Slip Systems In Single Crystals Research Articles

Energy approach to the selection of deformation pattern and active slip systems in single crystals

The recently introduced quasi-extremal energy principle for incremental non-potential problems in rate-independent plasticity is applied to select the deformation pattern and active slip systems in single crystals. The standard crystal plasticity framework with a non-symmetric slip-system interaction matrix at finite deformation is used. The incremental work criterion for the formation of deformation bands is combined with the quasi-extremal energy principle for determining the active slip systems and slip increments in the bands. In this way, the incremental energy minimization approach has been extended to the non-potential problem of deformation banding in metal single crystals. It is shown that fulfilment of the mathematical criterion for incipient deformation banding in a homogeneous crystal in the multiple-slip case under certain conditions requires non-positive determinant of the hardening moduli matrix. Numerical examples of energetically preferable patterns of deformation bands are presented for Cu and Ni single crystals.

A conventional theory of strain gradient crystal plasticity based on the Taylor dislocation model

Single crystal metallic materials display strong size effects when the characteristic length of plastic deformation is on the order of microns. The classical crystal plasticity theory cannot explain the size effects since its constitutive model possesses no intrinsic material length. The strain gradient crystal plasticity theory [Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005a. Mechanism-based strain gradient crystal plasticity – I. Theory. Journal of the Mechanics and Physics of Solids 53, 1188–1203; Han, C.S., Gao, H.J., Huang, Y., Nix, W.D., 2005b. Mechanism-based strain gradient crystal plasticity – II. Analysis. Journal of the Mechanics and Physics of Solids 53, 1204–1222] has been modified to incorporate a new quasi rate-independent formulation for the slip rate. Its major advantage is that it is not necessary to distinguish plastic loading and unloading in a rate-independent formulation, and therefore avoids the complexity of determining the set of active slip systems in single crystals. The intrinsic material length is identified from the Taylor dislocation model as l = α 2 ( μ τ 0 ) 2 b , where μ is the shear modulus, τ 0 is the initial yield stress (critical resolved shear stress) in slip systems, b is the magnitude of Burgers vector, and α is an empirical coefficient between 0.3 and 0.5. For non-uniform plastic deformation with the characteristic length of deformation comparable to the intrinsic material length l, the present theory gives higher plastic work hardening than the classical crystal plasticity theory due to geometrically necessary dislocations.

Dislocation glide and grain boundary decohesion in polycrystalline molybdenum disilicide during plastic deformation

Molybdenum disilicide polycrystals were deformed in constant strain rate tests in compression followed by analyses of the deformed specimens by means of optical microscopy and scanning and transmission electron microscopy. The strain rate sensitivity was measured by stress relaxation tests. Using a low strain rate of 2.5×10 −7 s −1, it was possible for the first time to achieve plastic flow at low-temperatures down to 495 °C and thus in the temperature range of the flow stress anomalies of different slip systems in single crystals. In addition, in situ straining experiments in a high-voltage electron microscope were performed to observe the deformation processes directly. The deformation is controlled by dislocation glide on the {0 1 1}〈1 0 0〉 and {1 1 0}〈1 1 1〉 slip systems below 1000 °C, however, by visco-elastic grain boundary glide and decohesion above this temperature.

Deformation Behavior of Polycrystalline MoSi2 Between 495°C and 1250°C

ABSTRACTIn order to study the deformation processes of reaction-sintered and hot pressed MoSi2, compression tests have been performed and the microstructure of the deformed samples has been investigated by optical, scanning and transmission electron microscopy. At a low strain rate of 2.5× 10−7 S−1 permanent deformation has been achieved at 1250°C. The deformation behaviour is controlled by different microprocesses within different temperature ranges. Below 1000°C, hardening occurs beyond the upper and lower yield points. Inside the grains, dislocations glide at sufficiently high stresses in a homogeneous way as well as in localized slip bands. A plateau in the dependence of the yield stress on temperaturecorresponds to the flow stress anomaly of easy slip systems in single crystals. However, since there are not enough independent slip systems to satisfy the van Mises criterion, the material does not deform homogeneously in all grains. Intergranular and intragranular cracks, which are formed after the yield point, carry an increasing part of strain at decreasing temperatures. Above 1000°C, softening occurs after the yield point. A grain boundary phase flows viscously and carries most of the deformation. Since the grains do not deform themselves, intergranular cracks develop also at high temperatures.

Deformation behavior of FeAl single crystals

The operative slip systems in single crystals of CsCl-type intermetallic compound FeAl deformed in compression at 77°, 300° and 473°K were determined for three different crystal orientations. The slip mode and yield stress were strongly dependent on crystal orientation and deformation temperature. For orientation with maximum shear stress on the ( 2 11) [111] or ( 1 01) [111] system, slip occurred on a system of ( 2 11) [111] at low temperature, but a higher temperatures the ( 1 01) [111] slip became more favorable. Crystals of orientation with maximum shear stress on the ( 11 2) [111] system exhibited complex cross slip pattern on the ( 11 2), (0 1 1), ( 12 3), ( 21 3) and ( 1 01) planes at 77°K, but no definite slip line was observed at higher temperatures. The critical shear stress resolved on the ( 2 11) [111] slip system showed hardly any temperature dependence between 77° and 300°K. The asymmetry for slip mode and CRSS to the twinning and antitwinning direction on the {112} plane was found at 77°K.

Determination of the slip systems in single crystals of tungsten monocarbide

Abstract Slip in single crystals of tungsten monocarbide has been observed around Vickers pyramid hardness indentations. The slip plane is {l100} at room temperature and the slip directions are postulated to be the and . The Vickers hardness value on a (0001) face is approximately twice the value determined for a (1100) face. This is attributed to the ease of motion of dislocations with Burgers vectors as opposed to the dislocations having Burgers vectors since the former can dissociate into partial dislocations. The occurrence of a {1100} slip plane is explained on the basis of the fact that a minimum number of only two covalent tungsten-carbon bonds need be broken for a unit of slip on this plane.