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International audience; Ultrasonic fatigue testing at 20 kHz was developed to accelerate fatigue tests and explore the very high cycle fatigue range. However, the use of ultrasonic fatigue systems raises the open question of the impact of frequency on the material fatigue response. In this paper, the impact of the loading frequency on the fatigue response of face-centered cubic polycrystalline copper is investigated. Firstly, experiments with conventional fatigue devices inducing loading frequencies lower than 100 Hz were carried out and compared with previously published results obtained with an ultrasonic fatigue machine at 20 kHz. At a stress amplitude of 100 MPa, the number of cycles required for failure was found to be more than 200 times greater for tests at 20 kHz than for tests at frequencies below 100 Hz. Secondly, for both types of fatigue tests, the conditions in stress amplitude and number of cycles needed for the emergence of the early slip markings were investigated. The early slip marking S–N curve was found to have the same sensitivity as the failure S–N curve to the frequency effect. Thirdly, the different possible reasons responsible for this frequency effect are discussed. It is concluded that the physical mechanisms of slip marking formation is preserved while their kinetics is sensitive to the loading frequency. Finally, two simplified models were considered and for the first time, the frequency effect on the fatigue response of copper is quantitatively correlated with the occurrence of time-dependent dislocations cross slip and vacancies production/diffusion involved in the persistent slip band formation for face-centered cubic structure. The obtained results could be extended to a full class of materials where slip band formation plays a key role in the crack initiation process while suggesting no frequency effect for materials with a lower degree of plasticity development at crack initiation (High Strength Steels for example).

The DISFAT project is a French project financially supported by the French National Agency for Research (ANR). It aims at a deeper understanding of mechanisms leading to crack initiation in metals and alloys under Very High Cycle Fatigue loading (VHCF). The VHCF regime is associated with stress magnitudes lower than the conventional fatigue limit and as a result, numbers of cycles higher than 109. Tests were carried out using an ultrasonic technique at loading frequency of 20 kHz. In the case of pure copper polycrystals, we previously showed that slip band (SB) activity and intrinsic dissipation were closely related. Dissipation and slip band amount increased with the number of cycles. At very small stress amplitudes, no slip band appeared at the specimen surface up to 108 cycles but the material was found to dissipate energy. These results revealed that the material never reached a steady state and so could break at higher number of cycles. In this paper, the morphology and the location of slip bands were characterized. Different types of slip bands depending on the stress amplitudes appeared at the specimen surface. The stress amplitude required to show the first slip bands decreases with the number of cycles. It is twice lower than the stress amplitude required to break the specimen for the same number of cycles. At the smallest stress amplitudes, slip bands were mostly found at twin boundaries. Quasi 3D finite element simulations taking into account the polycrystalline nature of the material emphasized the key role of the elastic anisotropy in slip band initiation. A criterion for slip band appearance was finally proposed. The authors are grateful for financial support from Agence Nationale de la Recherche France ANR-09-BLAN-0025-01 and to company Griset for supplying copper. The authors thank also very much Professor Haël Mughrabi for the scientific discussions.

Controlled laser experiments were used to generate ultra-short shock pulses of approximately 5 ns duration in monocrystalline copper specimens with [001] orientation. Transmission electron microscopy revealed features consistent with previous observations of shock-compressed copper, albeit at pulse durations in the µs regime. At pressures of 12 and 20 GPa, the structure consists primarily of dislocation cells; at 40 GPa, twinning and stacking-fault bundles are the principal defect structures; and at a pressure of 55–60 GPa, the structure shows micro-twinning and the effects of thermal recovery (elongated sub-grains). The results suggest that the defect structure is generated at the shock front; the substructures observed are similar to the ones at much larger durations. The dislocation generation is discussed, providing a constitutive description of plastic deformation. It is proposed that thermally activated loop nucleation at the front is the mechanism for dislocation generation. A calculational method for dislocation densities is proposed, based on nucleation of loops at the shock front and their extension due to the residual shear stresses behind the front. Calculated dislocation densities compare favorably with experimentally observed results. It is proposed that simultaneous diffraction by Laue and Bragg of different lattice planes at the shock front can give the strain state and the associated stress level at the front. This enables the calculation of the plastic flow resistance at the imposed strain rate. An estimated strength of 435 MPa is obtained, for a strain rate of 1.3 × 10 7 s 1 . The threshold stress for deformation twinning in shock compression is calculated from the constitutive equations for slip, twinning, and the Swegle–Grady relationship. The calculated threshold pressure for the [001] orientation is 16.3 GPa.  2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

The evolution of microstructure and the mechanical response of copper subjected to severe plastic deformation using equal channel angular pressing (ECAP) was investigated. Samples were subjected to ECAP under three different processing routes: BC, A and C. The microstructural refinement was dependent on processing with route BC being the most effective. The mechanical response is modeled by an equation containing two dislocation evolution terms: one for the cells/subgrain interiors and one for the cells/subgrain walls. The deformation structure evolves from elongated dislocation cells to subgrains to equiaxed grains with diameters of � 200–500 nm. The misorientation between adjacent regions, measured by electron backscatter diffraction, gradually increases. The mechanical response is well represented by a Voce equation with a saturation stress of 450 MPa. Interestingly, the microstructures produced through adiabatic shear localization during high strain rate deformation and ECAP are very similar, leading to the same grain size. It is shown that both processes have very close Zener–Hollomon parameters (ln Z � 25). Calculations show that grain boundaries with size of 200 nm can rotate by � 30� during ECAP, thereby generating and retaining a steady-state equiaxed structure. This is confirmed by a grain-boundary mobility calculation which shows that their velocity is 40 nm/s for a 200 nm grain size at 350 K, which is typical of an ECAP process. This can lead to the grain-boundary movement necessary to retain an equiaxed structure.

The mechanisms of microstructural evolution in copper subjected to equal channel angular pressing (ECAP) have been investigated after successive passes. The first few passes are the most efficient in grain refinement while the microstructure becomes gradually more equiaxed as the number of passes increases. The texture evolution is discussed based on electron back scattered diffraction (EBSD) results. These experimental results are interpreted in terms of a preliminary model with four successive stages: homogeneous dislocation distribution; elongated sub-cell formation; elongated subgrain formation; break-up of subgrains into equiaxed units; sharpening of grain boundaries and final equiaxed ultrafine structure.

We study the transformation of lattice defects in γ-TiAl upon intersection by deformation twins. A faulted dipole is chopped forming a dislocation loop faulted on the cube plane of the twin; faulted dipoles and twin loops may shrink at different rates. Dislocations with 1/2

Pure copper monocrystals with [001] and [\(\bar 1\)34] orientations were subjected to ultrashort shock pulses ranging in initial duration from 2.5 to 10 ns, induced by a laser at energies ranging from 10 to 70 MJ/m2. The deformation structure was significantly dependent on the crystallographic orientation and depth from the laser-impacted surface, as characterized by transmission electron microscopy (TEM). The threshold pressure for twinning in the [001] direction was observed to be in the range of 20 to 40 GPa compared with 40 to 60 GPa for the [\(\bar 1\)34] orientation. Dislocation densities were also different for the two orientations, under similar shock conditions. The [\(\bar 1\)34] dislocation density was systematically lower. This is attributed to the activation of fewer slip systems resulting in a lower rate of hardening. The different results found for [001] and [\(\bar 1\)34] copper single crystals are described and effects of pressure decay in [\(\bar 1\)34] specimens are discussed. Differences in the mechanical response between the two orientations are responsible for differences in the shear stress in the specimens at the imposed pressures and associated strains. The [\(\bar 1\)34] orientation is initially subjected to deformation by single slip, (111)[101], which has a Schmid factor of 0.4711 and a well-defined easy glide region followed by a cross-slip regime with secondary slip. The [001] orientation has eight slip systems {111}〈110〉 with identical Schmid factors of 0.4082, which lead to immediate work hardening. At an imposed and prescribed pressure (that establishes the strain), the [\(\bar 1\)34] orientation exhibits a lower shear stress. The orientation dependence of the twinning stress is much lower, as expressed by Schmidt factors. This higher stress for [001] predisposes the onset of twinning in this orientation. The results are interpreted in terms of a criterion in which slip and twinning are considered as competing mechanisms. A constitutive description using a modified mechanical threshold stress (MTS) model is applied to the two orientations, incorporating both slip and twinning. The threshold pressure for twinning is calculated, considering the effect of shock heating. The constitutive description provides a rationale for the experimental results: the calculated thresholds are 17 GPa for [001] and 25 GPa for [\(\bar 1\)34].

Copper with two orientations ([001] and [134]) was subjected to high intensity laser (energy levels of 40-300 J; energy densities of 15-70 MJ/m 2 and durations below 10 ns). The defects created are characterized by transmission electron microscopy. An orientation-dependent threshold stress for twinning is observed. The results are rationalized in terms of a criterion in which slip and twinning are considered as competing mechanisms. A constitutive description is applied to the two orientations, incorporating both slip and twinning. The predictions are in agreement with experiments. The threshold stress for twinning in the [001] orientation is 20-40 GPa, whereas the one for the [134] orientation is 40-60 GPa. The threshold stress is calculated, considering the effect of shock heating. The constitutive description provides a rationale for the experimental results; the calculated thresholds are 18 GPa for [001] and 25 GPa for [134]. A mechanism for void generation and growth based on the emission of geometrically necessary dislocations is proposed and analytically formulated.

Single crystal samples of n-(Ti-54.7 at.% Al) deformed to a permanent strain of 2% at room temperature under multiple-slip conditions contain faulted dipoles (FDs) whose density exhibits some dependence on load orientation. Although FDs are hard to observe after compression along [210], they are profuse and congregated in places in the [1 1 8.6] load orientation. They exhibit most of the topological characteristics of FDs formed under single slip as reported by Gregori and Veyssiere such as elongation in the screw direction of the primary d011] slip direction and a noticeable shape asymmetry. It is shown further that, in the [1 1 8.6] samples, bundles of FDs originate at jogs that result from intersection with forest dislocations of appropriate Burgers vectors. A mechanism for FD nucleation is proposed on the basis of asymmetrical dissociation of the parent d011] dislocation and specific impingements between the various partials on two adjacent octahedral planes. Implications of the FD nucleation at jogs ...

It is shown that certain varieties of dipolar debris usually interpreted in terms of a jog-trailing process result from the impact of a dislocation on individual loops or loop strings. A mechanism for spontaneous patterning in single slip is proposed that rests on the capture of dislocations of both signs by a string where they annihilate by pairs adding interlaced loop strings on to the initial embryo and building up a three-dimensional wall gradually. The process should apply to any crystal where the free-flight distance in the cross-slip plane is moderate. A manoeuvre for the conservative elimination of a loop string by a single dislocation is introduced.

Two mechanisms for the formation of strings of dislocation loops reported in part I of this work are explored. In one, strings result from the coalescence of two jogged segments originating from the same dislocation. In the second, strings result from local cross-slip annihilations of dipoles formed by two unjogged dislocations. The latter is the most consistent with observations.

Dislocation micromechanisms operating in an Al-rich γ-TiAl single crystal deformed by 1/2(110]{111} slip are investigated with particular attention paid to the generation and to the organization of prismatic loops and to the reactions of these with mobile dislocations. Loops are frequently arranged as staircase strings with one loop extremity aligned in the screw direction with the extremity of a nearby loop. Strings and dislocations tend to aggregate into loose walls. Also typical of deformation at room temperature are elongated loops piled up into multipoles whose extremities are often aligned with the screw direction. The causes of dislocation point-and hairpin-like pinning are discussed in the context of pre-existing models.

In γ-TiAl deformed at room temperature in single slip, prismatic loops ar often organized in a staircase-like configuration, called strings whose generation by cross-slip is facilitated by the dislocation tendency to form screw locks as described recently by Gregori and Veyssiere. The present letter is aimed at showing that strings may be encountered in virtually any crystal provided that the two impinging dislocations exhibit significantly different velocities. The crossslip annihilation mechanism of crossed dislocations considered by Tetelman is revisited and shown to evolve into a configuration significantly distinct from that originally predicted.

A transmission electron microscope investigation of the conditions of locking of 〈0 1 1] dislocations and related deformation debris is conducted in Al-rich γ-TiAl (L1 0 ordered structure) deformed in a temperature range relevant to the yield stress anomaly (YSA). Observations are paralleled with results previously obtained in L1 2 compounds (e.g. Ni 3 Al-based alloys) where a YSA occurs within a comparable range of deformation temperatures, involving an analogous type of dislocation with comparable dissociation modes and similar locking abilities. It is shown that in spite of differences in dislocation fine structure, the two systems to belong to the same class of YSA.

The influence of a pre-anneal on the yield stress peak of Al-rich γ-TiAl is demonstrated by arranging the available experimental data according to sample thermal history. The analysis is complemented by dedicated deformation tests and by microstructural observations. It is shown that mechanical properties may be markedly obscured by precipitation of interstitial atoms and to a lesser extent, by the Ti3Al5 short-range ordered phase.

In Al-rich γ-TiAl deformed at room temperature, faulted dipoles (FDs) are usually trailed by dislocations with

The plastic behaviour of single-phaseγ-TiAl poses a certain number of fundamental problems as to the origin of the flow stress anomaly and to how this is related to dislocation properties. Understanding these questions is of significant interest in the investigations of flow stress anomalies in intermetallics and in other materials. Also, it may reveal useful in the study of theγ-based lamellar alloys. The present contribution accounts for an investigation of mechanical properties and microstructural organization conducted in Al-richγ-TiAl single crystals oriented to activate single slip. Three separate topics are addressed. (I) 1/2 〈110] ordinary dislocations after deformation between room temperature and 800°C. The magnitude of the cusping appears to depend on the chronology of dislocation immobilization. The distribution of pinning points is analysed and the temperature dependence of their density confronted to that of the flow stress. (II) The core structure of 〈011] dislocations. After deformation at room temperature, 〈011] dislocations are dissociated into two partials separated by a stacking fault. The role of temperature and possible transitions of the dissociation are addressed. (III) The observation and analysis of background striations which cover the thin foils entirely. The striations are shown to be a deformation by-product resulting from the passage of perfect dislocations of the L10 structure, and from the interaction of these with a short-range ordered (SRO) Ti3Al5 phase. Striations can serve to discuss the absence of slip localization and the properties of cross-slip.

Transmission electron microscope images of aluminium-rich L10 TiAl samples deformed up to 400°C exhibit faint fringes spread uninterruptedly all over the thin foils. At variance from the fringe systems usually associated with stacking faults and/or antiphase boundaries, these faint striations show no clear spatial limitations by intersections with free surfaces or else by dislocations. The striation contrast is related to slip on {111} planes in either one of the 〈110] and 〈011] directions. It originates from modest atomic relaxations. The generation of the defects responsible for the striations is discussed in terms of non-localized slip in the presence of a short-range ordered phase, Ti3Al5, in Al-rich TiAl.

International audience; This paper present the ongoing DISFAT project financially supported by the French National Agency ANR and its white program. It aims at a deeper understanding of mechanisms leading to crack initiation in metals and alloys in Very High Cycle Fatigue (VHCF). In contrast to conventional fatigue tests, detecting irreversible microstructural changes using cyclic stress-strain curves analysis is no more possible, at least with conventional measurement systems, since the macroscopic behavior is quasi-elastic. To cope with this problem, we propose to use the energy signature of the deformation mechanisms. The main challenge of this project results from the fact that the energy and mechanical manifestations as well as the microstructural "evidences"of the mechanisms of interest involve very low signal. In this paper, we explain our strategy and present some results on fcc and bcc single-phase polycrystals.

Reverse Taylor impact tests have been carried out on ultrafine grained copper processed by Equal Channel Angular Pressing (ECAP). Tests were conducted on an as‐received OFHC Cu rod and specimens that had undergone sequential ECAP passes (2 and 8). The average grain size ranged from 30 μm for the initial sample to less than 0.5 μm for the 8‐pass samples. The dynamic deformation states of the samples, captured by high speed digital photography were compared with computer simulations run in AUTODYN‐2D using the Johnson‐Cook constitutive equation with constants obtained from stress‐strain data and by fitting to an experimentally measured free surface velocity trace. The constitutive response of copper of varying grain sizes was obtained through quasistatic and dynamic mechanical tests and incorporation into constitutive models.

Single crystal copper and copper 2‐wt% aluminum alloy with [134] and [001] orientations are compressed by means of a high energy short pulse laser. Pressures ranging from 20 GPa to 60 GPa are achieved. The shocked samples are recovered and the residual defect substructure is analyzed by transmission electron microscopy. Results show systematic differences depending on orientation and stacking fault energy. Samples with orientations [001] are symmetrical with simultaneous activation of eight slip systems. This leads to a higher work hardening rate. The [134] orientation is asymmetrical with one dominating slip system, and thus a reduced work hardening rate due to a prolonged easy glide region for dislocations. These differences in work hardening response affect the stresses required to achieve the twinning threshold pressure. The effects of stacking fault energy on the defect substructure and threshold twinning are also characterized. Experimental results are rationalized in terms of a constitutive description of the slip‐twinning transition using a modified MTS equation. Differences in the mechanical response of the orientations and the chemical compositions are responsible for differences in the shear stress in the specimens at the imposed pressures and associated strains.

Laser‐based experiments are being developed to study the response of solids under high pressure loading. Diagnostic techniques that have been applied include dynamic x‐ray diffraction, VISAR wave profile measurements, and post‐shock recovery and analysis. These techniques are presented with some results from shocked Si, Al, and Cu experiments.

Investigations conducted in our group on plastic properties of a variety of strained TiAl based alloys and resulting microstructures are reviewed. These include oriented single crystals of Al-rich γ-TiAl and semi-oriented polycrystals with γ + α2 lamellar structure. The wealth of micro-mechanisms encountered in this family of alloys is, to large extent, due to the decomposition of

Copper monocrystals were subjected to shock compression at pressures of 10–60 GPa by a short (3 ns initial) duration laser pulse. Transmission electron microscopy revealed features consistent with previous observations of shock-compressed copper, albeit at pulse durations in the µs regime. The results suggest that the defect structure is generated at the shock front. A mechanism for dislocation generation is presented, providing a realistic prediction of dislocation density as a function of pressure. The threshold stress for deformation twinning in shock compression is calculated from the constitutive equations for slip, twinning, and the Swegle-Grady relationship.

Prismatic loops generated by cross-slip are organised in staircase-like strings such that the beginning of a loop corresponds in the screw orientation with the end of its neighbour. Strings constitute nucleation sites for dislocation tangles thus offering an explanation for spontaneous patterning in single glide. A loop string can be partially and even totally eliminated by a single impacting dislocation. In dense walls, loop refinement can also take place conservatively by mutual annihilation of loops of opposite signs.

The temperature, TP, and the stress, σP, at which the yield stress of γ-TiAl alloys peaks are influenced by factors such as alloy composition and load orientation. Available data indicates that in the absence of adequate heat treatments, TP and σP are shifted towards values significantly higher than those of samples pre-annealed in order to precipitate interstitial atoms. Conditions under which precipitation influences the anomalous regime are revealed by dedicated tests. In addition to pointing out the clear effect of interstitials, these tests suggest that further ordering may contribute to the strength of Al-rich γ-TiAl.

Properties of ordinary dislocations and related debris are investigated in single crystals of γ-TiAl deformed in single slip at 20°C and 400°C. Typical of this temperature range are prismatic loops isolated or belonging to arrays, together with multipoles. The interaction of these with mobile ordinary dislocations generates various configurations including trailing-like hairpins. Certain features are consistent with an extrinsic origin for point pinning.

The flow stress of Al-rich γ-TiAl peaks at a temperature located between about 600°C and 1000°C. We present mechanical data on samples oriented so as to deform on a

A. Mishra , B.K. Kad , F. Gregori , M.A. Meyers a,* a Department of Mechanical and Aerospace Engineering, Materials Science and Engineering Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA b Department of Structural Engineering, University of California, San Diego, La Jolla, CA, USA c Laboratoire des Proprietes Mecaniques et Thermodynamiques des Materiaux (CNRS), Universite de Paris 13, France

The paper focuses on the formation and on the role of prismatic loops during deformation. The analysis is restricted to non-diffusive processes in fcc-related crystals. Double cross-slip and cross-slip dipolar annihilation yield strings of loops such that one loop extremity is aligned in the screw direction with the extremity of its nearest neighbour. Reactions between prismatic loops and mobile dislocations are at the origin of a number of microstructural reactions including recovery, dislocation entanglements and patterning in single slip, dislocation multiplication and there is indication that they may nucleate twins.

Nowadays there is a growing demand for the development of fast and robust fatigue life prediction methods in the very high cycle fatigue domain. In this way, ultrasonic fatigue technique which appeared in 1950 is very interesting for manufacturers. Because the typical frequency of these tests is 20 kHz, this technique is efficient to perform tests up to a very high number of cycles in a reasonable time (109 cycles are reached in 14 h). However, the frequency domain of these fatigue tests facilities raises the issue of the effect of frequency and more generally the validity of the obtained results for estimating fatigue life of structures loaded at frequencies three or four order of magnitude below ultrasonic frequencies. The objective of this work is to evaluate the effect of the loading frequency on the precursors of fatigue damage, namely the microplasticity at the grain scale. This thesis work deals with the case of polycrystalline pure copper loaded in fully reversed tensioncompression. To show the effect of frequency, the Wöhler or S-N curves were constructed at different frequencies. Then, the study focused on the mechanisms of microplasticity preceding crack initiation and several criteria were investigated: the morphologies of the slip bands and their locations in the microstructure, the thresholds of appearance of the slip bands, the evolution of the slip bands amount with the number of cycles, the distribution of the microplasticity in the grains, the dissipated energy during a fatigue cycle. Cross slip and vacancies production and diffusion are two mechanisms which play a part in the formation of slip bands and extrusions in surface. Their respective roles on the effects of frequency observed are discussed, Il existe actuellement une demande croissante pour le développement de méthodes expérimentales rapides et fiables permettant d'estimer la résistance à la fatigue dans le domaine de la fatigue à grands nombres de cycles. En ce sens, la fatigue ultrasonique apparue dans les années cinquante est très intéressante pour les industriels. En effet, la fréquence typique de ces essais est de 20 kHz ce qui permet d'atteindre le domaine des très grandes durées de vie en des temps d'essais raisonnables (109 cycles sont atteints en 14 h). Cependant ces essais posent le problème de l'effet de la fréquence et plus généralement de la validité des résultats obtenus pour estimer la durée de vie de structures chargées à des fréquences très inférieures à 20 kHz. L'objectif de ce travail est d'évaluer l'effet de la fréquence du chargement sur les mécanismes précurseurs de l'initiation de fissures et plus précisément sur les mécanismes de microplasticité à l'échelle du grain. Ce travail de thèse s’intéresse au cas du cuivre pur polycristallin sollicité en traction-compression alternée et symétrique. Pour mettre en évidence un effet de la fréquence, les courbes de Wöhler ont été construites à différentes fréquences. L’étude s’est ensuite focalisée sur les mécanismes de microplasticité précurseurs de l’initiation de fissures et plusieurs critères ont été examinés : les morphologies des bandes de glissement et leurs positions en lien avec la microstructure, les seuils d’apparition des bandes de glissement, le développement de ces bandes avec le nombre de cycles, la répartition de la microplasticité dans les grains, les valeurs d’énergie dissipée au cours d’un cycle. Le glissement dévié et la production-diffusion de lacunes sont deux mécanismes qui interviennent dans la formation des bandes de glissement et des extrusions en surface. Leurs rôles respectifs sur les effets de fréquence observés sont discutés.