J.M. Martínez-Esnaola

Cross-sectional nanoindentation: a new technique for thin film interfacial adhesion characterization

Abstract Interfacial adhesion is becoming a critical material property for improving the reliability of multilayer thin film structures used in microelectronics. Cross-sectional nanoindentation (CSN) is a new mechanical test especially designed for measuring the fracture toughness of thin film interfaces. Interfacial fracture is achieved by nanoindentation in the structure cross-section. A model based on the elastic plate theory has been developed to calculate numerically the interfacial critical energy release rate (Gci) for ceramic–ceramic systems from CSN test results. The model inputs are the thin film elastic properties, thin film thickness, interfacial crack area and maximum thin film deflection during the test. Closed form analytical solutions, obtained for two limiting cases, are consistent with the numerical approach. This technique has been successfully applied to silicon nitride–silicon oxide thin films, commonly used as electrical isolators in microelectronic devices.

Modelling the effect of oxidation on the creep behaviour of fibre-reinforced ceramic matrix composites

Abstract A creep-oxidation model is presented for continuous fibre-reinforced ceramic matrix composites at high temperature. The model includes the effects of interface and matrix oxidation, creep of the fibres and degradation of fibre strength with time. In particular, the influence of the glassy phases resulting from the oxidation of certain types of SiC based matrices is discussed. Model predictions are presented for the case of a woven Hi-Nicalon™/SiC composite and compared to experimental results at 1000 and 1100 °C. The fraction of broken fibres increases with time in an accelerated manner as a result of load transfer and fibre degradation. The model also predicts that a fraction of broken fibres of about 15% triggers the unstable failure of the composite.

Interfacial fracture induced by cross-sectional nanoindentation in metal–ceramic thin film structures

Abstract The cross-sectional nanoindentation (CSN) technique is extended to examine the fracture properties of thin film metal–ceramic interfaces. The methodology includes the selection of appropriate indentation parameters to achieve controlled interfacial delamination together with finite element modelling to estimate the contribution of plasticity of the metallic film to the overall interfacial fracture process. The results show good agreement with four-point bending, a method commonly used to measure thin film interfacial toughness, provided that mode mixities are similar. In addition, CSN allows observation of the interfacial crack by scanning electron microscopy and a local measurement of adhesion, with debonded areas in the range of 100–1000 μm2. The numerical modelling of the test provides an estimate of the intrinsic interfacial adhesion energy, separating the effects of metal plasticity.

Heterogeneous deformation and internal stresses developed in BCC wires by axisymmetric elongation

BCC wires macroscopically deformed by axisymmetric elongation (wire drawing) develop an intense <011> fibre texture and exhibit a characteristic non-uniform deformation of the grains evident in transverse sections (grain curling or “Van Gogh sky structure”). The extraordinary grain morphology induced by the <011> fibre texture is also accompanied by a peculiar constant strain hardening rate in single-phase BCC wires (exponentially increasing in case of BCC containing composite wires) that allows to reach very high strengths. Here we present a calculation of the elastoplastic axial elongation of such an aggregate of BCC grains with the ideal <011> fibre texture, using a slip-gradient dependent large-strain crystal plasticity constitutive equation incorporated into a finite element method (FEM) code, i.e., with proper account of the influence of the evolving shape and size of individual grains and of the local grain interactions. The results reproduce well the observed macroscopic behaviour (linear flow stress-strain curve at large strains) and the peculiar mesoscopic structural changes (grain curling in transverse sections). The simulation is focused on the analysis of strain and dislocation density heterogeneities and on the building up of mesoscopic (inter- and intra-granular) internal stresses during deformation. The computed average transverse tensile stresses acting normal to the axially oriented {100} planes approximately parallel to the boundaries of the flattened grains is close to 0.3 times the tensile flow stress of the aggregate, in good agreement with previous calculations based on the Taylor-Bishop-Hill model or on elasticplastic self-consistent calculations and with available neutron diffraction measurements. Such a high level of internal tensile stresses explains the well-known tendency of high strength BCC wires to fail by longitudinal splitting.

Simulation of the microstructural evolution during liquid phase sintering using a geometrical Monte Carlo model

The present paper proposes a Monte Carlo model to simulate the evolution of the microstructure during liquid phase sintering. The model mainly assumes that the system temperature is constant and that the composition of the liquid phase is completely homogeneous, but it is also capable of simulating the final cooling stage of the sintering process. It works with solidification, or melting, probabilities of volume elements (voxels) that are obtained accounting for the local geometry via the closest surrounding neighbours and avoiding the use of thermodynamic probabilities. This method reproduces an isotropic behaviour during solidification and melting and gives growth and melt rates proportional to surface curvatures. The proposed model provides realistic simulations of the microstructural evolution that takes place in real materials during liquid phase sintering.

Kinked cracks in anisotropic elastic materials

The problem of a kinked crack is analysed for the most general case of elastic anisotropy. The kinked crack is modelled by means of continuous distributions of dislocations which are assumed to be singular both at the crack tips and at the kink vertex. The resulting system of singular integral equations is solved numerically using Chebyshev polynomials and the reciprocal theorem. The stress intensity factors for modes I, II and III and the generalised stress intensity factor at the vertex are obtained directly from the dislocation densities.

Interfacial cracking in thin film structures

Abstract Interfacial fracture is a critical failure mode identified in reliability tests of multilayer thin film structures used in microelectronics. This paper reviews the main techniques developed so far to measure interfacial toughness in thin film sandwich structures, together with the models used to extract the fracture parameters of the interface. This background is used to present Cross Sectional Nanoindentation (CSN), a new mechanical test specifically designed for measuring the fracture toughness of thin film interfaces. The main advantages of this new technique are the high spatial resolution, which makes it suitable for studying patterned structures, and the direct observation of the interfacial crack front, not possible with other test configurations. A numerical model based on the elastic theory of plates has been used to calculate the interfacial toughness for ceramic-ceramic systems from CSN test results. Closed form analytical solutions, developed for two limiting cases, are consistent with the numerical approach. The CSN technique has been successfully applied to silicon nitride-silicon oxide thin films, commonly used as electrical isolators in microelectronic devices.

Analysis of sharp angular notches in anisotropic materials

The singular stresses at the tip of a sharp angular notch are analysed for the most general case of elastic anisotropy. The problem is stated in relation with the kinked crack and is modelled by means of continuous distributions of dislocations which are assumed to be singular at the notch vertex, the kind of the main singularity λ being unknown and weaker than at the crack tip. The Mellin transform is applied to obtain a system of simultaneous functional equations that enables one to find the parameter λ. The reciprocal theorem is used to compute the generalised stress intensity factor which characterises the singular stresses in a neighbourhood of the notch tip.

Original article: Diffusional Monte Carlo model of liquid-phase sintering

Abstract: Liquid-phase sintering (LPS) is a consolidation process for metallic and ceramic powders. At given temperature conditions, the process occurs with constant amount of liquid phase. However, the evolution of solid-particle shape is observed, namely, the rounding of particles and the growth of big particles at the expense of the small ones, which is known as Ostwald ripening. In this work, we propose a Monte Carlo (MC) model to simulate the microstructural evolution during LPS. The model considers the change of state of the discretising elements, namely voxels, of the system. The microstructural evolution proceeds accounting for both the geometrical characteristics of the particles, such as the number of solid neighbours, and the amount of solute contained in or surrounding a randomly chosen voxel. This has been implemented in terms of two probability distribution functions (PDFs). The diffusion of solute has also been considered by means of the implementation of a three-dimensional finite-difference algorithm. The diffusional MC model that we present is able to reproduce the Ostwald ripening behaviour and, in particular, results match the case in which the process is limited by the diffusion of the solute in the liquid phase.

Localized stress redistribution after fibre fracture in brittle matrix composites

Abstract A model is detailed that describes the redistribution of stress, after individual fibre failure, amongst the intact reinforcing fibres of a ceramic matrix composite. The load drop carried by a single fibre when it breaks is balanced by extra loads in the intact fibres which are calculated using elastic solutions and variational mechanics. The magnitude of stress redistribution is shown to follow a d − m relationship, where d is the distance from the broken fibre and m depends on the fibre volume fraction and a non-dimensional parameter that normalizes the influence of the stress and the elastic properties of the composite. The model has been applied to two composites, SiC/SiC and CAS/SiC. It is shown that the stress redistribution is localized in both composites, the stress increments in the closest intact fibres being more than one order of magnitude greater than predicted by the assumption of global stress redistribution.