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Ion beam implantations are widely performed to understand the effects of irradiation-induced displacement damage on nuclear structural materials. However, the volume of material that can be investigated is often limited by the maximum energies of accelerator facilitates, leading to a limitation in the thickness of samples whose mechanical properties can be evaluated. The Lawrence Berkeley National Laboratory's 88-Inch Cyclotron offers a wide range of ions and energies, allowing for material ion implantations at larger scales than typical. Four HT-9 SS-J-geometry tensile specimens were polished and then irradiated with deuterons at the 88-Inch Cyclotron to doses of approximately 0.2 dpa prior to small scale tensile testing. The results from this study show irradiation hardening characterized by the tensile test results and black dot irradiation defects. Additionally, a comprehensive look at low temperature irradiations of high-Cr F/M steels is presented and our results show agreement with the available data.

A well-established methodology to capture interphases in heterogeneous materials is to replace them by a zero-thickness interface model. Commonly accepted interface models intuitively assume that to satisfy the angular momentum balance, interfaces must coincide with the mid-layer of their corresponding interphases. Recently, via adopting weighted averages, an extended general interface model has been developed that allows for arbitrary interface positions while fulfilling the angular momentum balance. This manuscript incorporates this novel interface model into the Mori–Tanaka method within the framework of homogenization. Analytical solutions are developed to determine effective properties as well as average local fields for fiber-reinforced and particle-reinforced composites. Computational simulations using the finite element method (FEM) are carried out to compare with the analytical solutions. Through a set of numerical examples, the significance of the interface position on the overall response of heterogeneous materials is highlighted. Our extended framework clarifies various ambiguous observations originating from the trivial assumption of restricting the interface position to the mid-plane. One advantage of the current interface model is that it covers both the elastic and cohesive interface models at its limits and therefore the analytical solutions are widely applicable regardless of the interface type. A. Javili gratefully acknowledge the support provided by Scientific and Technological Research Council of Turkey (TÜBITAK) Career Development Program, grant number 218M700.

Although presenting attractive features in dealing with small-scale size effects, strain gradient plasticity (SGP) theories can lead to uncommon phenomena for some boundary value problems. Almost all non-incremental (Gurtin-type) SGP theories including thermodynamically-consistent higher-order dissipation predict elastic gaps under certain non-proportional loading conditions. An elastic gap is defined as a finite change in the equivalent yield stress after an infinitesimal change in the strain conditions, at the occurrence of the non-proportional loading source. The existence of such gaps in reality is largely questioned and represents a major source of uncertainty preventing the development of robust SGP theories for real small-scale applications. Using 3D discrete dislocation dynamics (3D-DDD), the present paper aims at investigating size effects within micron-scale single crystal structures under various non-proportional loading conditions, including tension-compression-passivation, bending-passivation and tension-bending. An in-depth investigation of the occurrence of elastic gaps under these conditions, which are known to entail such gaps when using classical non-incremental SGP theories, is conducted. The obtained 3D-DDD results reproduce well known experimentally confirmed size effects like Hall-Petch effect, Asaro’s type III kinematic hardening and reversible plasticity. However, no evidence of the phenomenon of elastic gaps is found, which constitutes a first indication that this phenomenon may not exist in reality. The simulations are performed on face-centered cubic (FCC) Nickel single grains with cuboid shapes ranging from 2 microns to 15 microns and different orientations. Agence Nationale de la Recherche (ANR-20-CE08-0010)

Growth and advancement in modern technologies and requirement of miniaturized parts in various field of manufacturing has attracted several micro fabrication processes. Advancements in micro manufacturing has grown tremendously and development in micro metallic parts are very much welcomed due to the high demand of micro parts by manufacturing industries for their ability to withstand difficult working conditions. With the miniaturization of parts and process, the so-called size effects influence the micro manufacturing process. Different categories of size effects, their nature of involvement during downscaling and their effects are discussed in this article. Influence of size effects based on materials used, process conditions, downscaling and other parameters affecting the production of micro parts especially focusing on micro hydroforming process and micro deep drawing process are studied through literature and discussed in detail.

International audience; Mechanical properties in tension of cobalt have been studied in a wide range of grain size d using thickness t of samples from 125 to 700 μm. The Hall and Petch (HP) relationship indicates that the yield stress strongly varies for t/d below a critical value around 14, highlighting the existence of a multicrystalline regime. The behavior becomes almost single crystalline when t/d is lower than 2.5, with a very small HP slope. The reduction of the t/d ratio has also a large influence on the work hardening of cobalt, especially in the beginning of plasticity, which mainly corresponds to the stage of basal slip mechanisms. However, these size effects tend to vanish when twinning becomes predominant. Nanoindentation measurements and application of a simple composite model show that the appearance of the multicrystalline regime is closely related to surface effects that develop through the thickness of the specimens. In addition, the Kocks - Mecking work hardening model predicts a significant increase of the average free path of dislocations in the basal slip stage. A quantitative analysis of dislocation pile-ups that develop during this stage supports the hypothesis that the mechanical softening observed in cobalt multicrystal is related to a higher activity of dislocations, which can escape more easily on free surfaces. When twinning becomes the main deformation mechanism, dislocation glide is restricted which reduced, in turn, the surface effect. Consequently, size effects gradually disappear with hardening.

Noticeable voltage shifts have been observed in the charge/discharge profiles of a three-electrode cell with a lithium metal reference electrode and having a deeply lithiated iron oxide (Fe/Li2O) negative electrode galvanostatically cycled in a limited potential range against a positive LiFePO4 counterpart. The origin of such shifts has been attributed to charge storage anomalies in the Fe/Li2O nanocomposite due to characteristic reduced Fe nanoparticle sizes. These shifts also affected the extreme points of the voltage profiles of the positive electrode, which was also independently monitored. A combined evaluation of voltage profile slippages with possible changes in internal resistance and/or Li+ inventory loss, including an aimed analysis of current interruptions at the end of each lithiation/de-lithiation half-cycle to monitor the internal resistance and diffusion resistance coefficient of the Fe/Li2O electrode, has enabled a clarification of its altered charge storage. An asymmetric behaviour of the Fe/Li2O electrode during Li+ uptake/release has been revealed, highlighting a progressive, diffusion-controlled-type voltage drift at low potentials vs. Li+/Li, and an unusual tendency to slight oxidation with capacitive variations during the reverse electrochemical processes at higher voltages, instead.

In the context of strain gradient plasticity (SGP), description of higher-order dissipation is the subject of extensive on-going discussions. In most existing SGP theories including thermodynamically-consistent higher-order dissipation, higher-order dissipative processes are described based on the decomposition of the higher-order stresses into recoverable and unrecoverable parts. This higher-order stress decomposition represents the basis of the so-called non-incremental (Gurtin-type) SGP theories, which are the most commonly used in the literature. As formulated, these theories satisfy the thermodynamic requirement of non-negative dissipation. However, they generally lead to unusual effects for some boundary value problems, such as the occurrence of elastic gaps under non-proportional loading conditions. The present work proposes an alternative way to describe higher-order dissipative effects, with an illustration within strain gradient crystal plasticity (SGCP) framework. Inspired by rheological models in series like Maxwell model, the higher-order stress decomposition is replaced by a decomposition of the plastic slip gradients into recoverable and unrecoverable parts. Effects of this decomposition technique are studied and compared with those obtained using higher-order stress decomposition. Capabilities of such a technique to deal with elastic gaps are also investigated. Agence nationale de la recherche : ANR-20-CE08-0010 (Projet SGP-GAPS)

The influence of the ratio between specimen thickness () and grain size () on the tensile and fatigue properties of plain and notched aluminium plate specimens has been studied. Grain sizes ranging from 66 m to 9.74 mm have been prepared and used in the tests. The observed decrease on tensile properties when is comparable, or even exceeds, can be accounted for by adding an additional negative exponential term to the Hall–Petch equation. An exponential decrease has also been found in endurance limits as grain size approaches plate thickness in plain specimens. In notched specimens, however, increasing grain size has two opposing effects, namely: a decrease in the plain endurance limit associated with the decrease in thickness relative to grain size and an increase in notched fatigue strengths brought about by a decrease in notch sensitivity.

peer-reviewed The full text of this article will not be available in ULIR until the embargo expires on the 28/03/2021 Inelastic deformation of a high-strength martensitic steel (P91) is investigated using a strain gradient crystal plasticity model implemented using the finite element method. Voronoi tessellation is used to model the hierarchical structure, prior austenite grain (PAG)/packet/block, of the martensitic steel and the effect of PAG/packet/block size on the macro- and micro-scale mechanical response is analysed numerically. The role of lath interaction and the influence of dislocation type (statistically stored and geometrically necessary dislocations) are investigated. It is found that block size determines the overall mechanical response, consistent with the Hall-Petch relation, while packet and block diameters influence the microplastic strain distribution. A modified Hall-Petch relation is examined which provides a relationship between material flow strength and block diameter (size) which holds for a wide range of initial dislocation densities and block diameters peer-reviewed

Monocrystalline, cast aluminium microwires of diameter (D) below 25 mu m free of micromilling artefacts are annealed under protective atmosphere. Annealing increases the flow stress of all tested microwires, by an amount that is found, in a Haasen plot of measured activation area values, to be an athermal contribution to the flow stress that is attributed to surface oxide layer thickening. Microwires oriented for single slip with D similar to 14 mu m behave as do as-cast microwires with D similar to 7 mu m, showing a transition to higher and more stochastic flow stress values; this effect is attributed to a greater scarcity of dislocation sources after annealing. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd.

The yield surface in crystal plasticity can be approached from various directions during mechanical loading. We consider the competition between nanoindentation and tensile loading towards plastic yielding. For this purpose, we develop a two-dimensional discrete dislocation model that is then utilized to investigate the hardness and pop-in event statistics during nanoindentation of single crystal under tensile pre-stress. Indentation is performed by using cylindrical (circular in 2D) indentation with varying radius and under both displacement and load control. Tensile in-plane stress, varying from zero to yield strength, is assigned to investigate the effect of pre-stress on hardness and pop-in statistics. At small indentation depths, the measured hardness is found to be smaller for larger tensile pre-stress; therefore, we conclude that nanoindentation can be used to detect plasticity. When indentation depth is larger, the effect of pre-stress is barely seen. Moreover, we discuss event statistics and the related effect of pre-stress., 27 pages, 13 figures

The present study aims to quantify the influence of void size effect on crack initiation and growth in mode I tearing of large ductile plates. Specifically, the aim is to demonstrate how size effects influence the transition from crack initiation to steady-state tearing and reveal the evolution in both the traction-separation relation and the fracture energy dissipated in the tearing process when related to large-scale cohesive modeling. The study investigates mode I tearing by adopting the gradient enriched Gurson-Tvergaard-Needleman (GTN) model by Niordson and Tvergaard (2019), where the novelty lies in accounting for strain gradient hardening near growing micro-voids in relation to large-scale plate tearing. The steady-state crack growth conditions are compared to a 2D plane strain model setup, while the transition from crack initiation to steady-state is analyzed using full 3D plate tearing calculations. A discussion about the 2D versus 3D models’ capability, their differences, and agreement is presented. The results are related to the traction-separation relations fit for efficient large-scale simulations, e.g., using cohesive zone modeling. The present study shows that the material length parameter incorporated into the constitutive model has a negligible impact on the onset of plate thinning (or necking) but delays the onset of shear localization and, thus, increases the total cohesive fracture energy.

The fundamental equations for Form II of Mindlin's second strain gradient elasticity theory for isotropic materials are first derived. A corresponding simplified formulation is then proposed, with six and two higher-order material parameters for the strain and kinetic energy, respectively. This simplified model is still capable of accounting for free surface effects and surface tension arising in second strain gradient continua. Within the simplified model, at first, surface tension effects appearing in nano-scale solids near free boundaries are analyzed. Next, a thin strip under tension and shear is considered and closed-form solutions are provided for analyzing the free surface effects. Expressions for effective Poisson's ratio and effective shear modulus are proposed and found to be size-dependent. Most importantly, for each model problem a stability analysis is accomplished disallowing non-physical solutions (befallen but not exclusively disputed in a recent Form I article). Finally, a triangular macro-scale lattice structure of trusses is shown, as a mechanical metamaterial, to behave as a second strain gradient continuum. In particular, it is shown that initial stresses prescribed on boundaries can be associated to one of the higher-order material parameters, modulus of cohesion, giving rise to surface tension. For completeness, a numerical free vibration eigenvalue analysis is accomplished for both a fine-scale lattice model and the corresponding second-order continuum via standard and isogeometric finite element simulations , respectively, completing the calibration procedure for the higher-order material parameters. The eigenvalue analysis confirms the necessity of the second velocity gradient terms in the kinetic energy density .

The plane problem of a loaded Euler-Bernoulli beam of finite length in frictionless bilateral contact with a microstructured half-plane modelled by the couple stress theory of elasticity is considered here. The study is aimed to investigate the size effects induced on the beam internal forces and moments by the contact pressure and couple stress tractions transmitted across the contact region. Use is made of the Green’s functions for point force and point couple applied at the surface of the couple stress elastic half-plane. The problem is formulated by imposing compatibility of strain between the beam and the half-plane along the contact region and three alternative types of microstructural contact conditions, namely vanishing of couple stress tractions, vanishing of microrotations and compatibility between rotations of the beam cross sections and microrotations of the half-plane surface. The first two types of boundary conditions are usually assumed in the technical literature on micropolar materials, without any sound motivation, although the third boundary condition seems the most correct one. The problem is thus reduced to one or two (singular) integral equations for the unknown distributions of contact pressure and couple stress tractions, which are expanded in series of Chebyshev orthogonal polynomials displaying square-root singularity at the beam ends. By using a collocation method, the integral equations are reduced to a linear algebraic system of equations for the unknown coefficients of the series. The contact pressure and couple stress along the contact region and the shear force and bending moment along the beam are then calculated under various loading conditions applied to the beam, varying the flexural stiffness of the beam and the characteristic length of the elastic half-plane. The size effects due to the characteristic length of the half-plane and the implications of the generalized contact conditions are illustrated and discussed.

The present work investigates a new approach to formulating a rate-independent strain gradient theory for crystal plasticity. The approach takes as offset recent discussions published in the literature for isotropic plasticity, and a key ingredient of the present work is the manner in which a gradient enhanced effective slip measure governs hardening evolution. The effect of both plastic strains and plastic strain gradients are combined into this scalar effective slip quantity, the energy associated with plastic strain is dissipative (unrecoverable), while the energy from plastic strain gradients is recoverable (free). The framework developed forms the basis of a finite element implementation and is demonstrated on benchmark problems designed to bring out effects such as strengthening and hardening. Monotonic loading and plane strain deformation is assumed throughout, but despite this, non-proportional straining is predicted in the plastic regime even under pure shear conditions. Results of single slip and symmetric double slip reveal that strengthening and hardening are governed by the slip system orientation and the material length parameter only.

A crystal plasticity computational framework is developed and validated to investigate the microstructure sensitivity of crack initiation in fretting. Randomly distributed microstructure geometries are incorporated into a partial-slip finite element fretting model. The number of cycles to fretting crack initiation is shown to be sensitive to average grain size and microstructure morphology. Scatter in the number of cycles to crack initiation is shown to increase as the number of grains across the contact width decreases due to statistical size effects. Average number of cycles to crack initiation is shown to increase with decreasing number of grains in the contact. Microstructure morphology is shown to have a negligible influence on the effect of stroke for the partial slip cases considered here. Irish Research Council (GOIPG/2014/549) peer-reviewed 2018-09-20

Wire drawing processes at the micron scale have received increased interest as micro wires are increasingly required in electrical components. It is well-established that size effects due to large strain gradient effects play an important role at this scale and the present study aims to quantify these effects for the wire drawing process. Focus will be on investigating the impact of size effects on the most favourable tool geometry (in terms of minimizing the drawing force) for various conditions between the wire/tool interface. The numerical analysis is based on a steady-state framework that enables convergence without dealing with the transient regime, but still fully accounts for the history dependence as-well as the elastic unloading. Thus, it forms the basis for a comprehensive parameter study. During the deformation process in wire drawing, large plastic strain gradients evolve in the contact region. This creates a need for a higher order plasticity theory to accurately predict the material behaviour across the multiple scales involved. The present study reveals that the contribution from an energetic (recoverable) length parameter is limited, while the corresponding dissipative contribution dominates and tends to shift the drawing force to a higher level. As a direct consequence, the strain gradient hardening effect reduces the most favourable tool angle of a sharp tool with up to 50% (in terms of the required drawing force), whereas a circular shaped tool is proven less sensitive to scaling effects. By considering the contact force profile between tool and material it becomes clear that the strain gradients have a smoothing effect and both the magnitude and position of the peak pressure are affected significantly. A round tool is found to reduce the peak force, while the location of the peak is found to move from outlet to inlet depending on the tool geometry.

In this paper the SED-approach is applied to a set of experimental data reported in the literature. Data are referred to mixed mode fracture resistance of Guiting Limestone, a sedimentary soft rock. Two types of specimens have been investigated: cracked Brazilian disk (BD) specimens under diametral compression and edge cracked semicircular bend (SCB) specimens under three-point bend loading. To evaluate size dependent behavior, specimens characterized by four different radii were tested under different mode mixities. To assess the static strength of cracked components the strain energy density (SED) criterion has been used. It is shown that this criterion can predict the size-dependent fracture behavior of Guiting Limestone. Critical experimental loads have been compared with the theoretical ones, estimated keeping constant the critical value of strain energy density (SED). The dimension of the control volume was found to be a function of specimen size and geometry.

Under longitudinal compressive loading, periodically layered composites are prone to micro-buckling, which is often the decisive mechanism determining their strength. This paper is concerned with the load carrying capacity of structures made of layered composites with respect to micro-buckling related failure in regions of stress concentrations. A series of parametric studies show the effect of non-uniform stress distributions due to bending loads and the presence of geometrical features such as notches and holes on the initiation of micro-buckling. The contribution of the bending stiffness of the reinforcing layers on the resistance against micro-buckling introduces a dependence on the layer thickness, resulting in size-scale dependent strength limits. Therefore, both the shape and dimensions of the considered geometrical features and the layering thickness of the micro-structure are varied as part of the parametric studies. Moreover, the impact of imperfections in the composite micro-structure on the strength of the considered specimens is investigated.

The concept of translaminar fracture toughness of 0° plies has enabled the development of a considerable number of ply-level numerical models for structural failure of laminated composites. Using thin-ply pre-pregs, this paper demonstrates that this translaminar toughness is not an absolute, but rather in-situ, property and depends strongly on the 0° ply-block thickness, even in situations where delamination and diffuse damage are inhibited. We used two different grades of a thin-ply carbon-epoxy system to produce four different 0° ply-block thicknesses ranging from 0.03 mm to 0.12 mm, and measured the respective translaminar fracture toughness using compact tension tests. SEM and X-ray analysis showed no delamination nor diffuse damage. Yet, the translaminar fracture toughness increased from 46 to 104 kJ/m2 (initiation), and from 49 to 160 kJ/m2 (propagation), for the thickness range above. This finding has significant implications for the development and use of ply-level numerical failure models, for structural design with thin-ply composites, and for the development of thin-ply material systems.

Size effects in metal plasticity are widely accepted, and different theoretical approaches to handle the phenomenon are developing in the literature. The present work considers the Fleck and Willis (2009b) framework, and creates a new gradient enhanced rate-independent crystal plasticity FE-implementation. The study considers both energetic and dissipative gradient hardening and strengthening, and adopts a general form of the gradient enhanced effective slip rate. Monotonic and cyclic shearing of an infinite crystal slab containing a single slip system at an angle of 90° to the loading direction is a first benchmark case. A second case considers combined shear and tension in 2D of a constrained HCP single crystal. The HCP crystal is loaded in its basal plane by a so-called butterfly deformation path that inflicts repeated loading and unloading of the three crystallographic slip systems. Finally, the evolution and interaction of multiple plastic zones are demonstrated by considering a notched tensile sample. A direct comparison to visco-plastic (rate-dependent) simulations confirms that the proposed crystal plasticity framework forms a rate-independent limit for the gradient enhanced Fleck–Willis theory. The model response also reduces to that of conventional crystal plasticity in the limit of zero length parameters.

Creep properties of bulk materials are generally independent of the size of the materials. However, this is probably not true in submicron-thick metallic films. Thin films have a large surface-area-to-volume ratio compared with bulk counterparts, and films formed by vapor deposition generally consist of fine grains of size comparable with the film thickness. As surfaces and grain boundaries are favorable paths of diffusion, time-dependent deformation, i.e., creep, easily occurs in thin films even at room temperature. Another influencing factor is the surface tension which resists tensile creep deformation though the effect is negligible in a bulk. Owing to these effects, the creep properties of thin films are different from those of bulk counterparts and expected to show strong thickness dependence. On the other hand, as thin films generally have large dimensions except for the film thickness, creep fracture will be induced by crack propagation in the in-plane direction. Hence, it is important to clarify the creep crack propagation properties and the thickness effects of metallic thin films. For bulk metals, many experimental studies have confirmed that the creep J-integral J * is the effective parameter dominating creep crack propagation rate d a /d t under the large scale creep (LSC) condition. However, to the best of the authors’ knowledge, no experimental studies have been conducted on the creep crack propagation of submicron metallic films, and hence the validity of using fracture mechanics for such films has not been verified. The objective of this study is to clarify the creep crack propagation properties and the thickness effects of submicron gold (Au) films. We conducted creep crack propagation experiments on freestanding specimens with a center notch at room temperature. In the creep crack propagation experiments of the ~230 nm and ~400 nm-thick Au films, a crack began to propagate from the notch root, and the crack propagation rate d a /d t decreased in the very early stage. Then, its stable crack propagation was accompanied by large creep deformation in almost the entire crack propagation stage. The d a /d t was neither uniquely characterized by the stress intensity factor nor the net stress. Finite element analyses considering the creep of the film confirmed that the cracks in the experiments propagated under the steady-state or the LSC condition in almost the entire crack propagation stage. The steady-state creep J-integral J * s was estimated by an approximate equation using the experimental crack center opening displacement rate. The d a /d t - J * s relations were observed within a narrow band regardless of the specimen width and applied stress. The results indicated that the creep J-integral is the dominant mechanical parameter characterizing the creep crack propagation rate of the Au films. No significant differences in the d a /d t - J * s relations were recognized in both the specimens with thicknesses ~230 nm and ~400 nm.

The effects of a torque on a cylindrical bar, either solid or hollow, made of an anisotropic micropolar linear elastic material are analyzed. The elastic properties are supposed to be invariant along the cylinder axis. One of the principal directions of the material elasticity tensors is parallel to the cylinder axis; the other two are arbitrarily rotated in the plane of any cross-section of the bar. Closed-form, approximate solutions are obtained if the material internal length is much smaller or much larger than the cylinder outer radius; the latter solution applies for particular orientations of the material symmetry axes. In the general case, only numerical solutions of the governing equations can be derived. A parametric study is carried out on the effect of different parameters (material internal length, orientation of the symmetry axes, etc.) on the stress distribution and the torsional rigidity of the cylinder. The size effects associated with the material internal length are pointed out in terms of torsional rigidity, both for solid and hollow cylinders.

International audience; The present paper proposes a flexible Gurtin-type strain gradient crystal plasticity (SGCP) model based on generalized non-quadratic defect energy and uncoupled constitutive assumption for dissipative processes. A power-law defect energy, with adjustable order-controlling index n, is proposed to provide a comprehensive investigation into the energetic length scale effects under proportional and non-proportional loading conditions. Results of this investigation reveal quite different effects of the energetic length scale, depending on the value of n and the type of loading. For n ≥ 2, regardless of the loading type, the energetic length scale has only influence on the rate of the classical kinematic hardening, as reported in several SGCP works. However, in the range of n < 2, this parameter leads to unusual nonlinear kinematic hardening effects with inflection points in the macroscopic mechanical response, resulting in an apparent increase of the yield strength under monotonic loading. More complex effects, with additional inflection points, are obtained under non-proportional loading conditions, revealing new loading history memory-like effects of the energetic length scale. Concerning dissipation, to make the dissipative effects more easily controllable, dissipative processes due to plastic strains and their gradients are assumed to be uncoupled. Separate formulations, expressed using different effective plastic strain measures, are proposed to describe such processes. Results obtained using these formulations show the great flexibility of the proposed model in controlling some major dissipative effects, such as elastic gaps. A simple way to remove these gaps under certain non-proportional loading conditions is provided. Application of the proposed uncoupled formulations to simulate the mechanical response of a sheared strip has led to accurate prediction of the plastic strain distributions, which compare very favorably with those predicted using discrete dislocation mechanics.

International audience; Two analytical approaches are developed to determine the overall size-dependent response of composites embedding general interfaces. The first approach extends the composite sphere assemblage (CSA) approach and the generalized self-consistent method (GSCM) to account for the general interface model resulting in new bounds and estimates on the macroscopic properties of particulate composites. In the second approach, we develop an interface-enhanced Mori–Tanaka method that not only determines the effective properties but also provides the state of the stress and strain in each phase of the medium. The general interface model captures both elastic and cohesive interface models. Computational analysis is carried out using the finite element method to verify the analytical results. A remarkable agreement between the proposed analytical solutions and the computational results is obtained. A thorough parametric study is carried out to shed light on the role of the general interfaces in the overall behavior of composites. Motivated by the numerical and analytical findings, the material behavior is found to be bounded. Thus, two notions of ultimate bounds and size-dependent bounds are introduced and discussed.

Discrete dislocation plasticity (DDP) analysis of the high-temperature cyclic deformation of two- phase composites comprising a plastic matrix and elastic precipitates is presented. Deformation of the matrix is by climb-assisted glide of dislocations while the precipitates deform by a combination of bulk elasticity and stress-driven interfacial diffusion. The DDP calculations predict a cyclically softening response due to the formation of dislocation cell structures within the matrix. The dislocation cell sizes decrease with decreasing size of the unit cell (or equivalently matrix channels) and this results in an increased cyclic softening rate in composites with smaller unit cells. Interfacial diffusion also enhances the formation of dislocation cell structures and thereby promotes cyclic softening. These results are consistent with predictions of the creep behaviour that indicate that the increase in the creep rate (i.e. tertiary creep) is also associated with the formation of dislocation cell structures within the matrix.

In this work, we have focused on the size dependence of the magnetic properties and the surface effects of CoFe2O4 nanoparticles synthesized by high-temperature chemical method with diameter d~2, 4.5, and 7 nm, with narrow size distribution. transmission electron microscopy (TEM) images and X-ray diffraction (XRD) profiles indicates that samples with 7 and 4.5 nm present a high crystallinity while the 2 nm sample has a poor one. We have investigated by magnetization measurements and in-field Mössbauer spectroscopy the influence of the surface in the internal magnetic order of the particles. Particles with d=7 nm have almost single domain behavior and the monodomain occupies approximately the whole particle. In the sample with d=4.5 nm the surface anisotropy is large enough to alter the ferrimagnetic order in the particle shell. Then, a surface/volume ratio of ~60% is the crossover between a single domain nanoparticle and a frustrated order in a magnetic core-shell structure, due to the competition between surface anisotropy and exchange interaction+crystalline anisotropy in cobalt ferrite. In the d=2 nm sample the poor crystallinity and the large surface/volume ratio avoid the ferrimagnetic order in the particle down to T=5 K. Fil: Pianciola, Betiana Noelia. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina Fil: Lima, Enio Junior. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina Fil: Troiani, Horacio Esteban. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina Fil: Nagamine, Luiz C.C.M.. Universidade de Sao Paulo; Brasil Fil: Cohen, R.. Universidade de Sao Paulo; Brasil Fil: Zysler, Roberto Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina

In 2014, with increasing use of multi-purpose, tablets remain the leading entry points of mobile connectivity for global consumers. It is expected to see more competitive overlap among display sizes for tablet PCs, notebook PCs, and smartphones. In fact, no matter what type of task is applied, the size effect impacts productivity, portability and user's experience of device usage on any form factors of mobile devices. However, research seldom studied the size effects regarding the trade-offs between performance and portability of tablets. To further investigate the size effects of the display and touchscreens on their performances, this study compared the operation time and error rate for the touch-input methods of 3 different sizes of tablets in 3 applied tasks. Our lab's study on the usage of tablets showed that browsing the Internet, shopping online, watching videos, viewing and editing email (words processing and/or photos sharing) were the most common applications mostly using online real-time communication software, Internet browsers and other related software. This result was used as the base to design the applied tasks of the present study. Accordingly, the software and task types were divided into multi-direction pointing and tapping, multi-direction dragging and dropping, and on-screen typing. Overall, it seems that the closer the sizes of displays and on-screen keyboards to those sizes of a generic laptops, the shorter the operation times. As these objective measures confirmed by the subjective assessments, the 10.1” tablets was most preferred; while the differences in the satisfactions were not significant among the three tablets. The results rationalized the phenomena in the tablet PC market that the 8.1” and 10.1” diagonal screens were popular especially for applied tapping tasks (e.g., Internet browsing) and on-screen typing tasks (e.g., word processing for email messages), respectively.

Large-scale thin-walled structures with a low weight-to-stiffness ratio provide the means for cost and energy efficiency in structural design. However, the design of such structures for crash and impact resistance requires reliable FE simulations. Large shell elements are used in those simulations. Simulations require the knowledge of the true stress–strain response of the material until fracture initiation. Because of the size effects, local material relation determined with experiments is not applicable to large shell elements. Therefore, a numerical method is outlined to determine the effect of element size on the macroscopic response of large structural shell elements until fracture initiation. Macroscopic response is determined by introducing averaging unit into the numerical model over which volume averaged equivalent stress and plastic strain are evaluated. Three different stress states are considered in this investigation: uniaxial, plane strain and equi-biaxial tension. The results demonstrate that fracture strain is highly sensitive to size effects in uniaxial tension whereas in plane strain or equi-biaxial tension size effects are much weaker. In uniaxial and plane strain tension the fracture strain for large shell elements approaches the Swift diffuse necking condition.

Experiments on soft polycrystalline aluminum have yielded evidence that, besides the required punch load, both the size and shape of imprinted features are affected by the scale of the set-up, e.g. substantial details are lost when the characteristic length is on the order of 10 μ m . The objective of this work is to clarify the role played by strain gradients on this issue, and to shed light on the underlying mechanisms. For this, indentation by a periodic array of flat punch indenters is considered, and a gradient enhanced material model that allows for a numerical investigation of the fundamentals are employed. During a largely non-homogeneous deformation, the material is forced up in between the indenters so that an array of identical imprinted features is formed once the tool is retreated. It is confirmed that the additional hardening owing to plastic strain gradients severely affects both the size and shape of these imprinted features. In particular, this is tied to a large increase in the mean contact pressure underneath the punch, which gives rise to significant elastic spring-back effects during unloading.

In this paper, using time series data for the period 2 January 1998 to 31 December 2008 for 560 firms listed on the NYSE, we examine whether firm volatility is related to market volatility. The main contribution of this paper is that we develop an analytical framework motivating the firm-market volatility relationship. We present three new findings on volatility. First, we discover significant evidence of common volatility; for 12 out of 14 sectors, market volatility has a statistically significant effect on firm volatility for at least 50 percent of firms. Second, we discover significant evidence of size effects: for small-sized firms, there is weak evidence of commonality in volatility, while for large-sized firms there is high evidence (for as much as 75 percent of firms) of commonality in volatility. Third, we find that market volatility predicts firm volatility for firms belonging to five of the 14 sectors.

The translaminar fracture toughness of fibre-reinforced composites is a size-dependent property which governs the damage tolerance and failure of these materials. This paper presents the development, implementation and validation of an original analytical model to predict the tensile translaminar (fibre-dominated) toughness of composite plies and bundles, as well as the associated size effect. The model considers, as energy dissipation mechanisms, debonding and pull-out of bundles from quasi-fractal fracture surfaces; the corresponding lengths are stochastic variables predicted by the model, based on the respective bundle strength distributions and fracture mechanics. Parametric studies show that composites are toughened by stronger fibres with large strength variability, and intermediate values of interfacial toughness and friction. Predictions are validated against four different composite ply systems tested in the literature, proving the model’s ability to capture not only size effects, but also the influence of different fibres and resins.

The plastic deformation of metals is the result of the motion and interaction of dislocations, line defects of the crystalline structure. Continuum models of plasticity, however, remain largely phenomenological to date, usually do not consider dislocation motion, and fail when materials behavior becomes size dependent. In this work we present a novel plasticity theory based on systematic physical averages of the kinematics and dynamics of dislocation systems. We demonstrate that this theory can predict microstructure evolution and size effects in accordance with experiments and discrete dislocation simulations. The theory is based on only four internal variables per slip system and features physical boundary conditions, dislocation pile ups, dislocation curvature, dislocation multiplication and dislocation loss. The presented theory therefore marks a major step towards a physically based theory of crystal plasticity.

The deformation behavior of metal sheets is strongly influenced by the extent of miniaturization due to the size effects (specimen size and grain size). In this paper, the effect of thickness and grain size on the flow stress of very thin brass sheets has been investigated by conducting microstructural studies and uni axial tensile tests on annealed specimens of thickness in the range 50 μm-200 μm.To obtain a large variation in thickness to grain size (t/d) ratio, different combinations of annealing temperature and time have been chosen. The effect of t/d ratio on yield stress and flow stress has been analysed using the tensile test data. For larger values of t/d ratio (6 -18), yield strength and flow stress at different strain levels increased with increase in t/d ratio. But flow stress decreases with increasing t/d when the values of t/d ratio are less than 3 due to the size effects.

Recently there has been a major thrust to develop novel nanomaterials exhibiting unique properties. These nanostructures are envisioned as building blocks for the next generation of electronic and energy harvesting systems. In this context, identification of their size-dependent properties is essential, but due to challenges in nanoscale experimentation, unambiguous characterization of mechanical and electromechanical behavior has been elusive. However, in the past few years, in-situ experimentation has emerged as a powerful technique to overcome these challenges. Furthermore, the coupling of such experimental findings to atomistic simulations has shown to have the potential to reveal mechanistic insights, essential for the deep understanding of nanoscale behavior. Here, we present a summary of a few significant results obtained by our group using this approach. Specifically, we discuss size effects that influence the mechanical and electromechanical properties of metallic and semiconducting nanowires.

An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type, is shown to be governed by a thermodynamically consistent differential problem with proper constitutive boundary conditions. The new thermoelastic strategy is illustrated by investigating a set of examples. It is demonstrated that in nonisothermal statically indeterminate problems rather complex structural behaviours can appear and that both the shift of the neutral surface and nonlocality have a dominating influence at small-scales.

International audience; Mechanical size effects in Zr65Ni35 Thin Film Metallic Glass (TFMG) are studied with an emphasis on a transition in failure mechanisms occurring below 500 nm. XRD and TEM analyses of Zr65Ni35 TFMG confirm the absence of a crystalline phase. The thickness effect on the mechanical properties of Zr65Ni35 TFMGs is investigated using nanoindentation, Brillouin spectroscopy, and fracture tests. Brillouin spectroscopy shows no variation of the elastic constants, while the hardness - measured by nanoindentation - presents a continuous increase with decreasing film thickness. The fracture surface of the TFMGs involves corrugations which disappear when the thickness is reduced below 500 nm.

A geometrically non-linear framework for micro-to-macro transitions is developed that accounts for the effect of size at the microscopic scale. This is done by endowing the surfaces of the microscopic features with their own (energetic) structure using the theory of surface elasticity. Following a standard first-order ansatz on the microscopic motion in terms of the macroscopic deformation gradient, a Hill-type averaging condition is used to link the two scales. The surface elasticity theory introduces two additional microscopic length scales: the ratio of the bulk volume to the energetic surface area, and the ratio of the surface and bulk Helmholtz energies. The influence of these microscopic length scales is elucidated via a series of numerical examples performed using the finite element method.

International audience; The influence of dimensions on the mechanical behavior of f.c.c. single crystals with dimensions larger than a few micrometers has been the topic of many experimental investigations and controversies during the 1970s and this question is still open. The objective of this article is to shed new light on this point by performing finite element simulations thanks to a strain gradient crystal plasticity model. Based on the model identification for nickel, several single crystal samples with various thicknesses and orientations were tested numerically in tension. The effect of dimensions was then analyzed considering the spatial distribution of dislocation densities. Near loading boundaries, dislocation density gradients appeared perpendicular to the Burgers vector direction of the primary activated slip system which modified the mechanical behavior. These gradients are discussed in terms of boundary conditions, crystal orientation and dislocation interactions with surfaces.

The asymptotic expansion treatment of the homogenization problem for nonlinear purely mechanical or thermal problems exists, together with the treatment of the coupled problem in the linearized setting. In this contribution, an asymptotic expansion approach to homogenization in finite thermoelasticity is presented. The treatment naturally enforces a separation of scales, thereby inducing a first-order homogenization framework that is suitable for computational implementation. Within this framework two microscopically uncoupled cell problems, where a purely mechanical one is followed by a purely thermal one, are obtained. The results are in agreement with a recently proposed approach based on the explicit enforcement of the macroscopic temperature, thereby ensuring thermodynamic consistency across the scales. Numerical investigations additionally demonstrate the computational efficiency of the two-phase homogenization framework in characterizing deformation-induced thermal anisotropy as well as its theoretical advantages in avoiding spurious size effects. (C) 2012 Elsevier Ltd. All rights reserved.

International audience; Discrete dislocation plasticity models and strain-gradient plasticity theories are used to investigate the role of interfaces in the elastic–plastic response of a sheared single crystal. The upper and lower faces of a single crystal are bonded to rigid adherends via interfaces of finite thickness. The sandwich system is subjected to simple shear, and the effect of thickness of crystal layer and of interfaces upon the overall response are explored. When the interface has a modulus less than that of the bulk material, both the predicted plastic size effect and the Bauschinger effect are considerably reduced. This is due to the relaxation of the dislocation stress field by the relatively compliant surface layer. On the other hand, when the interface has a modulus equal to that of the bulk material a strong size effect in hardening as well as a significant reverse plasticity are observed in small specimens. These effects are attributed to the energy stored in the elastic fields of the geometrically necessary dislocations (GNDs).

The mechanical response of thin metallic films is simulated using a two-dimensional strain gradient plasticity finite-element model involving grain boundaries in order to investigate the effect of the thickness, grain shape and surface constraint on the strength, ductility and back-stress. The grain boundaries and surface layers are modeled as initially impenetrable to dislocations while allowing for relaxation at a critical stress level. The model captures the variation of the strength with grain size, film thickness, and with the presence or not of constraining surface layers, in agreement with experimental results on Al and Cu films. A decrease in the uniform elongation is predicted with decreasing film thickness due to a loss of strain-hardening capacity and the possible presence of imperfections. These two effects dominate over the stabilizing contribution of the plastic strain gradients. Accounting for the relaxation of the interface constraint affects the magnitude of the back-stress as well as the drop in ductility. Institute of Mechanics, Materials and Civil Engineering, Universite´ catholique de Louvain, 1348 Louvain-la-Neuve, Belgium b Universite´ Libre de Bruxelles, Building, Architecture & Town Planning Dept. (BATir) CP 194/02, Avenue F.D. Roosevelt 50, 1050 Bruxelles, Belgium

International audience; In this paper, the Cosserat multiparticle model (CM2) for 3D periodically layered materials is proposed in order to reproduce both size and boundary effects in these materials. This model can handle n- phase periodically layered materials with 4n+1 kinematic variables at each 3D geometric point: two in-plane displacements and two rotations per phase plus one common out-of-plane displacement. The model gives excellent agreement with full finite element results for out-of-plane shearing.

An analytical solution in couple stress elasto-plastic theory is presented for the pure bending beam under small deformation. This solution considers the effects of both elastic deformation and plastic deformation, and gives the relationship between the moment M and the curvature κ implicitly. This solution can eliminate the shortcomings in the rigid-plastic solutions by Stolken and Evans (1998), Chen and Wang (2000, 2001) et al., and is proved to be more effective in materials with high plastic hardening or small plastic deformation. Moreover, numerical results show that the solution can be used to predict the size effects in the microbend tests and to measure their material length parameter.

Lasers offer a reproducible and controllable energy input into a highly localized area. This enables lasers as flexible forming tools. Although mechanisms of laser forming are known in principle, the application of laser forming is limited due to a lack of understanding of the quantitative process analysis. The presented article shows how laser forming processes can overcome the limits of conventional thermal forming by means of laser shock forming and laser assisted free head forming. Furthermore a concept is presented how to optimize a thermal forming process with the help of scaling rules.

The nanocrystalline lead zirconate titanate (PZT) with the composition Pb(Zr0.53Ti0.47)O3 has been synthesized by mechanical activation, without calcination at intermediate temperature. The PZT powder that has been mechanically activated for 10, 20 and 30 h shows crystallite size of 15, 12 and 8 nm, respectively. Size effect on PZT formation, tetragonality factor and dielectric constant has been investigated in detail. TEM and AFM studies have been carried out to confirm the formation of nanocrystalline PZT. The temperature dependence of dielectric constant at different frequencies was also measured, to study the size effects in PZT ferroelectrics. The nanocrystalline PZT obtained by this route has high dielectric constant at Curie temperature in comparison to that prepared conventionally. � 2009 Elsevier B.V. All rights reserved.

The purpose of this paper is to develop a homogeneous, orthotropic couple-stress continuum model to take the place of the periodic heterogeneous cellular solids. Through generalizing the definition of the characteristic length for isotropic couple-stress continuum, four characteristic lengths are introduced as material engineering constants for such kind of continuum. In order to determine the effective moduli and the characteristic lengths of the effective couple-stress continuum, a Representative Volume Element (RVE) method is constructed. The effective properties are obtained based on the response of the RVE under prescribed boundary conditions, and our results agree with the analytical solutions in literature. In addition, the influences of the relative density, the topology, the size, and the properties of the solid material of cellular materials on the effective moduli as well as the characteristic lengths are discussed, respectively. Furthermore, the size effects in cellular solid beams are investigated using our effective couple-stress continuum model. The results show that the developed continuum model in this paper can precisely capture the size effects in cellular solids.

The grain size dependence of the flow strength of polycrystals is analyzed using plane strain, discrete dislocation plasticity. Dislocations are modeled as line singularities in a linear elastic solid and plasticity occurs through the collective motion of large numbers of dislocations. Constitutive rules are used to model lattice resistance to dislocation motion, as well as dislocation nucleation, dislocation annihilation and the interaction with obstacles. The materials analyzed consist of micron scale grains having either one or three slip systems and two types of grain arrangements: either a checker-board pattern or randomly dispersed with a specified volume fraction. Calculations are carried out for materials with either a high density of dislocation sources or a low density of dislocation sources. In all cases, the grain boundaries are taken to be impenetrable to dislocations. A Hall-Petch type relation is predicted with Hall-Petch exponents ranging from approximate to 0.3 to approximate to 1.6 depending on the number of slip systems, the grain arrangement, the dislocation source density and the range of grain sizes to which a Hall-Petch expression is fit. The grain size dependence of the flow strength is obtained even when no slip incompatibility exists between grains suggesting that slip blocking/transmission governs the Hall-Petch effect in the simulations. (c) 2007 Elsevier Ltd. All rights reserved.

In a recent publication, we derived the mesoscale continuum theory of plasticity for multiple-slip systems of parallel edge dislocations, motivated by the statistical-based nonlocal continuum crystal plasticity theory for single-glide due to Yefimov et al. (2004b). In this dislocation field theory (DiFT) the transport equations for both the total dislocation densities and geometrically necessary dislocation densities on each slip system were obtained from the Peach-Koehler interactions through both single and pair dislocation correlations. The effect of pair correlation interactions manifested itself in the form of a back stress in addition to the external shear and the self-consistent internal stress. We here present the study of size effects in single crystalline thin films with symmetric double slip using the novel continuum theory. Two boundary value problems are analyzed: (1) stress relaxation in thin films on substrates subject to thermal loading, and (2) simple shear in constrained films. In these problems, earlier discrete dislocation simulations had shown that size effects are born out of layers of dislocations developing near constrained interfaces. These boundary layers depend on slip orientations and applied loading but are insensitive to the film thickness. We investigate stress response to changes in controlled parameters in both problems. Comparisons with previous discrete dislocation simulations are discussed., Comment: 20 pages, 11 figures