Tresca and von Mises yield criteria: a view from strain space

In this paper, we present a study of Tresca and von Mises criteria in strain space. The plastic strains that can meet these criteria are found analytically for the Tresca criterion and numerically for the von Mises criterion. Such information will be useful for determining the relationship between yield criterion and the lattice structure of a material.     

Shear band evolution during large plastic deformation of brittle and ductile metallic glasses

Four monolithic metallic glasses (MMGs) with different plasticities varying from brittle to ductile behavior under unconstrained loading were subjected to small punch testing. All specimens undergo large plastic deformation with multiple cobweb-like shear bands under these conditions. The process of shear band evolution was carefully controlled and investigated. Plasticity of MMGs is characterized by equivalent plastic strain ε* (product of shear band density and critical shear offset). Thus, this article provides an experimental basis for a better understanding of the shear band evolution during plastic deformation of MMGs.     

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.     

Influence of mode of deformation on microstructural heterogeneities in Ni subjected to large strain deformation

In the present work, the effect of deformation mode (uniaxial compression, rolling and torsion) on the microstructural heterogeneities in a commercial purity Ni is reported. For a given equivalent von Mises strain, samples subjected to torsion have shown higher fraction of high-angle boundaries, kernel average misorientation and recrystallization nuclei when compared to uniaxially compressed and rolled samples. This is attributed to the differences in the slip system activity under different modes of deformation.     

Crystallographic analysis of the fcc-to-fct martensitic transformation in an In22.73at.%Tl alloy

Analytical solutions for various crystallographic parameters have been obtained from the application of the infinitesimal deformation (ID) approach to the fcc M fct martensitic transformation with the (101) g [101] g twinning shear as the lattice invariant shear deformation. All crystallographic parameters were calculated for an In-22.73at.%Tl alloy. In order to compare numerical solutions between the ID approach and phenomenological crystallographic theory, the corresponding crystallographic parameters were also calculated using the Wechsler-Lieberman-Read (WLR) theory. Agreement between the two results obtained from the ID approach and the WLR theory is found to be excellent.     

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.     

Accelerating heterogeneous nucleation to increase hardness and electrical conductivity by deformation prior to ageing for Cu-4 at.% Ti alloy

ABSTRACT

Deformation bands, especially shear bands were intentionally formed in supersaturated Cu-4 at.% Ti alloy by groove-rolling with 75% area reduction. Cold deformation prior to the ageing process changed the precipitation behaviour of the alloy. The deformed structure with shear bands was maintained, without showing recovery and recrystallisation, even after prolonged ageing at 450°C for more than one day. The thermally stable shear bands act as nucleation initiation sites and prevent the expansion of discontinuous cellular precipitates. The hardness reached a value of 305?Hv and an electrical conductivity of 15% IACS (IACS?=?International Annealed Copper Standard. 100% IACS is defined as the conductivity corresponding to a volume resistivity at 20°C of 17.241?nΩ), compared to 283?Hv and 13% IACS for conventional solid-solutioned and peak-hardened alloy. In addition, the ageing time to reach the highest hardness was shortened from 720 to 180?min at 450°C.     

Effect of severe plastic deformation on the coercivity of Co–Cu alloys

Cast Co–5.6 wt% Cu and Co–13.6 wt% Cu alloys were subjected to severe plastic deformation (SPD) by high-pressure torsion (HPT). The HPT treatment drastically decreases the size of the Co grains (from 20 µm to 100 nm) and the Cu precipitates (from 2 µm to 10 nm). As a result, the coercivity H _c of both the alloys radically increases. The saturation magnetization, M _s, remains almost unchanged. Thus, SPD of the bulk samples opens the way for drastic increase in the coercivity for the Co-based alloys.     

Influence of twist boundary on deformation behaviour of 〈1 0 0〉 BCC Fe nanowires

Molecular dynamics simulations revealed significant difference in deformation behaviour of 〈1?0?0〉 BCC Fe nanowires with and without twist boundary. The plastic deformation in perfect 〈1?0?0〉 BCC Fe nanowire was dominated by twinning and reorientation to 〈1?1?0〉 followed by further deformation by slip mode. On the contrary, 〈1?0?0〉 BCC Fe nanowire with a twist boundary deformed by slip at low plastic strains followed by twinning at high strains and absence of full reorientation. The results suggest that the deformation in 〈1?0?0〉 BCC Fe nanowire by dislocation slip is preferred over twinning in the presence of initial dislocations or dislocation networks. The results also explain the absence of extensive twinning in bulk materials, which inherently contains large number of dislocations.     

Large apparent compressive strain of metallic glasses

Very high plastic strains exceeding 20% in uniaxial compression tests, which show an inflection in the stress–strain curves of Zr-based bulk metallic glasses, are shown to be a spurious effect due to mechanical interlocking of cracks with shear bands. This type of stress–strain behaviour is misinterpreted as an actual deformation in the literature. The effect of mechanical interlocking is explained by fractographic analysis.     

Shape effect related to crystallographic orientation of deformation behaviour in copper single crystals

The deformation behaviour of pure copper single crystals has been investigated by scanning electron microscopy and synchrotron radiation using the in situ reflection Laue method. Two types of sample with the same orientation of tensile axes, but with different crystallographic orientations in the directions of the width and thickness of the samples, have been studied. They showed different characteristics of deformation behaviour, such as the activated slip systems, the movement of the tensile axis, and the mode of fracture.     

Disclinations and rotational deformation in fine-grained materials

A theoretical model is presented which describes a new mechanism of plastic deformation in fine-grained materials. In the framework of the model, rotational deformation occurs via motion of dipoles of grain-boundary disclinations and is associated with the emission of lattice dislocations from grain boundaries into adjacent grain interiors. Ranges of defect system parameters are identified in which the disclination motion is energetically favourable. It is shown that the mechanism can contribute to plastic flow in fine-grained materials prepared by highly non-equilibrium methods such as ball milling, severe deformation and high-pressure compaction.     

Enhanced plastic deformation in a metallic glass induced by notches

It is shown that the compressive plasticity of a metallic glass, namely Zr_52.5Ni_14.6Al₁₀Cu_17.9Ti₅, can be improved by the introduction of two symmetrical notches. The enhanced plasticity may be ascribed to a blocking effect of the propagation of shear bands caused by large stress gradients around the notches. In contrast to ceramic specimens with similar notches, the plasticity enhancement of metallic glass induced by notches can provide a new approach to understanding its unique mechanism of deformation.     

Measurement of the size effect in the yield strength of nickel foils

There is a growing consensus that materials become stronger in small volumes and in the presence of large strain gradients. It has not been clear whether this is due to increased resistance to the motion of dislocations, fewer dislocations, or increased difficulty of multiplying dislocations in these situations. A classic experiment by Stölken and Evans (J.S. Stölken and A.G. Evans, Acta metall. 46 5109 (1998)) showed that thin nickel foils under bending display increased strengthening at large plastic strain values and, correspondingly, large plastic strain gradients. We have adapted their technique to small strains, and report preliminary data for the stress–strain curves of thin nickel foils through the elastic–plastic transition. These data show unambiguously that the yield strength is greater in the thinner foils. The strengthening is additive to the Hall–Petch effect, and is consistent with a size effect at the onset of plastic deformation.     

Voidites in pure type IaB diamonds

Abstract

Electron microscopy of five pure type IaB diamonds (showing no trace whatever of a B′ infrared absorption peak due to {001} platelets) reveals voidite distributions unlike any reported before. In three of the crystals the voidites are distributed at random, and are not associated with degraded platelets, which themselves are not present in these specimens. These observations show that voidite formation and platelet degradation are distinct independent phenomena. The other two speamens showed only arrays of dislocations that patently resulted from plastic deformation: no voidites were seen. The non-formation of platelets in diamonds showing such an advanced stage of nitrogen aggregation is unexpected, and places these diamonds in a category distinct from that called ‘irregular’, in which platelets have indeed formed, but then experienced, to some degree, a process of transformation to perfect dislocation loops.     

The effect of strain upon the topology of a soap froth

Abstract

The question of the effect of an imposed strain on the topology of a soap froth is addressed through numerical simulations. Both the standard model of a ‘dry’ twodimensional foam and the case of small liquid fraction are explored. The froths are subjected to both extensional deformation and simple shear. The counter-intuitive result that application of strain can induce ordering in a disordered froth is obtained, quantified and discussed. A qualitative dynamical explanation is proposed.     

Characterization of room-temperature plastic deformation of ß-Si3N4 by atomic force microscopy and transmission electron microscopy

Dislocation microstructures induced by room-temperature microhardness tests have been investigated in silicon nitride. Surface analysis of the residual indent by atomic force microscopy reveals intragranular slip bands and demonstrates that room-temperature plastic deformation involves dislocation motion as well as cross-slip events. Cross-slip events have been found to occur between {1010} prismatic planes. Transmission electron microscopy shows that dislocations have a Burgers vector b = [0001] and are located along the screw direction. Based on these observations, specific dislocation core configurations are discussed.     

The fatigue limits of copper single crystals cyclically deformed at constant plastic strain amplitudes

Based on systematic surface observations, experimental measurements on the fatigue limits of differently oriented copper single crystals cyclically deformed at constant plastic strain amplitudes are summarized, and an orientation dependence of the fatigue limit is sketched. It was found that the fatigue limits of crystals depend mainly upon the low-strain-amplitude dislocation structures, which are characteristic of the particular crystal orientations. When multiple-slip deformation is the main mode of deformation and ultimately produces stable lowenergy dislocation structures such as labyrinth and cell structures, the fatigue limit can be improved notably.     

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.     

Two different types of shear-deformation behaviour in Au–Cu multilayers

Localised shear deformation of a material is usually identified as a particular feature of deformation inhomogeneity. Here, we show two different types of shear deformation-behaviour that occurred in Au–Cu multilayers subjected to microindentation load, namely, a cooperative-layer-buckling-induced shear banding in a nanoscale multilayer and a direct localised shearing across a layer interface along a shear plane in a submicron-scale multilayer. Theoretical analysis indicates that the formation of the two different types of shear deformation in the multilayers depends on a competition between the dislocation-pile-up-induced stress concentration at the layer interface and the barrier strength of the layer interface for glissile dislocation transmission.