Single Slip Plane Research Articles

Probing deformation behavior of a refractory high-entropy alloy using in situ neutron diffraction

The grain orientation-dependent lattice strain evolution of a (TiZrHfNb)98N2 refractory high-entropy alloy (HEA) during tensile loading has been investigated using in situ neutron diffraction. The equivalent strain-hardening rate of each of the primary <hkl>-oriented grain families was found to be relatively low, manifesting the macroscopically weak work-hardening ability of such a body-centered cubic (BCC)-structured HEA. This finding, along with the post-mortem transmission electron microscopy (TEM) characterization, is indicative of a dislocation planar slip mode that is confined in a few single-slip planes and leads to in-plane softening by high pile-up stresses. In particular, during plastic deformation, the <110>-oriented grains yield preferentially, followed by lattice relaxation, while the load transfers to the <200>-oriented grains as a result of plastic anisotropy. Our work provides a new perspective for understanding the strain-hardening behavior and the role of planar slip in the plastic deformation of BCC-structured HEAs.

Atomistic investigations of Cr effect on the deformation mechanisms and mechanical properties of CrCoFeNi alloys

The emerging class of multi-principal element alloy (MPEA) processes superior mechanical properties and has great potential for applications in extreme environments. In this work, the synergic effect of the Cr content and crystallographic orientation on the deformation behaviors of single-crystal CrCoFeNi MPEAs has been investigated by atomistic simulations. We have found distinct differences in dislocation activities, deformation microstructures, and mechanical behaviors in the model MPEAs, which depend on crystallographic orientations, Cr concentration, and the number of activated slip systems. When multiple slip systems are triggered along [100] and [111] orientations, Shockley partial activation and their interaction are predominant, leading to the formation of sessile dislocations and a dense dislocation network. When only two slip systems of Shockley partials are favored along the [110] direction, the influence of Cr concentration and planner defect energies emerges. At low Cr concentration, the double planar slip of Shockley partials results in deformation-induced nanotwins. At high Cr concentration, the partial dislocations of a single slip plane become dominant, attaining the highest volume fraction of deformation-induced phase transformation. The results provide a fundamental understanding of deformation mechanisms in MPEAs, elucidating the synergic effect of crystal orientation and composition on tunning the mechanical behaviors.

Earthquake fault slip and nonlinear dynamics

Earthquake fault slip under shear forcing can be envisioned as a nonlinear dynamical process dominated by a single slip plane. In contrast, nonlinear behavior in Earth materials (e.g., rock) is driven by a strain-induced ensemble activation and slip of a large number of distributed features—cracks and grain boundary slip across many scales in the volume. The bulk recovery of a fault post-failure and that of a rock sample post dynamic or static forcing (”aging” or the “slow dynamics”) is very similar with approximate log(time) dependence for much of the recovery. In our work, we analyze large amounts of continuous acoustic emission (AE) data from a laboratory “earthquake machine,” applying machine learning, with the task of determining what information regarding fault slip the AE signal may carry. Applying the continuous AE as input to machine learning models and using measured fault friction, displacement, etc., as model labels, we find that the AE are imprinted with information regarding the fault friction and displacement. We are currently developing approaches to probe stick-slip on Earth faults, those that are responsible for damaging earthquakes. A related goal is to quantitatively relate nonlinear elastic theory (e.g., PM space, Arrhenius) to frictional theory (e.g., rate-state).

Micromechanical Tension Testing of Additively Manufactured 17-4 PH Stainless Steel Specimens

This study presents a methodology for the rapid fabrication and micro-tensile testing of additively manufactured (AM) 17-4PH stainless steels by combining photolithography, wet-etching, focused ion beam (FIB) milling, and modified nanoindentation. Detailed procedures for proper sample surface preparation, photo-resist placement, etchant preparation, and FIB sequencing are described herein to allow for high throughput (rapid) specimen fabrication from bulk AM 17-4PH stainless steel volumes. Additionally, procedures for the nano-indenter tip modification to allow tensile testing are presented and a representative micro specimen is fabricated and tested to failure in tension. Tensile-grip-to-specimen alignment and sample engagement were the main challenges of the micro-tensile testing; however, by reducing the indenter tip dimensions, alignment and engagement between the tensile grip and specimen were improved. Results from the representative micro-scale in situ SEM tensile test indicate a single slip plane specimen fracture (typical of a ductile single crystal failure), differing from macro-scale AM 17-4PH post-yield tensile behavior.

Laser shock peening of copper poly- and single crystals

In this paper, the effect of laser shock peening (LSP) of mono- and polycrystalline copper was studied. It is shown that the residual stress caused by this process is accumulated at the LSP treated surface of the material, the thickness of which is several hundreds of micrometers. The affected layer contains an enhanced density of dislocations. These dislocations are homogeneously distributed on the cross-section in the single crystal along the single slip plane. The dislocations in the polycrystal are distributed heterogeneously on the sample cross-section. This heterogeneity is discussed from the viewpoint of the orientation dependence of individual grains and varied values of the Schmid factor and confirms the compressive nature of the stress caused by LSP. Depth dependence of the microhardness of the material decreases from the LSP treated surface in direction to the sample center correspondingly.

Plane waves in anisotropic elastic–plastic material with voids

Dispersion equation is derived for the propagation of one-dimensional plane waves in a general linear anisotropic isothermal elastic–plastic material with voids. The plasticity of the considered material is defined through the dislocation of a single slip plane and direction. The derived dispersion equation is then reduced for the relevant wave propagation in particular media, namely, monoclinic, orthotropic, transversely isotropic, and isotropic elastic–plastic material with voids. In general, it is found that there exist four basic waves traveling with distinct speeds in these specific anisotropic elastic–plastic materials with voids. A new wave is found to appear because of the presence of plasticity in the material. Out of the four basic waves traveling in an orthotropic/transversely isotropic material with voids, a wave travels independent of plasticity and void parameters, whereas the remaining three waves depend on plasticity as well as on the presence of voids. The one which is traveling independent of plasticity and voids is nondispersive and nonattenuating, whereas the other waves are dispersive in nature. The speeds of all the existing waves are computed numerically for a specific model, displayed graphically, and discussed.

Data rich imaging approaches assessing fatigue crack initiation and early propagation in a DS superalloy at room temperature

Crack initiation and early propagation behavior of the directionally solidified (DS) superalloy CM247LC has been assessed by data rich imaging approaches. These include conventional characterization methods such as replica record analysis, 3D optical surface imaging, optical and scanning electron microscopy (SEM) as well as more recent techniques like digital image correlation (DIC) and synchrotron radiation computed tomography (SRCT). Three modes of secondary crack behaviors were found during evaluation of the fatigue process. The early stages of fatigue damage were controlled by microstructure-induced cracking, mainly consisting of carbide cracking. Fatigue damage was then promoted via slip band cracking and opening mode controlled carbide-cracking. The mechanisms of these different cracking behaviors are associated with the plastic zone of the main crack tip. Even though the early localized strain levels were of the same intensity within slip bands and at the intersection sites with carbides, carbide-induced cracking occurred prior to slip band cracking, characterized by SEM-DIC. This indicated that carbide-induced cracking was more likely to occur in the early stages of the fatigue process. Early crack growth behaviors were further investigated in situ at the microstructural scale via SRCT. The effect of carbides on crack initiation and propagation processes were evaluated in 3D. This revealed the phenomenon around pores, that cracks simultaneously grew on different slip planes in 3D, contrary to previous theories that such cracks tend to grow on a single favourable slip plane (in polycrystalline alloys). The SRCT result demonstrates the importance and necessity of 3D characterization of the crack propagation behavior at sub-surface, which is not fully analyzed by 2D characterization.

Wave propagation in elastic–plastic material with voids

Constitutive relations and governing equations have been developed for an elastic–plastic material with voids having single slip-plane and direction. The plasticity of the material is considered through the dislocation of slip-plane. The propagation of unidirectional plane waves has been explored in an infinite elastic–plastic material with voids, and it has been found that there exist four basic waves consisting of three coupled elastic–plastic waves and a lone transverse wave. The speeds of propagation of all the coupled elastic–plastic waves are found to be affected by the plasticity and void parameters, in general, while the transverse wave is not affected by the plasticity and void parameters at all and travels with the speed of classical transverse waves. Out of the three coupled elastic–plastic waves, two waves are the counterpart of the waves existing in elastic materials with voids, while the third wave is new and has appeared due to the presence of plasticity in the material. One of the coupled elastic–plastic waves that is least affected by the plasticity faces a critical frequency, below which the wave is a nonpropagating wave. This critical frequency arises due to the presence of voids in the medium. The speed of various waves is computed for a specific model and the results that are obtained are presented graphically. At large frequencies, all the coupled elastic–plastic waves propagate with constant speeds, but at low frequencies, they propagate with speeds less than that of the longitudinal wave of classical elasticity. Several earlier known results have been recovered as special cases from the present formulation.

Screw dislocation–spherical void interactions in fcc metals and their dependence on stacking fault energy

We performed molecular dynamics simulations to evaluate the effects of stacking fault energy (SFE) on interactions between a screw dislocation and spherical voids in face-centered cubic (fcc) metals. It was observed that the frequency of the cross-slips is a critical factor affecting the interaction, with primarily three different interaction morphologies being observed: (1) the two partial dislocations detach from the void independently with a time lag, (2) the two partial dislocations detach from the void almost simultaneously on a single slip plane, and (3) the two partial dislocations detach from the void almost simultaneously while involving more than one cross-slip and a jog formation. The magnitude of the critical resolved shear stress (CRSS) increases in the order mentioned above. The CRSS values for interaction morphology (2), which was observed most frequently in this study, were in good agreement with those predicted analytically by adjusting the parameters dependent on the SFE. Based on the obtained results, we discussed the applicability of the analytical model for void hardening in fcc metals. The results of this work contribute significantly to the modeling of mechanical property degradation in irradiated metals.

銅単結晶ナノ薄膜における疲労き裂発生

An in-situ FESEM fatigue crack initiation experiment of a 760-nm-thick freestanding single crystalline copper (Cu) film was conducted to clarify the intrinsic mechanisms of fatigue crack initiation excluding the effect of microstructure such as twin boundaries. An hourglass-shaped film specimen with a single-side-edge notch was prepared. The specimen had (001) surface and [110] loading direction. FESEM observations showed that slip lines were formed at the notch root in [110] direction perpendicular to the loading axis. Intrusions/extrusions were then formed along a single slip plane, or (111) plane, and a crack occurred along the slip plane.

A crystal plasticity framework based on the Continuum Dislocation Dynamics theory: relaxation of an idealized micropillar

AbstractThe motion and interaction of dislocation lines are the physical basis of the plastic deformation of metals. Although ‘discrete dislocation dynamic’ (DDD) simulations are able to predict the kinematics of dislocation microstructure (i.e. the motion of dislocations in a given velocity field) and therefore the plastic behavior of crystals in small length scales, the computational cost makes DDD less feasible for systems larger than a few micro meters. To overcome this problem, the Continuum Dislocation Dynamics (CDD) theory was developed. CDD describes the kinematics of dislocation microstructure based on statistical averages of internal properties of dislocation systems. In this paper we present a crystal plasticity framework based on the CDD theory. It consists of two separate parts: a classical 3D elastic boundary value problem and the evolution of dislocation microstructure within slip planes according to the CDD constitutional equations. We demonstrate the evolution of dislocation density in a micropillar with a single slip plane. (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

An analysis of the pile-up of infinite periodic walls of edge dislocations

We analyse the equilibrium pile-up configurations of infinite periodic walls of edge dislocations which are forced against an impenetrable obstacle by a constant applied shear stress. Numerically generated density distributions exhibit two distinct regions, for each of which we provide an interpretation and an analytical prediction. Near the obstacle, the influence of neighbouring slip planes may be neglected and the classical solution for a single slip plane applies. At a larger distance a linear decay is obtained. The characteristic length scales of the two parts of the pile-up are shown to depend differently on the parameters of the problem.

Transition of crack propagation from a transgranular to an intergranular path in an overaged Al-Zn-Mg-Cu alloy during cyclic loading

The fatigue crack propagation behavior in the overaged Al-Zn-Mg-Cu alloy was characterized by optical microscopy, scanning electron microscopy, transmission electron microscopy and electron backscatter diffraction. The results revealed that a fatigue crack tended to transgranularly propagate in the near-threshold regime, whereas intergranular crack propagation was dominant at the high ΔK regime. The transition of crack propagation from a transgranular to an intergranular path that occurred in the Paris regime was strongly influenced by the misorientation of adjacent grains and precipitate free zones. In addition, a crystallographic model of crack propagation was proposed to interpret the transition. The fatigue short crack propagation on a single slip plane was responsible for the formation of a transgranular propagation path in the near-threshold regime. The fatigue long crack propagation, which was conducted by a duplex slip mechanism in the Paris regime, led to the formation of fatigue striations. The formation of a zigzag crack in the near-threshold regime was ascribed to the high misorientation of adjacent grains.

Homogenization of the Peierls–Nabarro model for dislocation dynamics

This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic Lévy operator of order 1 and a potential depending periodically on u/ϵ. The limit equation is a non-local Hamilton–Jacobi equation, which is an effective plastic law for densities of dislocations moving in a single slip plane.

A comparative study of fracture in Al: Quantum mechanical vs. empirical atomistic description

A comparative study of fracture in Al is carried out by using quantum mechanical and empirical atomistic description of atomic interaction at crack tip. The former is accomplished with the density functional theory (DFT) based quasicontinuum method (QCDFT) and the latter with the original quasicontinuum method (EAM-QC). Aside from quantitative differences, the two descriptions also yield qualitatively distinctive fracture behavior. While EAM-QC predicts a straight crack front and a micro-twinning at the crack tip, QCDFT finds a more rounded crack profile and the absence of twinning. Although many dislocations are emitted from the crack tip in EAM-QC, they all glide on a single slip plane. In contrast, only two dislocations are nucleated under the maximum load applied in QCDFT, and they glide on two adjacent slip planes. The electron charge density develops “sharp corners” at the crack tip in EAM-QC, while it is smoother in QCDFT. The physics underlying these differences is discussed.

A 3-D view on the mechanisms of short fatigue cracks interacting with grain boundaries

Short fatigue cracks propagate with a fluctuating crack growth rate while interacting with microstructural barriers. Although some models of the interaction exist, it is not clear what determines the strength of the resistance of a grain boundary to crack propagation. Therefore we developed a method for artificial crack initiation which uses a focused ion beam (FIB) to nucleate cracks crystallographically on single slip planes identical to natural stage I cracks. The crack parameters as well as the grain boundary parameters can be varied independently for systematic experiments. For the first time the crack path through a grain boundary is shown in 3-D by FIB tomography. This enables the interaction between microcracks and grain boundaries to be observed in 3-D with a high spatial resolution. It is not only the inclination angle between the active slip systems, but also the inclination angle of the grain boundary, which determines the strength of these microstructural barriers.

Microstructure Characteristics of an Fe-Mn-C TWIP Steel After Deformation

The microstructure characteristics of an Fe-Mn-C TWIP steel after deformation are investigated. The results show that the hot-rolled, cold-rolled and then annealed sample of the Fe-Mn-C TWIP steel has excellent mechanical properties, and the true stress-true strain curve from tension tests exhibits repeated serrations. The deformed microstructure exhibits the typical planar glide characteristics such as no cell formation, dislocation pile-ups on a single slip plane, mechanical twins and stacking faults. There are equiaxial and deep dimple structures in the fractograph, indicative of a ductile fracture. Microcracks initiate from inclusions and twin-twin intersections. Deformation and fracture processes are the formation, growth and coalescence of microvoids.

Simulation of stage I‐crack growth using a 3D‐model

AbstractA three‐dimensional model for stage I‐short crack propagation on a single slip plane is presented. It considers elastic plastic material behaviour by allowing sliding on the active slip plane in a defined slip direction. A crack propagation law based on the crack tip slide displacement is implemented to simulate crack propagation. The model is solved numerically using the dislocation loop technique. (© 2009 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Texture characteristics controlled by single slip plane slipping in the warm-rolled Fe-14Mn-5Si-9Cr-5Ni shape memory alloy

To clarify the texture evolution mechanism of Fe-Mn-Si-based shape memory alloys, the rolling texture of an Fe-14Mn-5Si-9Cr-5Ni shape memory alloy is investigated during rolling to a final reduction of 82% at 873 K. A new rolling texture caused by single slip plane slipping is observed from such alloy, which is different from the conventional copper-type and brass-type textures. By means of the {111} pole figure scattering analysis of the local deformation structure, we conclude that such single slip plane slipping results in the weakness of brass orientation in the α fiber and the great enhancement of β fiber connecting S′ {331}&lt;213&gt; and B′ orientations {110}&lt;114&gt;.

Homogenization of First Order Equations with (u/ϵ)-Periodic Hamiltonians Part II: Application to Dislocations Dynamics

This paper is concerned with a result of homogenization of a non-local first order Hamilton–Jacobi equation describing the dislocations dynamics. Our model for the interaction between dislocations involves both an integro-differential operator and a (local) Hamiltonian depending periodicly on u/ϵ. The first two authors studied in a previous work homogenization problems involving such local Hamiltonians. Two main ideas of this previous work are used: on the one hand, we prove an ergodicity property of this equation by constructing approximate correctors which are necessarily non periodic in space in general; on the other hand, the proof of the convergence of the solution uses here a twisted perturbed test function for a higher dimensional problem. The limit equation is a nonlinear diffusion equation involving a first order Lévy operator; the nonlinearity keeps memory of the short range interaction, while the Lévy operator keeps memory of long ones. The homogenized equation is a kind of effective plastic law for densities of dislocations moving in a single slip plane.