Number Of Independent Slip Systems Research Articles

Importance of grain boundary processes for plasticity in the quartz-dominated crust: Implications for flow laws

When H2O is present along grain boundaries, the deformation processes responsible for plasticity in silicate mineral aggregates can deviate from what may be conventionally expected. Although a necessary component of understanding crustal deformation processes, there is no theoretical framework that incorporates grain boundary processes into polycrystalline quartz rheology. To address this issue, we carried out high-pressure and high-temperature deformation experiments on fine-grained quartz aggregates. Our study illustrates that grain boundary migration (GBM) through dissolution-precipitation (in the presence of an aqueous fluid) and grain boundary sliding (GBS) may act as accommodation mechanisms to prevent hardening from dislocation glide. GBM and GBS can relax incompatibilities resulting from an inadequate number of independent slip systems, plastic anisotropy between neighbouring grains, and non-planar grain boundaries together with grain boundary junctions. As demonstrated earlier in the literature, GBM may act as a recrystallization mechanism counteracting hardening, but also is a potential mechanism that allow H2O to enter in the quartz crystal (hydrolization) at the experimental time-scale. The above serial processes occur over a range of more than two orders of magnitude in grain size (∼3 to 200 μm) and explain a grain-size-insensitive stress exponent (n = 2) and low activation energy (Q = 110 kJ/mol). In the absence of a switch to grain size sensitive deformation mechanisms induced by grain size reduction, our results imply that only a modest weakening (∼5 times the strength of the protolith) is needed (or possible) to localize shear zones in the Earth's crust.

Transition of dominant deformation mode in bulk polycrystalline pure Mg by ultra-grain refinement down to sub-micrometer

Magnesium (Mg) and its alloys usually show relatively low strength and poor ductility at room temperature due to their anisotropic hexagonal close-packed (HCP) crystal structure that provides a limited number of independent slip systems. Here we report that unique combinations of strength and ductility can be realized in bulk polycrystalline pure Mg by tuning the predominant deformation mode. We succeeded in obtaining the fully recrystallized specimens of pure Mg having a wide range of average grain sizes, of which minimum grain size was 650 nm, and clarified mechanical properties and deformation mechanisms at room temperature systematically as a function of the grain size. Deformation twinning and basal slip governed plastic deformation in the conventional coarse-grained region, but twinning was suppressed when the grain size was refined down to several micro-meters. Eventually, grain boundary mediated plasticity, i.e., grain boundary sliding became dominant in the ultrafine-grained (UFG) specimen having a mean grain size smaller than 1 μm. The transition of the deformation modes led to a significant increase of tensile elongation and breakdown of Hall-Petch relationship. It was quantitatively confirmed by detailed microstructural observation and theoretical calculation that the change in strength and ductility arose from the distinct grain size dependence of the critical shear stress for activating different deformation modes.

Effect of Numbers of Turns of High‐Pressure Torsion on the Development of Exceptional Ductility in Pure Magnesium

The low ductility of magnesium at room temperature is usually attributed to an insufficient number of independent slip systems. Recent research has shown that refining the grain structure of pure magnesium promotes a breakdown in the Hall‐Petch relationship at low strain rates and may lead to the development of exceptional ductilities. This report describes the evolution of microstructure and the mechanical behaviour of pure magnesium using different amounts of imposed plastic deformation by high‐pressure torsion (HPT). It is shown that the initial coarse grains undergo twinning followed by a gradual grain refinement. The flow stress at low strain rates decreases as the grain size is reduced, thereby confirming an inverse Hall‐Petch behaviour. The elongation to failure increases with grain refinement and elongations over 300% are achieved after 1/2 turn of HPT. These experimental data agree with a model for the low temperature deformation behaviour of fine‐grained pure magnesium.

Plastic deformation of B2-NiTi – is it slip or twinning?

The work addresses two main questions that have baffled the shape memory research community. Firstly, the superb ductility of B2-NiTi cannot be solely attributed to slip on {0 1 1} planes, because there are not a sufficient number of independent slip systems under arbitrary deformations. We show unequivocally, upon diffraction measurements and local strain field traces, that deformation twinning on {1 1 4} planes that can provide additional systems to accommodate plastic flow is activated. Secondly, the slip direction on the {0 1 1} planes has not been established in NiTi with certainty. It is proved precisely to be in 0 0 1 direction based on crystallographic shear analysis producing the specific strain tensor components (measured at mesoscale with digital image correlation, DIC). Based on the single-crystal experiments, the CRSSs (critical resolved shear stress) are established as 250 and 330 MPa for slip and twinning, respectively. The results have implications in devising correct crystal plasticity formulations for shape memory alloys.

Enhanced strength and ductility of AZ80 Mg alloys by spray forming and ECAP

The relatively low strength and poor ductility of conventional AZ80 Mg alloys have been attributed to the limited number of independent slip systems, in combination with the formation of fragile eutectic β-Mg17Al12 networks at grain boundaries. In an effort to overcome these limitations, spray forming followed by equal channel angular pressing (ECAP) was employed to obtain a unique bi-modal microstructure: coarse grains were separated and surrounded by deformation networks consisting of ultrafine-grained Mg with an average grain size of 0.6µm and ellipsoidal shaped β-Mg17Al12 particles with sizes of 200–300nm. Tensile tests revealed the advantage of this structure: a yield strength of 235MPa combined with an elongation to failure of 14%; the values are significantly higher than those of their conventional counterparts (100MPa-12%, and 140 MPa-5%). The underlying strengthening and deformation mechanisms of this particular microstructure are discussed and analyzed.

Evolution of Microstructure in Rolled Mg-Based Alloy. Textural Aspect / Ewolucja Mikrostruktury W Walcowanym Stopie Na Bazie Mg. Aspekt Teksturowy

Magnesium alloys are the lightest structural materials, which makes them particularly suitable for use in the aircraft and automotive industry. However, due to hexagonal close-packed crystal structure, resulting in insufficient number of independent slip systems, magnesium alloys exhibit poor formability at room temperature. Conventional methods of work hardening of magnesium alloys requires the temperature about 300°C, which favours simultaneously processes of thermal recovery and grain growth, but decreases beneficial microstructure strengthening effect. Thus, it is a crucial to undertake development of a technology for semi-finished magnesium alloys elements, which will ensure better mechanical properties of the final products by forming desirable microstructure. In the paper we present the development of crystallographic texture of the Mg-based alloy (Mg-AZ31) in the form of pipe extruded at 430°C and subjected to pilger rolling at relatively low temperature.

On the deformation twinning of Mg AZ31B: A three-dimensional synchrotron X-ray diffraction experiment and crystal plasticity finite element model

Crystals with a hexagonal close-packed (HCP) structure are inherently anisotropic, and have a limited number of independent slip systems, which leads to strong deformation textures and reduced formability in polycrystalline products. Tension along the c-axis of the crystal ideally activates extension twinning as a deformation mode due to the lack of easy-slip systems. In this work, experiments were devised to study extension twinning in a polycrystalline Mg alloy AZ31B with a strong basal rolling texture by tensile deformation parallel to the plate normal. Three-dimensional synchrotron X-ray diffraction (3DXRD) was used to map the center-of-mass positions, volumes, orientations, elastic strains, and stress tensors of over 1400 grains in-situ up to a true strain of 1.4%. More than 700 tensile twins were observed to form in the mapped volume under deformation. The measured center-of-mass positions and grain volumes are used to construct various 3D microstructures and model them with a Crystal Plasticity Finite Element (CPFE) code. It is observed that the average grain-resolved stress did not always select the highest ranked Schmid factor twin variant. In fact, the contribution of lower ranked variants was non-negligible. The CPFE simulation indicates that there is a small variation in the stress within each grain in the elastic regime, which increases drastically upon the onset of plasticity. One of the significant outcomes of this work is the new statistical information on the interaction between twin and parent grain. It is shown that, on average, there is a small difference between the stress normal to the twin habit plane in the parent and twin, but that this is not the case for the shear acting on the habit plane.

In-situ EBSD study of the active slip systems and lattice rotation behavior of surface grains in aluminum alloy during tensile deformation

This paper reports an in-situ study of the plastic deformation behavior of surface grains in a polycrystalline aluminum alloy, in particular the active slip systems and lattice rotation, by means of the electron backscattered diffraction method. The experimental analysis is conducted at a spatial resolution of 1μm, thus allowing detailed analysis at subgrain levels, enabling elucidation of fine details of the deformation process that are not commonly seen in the literature. It is found that the grains rotate gradually with increasing strain during tensile deformation. The lattice rotation, in terms of both rotation path and rotation rate, is highly inhomogeneous both among the grains and within individual grains, leading to the formation of subgrains. The rotation behavior can be adequately described by the activation of slip systems with the maximum and second maximum Schmid factors. The number of independent slip systems in surface grains is much fewer than that in interior grains, as predicted by crystal plasticity theories. The lattice rotation rate is also heterogeneous among grains and subregions and for different deformation stages. The differences in rotation rate provide another mechanism for the accommodation of plastic strains and for the creation of subgrains. These findings are of importance for the mechanical processing of thin sheet materials or the deformation behavior of miniature components, where the majority of grains are on the surfaces.

AZ80 마그네슘 합금 압출재의 압축 성형조건에 따른 방위특성 분석

With the increasing demand for light-weight materials to reduce fuel consumption, the automobile industry has extensively studied magnesium alloys which are light weight metals. The intrinsic poor formability and poor ductility at ambient temperature due to the hexagonal close-packed (HCP) crystal structure and the associated insufficient number of independent slip systems restricts the practical usage of these alloys. Hot working of magnesium alloys using a forging or extrusion enables net-shape manufacturing with enhanced formability and ductility since there are several operative non-basal slip systems in addition to basal slip plane, which increases the workability. In this research, the thermomechanical properties of AZ80 Mg alloy were obtained by compression testing at the various temperatures and strain rates. Optical microscopy and EBSD were used to study the microstructural behavior such as misorientation distribution and dynamic recrystallization. The results were correlated to the hardening and the softening of the alloy. The experimental data in conjunction with a physical explanation provide the optimal conditions for net-shape forging under hot or warm temperatures through control of the grain refinement and the working conditions.

Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations

We present a detailed description of the numerical implementation, within the widely used viscoplastic self-consistent (VPSC) code, of a rigorous second-order (SO) homogenization procedure for non-linear polycrystals. The method is based on a linearization scheme, making explicit use of the covariance of the fluctuations of the local fields in a certain linear comparison material, whose properties are, in turn, determined by means of a suitably designed variational principle. We discuss the differences between this second-order approach and several first-order self-consistent (SC) formulations (secant, tangent and affine approximations) by comparing their predictions with exact full-field solutions. We do so for crystals with different symmetries, as a function of anisotropy, number of independent slip systems and degree of non-linearity. In this comparison, the second-order estimates show the best overall agreement with the full-field solutions. Finally, the different SC approaches are applied to simulate texture evolution in two strongly heterogeneous systems and, in both cases, the SO formulation yields results in better agreement with experimental evidence than the first-order approximations. In the case of cold-rolling of low-SFE fcc polycrystals, the SO formulation predicts the formation of a texture with most of the characteristic features of a brass-type texture. In the case of polycrystalline ice, deforming in uniaxial compression to large strain, the SO predicts a substantial and persistent accommodation of deformation by basal slip, even when the basal poles become strongly aligned with the compression direction.

Low temperature deformation and dislocation substructure of ruthenium aluminide polycrystals

The flow behavior and dislocation substructure present in ruthenium aluminide polycrystals due to deformation at room temperature and 77 K have been studied. Dislocations with three different types of Burgers vectors have been identified after 1–2% deformation in compression at 77 K and room temperature: 〈100〉, 〈110〉 and 〈111〉. The 〈100〉 and 〈110〉 dislocations are present with approximately equal densities, while the 〈111〉 are only occasionally observed. Trace analyses show that the majority of the dislocations are mixed in character and lie on {110} type planes. The implications of these observations with regard to the number of independent slip systems and the intrinsic deformability of this material are discussed.

On Material Removal Mechanisms in Finishing of Advanced Ceramics and Glasses

Fundamental considerations on the interactions between the abrasive and the work material as well as the micromechanisms of material removal and surface generation process in finishing of advanced ceramics and glasses are addressed. In developing plausible mechanisms, an attempt is made to delineate the failure mechanisms operable in polycrystalline ceramics and glasses versus metals. This is necessary because of the significant differences in the nature of bonding, restrictions on the extent of plastic deformation (including the number of independent slip systems required), microstructure, tribochemistry, and, flaws generated during processing of these materials and their consequent effect on the failure mechanisms associated.

On the plasticity of low symmetry crystals lacking five independent slip systems

Abstract The modified viscoplastic Taylor model proposed recently by Parks and Ahzi (1990, J. Mech. Phys. Solids 38, 701) for crystals possessing less than five independent slip systems is re-formulated. The proposed formulation can be applied to study the plasticity and texture evolution in crystals possessing five or less than five physically distinct and independent slip systems. This formulation has the advantages of providing explicit solutions and of not having to explicitly identify the kinematic constraints associated with the insufficient number of independent slip systems. This model is employed to simulate the plane strain compression of idealized 100% crystalline poly(ethylene terephthalate). Predicted crystallographic textures are in excellent agreement with experimental results. This example illustrates one of the many applications of this new formulation of the modified Taylor model.

Testing of soft-oriented NiAl single crystals in simple shear

The intermetallic NiAl has been of considerable interest recently as a prospective replacement for superalloys in turbine engines because of its higher melting point, lower density and good oxidation resistance. In addition, its B2 crystal structure is considered to have good potential for ductility enhancement due to its high symmetry and simple slip directions. Unfortunately, limited room temperature ductility has hindered the development of NiAl alloys. This is primarily due to an insufficient number of independent slip systems to satisfy Von Mises' criterion for uniform deformation. However, the presence of complex dislocation core structures has also been suggested to play a role in the deformation behavior of NiAl. At room temperature, NiAl rarely exhibits slip and deforms primarily by slip on either [001] or [011] type planes. Simulations of a dislocations in NiAl suggest cores spread out of the observed slip plane, which is generally expected to give rise to Schmid's law violations. In addition, based on Schmid's law analysis, slip of a dislocations on [100] planes has been reported to occur at lower stresses than on the more closely packed [110] planes which is unexpected from Peierls stress estimates. Furthermore, Takasugi et al. observed that in compressionmore » the critical resolved shear stresses (CRSSs) were higher than in tension for a given orientation (i.e., stress asymmetry). Therefore, it is likely that Schmid's law is not observed in NiAl and simple shear tests are needed to determine the actual critical shear stress (CSS) for deformation. In the present study, CSS values were measured for slip on both [001] and [011] planes. These values are compared to CRSS values obtained from compression test using Schmid factor calculations. Prismatic punch testing was conducted to investigate the possibility of a [hk0] slip in NiAl.« less

Phase Transitions Between β and γ (Mg, Fe) 2 SiO 4 in the Earth's Mantle: Mechanisms and Rheological Implications

The mechanisms of the phase transformations between the spinel (gamma) and modified spinel (beta) polymorphs of Mg(2)SiO(4) have been studied experimentally between 15 and 20 gigapascals and 800 degrees to 950 degrees C. The gamma to beta transformation occurs by a shear mechanism, whereas the beta to gamma transformation involves grain-boundary nucleation and interface-controlled growth. These contrasting mechanisms are a consequence of the number of independent slip systems that are available in the respective crystal structures. This result leads to the prediction that in subduction zones and perhaps also rising plumes in the Earth's mantle, the gamma to beta transformation should be accompanied by a transient reduction in strength.

Solid solution limits and selected mechanical properties of the quaternary L1 2 trialuminide AlTiMnMo

Intermetallics based on the trialuminide Al[sub 3]Ti, or on Al[sub 11]Ti[sub 5], have been extensively researched in recent years. Alloying with approximately 10 at.% of first-row transition elements, such as Cr or Mn, converts the DO[sub 22] structure of Al[sub 3]Ti to L1[sub 2]. Although this transition to the L1[sub 2] structure increases the number of independent slip systems to five and causes substantial softening, room-temperature tensile ductilities and fracture toughnesses remain low. Typical values for the room-temperature ductilities of Al-25Ti-8Cr and Al-25Ti-9Mn are 0.2% and room-temperature fracture toughnesses of trialuminides range from 2 to 5 MPa m[sup 1/2]. Reasons for the low fracture toughness of trialuminides have been discussed by Turner et al. and George et al. On a phenomenological basis, it appears that fracture toughnesses might improve, if either Poisson's ratio or the ratio of the bulk and shear moduli can be increased. In principle, this might be achieved by macroalloying ternary L1[sub 2] trialuminides, while at the same time maintaining the L1[sub 2] crystal structure. Focusing on first-row transition elements, Kumar and Brown investigated a range of such quaternary compounds. They did not observe any improvement in ductility, as compared to the ternary compounds. In the presentmore » work, it was decided to focus on a second-row transition element, namely, 2 molybdenum. As compared to Cr and Mn, which are only slightly soluble in Al[sub 3]Ti, up to 20 at. % Mo dissolves in Al[sub 3]Ti at 1,198 K. This raises the question whether substantial amounts of Mo also dissolve in the cubic ternary trialuminides such as Al-Ti-Mn. In order to verify this possibility, the extent of the single-phase region of cubic Al-Ti-Mn-Mo intermetallic was mapped out at 1,473 K. In addition, a limited characterization of room-temperature mechanical properties was carried out.« less

The effects of chromium on NiAl intermetallic alloys: Part II. Slip systems

One of the principal obstacles to room temperature tensile ductility in NiAl is an insufficient number of independent slip systems, due to the sole operation of the <100> {011} system. It has been both predicted and reported that Cr additions to NiAl induce <111>{112} slip, increasing the number of independent slip systems to five, a number sufficient for general plasticity. However, no attendant increase in tensile ductility has been observed. The present study reexamines the effects of Cr on the predominant room temperature slip system in polycrystalline NiAl, as a function of Cr content, Ni/Al ratio and processing route. It is shown that Cr has essentially no effect on the slip system in NiAl at room temperature, while processing by extrusion, compared with casting and homogenization, produces a small, yet significant, proportion of <110>{110} dislocations. Possible explanations for the discrepancy of the present results with those of previous work are discussed, as well as the presence and implications of the <110>{110} dislocations.

A simplified method for determining the number of independent slip systems in crystals

A novel method for determining the number of independent slip systems for any family or a combination of families of slip systems is proposed, which is more direct than previous approaches. This technique makes it possible to easily determine, from the known operative slip systems, if the material is slip-system-deficient. The method also makes it possible to determine if twinning may contribute additional deformation modes.

Dislocation Substructures Produced During Tensile, Creep, and Fatigue Deformation of Ti3Al at 700°C

Ti3Al is an ordered intermetallic compound having the DO19-type superlattice structure. The compound exhibits very limited ductility in tension below 700°C because of a pronounced planarity of slip and the absence of a sufficient number of independent slip systems. Significant differences in slip behavior in the compound as a result of differences in strain rate and mode of deformation are reported here.Figure 1 is a comparison of dislocation substructures in polycrystalline Ti3Al specimens deformed in tension, creep, and fatigue. Slip activity on both the basal and prism planes is observed for each mode of deformation. The dominant slip vector in unidirectional deformation is the a-type (b) = &lt;1120&gt;) (Fig. la). The dislocations are straight, occur for the most part in a screw orientation, and are arranged in planar bands. In contrast, the dislocation distribution in specimens crept at 700°C (Fig. lb) is characterized by a much reduced planarity of slip, a tangled dislocation arrangement instead of planar bands, and an increased incidence of nonbasal slip vectors.

DEPENDENCE OF CRACK FORMATION ON CRYSTALLOGRAPHIC ORIENTATION FOR ICE

Observations are reported of crack propagation in columnar-grain, polycrystalline ice subjected to constant compressive load applied perpendicular to the long axis of the columns. About three-quarters of the cracks observed were transcrystalline and the remainder occurred at grain boundaries. The plane of the cracks tended to be parallel to the direction of the applied load. Transcrystalline cracks tended to propagate either parallel or perpendicular to the basal plane. At least two-thirds of the grain boundary cracks were associated with boundaries for which the slip plane of one or both of the adjacent grains was close to parallel or perpendicular to the boundary. It is shown that the observations are consistent with the hypothesis that a minimum number of independent slip systems are required for a grain to conform to an arbitrary deformation under constraints imposed by neighboring grains.