Discrete Slip Planes Research Articles

Characterization of the strain rate sensitivity of basal, prismatic and pyramidal slip in Zircaloy-4 using micropillar compression

The slip strength of individual slip systems at different strain rates will control the mechanical response and strongly influence the anisotropy of plastic deformation. In this work, the slip activity and strain rate sensitivity of the <a> basal, <a> prismatic, and <c+a> pyramidal slip systems are explored by testing at variable strain rates (from 10−4 s−1 to 125 s−1) using single crystal micropillar compression tests. These systematic experiments enable the direct fitting of the strain rate sensitivities of the different slips using a simple analytical model and this model reveals that deformation in polycrystals will be accommodated using different slip systems depending on the strain rate of deformation in addition to the stress state (i.e. Schmid's law). It was found that the engineering yield stress increases with strain rate, and this varied by slip systems. Activation of the prismatic slip system results in a high density of parallel, clearly discrete slip planes, while the activation of the <c+a> pyramidal slip leads to the plastic collapse of the pillar, leading to a ‘mushroom’ morphology of the deformed pillar. This characterization and model provide insight that helps inform metal forming and understanding of the mechanical performance of these engineering alloys in the extremes of service conditions.

An effective anisotropic visco-plastic model dedicated to high contrast ductile laminated microstructures: Application to lath martensite substructure

In particular types of layer- or lamellar-like microstructures such as pearlite and lath martensite, plastic slip occurs favorably in directions parallel to inter-lamellar boundaries. This may be due to the interplay between morphology and crystallographic orientation or, more generally, due to constraints imposed on the plastic slip due to the lamellar microstructural geometry. This paper proposes a micromechanics based, computationally efficient, scale independent model for a particular type of lamellar microstructures containing softer lamellae which are sufficiently thin to be considered as discrete slip planes embedded in a matrix representing the harder lamellae. Accordingly, the model is constructed as an isotropic visco-plastic model which is enriched with an additional orientation-dependent planar plastic deformation mechanism. This additional mode is activated when the applied load, projected on the direction of the soft films, induces a significant amount of shear stress. Otherwise, the plastic deformation is governed solely by the isotropic part of the model. The response of the proposed model is assessed via a comparison to an infinite periodic two-phase laminate. It is shown that the yielding of the model follows the same behavior as the reference model. The proposed model is highly anisotropic, and the degree of anisotropy depends on the contrast between the slip resistance of the planar mode versus that of the isotropic part. The framework is applied to the substructure of lath martensite with thin films of inter-lath retained austenite, and exploited in a mesoscale simulation of a dual-phase steel microstructure. The results are compared with those of a standard isotropic model and a full crystal plasticity model which does not have the additional planar plastic mechanism. Predictions made with the proposed model show distinct differences compared with the crystal plasticity results, while keeping the computational cost comparable to that of the isotropic model — and significantly lower than that of the crystal plasticity simulation.

Cohesional Slip on a Plate Subduction Boundary During a Large Earthquake

AbstractThe frontal part of the Japan Trench plate boundary fault, which slipped during the 2011 Tohoku‐Oki earthquake (Mw 9.0), is enriched in smectite and is intrinsically weak owing to the high swelling pressure of this mineral. Our rheometric experiments using analog fault materials demonstrate that “cohesional slip,” rather than frictional slip, is a realistic faulting process in the studied fault zone. The cohesional slip can be described by the Bingham plastic model. Consequently, the coseismic shear stress is described by the yield stress and plastic viscosity. Comparison of the results with the average shear stress derived from a previous study suggests that the slip zone thickness for cohesional slip is ~1.3 cm or less. This finding is consistent with textures characterized by discrete slip planes of comparable thickness observed in the recovered fault rocks, suggesting that these slip planes were activated during the Tohoku‐Oki earthquake.

Influence of hydrogen on the deformation morphology of vanadium (1 0 0) micropillars in the α-phase of the vanadium–hydrogen system

The effect of dissolved hydrogen in a (1 0 0) vanadium single crystal was studied using compression tests of micropillars. It is observed that the shape of the deformed pillars changes with hydrogen concentration. At low concentrations the pillars deform on a few discrete slip planes and at high hydrogen concentrations the pillars deform to a barrel-like shape. Furthermore, the flow stress increases with hydrogen concentration. Both observations can be attributed to an elevated dislocation activity due to hydrogen.

Evaluation of fatigue crack initiation in a notched single-crystal superalloy component

The fatigue crack initiation in a notched single-crystal nickel-base superalloy component at 500°C was investigated and analysed. A critical plane approach in combination with a critical distance method has been adopted, in which the total shear strain ranges on the discrete slip planes are evaluated. Furthermore, a Coffin-Manson type of expression is used to predict the number of cycles to fatigue crack initiation. The experimental test specimens were studied by microscopy to determine on which crystallographic plane the fatigue initiation occurred. A good correlation between the experimental results and the simulated results were found.

Fatigue crack initiation in a notched single-crystal superalloy component

In this paper, the fatigue crack initiation in notched single-crystal test specimens of material MD2 is investigated and analysed. A critical plane approach is adopted, in which the total strain ranges on the discrete slip planes are evaluated. Furthermore, a Coffin-Manson type of expression is used to describe the number of cycles to fatigue crack initiation. This relation is determined from a set of smooth test specimens loaded uniaxially in the [001], [011] and [1̄11] directions at 500 °C with Rε=−1. The numerical procedure is then applied to a series of experiments, in which notched single-crystal test specimens were exposed to uniaxial cyclic loading in the [001] direction at 500 °C with Rε=0.

Energies and distributions of dislocations in stacked pile-ups

To understand the kinematic and thermodynamic effects of representing discrete dislocations as continuous distributions in their slip planes, we consider stacked double ended pile-ups of edge and screw dislocations and compute their distributions and microstructural energies, i.e., the elastic interaction energies of geometrically necessary dislocations (GNDs). In general, three kinds of representations of GNDs are used: discrete, semi-discrete, and, continuous representation. The discrete representations are closest to reality. Therefore, the corresponding solutions are considered exact. In the semi-discrete representation, the discrete dislocations are smeared out into continuous planar distributions within discrete slip planes. The solutions to problems formulated using different descriptions are different. We consider the errors in: dislocation distributions (number of dislocations), and, microstructural energies; when the discrete description is replaced by the semi-discrete one. Asymptotic expressions are derived for: number of dislocations, maximum slip, and, microstructural energy density. They provide a powerful insight into the behavior of the system, and are accurate for a wide range of parameters. Two characteristic lengths emerge from the analysis: the ratio of pile-up length to slip plane spacing (lambda), and, the ratio of slip plane spacing to the Burgers vector. For large enough lambda and large enough number of dislocations, both the discrete and semi-discrete solutions are well-approximated by asymptotic solutions. Results of a comprehensive numerical study are presented.

Earthquake-related deformation beneath gently inclined ground

The experimental data from an investigation of the response of sand slopes to centrifuge model earthquakes are presented. In each test a condition of steady state seepage was established parallel to the base of the model slope before triggering a single earthquake. Discrete slip planes are not observed; the predominant form of instability beneath both steeper and more gentle slopes is shear strain deformation. The deformation is continuous, though not linear, with depth. The data recorded by acceleration and pore pressure transducers are used to establish time histories of effective stress beneath slopes of different gradient. The mechanisms of deformation are then identified through the concept of characteristic state theory (phase transformation). It is shown that inertial loading is predominant in mechanisms associated with the deformation of slopes of moderate inclination, while transient pore pressure increase (with loss of shear strength and subsequent gravity effects) predominates in mechanisms associated with the deformation of more gentle slopes. Ĺauteur présente les données expérimentales de recherches sur la réaction de talus de sable &amp;garve; des modélisations de tremblement de terre en centrifugeuse. Dans chaque essai, on a établi un régime permanent de suintement parallèlement à la base du talus modé1isé avant de déclencher un tremblement de terre. On ńobserve aucun plan de glissement distinct, et le cisaillement est la forme prédominante &amp;acute;instabilité sous les pentes abruptes comme sous les pentes plus douces. La déformation est continue, mais pas linéaire, en profondeur. Les données enregistrées par les capteurs d'accé1ération et de pression &amp;acute;ean interstitielle servent à établir les diagrammes &amp;acute;évolution des contraintes intergranulaires sous des talus de pente variée. Les m6canismes de déformation sont alors identifiés à ĺaide du concept de la Worie de ĺétat caractéristique (transition de phase). On montre que le chargement inertiel est prédominant dans les mécanismes associés à la déformation des talus de pente modérée, tandis que ĺaugmentation transitoire de la pression &amp;acute;ean interstitielle (avec perte de r6sistance au cisaillement et effets de gravité subséquents) prédomine dans les mé- canismes associés à la déformation de talus à pente plus modérée.

Transmission electron microscopyin situstraining of multiphase Ni-20at.%Al-30at.%Fe

Abstract Transmission electron microscopy in situ straining experiments have been performed on the multiphase alloy Ni-20Al-30Fe (where the composition is in atomic per cent). This alloy consists of the B2 (ordered b.c.c.) phase Ni-30Al-20Fe and the phase Ni-12Al-40Fe which is f.c.c. with fine Ll2 (ordered f.c.c.) particles. Slip in the B2 phase was by the movement of ⟨100⟩ dislocations occurring either on discrete slip planes or in bands and produced loops as debris behind the gliding dislocations. Slip in the f.c.c. Ll2 phase was by the glide of pairs of (a/2)⟨110⟩ dislocations and occurred on discrete slip planes. The separation of the (a/2)⟨110⟩ dislocation pairs increased with increasing distance from the head of the slip band, because of disordering of the Ll2 particles. Pile-ups occurred in both phases at the two-phase interface. Slip propagation was observed to occur across the interfaces both from the B2 phase to the f.c.c. Ll2 phase and vice versa; there was also some evidence that dislocations could be nucleated into both phases from the internal two-phase interfaces.

On the theory of perfectly plastic anti-plane straining

A general formulation of two-dimensional elastic-perfectly-plastic anti-plane straining is presented for materials with arbitrary anisotropic convex yield surfaces. Stress and strain distributions in plastic regions adjoining portions of the boundary are obtained directly in terms of the yield surface geometry. When specialized to the classical torsion problem, results lead directly to a generalization of the well-known plastic roof construction for limit loads. Examples of the determination of fully plastic stress distributions and corresponding limit torques are given for circular and rectangular shafts with various yield conditions. Another specialization is made to the contained plastic deformation created by longitudinal shearing of a body containing a sharp edge notch. Here the determination of the elastic-plastic boundary and strain distribution is reduced to a potential theory problem for a region in the stress plane bounded by straight line segments and a portion of the yield surface, and a membrane analogy is presented which allows effective visualization of the solution. A solution valid for small scale yielding near a crack is given in terms of a conformal transformation of the yield surface to a unit circle, and some specific examples are worked. Particular attention is given to single crystal type yield surfaces made up of straight line segments corresponding to discrete slip planes.

The geometry of slip processes at a propagating fatigue crack—II

A previously published model of fatigue crack propagation is refined and the resulting slip geometry at the crack tip is calculated. The essential features of this refined model are: The slip on both sides of the crack is assumed to occur on slip bands instead of the discrete slip planes used in the old model. Slip is represented by finite matrices, shape changes of the crack tip as well as the anisotropy of slip are fully taken into account. It is shown, that the geometric mean of the average strains on both sides of the crack cannot be chosen independently but is a unique function of material parameters c 1, c 2 (characterizing the inhomogeneity of slip on both slip systems involved) and the angle α between the two slip planes. Whenever such strains—which must typically be of the order of one—can be produced by the applied stress, ductile crack propagation is possible (ductile fracture criterion). The crack tip angle and the ratio of crack advance per cycle and crack opening displacement are also given in terms of c 1, c 2 and α. Finally it is demonstrated that only the surface production by slip on intersecting slip planes cannot be reversed by slip reversal in the compression phase.