Parallel Slip Planes Research Articles

Short crack propagation near coherent twin boundaries in nickel-based superalloy

Short crack propagation near a coherent twin boundary in polycrystal nickel alloy is investigated with 3D crystal plasticity extended finite element modelling (CP-XFEM), utilising reconstructed experimentally characterised microstructures and crack path observations. Short 3D cracks at coherent twin boundaries are shown to grow on parallel (111) slip planes at very high rate so as to be an intrinsic part of the nucleation process. This is found to occur predominantly because of the stress states established by twin/parent constraint driven by the local elastic anisotropy. If elastic isotropy is modelled, crack growth is found to be non-planar and inclined to the twin boundary. The twin/parent twist angle is also found to influence local stress state, such that the actual 60° twist angle gives rise to the highest local stresses, preferential crack nucleation and rapid growth parallel to the twin boundary, and the deviations from 60° change the crack morphology and rate of growth.

Shear stress relaxation through the motion of edge dislocations in Cu and Cu–Ni solid solution: A molecular dynamics and discrete dislocation study

Shear stress relaxation through the motion of multiple edge dislocations in a periodic cell is studied by molecular dynamics and discrete dislocation methods. In both methods, we consider systems with an initial edge dislocation on the parallel slip planes. The initial shear strain is applied to the system along the Burgers vector of the dislocations. The velocity profile for a single edge dislocation fitted from a molecular dynamics (Bryukhanov, 2020) is used as the input to discrete dislocation dynamics. The dependence of shear stress, plastic strain, and plastic strain rate on time are analyzed. We show that when dislocations are sufficiently far from each other, relaxation occurs due to dislocation motion, and dislocation velocity can exceed the anisotropic speed of sound. If the dislocations are closer together, relaxation is due to the growth of stacking faults. We find that the stress at which the stress relaxation mechanism changes decreases with increasing dislocation density. Stress relaxation in a Cu–Ni solid solution occurs faster than in pure Cu due to a higher dislocation velocity in the high-velocity regime. However, the shear stress at which nickel atoms increase the plastic strain rate increases with an increase in dislocation density. The dependence of the relaxation time on the dislocation density obtained in discrete dislocation simulations is approximated using the power law. The elastic interaction between dislocations reduces the exponent of the power law from 1/ρ to approximately 1/ρ0.8 for both pure Cu and Cu–Ni solid solutions.

Surface and Subsurface Analysis of Stainless Steel and Titanium Alloys Exposed to Ultrasonic Pulsating Water Jet.

This article deals with the effect of periodically acting liquid droplets on the polished surfaces of AISI 316L stainless steel and Ti6Al4V titanium alloy. These materials were exposed to a pulsating water jet produced using an ultrasonic sonotrode with an oscillation frequency of 21 kHz placed in a pressure chamber. The only variable in the experiments was the time for which the materials were exposed to water droplets, i.e., the number of impingements; the other parameters were kept constant. We chose a low number of impingements to study the incubation stages of the deformation caused by the pulsating water jet. The surfaces of the specimens were studied using (1) confocal microscopy for characterizing the surface profile induced by the water jet, (2) scanning electron microscopy for detailed surface observation, and (3) transmission electron microscopy for detecting the changes in the near-surface microstructure. The surface described by the height of the primary profile of the surface increased with the number of impingements, and was substantially more intense in the austenitic steel than in the Ti alloy. Irregular surface depressions, slip lines, and short cracks were observed in the Ti alloy, whereas pronounced straight slip bands formed in the austenitic steel. The dislocation density near the surface was measured quantitatively, reaching high values of the order of 1014 m−2 in the austenitic steel and even higher values (up to 3 × 1015 m−2) in the Ti alloy. The origins of the mentioned surface features differed in the two materials: an intense dislocation slip on parallel slip planes for the Ti alloy and mechanical twinning combined with dislocation slip for the austenitic steel.

Atomistic study of shock Hugoniot in columnar nanocrystalline copper

Understanding the shock behavior of polycrystals is challenging due to the effects of grain size, defect, and orientation. In this study, we focus on the grain size and defect effects on the shock Hugoniot of polycrystals using columnar nanocrystalline copper. The dominant deformation mechanism is clarified under the impact velocities ranging from 300 m/s to 1200 m/s. The main findings from this study are as follows. The shock Hugoniot relation between pressure and specific volume has no clear dependence on the grain size, whereas the corresponding Hugoniot shear stress exhibits a grain size dependence. The primary defects of shock plasticity change from dislocation to stacking fault and finally twinning with the increase of impact velocity. As the impact velocity exceeds 1000 m/s, the shielding effect becomes prominent as a result of the defect formation on the parallel slip planes within a grain.

Microstructure evolution and crystallographic slip modes during grind hardening in TC21 titanium alloy

In this work, the microstructure evolution and slip mechanism of TC21 titanium alloy in grind hardening (GH) and grind hardening and aging treatment (GHAG) were comparatively investigated. The experimental results showed that the hardened layer formed in both GH and GHAG is mainly composed of TiN, while their internal microstructure is quite different. Compared with as-received alloy, the tensile strength and elongation after GH process increased by 110 MPa and 1.5%, respectively. The tensile strength after GH process increased by 50 MPa but the elongation decreased by 0.2%. Moreover, A method to deduce slip systems by using interior crystall misorientation axis (ICMA) was demonstrated in this paper. The distribution of ICMA indicated that three major slip systems were activated which was verified by texture components in ODF sections. The slipping results in two kinds of crystal orientation distribution: (a) the activated slip plane parallel to loading stress; (b) the slip direction parallel to loading stress, but existing a deviation angle between slip plane and loading stress.

Material modeling of ferritic steel on microscopic length scale under cyclic loading

AbstractA material model for the polycrystalline microstructure of formable steels is developed to determine the residual stress state resulting from incompatible plastic deformation of individual grains under non‐monotonic loading. The glide of mobile dislocations on a specific slip system mainly governs the shear rates. During the movement, dislocations experience several types of resistance. The existing immobile dislocation structures on non‐parallel slip planes reduce the slip activities. This is reflected in a nonlinear isotropic hardening criterion. Furthermore, piled up dislocations on parallel slip planes also create hindrance to mobile dislocations. This effect creates residual stresses within the material which are taken into account by an additional kinematic hardening law. Residual stresses play a crucial role as well, especially during cyclic loading. Both, nonlinear isotropic and kinematic hardening criteria can define the plastic character of ferritic steel under non‐monotonic loadings.

Characterisation of dislocation patterning behaviour with a continuum dislocation dynamics model on two parallel slip planes equipped with a deep neural network resolving local microstructures

The self-organisation behaviour of dislocation upon loading is still a mechanistically mysterious phenomenon. The present article aims to present a computationally tractable dislocation dynamics model, which can be used for helping analyse the mechanism behind dislocation pattern formation. With an integrated use of asymptotic analysis and machine learning tools, the discrete dislocation dynamics on two parallel slip planes is self-consistently reformulated at a coarse-grained level. For the present case, asymptotic analysis helps in 1) reformulating the original globally discrete problem by a continuum model underpinned by a database resolving the almost singular short-range elastic interaction of discrete dislocations; 2) identifying the proper input and output quantities for implementing machine learning tools; 3) digging out a hidden but explicit interrelation between mean-field quantities to reduce the dimensionality of the data space. Machine learning tools serve for 1) inferring the inherently implicit interrelationships between continuum quantities; 2) capturing a low-dimensional manifold in the data space corresponding to the local flow stress. The non-monotonically increasing profile of the flow stress - density relationship, as revealed by machine learning, is found to play a key role in the onset of dislocation patterning behaviour seen in the simulation results. A scaling law relating the applied stress to pattern wavelength is also derived, providing a rationale to the widely used empirical similitude relation. The experimentally observed swing in similitude coefficient value is attributed to the randomness in slip plane distributions. In a methodological viewpoint, the treatment of using asymptotic analysis to help design the curriculum for implementing machine learning tools, offers a paradigm for self-consistently upscaling more complicated multiscale systems.

Plastically Deformable and Exfoliating Molecular Crystals of a 2-D Coordination Polymer and Its Ligand

4-n-Hexyloxybenzoic acid and the corresponding potassium salt were synthesized and crystallized, and their force-induced mechanical response was studied. 4-n-Hexyloxybenzoic acid is crystallized as large single crystals of the reported monoclinic polymorph, whereas, its potassium salt forms a 2D polymeric structure. When a localized mechanical force is applied, crystals of both materials undergo plastic deformation to the extent that they can be folded to resemble characters of the English alphabet. With few cycles of bending and unbending, the crystals can be exfoliated, and crystalline layers can be separated. In both structures, van der Waals interactions of the hexyl chains contribute toward the formation of slip plane parallel to the wider face of the crystals, which is necessary for their plastic deformability. Reported crystal structures of 4-n-alkoxybenzoic acids with alkyl chain length ranging from C1 to C10 and their inorganic salts were analyzed, and it was found that packing of alkyl chains su...

Effect of Temperature on Small-Scale Deformation of Individual FCC and BCC Phases of Al0.7CoCrFeNi High Entropy Alloy

High Entropy Alloys (HEAs) represent an important class of structural materials because of their high strength, ductility, and thermal stability due to the solid solution nature of the multi-component metallic system. Understanding the mechanical response of isolated phases (FCC and BCC) of a dual-phase HEA is integral to understanding mechanical properties of these special alloys in bulk. We investigate the compressive response of single crystalline cylinders with diameters between 400 nm and 2 µm excised from individual grains within FCC and BCC phases of Al0.7CoCrFeNi HEA at 295 K, 143 K and 40 K. Micro-compression experiments were conducted in an in-situ SEM equipped with a custom-constructed cryogenic setup; FCC samples had a [324] crystallographic orientation, and those extracted from the BCC phase had a [001] orientation. We observed a smaller is stronger size effect in the yield strength as a function of pillar diameter, D, of both alloy phases for all temperatures, τ_y ∝D^m with a power law exponent, m, decreasing from -0.68 at 295K to -0.47 at 143K to -0.38 at 40K for FCC phase, and remaining constant at ~-0.33 for all temperatures for the BCC phase. We also observed reduced work hardening rates and more extensive strain bursts during deformation at lower temperatures in all samples. All deformed FCC samples contained multiple parallel slip offsets for all pillar sizes and temperatures; compressed BCC pillars had wavy slip traces, which are evidence of multiple intersecting slip systems. Transmission Electron Microscopy (TEM) microstructural analysis of the compressed FCC samples reveals parallel slip lines and distorted slip planes, while compressed BCC samples contained entangled dislocation networks, as well as several twinned regions in samples deformed at 40 K. Molecular dynamics (MD) simulations of representative FCC and BCC HEA compressions reveal that deformation in FCC HEAs is dominated by nucleation and propagation of partial dislocations along parallel slip planes but by partial dislocation/twinning in the BCC HEA at all temperatures. Simulations also predict a decrease in stacking fault energy with increased alloying. For example, a reduction in the stable stacking fault energy of the FCC HEA up to 55% with respect to pure constituents is observed. This reduction in stable stacking fault energy may drive the observed deformation mechanisms. We also discuss theories of low-temperature strengthening in HEAs, compare them to our experimental data and assess how they manifest in the observed temperature-dependent size effect.

Dislocation interactions at reduced strain rates in atomistic simulations of nanocrystalline Al

Molecular dynamics simulations of transient stress drops have been carried out in different regimes on a nanocrystalline Aluminum sample with average grain size of 12 nm. Besides confirming the interpretation of experimental results obtained during in situ X-ray diffraction, the creep simulations performed at 2 or 3 orders of magnitude lower strain rates than usual reveal deformation mechanisms that have not been observed previously. First of all, it is evidenced that the misfit dislocations available at the GB assist the propagation of a lattice dislocation on a plane with low resolved shear stress. Furthermore, it is shown that the interaction of two dislocations gliding on parallel slip planes can result in the emission of a vacancy in the grain interior. Finally, the importance of the Schmid factor in the activation of slip in nanocrystalline structures is discussed.

Continuum dynamics of the formation, migration and dissociation of self-locked dislocation structures on parallel slip planes

In continuum models of dislocations, proper formulations of short-range elastic interactions of dislocations are crucial for capturing various types of dislocation patterns formed in crystalline materials. In this article, the continuum dynamics of straight dislocations distributed on two parallel slip planes is modelled through upscaling the underlying discrete dislocation dynamics. Two continuum velocity field quantities are introduced to facilitate the discrete-to-continuum transition. The first one is the local migration velocity of dislocation ensembles which is found fully independent of the short-range dislocation correlations. The second one is the decoupling velocity of dislocation pairs controlled by a threshold stress value, which is proposed to be the effective flow stress for single slip systems. Compared to the almost ubiquitously adopted Taylor relationship, the derived flow stress formula exhibits two features that are more consistent with the underlying discrete dislocation dynamics: (i) the flow stress increases with the in-plane component of the dislocation density only up to a certain value, hence the derived formula admits a minimum inter-dislocation distance within slip planes; (ii) the flow stress smoothly transits to zero when all dislocations become geometrically necessary dislocations. A regime under which inhomogeneities in dislocation density grow is identified, and is further validated through comparison with discrete dislocation dynamical simulation results. Based on the findings in this article and in our previous works, a general strategy for incorporating short-range dislocation correlations into continuum models of dislocations is proposed.

Calculating the fatigue life of smooth specimens of two-phase titanium alloys subject to symmetric uniaxial cyclic load of constant amplitude

A system of microstructure-dependent fatigue failure models that allows calculating the number of stress cycles to failure of smooth specimens in the absence of data on the fatigue resistance of the material is proposed. Fatigue life is represented as the sum of the number of stress cycles to the initiation of a microstructurally short crack with a depth equal to one grain size and the number of stress cycles to the instant the growing physically small and long crack reaches the depth taken as a fatigue failure criterion. To fill the models, it is necessary to test standard specimens under monotonic short-term tension to determine the elastic modulus, Poisson’s ratio, and the proportional limit and to analyze the microstructure and texture of the material to determine the Taylor factor, the magnitude of the Burgers vector, and the distance between neighboring parallel slip planes in the lattice, depending on which slip system is activated relative to the tension direction. The models are applicable to metals and alloys in which a fatigue crack is initiated along a persistent slip band in a surface grain under high-cycle loading. The models are validated against fatigue test data for flat specimens of different two-phase titanium alloys (VT3-1, IMI 834, Ti–6Al–4V, VT6, VT16, VT22, VT23, LCB) with different types of microstructure (bimodal, globular, fine-grained β-transformed) subject to symmetric in-plane bending. The plotted S–N curves are in a satisfactory agreement with experimental data.

A Phase‐field Model of Dislocations on Parallel Slip Planes

AbstractWe establish a line‐tension energy for dislocation networks concentrated in finitely many parallel slip planes as the limit of a Peierls‐Nabarro energy. Dislocations in different planes interact depending on their distance. At intermediate distances a two‐scale dislocation microstructure is optimal. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mechanics of fatigue crack initiation in submicron-thick freestanding copper films

The mechanics of fatigue crack initiation in roughly 500-nm-thick freestanding copper (Cu) films were investigated by using single-side-edge-notched specimens and elastic finite element method (FEM) analyses. By applying cyclic loading at a stress ratio R=0, an intrusion/extrusion was formed near a notch root, and a fatigue crack then initiated at the intrusion/extrusion, which penetrated the film in the thickness direction on a slip plane parallel to a Σ3 twin boundary. Local stress distributions were evaluated by three-dimensional FEM analyses, taking account of the individual grain shape and crystal orientation around the fatigue crack initiation sites. The results revealed that a fatigue crack was initiated on slip systems where (i) the slip deformation penetrated the film in the thickness direction without being blocked by grain boundaries or twin boundaries, and (ii) a high resolved shear stress occurred under the conditions in (i). The number of cycles to fatigue crack initiation increased as the intensity of the resolved shear stress field at the fatigue crack initiation site decreased. The resolved shear stress required for fatigue crack initiation in the Cu films is roughly one order of magnitude higher than that in a bicrystal or single-crystal bulk Cu of 30–35MPa.

In situ measurements of a homogeneous to heterogeneous transition in the plastic response of ion-irradiated 〈1 1 1〉 Ni microspecimens

We report on the use of quantitative in situ microcompression experiments in a scanning electron microscope to systematically investigate the effect of self-ion irradiation damage on the full plastic response of 〈111〉 Ni. In addition to the well-known irradiation-induced increases in the yield and flow strengths with increasing dose, we measure substantial changes in plastic flow intermittency behavior, manifested as stress drops accompanying energy releases as the driven material transits critical states. At low irradiation doses, the magnitude of stress drops reduces relative to the unirradiated material and plastic slip proceeds on multiple slip systems, leading to quasi-homogeneous plastic flow. In contrast, highly irradiated specimens exhibit pronounced shear localization on parallel slip planes, which we ascribe to the onset of defect free channels normally seen in bulk irradiated materials. Our in situ testing system and approach allows for a quantitative study of the energy release and dynamics associated with defect free channel formation and subsequent localization. This study provides fundamental insight into the nature of interactions between mobile dislocations and irradiation-mediated and damage-dependent defect structures.

Partition of Cyclic Plasticity in an Austenitic-Ferritic Duplex Stainless Steel and its Significance for Fatigue Crack Initiation under High and Very High Cycle Fatigue Loading Conditions

The present study documents that at loading amplitudes close to the fatigue limit, cyclic irreversible plastic deformation in form of slip band generation in the austenitic-ferritic duplex stainless steel X2CrNiMoN22-5-3 (318 LN) mainly takes place in few austenite grains without any microcrack initiation in these grains. This was shown by means of focused ion beam (FIB) cutting in combination with high resolution scanning electron microscopy (SEM) at pronounced extrusion-intrusion-pairs in several austenite grains. Investigations by means of confocal laser scanning microscopy (CLSM) revealed that the slip band density in these grains increases with the number of loading cycles and remains constant in the very high cycle fatigue (VHCF) regime. Under such loading conditions, fatigue cracks frequently initiate in the ferrite phase due to anisotropy stresses which are strongly superimposed by stress intensifications at the tip of austenite slip bands. TEM investigations revealed that austenite slip bands, which are piling up against phase boundaries, cause localized dislocation generation and motion in neighboring ferrite grains. The cyclic irreversible motion of these dislocations on several parallel slip planes is correlated with the stage of fatigue crack initiation. A crystal plasticity model based on a finite element program, which considers anisotropic elasticity, allows for the determination of crack initiation sites in real microstructures according to the above mentioned mechanisms. Crystallographic orientations, measured by means of the electron back scatter diffraction (EBSD) technique, serve as input parameters for the calculations regarding microcrack initiation as well as for the analysis of the subsequent short fatigue crack propagation, which is strongly affected by microstructural barriers such as grain and phase boundaries.

Strain localization at dislocation channel–grain boundary intersections in irradiated stainless steel

The interaction of dislocation channels with grain boundaries in irradiated stainless steel was observed on multiple length scales using scanning electron microscopy (SEM) digital image correlation (DIC) and confocal microscopy (micro-scale), in situ straining and transmission electron microscopy (TEM) (nano-scale), and atomistic modeling (atomic scale). Interactions were divided into three classifications; slip transmission, discontinuous slip, and discontinuous slip that induced grain boundary slip. DIC and confocal microscopy were used to quantify the plastic strain at dislocation channel–GB intersections. In situ TEM was used to image dislocations inside of channels as they interacted with the grain boundary. Slip in the dislocation channels, as observed by TEM, was found to involve cross slip between different slip planes, as well as the possibility of different slip systems activated on parallel slip planes. Atomistic simulations agreed well with experiments on the nature of channel-grain boundary interactions and also showed elevated levels of elastic stress at DC–GB intersections where slip was discontinuous with no slip transmission. The two distinct classifications of discontinuous slip are significant, suggesting two possible cracking mechanisms that both lead to the rupture of the oxide over the grain boundary.

Basal Plane Dislocation Multiplication via the Hopping Frank-Read Source Mechanism and Observations of Prismatic Glide in 4H-SiC

In this paper, we report on the synchrotron white beam topographic (SWBXT) observation of “hopping” Frank-Read sources in 4H-SiC. A detailed mechanism for this process is presented which involves threading edge dislocations experiencing a double deflection process involving overgrowth by a macrostep (MP) followed by impingement of that macrostep against a step moving in the opposite direction. These processes enable the single-ended Frank-Read sources created by the pinning of the deflected basal plane dislocation segments at the less mobile threading edge dislocation segments to “hop” from one slip plane to other parallel slip planes. We also report on the nucleation of 1/3< >{ } prismatic dislocation half-loops at the hollow cores of micropipes and their glide under thermal shear stress.

Atomistic simulation of twin boundaries effect on nanoindentation of Ag(1 1 1) films

Atomistic simulations were employed to study the effect of a single twin boundary parallel with the indented surface on nanoindentation of Ag(111) films. The results show that the twin boundary has little influence on the elastic modulus of films. The load for the initial yield is observably reduced when the twin boundary is very near the indented surface due to the nucleation of the glissile dislocations on the slip plane parallel to the surface, rather than the formation of the tetrahedral sessile lock when nanoindentation on the perfect film. Twin boundaries are effective obstacles to the motion of dislocations, and change the dislocation patterns dominating the deformation, resulting in the hardening of films. In addition, twin boundaries can act as dislocation sources before losing their coherency.

Mechanical behavior of fcc crystal simulated by 3-D discrete dislocation dynamics

To simulate the mechanical behavior of the FCC crystal with the lower Peierls stress, the stiff property and physical meaning of the differential equation group consisting of dislocation evolution and mechanical state was investigated based on the 3-D discrete dislocation dynamics; the results indicate that the differential equation group is serious stiff, namely the external stress changes more quickly than dislocation evolution. Using the established numerical algorithm, the mechanical behavior of FCC crystal was simulated with the dislocations located in the parallel slip planes, and the effect of strain rate on the dislocation configuration and mechanical behavior, and the saturation process of mobile dislocation were discussed. The simulation results indicate that the numerical algorithm can efficiently simulate the dislocation dipole and the low strain rate loading.