Cross-slip Activation Research Articles

High cycle fatigue behavior and strengthening mechanisms of laser powder bed fusion pure tantalum

The fatigue behavior and strengthening mechanisms of the laser powder bed fusion pure tantalum (LPBF-Ta), coupled with a fatigue life prediction model, were originally explored. The fatigue strength of LPBF-Ta fabricated at the optimal laser energy density (154.16 J/mm3) is 348 MPa (106 cycles), showing a remarkable improvement of about 80 % and 50 % compared with that of the annealed and cold worked commercially pure tantalum, respectively. The microstructural analysis identifies that cellular structures averaging 300 nm in size contribute 438.2 MPa to strengthening, serving as the main contributor to fatigue strength. The breaching of cell walls by dislocations, along with the activation of cross-slip, ensures plasticity and ultimately enhances fatigue strength. Besides, the analysis of the defects reveals that the internal lack of fusion pore can induce the secondary fatigue crack, resulting in a region of brittle crack propagation. Furthermore, a finite life prediction model is established by originally incorporating the size of the crack source defect, and it significantly improves the prediction accuracy of the fatigue life. These results provide guidance for the development of fatigue strengthening strategies for LPBF-Ta.

Critical role of dynamic precipitation on enhanced creep resistance in Mg–Zn alloy by Mn substitution for Zr

Mg alloys with excellent creep resistance are able to withstand fatigue and damage under high temperature and complex load. Adding alloying elements rather than rare earth elements, such as Mn, can further reduce the cost and thus facilities the widespread applications of Mg alloys. In this paper, the individual effect of Mn and Zr elements on the dynamic microstructural evolution of Mg–Zn alloys during creep is evaluated, on the basis of identical initial microstructure before creep. And the essential origin of Mn substitution for Zr improving the creep resistance of Mg–Zn alloys by one order of magnitude is revealed. Experimental investigations and first principle calculations reveal that prior-precipitation of α-Mn particles serve as the heterogeneous nucleation sites for the precipitation of β1′ phases, and Mn partitioning in MgZn2 phases promote the nucleation and thermal stability of β1′ precipitates during creep. High number density of fine precipitates can effectively inhibit the occurrence of continuous dynamical recrystallization (CDRX), pin dislocations and impede the activation of cross-slip, which are the main reasons for the enhanced creep resistance in ZM60 alloy. As Zr does not participate in the formation of precipitates in ZK60 alloy, the MgZn2 phases with low thermal stability are prone to growth and coarsening during long-term creep. Large number of fine CDRXed grains and sparse coarse precipitates in ZK60 alloy cannot effectively impede the dislocation movement, which contributes to the occurrence of cross-slip and deteriorate the creep resistance. This work provides new insights for designing and fabricating outstanding heat-resistance Mg alloys.

A data driven approach for cross-slip modelling in continuum dislocation dynamics

Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that is a function of the screw segment length and the stress acting on the dislocation. In continuum dislocation dynamics (CDD), the information regarding the length of the screw dislocation segment and local stress state on dislocations are lost due to the coarse-grained representation of the density. In this work, a data driven approach to characterize the lost information by analyzing the discrete dislocation configurations is proposed to enable cross-slip modeling in the CDD framework in terms of the coarse-grained dislocation density and stress fields. The analysis showed that the screw segment length follows an exponential distribution, and the stress fluctuations, defined as the difference between the stress on the dislocations and the mean field stress in CDD, follows a Lorentzian distribution. A novel approach for cross slip implementation in CDD employing the screw segment length and stress fluctuation statistics was proposed and rigorously tested by comparing the CDD cross-slip rates with discrete dislocation dynamics (DDD) rates. This approach has been applied in conjunction with three cross-slip models used in DDD simulations differing mainly in the functional form of cross slip activation energy. It was found that different cross-slip activation energy formulations yielded different cross-slip rates, yet the effect on mechanical stress-strain response and dislocation density evolution was minimal for the [001] type loading.

Microstructure and Mechanical Properties of Biomedical Ti-Zr-Nb-Ta-Sn High-Entropy Alloys

Ti(50-x)Zr38NbxTa8Sn4 high-entropy alloys with x = 0, 10, and 20 at.% were produced by vacuum arc melting in a high-purity argon atmosphere. The initial microstructures consisted of equiaxial bcc grains with sizes of 115 ± 30 µm, 250 ± 60 µm, and 280 ± 70 µm for the Ti30Nb20, Ti40Nb10, and Ti50Nb0 alloys, respectively. The Ti30Nb20 and Ti40Nb10 alloys showed untypical mechanical behavior with a short strain-hardening stage followed by a gradual decrease in flow stress after reaching the yield point. Although these two alloys had some inclination toward macroscopic strain localization, their tensile elongation was similar to that obtained in the Ti50Nb0 alloy, which had a more extended stage of uniform deformation. The differences were associated with distinct microstructures observed after deformation to fracture. The formation of dislocation bands and the activation of cross-slip at the microscale, as well as the appearance of kink bands at the mesoscale, can result in plastic instability. In contrast, a lamellar-like microstructure with parallel dislocation bands, such as the one observed in the Ti50Nb0 alloy, can ensure a more stable mechanical behavior. The developed alloys (Ti30Nb20 and Ti40Nb10) have properties that make them highly attractive for biomedical application due to a combination of very high yield strengths (1090 and 930 MPa, respectively), low Young’s moduli (~78 and ~69 GPa, respectively), reasonable ductility, and excellent biocompatibility.

An improved combination of tensile strength and ductility in titanium alloys via oxygen ordering

Oxygen content has always been limited in commercial titanium and titanium alloys due to its propensity to induce a severe ductility loss. Yet, its effect on the macroscopical behavior has never been clearly understood and is still rather unclear considering the wide variability in the literature results. Here, we investigate the tensile properties of α-titanium with oxygen contents ranging from 0.15 to 0.80 weight percent (wt%). While the strain-hardening ability of oxygen is maintained, no ductility drop is observed up to 0.60 wt% of oxygen, thus allowing exceptional combinations of mechanical properties with an ultimate tensile strength (UTS) of 800 MPa and 29% of elongation at fracture for the Ti-0.6O alloy. Both high strength and ductility of these alloys result from the dislocations/precipitate's interactions. It is proposed that these interactions induce an important cross-slip activity responsible for a dislocation multiplication and a high work-hardening rate. With the addition of Zr, alloys exhibit an even more promising combination of mechanical properties, achieving 1,075 MPa of UTS and 28% of elongation at fracture for the Ti-4.5Zr-0.8O alloy. The mechanical properties of TiO and TiZrO alloys brought out in this study surpass those of Ti–6Al–4V alloy and open significant prospects for developing a new generation of oxygen-tolerant titanium alloys.

History and temperature dependent cyclic crystal plasticity model with material-invariant parameters

Cyclic deformation of metallic materials depends on the interaction of multiple mechanisms across different length scales. Solid solution atoms, vacancies, grain boundaries, and forest dislocations interfere with dislocation glide and increase the macroscopic strength. In single phase metallic materials under cyclic loading, the localization of dislocation densities in sessile substructures explains a significant fraction of the strain hardening. Upon cycling, these dislocation structures evolve across stable configurations, which depend on the strain accumulation.This work advances substructure-sensitive crystal plasticity models capable of quantifying the cyclic hardening history at various temperatures for single phase FCC materials. The framework predicts the cyclic evolution of dislocation substructure based on the activation of cross slip activation for Al, Cu, and Ni single- and poly-crystals up to 0.5 homologous temperature. The increase in cross slip with temperature and deformation induces a transformation in dislocation structures, which predicts secondary hardening without any additional provision. Moreover, the approach relies on material-invariant mesoscale parameters that are specific to dislocation substructures rather than a material system. Hence, we demonstrate that crystal plasticity predictive power can be augmented by parameterizing the model with single crystal experimental data from multiple materials with common substructures. As a result, the crystal plasticity model shares parameter information across materials without the need for additional single crystal experimental data for calibration.

Ultra-strong heavy-drawn eutectic high entropy alloy wire

Metallic wires with high strength-ductility at both room and cryogenic temperatures are always pursued for engineering applications. However, traditional metallic wires are tortured inevitably by strength-ductility trade-off dilemma. In this work, a gradient heterogeneous lamella structure, characterized with hard gradient-distributed B2 lamellae embedded in soft FCC lamellae matrix, is introduced into AlCoCrFeNi2.1 eutectic high entropy alloy (EHEA) wire by well-designed multiple-stage heavy-drawn and heat treatment processes, which achieves an outstanding strength-ductility synergy. This EHEA wire exhibits not only high tensile strength of 1.85 GPa and sufficient uniform elongation of ∼12% at room temperature, but also ultra-high tensile strength of 2.52 GPa and even slightly elevated uniform elongation of ∼14% at cryogenic temperature. In-depth microstructure characterization indicates that the gradient heterogeneous lamella structure facilitates a radial gradient distribution of geometrically necessary dislocation (GND) during tension, i.e., the GND density decreases gradually from the surface region to the central region of EHEA wire, which induces pronounced strain gradient strengthening effect and thus greatly benefits the mechanical properties. Intriguingly, at cryogenic temperature, dense cross-slip which gives rise to intensively dynamic microstructure refinement is firstly observed in the B2 phase of EHEA wire. The activation of cross-slip provides sufficient ductility while inducing evidently dynamic Hall-Petch effect, becoming the most effective deformation mechanism contributing to the unprecedented cryogenic tension properties. This work sheds light on designing ultra-strong EHEA wire and other advanced metallic wires.

Deformation mechanism of commercially pure titanium under biaxial loading at ambient and elevated temperatures

Commercially pure (CP) titanium is thermally processed and subjected to biaxial stress. However, the evolution of the microstructural deformation mechanisms under such circumstances is not adequately understood. In this study, the mechanical responses and microstructural deformation mechanisms of TA2 CP titanium sheets under equi-biaxial loading at room temperature (RT), 300 °C, and 400 °C were studied. The activated slip and twinning systems were investigated by transmission electron microscopy (TEM) after polished cruciform specimens were biaxially tensile-tested at RT and elevated temperatures. The results show that {112¯2} contraction twinning and {101¯2} extension twinning are the main deformation mechanisms of RT biaxial deformation, while dislocation glide is predominant in biaxial deformation at 300 °C and 400 °C. This difference yields varied work-hardening behaviors at RT and elevated temperatures. In biaxial deformation at 400 °C, the main slip trace type is multiple slip. The interaction of different slip systems in multiple slip created shear deformation concentration areas and further induced cross-slip. However, in biaxial deformation at 300 °C, the amounts of simplex and multiple slip were significantly reduced compared to those at 400 °C because the lower temperature increased the critical resolved shear stress and insufficient activated slip systems were available for grain deformation. Therefore, several stress-concentration areas were generated with the activation of cross-slip.

On the investigation of size effect in bcc α-iron under high strain rate and high temperature: Multiscale dislocations dynamics simulations

Size effect for BCC α-iron is investigated for micro-polycrystalline grains. MDDP simulations were performed to mimic impenetrable grain boundaries at sizes ranging between 0.5 μm and 2 μm at an applied rate of 105 s−1 at 300 K, 600 K and 900 K temperatures. For the three deformation temperatures, the Hall-Petch effect and the Orowan effect are reproduced. A comprehensive study of the microstructure evolution shows that screw dislocations control the plastic deformation of the polycrystalline materials via the activation of cross-slip mechanisms. Hardening is seen at low sizes for all temperatures at low strain range due to the dislocations pile up inside the grains prior to cross-slip activation. Once cross-slip is thermally activated, self-multiplication of dislocations is detected resulting in strain softening indicating that Orowan fit represented better the size effect in micro-polycrystalline BCC α-iron.

Microplasticity in inhomogeneous alloys

We report on a preliminary modelling effort to understand the influence of compositional inhomogeneity on alloy microplasticity from a dislocation dynamics perspective. We tackle this problem by multiscale simulations in three steps: (1) analysis of the 3D composition morphology in alloys with tendency to undergo spinodal instability both thermally and under irradiation, with bcc FeCrAl alloys as a model system, (2) atomistic simulation of the dislocation mobility as a function of the local alloy composition, and (3) using dislocation dynamics simulations to understand the impact of composition inhomogeneity on microplasticity. The dislocation dynamics model takes into consideration the coherency stress associated with composition inhomogeneity when computing the forces driving the dislocation motion and on cross slip. Our preliminary investigation shows that the stress-strain response of the alloy and the dislocation density evolution depend on the wavelength of the composition fluctuations. Our investigation also shows that the alloy inhomogeneity may alter the cross-slip activity, which, in turn, influences the dislocation density evolution. The dependence of the dislocation mobility and coherency stress on local composition and its variation, as well as the altered cross slip rates, cause the dislocation microstructure to differ relative to that in the homogeneous alloy of the same average composition.

Effect of solid-solution strengthening on deformation mechanisms and strain hardening in medium-entropy V1-Cr CoNi alloys

• The solid-solution strength linearly increases with v in V 1- x Cr x CoNi alloys. • Addition of v highly increases SFE and induces planar slip behavior. • The V -abundant VCrCoNi alloys exhibit higher strain-hardening than TWIP CrCoNi alloy. • High friction stress is predominant than SFE in determining deformation mechanism. • High friction stress lowers cross-slip activation and dislocation annhiliation rate. High- and medium-entropy alloys (HEAs and MEAs) possess high solid-solution strength. Numerous investigations have been conducted on its impact on yield strength, however, there are limited reports regarding the relation between solid-solution strengthening and strain-hardening rate. In addition, no attempt has been made to account for the dislocation-mediated plasticity; most works focused on twinning- or transformation-induced plasticity (TWIP or TRIP). In this work we reveal the role of solid-solution strengthening on the strain-hardening rate via systematically investigating evolutions of deformation structures by controlling the Cr/V ratio in prototypical V 1- x Cr x CoNi alloys. Comparing the TWIP of CrCoNi with the dislocation slip of V 0.4 Cr 0.6 CoNi, the hardening rate of CrCoNi was superior to slip-band refinements of V 0.4 Cr 0.6 CoNi due to the dynamic Hall-Petch effect. However, as V content increased further to V 0.7 Cr 0.3 CoNi and VCoNi, their rate of slip-band refinement in V 0.7 Cr 0.3 CoNi and VCoNi with high solid-solution strength surpassed that of CrCoNi. Although it is generally accepted in conventional alloys that deformation twinning results in a higher strain-hardening rate than dislocation-mediated plasticity, we observed that the latter can be predominant in the former under an activated huge solid-solution strengthening effect. The high solid-solution strength lowered the cross-slip activation and consequently retarded the dislocation rearrangement rate, i.e., the dynamic recovery. This delay in the hardening rate decrease, therefore, increased the strain-hardening rate, results in an overall higher strain-hardening rate of V -rich alloys.

The influence of temperature on the strain-hardening behavior of Fe-22/25/28Mn-3Al-3Si TRIP/TWIP steels

The influence of temperature and stacking fault energy (SFE) on the strain-hardening behavior and critical resolved shear stress for twinning was investigated for three Fe–22/25/28Mn–3Al–3Si wt.% transformation- and twinning-induced plasticity (TRIP/TWIP) steels. The SFEs were calculated by two different methods, density functional theory and statistical thermodynamic modeling. The dislocation structure, observed at low levels of plastic deformation, transitions from “planar” to “wavy” dislocation glide with an increase in temperature, Mn content, and/or SFE. The change in dislocation glide mechanisms from planar to wavy reduces the strain hardening rate, in part due to fewer planar obstacles and greater cross slip activity. In addition, the alloys exhibit a large decrease in strength and ductility with increasing temperature from 25 to 200 °C, attributed to a substantial reduction in the thermally activated component of the flow stress, predominate suppression of TRIP and TWIP, and a significant increase in the critical resolved shear stress for mechanical twinning. Interestingly, the increase in SFE with temperature had a rather minor influence on the critical resolved shear stress for mechanical twinning, and other temperature dependent factors which likely play a more dominant role are discussed.

Modeling the effect of short-range order on cross-slip in an FCC solid solution

Short-range ordering (SRO) in single-phase face-centered cubic solid solution alloys has been linked to changes in mechanical behavior that are correlated with pronounced changes in deformation microstructure. More specifically, it has been linked with the rise of localized planar slip, which is associated with a glide softening effect due to the destruction of SRO in a slip plane by lead dislocations in an array. While the glide softening effect has been well studied, what remains less clear is the effect of SRO on cross-slip. While it is apparently suppressed in the planar slip mode, the energetic factors governing this phenomenon have not been investigated in detail. In this study, cross-slip in a model Ni-10%Al alloy is studied through the use of atomistic simulations, comparing configurations with random configurational disorder and SRO. The resulting cross-slip activation barriers are found to depend not only on the overall state of SRO in the alloy, but also on the presence or absence of a diffuse anti-phase boundary in the slip plane. The results from this study demonstrate an increase in the cross-slip energy barrier due to an increase in energy per unit length of the final state for dislocations in a planar slip array, and the possibility of correlated cross-slip, and suggest also a reduction in dynamic recovery with the onset of SRO.

Advanced method for structure-strength-ductility assessment of dispersion-strengthened FCC metals using activation work, mean slip distance and constitutive relation analyses: Decoding the Haasen plot

The role of cross-slip activation on controlling dislocation mechanisms and deformation debris creation in a dispersion-strengthened matrix (DSM) face-centred cubic metal, GlidCop®, has been elucidated using experimental measurement of the strain rate sensitivity, S, the mean slip distance, λ, and constitutive relation analyses (CRA) from 78 to 473 K. If the stress for cross-slip activation is larger than that of DSM yield stress, geometrically necessary prismatic loops (GNPL) are generated, but the rate controlling kinetics is that of vacancy-drag for cube-textured copper wire-specimens. With increasing temperature, percolation continues to occur by Orowan looping. However, upon yielding, GNPL formation is replaced by various types of dipole loop creation due to dislocation intersections from multiple slip. Loops that convert to stacking fault tetrahedra are measurable, but opposite sign dipoles are dynamically annihilated by pipe diffusion reducing debris retention. The rate controlling mechanisms are identified in the temperature range in which S is constant and the activation energy to overcome the obstacle becomes identical to the measurable activation work. This study shows that cross-slip activation stress determined by CRA, when superposed on the yield stress versus temperature plot of DSM alloys, can identify the mechanism-change temperatures. Subsequent S versus temperature profiles, determined from a new method of Haasen plot analysis of up- and down-strain-rate change tests, can delineate the prime rate-controlling mechanisms, characterize the stored debris and determine whether non-shearing or shearing of particles had occurred. Hence, an advanced method to characterize plastic behavior of DSM alloys has been developed.

The effect of local chemical ordering on dislocation activity in multi-principle element alloys: A three-dimensional discrete dislocation dynamics study

The exceptional combination of strength and ductility in multi-component alloys is often attributed to the interaction of dislocations with the various solute atoms in the alloy. To study these effects on the mechanical properties of such alloys there is a need to develop a modeling framework capable of quantifying the effect of these solutes on the evolution of dislocation networks. Large scale three-dimensional (3D) Discrete dislocation dynamics (DDD) simulations can provide access to such studies but to date no relevant approaches are available that aim for a complete representation of real alloys with arbitrary chemical compositions. Here, we introduce a formulation of dislocation interaction with substitutional solute atoms in fcc alloys in 3D DDD simulations that accounts for solute strengthening induced by atomic misfit as well as fluctuations in the cross-slip activation energy. Using this model, we show that local fluctuations in the chemical composition of various CrFeCoNi-based multi-principal element alloys (MPEA) lead to sluggish dislocation motion, frequent cross-slip and alignment of dislocations with solute aggregation features, explaining experimental observations related to mechanical behavior and dislocation activity. It is also demonstrated, that this behavior observed for certain MPEAs cannot be reproduced by assuming a perfect solid solution. The developed method also provides a basis for further investigations of dislocation plasticity in any real arbitrary fcc alloy with substitutional solutes.

Microstructure and mechanical properties of high-Mn-ODS steels

The contribution of dislocation density to strength of Cr–Ni containing austenitic ODS steels is assumed to be limited by dynamic recovery during consolidation of mechanically alloyed powder [Seils et al. Materials Science and Engineering A 786 (2020) 139452]. In order to prevent the reduction in dislocation density by dislocation annihilation subsequent to thermally activated cross slip during recovery, Cr and Ni were replaced by 24 and 34 wt% of Mn in the present study. The comparably lower stacking fault energy leads to larger stacking fault widths and, hence, lower probability of cross slip. The Mn-ODS steels were successfully manufactured by mechanical alloying and subsequent field assisted sintering. X-ray diffraction analysis revealed increased dislocation densities for both Mn-ODS alloys compared to a previously reported Cr–Ni-ODS steel. Formation of additional ε-phase was observed in the lower Mn alloy. Compression and hardness tests confirmed an improved strength and hardness of the Mn-ODS steels. Less thermal stability was found compared to the Cr–Ni-ODS steels due to pronounced ripening of oxide particles as well as grain coarsening in both investigated alloys.

Deformation mechanisms of Mg-Ca-Zn alloys studied by means of micropillar compression tests

The effect of Ca and Zn in solid solution on the critical resolved shear stress (CRSS) of <a> basal slip, tensile twinning and <c+a> pyramidal slip in Mg alloys has been measured through compression tests on single crystal micropillars with different orientations. The solute atoms increased the CRSS for basal slip to ~ 13.5 MPa, while the CRSS for pyramidal slip was lower than 85 MPa, reducing significantly the plastic anisotropy in comparison with pure Mg. Moreover, the CRSSs for twin nucleation and growth were very similar (~ 37 MPa) and the large value of the CRSS for twin growth hindered the growth of twins during thermo-mechanical processing. Finally, evidence of <a> prismatic slip and cross-slip between basal and prismatic dislocations was found. It is concluded that the reduction of plastic anisotropy, the activation of different slip systems and cross-slip and the weak basal texture promoted by the large CRSS for twin growth are responsible for the improved ductility and formability of Mg-Ca-Zn alloys.

Effects of cross-slip activity on low-cycle fatigue behavior and dislocation structure in pure aluminum single crystals with single-slip orientation

Fully reversed tension-compression low-cycle fatigue tests were performed at room temperature (RT) and 77 K on single-slip-oriented pure aluminum single crystals having different Schmid factor (SF) values (0, 0.14 and 0.24) for the cross-slip system under constant plastic shear-strain amplitudes. Cyclic deformation curves showed no stress saturation at RT, regardless of the applied strain amplitude. The cyclic deformation behavior at RT was as follows: initial hardening, softening and secondary hardening in the specimens with non-zero SF, whereas the specimens with SF = 0 exhibited monotonic hardening. However, all the specimens formed and developed the cell structure from the early stage of fatigue. On the other hand, no differences were observed in the cyclic deformation of the three specimens at 77 K. Shear stress amplitudes revealed initial hardening followed by saturation at any shear strain amplitudes applied, and a plateau stress region with a value of 42 MPa appeared in the cyclic stress-strain curve obtained at 77 K. Dislocation structures in the tested specimens were almost identical to those observed in single-slip-oriented pure Cu single crystals fatigued at RT.

High temperature nanoindentation as a tool to investigate plasticity upon phase transformations demonstrated on Cobalt

A new field of application for high temperature nanoindentation as a complimentary method to understand the mechanics of plasticity upon bulk phase transformations in thermodynamic equilibrium is introduced. The feasibility is outlined on polycrystalline Cobalt involving a low-temperature hexagonal closed packed phase, and above 700K, a high-temperature face centered cubic phase, which was conventionally characterized by means of differential scanning calorimetry and high temperature X-ray diffraction. Strain rate sensitivity, activation volume and activation energy of plastic deformation were determined up to 873 K to identify the rate-controlling deformation mechanism. From RT to 473 K plasticity was found to be controlled by lattice friction on the basal plane, where dislocations have to overcome the Peierls barrier and deformation twinning was apparent in the hexagonal phase. The thermal activation of cross slip lead to reduced twinning actions when the phase transition temperature is approached. In the high temperature face centered cubic phase deformation was found to be controlled by cutting of forest dislocations and no deformation twinning was observed.

Correlation between anelastic response and microstructure of 5N-Al thin foils

The anelastic behavior of 5N-Al thin foils with three different thicknesses (10, 50 and 125 µm) was investigated in the temperature range from 300 to 720 K through Mechanical Spectroscopy (MS) measurements performed by using a completely automated vibrating reed analyser. Two relaxation peaks P1 and P2 and a relevant high temperature background were observed in the thinnest samples whereas only the grain boundary peak (PGB) was observed in the thickest ones. Detailed TEM observations and X-ray diffraction (XRD) measurements indicate that defective structures depend on foil thickness and suggest that the origin of P1 and P2 peaks is connected to the vibration dynamics of isolated dislocations not organized in networks. P1 has been attributed to the combination of dislocatio n motion through the stress field of other dislocations and thermally activated cross slip, while P2 is due to the movement of jogs assisted by pipe diffusion. In addition to anelastic effects due to dislocation vibration, permanent grain boundary sliding seems to contribute to the high temperature background observed in the thinnest foils.