Loop Patches Research Articles

Loop patch orientations in the matrix structure of cyclically deformed copper

A detailed analysis was performed of two regions of matrix or loop patch structure of cyclically deformed copper, each containing a single orientation of persistent slip bands (PSBs). Each loop patch orientation identified agreed with a wall geometrically predicted from a dipole-loop-stacking model for the occurrence of primary slip in combination with a slip system involving a secondary Burgers vector. The wall orientations identified were mechanistically favoured, based on dislocation-sweeping angle considerations, and also were those best able to accommodate excess primary slip dipole loops. The occurrence of {135} walls emphasized the importance of mechanistic considerations in determining wall orientations. The loop patch orientations identified generally contained 〈112〉 parallel to the primary edge dislocations, permitting a high percentage of walls and loop patches to coincide at PSB interfaces. The same geometrical condition enables us to understand wall rotations within PSBs. Additional evidence was obtained related to the influence of dislocation-sweeping angles on wall spacing and on dipolar structures in the immediate vicinity of twin boundaries.

Some aspects of the dislocation microstructures in fatigued FeCrAl alloys

Fe25Cr4Al and Fe25Cr2Al (wt.%) alloys were cyclically deformed in air at various total strain amplitudes. Four different structures were observed, in order of decreasing strain: ordinary dislocation cell structures in both alloys at about 1% total strain and above; and “maze” or “labyrinth” structures at intermediate strains, again for both alloys; however, at the lowest strain rates, a typical loop patch structure was found in the 2% aluminium alloy but a precursor to the maze (labyrinth) structure was found in the 4% alloy. That precursor structure seems to be the same as that observed by Mori et al. It would thus appear that the difference between the two alloys lies in the bypassing of the loop-patch structure in the 4% alloy, with, instead, direct construction of dipolar or multipolar walls. Thus the softening observed in the 2% alloy is due to the formation of the loop patches.

Transmission electron microscopy studies of the dislocation microstructures in fatigued Fe-8.7Al-29.7Mn-1.04C alloy

Austenitic Fe-8.7Al-29.7Mn-1.04C alloy (where the composition is in approximate weight per cent) was cyclically deformed at various total strain amplitudes. The microstructural changes induced by fatigue at room temperature were examined by transmission electron microscopy. At low strain amplitudes, it was found that the substructure consisted of well-developed loop patches and veins. However, at high strain amplitudes a series of closely spaced ladder-like persistent slip bands was formed in the alloy investigated. Furthermore, K phase Fe 3AlC x particles were induced in the Fe-8.7Al-29.7Mn-1.04C alloy during cycling at high strain amplitudes.

The three-dimensional shape of loop patches produced by cyclic deformation

Loop patches produced by cyclic deformation often have an elongated shape. The elongation aspects inferred from observations in the literature on f.c.c. single crystals and the elongation direction identified for h.c.p. titanium and zirconium are shown to be consistent with recent proposals to explain the orientations of dislocation structures consisting of dipole loops.

Dislocation arrangements in cyclically deformed copper single crystals

Detailed transmission electron microscopy (TEM) studies of dislocation arrangements in single-crystal copper samples, fatigued at a constant plastic shear strain amplitude of 0.15%, revealed clear differences between single- and multiple-slip-oriented crystals. In single-slip-oriented samples the dislocation arrangement consisted of loop patches and persistent slip bands (PSBs) with a ladder structure but, in addition, some cell formation also appeared in the PSBs. In multiple-slip-oriented crystals the dislocation matrix arrangement consisted of channel and wall layers lying nearly perpendicular to the loading axis. Ladder-type PSBs were also observed in these crystals, but they were normally separated from the matrix by cells and, in addition, PSBs seemed to have developed through cell formation. The resistance of PSBs to deformation can also locally vary because the proportional amounts of cells and ladder-like structures were not constant. On the basis of the present findings, PSBs should be considered only as structural elements into which the deformation concentrates during fatigue, regardless of their exact dislocation arrangement, which may contain ladder-type structures, cells and other possible dislocation configurations. As the role of point defects may also be significant in the initiation and, in particular, to the propagation of fatigue cracks, TEM observations were supplemented by small-angle neutron scattering and positron annihilation measurements which gave additional information about the point defect agglomerations.

Geometrical factors influencing the orientations of dipolar dislocation structures produced by cyclic deformation of f.c.c. metals

A recently proposed geometrical model to explain the orientations of labyrinth dipolar walls produced by cyclic deformation of f.c.c. metals is extended to explain the orientations of loop patches, channels within the matrix structure, and dipolar walls within persistent slip bands. The model is based on determining favourable stacking arrangements for dipolar loops involving one or two Burgers vectors and slip systems and on determining the directions in which stacking should be limited. The stacking of dipolar loops into regular networks results evidently in low energy dislocation structures. The dipolar loops are assumed to be swept into the dipolar dislocation arrangements by edge dislocations. When excess dipolar loops of one slip system are present, the ability of the dipolar arrangements to accommodate these becomes important. Good agreement is found between the predictions of this model and the available experimental evidence.

Loop patch behavior as affected by incremental loading and cyclic frequency in fatigue

Fatigue tests of copper single crystals initiated by a ramp-loading program yield a higher saturation stress (32 MPa) than the accepted stress (28 MPa) for the plateau of the cyclic stress-strain curve. In order to understand this difference, the dislocation structures of a ramp-loaded crystal have been studied by transmission electron microscopy, and the effect of frequency on the nucleation of persistent slip bands (PSBs) has also been studied. The loop patches thus found in a ramp-loaded crystal are not much different from those produced in a regular test at constant strain amplitude, except that they contain a higher and more uniform content of secondary dislocations. The higher flow stress observed for ramp loading is explained by training of the loop patches. The nucleation of PSBs was found to be strain rate dependent.

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.

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.

Dislocation structures in copper single crystals fatigued at low amplitudes

Abstract Single crystals cycled over a wide range of strains, below and up to those of the plateau in the cyclic stress-strain curve, have been prepared by ultrasonic fatigue. The dislocation structures of these specimens have been examined by transmission electron microscopy (TEM) and details of the structures, including the dimensions and varieties of the structures and the identities of the dislocations, have been documented. Special attention has been given to the occurrence of secondary dislocations and their role in the dislocation mechanisms, such as the transformation of loop patches into persistent slip bands.

Crack initiation mechanisms in copper polycrystals cycled under constant strain amplitudes and in step tests

Crack nucleation mechanisms at plastic strain amplitudes of 10 −3 and 10 −4 are reported for polycrystalline pure copper. In specimens cycled at 10 −3, cell structures are formed and, as well known, cracks nucleate at the grain boundaries. At the lower amplitude the dislocation structures consist of persistent slip bands (PSBs) and loop patches. Nevertheless, while some cracks do nucleate in the PSBs, the grain boundaries are the preferred site, rather surprisingly, for both crack nucleation and crack propagation. Crack nucleation mechanisms for low-high and high-low step tests using these two amplitudes were also explored. In low-high tests, for a rather wide range of fatigue life fractions the subsequent cycles at the high amplitude tend to ignore the damage produced first at the low amplitude. The potency of the damage interaction is much greater in high-low tests for the conditions studied here.

Glide and climb stresses on secondary slip systems in F.C.C. crystals due to isolated primary edge and screw dislocations

The climb and glide stresses resulting from an isolated 1 2 [ 10] (111) edge dislocation as well as from an isolated 1 2 [ 101] screw dislocation were calculated for all possible 〈110〉 {111} and 〈110〉 {100} slip systems. Knowledge of these stresses is needed in studies of glide on non-primary slips systems as affected by agglomerations of primary dislocations, especially pile-ups, or the loop patches and dipolar walls observed in fatigued specimens. The same data are believed also to be highly applicable to fracture studies in that the stresses about a mode I crack resemble those of a set of edge dislocations along the crack edge with their Burgers vectors normal to the plane of the crack. Similarly, a mode II crack may be simulated by an edge dislocation whose Burgers vector lies in the plane of the crack normal to the crack edge, and amode III crack may be simulated by a screw dislocation.

Dislocation behavior in fatigue V: Breakdown of loop patches and formation of persistent slip bands and of dislocation cells

The loop patch and channel structure in fatigued cooper becomes unstable at a resolved sgear stress of about 30 MPa at room temperature and is replaced by persistent slip bands (PSBs). This instability depends little, if at all, on frequency of cycling and strain amplitude. It appears to be a function only of the dislocation density in the loop patches but includes a temperature dependence (i.e. the critical stress rises to about 70 MPa at 4 K) which suggests that cross-slip, defect dragging and/or “forest cutting” are involved. In view of the available evidence it is suggested that the discussed instability is due to secondary glide on systems intersecting the primary slip plane which, through moving primary edge dislocations normal to their slip planes, permits their mutual annihilation. It is envisaged that such secondary glide takes place on a small scale in a very large number of places in the loop patches once the critical dislocation density is reached. A semiquantitative analysis of the stresses involved in conjunction with micrographical evidence indicates that the intersecting glide occurs at least partly on cube planes. If this interpretation is correct, the removal of the primary loops leaves behind dislocations which are faulted but are fairly mobile and are liable to annihilate each other mutually to a large extent and to leave “debris” which is then swept into the dipolar walls in the PSBs, all in agreement with micrographical evidence. Cell formation in the PSBs is believed to result at stresses high enough to introduce secondary glide in the PSBs. Loop patches, consisting as they do of mobile dislocations, must be attracted to the surfaces on account of the (mild) dislocation surpluses at their boundaries with the channels and the image forces arising therefrom. Such image forces are virtually independent of the presence of thin surface films, but such surface films can inhibit the escape of the prismatic loops out of the metal. Correspondingly, loop patches will be either enriched or depleted at surfaces, to a depth comparable with the average loop patch diameter, depending on whether the surface films are or are not so thick as to bar the egress of the loops. One probable example of each case is discussed.

Dislocation behavior in fatigue IV. Quantitative interpretation of friction stress and back stress derived from hysteresis loops

The dislocation model developed in Parts I – III is examined quantitatively. According to this model loop patches result from random trapping of glide dislocations whereby a constant fraction of them are incorporated into the loop patches in each cycle. The dislocation density in these is equilibrated rather easily because of the low friction stress on the loops in prismatic glide. As another result of the low friction against prismatic glide the loop patches adjust towards optimum dislocation density such that the stored energy is minimized. This imparts to them volume elasticity and properties similar to Taylor lattices. The back stress, which was determined in Part II from an analysis of the hysteresis loops, is identified with the maximum elastic reaction of the dislocation lattice against the imposed strain at the end of each cycle. Correlated with this is a friction stress of closely similar magnitude arising firstly because relative motions of the dislocation lattices beyond the confines of their immediate energy minima are irreversible and secondly because of the anchoring of glide dislocations at loop patch surfaces through local loop polarization. This feature explains a major experimental result of Part II, namely the equality of the friction stress and the back stress except for that part of the friction stress which can be ascribed to jog dragging and point-defect hardening. With respect to deformations within the momentary energy valley the dislocations in the loop patches respond quasi-elastically as if the elastic constant of the material was too low. The magnitude of the apparent elastic constant depends on the configuration of the dislocation lattice. Comparison with the experimentally observed quasi-elastic behavior indicates that the lattice is nearly close packed. Further, comparison with the experimentally determined dislocation density in the loop patches at saturation suggests that in all cases about 10% of the glide dislocations become trapped in the loop patches. The magnitude of the back stress and its dependence on the number of cycles and fatigue strain range derived from the model is in almost perfect agreement with observations; in fact it is well within the limits of reliability of both theory and experiment. Another check of the theory is possible via the changes in hysteresis loop shape with the number of cycles beyond the cumulative strain at which the loop patches can accommodate the fatigue strain by simple “flipping”. The agreement between the predicted transformation of both stress and strain in proportion to the square root of the number of cycles and the observed changes in hysteresis loop shape was found to be excellent. These results and those of Parts II and III apply to the whole range of fatigue amplitude in the plateau region which is characterized by the formation of persistent slip bands at a stress of about 30 MPa.

Dislocation behavior in fatigue III. Properties of loop patches — Do they participate in fatigue cycling?

The fundamental question of whether the loops in the loop patches “flip” rhythmically with fatigue cycling (model 1) or remain randomly nriented throughout (model 2) is considered. It is shown that model 2, but not model 1, gives rise to apparently insurmountable difficulties. These include the fact that the back stress τ B derived on the basis of model 2 apparently has very different characteristics from those observed. In contrast, model 1 yields qualitative agreement between the predicted and observed properties of the back stress. Further, the remarkable equality τ B = τ F − τ S, where τ F is the friction stress and τ S that part of the friction stress which has previously been identified with point-defect hardening and jog dragging, is a direct consequence of model 1 but appears to be in irreconcilable conflict with model 2. For these reasons it is concluded that the loops do participate in fatigue cycling, i.e. model 1 applies. Loop patches will behave like Taylor dislocation lattices provided that the frictional stress against prismatic glide of the loops is small. This is believed to be established by the result given in Part II of this series that the contribution to τ S due to jog dragging is much larger than that ascribable to point-defect hardening and that τ S is typically much smaller than the applied stress. As a consequence loop patches have a total volume that is determined by the amount of dipoles in the specimen. These are formed by random trapping of glide dislocations. Since the channel width appears to be nearly constant, probably regulated by jog formation as shown in Part II, the average loop patch diameter is thus determined. Also, in contrast to the assumption in Part I of this series, it is now concluded that the properties of the loop patches, except for the surfaces immediately interacting with the glide dislocations, are essentially homogeneous throughout. Except for this correction, the concepts and model developed in this and subsequent parts of the series are largely based on Part I. A quantitative treatment of the back stress as a function of the number of cycles and the fatigue strain amplitude, and of the evolution of the hysteresis loops, will be given in Part IV. The conversion of the matrix structure into persistent slip bands (PSBs) will be the subject of Part V. This series of papers pertains to fatigue strain amplitudes in the “plateau region” in which PSB formation ensues at about 30 MPa stress.

Mechanisms of fatigue hardening in copper single crystals

Copper single crystals were cycled in push-pull at a constant total shear-strain amplitude, γ t , of ±0.0075, which gave a fatigue life, N f , of 42,500 cycles. Dislocation arrangements were determined as a function of the number of elapsed cycles and were correlated with the fatigue-hardening curve. The cyclic stress-strain curve was determined over the range γ t = ±0.0016–0.016. Results have been compared with other recent fatigue-hardening studies. Dislocation bundles in dipole and multipole configurations are formed by a mutual-trapping mechanism during rapid hardening. The bundles contribute to rapid hardening by providing effective barriers to continued dislocation motion on the primary and secondary slip systems. Dislocation structures in the earliest stages of rapid hardening were found to be analogous to unidirectional dislocation structures; the similarity rapidly fades, however, with continued cycling and the progressive development of a cell structure, until at saturation hardening (≈0.5 per cent N f ), a dislocation structure uniquely characteristic of cyclic deformation is developed. Strain accommodation during saturation hardening can be accomplished by the cooperative movement of dislocations within cell walls (or loop patches) and by the traffic of dislocations across cells (or between loop patches), with ∼50 per cent of the dissipated energy estimated to be available for point-defect production. The present results lead to a unified view of fatigue hardening for high- and low-strain amplitudes. The dislocation structures in low-amplitude loop patches and in high-amplitude cell walls appear to be identical, each being a product of the early mutual-trapping mechanism. A correlation is suggested between the occurrence of the Bauschinger effect and the development of simple dislocation bundles (Stage I type dislocation structure). It is postulated that the Bauschinger effect is a result of the relaxation of dislocations within these dislocation bundles.