Main Slip Systems Research Articles

Effect of micron-scale nonmetallic inclusions on fatigue crack nucleation in a nickel-based superalloy

Micron-level nonmetallic inclusions are likely to be a limiting factor for further improvement in the fatigue resistance of nickel-based superalloys. To investigate the fatigue response of nickel-based superalloys containing micro-inclusions, a dislocation-based crystal plasticity model was employed for numerical simulations, and the local energy storage density criterion was used for damage evolution analysis. The results showed that, as a hard phase, micro-inclusions interfered with the plastic deformation of the matrix, as evidenced by the inhomogeneous slipping of the main slip systems and the activation of new slip systems. Additionally, micro-inclusions induced the accumulation of geometrically necessary dislocations (GNDs) around them. When micro-inclusions appeared on grain boundaries, the above factors changed the energy required for local deformation through potential hardening effects in the model and ultimately affected the evolution of the local energy storage density. When micro-inclusions appeared inside grains, the evolution of local energy storage was often dominated by plastic deformation only. The above mechanism is microstructure sensitive and spatially limited, which leads to the dispersion of lifetimes and negligible effect of micro-inclusions on distal grains.

Temperature- and pressure-induced structural transformations in NbN: A first-principles study

Structural transformations at high temperatures and pressures, elastic moduli, hardness, fracture toughness, Debye temperature, stress-shear strain relations, electronic structure, and lattice dynamics in the experimentaly observed NaCl–NbN (δ, Fm-3m), anti-TiP-NbN (ε, P63/mmc), anti-NiAs-NbN (δ′, P63/mmc), WC-NbN (η, P-6m2), and TiP–NbN (ε′, P63/mmc) phases and hypothetical new tP4-129 (P4/nmm), hP6-189 (P-62m), oP8-25 (Pmm2) and cP2-221 (Pm-3m) structures are studied by using first-principles calculations and molecular dynamics simulations. The possible mechanisms of the phase transitions between these structures based on the condensation of a certain phonon mode with subsequent spontaneous strains are suggested. The ε, η and δ′, and cP2-221 structures are brittle materials and exhibit highest shear moduli (200.5–216.8 GPa), Young moduli (492.4–528.8 GPa), Vickers hardness (23.9–27.1 GPa), fracture toughness (4.54–4.72 MPa m1/2), and Debye temperatures (730.5–767.0 K). It is found that the main slip systems should be (0001)<10-10> for ε and η, and both (0001)<10-10> and (0001)<-12-10> for δ’.

Cold dwell behaviour of Ti6Al alloy: Understanding load shedding using digital image correlation and dislocation based crystal plasticity simulations

• The cold dwell behaviour of Ti6Al is analysed by a combination of digital image correlation, electron backscatter diffraction and dislocation based crystal plasticity simulations • Experiments and simulations are carried out between room temperature and 230°C to understand the worst case scenario for cold dwell and understand its physical origin • A data set of pairs of grains is analysed: some pairs of grains show the “rogue” and “non-rogue” behaviour respectively, while a novel behaviour called “non-typical rogue” is observed, in which a moderate load shedding takes place during cold dwell • The correlation between stress discontinuity at the grain boundary in “rogue” grain pairs and the distribution of geometrically necessary dislocations is analysed • The worst case scenario at 120°C is explained by the temperature dependence of the strain rate sensitivity of basal and prismatic slip systems, and the temperature dependence of the spread of geometrically necessary dislocations around the grain boundary Digital image correlation (DIC) and dislocation based crystal plasticity simulation were utilised to study cold dwell behaviour in a coarse grain Ti-6Al alloy at 3 different temperatures up to 230 °C. Strains extracted from large volume grains were measured during creep by DIC and were used to calibrate the crystal plasticity model. The values of critical resolved shear stresses (CRSS) of the two main slip systems (basal and prismatic) were determined as a function of temperature. Stress along paths across the boundaries of four grain pairs, three “rogue” grain pairs and one “non-rogue” grain pair, were determined at different temperatures. Large load shedding was observed in one of the “rogue” grain pairs, where a stress increment during the creep period was found in the “hard” grain. A minor load shedding mechanism was observed in two non-typical “rogue” grain pairs, in which the plastic deformation is nonuniform inside the grains and geometrically necessary dislocations accumulate in the centre of the grains. At elevated temperatures, 120 °C was found to be the worst case scenario as the stress difference at the grain boundaries of these four grain pairs was found to be the largest among the three temperatures analysed. The origin of this critical temperature is debated in the literature and it is investigated for the first time in the present work by analysing the simultaneous effects of the geometrically necessary dislocations (GND) and the strain rate sensitivity (SRS) of the slip systems. The analysis shows that the combined effects of the peak SRS of both prismatic and basal slip systems at 80 °C and of the increase of the spread of the GND distribution around the grain boundary at higher temperatures are the origin of the observed worst case scenario.

Fatigue crack initiation and propagation behavior of nickel-based single crystal DD6 under different drilling processes

The fatigue crack initiation and propagation behavior of film cooling holes (FCHs) under different drilling processes are of great significance to key structural parts. In this paper, it mainly comprehensively and systematically summarized the difference in surface condition caused by different drilling processes of nickel-based superalloys combining several characterization devices and described whole process from crack initiation to fracture in detail. The in-situ fatigue crack growth test at room temperature on the plate specimens with a different drilling FCHs (EDM and LDM) made of [001] nickel-based single crystal was carried out, and proposed a comprehensive evaluation method for the crack initiation mechanism from the three dimensions of geometry, metallurgy and mechanics. The four main octahedral slip systems are proved by finite element simulation. Then, we clarified the difference of fracture surface, crack path and fracture morphology of different drillings, and the competition mechanism between crack propagation path and slip surface was investigated. Finally, a simple unified model of fatigue crack growth rate was proposed, which provides a useful crack propagation law of different drilling hole.

Cold Dwell Behaviour of Ti6Al Alloy: Understanding Load Shedding Using Digital Image Correlation and Crystal Plasticity Simulations

Digital image correlation (DIC) and crystal plasticity simulation were utilised to study cold dwell behaviour in a coarse grain Ti-6Al alloy at 3 different temperatures up to 230 °C. Strains extracted from large volume grains were measured during creep by DIC and were used to calibrate the crystal plasticity model. The values of critical resolved shear stresses (CRSS) of the two main slip systems (basal and prismatic) were determined as a function of temperature. Stress along paths across the boundaries of two grain pairs, (1) a `rogue' grain pair and (2) a `non-rogue' grain pair, were determined at different temperatures. Load shedding was observed in the `rogue' grain pair, where a stress increment during the creep period was found in the `hard' grain. At elevated temperatures, 120 °C was found to be the worst case scenario as the stress difference at the grain boundaries of these two grain pairs were found to be the largest among the three temperatures. This can be attributed to the fact that the strain rate sensitivity of both prismatic and basal slip systems is at its greatest in this worst case scenario temperature.

Role of criston shear sources in the formation of Chernov-Luders bands

Shear bands often appear during plastic deformation. The Chernov-Luders band is an example of a complex multiscale heterogeneous structure containing shear bands. The article is devoted to the analysis of a part of the experimental data on the formation (under tension) of Chernov-Luders band in textured polycrystalline steel samples with fine grain, pre-deformed by rolling. The main attention is focused on the criston mechanism of formation of the observed texture components. The essence of the criston approach, associated with the contact interaction of dislocations at the intersection of slip planes, is briefly described. Information on the observed types of texture is given and a sufficiently detailed analysis of the reconstruction of the mechanism of the appearance of several texture components is carried out taking into account the interaction of the main dislocation slip systems for a body-centered cubic (bcc) lattice. It is shown that some of the real shear directions correspond to the interaction of more than two dislocation slip systems, that is, in fact, there are criston-cristons combinations. A summary table of the results of the analysis of the "composition" of cristons for all texture components is presented, reflecting the fractional contribution of dislocations belonging to interacting slip systems. The analysis has shown that practically all systems of standard slip along the planes of the {110}, {112}, {123} families play an active role in the formation of cristons and, accordingly, the observed texture. Brief summary comments are provided. In particular, it was noted that, with a sequential criston approach, the issue of non-Schmidian slip variants can be eliminated. The important role of texturing is also noted for the ordering of the intergranular medium and the appearance of macroconcentrators in groups of contacting grains, which, as experience shows, are important in the formation of Chernov-Luders band.

A topologized resolved shear stress method for the life prediction of nickel-base single crystal superalloys

Fifteen multiaxial critical-plane fatigue damage parameters of isotropic metal materials are applied to the life evaluation of nickel-base single crystal superalloys. These parameters are classified into stress-, strain- and strain-energy parameters, and their predictive abilities are evaluated by 12 groups of single crystal fatigue data obtained from mainly an intermediate temperature range (500–760 °C) where the slip deformation is the main damage mode. The results show that the strain energy group exhibits the best fitting characteristics with correlation coefficients. A topologized resolved shear stress method (TRSS) considering the interaction of main slip systems is further proposed. The dispersion degree of resolved shear stress among the main slip systems is quantified by a dispersion factor, and the real driving capacity of resolved shear stress is amended according to the topology of driving force. The obtained results show that the proposed method has achieved an improvement of correlation ability.

Temperature effect on mechanical response of c-plane monocrystalline gallium nitride in nanoindentation: A molecular dynamics study

A series of three-dimensional molecular dynamics (MD) simulations was performed to investigate the effect of temperature on the nanoscale deformation behaviour and mechanical properties of c-plane monocrystalline gallium nitride (GaN) under nanoindentation. Simulation results showed that the atomic displacement and strain increased with increasing temperature. Thus, the nucleation and propagation of dislocations in the main slip systems were promoted to intensify the plastic deformation of GaN crystal. Increasing the temperature also contributed to the increase in local phase transition from the wurtzite crystal structure (B4-GaN) to the zinc-blende crystal structure (B3-GaN) and a very evident amorphization of GaN in the indentation zone. Based on the analysis of the load-depth curves, it was found that both the hardness and Young's modulus decreased as the temperature increased. This work can enrich the atomic-level understanding of the effect of temperature on the mechanical response of monocrystalline GaN when subjected to the external loads.

How hard metal becomes soft: crystallographic analysis on the mechanical behavior of ultra-coarse cemented carbide.

Investigation into the temperature dependence of the mechanical behavior of ultra-coarse grained cemented carbide materials is highly demanded due to its service conditions of concurrent applied stress and high temperature. In the present study, based on the designed experiments and microstructural characterization combined with crystallographic analysis, the evolution of slip systems, motion and interaction of dislocations with temperature are quantified for the WC hard phase. Mechanisms are proposed for the formation of the sessile dislocations in the main slip systems at the room temperature and the glissile dislocations in the new slip systems activated at high temperatures. Furthermore, the correlation of the plastic strain and fracture toughness with the temperature-dependent slip activation, dislocation reaction and transformation is explained quantitatively. Enlightened by the present findings, potential approach to enhance the high-temperature strength of ultra-coarse cemented carbides based on WC strengthening was suggested.

Crystallographic preferred orientations of plagioclase via grain boundary sliding in a lower-crustal anorthositic ultramylonite

To clarify the rheological properties and deformational mechanisms that operate within lower-crustal shear zones, we analyzed deformation microstructures and fabrics in plagioclase grains from high-strain regions of intrafolial drag folds of an anorthositic ultramylonite from Langoya, Vesteralen, northern Norway. These grains have developed weak crystallographic preferred orientations (CPOs). Other than deformation twinning, they do not show any indications of intracrystalline plasticity or dynamic recrystallization. In some domains of the drag fold, plagioclase CPOs are more distinct, but the majority of inferred slip systems are not consistent with the main slip systems in plagioclase. These suggest that neither dislocation creep nor dislocation-accommodated grain boundary sliding (GBS) produced the plagioclase CPOs but rather grain rotation via GBS along specific grain boundaries parallel or subparallel to crystallographic planes of (010), (100) or (110), which led to an alignment of the easy-slip grain boundaries in the flow direction that produced the observed CPO patterns. The anisotropy of dissolution and growth rates may have been responsible for the development of the specific grain boundaries.

Towards high ductility in magnesium alloys - The role of intergranular deformation

This paper investigates the intergranular deformation behavior and its effect on the overall ductility of a Mg-Gd-Y alloy, using in-situ tension in scanning electron microscopy (SEM) combined with electron backscattered diffraction (EBSD) and digital image correlation (DIC) techniques. At regions surrounding grain boundaries, the majority of activated dislocation slip traces were found to form in pairs across grain boundary, and the basal-to-basal (B-B) slip pair is the dominant type. Strain accommodation around the grain boundary interfaces is affected by both Schmid factor in the adjacent grains and the m’ value between these main slip systems. A mk value was proposed in this paper as the maximum value of the product of the Schmid factor and the m’ value of the adjacent grains to measure strain accommodation around the grain boundary interface, where a higher mk value would mean a larger local strain. It is suggested that the overall ductility of a Mg alloy could be evaluated by measuring its average mk value. As an evidence, the Mg-Gd-Y alloy tubes with higher mk value generally show higher elongations during tensile tests in this study.

Determination of the single-phase constitutive relations of α/β dual phase TC6 titanium alloy

The constitutive relations of α and β phases in a TC6 titanium alloy were determined by implementing a two-phase elastic-plastic self-consistent (EPSC) framework combined with the evolution of lattice strains; these strains were obtained via in-situ tensile loading synchrotron-based x-ray diffraction experiments. It was found that the {200}β reflection has the lowest stiffness and load partitions prior to the α phase during the elastic loading stage in this alloy. The simulated parameters including the diffraction elastic constant and initial yield stress of lattice reflections exhibited satisfactory correspondence with the experimental results. Further analysis of the characteristics of the Schmid Factor (SF) distributions of the main slip systems revealed that the elastic-plastic transition process in the α phase occurs over a prolonged period. In contrast, the β phase undergoes a transient process owing to its relatively more concentrated SF frequency distributions, than those of the α phase. In addition, the fitted stress-strain curve of each phase was compared with the measured macro stress-strain curve obtained from the in-situ experiment. It revealed Young's moduli of 110.3GPa and 104.5GPa, and yield stresses of 877.8MPa and 969MPa, for the α and β phases, respectively.

Molecular dynamics simulation study of deformation mechanisms in 3C–SiC during nanometric cutting at elevated temperatures

Molecular dynamics (MD) simulation was employed in this study to elucidate the dislocation/amorphization-based plasticity mechanisms in single crystal 3C–SiC during nanometric cutting on different crystallographic orientations across a range of cutting temperatures, 300K to 3000K, using two sorts of interatomic potentials namely analytical bond order potential (ABOP) and Tersoff potential. Of particular interesting finding while cutting the (110)<001̅> was the formation and subsequent annihilation of stacking fault-couple and Lomer–Cottrell (L–C) lock at high temperatures, i.e. 2000K and 3000K, and generation of the cross-junctions between pairs of counter stacking faults meditated by the gliding of Shockley partials at 3000K. Another point of interest was the directional dependency of the mode of nanoscale plasticity, i.e. while dislocation nucleation and stacking fault formation were observed to be dominant during cutting the (110)<001̅>, low defect activity was witnessed for the (010)<100> and (111)<1̅10> crystal setups. Nonetheless, the initial response of 3C–SiC substrate was found to be solid-state amorphization for all the studied cases. Further analysis through virtual X-ray diffraction (XRD) and radial distribution function (RDF) showed the crystal quality and structural changes of the substrate during nanometric cutting. A key observation was that the von Mises stress to cause yielding was reduced by 49% on the (110) crystal plane at 3000K compared to what it took to cut at 300K. The simulation results were supplemented by additional calculations of mechanical properties, generalized stacking faults energy (GSFE) surfaces and ideal shear stresses for the two main slip systems of 3C–SiC given by the employed interatomic potentials.

Deformation behaviors in isotactic polypropylene during rolling

Wide angle X-ray diffraction is used to measure the texture evolution of isotactic polypropylene (iPP) during rolling. Pole figures, orientation distribution functions and crystallinities of the rolled iPP are obtained and calculated. The texture evolution is also simulated by the modeling. It can be drawn that the main deformation mechanisms occurred at low strain is the coarse slips on few planes and the amorphization because of the special mother and daughter lamellae of the material, which leads to the crystallinity decreases greatly. As the true strain increases, mother and daughter lamellae are broken, then, the following deformation does not be controlled by the special structure of α-iPP. The basic deformation mechanisms in the rolled iPP is the crystallographic slips, and the main slip systems are (010)[001] and (100)[001] chain slips and (010)[100] transverse slip and so on. Amorphization is also a deformation mechanism which may take place as an alternative to crystallographic slip depending on the crystallographic orientation of a lamella. The [001]‖RD fiber texture, which includes several (hk0)[001] texture components is the main texture component in the rolled iPP.

Simulations of texture evolution for HCP metals: Influence of the main slip systems

Deformation of hexagonal close packed (HCP) metals is accompanied by the development of a strong texture, which depends on the predominant deformation mechanism of the metal and the deformation path. This study investigates texture rotations in HCP deforming by basal 〈a〉 , prismatic 〈a〉 , pyramidal 〈a〉 or pyramidal 〈c+a〉 slip. This study uses crystal plasticity models to simulate the development of tension, compression and plane strain deformation textures. Basal slip causes rotation of the 〈c〉 axis toward the compression direction, as well as pyramidal 〈a〉 slip, whereas pyramidal 〈c+a〉 slip makes the 〈c〉 axis rotate toward the extension direction. Prismatic slip generates a rotation of the lattice around its 〈c〉 axis, but the 〈c〉 axis position does not change; however a prismatic plane rotates toward the extension direction. The development of textures in constrained crystals deforming with multiple slip modes is compared with the effect of the dominant slip system activity.

Fabric transitions in quartz via viscoplastic self-consistent modeling part I: Axial compression and simple shear under constant strain

Quartz is a common crustal mineral that deforms plastically in a wide range of temperatures and pressures, leading to the development of different types of crystallographic preferred orientation (CPO) patterns. In this contribution we present the results of an extensive modeling of quartz fabric transitions via a viscoplastic self-consistent (VPSC) approach. For that, we have performed systematic simulations using different sets of relative critical resolved shear stress of the main quartz slip systems. We have performed these simulations in axial compression and simple shear regimes under constant Von Mises equivalent strain of 100% (γ=1.73), assuming that the aggregates deformed exclusively by dislocation glide. Some of the predicted CPOs patterns are similar to those observed in naturally and experimentally deformed quartz. Nevertheless, some classical CPO patterns usually interpreted as result from dislocation glide (e.g. Y-maxima due to prism <a> slip) are clearly not developed in the simulated conditions. In addition we reported new potential preferred orientation patterns that might happen in high temperature conditions, both in axial compression and simple shear. We have demonstrated that CPOs generated under axial compression are usually stronger that those predicted under simple shear, due to the continuous rotation observed in the later simulations. The fabric strength depends essentially on the dominant active slip system, and normally the stronger CPOs result from dominant basal slip in <a>, followed by rhomb <a> and prism [c] slip, whereas prism <a> slip does not produce strong fabrics. The opening angle of quartz [0001] fabric used as a proxy of temperature seems to be reliable for deformation temperatures of ~400°C, when the main slip systems have similar behaviors.

Synthetic seismic anisotropy models within a slab impinging on the core–mantle boundary

The lowermost few hundreds of kilometres of the Earth's mantle are elastically anisotropic; seismic velocities vary with direction of propagation and polarization. Observations of strong seismic anisotropy correlate with regions where subducted slab material is expected. In this study, we evaluate the hypothesis that crystal preferred orientation (CPO) in a slab, as it impinges on the core–mantle boundary, is the cause of the observed anisotropy. Next, we determine if fast polarization directions seen by shear waves can be mapped to directions of geodynamic flow. This approach is similar to our previous study performed for a 2-D geodynamic model. In this study, we employ a 3-D geodynamic model with temperature-dependent viscosity and kinematic velocity boundary conditions defined at the surface of the Earth to create a broad downwelling slab. Tracers track the deformation that we assume to be accommodated by dislocation creep. We evaluate the models for the presence of perovskite or post-perovskite and for different main slip systems along which dislocation creep may occur in post-perovskite [(100),(010) and (001)]—resulting in four different mineralogical models of CPO. Combining the crystal pole orientations with single crystal elastic constants results in seismically distinguishable models of seismic anisotropy. The models are evaluated against published seismic observations by analysing different anisotropic components: the radial anisotropy, the splitting for (sub-)vertical phases (i.e. azimuthal anisotropy), and the splitting for subhorizontal phases. The patterns in radial anisotropy confirm our earlier results in 2-D. Observations of radial anisotropy and splitting in subhorizontal phases are mostly consistent with our models of post-perovskite with (010)-slip and (001)-slip. Our model of (001)-slip predicts stronger splitting than for (010)-slip for horizontally propagating phases in all directions. The strongest seismic anisotropy in this model occurs where the slab impinges on the core–mantle boundary. The azimuthal anisotropy pattern for (001)-slip shows fast axis directions at the edges of the slab (sub-)parallel to flow directions, suggesting horizontal flows may be mapped out in the lowermost mantle using seismic observations.

Modelling the effect of pressure on the critical shear stress of MgO single crystals

A hierarchical multi-scale model was used to study the effect of high pressure on the critical shear stresses of MgO. The two main slip systems, ½⟨110⟩{110} and ½⟨110⟩{100}, were considered. Based on a generalised Peierls–Nabarro model, it is shown that the core structure of ½⟨110⟩ screw dislocations is strongly sensitive to pressure. Mostly planar and spread in {110} at ambient pressure, the core of screw dislocations tends to spread in {100} with increasing pressure. Subsequently, an inversion of the easiest slip systems is observed between 30 and 60 GPa. At high pressure, the plasticity of MgO single crystals is expected to be controlled by ½⟨110⟩{100} slip systems, except at high temperature where both slip systems become active. Pressure is also found to increase the critical resolved shear stresses and to shift the athermal temperature toward higher temperatures. Under high pressure, MgO is thus characterised by a significant lattice friction on both slip systems.

The Discussion of {111}∥ND Formation Mechanism

{111}∥ND forms at deformation stage, it is connected with main slip systems, by analyzing main slip systems and its performance, {111}∥ND formation mechanism can be drawn. In addition, by analyzing cold reduction’s effect on main slip systems, the relationship between {111}∥ND and cold reduction can be drawn, and some experiments can be explained.

Evaluating quartz crystallographic preferred orientations and the role of deformation partitioning using EBSD and fabric analyser techniques

Quartz crystallographic preferred orientations (CPO) from three distinct orthogneisses using both the Electron Back Scatter Diffraction (EBSD) and Fabric Analyser (FA) techniques reveal a clear trend from basal <a> and rhomb <a + c> slip for high P–T conditions (670 ± 20 °C/9 kbar), rhomb <a + c> and basal <a> slip for medium P–T (590 ± 15 °C/6 kbar) and a dominance of prism <a> slip for lower P–T conditions (<570 °C/4–5 kbar). The textural variations are interpreted in terms of a temperature field gradient and microscale strain partitioning controlled by a weak feldspar matrix that can locally invert the expected slip system sequences. Locally quartz CPOs are different within one thin section, and in comparison to bulk orientation measurements both, EBSD and the Fabric Analyser techniques are ideal to determine such textural heterogeneities. While the EBSD is a powerful technique to determine the full CPO, measurements from similar locations inside several quartz grains from the orthogneisses and an annealed and undeformed quartzite show that the FA is an accurate tool to determine CPOs of c-axis orientations in uniaxial materials. In a CPO focussed study the FA is a cheap alternative to EBSD as the analysis of whole thin section can be accomplished in a very short time, with minimal sample preparation. With the FA it is possible to evaluate the CPOs of several samples quickly with an accuracy that allows identification of the main slip systems and their homogeneity.