loads (2mN), plastic-flow enhancement was observed in the compliant structure. The results are discussed in the light of the arrangement of dislocations observed in the plastic zones.     

Influencing surface plastic flow in metals using common chemical media

We demonstrate a unique mechanochemical effect – change in surface plastic flow by action of chemical media such as inks and glues – in large-strain deformation of metals. Unlike other well-known phenomena such as stress corrosion cracking and liquid metal embrittlement, the effect is not catastrophic and is largely material independent. High-speed in situ imaging shows that the media influence the flow by effecting a local ductile-to-brittle transition – from unsteady, large-amplitude, plastic folding, to repeated fracture and segmentation – with large decrease in deformation forces. The benign nature of the media offers opportunities for enhancing performance of metal cutting and deformation processes.     

Fragmentation testing for ductile thin films on polymer substrates

Fragmentation testing of thin films on substrates has in the past been mostly performed in situ using optical and scanning electron microscopy. While these techniques work well for brittle materials, they cannot always discern the difference between through-thickness cracks (TTCs) and localized plastic deformation of ductile films. Here, we describe fragmentation testing with atomic force microscopy and present criterion to distinguish TTCs and localized deformation for ductile films.     

Deformation strengthening of grain-boundary sliding in a Pb-62wt% Sn alloy

Abstract

Direct observation in a scanning electron microscope of the evolution of the grain-boundary sliding (GBS) process in a Pb-62wt%Sn eutectic alloy during superplastic deformation in shear is reported. The distribution of GBS along the shear surface is found to be inhomogeneous and there is evidence of coupling of the processes of GBS and grain-boundary migration. The rate of GBS increases at small stages of strain (up to about 0·8) and decreases thereafter, indicating that the GBS process is eventually accompanied by strain hardening. The observations are compatible with the dislocation model for GBS.     

Influence of In substitution and plastic deformation on AsGa-related photoluminescence in GaAs

Abstract

Low-temperature photoluminescence experiments have been carried out on semi-insulating GaAs crystals undoped or containing ～5 × 10¹⁹ In atoms cm^?3. A broad band peaking around 0·8eV is observed which is generally related to the antisite defect As_Ga. The effect of In substitution or plastic deformation is to shift this band towards higher energies by 10–25 meV. This positive energy shift is quantitatively accounted for by considering the stress fields induced by the incorporation of indium or the creation of dislocations.     

Deformation behaviour and 6H-LPSO structure formation at nanoindentation in lamellar high Nb containing TiAl alloy

Microstructure and deformation mechanisms at a nanoindentation in the lamellar colony of high Nb containing TiAl alloy have been studied using the focused ion beam and the transmission electron microscopy. Considerable deformation twins are observed around the nanoindentation, and a strain gradient is generated. A continuous change in the bending angle of the lamellar structure can be derived, and a strain-induced grain refinement process is observed as various active deformations split the γ grains into subgrains. In addition to all possible deformation mechanisms (ordinary dislocation, super-dislocation and deformation twining) activated due to the heavy plastic deformation, a 6-layer hexagonal (6H) long-period stacking ordered structure is identified for the first time near the contact zone and is thought to be closely related to the glide of partial dislocations.     

Presence of ε-martensite as an intermediate phase during the strain-induced transformation of SUS304 stainless steel

We have investigated the formation process of α′-martensite from the γ-phase induced by external strain using in situ synchrotron diffraction experiments, combined with Lorentz transmission electron microscopy (TEM) and high-resolution TEM observations. It is clearly demonstrated that ε-martensite with hexagonal symmetry appears as an intermediate structure during the plastic deformation of SUS304 stainless steel. In addition to stacking faults and dislocations, interfaces between the twin structures presumably play a key role in the formation of ε-martensite.     

Effect of aspect ratio on the compressive deformation and fracture behaviour of Zr-based bulk metallic glass

The compressive deformation and fracture features of Zr₅₉Cu₂₀Al₁₀Ni₈Ti₃ bulk metallic glassy samples with aspect ratios in the range of 0.67–2.00 have been investigated. The compressive plastic strain of the glass monotonically increases with decreasing aspect ratio, but the maximum strength almost maintains a constant value of 1.77–1.88?GPa. All the compressive shear-band angles are equal to?～40° if modified by the rotation of the primary shear bands.     

Highly inhomogeneous compressive plasticity in nanocrystal-toughened Zr–Cu–Ni–Al bulk metallic glass

A Zr₆₂Cu_15.5Al₁₀Ni_12.5 bulk metallic glass with a large supercooled liquid region of 90 K, produced by copper-mould casting, exhibits a high strength of 1730 MPa and superior but highly inhomogeneous plasticity under uniaxial compression at ambient temperature. Micro-X-ray diffraction shows that compressive loading facilitates crystallization in the monolithic glassy alloy, resulting in room-temperature plasticity. The plastic deformation of the Zr₆₂Cu_15.5Al₁₀Ni_12.5 BMG may be attributed to in situ precipitation of nanocrystals during compression in heavily deformed areas.     

Understanding the shear band interaction in metallic glass

Qualitative and quantitative models were proposed to understand the shear band (SB) interaction scenario found in the compressive tests on specimen with two symmetrical semi-circular notches. The so-called ‘work-hardening’ behavior could be ascribed as the stress interaction which was caused by stress fields around the SB tips. Besides, the SB bending was observed along propagation orientation. The quantitative analysis based on traditional shear deformation mechanism could reasonably account for how the SB was bent. It is anticipated that the present work could provide a pathway to understand the deep SB deformation mechanism of metallic glass.     

Unusual room-temperature compressive plasticity in nanocrystal-toughened bulk copper-zirconium glass

Cast Cu₅₀Zr₅₀ alloy rods with a diameter of 1?mm have been found to consist of a glassy phase containing fine crystalline particles with a size of about 5?nm. They have a glass transition temperature T _g of 675?K, and a large supercooled-liquid region extending 57?K above T _g. The rods exhibit a high yield strength of 1860?MPa and a Young's modulus of 104?GPa. Because they contain a dispersion of embedded nanocrystals, the as-cast bulk metallic glass rods can sustain a compressive plastic strain at room temperature of more than 50%, an exceptional value which is explicable by compensation of any shear softening by nanocrystal coalescence and pinning of shear bands.     

Formation of FeNi with L10-ordered structure using high-pressure torsion

FeNi with the L1₀-ordered structure is formed over an astronomical timescale in meteorites. In this study, severe plastic deformation using high-pressure torsion (HPT) is employed for the production of the L1₀ structure in the laboratory. Its formation is confirmed by X-ray diffraction analysis and transmission electron microscopy. Processing of elemental nanopowders by HPT is an effective method for the formation of the L1₀ phase, which is enhanced by the addition of Co to FeNi or annealing after HPT. The formation of the phase must be associated with enhanced diffusion through HPT.