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Dislocation storage in single slip oriented Cu micro-tensile samples: New insights by X-ray microdiffraction
Abstract
Synchrotron X-ray microdiffraction was used to characterize the deformation structure of single crystalline Cu micro-tensile specimens which were oriented for single slip. The 3-mm thick samples were strained in situ in a scanning electron microscope (SEM). Electron microscopy observations revealed glide steps at the surface indicating single slip. While the slip steps
at the surface must have formed by the predominant activation of the primary glide system, analysis of Laue peak streaking directions revealed that, even at low strains, dislocations had been activated and stored on an unpredicted slip system. Furthermore, the µLaue scans showed that multiple slip takes over at a later state of deformation.
... Section 5.3 lists a series of examples of application, briefly describing two of them. Section 5.4 focuses on one particular application (Kirchlechner et al., 2011a(Kirchlechner et al., , 2011b, the in situ study of single-crystalline micropillars during mechanical tests. The chapter concludes with a consideration of optimal geometry for cutting micropillars and for choosing their orientation with respect to the incident beam, the setup's future possibilities and a number of open-ended questions. ...
... • How does the size of a crystal influence its plastic properties (Kirchlechner et al., 2011a(Kirchlechner et al., , 2011b(Kirchlechner et al., , 2011c(Kirchlechner et al., , 2012? Three examples will be described: two briefly in Section 5.3.2, and a third in more detail in Section 5.4. ...
... This study followed that of Uchic et al. (2004), whose authors showed a strong size effect in compressive tests in micro-objects: small singlecrystalline samples show a significantly larger flow stress than their macroscopic counterpart. In order to better understand the plasticity mechanisms that operate during mechanical tests on small objects, (Kirchlechner et al., 2011a(Kirchlechner et al., , 2011b(Kirchlechner et al., , 2011c(Kirchlechner et al., , 2012 used Laue microdiffraction to monitor the fields of crystal orientation and orientation gradient in single-crystalline copper micropillars, during compressive and tensile tests, following the approach of Maaß et al. (2006Maaß et al. ( , 2007. Face-centered cubic (FCC) crystal plasticity is mediated by dislocation glide, at least for the temperature of interest here (room temperature). ...
... Section 5.3 lists a series of examples of application, briefly describing two of them. Section 5.4 focuses on one particular application (Kirchlechner et al., 2011a(Kirchlechner et al., , 2011b, the in situ study of single-crystalline micropillars during mechanical tests. The chapter concludes with a consideration of optimal geometry for cutting micropillars and for choosing their orientation with respect to the incident beam, the setup's future possibilities and a number of open-ended questions. ...
... O. Robach et al. • How does the size of a crystal influence its plastic properties (Kirchlechner et al., 2011a(Kirchlechner et al., , 2011b(Kirchlechner et al., , 2011c(Kirchlechner et al., , 2012? Three examples will be described: two briefly in Section 5.3.2, and a third in more detail in Section 5.4. ...
... This study followed that of Uchic et al. (2004), whose authors showed a strong size effect in compressive tests in micro-objects: small singlecrystalline samples show a significantly larger flow stress than their macroscopic counterpart. In order to better understand the plasticity mechanisms that operate during mechanical tests on small objects, (Kirchlechner et al., 2011a(Kirchlechner et al., , 2011b(Kirchlechner et al., , 2011c(Kirchlechner et al., , 2012 used Laue microdiffraction to monitor the fields of crystal orientation and orientation gradient in single-crystalline copper micropillars, during compressive and tensile tests, following the approach of Maaß et al. (2006Maaß et al. ( , 2007. Face-centered cubic (FCC) crystal plasticity is mediated by dislocation glide, at least for the temperature of interest here (room temperature). ...
This chapter describes the Laue microdiffraction station of the French CEACNRS CRG-IF BM32 beamline at the European Synchrotron Radiation Facility (ESRF), with its available special methods and planned upgrades. Applications are discussed, with an overview of scientific questions addressed by users. Three examples of user studies are presented. Two of them, concerning shape memory alloys and solid oxide fuel cells, are only briefly described. The third example, concerning compressive and tensile tests on single-crystalline micropillars, is described more extensively. Here, the data from two papers are examined in an attempt to i) separate intrinsic effects (e.g. size effects) from extrinsic effects (due to non-ideal boundary conditions at the ends of the pillars), and ii) include in the description the crystallographic orientation of the pillar-free surfaces, in order to find the best conditions for detecting edge dislocations of the most activated glide system possibly piled up against a surface barrier.
... (Katrin Schulz), ispanovity.peter@ttk.elte.hu (Péter Dusán Ispánovity) microcompression [13,2,14], microtension [15,16,17], microshear [18,19], microtorsion [20], microbending [21,22] and microfatigue [23,24]. ...
... In the so-called dislocation starved regime, when the sample dimension is below approx. 1 µm, the number of dislocation lines and disloca-30 tion sources is so small, that dislocation interactions (such as annihilation, junction formation or cross-slip events) hardly take place and the plastic response and size effects are dominated by individual dislocation mechanisms (such as source activation) [2,7]. In the so-called storage regime, on the other hand, dislocation interactions do happen in an increasingly large amount during deformation, leading to the build-up of a complex dislocation network and the increase of the dislocation density [25,8,17,26]. The observed size effects and strain hardening can be of- 40 ten related to the development of strain gradients and the corresponding geometrically necessary dislocation (GND) content. ...
In metals geometrically necessary dislocations (GNDs) are generated primarily to accommodate strain gradients and they play a key role in the Bauschinger effect, strain hardening, micron-scale size effects and fatigue. During bending large strain gradients naturally emerge which makes this deformation mode exceptionally suitable to study the evolution of GNDs. Here we present bi-directional bending experiment of a Cu single crystalline microcantilever with in situ characterisation of the dislocation microstructure in terms of high-resolution electron backscatter diffraction (HR-EBSD). The experiments are complemented with dislocation density modelling to provide physical understanding of the collective dislocation phenomena. We find that dislocation pile-ups form around the neutral zone during initial bending, however, these do not dissolve upon reversed loading, rather they contribute to the development of a much more complex GND dominated microstructure. This irreversible process is analysed in detail in terms of the involved Burgers vectors and slip systems to provide an in-depth explanation of the Bauschinger-effect and strain hardening at this scale. We conclude that the most dominant role in this behaviour is played by short-range dislocation interactions.
... In situ microdiffraction experiments of Maaß et al. also reports about the development of an inhomogeneous stress state and a large GND density in Cu pillars under multiple slip [20]. In a similar experiment performed on tensile specimens oriented for single slip Kirchlechner et al. concluded that although slip occurred on the primary slip system, GNDs were generated and stored in a large number on the inactive slip systems [21]. ...
... The experimental results, see Figure 4, as well as the simulation results, see Figure 12, show, that the allocation of the GND density is dominated by slip systems that are not mainly responsible for the production of plastic slip. This observation has also reported by Kirchlechner et al. who considered tension tests of single crystalline copper specimen orientated for single slip and presented analyses of in situ scanning electron microscopy and post mortem µLaue diffraction [21]. The simulation results in Figure 12 also show that there is an amount of GND density on active slip systems at the beginning of loading, but it is not preserved in the system during further loading and can leave the system via the surface. ...
With decreasing system sizes, the mechanical properties and dominant deformation mechanisms of metals change. For larger scales, bulk behavior is observed that is characterized by a preservation and significant increase of dislocation content during deformation whereas at the submicron scale very localized dislocation activity as well as dislocation starvation is observed. In the transition regime it is not clear how the dislocation content is built up. This dislocation storage regime and its underlying physical mechanisms are still an open field of research. In this paper, the microstructure evolution of single crystalline copper micropillars with a ⟨110⟩ crystal orientation and varying sizes between 1 to 10 μm is analysed under compression loading. Experimental in situ HR-EBSD measurements as well as 3D continuum dislocation dynamics simulations are presented. The experimental results provide insights into the material deformation and evolution of dislocation structures during continuous loading. This is complemented by the simulation of the dislocation density evolution considering dislocation dynamics, interactions, and reactions of the individual slip systems providing direct access to these quantities. Results are presented that show, how the plastic deformation of the material takes place and how the different slip systems are involved. A central finding is, that an increasing amount of GND density is stored in the system during loading that is located dominantly on the slip systems that are not mainly responsible for the production of plastic slip. This might be a characteristic feature of the considered size regime that has direct impact on further dislocation network formation and the corresponding contribution to plastic hardening.
... In situ microdiffraction experiments of Maaß et al. also reports about the development of an inhomogeneous stress state and a large GND density in Cu pillars under multiple slip [20]. In a similar experiment performed on tensile specimens oriented for single slip Kirchlechner et al. concluded that although slip occurred on the primary slip system, GNDs were generated and stored in a large number on the inactive slip systems [21]. ...
... The experimental results, see Figure 4, as well as the simulation results, see Figure 12, show, that the allocation of the GND density is dominated by slip systems that are not mainly responsible for the production of plastic slip. This observation has also reported by Kirchlechner et al. who considered tension tests of single crystalline copper specimen orientated for single slip and presented analyses of in situ scanning electron microscopy and post mortem µLaue diffraction [21]. The simulation results in Figure 12 also show that there is an amount of GND density on active slip systems at the beginning of loading, but it is not preserved in the system during further loading and can leave the system via the surface. ...
With decreasing system sizes, the mechanical properties and dominant deformation mechanisms of metals change. For larger scales, bulk behavior is observed that is characterized by a preservation and significant increase of dislocation content during deformation whereas at the submicron scale very localized dislocation activity as well as dislocation starvation is observed. In the transition regime it is not clear how the dislocation content is built up. This dislocation storage regime and its underlying physical mechanisms are still an open field of research. In this paper, the microstructure evolution of single crystalline copper micropillars with a crystal orientation and varying sizes between 1 to is analysed under compression loading. Experimental in situ HR-EBSD measurements as well as 3d continuum dislocation dynamics simulations are presented. The experimental results provide insights into the material deformation and evolution of dislocation structures during continuous loading. This is complemented by the simulation of the dislocation density evolution considering dislocation dynamics, interactions, and reactions of the individual slip systems providing direct access to these quantities. Results are presented that show, how the plastic deformation of the material takes place and how the different slip systems are involved. A central finding is, that an increasing amount of GND density is stored in the system during loading that is located dominantly on the slip systems that are not mainly responsible for the production of plastic slip. This might be a characteristic feature of the considered size regime that has direct impact on further dislocation network formation and the corresponding contribution to plastic hardening.
... Laue microdiffraction has been used before on small-scale samples: Barabash et al. showed that (i) the continuous streaking of Laue diffraction peaks can be related to internal strain gradients and (ii) discontinuous streaking happens in the presence of dislocation walls forming geometrically necessary boundaries [16]. Since then, Laue microdiffraction has been established as a powerful technique in the study of mechanisms that govern plastic deformation at the micro scale [17][18][19][20][21]. For instance, Maaß et al. [18] performed in situ compression tests on ion-milled Au micropillars. ...
... Although GND values are lower bounds on the actual stored dislocation density within the wire, the difference between the two values is sufficiently high for the conclusion to be reached that most dislocations escaped the microcast wires while they were being deformed in tension. A similar conclusion was found by Kirchlechner et al. [19] by analysing peak streaking during tensile deformation of Cu single microcrystals (aspect ratio of 1:5) initially oriented for single slip. ...
Single-crystalline cast aluminium microwires with a diameter near 15 μm are characterised by Laue microdiffraction. A microwire in the as-cast condition exhibits a misorientation below 1∘ over a length of 500 μm. The measured density of geometrically necessary dislocations is low, <1012 m⁻², though local maxima up to one order of magnitude higher are found. After tensile deformation to failure, the dislocation density is significantly increased in microwires that have mostly deformed in single slip ( ≈2×1013 m⁻²), and yet higher when deformation has occurred by multiple slip ( ≈6×1013 m⁻²). In deformed single slip oriented microwires, the streaking directions of Laue spots show that dislocations are stored (though not exclusively) on the primary slip system. Results are consistent with a deformation mechanism governed by rotating, likely single-arm, sources.
... In addition, Laue microdiffraction revealed dislocations of an unpredicted slip system at low strains which were not able to escape to the surface in larger numbers and, thus no similar slip steps were observed on the sample surface. Moreover, Laue microdiffraction experiments by Kirchlechner et al. showed that multiple slip takes over at later deformation states [85]. Results obtained by Laue microdiffraction will be reviewed and discussed in further detail in section III.1. ...
... As described before FIB milling allows for fabricating dedicated specimen for micro-mechanical Note that SEM is a surface sensitive tool giving access solely to defects which exit at the surface while stored dislocations cannot be investigated. Ex situ Laue microdiffraction experiments on Cu microstructures which were strained by 22 % evidenced that all dislocations escaped from the strongly deformed crystal while they were stored at the ends of the structure where the sample looks perfect in the SEM [85]. ...
In recent years, the mechanical behavior of low-dimensional materials has been attracting lots of attention triggered both by the ongoing miniaturization and the extraordinary properties demonstrated for nanostructures. It is now well established that mechanical properties of small objects differ fundamentally from their bulk counterpart and in particular that "smaller is stronger" but many questions on the deformation mechanisms remain open. Most of the knowledge obtained on small- scale mechanics is based on ex-situ and in-situ characterizations using electron microscopy. However, these techniques suffer from the fact that imaging or scattering information is either limited to the surface or from a 2D projection of a thin foil of material. Within the last two decades tremendous progress was achieved at 3rd generation synchrotrons making it possible to focus hard X-ray beams down to the 100-nm scale. Modern synchrotron X-ray diffraction methods may thus provide structural information with good spatial resolution and fully 3D. In this review, we discuss the progress achieved on in-situ micro- and nano-mechanical tests coupled with different synchrotron X-ray diffraction techniques to monitor the elastic and plastic deformation, highlighting the advantages of these approaches, which offer at the same time versatile sample environments and extreme precision in displacement fields.
... The analysis of GND densities by lattice curvature requires strong assumptions on the strain and rotation tensors [7]. In Laüe micro-diffraction two methods are possible, the first is analogous to the one using EBSD, the local disorientation is evaluated from the diffraction patterns [8]. The second uses the broadening of the diffraction lines [9]. ...
The classical method of evaluating the density of geometrically necessary dislocations, (GND), is based on crystallographic orientation data obtained by electron diffraction in a scanning microscope or by Laüe micro-diffraction. These data allow the measurement of the curvature of the crystal lattice from which the GND is calculated. This method requires strong assumptions on the strain and rotation tensors. In the present study, we propose an original approach for the evaluation of GND which is based on the analysis of the topography of the slip bands and which does not require particular assumptions. The topography is measured by atomic force microscopy. The plastic displacement field is obtained by correcting the topography for plastic rotation. This method of analyzing the plastic displacement field has been presented in two previous papers on the comparative plasticity of iron and single crystal copper. An analytical model is used to model the displacement field. The orientation measurement of the crystal allows to express the plastic displacement field in the reference frame associated with the sliding system. It is then possible to calculate the gradient tensor of the plastic displacement by derivation of the displacement field and then by taking the rotational of the latter to obtain the Nye tensor.
... Focused ion beam milling (FIB) has fundamentally changed nanomechanical testing, inasmuch as it has allowed unprecedented experimental designs, which are useful for targeting specific material properties at the nanometer scale [1,2]. For example, FIB-machined samples were pivotal to the discovery of geometric size effects on strength [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. FIB-based techniques also have the unique ability to isolate and investigate the mechanical contribution of microstructural features and defects-such as grain and twin boundaries [21][22][23][24][25]-and are increasingly used to study the fracture mechanisms at the nanometer scale, for instance in thin films [26][27][28][29][30][31]. ...
Focused ion beam (FIB) milling is an increasingly popular technique for fabricating micro-sized samples for nanomechanical characterization. Previous investigations have cautioned that exposure to a gallium ion beam can significantly alter the mechanical behavior of materials. In the present study, the effects of gallium, neon, and xenon ions are scrutinized. We demonstrate that fracture toughness measurements on freestanding gold thin films are unaffected by the choice of the ion species and milling parameters. This is likely because the crack initiation is controlled by the local microstructure and grain boundaries at the notch, rather than by the damaged area introduced by FIB milling. Additionally, gold is not susceptible to chemical embrittlement by common FIB ion species. This confirms the validity of microscale fracture measurements based on similar experimental designs.
Graphical abstract
... D'autres études se sont focalisées sur les liens entre densités de dislocations et gradients d'orientation, dans plusieurs matériaux métalliques [Barabash et al., 2009, Kirchlechner et al., 2011. Ces densités sont extraites du gradient d'orientation que l'on peut extraire à partir de la forme des taches de Laue, ou Laue résolue en profondeur (cf. ...
La caractérisation des contraintes internes présentes dans les matériaux de structure ou fonctionnels est primordiale pour une optimisation de leurs propriétés et de leur tenue en service. Ce travail de thèse est une contribution au développement d'une technique de microscopie par diffraction des rayons X, appelée "Differential Aperture X-ray Microscopy", (DAXM, permettant la caractérisation 3D et non-destructive de la microstructure de matériaux cristallins et des contraintes internes présentes dans le matériau. Cette technique est basée sur l'utilisation du rayonnement synchrotron; nous avons utilisé la ligne CRG BM32 du synchrotron européen ESRF. Le faisceau de rayons incident est polychromatique (5-25keV) et fortement focalisé (section sub-micrométrique). En raison la pénétration du faisceau dans le matériau, qui est typiquement de quelques dizaines de microns, l'image de diffraction collectée est une superposition des diagrammes de Laue de tous les cristaux situés sur le trajet du faisceau incident. La DAXM utilise, en supplément de la microdiffraction Laue "classique", un masque mobile (ici un fin fil de tungstène) qui absorbe une partie des faisceaux diffractés. L'analyse de l'évolution des niveaux de gris des pixels de l'image en fonction de la position du masque permet non seulement de reconstruire la microstructure du matériau en profondeur mais aussi d'accéder à la distribution 3D des déformations élastiques (et des contraintes associées). L'un des avantages de la DAXM est sa résolution spatiale, de l'ordre du micromètre, qui permet d'envisager l'analyse des concentrations de contraintes dans les matériaux polycristallins, dans le cadre des approches micromécaniques expérimentales.Le travail mené dans cette thèse avait pour but d'améliorer le dispositif expérimental existant,de mettre en place la formulation théorique du problème, et de développer les outils numériques permettant le traitement des données.Du point de vue expérimental, nous avons notamment développé une machine d'essai mécanique in-situ (flexion 4-points) adaptée à la ligne BM32, et nous proposons un masque multi-fil qui devrait permettre de réduire significativement la durée de l'acquisition des données.Nous avons établi les équations de triangulation reliant la position des pixels du détecteur,la position du fil, et la profondeur de la source le long du faisceau incident. On montre ainsi que la reconstruction 3D nécessite une procédure de dérivation des niveaux de gris; nous nous sommes limités dans ce travail à une dérivation par différence finie d'ordre 1, qui reste sensible au bruit d'image. Ces équations font apparaître la nécessité de déterminer la géométrie du montage avec grande précision. On propose pour cela l'utilisation de la fluorescence de l'échantillon. On adjoint aux équations géométriques une description mathématique simplifiée de l'atténuation du faisceau par l'échantillon, prenant en compte un coefficient d'absorption unique. Le modèle de calibration est testé sur plusieurs matériaux, avec de très bons résultats.La capacité de la DAXM à reconstruire une microstructure est testée sur des échantillons modèles pour lesquels la géométrie 3D de la microstructure est parfaitement connue : empilement de fin fils de GaN sur un substrat, et plan de macle dans un polycristal d'acier inoxydable (316L). On montre que la résolution de la DAXM est variable d'un pixel à l'autre du détecteur; la microstructure peut cependant être reconstruite avec une précision de l'ordre du micromètre.La DAXM est ensuite testée sur un échantillon d'UO2 implanté d'ions Kr, créant une couche de surface d'épaisseur micrométrique fortement déformée (collaboration CEA-Cadarache). On observe que la méthode de reconstruction proposée produit d'importants artefacts, qui sont dus à la transmission variable des faisceaux diffractés dans le masque. Nous mettons en place la formulation permettant de prendre en compte cet effet.
... By far, the best spatial resolution is obtained with Bragg coherent diffraction imaging (BCDI), which is a lensless imaging technique, with a typical resolution of 8-10 nm (Labat et al., 2015). In addition, with the aid of phase retrieval algorithm (Fienup, 1982;Minkevich et al., 2008), it allows for spatially characterizing individual defects and dislocation networks in crystals (Labat et al., 2015;Kirchlechner et al., 2011;Hofmann et al., 2017;Clark et al., 2015) as well as the full elastic strain tensor deduced from crystallographically resolved displacement fields (Haag et al., 2013;Newton et al., 2010). X-ray experiments offering the unique advantages of being nondestructive, volume probing, and exquisitely sensitive to small strains makes BCDI an ideal tool for such nanomechanical testing, yet in situ experiments using these new modalities are still nascent (Miao et al., 2015;Leclere et al., 2015;Ren et al., 2014;Maaß et al., 2009;Dupraz et al., 2017). ...
Systematic tensile tests were performed on single defect-free 〈110〉 Au nanowires grown by physical vapor deposition while simultaneously recording three-dimensional Bragg peaks using coherent X-rays. The trajectory of three-dimensional Bragg peaks in reciprocal space during tensile testing allowed for measurements of the evolution of strains and rotations of the nanowire, thus sensitively uncovering the full deformation geometry of the nanowire. The transition from elastic to plastic deformation is accompanied by rotations of the nanowire as quantified by analysis of the motion of Bragg peaks, showing the importance of boundary conditions in interpreting nanoscale mechanical deformations.
... The different probing volumes of the different orientations further complicated the analysis. Laue micro-diffraction is well suited for strain and orientation mapping in miscellaneous materials Tamura et al., 1999;Ice & Larson, 2000;MacDowell et al., 2001;Larson et al., 2002;Tamura et al., 2002b;Tamura et al., 2002a;Tamura et al., 2003;Rogan et al., 2003;Ice et al., 2005;Maaß et al., 2006;Kunz et al., 2009;Ice & Pang, 2009;Kirchlechner et al., 2011b;Kirchlechner et al., 2011a;Robach et al., 2011;Villanova et al., 2012;Chen et al., 2012;Richard et al., 2012;Hofmann et al., 2013;Ibrahim et al., 2015;Dejoie et al., 2015). Recently, local Laue micro-diffraction measurements of the strain have also been performed in nano-objects, such as Au nanowires (Leclere et al., 2015) or Ge nanowires . ...
Laue micro-diffraction and simultaneous rainbow-filtered micro-diffraction were used to measure accurately the full strain tensor and the lattice orientation distribution at the sub-micrometre scale in highly strained, suspended Ge micro-devices. A numerical approach to obtain the full strain tensor from the deviatoric strain measurement alone is also demonstrated and used for faster full strain mapping. The measurements were performed in a series of micro-devices under either uniaxial or biaxial stress and an excellent agreement with numerical simulations was found. This shows the superior potential of Laue micro-diffraction for the investigation of highly strained micro-devices.
... For the reliable design, we have to know the precise mechanical properties of constituent materials. However, though characteristic mechanical properties of nano-scaled materials, which are substantially different from those of bulk, have been pointed out (Dimiduk, et al., 2005), (Greer and Nix, 2006b), (Kirchlechner, et al., 2011), and (Kiener, et al., 2008), the research has not been enough. ...
Nanometer-scale components (nano-components) often exhibit characteristic mechanical behavior different from those of bulk counterparts. In this paper, we review a series of experimental studies on the mechanics of their fracture focusing especially on the interfacial strength in the nano-components, which consist of dissimilar nano-layers. Since the stress concentrated region is proportionally scaled down for shrinkage of component size, it becomes a few nanometers or at most a few tens of nanometers in the nano-components. We particularly pay attention to the availability of "stress" as the governing quantity of cracking, which is on the basis of the concept of continuum mechanics. We also investigate the effect of nano-scale stress concentration on the fatigue behavior of metals in nano-components. Finally, we discuss future directions on the further experimental exploration on the fracture mechanics in nano-components; the tensile testing of nano-rod and the fracture due to the stress concentration in the single nanometer scale.
... Le cuivre, en tant que matériau modèle fréquemmentétudié dans la littérature, a servi de basè a la plupart desétudes des mécanismes de déformation plastique du monocristal réalisées par microdiffraction Laue. Les structures de dislocations résultant de la déformation d'échantillons monocristallins de cuivre en traction ont ainsiétéétudiées, soità travers l'étude de la courbure du réseau cristallin basée sur des mesures d'orientation cristalline (Pang et al. (2010)), soit directementà partir de l'étalement de pics de diffraction (Kirchlechner et al. (2011b)). Magid et al. (Magid et al. (2009);Field et al. (2010)) ont quantà euxétudié les mécanismes de déformation plastiqueà l'oeuvre dans un monocristal de cuivre déformé en compression uniaxiale, dans une configuration d'orientation visantà favoriser le glissement simple,à 10% de déformation. ...
The modeling of strain hardening in polycrystals is a difficult and still standing task. Current existing models are partly phenomenological, as they always consider constitutive parameters adjusted on the experiment. The aim of the present study is to design a physically based model for the basic problem of monotonic deformation in the FCC polycrystal. Laue microdiffraction is used to measure the mechanical fields in the vicinity of grain boundaries in a copper tricrystal compress at 0.2%. These measurements aim to characterize the plastic phenomena involved and to provide experimental data as bench results for the simulations. Evidences of geometrically necessary dislocations (GND) storage close to the grain boundaries are given in relation with the apparition of longrange internal stresses. Dislocations Dynamics simulations are used to study the plastic strain close to a grain boundary in Cu bicrystals. We show that close to the boundaries plastic strain is associated to the storage of heterogeneous GNDs in complex 3D microstructures. The mechanical properties associate to such microstructure can be described with continuous laws based on a theoretical approximation assuming a 1D pile-up. The corresponding constitutive laws are then introduced in a crystal plasticity model initially devoted to FCC single crystal plasticity and solved with Finite Elements simulations. The new model we propose as now the capacity to reproduce or predict the experimental results we first obtained in the Cu tricrystal. In conclusion, a physically justified model is proposed to predict plastic deformation for the FCC polycrystal in monotonic deformation.
... Micro bending cantilevers were produced similar to the approach in [23]: copper rods with 1 Â 1 Â 20 mm 3 with a nominal 1 1 2 crystal direction parallel to the beam length axis were cut from a macroscopic single crystal using a diamond wire and then etched to a needle. The cone angle was in the order of 10°with a top radius of 5 lm. ...
The evolution of low cycle fatigue damage in copper is studied by in situ micro Laue diffraction. Free standing single crystalline micro-cantilevers with a cross-section of 10 × 10 μm2 were loaded in displacement controlled mode with a surface strain amplitude up to 5%. The point to point misorientation and the diffraction peak width as a measure of geometrically necessary dislocation density was analyzed locally during deformation and globally after 0, 1/4, 1/2, 3/4, 1 and multiples up to a maximum of 22 full cycles. Two different behaviors were observed (i) samples geometrically suppressing cross-slip show a steady state deformation pattern with dislocations in a pile-up. (ii) The sample with cross-slip does not reach a steady state with dislocations accumulating at the neutral plane.
... [ 22,23 ] This either micro-or nano-compression experiment has subsequently been developed further to in-situ techniques in combination with transmission electron microscopy (TEM), [ 24 ] scanning electron microscopy (SEM), [ 25,26 ] and micro-diffraction methods. [27][28][29] Besides reinvigorating interest in intermittent plastic fl ow, small scale mechanical testing has revealed intriguing extrinsic size-scaling effects. [30][31][32][33] In this work, we use the high displacement resolution of a displacement controlled micro-compression experiment, combined with kHz data acquisition rates (DAR) to study the spatio-temporal properties of intermittent collective dislocation activity in the form of displacement jumps. ...
Directly tracing the spatiotemporal dynamics of intermittent plasticity at the micro- and nanoscale reveals that the obtained slip dynamics are independent of applied stress over a range of up to ∼400 MPa, as well as being independent of plastic strain. Whilst this insensitivity to applied stress is unexpected for dislocation plasticity, the stress integrated statistical properties of both the slip size magnitude and the slip velocity follow known theoretical predictions for dislocation plasticity. Based on these findings, a link between the crystallographic slip velocities and an underlying dislocation avalanche velocity is proposed. Supporting dislocation dynamics simulations exhibit a similar regime during microplastic flow, where the mean dislocation velocity is insensitive to the applied stress. Combining both experimental and modeling observations, the results are discussed in a framework that firmly places the plasticity of nano- and micropillars in the microplastic regime of bulk crystals.
... As no additional streaking can be detected, it seems that slip on these slip systems is rather unconstrained and no dislocations are stored on these slip systems [54]. Fig. 9 shows TEM bright field and dark field images of a 190 nm diameter Ni [111] pillar which was 5% pre-strained prior to FIB fabrication before and after in situ compression using the g 1-10 diffraction condition. ...
Micro-compression tests were performed on pre-strained nickel (Ni) single crystals in order to investigate the influence of the initial dislocation arrangement on the size dependence of small-scale metal structures. A bulk Ni sample was grown using the Czochralski method and sectioned into four compression samples, which were then pre-strained to nominal strains of 5, 10, 15 and 20%. Bulk samples were then characterized using transmission electron microscopy (TEM), micro-Laue diffraction, and electron backscatter diffraction. TEM results show that a dislocation cell structure was present for all deformed samples, and Laue diffraction demonstrated that the internal strain increased with increased amount of pre-straining. Small-scale pillars with diameters from 200 nm to 5 μm were focused ion beam (FIB) machined from each of the four deformed bulk samples and further compressed via a nanoindenter equipped with a flat diamond punch. Results demonstrate that bulk pre-straining inhibits the sample size effect. For heavily pre-strained bulk samples, the deformation history does not affect the stress–strain behavior, as the pillars demonstrated elevated strength and rather low strain hardening over the whole investigated size range. In situ TEM and micro-Laue diffraction measurements of pillars confirmed little change in dislocation density during pillar compression. Thus, the dislocation cell walls created by heavy bulk pre-straining become the relevant internal material structure controlling the mechanical properties, dominating the sample size effect observed in the low dislocation density regime.
Microwires have become of increasing interest for the miniaturization of structural components. A profound understanding of the deformation behavior of microwires is important for the assessment of their applicability and lifetime in specific components. In particular, the deformation behavior under torsional loading and the associated microstructure evolution are of interest. The exact involvement of individual slip systems and their activities in the complex stress field under torsional loading are mostly unknown. In this paper, the microstructure evolution of single crystalline gold microwires under torsion have been analyzed for the high-symmetry crystal orientations 〈100〉, 〈110〉, and 〈111〉 using simulation and experimental results. It is shown that a classification of the slip systems can be derived a priori by theoretical considerations. It is found, that the slip system activity, stress relaxation mechanism, as well as screw and edge composition of the piled-up dislocation density depends on specific slip system groups. Furthermore, the misorientation and its rotational axes including the identification of the slip system activities are discussed.
Development of non-conventional mechanical testing techniques was primarily driven by the requirement to measure mechanical properties at smaller length scales with increasing miniaturization of devices, as well as the need for microstructure design from bottom up. This review covers the techniques involved in determining the small-scale deformation and fracture response of materials under different stress states. This is an attempt to provide a summary of choices and test protocols to potential users based on the property of interest to them. It begins with the basics of test instrumentation and sample preparation, followed by a short introduction to modeling tools that accompany testing, and later gets into the details of individual tests and their advantages and limitations. Selected applications from recent published works are presented to provide a flavor of material systems whose behaviour differs significantly from the macro-scale due to their size and/or architecture. At the end fallacies in data interpretation and a roadmap to standardization followed by ideas and future scope for non-conventional small-scale testing are given.
The description of the eXtreme Mechanics (XM) principles as new insights as well as updates of the classical mechanics laws is presented in Chap. 2: Extreme Mechanics in Advanced, Emerging Materials. This section consists of the most recent updates of the mechanics of materials (i.e. the “eXtreme Mechanics”) for the cutting-edge design in the advanced micro/nanoscale materials. How they have crucially affected the state of the art of design and technology of today’s most important and tomorrow’s emerging devices and systems will be highlighted in this book through real-world cases in several major areas of the modern technological world. Three emphasized clusters of industries have been identified as our focus in this book—advanced nano/microelectronics (3D IC, advanced packaging, MEMS, etc.), smart energy technology (battery, photovoltaics, etc.), and emerging flexible electronics (and other extreme technologies). This book consists of the most recent updates of the mechanics of materials (i.e. the “eXtreme Mechanics”) for the cutting-edge design in the advanced micro/nanoscale materials. How they have crucially affected the state of the art of design and technology of today’s most important and tomorrow’s emerging devices and systems will be highlighted in this book through real-world cases in several major areas of the modern technological world. Three emphasized clusters of industries have been identified as our focus in this book—advanced nano/microelectronics (3D IC, advanced packaging, MEMS, etc.), smart energy technology (battery, photovoltaics, etc.), and emerging flexible electronics (and other extreme technologies).
In this paper, microtensile testing is demonstrated to be a viable technique for measuring irradiation hardening and reduction of ductility of ion irradiated hot isostatic pressed SA508 ferritic/bainitic steel. Ion irradiation with He²⁺ was used as a surrogate for neutron irradiation to reach a damage level of 0.6 dpa (Kinchin-Pease). The mechanical properties of four unirradiated microtensile steel specimens were measured and compared to the bulk properties: when averaged the 0.2% proof stress was 501.6 ± 56.0 MPa, in good agreement with the macrotensile 0.2% proof stress of 456.2 ± 1.7 MPa. On the basis of the agreement between microtensile and standard tensile 0.2% proof stress in the unirradiated material, it was possible to directly measure irradiation induced hardening from ion irradiation performed with He²⁺ ions to a dose of 0.6 dpa. Microtensile testing of the ion irradiated steel revealed an increase in 0.2% proof stress of approximately 730 MPa. The irradiation hardening measured by nanoindentation was 3.22 ± 0.29 GPa. Irradiation hardening was higher than that previously observed in neutron irradiated low alloy steels exposed to similar doses at low temperatures (<100 °C). The reason for the higher hardening was related to the presence of fine helium bubbles implanted in the irradiated layer that, alone, was calculated to produce a 707 ± 99 MPa increase in yield stress.
In situ nanomechanical testing provides critical insight into the fundamental processes that lead to deformation phenomena in materials. Often, in situ tests are performed in relevant conditions such as high or low temperatures, tribological contact, gas environments, or under radiation exposure. Modern diffraction and imaging methods of materials under load provide high spatial resolution and enable extraction of quantitative mechanical data from local microstructure components or nano-sized objects. The articles in this issue cover recent advances in different types of in situ nanomechanical testing methods, spanning from dedicated nanomechanical testing platforms and microelectromechanical systems devices to deformation analyses via in situ diffraction and imaging methods. This includes scanning electron microscopy, advanced scanning transmission electron microscopy, electron diffraction, x-ray diffraction, and synchrotron techniques. Emerging areas such as in situ tribology enable novel insights into the origin of deformation mechanisms, while the evolution of microelectromechanical systems for controlled in situ testing provide opportunities for advanced control and loading strategies. Discussion on the current state of the art for in situ nanomechanical testing and future opportunities in imaging, strain sensing, and testing environments are also addressed.
https://authors.elsevier.com/a/1Z87P4r9SUFF3p
Although the effect of specimen size on strength has been well documented for metal micro-samples significantly larger than ~1 μm, less is known about the deformation induced dislocation structure, especially just above the size at which dislocation starvation happens. Here, uniaxial compression tests were performed on cylindrical [011] oriented copper micropillars with diameters of 1 μm, 3 μm and 5 μm. Dislocation cells formed in a fractal geometry in the 3 μm and 5 μm pillars, while dislocations were not retained in the 1 μm pillars. The effects of strain and strain rate on cell formation were also investigated.
The mechanical behavior of several micron sized Cu bi-crystals with a single coherent twin boundary (TB) is studied by in situ Laue microdiffraction (μLaue) compression with the aim to unravel the slip transfer mechanisms through TBs. Single crystalline pillars (SCP) are additionally tested and used as reference samples. Engineering stress-strain curves and post mortem scanning electron microscopy (SEM) images were correlated to the local evolution of the TB angle, the storage of geometrically necessary dislocations and crystal orientations investigated by in situ X-ray Laue microdiffraction (μLaue). Both μLaue and post mortem SEM demonstrate multiple transmission events through the TB without significant storage of geometrically necessary dislocations in the crystals or at the boundary, independent on the compression direction. Nevertheless, at engineering strains larger than 5% a small dislocation pile-up was once observed temporarily at the boundary. Upper and lower bounds for the transmission stress are discussed based on the current experimental results.
Uchic and co-workers were the first ones who performed uniaxial compression tests on micron-sized samples and inspired scientists worldwide to perform similar microcompression, tension, or bending experiments. The straining device is able to perform compression, tensile, or bending experiments. Complementary fine energy scans can be performed by inserting a tunable monochro-mator or a multi-colored rainbow filter in the white beam path in order to determine the energy of selected reflections and to further analyze the full strain tensor. For Laue diffraction experiments, a white X-ray beam consisting of a broad energy band pass is used. Nevertheless, scanning electron microscopy (SEM) just probes the sample surface and, therefore, is only able to monitor glide steps formed by dislocations escaping at the sample surface. These glide steps imply that the activation of discrete dislocation sources are responsible for the plastic deformation of metallic structures.
Diffraction methods using neutrons and/or high-energy X-rays offer unique opportunities for investigating various aspects of importance for the development of intermetallic titanium aluminides (TiAl) alloys. Despite their different nature, high-energy X-rays and neutrons are both suited for performing diffraction as well as scattering experiments in materials science. A common feature of structural materials, including TiAl alloys, is the dependency of their properties on phase composition and the arrangement of the constituting phases. Employing high-energy X-ray diffraction (HEXRD) allowed for in situ monitoring of the phases evolution. Transmission electron microscopy (TEM) is a method that would allow determining phase fractions in lamellar grains, although at the expense of time-consuming sample preparation and the restriction to small sample volumes. By diffraction methods, the phase fractions can be determined with high accuracy even in the instance that lamellar colonies are present in the material.
Compression of micropillars is routinely used to measure the material response under uniaxial load. In bi-crystalline pillars an S-shaped grain-boundary together with an S-shaped pillar is often observed after deformation raising the question of its origin and consequences for stress-strain materials data. In addition to dislocation and grain-boundary based mechanisms, this observation can be caused by buckling and subsequent post-buckling deformation. Deviations from the classical pre- and post-buckling deformation behavior are assigned to imperfections, which are categorized in extrinsic and intrinsic imperfections in this work. In the present paper, the S-shaped actual deformation state is particularly promoted by an intrinsic imperfection, caused by a material heterogeneity (due to the bi-crystal arrangement). This kind of deformation behavior is investigated by micro-compression experiments on 7 × 7 × 21 μm³ sized bi-crystal copper pillars with nearly elastic (axial Young's modulus) homogeneity and identical Schmid factors for both grain orientations. Complementary finite element simulations are performed, in which also the role of friction and of an extrinsic imperfection in the form of initial misalignment of the loading on the S-shape are considered. There, a material model describing the flow stress distribution caused by a dislocation pile-up at the grain-boundary is applied. Finally, suggestions to prevent buckling and, thus, transversal post-buckling displacements during micropillar compression tests are given with the goal to extract engineering stress-strain curves.
Load-displacement curves measured during indentation experiments on thin films depend on non-homogeneous intrinsic film microstructure and residual stress gradients as well as on their changes during indenter penetration into the material. To date, microstructural changes and local stress concentrations resulting in plastic deformation and fracture were quantified exclusively using numerical models which suffer from poor knowledge of size dependent material properties and the unknown intrinsic gradients. Here, we report the first in-situ characterization of microstructural changes and multi-axial stress distributions in a wedge-indented 9 μm thick nanocrystalline TiN film volume performed using synchrotron cross-sectional X-ray nanodiffraction. During the indentation, needle-like TiN crystallites are tilted up to 15 degrees away from the indenter axis in the imprint area and strongly anisotropic diffraction peak broadening indicates strain variation within the X-ray nanoprobe caused by gradients of giant compressive stresses. The morphology of the multiaxial stress distributions with local concentrations up to −16.5 GPa correlate well with the observed fracture modes. The crack growth is influenced decisively by the film microstructure, especially by the micro- and nano-scopic interfaces. This novel experimental approach offers the capability to interpret indentation response and indenter imprint morphology of small graded nanostructured features.
Grain boundary sliding is an important deformation mechanism that contributes to creep and superplastic forming. In tin-based lead-free solders grain boundary sliding can make significant contributions to in service performance. Novel micro-compression tests designed to isolate individual grain boundaries and assess their mechanical resistance to sliding were conducted on tin. The boundary sliding deformation was more obvious for smaller sample cross-sections and made a larger contribution to the overall deformation. As with dislocation and twinning mediated plasticity there was a significant size effect in which the resistance to grain boundary sliding increases as the sample size is reduced.
In this study, the evolution of dislocation densities during compressive deformation of nanoscale Cu/Nb single crystal multilayers with individual layer thickness of 20 nm is investigated using Synchrotron X-ray micro-diraction. The samples were subjected to successive compression straining up to a cumulative strain of 35%. The nanolayer composite exhibited a maximum ow strength of ∼ 1.6 GPa at approximately 24% compressive strain. Synchrotron X-ray micro-diraction experiments, using a monochromatic beam of 10 keV energy were performed after each compression strain increment. We observed a signicant increase in X-ray ring width peak broadening in both Cu and Nb layers up to strains of ∼ 3.5% followed by saturation broadening at higher strains. This observation indicates that the interfaces of the Cu/Nb nanolayers are very effective in trapping and annihilating dislocation content during mechanical deformation.
Deforming metals during recording X-ray diffraction patterns is a useful tool to get a deeper understanding of the coupling between microstructure and mechanical behaviour. With the advances in flux, detector speed and focussing techniques at synchrotron facilities, in-situ mechanical testing is now possible during powder diffraction and Laue diffraction. The basic principle is explained together with illustrative examples.
We develop a new test method for evaluating tensile properties of nano-mateirals and apply it to a single crystalline gold nanorod with a square section of 189nm. The nanorod, which is carved out of a bulk material by focused ion beam processing, is mounted on a lozenge-shaped silicon frame and is pulled by a compressive load on the top face of the frame. Although the applied load increases monotonically in the early stages of deformation, it drops rapidly at a certain displacement. In-situ TEM observation indicates that the rapid decrease of applied load is due to crystallographic slip generation in the nanorod. The critical resolved shear stress on the primary slip system at yielding is evaluated to be 325.8MPa, which is about 600 times larger than that of bulk. When the tensile elongation becomes large, the nanorod shows necking and isotropic plastic behavior independent on crystalline structure.
In sample‐scanning Laue microdiffraction, the local crystal orientation and local deviatoric strain tensor are obtained by illuminating the polycrystalline sample with a broadband `white' (5–30 keV) X‐ray microbeam and analyzing the spot positions in the resulting local Laue pattern. Mapping local hydrostatic strain is usually slower, owing to the need to alternate between white and tunable‐energy monochromatic microbeams. A technique has been developed to measure hydrostatic strain while keeping the white beam. The energy of one of the Laue spots of the grain of interest is measured using an energy‐dispersive point detector, while simultaneously recording the Laue pattern on the two‐dimensional detector. The experimental spot energy, E exp, is therefore measured at the same time as E theor, the theoretical spot energy for zero hydrostatic strain, which is derived from the analysis of the Laue pattern. The performance of the technique was compared with that of the monochromatic beam technique in two test cases: a Ge single crystal and a micrometre‐sized UO2 grain in a polycrystal. Accuracies on the hydrostatic strain Δa/a of ±0.4 × 10−4 and ±1.3 × 10−4 were obtained for Ge and UO2, respectively. Measurement strategies to limit the remaining uncertainties on E theor are discussed.
Strain heterogeneities in polycrystalline thin films are of great interest in technology because many fabrication and reliability problems are stress related. Nevertheless measuring local strains in sub-micron grains remains a real experimental challenge. This thesis is focused on recent and promising results in the field of strain measurements in small dimensions via X-ray micro-diffraction. A 3D mapping of 111 Bragg reflection from a Au sub-micron single grain was measured during a thermal cycle. Coherent properties of the beam has been used to retrieve a component of the displacement field in 3D from this single grain with a resolution around 17 x 17 x 22 nm via phase retrieval procedures. However algorithms do not always converge when the grain is highly strained. Thus alternative techniques are proposed and tested to overcome this stagnation. Complementary results from laboratory diffraction and micro 3D X-Ray Diffraction have also been analysed to compare strain at different scales. Strong strain heterogeneities has been evidenced between grains.
White beam x-ray Laue microdiffraction allows fast mapping of crystal
orientation and strain fields in polycrystals, with a submicron spatial
resolution in two dimensions. In the well crystallized parts of the
grains, the analysis of Laue spot positions provides the local
deviatoric strain tensor. The hydrostatic part of the strain tensor may
also be obtained, at the cost of a longer measuring time, by measuring
the energy profiles of the Laue spots using a variable-energy
monochromatic beam. A new "Rainbow" method is presented, which allows
measuring the energy profiles of the Laue spots while remaining in the
white-beam mode. It offers mostly the same information as the latter
monochromatic method, but with two advantages : i) the simultaneous
measurement of the energy profiles and the Laue pattern; ii) the rapid
access to energy profiles of a larger number of spots, for equivalent
scans on the angle of the optical element. The method proceeds in the
opposite way compared to a monochromator-based method, by simultaneously
removing several sharp energy bands from the incident beam, instead of
selecting a single one. It uses a diamond single crystal placed upstream
of the sample. Each Laue diffraction by diamond lattice planes
attenuates the corresponding energy in the incident spectrum. By
rotating the crystal, the filtered-out energies can be varied in a
controlled manner, allowing one to determine the extinction energies of
several Laue spots of the studied sample. The energies filtered-out by
the diamond crystal are obtained by measuring its Laue pattern with an
other 2D detector, at each rotation step. This article demonstrates the
feasibility of the method, and its validation through the measurement of
a known lattice parameter.
In situ scanning electron microscopy compression tests clearly demonstrate that a multilayered arrangement of CrN and AlN – when stabilized by coherency strains to its cubic metastable phase for AlN layer thicknesses below 3 nm – exhibits increased fracture toughness as compared to single-layered CrN. This allows increasing the maximum loading from ∼5.25 to 6.80 GPa. If the AlN layers mainly crystallize in their stable wurtzite structure – for thicknesses above 3 nm – spontaneous and fatal cracking occurs under loads as small as 3.80 GPa.
The observed mechanical behaviour of micron-sized samples raises fundamental questions about the influence of size on the underlying dislocation plasticity. In situ µLaue diffraction on a single crystalline copper bending beam was performed to study the feasibility of bending tests and their contribution to our understanding of size-dependent dislocation plasticity. Theoretical considerations lead to a minimum sample size where in situ µLaue experiments are useable. A critical size is evidenced below which, depending on Young's modulus and maximum stress, the elastic and plastic contributions to the lattice curvature cannot be separated. The experiment shows the increase in geometrically necessary dislocations during plastic deformation followed by a decrease during unloading. This can be explained by the formation and dissolution of a dislocation pile-up at the neutral axis of the bending cantilever. The dissolution of the dislocation pile-up is caused by the back stress of the pile-up and a direct observation of the Bauschinger effect, which is consistent with the non-purely elastic mechanical behaviour when unloading the sample.
Polycrystalline copper wires with diameters of 25, 30 and 50 µm were annealed at temperatures between 200°C and 900°C, resulting in different microstructures with ratios of wire diameter to grain size between 1.1 and 15.6. The microstructure evolution and tensile behavior were studied systematically. In comparison with experimental data available in the literature, the results revealed that the tensile yield stresses of these micro-sized wires are influenced not only by the grain size but also by the ratio of wire diameter to grain size. This is clearly seen when comparing identical grain sizes but different wire diameters where thinner wires reveal smaller flow stress values. A model is proposed to explain the ‘smaller is softer’ phenomenon, taking into account the higher strengthening effect of grain boundaries compared to the free surface.
In situ micro-Laue diffraction was used to study the plasticity in three 7μm, initially identical, single-crystalline Cu pillars during compression. Movements of the Laue spot as well as Laue spot streaking were analyzed to obtain real-time insights into the storage of excess dislocations and the possible formation of dislocation cell structures. The results reveal that instrumental constraints lead to dislocation storage at the sample base and top, but will not affect the storage of excess dislocations in the sample center in case of an ideal alignment. In contrast, misaligned samples show early yielding due to the activation of an unpredicted slip system, storage of excess dislocations also in the sample center and, at a later stage, the formation of a complex dislocation substructure.
The study of mechanical properties in micron and submicron sized metal crystals raises fundamental questions about the influence of size on different aspects of plasticity. In situ characterization of the microstructure evolution during loading is necessary to understand the physics underlying crystal deformation. In situ μLaue diffraction is able to provide unique statistical information on the evolution of type and density of stored dislocations. Here we show macroscopically expected and unexpected plastic behavior at low strains, observed during in situ μLaue tensile tests on micron sized, single slip oriented Cu samples. Regardless of the initial behavior, a steady state is reached which qualifies a technical yield criterion at the micron scale.
The mechanical properties and strain rate sensitivity of nanocrystalline nickel was studied as a function of grain size at different temperatures in tensile tests and with a nanoindenter in order to examine the different deformation mechanisms of nanocrystalline materials. The effect of lateral boundaries and hydrogen on the nucleation of dislocations was studied in detail. For the first time it was possible to observe the reduction of the dislocation nucleation stress on a nanoscale. In addition the experiments yielded, depending on temperature and strain rate, the strain rate sensitivity, the activation volume and the creep exponents as a function of stress and grain size. From the creep experiments the transition between grain boundary sliding and dislocation climb as a function of temperature was obtained. The strain rate jump tests gave extremely small activation volumes, nearly a factor of 100 smaller than in conventional nickel as a function of grain size. To help in understanding this behaviour the strain rate sensitivity of single grains was tested with a nanoindenter. The results clearly showed that the primary interaction of dislocations with grain boundaries is the reason for the observed strong rate effects and small activation volumes.
IntroductionAvailable Straining TechniquesDislocation Mechanisms in Thermally Strained Metallic FilmsSize-Dependent Dislocation Plasticity in MetalsConclusions and Future DirectionsReferences
There is much interest in the recent years in the nanoscale metallic multilayered composite materials due to their unusual mechanical properties, such as very high flow strength and stable plastic flow to large strains. These unique mechanical properties have been proposed to result from the interface-dominated plasticity mechanisms in nanoscale composite materials. Studying how the dislocation configurations and densities evolve during deformation will be crucial in understanding the yield, work hardening, and recovery mechanisms in the nanolayered materials. In an effort to shed light on these topics, uniaxial compression experiments on nanoscale Cu/Nb single-crystal multilayer pillars using ex situ synchrotron-based Laue x-ray microdiffraction technique were conducted. Using this approach, we studied the nanoscale Cu/Nb multilayer pillars before and after uniaxial compression to about 14% of plastic strain and found significant Laue peak broadening in the Cu phase, which indicates storage of statistically stored dislocations, while no significant Laue peak broadening was observed in the Nb phase in the nanoscale multilayers. These observations suggest that at 14% plastic strain of the nanolayered pillars, the deformation was dominated by plasticity in the Cu nanolayers and elasticity or possibly a zero net plasticity (due to the possibility of annihilation of interface dislocations) in the Nb nanolayers.
µLaue diffraction sheds light onto the deformation behavior of miniaturized samples. Here we present a new instrumental setup for the in situ deformation of micron sized specimens at BM32 of the ESRF synchrotron source. Furthermore, a compression test of a 7 µm sized single slip oriented copper pillar is presented, showing the activation of an unpredicted slip system due to misalignment and the formation of several sub-grains. The results of the compressed pillar as well as possibilities and crucial points for measuring and data evaluation are discussed.
Intermetallic γ-TiAl based alloys are a novel class of lightweight structural materials that exhibit excellent high-temperature strength while having low density. These properties make them ideal candidates for replacing dense Ni base alloys currently used in the temperature range from 550 to 750 °C. Therefore, extensive research activities were conducted during the last 20 years to make this innovative class of materials fit for service. In this task, diffraction methods have been an important tool for promoting the development of TiAl alloys. The ability to perform experiments in situ and to determine phase fractions even in cases where two phases are present in ultrafine lamellar structures are only two examples for applications in which diffraction methods are indispensable. In this work, a review is given concerning the use of diffraction methods in the development of TiAl alloys. Different methods are introduced and highlighted by examples. This review lists the advantages of diffraction experiments and critically discusses the limits of the individual methods.
The high strength of micro-crystals is determined in the early flow regime, where a transition from elastic to plastic flow is obscured if compared to stress–strain data from bulk single crystals. In the present work we therefore focus on the evolution of dislocation structures in Ni micro-pillars during early deformation by employing in-situ Laue micro-diffraction. It will be shown that substantial changes in the lattice fine structure, such as multiple subgrain formation and significant rotational gradients, can be resolved prior to the onset of large strain generation. The results reveal more pronounced effects for smaller sample dimensions and also suggest that most of the evolving dislocation structure is formed prior to the occurrence of large strain bursts. A clear increase in dislocation density as a function of strain is observed, which we discuss in the context of size-dependent strain hardening and exhaustion hardening.
Uniaxial compression tests have been performed on single crystal Au columns ranging in diameter from 180 nm to 8 µm. The columns were machined into the surface of a large-grained Au sheet using a focused ion beam microscope and then mechanically tested using a nanoindenter outfitted with a flat diamond punch. Images of the compressed columns show that deformation occurs by localized shear on the slip systems with the largest resolved shear stresses. After an elastic loading regime, the columns exhibit yielding in discrete strain bursts. The compressive yield stress scales roughly as the inverse square root of the column diameter. The apparent strain hardening rate also increases strongly with decreasing column diameter and stresses as large as 1 GPa are reached. Both of these size effects are attributed to dislocation source-limited behaviour in small volumes.
This paper concerns instanton contributions to two-point correlation functions of Berenstein-Maldacena-Nastase (BMN) operators in N 4 supersymmetric Yang-Mills theory that vanish in planar perturbation theory. Two-point functions of operators with even numbers of fermionic impurities (dual to R R string states) and with purely scalar impurities (dual to NS NS string states) are considered. This includes mixed R R–NS NS two-point functions. The gauge theory correlation functions are shown to respect BMN scaling and their behavior is found to be in good agreement with the corresponding D-instanton contributions to two-point amplitudes in the maximally supersymmetric IIB plane wave string theory. The string theory calculation also shows a simple dependence of the mass matrix elements on the mode numbers of states with an arbitrary number of impurities, which is difficult to extract from the gauge theory. For completeness, a discussion is also given of the perturbative mixing of two impurity states in the R R and NS NS sectors at the first nonplanar level.
Single-crystal micro-pillars of a molybdenum alloy were prepared by a new technique that involves chemically etching away the matrix of a directionally solidified NiAl–Mo eutectic. The square cross-section pillars had edge dimensions ranging from ∼360 to ∼1000 nm. When tested in compression with a nanoindentation system, the pillars all yielded, regardless of size, at a critical resolved shear stress of 4.3 GPa, or G/26, where G is the shear modulus. This shear yield strength is in the range expected for the theoretical strength, G/30 to G/10.
White beam x-ray microdiffraction is used to investigate the microstructure of micron-sized Si, Au, and Al pillars fabricated by focused ion beam (FIB) machining. Comparison with a Laue pattern obtained from a Si pillar made by reactive ion etching reveals that the FIB damages the Si structure. The Laue reflections obtained from the metallic pillars fabricated by FIB show continuous and discontinuous streakings, demonstrating the presence of strain gradients. (c) 2006 American Institute of Physics.
It has been known for more than half a century that crystals can be made stronger by introducing defects into them, i.e., by strain-hardening. As the number of defects increases, their movement and multiplication is impeded, thus strengthening the material. In the present work we show hardening by dislocation starvation, a fundamentally different strengthening mechanism based on the elimination of defects from the crystal. We demonstrate that submicrometer sized gold crystals can be 50 times stronger than their bulk counterparts due to the elimination of defects from the crystal in the course of deformation.
The availability of high brilliance rd generation synchrotron sources together with progress in achromatic focusing optics allow to add submicron spatial resolution to the conventional century-old X-ray diffraction technique. The new capabilities include the possibility to map in-situ, grain orientations, crystalline phase distribution and full strain/stress tensors at a very local level, by combining white and monochromatic X-ray microbeam diffraction. This is particularly relevant for high technology industry where the understanding of material properties at a microstructural level becomes increasingly important. After describing the latest advances in the submicron X-ray diffraction techniques at the ALS, we will give some examples of its application in material science for the measurement of strain/stress in metallic thin films and interconnects. Its use in the field of environmental science will also be discussed.
When a crystal deforms plastically, phenomena such as dislocation storage, multiplication, motion, pinning, and nucleation
occur over the submicron-to-nanometer scale. Here we report measurements of plastic yielding for single crystals of micrometer-sized
dimensions for three different types of metals. We find that within the tests, the overall sample dimensions artificially
limit the length scales available for plastic processes. The results show dramatic size effects at surprisingly large sample
dimensions. These results emphasize that at the micrometer scale, one must define both the external geometry and internal
structure to characterize the strength of a material.
We demonstrate real-time resolved white beam Laue diffraction during compression of micron-sized focused ion beam milled single crystals Au pillars, revealing the dynamical correlation between microstructure and plasticity. The evolution of the Laue patterns of the Au pillars demonstrates the occurrence of crystal rotation and strengthening is explained by plasticity starting on a slip system that is geometrically not predicted but selected because of the character of the preexisting strain gradient.
Under stress, many crystalline materials exhibit irreversible plastic deformation caused by the motion of lattice dislocations.
In plastically deformed microcrystals, internal dislocation avalanches lead to jumps in the stress-strain curves (strain bursts),
whereas in macroscopic samples plasticity appears as a smooth process. By combining three-dimensional simulations of the dynamics
of interacting dislocations with statistical analysis of the corresponding deformation behavior, we determined the distribution
of strain changes during dislocation avalanches and established its dependence on microcrystal size. Our results suggest that
for sample dimensions on the micrometer and submicrometer scale, large strain fluctuations may make it difficult to control
the resulting shape in a plastic-forming process.
The validity of Schmid’s law in micropillar samples is assessed by a simulation scheme in which the critical stress to operate a slip system is determined by the free lengths of dislocations pinned by intersection points imposed by dislocations lying on other slip planes. At fixed dislocation density, yielding occurs predominantly on the slip system with the maximum Schmid factor when the sample size is large, but as the sample size reduces, other slip systems have an increasing probability of operating.
Spatial scales in crystal plasticity are understood to influence flow stresses and work-hardening rates. A direct assessment of the crystal-size dependence of the critical resolved shear stress has been made for single-slip oriented crystals of pure Ni having sample diameters that range from 40 to 1.0μm. The sample dimensions directly limit the length scales available for plasticity, but without significant external or kinematical constraint. The results show strength increases of up to 15 times over pure Ni and size-affected hardening rates. Stresses are lower, but strengthening persists to larger sizes than for the prior work on face-centered cubic metal whiskers. The results emphasize that at the micron-size scale and below both external geometry and internal structure affect the micromechanisms of deformation and strength.
The authors have experimentally investigated the compressive strength of GaAs pillars with a diameter of 1 μm by uniaxial compression tests. The tests were performed at room temperature and, contrary to macroscopic tests, the micropillars were found to exhibit ductile plasticity comparable to that of metal single crystal micropillars. The yield stress was 1.8±0.4 GPa and, for one pillar that was more closely examined, a total deformation of 24% was observed. In the diffraction patterns from transmission electron microscopy studies of this pillar, a high density of twins was observed.
A novel method for in situ scanning electron microscope (SEM) micro-compression tests is presented. The direct SEM observation during the instrumented compression testing allows for very efficient positioning and assessment of the failure mechanism. Compression tests on micromachined Si pillars with volumes down to 2 μm3 are performed inside the SEM, and the results demonstrate the potential of the method. In situ observation shows that small diameter pillars tend to buckle while larger ones tend to crack before failure. Compressive strength increases with decreasing pillar diameter and reaches almost 9 GPa for submicrometer diameter pillars. This result is in agreement with earlier bending experiments on Si. Difficulties associated with precise strain measurements are discussed.
Micro-bending and micro-compression experiments that were conducted on single crystal oriented copper (Cu) specimens to determine its mechanical properties are discussed. Both kinds of experiments exhibited a strong size effect on the flow stress with decreasing sample size. The exponents of a power-law fitted to the experimental data were found to be -0.8 for the micro-bending specimen and 0.4 for the micro-compression specimen. Models proposed in the literature dealing with dislocation starvation, dislocation nucleation, and dislocation pile-up were discussed. The damaged surface due to the Ga+ ion bombardment during focused ion beam (FIB) preparation was investigated using Auger electron microscopy. The results of the experiments show that the substantial depth of implantation up to 35 nm and Ga content reaching 20% may cause dislocation pile-ups, which in turn would alter the deformation behavior expected compared the undamaged Cu.
Mechanical testing of micron-size samples provides distinct advantages over macroscopic testing for quantifying the fundamental processes governing plastic flow, such as the exploration of intrinsic size effects and direct, quantitative measures of strain heterogeneity and intermittency. Future advances include an expanded range of testing and data acquisition parameters, including spatially-localized displacement measurements. (c) 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Recent experimental studies have revealed that micrometer-scale face-centered cubic (fcc) crystals show strong strengthening effects, even at high initial dislocation densities. We use large-scale three-dimensional discrete dislocation simulations (DDS) to explicitly model the deformation behavior of fcc Ni microcrystals in the size range of 0.5–20 μm. This study shows that two size-sensitive athermal hardening processes, beyond forest hardening, are sufficient to develop the dimensional scaling of the flow stress, stochastic stress variation, flow intermittency and high initial strain-hardening rates, similar to experimental observations for various materials. One mechanism, source-truncation hardening, is especially potent in micrometer-scale volumes. A second mechanism, termed exhaustion hardening, results from a breakdown of the mean-field conditions for forest hardening in small volumes, thus biasing the statistics of ordinary dislocation processes.
A method for in situ testing of miniaturized tension specimen was developed. The size effects of the plastic deformation behavior of copper single crystals loaded along the <-2 3 4> direction were investigated. The diameter was varied between 0.5 [mu]m and 8 [mu]m, and the aspect ratio, gauge length to side length, between 1:1 and 13.5:1. At high aspect ratios hardening was negligible. However, an increase of the flow stress with decreasing diameter was observed. This increase was small for diameters above 2 [mu]m, and somewhat larger below 2 [mu]m. These findings are explained by individual dislocation sources which govern the plastic deformation. For low aspect ratios the behavior is significantly different. A pronounced hardening and a very strong size effect was observed. Both are a result of dislocation pile-ups due to the constrained glide of the dislocations caused by the sample geometry.
Recent investigations have reported significantly higher flow stresses for microcompression compared to microtensile testing. To
clarify this point a load reversal test was performed on a microtensile specimen and equal flow stresses in tension and compression were observed. In contrast, if the lateral sample compliance constrains the deformation, microcompression testing overestimates the flow stresses. Additional contributions to the measured flow stresses stem from the aspect ratio of the sample and dislocation pile-ups.
Under stress, crystals irreversibly deform through complex dislocation processes that intermittently change the microscopic
material shape through isolated slip events. These underlying processes can be revealed in the statistics of the discrete
changes. Through ultraprecise nanoscale measurements on nickel microcrystals, we directly determined the size of discrete
slip events. The sizes ranged over nearly three orders of magnitude and exhibited a shock-and-aftershock, earthquake-like
behavior over time. Analysis of the events reveals power-law scaling between the number of events and their magnitude, or
scale-free flow. We show that dislocated crystals are a model system for studying scale-free behavior as observed in many
macroscopic systems. In analogy to plate tectonics, smooth macroscopic-scale crystalline glide arises from the spatial and
time averages of disruptive earthquake-like events at the nanometer scale.
The fundamental processes that govern plasticity and determine strength in crystalline materials at small length scales have been studied for over fifty years. Recent studies of single-crystal metallic pillars with diameters of a few tens of micrometres or less have clearly demonstrated that the strengths of these pillars increase as their diameters decrease, leading to attempts to augment existing ideas about pronounced size effects with new models and simulations. Through in situ nanocompression experiments inside a transmission electron microscope we can directly observe the deformation of these pillar structures and correlate the measured stress values with discrete plastic events. Our experiments show that submicrometre nickel crystals microfabricated into pillar structures contain a high density of initial defects after processing but can be made dislocation free by applying purely mechanical stress. This phenomenon, termed 'mechanical annealing', leads to clear evidence of source-limited deformation where atypical hardening occurs through the progressive activation and exhaustion of dislocation sources.
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