Dislocations, kink bands, and room-temperature plasticity of Ti3SiC2

Transmission electron microscopy (TEM) of aligned, macrograined samples of Ti₃SiC₂, deformed at room temperature, shows that the deformed microstructure is characterized by a high density of perfect basal-plane dislocations with a Burgers vector of 1/3〈112 0〉. The dislocations are overwhelmingly arranged either in arrays, wherein the dislocations exist on identical slip planes, or in dislocations walls, wherein the same dislocations form a low-angle grain boundary normal to the basal planes. The arrays propagate across entire grains and are responsible for deformation by shear. The walls form as a result of the formation of kink bands. A dislocation-based model, that builds on earlier ideas proposed for kink-band formation in hexagonal metallic single crystals, is presented, which explains most of the microstructural features. The basic elements of the model are shear deformation by dislocation arrays, cavitation, creation of dislocation walls and kink boundaries, buckling, and delamination. The delaminations are not random, but successively bisect the delaminating sections. The delaminations and associated damage are contained by the kink boundaries. This containment of damage is believed to play a major role in endowing Ti₃SiC₂ and, by extension, related ternary carbides and nitrides with their damage-tolerant properties.     

Surface nanocrystallization in AISI 52100 steel induced by surface mechanical grinding treatment(SMGT)

Surface nanocrystallization(SNC) has proved to be an effective approach to improve the overall properties of bulk metallic materials.Recently,a new surface nanocrystallization technique,i.e.,surface mechanical grinding treatment(SMGT),was developed.In this work,a gradient nano-micro structure was achieved in the surface layer of the AISI 52100 steel by using SMGT.We obtained a minimum grain size of about 7nm in the top surface layer.The total thickness of the deformed layer is over 200 micrometer.Meanwhile the surface roughness is rather low. Ferrite grains were deformed to different extents varying with depth from the top surface.Gradient grain sizes were formed from top surface to deep matrix which offered a great opportunity to study the refinement process of the ferrite grains.It is found that dislocation activities play a dominant role in the process.At the initiate stage, dislocations accumulated and interacted to form dense dislocation walls and cells.Increasing strain and strain rate induced more dislocation walls in cells,forming finer cells.This procedure continued until nanograins formed at the top most surface. The existence of cementite particles in ferrite matrix greatly facilitates the ferrite refinement process.Boundaries between ferrites and cementites offered many dislocation sources which accelerate the propagation of dislocations. Dislocation walls were blocked by cementites which certainly lead to finer dislocation cells.The existence of cementites makes it easier to generate fresh dislocation walls in sub-micron grains.A strain gradient was formed from a cementite particle to surrounding ferrite grains.This strain gradient gives rise to more geometric necessary dislocations. As ferrite grain size decreased less than that of cementite particles,fragmentation occurred in cementites.Hard second phase was usually considered as brittle.In this work,evidences of deformation(traces of dislocation activities) in cementites were distinct.Since the stress concentration in the phase boundary(especially triple junction) excesses the shear modulus of cementite,dislocation emission was triggered.It is found in this work that dislocations tend to slip along parallel planes,possibly on(001),(01 0),(100),(110),(10 1 ) and(011) planes,depending upon as the load directions.     

Crack-tip dislocation emission arrangements for equilibrium—II. Comparisons to analytical and computer simulation models

Theoretical analyses of thin film effects on an apparent dislocation free zone (DFZ), grain boundary effects on the number of dislocations required for equilibrium and a tip-emission condition to avoid the Rice paradox are compared to the in situ TEM study of Part I. It is first shown that the apparent DFZ is a thin film artifact and, second, that a grain boundary blocked slip band may require half as many dislocations for equilibrium compared to no blockage. It is further shown that the “DFZ” becomes diminishingly small for even relatively low applied stress intensities. Based on a disappearing “DFZ”, an asymptotical solution of Li's grain size analysis leads to the number of dislocations in equilibrium for a given applied stress intensity, friction stress and grain size. With an ad hoc failure criterion, this gives a first order prediction of fracture toughness for a large number of ferritic and ferrite-pearlites steels. Finally, based on local stress distributions obtained from a solution containing tip-emission conditions, it is suggested that a local stress intensity presents a more easily defined brittle fracture criterion. This is applied to observations of dislocation arrangements at large applied stress intensity in Part III.     

Dislocation interactions with internal coherency stresses in age-hardened Cu-Ni-Fe alloys

The effects of internal coherency stresses on dislocation configurations and dislocation radii of curvature were investigated for age-hardened Cu-Ni-Fe alloys. Biaxial compression and tensile stresses were calculated from tetragonal crystal structure data for the two coherent precipitate phases, which were assumed to be elastically strained cubic phases. Shear stresses on slip planes were resolved from the biaxial coherency stresses and they correctly predicted the dislocation configurations observed in a transmission electron micrograph. Dislocations oriented perpendicular to the platelets were wavy because the shear stress on the slip plane abruptly changed sign (direction) at the platelet boundaries. Dislocation radii of curvature in the wavy sections were both calculated and observed to be about 300å. The analysis indicated both dislocations with Burgers vectors parallel to the platelets and wavy dislocation sections would move freely under small applied loads, but dislocations trapped between platelets would not.     

Dislocations motion in alloys with a periodic antiphase boundaries structure

Some peculiarities of the propagation of dislocations across a periodic antiphase boundaries structure are discussed. Examination of the effective surface tension acting on each dislocation shows that their equilibrium configuration mainly depends on the relative energies of the geometrical stacking fault and the shear antiphase boundary bounded by a unit dislocation, as well as the average separation of the periodic antiphase boundaries. Such an analysis allows to explain the occurrence of various deformation modes in these alloys: microtwinning in Ni₃ V or propagation of dislocations in planes with disturbed long range order in Cu₃ Pd.     

A quantitative assessment of forest-hardening in f.c.c. metals

Macroplastic deformation results from the long-distance movement of dislocations. In singlephase crystals it implies cutting the dislocation forest traversing the slip plane of the running dislocations and, as a consequence of the non-regular distribution of the “trees”, dislocation loops are left around the harder islands in their slip planes. The dislocation length so stored represents an increment of the obstacle density already present in other non-coplanar slip systems and thus contributes to their work-hardening. This work presents quantitative results on the contribution by forest cutting in a f.c.c. metal upon flow stress and work hardening rate. It has been obtained by computer simulation of dislocation glide through a mixture of punctual and linear obstacles whose strengths reproduce approximately the strength spectrum of a f.c.c. forest as derived by Shoeck and Frydman. Simulations have been conducted for random arrays of obstacles and for more realistic spatial dislocation distributions (cells, subgrains). Both the flow stress (and its temperature and strain rate dependence) and the athermal work-hardening rate so obtained are in good agreement with those measured for f.c.c. polycrystals in experiments covering up to large strains.     

Dislocation interactions with internal coherency stresses in age-hardened Cu-Ni-Fe alloys

The effects of internal coherency stresses on dislocation configurations and dislocation radii of curvature were investigated for age-hardened Cu-Ni-Fe alloys. Biaxial compression and tensile stresses were calculated from tetragonal crystal structure data for the two coherent precipitate phases, which were assumed to be elastically strained cubic phases. Shear stresses on slip planes were resolved from the biaxial coherency stresses and they correctly predicted the dislocation configurations observed in a transmission electron micrograph. Dislocations oriented perpendicular to the platelets were wavy because the shear stress on the slip plane abruptly changed sign (direction) at the platelet boundaries. Dislocation radii of curvature in the wavy sections were both calculated and observed to be about 300å. The analysis indicated both dislocations with Burgers vectors parallel to the platelets and wavy dislocation sections would move freely under small applied loads, but dislocations trapped between platelets would not.      

Cracks and screw dislocation arrays in anisotropie bimaterial plates

This article examines the equilibrium configuration of dislocation arrays in anisotropic bimaterial plates. Both components in the plate are assumed to be orthotropic with respect to plate axes. Forces on dislocations due to external loadings are found in closed form.Image forces due to phase boundary and free surfaces are also taken into consideration.Discussions on the behavior of screw dislocation arrays can be easily extended to the behavior of antiplane shear cracks. The crack opening displacements for several biomaterial systems have been calculated. In these systems, the crack opening displacements are found to be insensitive to the variation of plate thickness. However, they are strongly affected by the relative magnitude of elastic constants of the component phases. This is demonstrated in several diagrams. Formerly Graduate Student, Department of Mechanical and Aerospace Engineering, University of Delaware     

Equilibrium position of misfit dislocations at planar interfaces

The equilibrium position of misfit dislocations at interfaces is analysed within linear elasticity theory. Calculations are performed for an isolated dislocation as well as for an infinite array of dislocations in an infinite bicrystal. Analytic expressions are obtained for the image forces on the dislocation array due to the elasticity discontinuity. The position of the dislocations is determined by the balance between image forces and coherency forces on the dislocations. An equilibrium position is obtained in crystal I with smaller shear modulus G₁. The equilibrium stand-off distance is proportional to the inverse of the lattice misfit and increases with the ratio of the shear moduli, G₂/G₁, and of the Poisson's ratios, ν₂/ν₁, respectively. The calculated stand-off distance of misfit dislocations in Nb adjacent to a NbAl₂O₃ interface is smaller by a factor of 2 than the experimentally observed distance. This discrepancy can be explained qualitatively by the higher core energy of a dislocation in the vicinity to the elastically rigid Al₂O₃ compared to the core energy of a dislocation in bulk Nb.     

The orientation and temperature dependence of the yield stress of Ni3 (Al,Nb) single crystals

The flow stress of Ni₃(Al, Nb) single crystals has been measured as a function of orientation in the temperature range 77 to 910 K. While the increasing flow stress behavior is similar to that observed in other Ni₃Al-based alloys, the absolute value of the stress was found to be much higher. Also, the effect of orientation changes was to produce much greater changes in the temperature at which the peak flow stress occurs than has been previously observed. The operative slip systems were analyzed by two surface slip trace analysis. Primary octahedral slip was found to be predominant at temperatures below the peak stress temperature, while primary cube slip is prevalent above the peak temperature. The anomalous increase in the flow stress of Ni₃(Al, Nb) with increasing temperature is generally consistent with the thermally activated cross-slip of a/2<110> dislocations from {111} planes onto {100} planes. The cross-slip is shown to be aided not only be the resolved shear stress on the {100} cross-slip plane but also by the stress tending to constrict the a/<112> Shockley partial dislocations on the primary glide plane.     

Influence of interstitial carbon,nitrogen, and hydrogen on the plasticity and brittleness of steel

The introduction of carbon, nitrogen, and hydrogen in steel is analyzed in terms of the electron structure, dislocation properties, hardening, and failure of the steel. The similarity and differences in the mechanical properties of the corresponding solution solutions are discussed in relation to the influence of these elements on the density of electron states at the Fermi level of iron and correspondingly on the concentration of free electrons. Carbon reduces the concentration of free electrons, while nitrogen and hydrogen have the opposite effect. Hence, the atomic interaction is changed: specifically, its covalent or metallic component will be intensified. The dislocation rate in deformation is analyzed in the approximation of mobile and immobile interstitial atoms. In the first case, the interstitial atoms obstruct dislocational slip; the mobility of the dislocations is determined by the binding enthalpy of the dislocations with impurity atoms. If the interstitial atoms may accompany dislocations, the atomic bond is locally changed in dislocational atmospheres. That affects the unit energy of the dislocations and the distance between them in the slip planes. On the basis of the research results, the significant similarity between the hydrogen brittleness of austenitic steel and the ductile–brittle transition in alloying with nitrogen is explained.     

Dislocation/precipitate interactions during coarsening of a plastically strained high-misfit nickel-base superalloy

The effects of dislocations on the coarsening of γ’ precipitates have been studied in INCONEL* X-750. Using a thermomechanical treatment that includes solution treatment, the addition of approximately 3 pct plastic strain at room temperature, followed by aging at 845 °C for 100 hours, a unique banded microstructure is obtained. The plastic strain results in the formation of intense planar slip bands, and the dislocations in these bands act as preferred coarsening sites by relieving γ’ misfit strains. Precipitates grow on only one side of a slip band, and hexagonal arrays of mixed a/2〈110〉 dislocations form on the precipitate faces in the plane of the slip band. The resulting microstructure consists of interconnected networks of dislocations and precipitates, separated by bands of the γ matrix phase that are relatively free of γ’. The equilibrium dislocation structure has been determined for the γ/γ’ interface by an O-lattice construction. Comparisons with experimental results have been made and interphase boundary dislocation reactions analyzed. A model has also been proposed by which matrix dislocations are incorporated into the hexagonal networks of mixed character. Some fundamental insight into the probable role of dislocations in stress coarsening can be gained from the study.     

Geometrically necessary,incidental and subgrain boundaries

During the deformation of polycrystals, the grains break up into domains within which the selection of operative slip systems differs. The domains then subdivide into “cell blocks”. Locally, each group of cell blocks comes near to fulfilling the Taylor criterion when taken collectively, but the number of active glide systems in any one cell block is fewer than predicted. The boundaries between cell blocks and/or domains accommodate the lattice misorientations which result from glide on the different slip system combinations. They are therefore named “geometrically necessary bpundaries”. They, like all boundaries capable of accommodating variable lattice misorientations, are composed of dislocations. Microscopically, such boundaries appear as “dense dislocation walls” and “microbands”. Geometrically necessary boundaries are distinguished from ordinary dislocation cell boundaries by the absence of a change of glide systems across the latter. In materials deforming with a cell structure, ordinary dislocation cell boundaries as well as traditional “deformation bands” arise from the mutual trapping of dislocations into low-energy configurations. Such cell boundaries or walls are therefore named “incidental dislocation boundaries”. The misorientation across incidental boundaries is typically much smaller than for geometrically necessary boundaries. A further distinction is their respective on the flow stress. The average spacing of dislocation cell walls is inverse proportional to the flow stress whereas geometrically necessary boundaries obey the Hall-Petch relationship. Since they tend to occur more frequently the incidental boundaries typically control the flow stress. At increasing strain the angles between dislocation cells increase and different slip system combinations can operate in neighbouring cells. Cell walls are then no longer incidental boundaries but geometrically necessary boundaries. Such boundaries are termed “subgrain boundaries”.     

TEM-in situ deformation of beryllium single crystals—a new explanation for the anomalous temperature dependence of the critical resolved shear stress for prismatic slip

The critical resolved shear stress for prismatic slip within beryllium single crystals passes through a maximum in the temperature range of 170–450 K. A valid explanation has not been found till now. In the present paper the experimental results of TEM-in situ deformation of single crystal beryllium are presented. Although the samples were oriented to promote prismatic slip, combined slip mechanisms on prismatic and basal planes were observed at room temperature. However, at 170 K plastic deformation only occurred by prismatic slip. A new model explaining the anomaly of the critical resolved shear stress is proposed which is based on elementary dislocation processes, i.e. formation and motion of salient points on dislocation lines. The same mechanisms might also result for other hexagoanl metals in a comparable anomaly of the plastic behavior.     

Spannungsverteilung und versetzungsvervielfachung in der sinterkontaktregion

Systematic sintering experiments with monocrystalline sphere-plate models and sphere arrays made of copper (99.999% pure) have shown that in the contact regions a spontaneous dislocation multiplication may occur and lead to the formation of dislocation zones. In the light of that, the results of calculations according to the finite element analysis are presented. It allows to state the spatial distribution of all the components of the stress tensor which are due to capillary forces, inclusive of the shear stresses that are decisive for dislocation formation in the slip planes of the sintering particles in dependence on parameters of structure, geometry and sintering. It is found that, in many cases, the amount and reach of the capillary forces are sufficient for causing a dislocation multiplication in regions being noticeably larger as the contact proper.     

单晶铜塑性变形的二维离散位错动力学模拟研究

针对亚微米尺度晶体元器件在加工和服役中出现的反常力学行为和动态变形等问题,基于离散位错动力学理论建立了单晶铜塑性变形过程的二维离散位错动力学模型。该模型考虑外加载荷、位错间相互力和自由表面镜像力对位错的作用机制,引入了截断位错速度准则。与微压缩实验对比验证了模型的正确性,并且能够描述力加载描述的位错雪崩现象。应用该模型分析了不同加载方式和应变率下位错演化及力学行为,结果表明:当外部约束为力加载和位移加载时,应力应变曲线分别呈现出台阶状的应变突增和锯齿状的应力陡降,位错雪崩效应的内在机制则分别归结为位错速度的随机性和位错源开动的间歇性;应变率在102～4×104 s?1范围内,单晶铜屈服应力的应变率敏感性发生改变,位错演化特征由单滑移转变为多滑移面激活的均匀变形,位错增殖逐渐代替位错源激活作为流动应力的主导机制。      

A crystallographic study of fatigue damage in titanium

Large grain specimens with average grain size of 0.0127 m made from commercial purity titanium were subjected to a torsional cyclic strain at two different amplitudes: ±0.008 and =0.003. Fatigue damage was studied by scanning electron microscopy and crystal orientations were determined by X-ray diffraction and surface trace analysis. It was found that cyclic strain amplitude influenced the deformation mode and the nature of the macroscopic crack propagation. At high strain amplitudes the normal slip processes were observed and microcracking was observed on the (0001), and {1100} slip planes. The macroscopic crack propagation was dominated by the Stage I shear mode; however, some Stage II tensile mode propagation was observed after extensive Stage I propagation. At low strain amplitude twin plane cracking was observed on the {1011}, {1010}, and {1123} planes in addition to normal slip plane cracking, and the macroscopic crack propagation was dominated by the Stage II tensile mode. However, microscopic examination showed the macroscopic tensile mode cracks to be composed of microscopic shear mode cracks along slip planes and twin planes. At both low and high strain amplitudes cracking was observed on the {1120} plane which is neither a slip or twin plane in titanium. It is proposed that this cracking mode was a result of a dislocation reaction forming sessile dislocations on the {1120} plane.