Time-dependent deformation of metals

The basic characteristics of timedependent deformation of metals are described in terms of dislocation properties. At high temperatures, diffusion controlled climb of edge dislocations is the rate limiting process, whereas at low temperatures, other forms of recovery involving cross-slip of screw dislocations operate. A composite model of plastic flow is used to describe the coupling between these recovery processes. The model is patterned after the persistent slip band structures observed in cyclically deformed fcc single crystals. Screw dislocations are allowed to move in the cell interiors and to deposit edge dislocations into the adjoining walls. Cross-slip and climb lead to dislocation rearrangement and annihilation in the two regions. These processes are coupled not only through the dislocation microstructure, but also through the mechanics of the composite structure. The model is used to describe various deformation properties of metals, including stage II, stage III, and stage IV strain hardening and saturation of the flow stress. The coupling of cross-slip and climb controlled recovery processes leads to gradual transitions in strain hardening and gives a natural account of the transition from low temperature deformation to high temperature creep. The model also leads to polarized dislocation structures, internal stresses, and anelastic creep properties. This paper is based on a presentation made at the symposium “50th Anniversary of the Introduction of Dislocations” held at the fall meeting of the TMS-AIME in Detroit, Michigan in October 1984 under the TMS-AIME Mechanical Metallurgy and Physical Metallurgy Committees.     

The effect of a locked screw dislocation on a pile-up of screw dislocations in a two phase system

The influence of an internal stress field of a locked screw dislocation of Burgers vector mb on a pile-up of screw dislocations in a two-phase system composed of two welded elastic half-planes is analyzed using the method of continuously distributed dislocations. The distribution function, the number of dislocations in the pile-up and the τ_yZ component of stress field on they =o plane are obtained. The results are discussed and applied to the fracture behavior of two-phase systems,     

Room-temperature deformation behavior of a directionally solidified β (B2)-(Ni-Fe-Al) intermetallic alloy

The room-temperature mechanical behavior of a directionally solidified columnar-grained, single-phase β (B2)-(Ni-20 at. pct Fe-30 at. pct A1) intermetallic alloy deformed along the “hard” 〈001〉 direction has been characterized. The 0.2 pct offset compressive yield stress was found to be comparable to that of 〈001〉 single crystals of stoichiometric NiAl. The dislocation substructure consisted of a preponderance of long, straight a〈111〉 screw dislocations on {112} planes, with cross-slip on {123} and {110} planes. The superpartials were not resolved by weak-beam imaging conditions, indicating that the antiphase boundary (APB) energy of NiAl is not reduced significantly by the Fe addition. The dislocation substructure was analyzed as a function of strain and compared to the dislocation substructure in 〈001〉 NiAl and body-centered cubic (bcc) metals deformed at low homologous temperatures. The debris left behind by a〈111〉 screw dislocations consisted of prismatic edge dipole loops 5 to 25 nm in diameter.     

Characteristics of lath martensite: Part II. The martensite-austenite interface

This investigation, using an Fe-20 pct Ni-5 pct Mn (wt pct) alloy, deals with the nature of the lath martensite-austenite interface. For the first time the misfit dislocation structure associated with a martensite interface has been observed experimentally. The interface consists of a single set of parallel dislocations having Burgers vector α/2[l?1l]_martensite = α/2[011]_austenite. Relative to the austenite, the observed dislocation line direction is [0?57], and the dislocation line deviates about 10 and 15 deg from the pure screw orientation in the austenite and martensite, respectively. However, the dislocations are in screw orientation on an atomic scale, although the interface step structure causes them to deviate from the exact screw orientation macroscopically. The spacing of the interface dislocations varies from 26 to 63Å. The observed interface dislocation array satisfies the requirements for a glissile interface, which suggests that the dislocations are misfit dislocations which accomplish the lattice invariant shear of the crystallographic theories.     

The role of intruder dislocations in modifying the misfit dislocation structures and growth kinetics of precipitate plates

Intruder dislocations formed at θ’ and η plates in Al-4 pet Cu and Al-0.2 pct Au alloys respectively by a small plastic strain partially compensate the misfit by single arrays ; the Burgers vector of the dislocations has a component normal to the plate interfaces. On subsequently aging such deformed microstructures, little change takes place in θ’ where the misfit is low. In η, on the other hand, the large misfit is sufficient to nucleate other compensatory arrays which interact with the intruder dislocations to form the lowest energy dislocation network and to annihilate the Burgers vector component directed normal to the plates. The lengthening kinetics of θ’ plates are unaffected by the intruder dislocations, but the thickening kinetics are briefly accelerated, probably by means of vacancy-enhanced diffusion associated with the plastic deformation. The thickening enhancement later falls off as the defects are annealed. In Al-Au, an interesting morphological instability develops and leads to the formation of elongated plates. These we believe are caused by a mechanism of sympathetic nucleation. R. Sankaran, formerly Department of Metallurgy and Materials Science, University of Pennsylvania, Philadelphia, Pa. 19174     

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.     

The orientations of dipolar dislocation structures produced by the cyclic deformation of B.C.C. metals

The orientations of dipolar walls produced by cyclic deformation in a renitrogenized mild steel and in literature observations on b.c.c. metals are shown generally to agree well with the predictions of a geometrical model of the dipolar wall, based on dipole loop stacking and on the sweeping of such loops into the walls by edge dislocations. Ladder-like walls within persistent slip bands are found to be perpendicular to the primary Burgers vector, as predicted for the dislocation activity of dislocations of a single Burgers vector. Literature observations of slip-bands containing rung-like walls not perpendicular to the primary Burgers vector are shown to be compatible with the two slip systems reported. Evidence for the occurrence of mutually perpendicular {100}-{210} and {311}-{110} combinations of labyrinth-like walls is also presented, with each combination predicted for a pair of {110}〈111〉 slip systems, the occurrence of which is compatible with the observations. In contrast to observations previously analyzed in f.c.c. metals, consideration of the cross-slip systems generally does not appear necessary to explain the observed wall orientations. It is suggested that the role of cross slip on influencing the orientations of the dipolar walls produced should depend on the test temperature and strain rate.     

Mechanism of Al2CuLi (T 1) nucleation and growth

Conventional strain contrast transmission electron microscopy (CTEM) and high-resolution transmission electron microscopy (HRTEM) were performed to establish the nucleation and growth mechanism of Al₂CuLi (T₁) precipitates in an Al-Li-Cu alloy. It is shown that the growth mechanism ofT ₁ precipitate plates occurs by the diffusional glide of growth ledges composed of b = 1/6〈112〉 partial dislocations on 111 matrix planes and that the growth ledges migrate by the ledge-kink mechanism, as previously suggested by Cassadaet al. 1 for this system.T ₁ plate nucleation is modeled as the dissociation of a perfect b = 1/2〈110〉 matrix dislocation in the vicinity of a dislocation jog. The coordinated dissociation of the dislocation line segments on each side of the sessile jog provides the displacement necessary for the formation of a new hexagonal plate or plate ledge. Strain contrast analysis of the Burgers vector of plate edges and the edges of growth ledges indicates the stacking of partial dislocations is of mixed displacement. Formerly Graduate Student, Department of Materials Science, University of Virginia,     

Dislocation substructure in Ta-Re-N alloys deformed at 77 K

High purity Ta, Ta-Re, and Ta-Re-N alloy single crystals were deformed in tension at 77 K, and the resulting dislocation arrangements were studied by transmission electron microscopy. Re and N have similar effects on the dislocation substructure. Alloying increases the fraction of primary screw dislocations at the expense of debris, tangling, and secondary dislocations. For a given increment in yield stress, Re causes much larger changes in the substructure than N. The substructures observed in Ta-Re-N alloys are similar to those in Ta-Re alloys, even though ternary alloys exhibit alloy softening and binary alloys exhibit alloy hardening. These observations can be explained in terms of the different intrinsic mobilities of edge and screw dislocations, the different interactions which substitutionals and interstitials have with edge and screw dislocations, and the large differences in concentration of substitutional and interstitial solutes.     

Dislocation substructure in Ta-Re-N alloys deformed at 77 K

High purity Ta, Ta-Re, and Ta-Re-N alloy single crystals were deformed in tension at 77 K, and the resulting dislocation arrangements were studied by transmission electron microscopy. Re and N have similar effects on the dislocation substructure. Alloying increases the fraction of primary screw dislocations at the expense of debris, tangling, and secondary dislocations. For a given increment in yield stress, Re causes much larger changes in the substructure than N. The substructures observed in Ta-Re-N alloys are similar to those in Ta-Re alloys, even though ternary alloys exhibit alloy softening and binary alloys exhibit alloy hardening. These observations can be explained in terms of the different intrinsic mobilities of edge and screw dislocations, the different interactions which substitutionals and interstitials have with edge and screw dislocations, and the large differences in concentration of substitutional and interstitial solutes.     

Determination of dislocation densities in HCP metals from X-ray diffraction line-broadening analysis

X-Ray diffraction (XRD) line-broadening analysis has been performed on highly textured Zr-2.5Nb specimens which had been deformed in tensile tests to produce well-controlled dislocation structures. An iterative deconvolution method has been applied to extract the broadening function for the material, using as standards, a Zr single crystal and a 0 pct deformed specimen. In both cases, for specific tensile tests, a significant contribution to the basal line broadening was observed, which was clearly not directly related to the dislocation structure generated by the deformation, i.e., so-called c-component dislocations having a component of their Burgers vectors perpendicular to the basal plane. Calculations showed that the extent of basal line broadening cannot be attributed to the secondary effect of strain from a-type dislocations, i.e., dislocations with Burgers vectors parallel with the basal plane. It is concluded that most of the line broadening observed was the result of intergranular strain distributions. These distributions are most prominent for grains oriented with their c-axes perpendicular to the tensile-deformation axis and resulted in basal-plane line broadening even when there were few, if any, c-component dislocations present. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science and Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

A comparison of the dislocation structures at small strains in copper deformed in tension and in torsion

OFHC copper specimens of 39 μm grain size were deformed in tension (to 8 pct tensile strain) and in pure torsion (to 8 pct shear strain) at 300 K and the resulting dislocation Burgers vectors, distributions and densities were determined using transmission electron microscopy. Employing the von Mises yield criterion and the total plastic-work hypothe-sis, good agreement was obtained between the tension and torsion test results for: (a) equivalent stress •σ versus equivalent strain •∈^P curves, (b) the dislocation Burgers vec-tors, distribution and density as a function of the equivalent strain and (c) the equivalent stress as a function of the square root of the dislocation density. These results imply that in the unidirectional straining of copper there results a constant dislocation struc-ture for a given amount of plastic work, irrespective of whether the deformation is in tension or torsion. However, equally good correlations were obtained on the basis of maximum shear stress and maximum shear strain and therefore a positive decision be-tween the two yield criteria could not be made.     

Contributions to the theory of jogged screw dislocation glide

The velocity of screw dislocations limited by the nonconservative motion of jogs is investigated. The vacancy concentration profile near a moving screw dislocation containing alternately signed jogs separated by a distance λb, whereb is the magnitude of the Burgers vector, has been calculated. It is shown that for λ > 20 the vacancy profile is essentially the same as that found previously for the case of a moving screw dislocation containing isolated jogs. It is shown that the jog-jog diffusion interaction does not change the stress dependence of the glide velocity as has been suggested. The steady state velocity of a gliding jogged screw dislocation responding to an effective stress τ_e is calculated using the quasiequilibrium approach to dislocation climb and the steady state vacancy concentration profile. It is shown that the glide velocity exhibits hyperbolic tangent stress dependence if the average vacancy concentration in the crystal equals the equilibrium vacancy concentration, C_o. If, however, the average vacancy concentration in the crystal follows the relation C_o cosh (λb ³ τ _e kT) during deformation, the glide velocity can be expressed as υ = πD_υb²C₀ sinh (λb ³ τ _e /kT whereD _υ is the diffusion coefficient for vacancies in the crystal. A model which suggests that the equilibrium vacancy concentration follows a relation similar to the hyperbolic cosine dependence is presented.     

Determination of dislocation densities in HCP metals from X-ray diffraction line-broadening analysis

X-Ray diffraction (XRD) line-broadening analysis has been performed on highly textured Zr-2.5Nb specimens which had been deformed in tensile tests to produce well-controlled dislocation structures. An iterative deconvolution method has been applied to extract the broadening function for the material, using as standards, a Zr single crystal and a 0 pct deformed specimen. In both cases, for specific tensile tests, a significant contribution to the basal line braodening was observed, which was clearly not directly related to the dislocation structure generated by the deformation, i.e., so-called c-component dislocations having a component of their Burgers vectors perpendicular to the basal plane. Calculations showed that the extent of basal line broadening cannot be attributed to the secondary effect of strain from a-type dislocations, i.e., dislocations with Burgers vectors parallel with the basal plane. It is concluded that most of the line broadening observed was the result of intergranular strain distributions. These distributions are most prominent for grains oriented with their c-axes perpendicular to the tensile-deformation axis and resulted in basal-plane line broadening even when there were few, if any, c-component dislocations present. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science and Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Interfacial structure and crystallographic studies of transformations in βt$́and β CuZn alloys—II. martensitic formation of α1′ plates in β′

A TEM study of the interphase boundary structure of 9R orthorhombic α₁' martensite formed in β′ CuZn alloys shows that it consists of a single array of dislocations with Burgers vector parallel to 〈110〉_β′ and spaced about 3.5 nm apart. This Burgers vector lies out of the interface plane; hence the interface dislocations are glissile. Unexpectedly, though, the Burgers vectors of these dislocations are not parallel when referenced to the matrix and the martensite lattices. This finding is rationalized on published hard sphere models as a consequence of relaxation of a resultant of the Bain strain and lattice invariant shear displacements within the matrix phase.     

Effect of temperature and shear direction on yield stress by {11\bar 22}〈\overline {11} 23〉 slip in HCP metals23〉 slip in HCP metals

The yield shear stress τ _y due to {11 $\bar 2$ 2}〈 $\overline {11} $ 23〉 second-order pyramidal slip system in cadmium, zinc, and magnesium hcp crystals increased with increasing temperature. This result is interpreted by two thermally activated processes as follows: (1) the dissociation of a (c+a) edge dislocation with a Burgers vector of 1/3〈 $\overline {11} $ 23〉 into a c sessile dislocation and an a glissile basal dislocation, and the subsequent immobilization of the (c+a) edge dislocation; (2) consequently, the double-cross slip of (c+a) screw dislocations must be activated thermally by an increment of applied stress to increase propagation velocity of slip band width. Moreover, τ _y is affected strongly by a direction of applied shear force due to second-order pyramidal slip in zinc as well as in cadmium. The anomalous behaviors of yielding would be caused by the nonsymmetrical core structure of the (c + a) dislocation due to the lattice heterogeneity in hcp metals.     

The orientation dependence of deformation mode and structure in stoichiometric NiAl single crystals deformed by high temperature steady-state creep

Single crystals of stoichiometric NiAl having predetermined orientations have been deformed by steady-state creep in the temperature range 750° to 1055°C, the stresses being varied from 1.76 to 7.02 kg mm_-2. In crystals oriented 7.5 deg from [101], only (100) slip was observed; the primary slip plane was 100 although secondary slip occurred on 110. As predicted by elastic anisotropy considerations, dislocations on 100 with b = α(100) have a zig-zag shape with the segments aligned along (110). On 110 they tend to lie along (111) and (112). Cross-slip of short segments having screw orientations can occur between l00 and 110, giving rise to dipoles and prismatic loops. Crystals with tensile axes 14 deg from [1ll] slip in all three (100) directions on both cube and dodecahedral planes. Characteristic structures are dislocation entanglements, dipoles, loops, and networks containing nodes. Often two (100) type dislocations react and form a segment of (110) dislocation. Crystals approximately 19 deg from the cube orientation slip in both the (100) and (110) directions, and the contribution of (110) slip to the total glide strain increases at higher temperatures. The (110) dislocations are mostly pure screw as predicted by elastic anisotropy. Two sets of α(100) dislocations with mutually perpendicular Burgers vectors can form a network of twist or mixed character. If the contact plane is not one of the cube planes, the network is lozenge shaped, and small (110) segments form at the node points. Slip in the (111) direction was not observed with certainty; (100) slip occurred in all specimens, and (110) slip only in crystals reasonably close to the cube orientation.     

Fatigue deformation of silver single crystals

The defect microstructure at saturation of silver single crystals subjected to constant plastic strain amplitude, γ_p, fatigue tests in the range γ_p = ±0.0025 to ±0.025 was studied by transmission electron microscopy. The rate of fatigue hardening and the saturation stress increase with increasing plastic strain amplitude. The dislocation microstructure at saturation changes from an open band structure at small plastic strain amplitudes to a closed cell structure at large plastic strain amplitude. The defect microstructure at saturation can be characterized by the density and distribution of point defect clusters and the dislocation wall spacing along the primary Burgers vector direction. The saturation stress is inversely proportional to the dislocation wall spacing along the primary Burgers vector direction and to the spacing of the point defect clusters on the primary slip plane. There is no significant difference between the fatigue hardening, the cyclic stress-strain curve and the dislocation microstructure at saturation of silver and copper single crystals.