Room temperature deformation mechanisms in Nimonic 80A

The deformation mechanisms occurring during room temperature tensile and low cycle fatigue testing were investigated. During fatigue the ordered γ′ precipitates restricted the dislocation movement to isolated {111} slip planes. The dislocations often moved in pairs as a result of γ′ shearing. Surface grains deformed more homogeneously as indicated by the dislocation cells. A band structure was also observed which resembled persistent slip bands in other age hardened alloys. These bands produced lamellar extrusions on the gauge surface. At higher strain ranges (Δε, > 2%), the strain was also accommodated through micro-twinning and grain rotation. The rotation of the grains produced an asterism in the TEM diffraction patterns which was also observed at higher strains in the tensile specimens.     

Application of minimum energy formalism in a multiple slip band model for fatigue—II. Crack nucleation and derivation of a generalised Coffin-Manson law

A situation of multiple parallel slip bands is considered. Each slip band is modelled as an accumulation of edge dipoles. The dislocation dipole density within the slip bands continually increases with fatigue cycling. The strain energy density within the slip bands consequently builds up with cycling until a critical cycle number when it becomes energetically favorable to nucleate a microcrack within one of the slip bands. This is proposed to be the crack nucleation cycle number. The above criterion based on the strain energy density is used to derive an explicit expression for the number of cycles for crack nucleation. It is shown that there is a parallel between this criterion for crack nucleation and other criteria that are based on the accumulation of a certain critical amount of damage. A generalised Coffin-Manson law for crack initiation is also derived. The size and most likely site of the just-nucleated crack is discussed.     

Numerical simulation of persistent slip band formation

The properties of persistent slip bands in metals under fatigue and their formation out of the matrix structure are compared with the numerical simulations of a model based on nonlinear reaction-diffusion equations. The persistent slip band structure results from the competition between the mutual interactions of the dislocations and their movement in the slip direction. Numerical simulations of the model equations reproduce the pattern wavelength, the dislocation densities, the wall size and the growth mechanisms experimentally observed.     

An analysis of equilibrium dislocation distributions

Equilibrium distributions of collections of discrete dislocations are analyzed, with the dislocations modelled as line defects in a linear elastic medium. The dislocated equilibrium configuration is determined by finding a minimum potential energy configuration, with respect to variations in the dislocation positions, for a fixed number and type of dislocations. Numerical results are presented for finite and infinite bodies with distributions of edge dislocations under plane strain conditions. Calculations involving doubly periodic arrays of cells, within which there is a single set of parallel slip planes, show a strong tendency for sharp dislocation walls to form. Perturbations of the wall structure due to the presence of pinned dislocations, vacant slip planes and free surfaces are illustrated. The stress fields due to the dislocation walls are calculated and large shear stress values are found away from any dislocation core. Pileups involving dislocations on two sets of intersecting slip planes are found to give rise to equilibrium configurations involving dislocation free regions. The response of dislocation patterns in an infinite medium to an imposed shear stress is also analyzed.     

The phenomenon of strain avalanches in cyclic deformation

By studying cyclic deformation of both mono- and polycrystalline copper with a fast response recorder, we have discovered an interesting substructure in hysteresis loops. This effect is caused by strain avalanches, which occur in loop patches, persistent slip bands and cellular dislocation structures. The behavior of the strain avalanches changes as life is expended and offers a means of measuring the current state of fatigue damage. They are especially pronounced when cracks are propagating. We believe that strain avalanches provide a useful tool for understanding cyclic deformation and fracture and for a novel method of nondestructive testing.     

A point defect model for fatigue crack initiation in Ni3Al+B single crystals

Transmission electron microscopy of boron-doped Ni₃Al single crystals, oriented for single slip and cyclically deformed at room temperature, revealed a high density of dislocation dipoles and point defect clusters. Observations of circular perfect dislocation loops, Frank loops, vacancy tetrahedra and spherical voids provide evidence of vacancy condensation during fatigue cycling at room temperature. It is suggested that lattice misfit develops between persistent slip bands (PSB) and matrix as a result of the generation and coalescence of excess vacancies in PSBs. The misfit strain at PSB/matrix interfaces is considered to increase with increasing cumulative plastic strain. Together with SEM observations of surface topography, it is suggested that fatigue damage in Ni₃Al single crystals is initiated by the formation of microvoids (microcracks) at PSB/matrix interfaces. The microvoids (microcracks) break down the coherency of the PSB/matrix interfaces and thereby relieve the accumulated misfit strain at the interfaces. A model of fatigue crack initiation based upon a surface energy criterion is proposed.     

Orientation effects on the elevated temperature fatigue of copper single crystals

Effects of orientation on dislocation structures which evolve during the elevated temperature fatigue of copper single crystals have been studied using crystals oriented for double slip. The resulting dislocation reactions produce sessile jogs, Cottrell-Lomer locks, or cells formed by coplanar slip. The relative strengths of the reaction products vary markedly with increasing temperature. At room temperature coplanar slip crystals are strongest, crystals forming Cottrell-Lomer locks weakest. At 678 K (0.5 T_m) Cottrell-Lomer lock crystals are strongest, those forming sessile jogs weakest. The orientation dependence of the saturation stress is much greater at 678 K than at room temperature. A plateau in the saturation stress of about 14 MPa is observed in sessile jog and Lomer lock crystals cycled at 523 K. Persistent slip bands (PSBs) with the familiar ladder structure are observed by electron microscopy in these crystals. No saturation stress plateau or TEM evidence of PSB formation was found at 678 K. Only cells, usually equiaxed, were seen.     

Dislocation structures in fatigued polycrystalline copper

The dislocation structures in fatigued polycrystalline copper with small average grain size were investigated over a plastic strain range from 1.5 x 10⁻⁵ to 10⁻². It was found that the dislocation structures are arranged into three types of configurations, which correspond to the three regions in the cyclic stress-strain curve. Cylidirical loop patch structure are present in region A for low strain amplitudes, similar to those observed previously in coarse grained polycrystals. Moreover, irregular loop patches are also formed in this region for small grains polycrystals rather thanin region B at intermediate strain amplitudes for coarse grained polycrystals. In region B, persistent slip band (PSB) structures are formed but with a low volume content compared with the coarse grained polycrystals. In region C, at high plastic strains, the dislocation structures are dominated by dipolar walls. In addition, labyrinth structures are developed in region C instead of region B for coarse grained polycrystals. All the dislocation structures observed are viewed as forms of dipolized structures. A dipolized dislocation arrangement model is proposed to describe the formation process of dislocation structures. It is shown that all the dislocation configurations formed in cycled polycrystalline copper are low energy structures.     

The effect of strain on hydrogen-induced dislocation morphologies in single crystal iron

The details of the dislocation morphologies in iron single crystal during stage I plastic straining with and without the presence of a concurrent supply of hydrogen have been studied. Hydrogen was shown to greatly enhance the tendency of strain localization especially near hydrogen-containing spherical inclusions. Three different strongly operating slip systems have been identified in the localized dislocation tangled structure, in contrast to the surrounding matrix or the region around the same particles in hydrogen free specimens, where one primary slip system predominated. It was suggested that hydrogen not only enhances the mobility of primary screw dislocations, but also affects the local stress and strain associated with particles, to promote dislocation generation on those slip systems associated with twin formation. If there is no competing slip system, the twinning-sense dislocations catalyzed by hydrogen can lead to the formation of crystallographic identifiable twins. If, on the other hand, a strong anti-twinning primary slip operates, as in the present study, the twinning process is suppressed and the associated dislocations interact locally with the primary system to promote a dislocation tangled structure. Hydrogen-induced microcrack formation was found to have an orientation similar to the strain localization band, suggesting that a direct correspondence exists between the presence of hydrogen-induced strain localization bands and the initiation of hydrogen-induced cracks.     

Quantitative measurement of persistent slip band profiles and crack initiation

In many materials (which have no extended flaws) crack initiation happens by slip localisation in so-called persistent slip bands. The mechanism of this crack nucleation is not yet understood quantitatively and is not accessible by direct experimentation, since the rugged surface structure of the slip band hinders reliable observation of crack nuclei from the outside of the specimen. Therefore a sectioning technique was developed, which produces a section perpendicular to the average specimen surface with an edge accuracy of 20 nm (resolution of the SEM). With this technique the development of the surface topography until the nucleation of cracks was observed in copper crystals. The surface topography is non-random from the very beginning. Extrusions with a triangular cross section with a 2 μm base width are formed. Crack nucleation happens preferentially along the interface between persistent slip bands and matrix. The local plastic strain amplitude in the persistent slip bands was found to be the parameter which correlates best with the life via a Coffin-Manson type relationship.     

The cyclic stress-strain behavior of nickel-base superalloys—I. Polycrystals

The cyclic stress-strain behavior of a wrought, nickel-base superalloy has been investigated at ambient temperature and 843°C with a constant cyclic ramp rate of 10⁻²/s. At ambient temperature, the derived cyclic stress-strain curve exhibits three stage behavior, as has been reported under similar conditions for f.c.c. metals. At elevated temperature, the curve is reduced to a power law function with no indication of three stage behavior. The dislocation substructure produced in the intermediate strain range region consists, at both temperatures, of strong persistent slip bands shearing the strengthening γ′ precipitates in the grain interiors and dense dislocation tangles necessitated by near grain boundary strain accommodation. The shapes of the cyclic stress-strain curves are shown to be consistent with the observed dislocation substructures. The cyclic hardening response and details of hysteresis loop shapes were found to be substantially unchanged with temperature.     

Orientation dependence of dislocation structures in cyclically deformed Cu-16 At. Pct Al alloy single crystals

The dislocation structures induced by the cyclic deformation of Cu-16 at. pct Al alloy single crystals oriented, typically, as for single slip and [023] and for double slip, were studied by transmission electron microscopy (TEM) and compared with the results of Cu single crystals. Completely unlike the dislocation structures of Cu single crystals of corresponding orientations, the dislocation structures of these oriented Cu-16 at. pct Al alloy single crystals show a typical planar morphology. As the applied-plastic-stain amplitude increases, the dislocation configuration changes, on the whole, from multipolar arrays to dislocation tangles in the primary slip plane and from low-density planar slip bands to well-developed persistent Lüder’s bands (PLBs) in the planes normal to the primary slip plane, respectively. Secondary slips can be clearly observed to activate from very low plastic-strain amplitudes in all three Cu-16 at. pct Al single crystals investigated. Interestingly, the crystallographic orientation has almost no effect on the dislocation structure of Cu-16 at. pct Al single crystals.     

The influence of elastic anisotropy on dislocation stability in /gb-tin and lead

The effects of elastic anisotropy on the energy and thermodynamic stability of dislocations in β-tin and lead were assessed through computation of the dislocation energy factorK. The energy factors were utilized to construct an inverse Wulff plot, from which unstable dislocation orientations are defined by concave regions of the construction. Dislocation instabilities are predicted for β-tin near the melting point for four of six slip systems considered, the slip systems displaying the instabilities being (110) [001], (100) [001], (010) [101], and (101)[101]. An instability is predicted also for the slip system {111} <111> in lead, which is the first fcc metal found to display sufficient elastic anisotropy for instability. For the metals examined in this paper, the angular range over which instabilities occur narrows with decreasing temperature, and usually, below some critical temperature, the dislocation line becomes stable over all orientations. The occurrence of dislocation instabilities is a direct result of elastic anisotropy, and their possible influence on physical properties is discussed.     

Transient cyclic stress-strain response and cumulative damage in Cu-16at.% A1 single crystals fatigued under variable straining

In order to investigate the transient cyclic stress-strain response and cumulative damage behavior of Cu-16at.% A1 alloy, single crystals with a common single slip orientation were cyclically deformed under variable straining. Studies were made of hardening behavior, strain bursts, hysteresis loops, friction and back stresses, dislocation structures, damage accumulation and life behavior. During ascending step tests, hardening naturally occurred and the strain was found to be accommodated not by increasing the plastic strain of current active slip bands but by increasing the volume fraction of active slip bands. During descending step tests, however, the plastic strain per individual slip band decreases with decrease of strain amplitude. The transient response after a reduction of strain amplitude in Cu-16at.% Al single crystals is not softening as commonly occurs but hardening. Hardening in this case seems to be caused both by hardening of individual slip bands and by the decrease of the volume fraction of active slip bands, which is also an indication of hardening. With regard to damage behavior, in low-high step tests, the number of cracks was found to increase remarkably during high amplitude cycling whereas the number of cracks did not change much after the step to low amplitude cycling during a high-low test. Miner summations of fatigue life for H-L step tests were found to be smaller than unity because the stresses associated with the structure produced at high amplitude were high and the plastic strain localized in active slip bands increased with the decrease of the volume fraction of active slip bands, caused by continuous cycling at the reduced strain amplitude. In L-H step tests, the Miner summations for fatigue life were found to be greater than unity because the hardening and the damage accumulation associated with low amplitude cycling were relatively insignificant as compared to that at high amplitude and fresh damage developed during the high amplitude sequence. The Miner summation behavior in these alloy single crystals was found to be more typical of that in commercial metals, and different from behavior in copper.     

Application of minimum energy formalism in a multiple slip band model for fatigue — I. Calculation of slip band spacings

A theory of slip band spacing in fatigued materials has been developed based on a criterion of minimum strain energy accumulation within slip bands. A two-dimensional, quasi-monotonic, dipole pile-up model is employed for this purpose. Multiple parallel, equally spaced, mutally interacting slip bands are considered. Each slip band is modeled as an accumulation of dipoles. Partially irreversible slip processes with stochastic fluctuations are allowed in the model. It is shown that for a given imposed plastic work, there exists a unique configuration (number and spacing) of the bands that has the minimum internal energy stored within all bands. An expression for the optimum slip band spacing in polycrystalline materials has been derived based on all experimentally determinable parameters. The effects of plastic strain amplitude, temperature and environment on this optimum slip band spacing are assessed. There is reasonably good agreement between theory and experiment.     

Continuity of slip screw and mixed crystal dislocations across bicrystals of nickel at 573 K

Iso-axial symmetrical tilt bicryslals of pure nickel oriented lor either screw or mixed crystal slip were deformed in simple compression at 573 K (0.33 T_m) at a strain rate of 3 × 10⁻⁴s⁻¹. Observation of slip traces revealed that screw bands were generally continuous across the interface. The degree of slip continuity, however, depended on boundary structure. Boundaries related lo low Σ values exhibited a higher degree of slip continuity than high Σ boundaries. Dislocations with mixed character were discontinuous regardless of boundary Σ. When the results are interpreted in terms of reactions between lattice dislocations at the grain boundary plane, it emerges that slip continuity is related to

• 1.(a) the magnitude of the residual dislocation at the boundary
• 2.(b) the dissociation of the residual into smaller grain boundary dislocations.

A smaller residual and a larger Burgers vector of the grain boundary dislocation enhances the probability of slip continuity across the interface. The reasons for why grain boundaries are weak barriers to passage of screw dislocations but good traps for mixed dislocations are discussed.     

Dislocation structures of monocrystalline copper during corrosion fatigue in 0.1 M perchloric acid

We have studied the dislocation structures of single crystals of copper cycled in 0.1 M perchloric acid and under different polarization potentials. TEM samples were cut from representative specimens both after saturation and after fracture. Although much higher strain localization was observed in the crystals cycled at anodic potentials, the dislocation structures observed were very similar to those of specimens tested at cathodic potentials and in air. For a plastic shear strain amplitude of 2×10⁻³, regular loop patches and dipolar walls were observed. For a higher strain amplitude of 4×10⁻³, dipolar walls associated with secondary slip were found in addition to regular primary walls. We believe this structure to be associated with breaking the primary persistent slip bands (PSB's) into truncated groups, of which the truncations were lined up along the traces of the secondary slip plane. Dislocation structures observed after final fracture of the crystals were different from those formed by cycling just into saturation; dipolar walls formed first and cell structures developed later. Thus, we confirmed the transition of dipolar walls into cells, reported by other investigators. Moreover, the transition of loop patches into “rungs” structure, the embryo of the PSB, was also observed in the late stages of life. BENDA YAN, formerly with the University of Pennsylvania     

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.     

Microstructural aspects of strain localization in AlMg alloys

The literature contains a number of continuum plasticity models describing the onset of strain localization but little definitive work which describes the microstructural transitions which accompany localization. In the present study a range of metallographic methods have been used in order to observe the progression of localization from events within single grains to the spatial organization of these events across the entire sample. The deformation mode used was cold rolling and observations were made using a variety of orientations relative to the rolling direction. It is concluded that in the AlMg system, localization begins by a structural instability in the accumulated dislocation substructure and later becomes organized into macroscopic bands due to local stress concentrations. The structure of the macroscopic bands is complex. They contain some high angle boundaries suggesting that they form due to the rapid and cooperative action of a number of slip systems over distances of the order of 0.2 μm. The bands cross grain boundaries and are organized in a cooperative sense because they represent local softening events. Thus, the shear bands in AlMg appear to form without texture softening or the need for the precursor of a lamellar structure. They involve a dramatic local change in the process of dislocation accumulation which is essentially a form a local dynamic recovery. The events become spatially organized to form macroscopic bands inclined at approx. 35° to the rolling plane as required by continuum plasticity.     

Grain size effects in the strain hardening of polycrystals

The degree to which the flow stress of a polycrystal is sensitive to grain size is discussed in terms of the distribution of slip and dislocation structure that develops in the vicinity of grain boundaries as deformation proceeds. The point of view is taken that the two principal classes of grain boundary hardening models, namely, those based on dislocation pile-ups and those based on dislocation density concepts respectively represent special cases of a single rationale developed in this paper. Grain boundary strengthening is intimately related to strain hardening which is affected by slip mode,i.e., the number of slip systems and the ability to cross slip. The effects of substitutional solute elements on grain boundary strengthenings is considered to be a consequence of their influence on slip modes rather than on their interaction with dislocation sources.