The Influence of Grain Size and Temperature on the mechanical Deformation of Nanocrystalline Materials: Molecular Dynamics Simulation

Nanocrystalline (nc) materials are characterized by a typical grain size of 1-100nm. The uniaxial tensile deformation of computer-generated nc samples, with several average grain sizes ranging from 5.38 to 1.79nm, is simulated by using molecular dynamics with the Finnis-Sinclair potential. The influence of grain size and temperature on the mechanical deformation is studied in this paper. The simulated nc samples show a reverse Hall-Petch effect. Grain boundary sliding and motion, as well as grain rotation are mainly responsible for the plastic deformation. At low temperatures, partial dislocation activities play a minor role during the deformation. This role begins to occur at the strain of 5%, and is progressively remarkable with increasing average grain size. However, at elevated temperatures no dislocation activity is detected, and the diffusion of grain boundaries may come into play.

The effect of nucleation time on the growth of a microvoid in a viscoelastic material

In this paper, discussions are focused on the growth of a nucleated void in a viscoelastic material. The in situ tensile tests of specimens made of high-density polyethylene, filled with spherical glass beads (HDPE/GB) are carried out under SEM. The experimental result indicates that the microvoid nucleation is induced by the partially interfacial debonding of particles. By means of the Laplace transform and the Eshelby's equivalent inclusion method, a new analytical expression of the void strain at different nucleation times is derived. It can be seen that the strain of the nucleated void depends not only on the remote strain history, but also on the nucleation time. This expression is also illustrated by numerical examples, and is found to be of great usefulness in the study of damage evolution in viscoelastic materials.

Finite Element Solutions for Plane Strain Mode I Crack with Strain Grading Effect

In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom mu(i). omega(i) is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l(1). Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. (C) 2002 Elsevier Science Ltd. All rights reserved.

Analysis of Dislocation-Induced Strain Field in an Idealized Wafer-Bonded Microstructure

The localized dislocation at the interface induces uneven strain distribution in two wafer-bonded layers. Because of the different elastic properties of two bonding layers and this uneven strain distribution, the bilayered microstructure deflects and deflection relaxes the strains. Depending on the microstructure dimensions, elastic properties and lattice parameters, the contribution of deflection to strain field can be very significant. The interface condition also plays an important role in relaxing strain. Two models capable of describing different interface conditions are used for the analysis and offer a more comprehensive study on the dislocation-induced strain field in a wafer-bonded bilayered microstructure. The combined effect of microstructure dimensions and interface condition on the strain is presented and compared.

Interface crack problems with strain gradient effects

In this paper, the strain gradient theory proposed by Chen and Wang (2001 a, 2002b) is used to analyze an interface crack tip field at micron scales. Numerical results show that at a distance much larger than the dislocation spacing the classical continuum plasticity is applicable; but the stress level with the strain gradient effect is significantly higher than that in classical plasticity immediately ahead of the crack tip. The singularity of stresses in the strain gradient theory is higher than that in HRR field and it slightly exceeds or equals to the square root singularity and has no relation with the material hardening exponents. Several kinds of interface crack fields are calculated and compared. The interface crack tip field between an elastic-plastic material and a rigid substrate is different from that between two elastic-plastic solids. This study provides explanations for the crack growth in materials by decohesion at the atomic scale.

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.

Microstructure, strain fields and flow stress in deformed metal matrix composites

An experimental study of local orientations around whiskers in deformed metal matrix composites has been used to determine the strain gradients existing in the material following tensile deformation. These strain fields have been represented as arrays of geometrically necessary dislocations, and the material flow stress predicted using a standard dislocation hardening model. Whilst the correlation between this and the measured flow stress is reasonable, the experimentally determined strain gradients are lower by a factor of 5-10 than values obtained in previous estimates made using continuum plasticity finite element models. The local orientations around the whiskers contain a large amount of detailed information about the strain patterns in the material, and a novel approach is made to representing some of this information and to correlating it with microstructural observations. © 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.

Crack Tip Field and J-Integral with Strain Gradient Effect

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental version of the conventional J_2 deformation theory No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary value problem is the same as that in the conventional theory Two typical crack Problems are studied: (a) the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it. Consequently, the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.

Strain Rate Dependence of Plastic Flow in Ce-based Bulk Metallic Glass During Nanoindentation

The strain rate dependence of plastic deformation of Ce60Al15CU10Ni15 bulk metallic glass was studied by nanoindentation. Even though the ratio of room temperature to the glass transition temperature was very high (0.72) for this alloy, the plastic deformation was dominated by shear banding under nanoindentation. The alloy exhibited a critical loading rate dependent serrated flow feature. That is, with increasing loading rate, the alloy exhibited a transition from less prominent serrated flow to pronounced serrated flow during continuous loading but from serrated to smoother flow during stepped loading.

Mode I and Mode II Crack Tip Asymptotic Fields with Strain Gradient Effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

Some observations describing the electrochemical surface annealing of austenitic stainless steel

Cold-worked austenitic stainless steels have been subject to a pulsed electrochemical treatment in fairly concentrated aqueous solutions of sodium nitrite. The electrochemical reactions that occur transform the strain-induced martensite phase, originally formed by the cold work, back to the austenite phase. However, unlike the conventional thermal annealing process, electrochemically induced surface annealing also hardens the surface of the alloy. Because the process causes transformation of the surface martensite, we term it "electrochemical surface annealing", despite the fact that it results in an increase in surface hardness.

Onset of Adiabatic Shear Instability in Strain Gradient Dependent Metal Matrix Composites

In this paper, effect of strain gradient on adiabatic shear instability in particle reinforced metal matrix composites is investigated by making use of the strain gradient dependent constitutive equation developed by Dai et al. [9] and the linear perturbation analysis presented by Bai [10]. The results have shown that the onset of adiabatic shear instability in metal matrix composites reinforced with small particles is more prone to occur than in the composites reinforced with large particles. This means that the strain gradient provides a strong deriving force for onset of adiabatic shear instability in metal matrix composites.

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.

On the Formation of Periodic Segmentation Cracks in a Coating Plated on a Substrate with Periodic Subsurface Inclusions

The mechanism of the formation of periodic segmentation cracks of a coating plated on a substrate with periodic subsurface inclusions (PSI) is investigated. The internal stress in coating and subsequently the strain energy release rate (SERR) of the segmentation cracks are computed with finite element method (FEM). And the effect of the geometrical parameters of the PSI is studied. The results indicate that the ratio of the width of the inclusion to the period of the repeated structure has an optimum value, at which the maximum internal tensile stress and SERR arise. On the other hand, the ratio of the max-thickness of the inclusion to the thickness of the coating has a threshold value, above which the further increase of this ratio should seldom influence the internal stress or the SERR.