Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength. © 2002 Elsevier Science Ltd. All rights reserved.

Size Dependent Nanoindentation of a Soft Film on a Hard Substrate

Nanoindentation experiments on Al/glass systems show that, as the indentation depth increases, the hardness decreases during a shallow indentation, and increases when the indenter tip approaches the film–substrate interface. We associate the rise in hardness during two stages with the strong strain gradient effects, the first stage is related with the small scale effects and the second stage with the strain gradient between the indenter and the hard substrate. Using the strain gradient theory proposed by Chen and Wang and the classical plasticity theory, the observed nanoindentation behavior is modeled and analyzed by means of the finite element method, and it is found that the classical plasticity cannot explain the experiment results but the strain gradient theory can describe the experiment data at both shallow and deep indentation depths very well. The results prove that both the strain gradient effects and substrate effects exist in the nanoindentation of the film–substrate system.

Size Effect and Geometrical Effect of Solids in Micro-Indentation Test

Micro-indentation tests at scales of the order of sub-micron show that the measured hardness increases strongly with decreasing indent depth or indent size, which is frequently referred to as the size effect. At the same time, at micron or sub-micron scale, another effect, which is referred to as the geometrical size effects such as crystal grain size effect, thin film thickness effect, etc., also influences the measured material hardness. However, the trends are at odds with the size-independence implied by the conventional elastic-plastic theory. In the present research, the strain gradient plasticity theory (Fleck and Hutchinson) is used to model the composition effects (size effect and geometrical effect) for polycrystal material and metal thin film/ceramic substrate systems when materials undergo micro-indenting. The phenomena of the "pile-up" and "sink-in" appeared in the indentation test for the polycrystal materials are also discussed. Meanwhile, the micro-indentation experiments for the polycrystal Al and for the Ti/Si_3N_4 thin film/substrate system are carried out. By comparing the theoretical predictions with experimental measurements, the values and the variation trends of the micro-scale parameter included in the strain gradient plasticity theory are predicted.

Particulate Size Effects in the Particle-Reinforced Metal-Matrix Composites

The influences of I,article size on the mechanical properties of the particulate metal matrix composite;are obviously displayed in the experimental observations. However, the phenomenon can not be predicted directly using the conventional elastic-plastic theory. It is because that no length scale parameters are involved in the conventional theory. In the present research, using the strain gradient plasticity theory, a systematic research of the particle size effect in the particulate metal matrix composite is carried out. The roles of many composite factors, such as: the particle size, the Young's modulus of the particle, the particle aspect ratio and volume fraction, as well as the plastic strain hardening exponent of the matrix material, are studied in detail. In order to obtain a general understanding for the composite behavior, two kinds of particle shapes, ellipsoid and cylinder, are considered to check the strength dependence of the smooth or non-smooth particle surface. Finally, the prediction results will be applied to the several experiments about the ceramic particle-reinforced metal-matrix composites. The material length scale parameter is predicted.

Micro-scale Mechanics of the Surface-Nanocrystalline Al-Alloy Material

Based on the microscopic observations and measurements, the mechanical behavior of the surface-nanocrystallized Al-alloy material at microscale is investigated experimentally and theoretically. In the experimental research, the compressive stress-strain curves and the hardness depth curves are measured. In the theoretical simulation, based on the material microstructure characteristics and the experimental features of the compression and indentation, the microstructure cell models are developed and the strain gradient plasticity theory is adopted. The material compressive stress-strain curves and the hardness depth curves-are predicted and simulated. Through comparison of the experimental results with the simulation results, the material and model parameters are determined.

Toughness Of Ni/Al2O3 Interfaces As Dependent On Micron-Scale Plasticity And Atomistic-Scale Separation

Ceramic/metal interfaces were studied that fail by atomistic separation accompanied by plastic dissipation in the metal. The macroscopic toughness of the specific Ni alloy/Al2O3 interface considered is typically on the order of ten times the atomistic work of separation in mode I and even higher if combinations of mode I and mode II act on the interface. Inputs to the computational model of interface toughness are: (i) strain gradient plasticity applied to the Ni alloy with a length parameter determined by an indentation test, and (ii) a potential characterizing mixed mode separation of the interface fit to atomistic results. The roles of the several length parameters in the strain gradient plasticity are determined for indentation and crack growth. One of the parameters is shown to be of dominant importance, thus establishing that indentation can be used to measure the relevant length parameter. Recent results for separation of Ni/Al2O3 interfaces computed by atomistic methods are reviewed, including a set of results computed for mixed mode separation. An approximate potential fit to these results is characterized by the work of separation, the peak separation stress for normal separation and the traction-displacement relation in pure shearing of the interface. With these inputs, the model for steady-state crack growth is used to compute the toughness of the interface under mode I and under the full range of mode mix. The effect of interface strength and the work of separation on macroscopic toughness is computed. Fundamental implications for plasticity-enhanced toughness emerge.

Simulations of Mechanical Behavior of Polycrystalline Copper with Nano-Twins

Mechanical behavior and microstructure evolution of polycrystalline copper with nano-twins were investigated in the present work by finite element simulations. The fracture of grain boundaries are described by a cohesive interface constitutive model based on the strain gradient plasticity theory. A systematic study of the strength and ductility for different grain sizes and twin lamellae distributions is performed. The results show that the material strength and ductility strongly depend on the grain size and the distribution of twin lamellae microstructures in the polycrystalline copper.

Peeling Experiments Of Ductile Thin Films Along Ceramic Substrates - Critical Assessment Of Analytical Models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al2O3 substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al2O3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al2O3 substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case. (C) 2007 Elsevier Ltd. All rights reserved.

The Capillary Force In Micro- And Nano-Indentation With Different Indenter Shapes

The influence of the indenter shapes and various parameters on the magnitude of the capillary force is studied on the basis of models describing the wet adhesion of indenters and substrates joined by liquid bridges. In the former, we consider several shapes, such as conical, spherical and truncated conical one with a spherical end. In the latter, the effects of the contact angle, the radius of the wetting circle, the volume of the liquid bridge, the environmental humidity, the gap between the indenter and the substrate, the conical angle, the radius of the spherical indenter, the opening angle of the spherical end in the truncated conical indenter are included. The meniscus of the bridge is described using a circular approximation, which is reasonable under some conditions. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. The results can be applicable to the micro- and nano-indentation experiments. It shows that the measured hardness is underestimated due to the effect of the capillary force. (c) 2008 Elsevier Ltd. All rights reserved.

Formation of adiabatic shear band in metal matrix composites

A modified single-pulse loading split Hopkinson torsion bar (SSHTB) is introduced to investigate adiabatic shear banding behavior in SiCp particle reinforced 2024 Al composites in this work. The experimental results showed that formation of adiabatic shear band in the composite with smaller particles is more readily observed than that in the composite with larger particles. To characterize this size-dependent deformation localization behavior of particle reinforced metal matrix composites (MMCp), a strain gradient dependent shear instability analysis was performed. The result demonstrated that high strain gradient provides a deriving force for the formation of adiabatic shear banding in MMCp. (C) 2004 Elsevier Ltd. All rights reserved.

Investigation on mechanical properties and size effect of nanocrystalline twin copper

The stress-strain relations of nanocrystalline twin copper with variously sized grains and twins are studied by using FEM simulations based on the conventional theory of mechanism-based strain gradient plasticity (CMSG). A model of twin lamellae strengthening zone is proposed and a cohesive interface model is used to simulate grain-boundary sliding and separation. Effects of material parameters on stress-strain curves of polycrystalline twin copper are studied in detail. Furthermore, the effects of both twin lamellar spacing and twin lamellar distribution on the stress-strain relations are investigated under tension loading. The numerical simulations show that both the strain gradient effect and the material hardening increase with decreasing the grain size and twin lamellar spacing. The distribution of twin lamellae has a significant influence on the overall mechanical properties, and the effect is reduced as both the grain size and twin lamellar spacing decrease. Finally, the FEM prediction results are compared with the experimental data.

Determination of interface properties between micron-thick metal film and ceramic substrate using peel test

Peel test measurements have been performed to estimate both the interface toughness and the separation strength between copper thin film and Al2O3 substrate with film thicknesses ranging between 1 and 15 mu m. An inverse analysis based on the artificial neural network method is adopted to determine the interface parameters. The interface parameters are characterized by the cohesive zone (CZ) model. The results of finite element simulations based on the strain gradient plasticity theory are used to train the artificial neural network. Using both the trained neural network and the experimental measurements for one test result, both the interface toughness and the separation strength are determined. Finally, the finite element predictions adopting the determined interface parameters are performed for the other film thickness cases, and are in agreement with the experimental results.

Small scale, grain size and substrate effects in nano-indentation experiment of film-substrate systems

The mechanical properties of film-substrate systems have been investigated through nano-indentation experiments in our former paper (Chen, S.H., Liu, L., Wang, T.C., 2005. Investigation of the mechanical properties of thin films by nano-indentation, considering the effects of thickness and different coating-substrate combinations. Surf. Coat. Technol., 191, 25-32), in which Al-Glass with three different film thicknesses are adopted and it is found that the relation between the hardness H and normalized indentation depth h/t, where t denotes the film thickness, exhibits three different regimes: (i) the hardness decreases obviously with increasing indentation depth; (ii) then, the hardness keeps an almost constant value in the range of 0.1-0.7 of the normalized indentation depth h/t; (iii) after that, the hardness increases with increasing indentation depth. In this paper, the indentation image is further investigated and finite element method is used to analyze the nano-indentation phenomena with both classical plasticity and strain gradient plasticity theories. Not only the case with an ideal sharp indenter tip but also that with a round one is considered in both theories. Finally, we find that the classical plasticity theory can not predict the experimental results, even considering the indenter tip curvature. However, the strain gradient plasticity theory can describe the experimental data very well not only at a shallow indentation depth but also at a deep depth. Strain gradient and substrate effects are proved to coexist in film-substrate nano-indentation experiments. (c) 2006 Elsevier Ltd. All rights reserved.

The effects of capillary force in micro or nano-indentation

Models describing wet adhesion between indenters and substrates joined by liquid bridges are investigated. The influences of indenter shapes and various parameters of structures on capillary force are focused. In the former, we consider several shapes, such as conical, spherical and truncated conical indenter with a spherical end. In the latter, the effects of the contact angle, the environmental humidity, the gap between the indenter and the substrate, etc. are included. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. Most interesting finding is that applying the present results to micro- and nano-indentation experiments shows the size effect in indentation hardness not produced but underestimated by the effects of capillary force.(4 refs)

Analysis of micro-indentation problem of a soft film on a hard substrate

Two stages have been observed in micro-indentation experiment of a soft film on a hard substrate. In the first stage, the hardness of the thin film decreases with increasing depth of indentation when indentation is shallow; and in the second stage, the hardness of the film increases with increasing depth of indentation when the indenter tip approaches the hard substrate. In this paper, the new strain gradient theory is used to analyze the micro-indentation behavior of a soft film on a hard substrate. Meanwhile, the classic plastic theory is also applied to investigating the problem. Comparing two theoretical results with the experiment data, one can find that the strain gradient theory can describe the experiment data at both the shallow and deep indentation depths quite well, while the classic theory can't explain the experiment results.