Kinking and Cracking Caused by Slip in Single Crystals of Silicon Carbide

α-SiC single crystals were compressed parallel to the basal plane, (0001), at temperatures between 900° and 1500°C. Plastic deformation by slip on the basal planes which accompanied kinking occurred above 1000°C. At kink boundaries, two kinds of cracks were observed. One was the cracks elongated parallel to the basal plane. This kind of crack was initiated by the tensile stress produced by piled-up dislocations on the basal planes against a kink boundary. The other was on a kink boundary, and was induced by the stress of dislocations, heterogeneously distributed on the kink boundary. The initiation of cracks produced by dislocations was considered to be a possible cause of fracture in polycrystalline SiC at high temperatures.     

Mechanical Behavior of Magnesium Oxide at High Temperatures

Magnesium oxide crystals show a wide variety of deformation and fracture modes under tension. These modes are determined by the number of slip systems operating concurrently in a given volume. (1) At low temperatures, slip is confined to a single (110) (110) system and plasticity is limited by stress concentrations which develop where slip switches from one plane to another. (2) At intermediate temperatures, (110) (110) slip systems at 90° can interpenetrate but those at 60° cannot. Mechanical properties then depend on the initial slip distribution. When slip is confined to 90° systems there is little work hardening and crystals neck down to a knife-edge ductile fracture. When slip is confined to 60° systems, crystals work harden and fracture by cleavage. (3) At high temperatures, dislocations can interpenetrate on all systems and polygonization can occur. After easy glide the crystals work harden and elongate over 100% before fracturing in a completely ductile manner. The transition temperature from one mode to another depends on strain rate.     

Fracture-Strength Anisotropy of Sapphire

At 22°C, the bend strength of as-ground sapphire bars with different orientations of tensile surface and tensile axis varies from 4×10⁴ to 12×10⁴ psi as a result of the anisotropies of machining damage and fracture energy. Generally, the strength-controlling surface flaws caused by grinding are of constant size; failure from such flaws is affected by grinding-induced slip and twinning. Surface striations, which occur when there is negligible subsurface slip, can lead to stress concentrations, whereas twins can lead to increases in flaw size; each of these effects reduces strength. In addition, the large anisotropy in fracture strength, which is not predicted by the elastic anisotropy, is controlled by the anisotropic fracture energy. Approximation of the attractive forces across the fracture plane based on elastic moduli and interplanar distance can be used to understand the fracture energy anisotropy.     

Mechanical Behavior of Single-Crystal and Polycrystalline Cesium Bromide

Plastic-deformation studies were made of cesium bromide which exhibits no cleavage planes. Single crystals were found to be "soft" and ductile if they were favorably oriented relative to the loading axis to activate the {110}∝001〈 slip systems. Kink bands were formed by applying a compressive load normal to a {100} plane. Cross slip was found to occur during deformation at all test temperatures. Tensile loads applied normal to {100} and {110} planes caused fracture along {110} planes, whereas compressive loads normal to {100} planes forced fracture along {112} planes. The ductility of polycrystalline cesium bromide was found to be limited because of the lack of five independent slip systems. The specimens with smaller grains showed less strain at fracture and greater strain hardening than the larger-grained specimens. The mechanism fracture was intergranular up to 300° C.     

Mechanical Behavior of Lithium Fluoride at High Temperatures

Single crystals of lithium fluoride were pulled in tension at high temperatures; the results of these tests are compared with data for magnesium oxide. Interpenetration of {110}〈110〉 slip systems does not occur in LiF as readily as in MgO. Because of this lack of interpenetrability, plastic instability and completely ductile fracture do not occur in LiF below 700°C (0.87 T _mp); the high-temperature tensile strength of LiF decreased very little from 300° to 700°C. This lack of interpenetrability of slip systems in LiF at high temperatures also had a profound effect on the deformation processes, the development of substructure, and the strain-hardening and fracture characteristics of the material. This work emphasizes the importance of interpenetration of slip not only in the high-temperature ductility and strain-hardening processes but also in the maximum tensile strength which ionic crystals develop before fracture.     

Deformation Behavior of Sapphire Via the Prismatic Slip System

The deformation behavior of α -axis sapphire in tension from 1550° to 1850°C was studied in constant strain-rate, differential strain-rate, and differential-temperature tests. The crystals deformed via the prismatic system,     , resulting in stress-strain curves with a significant yield drop, a region of work-hardening which decreased in magnitude with increasing temperature, and a region of constant flow stress. The deformation was inhomogeneous with irregularly spaced slip bands containing a high density of glide dislocations and also basal dislocation debris. The flow behavior did not conform to simple diffusional or Peierls-process models but could be rationalized on the basis of the creation of a super saturation of vacancies generated by the motion of jogs on gliding screw dislocations.     

Prismatic Slip of A12O3 Single Crystals Below 1000°C in Compression Under Hydrostatic Pressure

Alumina single crystals were compressed perpendicular to the [0001] axis at a constant strain rate between 20° and 950°C. At r>200°C, failure was suppressed by_hydrostatic pressures of 500 to 1500 MPa. Prismatic slip {1120}〈1100〉 was deduced from optical observations of the lateral surfaces and from stress-optical features in thin sections cut from the specimens. The critical resolved shear stress (CRSS) decreased rapidly with increasing temperature, from a maximum of ∼3000 MPa at 200°C (strain rate 2±10-⁻⁵ s⁻¹). A simple linear law can be fitted with the logarithm of the CRSS as a function of temperature, up to 1800°C. The rate-controlling mechanism for dislocation glide is likely to be either the Peierls barrier or barriers due to dissociation out of the glide plane.     

Effect of Crystal Orientation on the Mechanical Behavior of Magnesium Oxide at High Temperatures

The high-temperature deformation of magnesia single crystals with a [110] tensile axis is described and related to previous observations on [001] crystals. The [110] tensile axis favors slip on systems with oblique vectors (i.e. at 120°). Two main modes of deformation are identified and distinguished by the interpenetrability of oblique slip: (1) Between 1400° and 1700°C interpenetration does not occur. The crystal becomes subdivided into distinct blocks slipping on different systems. These blocks are separated by sharp kink boundaries which act as barriers to further slip. Voids form in the kink interfaces and lead to brittle fracture. (2) Above 1700°C slip on all systems interpenetrates and a stable substructure develops throughout the gage section. At high strains the single crystal recrystallizes. The specimen work hardens and elongates 100% before necking down to completely ductile fracture. This behavior is discussed in terms of dislocation interactions.     

Deformation Microstructure in (001) Single Crystal Strontium Titanate by Vickers Indentation

Recent interests on the plastic deformation of strontium titanate (SrTiO₃) are derived from its unusual ductile-to-brittle-to-ductile transition (DBDT). The transition is divided into three regimes (A, B, and C) corresponding to the temperature range of 113–1053 K (−160° to 780°C), 1053 to ∼1503 K (780° to ∼1230°C), and ∼1503–1873 K (∼1230° to 1600°C), discovered by Sigle and colleagues in the MPI-Stuttgart. We report the dislocation substructures in (001) single crystal SrTiO₃ deformed by Vickers indentation at room temperature, studied by scanning and transmission electron microscopy. Dislocation dipoles of screw and edge character are observed and confirmed by inside–outside contrast using ± g -vector by weak-beam dark field imaging. They are formed by edge trapping, jog dragging, and cross slip pinching-off. Similar to dipole breaking off in deformed sapphire (α-Al₂O₃) at 1200°C and γ-TiAl intermetallic at room temperature, the dipoles pinch off at one end, and emit a string of loops at trail. Two sets of slip systems {110}〈     〉 and {100}〈011〉 are activated under both 100 g and 1 kg load. The suggestion is that plastic deformation has reached the stage II work hardening, which is characterized by multiplication of dislocations through cross slip, interactions between dislocations, and operating of multiple slip systems.     

Mechanical Properties of Magnesia Single Crystals Corn pression

Stress-strain curves of single crystals of magnesia compressed in the [100] direction are reported at temperatures from –196° to 1200°C.; curves are also shown for different rates of loading at room temperature. The crystals show considerable ductility at all temperatures and at room temperature can be deformed plastically about 6% before fracture at stresses which are about one-quarter of reported polycrystalline fracture strengths. The macroscopic yield drops apparently exponentially from an extrapolated value of 50,000 lb. per sq. in. at absolute zero to about 4500 lb. per sq. in. at temperatures of 900°C. and higher. Heat-treatment has an appreciable effect on the yield stress. The resistance of the material to deformation increases with the number of slip systems and bands activated because of the barriers to dislocation movements which occur at slip band intersections. At about 2 to 3% strain, stress concentrations begin to be relieved by small internal cracks which are not easily propagated. This effect is extensive before final macroscopic failure of the crystal occurs. Preliminary creep tests above the macroscopic yield stress and in the temperature range 800° to 1000°C. show large instantaneous plastic deformations followed by slow constant-rate creep.     

Effect of Crystal Orientation on Plastic Deformation of Magnesium Oxide

Stress-strain data for single crystals of MgO tested in compression with 〈110〉 and 〈111〉 loading axes are presented for temperatures ranging from 26〉 to 1250°C. Stress-strain data for polycrystalline MgO are also presented over the same temperature range. Single crystals with a 〈111〉 loading axis were found to deform plastically on the {100}〈110〉 slip systems at temperatures above 350°C. The total strain at fracture for polycrystalline MgO at room temperature was about 0.6%; above 600°C it was about 2%. The general inability of the {110}〈110〉 slip systems of this structure to satisfy the Taylor requirement, i.e., the necessity of five independent slip systems, ease of cleavage, and slip nonuniformity, limits polycrystalline ductility at low temperatures. At higher temperatures, slip can occur on {100}〈110〉 slip systems, thus providing the additional slip, systems necessary to satisfy Taylor's criterion; also, stress-induced climb and high dislocation mobility inhibit cleavage fracture.     

Fracture and Crack Healing in (U,Pu)C

The fracture stress of several types of (U,Pu)C_1+x pellets was measured from 25° to 1200°C at a fixed strain rate. The fracture stress increases with temperature and the fracture is predominantly transgranular up to ≊500°C. At >500°C, the fracture stress decreases as the temperature increases and the fracture becomes increasingly intergranular. The flow stress, σ_0.002, decreased rapidly between 1000° and 1600°C. An investigation of the stress dependence and kinetics of crack healing at 1300° to 1600°C indicates that strength may recover by a volume-diffusion-controlled mechanism.     

Brittle–Ductile Transition and Dislocation Mobility in Sapphire

The brittle-to-ductile transition (BDT) of Precracked sapphire in four-point bending was studied as a function of orientation and strain rate from room temperature to 1500°C. Plastic deformatiom of sapphire occurs via basal and prismatic slip during loading at high temperature (above 1030–1100°C, depending on orientation). The BDT temperature, T_c , varies with strain rate and crystallographic orientation of the fracture plane. The activation, derived from the strain rate variation of T_c , is approximately energy of the process controllingh the BDT in sapphire, derived from the strain rate variation of T_c is sapproximately 3.2 eV, close to that for dislocation glide. In one specimen orientation, "warm-prestressing" increases the room-temperature fracture stress.     

Creep Deformation of 0° Sapphire

Creep deformation of 0° sapphire was studied between 1600°and 1800°C at stresses up to 114 MN/m². Microscopical evidence (dislocation structures observed by transmission electron microscopy (TEM) and by etch pits) suggested that Nabarro climb was the predominant deformation mechanism. Both the experimental creep rates and stress exponents were in good agreement with those predicted by this model. Although non-basal dislocations with a ½〈101〉 Burgers vector were present, the good creep resistance of 0° sapphire was attributed to the difficulty of activating pyramidal slip.     

Structural Changes Accompanying Deformation in Pyrolytic Graphite

Electron microscopy and X-ray diffraction techniques were used to follow the structural changes in pyrolytic graphite which accompany deformation produced by applying a stress parallel to the substrate. Basal slip and an increase in preferred orientation account for deformations up to 14%. The mechanism by which deformation above 14% occurs is not well understood. Some evidence indicates that deformations above 14% may be associated with fracture across the basal planes with subsequent basal slip, an increase in porosity, and a very slight increase in preferred orientation. Rows of etch pits which may delineate an array of dislocations were observed in a specimen heated at 3000° C without load.     

Deformation and Fracture of Polycrystalline Lithium Fluoride

Techniques for the fabrication of polycrystalline LiF test specimens were developed and evaluated using single-crystal LiF as a control. An etch was developed which revealed dislocations on all crystallographic faces of LiF. Large-grained polycrystalline specimens tested in four-point loading underwent 0.076 to 0.798% plastic strain before fracture. In most cases their yield stress was similar to that for single crystals favorably oriented for flow on {110}〈110〉 slip systems. Deformation was inhomogeneous among the grains because of differences in orientation with respect to the applied stress and within individual grains because of interactions at grain boundaries. Grain boundaries were barriers to slip, but stresses resulting from slip in one grain were transmitted to neighboring grains and often caused local deformation near the boundary. In one case, local boundary slip occurred on an (010) plane. Three-grain junctions were areas of high residual stresses, and fractures originated at boundaries at or near three-grain junctions. Fractures were mixed transgranular and intergranular.     

Mechanical Properties of Polycrystalline TiC

The mechanical properties of fine-grained polycrystalline TiC were studied using both four-point bending and compression tests. The ductile-brittle transition (D-B) temperature in compression was determined to be =800°C and was found to depend on grain size. Yield-point behavior was observed for the first time in fine-grained TiC deformed in compression and was found to depend on grain size and test temperature. The yield stress as a function of grain size can be described by a Hall-Petch type of relation, i.e. yield stress α (grain size)-1/2. The dislocations resulting from deformation in compression at lower temperatures were predominately screw in character, with edge dipoles and dislocation loops being present. As the temperature of deformation was increased, the dipoles and loops were gradually annihilated by climb and the dislocations were observed in the form of hexagonal networks with a much-reduced dislocation density. A plot of log yield stress vs 1/T showed a change in slope, which suggests that two rate-controlling mechanisms are in operation during deformation at different test temperatures. Thermal activation analysis at T = 1050° to 1500°C suggested that the rate controlling mechanism during deformation in this temperature range is associated with cross slip.     

Damage Produced by Moving Dislocations in MgO

The dislocation substructures in single crystals of MgO deformed in four-point bending at temperatures from –196° to 1300°C have been observed by transmission electron microscopy. Elongated edge dislocation pairs were found at all deformation temperatures. The majority of pairs originated where screw dislocations intersected grown-in dislocations. Grown-in dislocations always contained impurity precipitates along their length and often did not lie exactly in a slip plane. Because of either one or both of these factors, grown-in dislocations remained immobile during deformation. The stability of dislocation pairs depended on the separation of the two dislocations and on the deformation temperature. Narrow pairs broke up into small prismatic loops at 750°C and above. The width of the largest observed pairs approached but never exceeded the calculated value:      

High Temperature Tensile Creep of Magnesium Oxide Single Crystals

The creep behavior and the dislocation substructure developed during creep were investigated for 〈011〉 oriented MgO single crystals creep tested in tension. Creep deformation was studied over stress and temperature ranges of 29.0 to 86.2 MN/m² and 1200 to 1500°C, and the minimum creep rate, ε, was found to obey the relation:

where σ = applied tensile stress, k = the Boltzmann constant, T = absolute temperature, n = 3.8 to 4.5, and A = ll × 10⁻² (MN/m²)^-4 s^-1. Dislocation substructures developed during creep were studied by transmission electron microscopy and etch pitting techniques. At 1400°C, the dislocation density, ρ , at 0.10 tensile creep strain depended on applied stress as ρασ ^2.1. Numerous dislocation loops and long straight dislocations were present, but subboundaries were seldom observed. The results are discussed in terms of two possible operative creep mechanisms: (1) a recovery process based on annealing out of dislocation dipoles and loops, and (2) dislocation glide limited by atmospheres of charged defects surrounding dislocations.     

High-Temperature Deformation of Alumina Double Bicrystals

Deformation and strength of alumina double bicrystals fabricated from verneuil-grown stock were studied as functions of temperature (1210° T 1820°C) and strain rate (0.0005 ε 0.05 min^-1). The oriented specimens had c axes parallel or perpendicular to the compressive stress axes; + a axes and c axes were matched and/or mismatched across the (1123) interfaces of the double bicrystals. Undoped ("pure") double bicrystals in which the c axes and stress axis were coincident deformed by rhombohedral twinning and, at T 1550°C, by slip. Double bicrystals containing crystal segments having c axes perpendicular to the stress axis deformed in part by basal kinking. Interfacial impurity additions of mullite or spinel thin films promoted grain-boundary fracture and sliding, whereas "pure" double bicrystals, even at stresses comparable to the ultimate strengths of single crystals in similar orientations, did not exhibit macrosliding of the grain boundary.