Campbell Laird

Strain localization in cyclic deformation of copper single crystals

Abstract The localization of plastic strain into macroscopic groups of persistent slip bands has been determined on copper single crystals strain-cycled into saturation. The macroscopic bands traverse the whole cross section and undergo complete reversibility of plastic strain with load reversibility. Although overall, surface slip steps form in proportion to the applied plastic strain, individual steps are not always completely reversed, leading to the rapid formation of a notch-peak topography within the bands. The dislocation structure of the persistent slip bands was determined, permitting a critical assessment of the various mechanisms proposed for saturation in low-strain cyclic deformation. Using existing ideas, an adequate model of saturation is based upon the cooperative movement of primary links between the persistent slip-band walls, but impeded in their motion by point-defect clusters and small dislocation debris.

Low energy dislocation structures produced by cyclic deformation

Abstract Cyclic deformation in push-pull straining provides ideal conditions for achieving low energy dislocation structures because large cumulative strains give rise to high dislocation densities and the to-and-fro dislocation motions enhance entrapment probabilities. At low strain amplitudes the structures are dominated by clusters of prismatic loops; evidence for the dislocation content and interaction of the clusters is reviewed and is shown to be consistent with the establishment of low energy arrays. At higher amplitudes the dislocation structures are dominated by dislocation walls which are strongly dipolar. The deformation which occurs in these structures at low numbers of cycles does not seem to be consistent with low energy arrays, or at least only with those of moderately low energy. However, with sufficient cycling, lower energy arrays seem to become established and to promote homogeneity of the strain. At still higher amplitudes, complex cellular structures are observed and the complications of these structures can be interpreted convincingly in terms of low energy dislocation structures.

Dislocation behavior in fatigue

Abstract Recognizing mechanistic similarities as well as differences between unidirectional and cyclic deformation, the authors apply recent advances in understanding mechanisms of unidirectional deformation to fatigue. Reinterpretations or new mechanisms are offered for the following: the formation of dislocation veins and of persistent slip bands (PSBs), the behavior of dislocations in established PSBs, and the transformation of PSB dipolar walls into dislocation cells. In addition, the nature of extrusions and intrusions is discussed.

Cyclic stress—strain response of two-phase alloys Part I. Microstructures containing particles penetrable by dislocations

Abstract Specimens of solution-treated Al-4% Cu alloy and aged alloy with coherent θ″ precipitates have been cycled under constant plastic strain over a wide range of fatigue life. The cyclic hardening and subsequent softening which occurs have been investigated by phenomenological experiments, electron and scanning microscopy and by optical microscopy. Hardening is interpreted by unidirectional concepts and softening by a disordering hypothesis, a new application with respect to fatigue. On the basis of these results, a general interpretation of cyclic response in this type of two-phase alloy has been obtained.

Dislocation behavior in fatigue II. Friction stress and back stress as inferred from an analysis of hysteresis loops

Abstract Fatigue hysteresis loops obtained by three different authors are evaluated to obtain data for the friction stress and back stress acting on the dislocations. Part of the friction stress is equal in magnitude to the back stress and like it rises roughly in proportion to the root of the cumulative plastic strain. The theoretical discussion of this contribution to friction stress will be given in conjunction with the discussion of the back stress in parts III and IV of this series. The smaller part of the friction stress depends more or less linearly on the number of cycles. It is identified primarily with the stress required for dragging the jogs on the screw dislocations which shuttle to and fro in the matrix channels in accordance with the deductions of part I of this series. Additionally, there may be a yet smaller contribution to the friction stress due to dispersed point defects. This, if it exists, comes to saturation after about 12 cycles. The fact that no contribution to the stress can be identified with the back stress due to the glide dislocations which are spun out and taken up again at the channel-loop patch interfaces indicates that their line tension is quite low. This is understandable on account of their arrangement into tilt wall configurations as well as the local screening of their stresses by reorienting loops in their vicinity. Following up on the corresponding hypothesis in part I, it is suggested that the channel widths in the matrix structure adjust such that, on the average, one jog resides on each screw dislocation segment. If so, the channel width should initially decrease inversely with the number of cycles, and then become constant.

MECHANISMS OF SLIP MODE MODIFICATION IN F.C.C. SOLID SOLUTIONS

While it is widely recognized that alloy factors other than stacking fault energy play a role in promoting planarity of slip, no detailed model has been advanced to explain the mechanism of planar vs wavy slip mode. Therefore, friction stress effects of alloying on disolcation behavior are reviewed, as well as the role of stacking fault structure in inhibiting the clustering of dislocations in planar slip metal. A model of cross-slip inhibition (and thus planar slip behavior) is developed from the idea that the joining of partials is resisted by frictional effects. Planarity of slip is promoted not only by low stacking fault energy but by increase in shear modulus, atomic size misfit and solute content. A critical solute concentration is predicted by the model for the transition from wavy slip to planar slip and this is shown to be in good agreement with observations for copper base solid solutions and other alloy systems.

Overview of fatigue behavior in copper single crystals—I. Surface morphology and stage I crack initiation sites for tests at constant strain amplitude

Abstract The sharp-corner technique coupled with scanning electron microscopy has been used here for observing morphological changes at the surfaces of fatigued copper monocrystals. This technique confirms a number of recently-reported observations on persistent slip band (PSB) and crack initiation behavior, but elaborates others and provides new insights. For example, it reveals PSB encroachments (i.e. negative protrusions) which indicate that one mechanism of protrusion propagation is a shuttling mechanism amongs PSB-matrix lamellae. It is also found that there is a tendency to form longer cracks preferentially at the leading edges of positive protrusions and at the valleys of encroachments, implying that Stage I crack initiation sites are biased by the surface geometry. Interferometric observations show that PSB strain is inhomogeneous, being more highly localized at PSB-matrix interfaces, another phenomenon causing enhanced crack initiation.

Crack nucleation and stage I propagation in high strain fatigue—II. mechanism

Abstract In order to establish the properties of the grain boundaries at which cracks nucleate in high strain fatigue, groups of grains adjacent to the free surface of polycrystalline copper have been analysed by X-ray and trace techniques prior to testing, and subsequently observed during testing to check the nucleation sites. It has thus been found that vulnerable boundaries are associated with highly misoriented grains, the dominant slip systems of which are directed over large slip distances at the intersection of the boundary with the surface. The role of deformation incompatibility in crack nucleation is discussed and the nature of Stage I growth (intergranular) in high strain fatigue is described and defined in terms of bulk slip in the grains adjacent to the crack.

The cyclic stress-strain response of copper at low strains—i. Constant amplitude testing

Abstract A controversy has arisen over whether or not the cyclic stress-strain (CSS) curve for polycrystalline copper can be correlated with that for monocrystals, particularly in showing a plateau and a fatigue limit at an equivalent stress and strain (equivalence being expressed via Taylors factor). Bhat and Laird suggested this correlation but Mughrabi opposed it on the grounds that interpretetion of the mechanical data was equivocal and he did not believe persistent slip band (PSBs) would exist in the bulk of polycrystals. To help settle this controversy, low strain tests under both constant strain-control and constant stress-control (Part I) have been carried out in polycrystals as well as extensive observations of the dislocation structures by TEM. It is concluded that the strain-control curve does not show a true plateau, in agreement with the views of Mughrabi. However, a definite change of slope occurs at a stress and strain corresponding to the fatigue limit and initial formation of PSBs in monocrystals, in agreement with the views of Bhat and Laird. Furthermore, the stress-control CSS curve tends strongly to a plateau, differing from the strain-control CSS curve at low strains; also dipolar wall structures analogous to those of monocrystalline PSBs but not so regularly ladder-like, are found in the bulk of polycrystalline copper. The dislocation structures corresponding to the different CSS curves in load and strain control are documented, and reasons for history dependence in CSS response are provided. Thus a close correlation between the CSS curves and cyclic response of polycrystals and monocrystals is demonstrated. In a companion paper (Part II), similar correlation is demonstrated for tests conducted under variable amplitudes.

Latent Hardening in Single Crystals I. Theory and Experiments

Accurate measurements of the initial yield stress on previously latent slip systems as well as a reinterpretation of widely reported experimental observations have led to a new description of single crystal hardening within the framework of the incremental (flow) theory of plasticity. Slip interactions and the history of slips are essential in explaining well-known physical phenomena such as stage II deformation and latent hardening. Guidelines for deriving the set of instantaneous hardening moduli are given in terms of inequality restrictions. Although time-independent behaviour is assumed throughout the present study, these restrictions are expected to apply as well to time-dependent creep behaviour at low to intermediate temperatures. In Part II, a complete constitutive theory is developed with analytical forms given for the instantaneous hardening moduli.