Limited Number Of Slip Systems Research Articles

Slip identification from HR-DIC/EBSD: Incorporating Crystal Plasticity constitutive laws

It is well known that dislocation slip plays a major role in plastic deformation of polycrystals. Depending on the crystal’s symmetry, only a limited number of Slip Systems (SSs) are possible, and their activities depend on the crystal orientation with respect to the applied stress. High Resolution Digital Image Correlation (HR-DIC) can be used to get the full-field measurements of displacement fields on the surface of the strained material during an in situ tensile test, whereas the EBSD technique provides local crystallographic orientations. Therefore, coupling them can lead to full description of the local slip activities. Recently, an algorithm (named SSLIP) was proposed in the literature to automatically estimate the plastic activity from HR-DIC and EBSD data. The aim of the present paper is first to improve this algorithm so that it works for incremental straining, and to propose a way to take account for the anisotropic behaviour through a well-known set of Crystal Plasticity (CP) constitutive laws. It is shown that slip identification, together with those CP laws, can be used to estimate the tensile stress at grain scale. The influence of the DIC resolution is investigated and “correction rules” for small grains are proposed. Finally, the experimental results are compared against those found using the CP Finite Element Method (CPFEM), showing good consistency, specially in terms of active SSs and local stress.

In-situ analysis of the effect of residual fcc phase and special grain boundaries on the deformation dynamics in pure cobalt

Polycrystalline hcp metals – an important class of engineering materials – typically exhibit complex plasticity because of a limited number of slip systems. Among these metals, deformation is even more complicated in cobalt as it commonly contains residual fcc phase due to the incomplete martensitic fcc→hcp transformation upon cooling. In this work, we employ a combination of in-situ (acoustic emission, AE) and ex-situ (scanning electron microscopy, SEM) techniques in order to examine deformation dynamics in pure polycrystalline cobalt varying in grain size and the content of residual fcc phase prepared using systematic thermal treatment and cycling. We reveal that the presence of the fcc phase and special ∼71∘ grain boundaries between different hcp martensite variants brings about higher deformability and strength. The fcc phase provides additional slip systems and also accommodates deformation via the stress-induced fcc→hcp transformation during loading. On the other hand, special boundaries enhance structural integrity and suppress the formation of critical defects. Both these non-trivial effects can dominate over the influence of grain size, being a traditional microstructural variable. The ex-situ SEM experiments further reveal that the stress-induced fcc→hcp transformation is sluggish and only partial even at high strains, and it does not give rise to detectable AE signals, unlike in other materials exhibiting martensitic transformation. In turn, these insights into cobalt plasticity provide new avenues for the microstructure and performance optimization towards the desired applications through the modern concept of grain boundary engineering.

Oxygen solutes-regulated low temperature embrittlement and high temperature toughness in vanadium

The plasticity of body-centered cubic (BCC) metals is sensitive to interstitial trace impurities. Owing to high oxygen affinity, vanadium (V) shows a tendency of embrittlement with increasing oxygen concentration. However, how oxygen solutes affect the ductile-to-brittle transition (DBT) behavior of V remains unclear. In this study, we investigate the DBT behavior of V with different oxygen solute concentrations using small-punch test. As oxygen content increases, the DBT temperature (DBTT) rises incrementally accompanied by a widening of the semi-brittle transition zone. The reduction of the lower fracture energy plateaus indicates a classical low-temperature embrittlement, while the rising of the upper fracture energy plateaus manifests a remarkable high-temperature toughening. Below DBTT, owing to the strong pinning effect of oxygen-vacancy complexes on dislocations, only a limited number of slip systems were activated with very low dislocation density, and all screw dislocations are immobile. Above DBTT, owing to the intensive interactions between dislocation and oxygen-vacancy complexes, frequent dislocation cross-slips trigger multiple slip systems and accelerate dislocation multiplication and storage, all of which contribute to the high-temperature toughness. These findings clarify the effect of oxygen solute on the DBT of V and guide the design of high-performance refractory metals.

Dislocation cross slip in molecular crystal cyclotetramethylene tetranitramine (β-HMX)

In this work, we explore the mechanism of cross-slip in the low symmetry molecular crystal cyclotetramethylene tetranitramine (β-HMX)—a secondary explosive. Cross-slip is well studied and understood in high symmetry crystals but virtually uninvestigated in molecular crystals. To this end, we use molecular simulations and observe that only screw dislocations with the [100] Burgers vector may cross-slip effectively. The process involves the (011), (010), (001), and (011¯) planes and takes place in both the positive and negative directions of dislocation motion in each of the respective slip systems. Resolved shear stresses larger than ∼0.6 of the critical resolved shear stress are necessary in at least two of the planes in order to activate cross-slip. The application of pressure does not prevent cross-slip from taking place. The phenomenon occurs at elevated pressures in the same slip systems as at zero pressure. However, due to the limited number of slip systems involved, cross-slip does not appear to be of central importance in β-HMX and, of course, remains relevant only as long as the dislocation-based mechanism of plasticity is not replaced by the shear localization mode, which becomes dominant at high pressure, under strong shock conditions.

Effect of Ca concentration on Microstructure formation behaviors in AZ61 magnesium alloy

Magnesium alloys have been paid attention as lightweight materials in various industrial fields. However, their use is limited by poor formability at room temperature which was caused by the limited number of slip systems. The texture control plays an important role in plastic workability of magnesium. Addition of Ca as alloying element is known to improve the general corrosion resistance and mechanical integrity of magnesium alloys in chloride environment. In order to investigate the Ca concentration on microstructure formation behaviors, Ca addition on AZ magnesium alloy were experimentally investigated by high-temperature uniaxial compression. Uniaxial compression test was conducted at 673K and 723K with a strain rate of 5.0×10−2s−1. The working softening was observed and the main component of texture and the sharpness of basal texture in two kinds of specimens varies depending on the deformation conditions.

Effect of hot working on the damping capacity and mechanical properties of AZ31 magnesium alloy

Magnesium alloys have received much attention for their lightweight and other excellent properties, such as low density, high specific strength, and good castability, for use in several industrial and commercial applications. However, both magnesium and its alloys show limited room-temperature formability owing to the limited number of slip systems associated with their hexagonal close-packed crystal structure. It is well known that crystallographic texture plays an important role in both plastic deformation and macroscopic anisotropy of magnesium alloys. Many authors have concentrated on improving the room- temperature formability of Mg alloys. However, despite having a lot of excellent properties in magnesium alloy, the study for various properties of magnesium alloy have not been clarified enough yet.Mg alloys are known to have a good damping capacity compared to other known metals and their alloys. Also, the damping properties of metals are generally recognized to be dependent on microstructural factors such as grain size and texture. However, there are very few studies on the relationship between the damping capacity and texture of Magnesium alloys. Therefore, in this study, specimens of the AZ31 magnesium alloy, were processed by hot working, and their texture and damping property investigated. A 60 mm × 60 mm × 40 mm rectangular plate was cut out by machining an ingot of AZ31 magnesium alloy (Mg-3Al-1Zn in mass%), and rolling was carried out at 673 K to a rolling reduction of 30%. Then, heat treatment was carried out at temperatures in the range of 573-723 K for durations in the range of 30-180 min. The samples were immediately quenched in oil after heat treatment to prevent any change in the microstructure. Texture was evaluated on the compression planes by the Schulz reflection method using nickel-filtered Cu Kα radiation. Electron backscatter diffraction measurements were conducted to observe the spatial distribution of various orientations. Specimens for damping capacity measurements were machined from the rolled specimen, to have a length of 120 mm, width of 20 mm, and thickness of 1 mm. The damping capacity was measured with a flexural internal friction measurement machine at room temperature. It was found that the damping capacity increases with both increasing heat-treatment temperature and time, due to grain growth and the increased pole densities of textures.

Molecular dynamics simulation study of the effect of temperature and grain size on the deformation behavior of polycrystalline cementite

Molecular dynamics simulations combined with quantitative atomic displacement analyses were performed to study the deformation behaviors of polycrystalline cementite (Fe3C). At low temperature and large grain size, dislocation glide acts as the preferred deformation mechanism. Due to the limited number of slip systems at low temperature, polycrystalline cementite breaks by forming voids at grain boundaries upon tensile loading. When the temperature rises or the grain size reduces, grain boundary sliding becomes the primary mechanism and plastic deformation is accommodated effectively.

마그네슘 합금 판재의 변형률, 변형률 속도 및 온도 환경을 고려한 유동응력 모델에 대한 연구

The formability of magnesium alloy sheets at room temperature is generally low because of the inherently limited number of slip systems, but higher at temperatures over <TEX>$150^{\circ}C$</TEX>. Therefore, prior to the practical application of these materials, the forming limits should be evaluated as a function of the temperature and strain rate. This can be achieved experimentally by performing a series of tests or analytically by deriving the corresponding modeling approaches. However, before the formability analysis can be conducted, a model of flow stress, which includes the effects of strain, strain rate and temperature, should be carefully identified. In this paper, such procedure is carried out for Mg alloy AZ31 and the concept of flow stress surface is proposed. Experimental flow stresses at four temperature levels (<TEX>$150^{\circ}C$</TEX>, <TEX>$200^{\circ}C$</TEX>, <TEX>$250^{\circ}C$</TEX>, <TEX>$300^{\circ}C$</TEX>) each with the pre-assigned strain rate levels of <TEX>$0.01s^{-1}$</TEX>, <TEX>$0.1s^{-1}$</TEX> and <TEX>$1.0s^{-1}$</TEX> are collected in order to establish the relationships between these variables. The temperature-compensated strain rate parameter which combines, in a single variable, the effects of temperature and strain rate, is introduced to capture these relationships in a compact manner. This study shows that the proposed concept of flow stress surface is practically relevant for the evaluation of temperature and strain dependent formability.

An experimental study of cyclic deformation of extruded AZ61A magnesium alloy

Thin-walled tubular specimens were employed to study the cyclic deformation of extruded AZ61A magnesium alloy. Experiments were conducted under fully reversed strain-controlled tension–compression, torsion, and combined axial–torsion in ambient air. Mechanical twinning was found to significantly influence the inelastic deformation of the material. Cyclic hardening was observed at all the strain amplitudes under investigation. For tension–compression at strain amplitudes higher than 0.5%, the stress–strain hysteresis loop was asymmetric with a positive mean stress. This was associated with mechanical twinning in the compression phase and detwinning in the subsequent tension phase. Under cyclic torsion, the stress–strain hysteresis loops were symmetric although mechanical twinning was observed at high shear strain amplitudes. When the material was subjected to combined axial–torsion loading, the alternative occurrence of twinning and detwinning processes under axial stress resulted in asymmetric shear stress–shear strain hysteresis loops. Nonproportional hardening was not observed due to limited number of slip systems and the formation of mechanical twins. Microstructures after the stabilization of cyclic deformation were observed and the dominant mechanisms governing cyclic deformation were discussed. Existing cyclic plasticity models were discussed in light of their capabilities for modeling the observed cyclic deformation of the magnesium alloy.

The nature of grain refinement in equal-channel angular pressing: a comparison of representative fcc and hcp metals

AbstractEqual-channel angular pressing is an effective tool for producing exceptional grain refinement in bulk polycrystalline metals. Typically, processing in this way refines the grains to the submicrometer level in a wide range of metals but recent experiments have established that the mechanism of grain refinement is different in fcc and hcp metals. Specifically, the refining of grains in aluminum involves the introduction of elongated bands of cells or subgrains and the subsequent evolution of this structure into an array of ultrafine grains whereas in magnesium the limited number of slip systems leads to the formation of new grains along the existing grain boundaries. Because of these limitations, magnesium alloys are especially susceptible to the production of materials having bimodal grain distributions.

Mechanical properties of ru-ni-ai alloys

The Ru-Ni-Al system is significant for a number of reasons, not least of which is the interest in the ruthenium and nickel aluminides for high-temperature structural applications. The widely disparate properties of the B2 structured compounds NiAl and RuAl, in particular, have enjoyed extensive study. Whereas various factors, including a limited number of slip systems, conspire to render NiAl brittle at room temperature. Fleischer et al. have drawn attention to the unusual room-temperature ductility and toughness that RuAl exhibits in combination with high-temperature strength, specific stiffness, and oxidation resistance. Since alloys based on platinum group metals (PGMs) have apparent cost implications, some effort has been expended in seeking ways to replace some of the Ru without adversely affecting the intrinsic ductility. One approach is to seek some convergence in the properties of RuAl and its less ductile B2 counterparts by isostructural substitution for the Ru. In this regard, the existence of a B2 NiAl phase makes Ni an obvious candidate.

RHEOLOGY OF PARTIALLY MOLTEN MANTLE ROCKS

▪ Abstract Over the past decade, significant progress has been made in understanding the rheological properties of partially molten mantle rocks. Laboratory experiments demonstrate that a few percent of melt can have an unexpectedly large effect on viscosity both in the diffusional creep regime and in the dislocation creep regime. In both cases, the enhancement in creep rate is much larger than anticipated based on deformation models because melt wets at least a fraction of the grain boundaries. For diffusion creep, the wetted interfaces provide a rapid diffusion path that is not included in analyses based on melt distribution in isotropic melt-crystal systems. For dislocation creep, two points require consideration. First, even without a melt phase present, fine-grained samples deformed in the dislocation creep field flow a factor of ∼10 faster than coarse-grained rocks due to contributions from grain boundary mechanisms to the deformation process. Second, melt has only a small effect on creep rate for coarse-grained rocks but has a relatively large effect for fine-grained samples. Thus, because olivine has only a limited number of slip systems, grain boundaries contribute significantly to deformation of fine-grained rocks in the dislocation creep regime, provided that deformation occurs near the transition between diffusional creep and dislocation creep. Based on laboratory measurements, this transition is expected to occur at a grain size of about 6 mm for a differential stress of 0.1 MPa. Therefore, under mantle conditions, even a few percent melt should reduce the viscosity by as much as a factor of 10. A broad range of problems related to deformation beneath mid-ocean ridges and in the mantle wedge above subducting slabs can now be addressed using experimentally determined rheologies for partially molten mantle rocks.

Nucleation and short crack growth in fatigued polycrystalline copper: Polak, J. and Liskutin, P. Fatigue Fract. Eng. Mater. Struct. 1990 13, (2), 119–133

Molecular dynamics simulations combined with quantitative atomic displacement analyses were performed to study the deformation behaviors of polycrystalline cementite (Fe3C). At low temperature and large grain size, dislocation glide acts as the preferred deformation mechanism. Due to the limited number of slip systems at low temperature, polycrystalline cementite breaks by forming voids at grain boundaries upon tensile loading. When the temperature rises or the grain size reduces, grain boundary sliding becomes the primary mechanism and plastic deformation is accommodated effectively.

Fatigue and fracture of a zinc die casting alloy

The fracture toughness and crack tearing response were measured for a common zinc die casting alloy, BS1004: 1972 Alloy A. Its fatigue crack growth behaviour was also examined for constant amplitude loading and for a single overload. The constant amplitude crack growth rate was dependent upon both the effective stress intensity range ΔK eff and the mean load of the fatigue cycle. Crack growth rates were faster than those in aluminium or in typical steels, when compared on the basis of ΔK/ E or ΔK eff/ E. These unsual features on the zinc alloy are due to its limited number of slip systems and susceptibility to cleavage. A tensile overload induces a transient retardation of fatigue crack growth rate. The primary cause of the retarded growth was found to be plasticity induced crack closure.

Deformation of biotite and muscovite: Tem microstructure and deformation model

Growth and deformation defects have been observed in 1M and 2M1 biotites and 2M1 muscovites using transmission electron microscope (TEM) techniques. These have been related to optical observations. In deformed biotite, the dislocation density increases as the strain increases. The density of stacking faults also increases with strain. The spatial ordering of stacking faults decreases as the strain increases. In muscovites selected from the same areas as the biotites, stacking fault and dislocation densities show little or no variation with deformation. The different responses of biotite and muscovite to deformation are explained, in part, by the physical and chemical differences between 1M biotite and 2M1 muscovite. There is strong evidence, in both the biotites and muscovites, that stacking faults may be result of deformation as well as a crystal growth process. The grain size of the deformed mica aggregates is reduced by the nucleation of new micas. There is also evidence for a grain size reduction mechanism (segmentation) in biotites. This mechanism appears to achieve the same result as recovery-recrystallization mechanisms, but not by the same method. Segmentation may be a mechanism which is favoured in strongly anisotropic minerals with a limited number of slip-systems. A model is proposed that attempts to correlate response of the biotite to deformation. The deformation is synchronous with, and post-dates, the nucleation of the new metamorphic micas.

Relationship between contractile strain ratioR and texture in zirconium alloy tubing

The crystallographic textures of zirconium alloy tubing used as cladding in nuclear reactor fuel are commonly characterized by the quantitative texture numbers F (Kaellstroem) and f/sub r/ (Kearns) which are derived from the direct and inverse pole figures. The texture numbers of zircaloy 2 and 4 tubes have been correlated experimentally with the value of the contractile strain ratio R which is a measure of the plastic anisotropy of the tube. The correlations were based on the results of 20 different tubing lots. The f/sub r/-R correlation shows much less data scatter than the F-R correlation. By assuming a simple plastic deformation model for zirconium alloys the following relations between texture and anisotropy are obtained: F = R-1/R+1 and f/sub r/ = R/R+1. The theoretically derived relations are in good agreement with the experimental data. The procedure of correlating texture with plastic anisotropy is not limited to zirconium alloy tubing, but should be equally applicable to textured sheet and plate materials and other alloys with a limited number of slip systems.

On the formation of the diamond grain configuration during high temperature creep and fatigue

A study has been made of the influence of test variables on the formation of the diamond grain configuration during high temperature creep and fatigue deformation of a wide variety of metals. The proposed mechanisms for the formation of this interesting grain morphology are reviewed. It is concluded that the diamond grain configuration arises from a balance between grain-boundary sliding, grain-boundary mobility, intragranular deformation and defect imbalance across the grain boundaries and that it tends to be stabilized by intergranular cavitation. While the phenomenon occurs during high temperature fatigue in a variety of metals irrespective of their crystal structure, during creep it has been observed only in to h c p metals. It is surmised that the occurrence of the diamond array of grain boundaries during creep deformation in h c p metals is aided by the limited number of slip systems which leads to high defect imbalances in adjacent grains and consequently high driving forces for grain-boundary migration. On the basis of quantitative metallography involving measurements of the number of edges per grain section, the number of grains meeting at vertices, angular distribution histograms and grain-boundary lengths in different angular orientations with respect to the stress axis in "annealed" and "diamond" microstructures, it is concluded that the shape of the "diamond" grain is essentially the same as that of the "annealed" grain but in a distorted form.

The deformation and twinning of graphite crystals under a point load

Abstract The deformation produced by point loading on the cleaved basal surfaces of graphite crystals has been studied in the scanning electron microscope. The experiments were of two types, viz. sliding and static contact. In the first a small tungsten stylus (tip radius ∼ 1 μm) was slid on the graphite surface inside the scanning electron microscope and the resulting damage observed as it occurred. The marked anisotropy and the limited number of slip systems of the graphite structure result in a characteristic deformation mode which involves the cleavage of thin flakes followed by folding of the partially separated layers. In the second type of experiment the deformation produced by a diamond indenter was studied. These experiments showed that the hardness value of c. 4.8 × 107 N/m2 for naturally-occurring graphite and 22 × 107 N/m2 for neutron-irradiated graphite are determined by a cleavage and folding process and are not related to the basal plane shear strength. It is suggested that the mechanism of folding in both types of experiment is one of mechanical twinning. An important feature of the deformation process is that the dislocation walls forming the twin boundaries are mobile under the applied stress and are free to run in the newly formed chips and flakes in a direction parallel to the basal plane. The greatly increased hardness of neutron-irradiated graphite is explained by the reduction in mobility of the twin boundaries due to the high point defect concentration.

The friction and deformation of clean metals at very low temperatures

A study has been carried out on the friction and surface damage between hemispheres and flats of the same metal at low sliding speeds at temperatures ranging from 25 K to room temperature in a vacuum of the order of 10 -10 Torr. All the metal specimens were polycrystalline and included gold, silver, copper and nickel (f .c. c.), tantalum, iron, molybdenum and tungsten (b. c. c.), zirconium, titanium, beryllium and cobalt (hexagonal). There are three main types of behavior. With f. c. c. metals at room temperature the friction is high ( μ ≂ 2.5) and the slider produces grooving in the lower surface. At very low temperatures a transition is observed: the friction falls to μ ≂ 1.5 and there is a change in the type of surface damage. This transition is associated with a marked rise in the work-hardening rate of the metal. With some of the b. c. c. metals there is a similar change at low temperatures but this is associated with a ductilebrittle transition. Under brittle conditions the friction does not exceed about μ = 1.0. With hexagonal metals the behaviour depends on the ductility of the metal. Zirconium and titanium behave like cubic metals. With beryllium and cobalt, which possess a limited number of slip systems, interfacial deformation is restricted and the friction and surface damage are small. The lowest friction ( μ = 0.5) and the least surface damage are observed between cobalt specimens in agreement with the recent work of Buckley &amp; Johnson (1968). With the relatively clean surfaces used in the present study the sliding process involves two main mechanisms. The first is junction-growth (Courtney-Pratt &amp; Eisner 1958). Because interfacial adhesion is strong and the slider deformable the action of a tangential stress is to enlarge the true area of metallic contact. The second is a ploughing action. The front of the slider ploughs out a groove in the lower surface displacing material ahead of and around it. These two processes interact and it is shown that, if junction-growth is appreciable, tensile stresses may develop in the trailing portion of the contact region. The way in which the metal can withstand these tensile stresses plays a crucial part in determining the friction and type of surface damage produced. The present work shows that under conditions of strong adhesion the most important material property is the ductility of the metal. This analysis represents an advance on the simple junction-growth model proposed by Tabor in 1959.