Bauschinger and size effects in thin-film plasticity

The Bauschinger and size effects in the thin-film plasticity theory arising from the defect-energy of geometrically necessary dislocations (GNDs) are analytically investigated in this paper. Firstly, this defect-energy is deduced based on the elastic interactions of coupling dislocations (or pile-ups) moving on the closed neighboring slip plane. This energy is a quadratic function of the GNDs density, and includes an elastic interaction coefficient and an energetic length scale L. By incorporating it into the workconjugate strain gradient plasticity theory of Gurtin, an energetic stress associated with this defect energy is obtained, which just plays the role of back stress in the kinematic hardening model. Then this back-stress hardening model is used to investigate the Bauschinger and size effects in the tension problem of single crystal Al films with passivation layers. The tension stress in the film shows a reverse dependence on the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L is determined, which is just several slip plane spacing, and accords well with our physical interpretation for the defectenergy. The Bauschinger effect after unloading is analyzed by combining this back-stress hardening model with a friction model. The effects of film thickness and pre-strain on the reversed plastic strain after unloading are quantified and qualitatively compared with experiment results.

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

The elasto-plastic responses of thin films subjected to cyclic tension-compression loading and bending are studied, with a focus on Bauschinger and size effects. For this purpose, a model is established by incorporating plastic recovery into the strain gradient plasticity theory we proposed recently. Elastic and plastic parts of strain and strain gradient, which are determined by the elasto-plastic decomposition according to the associative rule, are assumed to have a degree of material-dependent reversibility. Based on the above assumption, a dislocation reversibility-dependent rule is built to describe evolutions of different deformation components under cyclic loadings. Furthermore, a simple strategy is provided to implement the passivated boundary effects by introducing a gradual change to relevant material parameters in the yield function. Based on this theory, both bulge and bending tests under cyclic loading conditions are investigated. By comparing the present predictions with the existing experimental data, it is found that the yield function is able to exhibit the size effect, the Bauschinger effect, the influence of surface passivation and the hysteresis-loop phenomenon. Thus, the proposed model is deemed helpful in studying plastic deformations of micron-scale films.

A study of particle size effect and interface fracture in aluminum alloy composite via an extended conventional theory of mechanism-based strain-gradient plasticity

In a remarkable series of experiments, Elssner et al. (1994) and Korn et al. (2002) observed cleavage cracking along a bimaterial interface between Nb and sapphire. The stress required for cleavage cracking is around the theoretical strength of the material. Classical plasticity models fall short to reach such a high stress level. We use the conventional theory of mechanism-based strain gradient plasticity (Huang et al., 2004) to investigate the stress field around the tip of an interface crack between Nb and sapphire. The tensile stress at a distance of 0.1 µm to the interface crack tip reaches 13.3σY ,w hereσY is the yield stress of Nb. This stress is nearly 4 times of that predicted by classical plasticity theory (3.6σY ) at the same distance to the crack tip, and is high enough to trigger cleavage cracking in materials and interfaces. This is consistent with Elssner et al.'s (1994) and Korn et al.'s (2002) experimental observations.

Micromechanical modeling of damage evolution and fracture behavior in particle reinforced metal matrix composites based on the conventional theory of mechanism-based strain gradient plasticity

Recent micro- and nano-indentation experiments have shown strong indentation size effects at the micron and sub-micron scales. Classical plasticity theories cannot explain the indentation size effect because their constitutive models possess no intrinsic material lengths. The Mechanism-based Strain-Gradient (MSG) plasticity theory and its simplified version, the Conventional theory of Mechanism-based Strain-Gradient plasticity (CMSG), have been established from the Taylor dislocation model and have successfully explained the indentation size effect. This paper provides a review of these theories and their applications to study the indentation of face- and body-centred-cubic metals and thin films on hard or soft substrates.

The effects of film thickness and wake-up field cycling on the ferroelectricity in Hf0.5Zr0.5O2 films thinner than 8 nm were carefully examined. The Hf0.5Zr0.5O2 films became more antiferroelectric-like with decreasing film thickness in pristine state, whereas all the Hf0.5Zr0.5O2 films showed ferroelectric characteristics after wake-up process. The decrease in the coercive field with decreasing film thickness could be understood based on the depolarization correction. From the temperature-dependent characterization, the tetragonal-to-orthorhombic phase transition during wake-up process is believed to be a thermally activated process, and the estimated activation energy was ∼3.42 ± 0.17 kJ/mol.

An experimental study on copper leaching from Cu1.85S thin films is presented, wherein copper extraction is quantitatively evaluated by changes in film thickness measured by white light interferometric profilometry. Changes in the film morphology and elemental composition, as assessed by scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy, are used to confirm that the loss in film thickness is due to changes in the copper content and that the resultant film species is consistent with the mechanism of copper dissolution. The Cu1.85S thin films were synthesized by chemical bath deposition. The leaching behaviour of copper from the films was investigated in acidic ferric sulfate media at pHs 1, 2, and 3, and pH 1 at redox potentials of ~350–650 mV versus Ag/AgCl in 3 M KCl. The changes in the film thickness and copper sulfur ratio were shown to reflect copper dissolution behaviour from chalcocite. Leaching of the Cu1.85S films demonstrated a greater decrease in film thickness as pH decreased. In addition comparison of the order of reaction as a function of proton concentration in non-oxidative dissolution of Cu1.85S (0.06) and as a function of iron(iii) concentration in ferric oxidation of Cu1.85S (0.40) shows that the proton dissolution reaction is negligible. Leaching of the Cu1.85S films at redox potentials of up to ~476.4 mV versus Ag/AgCl in 3 M KCl produced covellite and demonstrated greater decreases in film thickness with increases in the redox potential. Leaching of the films above ~476.4 mV resulted in the formation of spionkopite and demonstrated a much lesser decrease in film thickness. These results are consistent with Eh-pH diagrams for the Cu–S–H2O system.

The effect of tablet porosity, surface roughness and film thickness on the adhesion of hydroxypropyl methyl cellulose films to placebo tablet substrates have been studied using a specially designed tensile tester (Fisher & Rowe, 4976). There were direct relations between measured adhesion and tablet porosity and also surface roughness and tablet porosity. The effect of film thickness on the measured adhesion is complex with an initial decrease with thicknesses up to 35 micron and then a gradual increase with thicknesses up to 140 micron dut to differences in the strees distribution within the film during testing. A knowledge of these effects is necessary if results from various sources are to be compared. The findings illustrate the potential capability of the extrapolation of measured adhesion results to zero porosity and zero thickness values in order to obtain a measure of the true or intrinsic adhesion at any film/tablet interface without the confusing elements of tablet porosity, surface roughness and residual stresses in the film.

Effect of film thickness on the polarization characteristics of a Pt anode on zircona electrolyte

We have investigated the crystallization of amorphous equiatomic NiTi thin films sandwiched between two protective silicon nitride barrier films using optical, atomic force, and transmission electron microscopies. Crystallite nucleation occurs homogeneously inside the NiTi films because small composition shifts at the interfaces between NiTi and surrounding layers suppress heterogeneous nucleation at these interfaces. The crystallite growth rate is independent of film thickness for films thicker than 600nm. Below 600nm, the growth rate decreases rapidly and has an apparent activation energy that increases with decreasing film thickness. We suggest that diffusion of hydrogen from the film interfaces may be responsible for this unusual behavior.

The indentation size effect in the spherical indentation of iridium: A study via the conventional theory of mechanism-based strain gradient plasticity

Films of a series of monodisperse, moderately syndiotactic poly(methyl methacrylate) (PMMA) standards, with Mw ranging from 2,900–428,000, were solution-cast and spun-cast from chloroform onto clean aluminium substrates. The polymers were thoroughly characterized by conventional spectroscopic and chromatographic techniques. The films were studied using x-ray photoelectron spectroscopy (XPS) and time-of-flight secondary-ion mass spectrometry (ToF SIMS). The effects of molecular weight and film thickness on SIMS spectra were investigated thoroughly by unit-mass and high-resolution ToF SIMS. Film thickness had a pronounced effect on the negative SIMS spectra, particularly in films a few monolayers thick. This was seen in both the total negative ion counts (m/z 31–200) and the key negative ion intensity ratios. A parallel effect was observed with respect to the effect of molecular weight. These differences are attributed to (i) the original end-group concentration in the surface which decreases with increasing molecular weight and (ii) the original end-group concentration in the surface which increases as film thickness decreases.

In consideration of the high-density dislocations from the lithiation process of high-capacity electrodes in Li-ion batteries, in this paper, a new elastoplastic model is established to describe the diffusion-induced deformation and damage fracture. With the help of the relative physical quantities and state of charge, the surface damage and fracture behaviors of electrode materials are discussed based on the elastic-perfectly plastic (PP) and the strain gradient plasticity (SGP) theories, respectively. The results show that the lithiation deformation could be alleviated by reducing the electrode scale, and the plastic flow can play an essential role in the extrusion ratcheting effect relating to the upper surface fracture. Furthermore, the interface damage is more likely to appear by increasing the initial bond stiffness at the upper surface, which has little effect on the later fracture. A strong size effect is also found in the damage and fracture critical curves for the PP and SGP models.