Size Effects In Deformation Research Articles

Long-term strength and deformation size effect of gangue cemented backfill in acid mine water

The mine water environment can seriously affect the long-term strength and deformation of the backfill body, thereby affecting the stability of the goaf. In this study, the gangue cemented backfill (GCB) of different sizes were placed in different environments (air, water, single H2SO4 solution, and H2SO4 solution coupled with load), the deformation and ultrasonic pulse velocity (UPV) of specimens were recorded with age. The compressive strength, acoustic emission (AE), and resistivity of GCB during the uniaxial compression at 360 days were monitored. In addition, the microscopic morphology of GCB was observed by scanning electron microscopy (SEM), and the damage model of GCB in the process of uniaxial compression was established. The research showed that: the deformation of GCB was fast in the first 90 days and gradually slowed down. The bigger the size was, the greater the instantaneous creep of the GCB was, and the faster the increase rate of the initial deformation was. The UPV of eroded GCB experienced three stages of growth-stability-decrease. The UPV of the smaller GCB increased rapidly in the early stage and decreased rapidly in the later stage. At 360 days, the order of compressive strength of GCB in different media is: water > air > single H2SO4 solution > H2SO4 solution coupled with load, and the compressive strength decreases with the increase of specimen size. In the process of uniaxial compression, the larger the size of the GCB, the larger the number of AE rings detected. The smaller the size of GCB, the stronger the AE characteristics appeared in the initial compaction stage. During the loading process, the resistivity curve of GCB changed approximately in a “U” shape. The smaller the size of GCB, the slower the increasing rate of resistivity in the post-peak failure stage. The abrupt change in the AE ring and the stable resistivity stage could be used to predict the failure of the GCB. The research could provide a reference for the design of the erosion resistance of GCB.

Influence of silicide and texture on the room temperature deformation size effect of Ti65 alloy sheets/foils and its constitutive model modification

In micro-scaled plastic deformation process such as micro-forming, material size effect is challenging to investigate and reveal using traditional material models. Since high-temperature titanium alloys have become the critical materials of micro-parts depending on outstanding mechanical properties, studying the effect of texture and silicide precipitate on size effect in microtensile deformation of a high-temperature titanium alloy is of great significance because the size effect of highly alloyed titanium alloys has been less studied. In the present study, various heating treatments were performed to regulate grain size and texture and obtain silicide precipitate. The room temperature tensile tests were carried out to investigate the effect of the texture and silicide precipitate on the size effect of plastic deformation behaviour. It is revealed that silicide precipitation in the heat-treated specimens can lead to a more obvious “smaller is weaker” phenomenon and the specimens with transverse textures show a better strength–ductility match. In addition, considering solution strengthening, grain boundary strengthening and precipitation strengthening, the material constitutive model is modified by the effect of silicide and texture on the size effect, allowing for an accurate description of the tensile deformation characteristics at the microscopic scale. The results of the physical experiments and the hybrid constitutive model provide a basis for understanding and further exploration of the microscale plastic deformation behaviour of high-temperature titanium alloys.

Наноиндентирование и механические свойства материалов в субмикро- и наношкале. Недавние результаты и достижения (О б з о р)

The review discusses the details of various materials mechanical behavior in submicro- and nanoscale. Significant advances in this scope result from the development of wide family of load based precise nanotesting techniques called nanoindentation. But nowadays, nanomechanical properties are studied not only by nanoindentation techniques in narrow sense, i.e. local loading of macro, micro and nanoscale objects. Nanomechanical load testing is discussed here within a wider scope employing precise deformation measurement with nanometer scale resolution caused by various types of low load application to the object under study including uniaxial compression or extension, shearing, bending or twisting, optionally accompanied by in situ monitoring sample microstructure using scanning and transmission electron microscopy and Laue microdiffraction technique. The main courses of experimental techniques development in recent ten years along with the results obtained using them in single, poly and nano crystalline materials, composites, films and coatings, amorphous solids and such biomaterials as tissues, living cells and macromolecules are described. Special attention is paid to deformation size effects and atomic mechanisms in nanoscale. This review is a natural continuation and development of the review published at Fiz.Tverd.Tela vol.50, issue 12, 2008 of the same author that discusses details of nanomechanical properties of solids. Current review includes wider range of nanomechanical testing concepts and recent achievements in the scope. The work was supported by RFBR grant for project #19-12-50235.

The size dependent strength of Fe, Nb and V micropillars at room and low temperature

The strength of focussed ion beam (FIB) machined [001] orientation single crystal micropillars of body centred cubic structured (bcc) metals Fe, Nb and V, with diameters 200–5000 nm, have been measured at 296 K and 193 K using nanoindentation equipment. The metals have similar critical temperatures for screw dislocation mobility, Tc, close to 350 K. All three metals deform on the (110) plane at both test temperatures and show very similar behaviour of the plastic flow stress, σp, normalised by the shear modulus resolved on the slip plane, μ, as a function of pillar diameter, d, normalised by the Burgers vector, b. At room temperature all metals show a size effect on strength described by power law relation σp/μ=A(d/b)n with n ≈ −0.6 and this is shown to mirror the behaviour of face centred cubic metals. At 193 K the three metals show a higher strength and larger size exponent n ≈ −0.3 and again their normalised flow data is very similar. The behaviour is consistent with the observation that the deformation size effect in bcc materials converges to that seen with face centred cubic (fcc) structure metals as testing temperature approaches Tc. The temperature and size dependence of the experimental data shows similarity with the prediction of strength models based on the geometric confinement of dislocation sources (the single dislocation arm model) and a temperature dependent friction stress. However the model cannot consistently capture the behaviour for the three metals studied.

Quantitative modeling and characterization of the size effects in microscale coining process of copper

This paper investigated size effects of copper in microscale coining process. By comparing experimental results with finite element analysis (FEA), the type and contribution of size effects could be identified. We found that the deformation size effect is the most pronounced in microscale coining where grains must be introduced into relatively small die cavities through severe plastic deformation. The magnitude of the deformation size effect was determined by the relative ratio of the grain size to the die cavity, and smaller size factor produced greater effect. We also found that feature height in microscale coining was related to grain size and flow stress of the material. Therefore, size effects could be quantitatively modeled and compensated by calculating equivalent grain size and flow stress correction. After compensating for size effects, the FEA model could accurately predict material forming performance.

Constitutive model based on dislocation density and ductile fracture of Monel 400 thin sheet under tension

In micro-scaled plastic deformation, material strength and ductile fracture behaviors of thin sheet in tension are quite different from those in macro-scale. In this study, uniaxial tensile tests of Monel 400 thin sheets with different microstructures were carried out to investigate the plastic deformation size effect in micro-scale. The experimental results indicate that the flow stress and fracture strain departure from the traditional empirical formula when there are only fewer grains across the thickness. And the number of dimples on the fracture surface is getting smaller with the decreasing ratio of specimen thickness to grain size. Then, a constitutive model based on dislocation density considering the free surface effect in micro-scale is proposed to reveal the mechanism of the flow stress size effect. In addition, a model is proposed considering the surface roughening inducing the thickness nonuniform and the decrease of micro-voids resulting from the reduction of grain boundary density with the decreasing ratio of specimen thickness to grain size. The interactive effects of the surface roughening and the decrease of micro-voids result in the earlier fracture in micro tension of the specimen with fewer grains across the thickness.

Plastic deformation size effects in micro-compression of pure nickel with a few grains across diameter

In microscale, it is hard to predict the plastic deformation behaviors because of size effects. In this study, size effects on plastic deformation behaviors in micro-compression were investigated experimentally at room temperature, including flow stress and inhomogeneous deformation. It is found that the flow stress decreases with the increase of grain size when there are more than 6.2 grains across the specimen diameter. The flow stress tends to increase when there are only 3–4 grains across the specimen diameter. Then, a flow stress size effect model considering both free surface and constrained surface effects is developed to model the flow stress size effect in microforming. The calculated results are in good agreement with experimental ones. The influence of the ratio of specimen diameter to grain size on the flow stress size effect is revealed. The experimental results also indicate that the inhomogeneous deformation in micro-compression increases with the increase of grain size. The surface folding occurs on the surfaces of some specimens with a few grains across the diameter. Then, the surface folding phenomenon is studied through Electron Backscattered Diffraction (EBSD) and the proposed model considering the microstructure distribution on the specimen surface. The reported results and models provide a basis for understanding of the size effects on plastic deformation behaviors in microforming.

Deformation Size Effects Due to Specimen and Grain Size in Microbending

Sheet metal forming often consists of bending processes in which gradients of deformation exists through the thickness of the workpiece in a localized deformation area. In microscale bending, these deformation gradients become much steeper, as the changes in the deformation occur over short distances (in the order of micrometers). In addition, with miniaturization, the number of grains that are present through the thickness decreases significantly. In this research, the effect of grain size and specimen size on the deformation distribution through the thickness of microbent sheet specimens was investigated via microhardness evaluations. It was found that the deformation distribution, i.e., hardness profile, is not affected significantly by the grain size when the sheet thickness is large (for 1.625 mm specimens) or by miniaturization of the specimen size when the grain size is fine. However, the deformation distribution of the coarse grained specimens deviates from the fine grained ones and from the 1.625 mm thick sheet specimens when the specimen size is miniaturized.

RESEARCH ON THE EFFECT OF LOADING CONDITIONS ON THE STRENGTH AND DEFORMATION BEHAVIORS OF ROCKS

The paper aims at a numerical study of strength and deformation behaviors of rocks under different loading conditions in uniaxial compression with an elasto-plastic cellular automaton (EPCA2D) code. Two loading conditions, i.e. with and without considering frictions between loading platens and rock specimen's ends, are used in the failure processes of heterogeneous rocks. Rock specimens are assumed to be the same heterogeneity, i.e. the specimens with different sizes have the same probability of containing flaws. Under this condition, it is concluded that the strength and deformation behaviors of rocks are influenced by the heterogeneity a little. The mismatch of elastic properties of the platen and the rock in influencing the stress distribution at the ends of the specimen is the dominant cause for the so-called strength and deformation size effects, which in turn affects the final failure patterns of rocks.

Observations of flow in Inx Ga1-xAs multilayers

Work elsewhere has shown that the hardnesses of coherent InxGa1-xAs multilayer structures in which the misfit stresses are controlled by varying the indium content in each layer are influenced by the thicknesses and the coherency strains in the layers. These results have been interpreted in terms of the length-scale for flow being greater than the layer thickness and associated with deformation size effects. However, nanoindentation of InxGa1-x As suggests an influence of the flow stress of the individual layers on the overall multilayer flow stress. Consequently, initiation of flow in the weaker layer is expected. A deformed multilayer has been characterized by measurement of the lattice rotations measured from energy-filtered convergent beam electron diffraction (CBED) patterns recorded in scanning transmission electron microscopy (STEM) mode. Based on the movement of Kikuchi lines as a result of rotations of the lattice the local orientation of the crystal can be extracted, allowing the local orientations to be estimated. The small probe-size in CBED of ∼1 nm used here ensures the region sampled is smaller than the thickness of the individual layers. These measurements have been used to construct a map of the axes of rotation in the lattice which demonstrates the ability to distinguish the individual layers.

A One-Dimensional Nonlocal Damage-Plasticity Model for Ductile Materials

This paper presents a new 1-D non-local damage-plasticity deformation model for ductile materials. It uses the thermodynamic framework described in Houlsby and Puzrin (2000) and holds, nevertheless, some similarities with Lemaitre’s (1971) approach. A 1D finite element (FE) model of a bar fixed at one end and loaded in tension at the other end is introduced. This simple model demonstrates how the approach can be implemented within the finite element framework, and that it is capable of capturing both the pre-peak hardening and post-peak softening (generally responsible for models instability) due to damage-induced stiffness and strength reduction characteristic of ductile materials. It is also shown that the approach has further advantages of achieving some degree of mesh independence, and of being able to capture deformation size effects. Finally, it is illustrated how the model permits the calculation of essential work of rupture (EWR), i.e. the specific energy per unit cross-sectional area that is needed to cause tensile failure of a specimen.

Investigation of Deformation Size Effects During Microextrusion

Microextrusion has recently emerged as a feasible manufacturing process to fabricate metallic micropins having characteristic dimensions on the order of less <1mm. At this length scale, the deformation of the workpiece is dominated by the so-called size effects, e.g., material property and frictional behavior variations at small length scales. In extrusion experiments performed to produce submillimeter-sized pins having a base diameter of 0.76mm and an extruded diameter of 0.57mm, the extruded pins exhibited a curving tendency when a workpiece with a relatively coarse grain size of 211μm was used. This phenomenon was not observed when workpieces with a finer grain size of 32μm were used. In this paper, results from microhardness tests and microstructure analyses for both grain sizes are presented to investigate this phenomenon and to characterize the deformation during microextrusion. The results obtained from this analysis show that as the grain size approaches the specimen feature size, the deformation characteristics of the extruded pins are dominated by the size and location of specific grains, leading to a nonuniform distribution of plastic strain and measured hardness and, thus, the curving tendency. Microhardness tests of the initial billet material and tensile test specimens are also presented as supplementary analyses.

3D FEA of Size Effects in Deformation of Thin Metallic Films

AbstractThe purpose of this work is to analyze size effects in the deformation occurring during nanoindentation‐tests of thin metallic films on ceramic substrates. It is well known that classical phenomenological theories of plasticity are hardly applicable in cases of very small dimensions of a body [1]. Thus, the dependency of the mechanical behavior of thin films on the thickness can not be studied in the framework of classical theories. In order to simulate numerically the deformation, a specific material model has been chosen which is able to account for size effects. It bases on the theory of ”Mechanism Strain Gradient” (MSG) plasticity [2] in conjunction with the deformation theory of plasticity. The material model has been implemented via the user defined element subroutine (UEL) in the commercial FE code ABAQUS/Standard as a ten‐node tetrahedron‐element. With the developed subroutine the deformation of thin copper films on Si substrates during nanoindentation‐tests has been simulated. Different material models of the indentor (rigid and elastic) as well as different friction conditions between the film and the pyramidal indentor were tested. Furthermore, the influence of an additional oxide layer on the films surface has been analysed. In order to verify the numerical investigations, results from nanoindentation experiments have been used for comparison [4]. The FE simulations for different thicknesses in the range of 100‐600nm showed a very good agreement with the experiments. In particular, the size dependency of the force‐displacement curves, calculated by using the developed subroutine, is in rather good agreement with experiments. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The analysis of deformation size effects using multiple gauge length extensometry and the essential work of rupture concept

Size dependence of the load–displacement and stress–strain curves is a phenomenon widely reported in the literature and readily observed in experiments. The present paper introduces two developments in the analysis of ductile rupture, one in the area of experimental technique and interpretation, and one in the area of numerical modelling. Firstly, the new experimental technique is described of multiple gauge length optical extensometry (laser scanning) that provides a uniquely powerful means of collecting the data needed for the study of size effects, from a single tensile test on a ductile specimen. The interpretation procedures are presented based on the considerations about the nature of deformation and energy expenditure within different material volumes in a tensile specimen. Consequently, the property of the specimen can be defined and identified that relates to the energy consumption per unit cross-sectional area required to rupture the specimen entirely (the essential work of rupture). Another energetic measure is also obtained from the test that relates to the plastic work dissipation per unit volume in pre-peak deformed material. Secondly, the observed size effects and specific energy determination procedures are discussed in the context of non-local coupled plasticity-damage modelling. Conventional local numerical models of inelastic deformation fail to predict the sequence of deformation responses observed in the tensile test, namely, uniform deformation followed by strain localisation, necking and rupture. It is shown here that coupled non-local damage-plasticity modelling is capable of capturing the hardening–softening and global–local plasticity transitions, and hence the trends observed in ductile fracture. The predictions of the coupled non-local damage-plasticity modelling for different deformation regimes are shown to agree qualitatively with the experimentally observed behaviour. The two aspects of the proposed approach, experimental and modelling, are presented here together since they are intimately linked at the fundamental level. The implications of the proposed approach are discussed for the deformation analysis of plastically deforming and damageable materials and structures at various scales, from macroscopic to miniature.