C. H. Hsueh

The importance of amorphous intergranular films in self-reinforced Si3N4 ceramics

Abstract High-fracture-strength and high-toughness β-Si 3 N 4 ceramics can be obtained by tailoring the size and number of the elongated bridging grains. However, these bridging mechanisms rely on debonding of the reinforcing grains from the matrix to increase toughness. Interfacial debonding is shown to be influenced by sintering aids incorporated in the amorphous intergranular films. In one case, the interface strength between the intergranular glass and the reinforcing grains increases with the aluminum and oxygen content of an interfacial epitaxial β-SiAlON layer. In another, the incorporation of fluorine in the intergranular film allows the crack to circumvent the grains. Atomic cluster calculations reveal that these two debonding processes are related to (1) strong Si–O and Al–O bonding across the glass/crystalline interface with an epitaxial SiAlON layer and (2) a weakening of the amorphous network of the intergranular film when difluorine substitutes for bridging oxygen.

Multiple film cracking in film/substrate systems with residual stresses and unidirectional loading

Multiple film cracking in film/substrate systems is analyzed in the present study. Specifically, the experimental measurements of multiple cracking of SiOx films of various thicknesses on polyethylene terephthalate substrates are analyzed. The system is subjected to both residual stresses and unidirectional tensile loading. Considering a three- dimensional geometry, an analytical model is developed to derive the stress distribution in the system, and the film-cracking problem is analyzed using both the strength and the energy criteria. Compared to the strength criterion, the energy criterion shows better agreement with the measurements of the crack density versus applied strain relation.

A modified analysis for stress transfer in fibre-reinforced composites with bonded fibre ends

The elastic stress transfer from the matrix to the embedded fibre in fibre-reinforced composites has been analysed previously when the loading direction is parallel to the fibre axis and the fibre is bonded to the matrix. Stress transfer occurs both at the interface along the fibre length and at the ends of the fibre. However, the boundary condition at the bonded ends is ambiguous, and various assumptions have been made to obtain solutions for this stress transfer problem. To satisfy more rigorously the boundary condition for the bonded ends, a new technique of assuming imaginary fibres in the composite is proposed in the present study. Compared to the previous analytical solution, the present analytical solution bears more physical meaning and is in better agreement with numerical and experimental results

Analyses of thermal expansion behavior of intergranular two-phase composites

Both analytical modeling and numerical simulations were performed to analyze residual thermal stresses and coefficients of thermal expansion (CTEs) of intergranular two-phase composites in a two-dimensional sense. A composite-circle model was adopted for analytical modeling. Model microstructures consisting of square-array, hexagon-array, and brick wall-array of grains with an intergranular phase as well as an actual microstructure of random-array grains with an intergranular phase were adopted for numerical simulations. The results showed that in predicting CTEs, the simple analytical model represents the two-dimensional composite well except that with brick wall-array grains, which induced significant anisotropic CTEs in the composite. The residual thermal stresses in composites were also discussed.

Pull-out of a ductile fibre from a brittle matrix

Pull-out of a ductile fibre from a brittle matrix has been analysed using a shear lag model. Debonding at the fibre-matrix interface and yielding of the fibre occurred during the pull-out process. Both Poissons contraction of the fibre and Coulomb friction of the debonded interface were considered. The debond length, which consists of an elastic zone length and a plastic zone length, was also analysed. When the fibre has a finite embedded length, it was found that necking prior to full pull-out of the fibre was required to optimize the toughening of a brittle matrix due to plastic deformation of the fibres. The essential material properties to achieve this are addressed.

Matrix cracking with frictional bridging fibres in continuous fibre ceramic composites

Interfacial debonding and matrix cracking due to residual axial stresses have been analysed for unidirectional fibre-reinforced ceramic composites. The analytical solutions for the crack-opening displacement, the axial displacement of the composite due to interfacial debonding, and the critical residual axial stress for matrix cracking have been obtained. The solutions were then compared with those for tensile loading in the fibre direction. Three issues related to Part I, i.e. the effective fracture toughness of the composite, the critical loading stress for matrix cracking in the presence of residual stresses, and the debonded fibre length due to loading, were also addressed in the present study.

Evaluations of residual axial stresses and interfacial friction in Nicalon fibre-reinforced macro-defect-free cement composites

The residual axial stress and the interfacial frictional stress of Nicalon fibre-reinforced macro-defect-free cement composites have been evaluated using the indentation technique. In these composites, both the residual axial stress in the fibre and the interfacial bonding are relatively high compared to other ceramic composites. Owing to the high residual axial stress, Poissons effect can be ignored in analysing the stress-displacement relation of the fibre, and the interfacial frictional stress along the sliding length can be assumed to be a constant during indentation loading and unloading. Because of the strong interfacial bonding, consideration of the upper bound of the sliding zone length during unloading is essential. The sliding zone length during unloading is limited by the debond length at peak loading. The theoretical predictions of stress-displacement relations are in excellent agreement with the experimental results.

Consideration of radial dependences of axial stresses in the shear-lag model for fibre pull-out

The shear-lag model has been used extensively to analyse stress transfer during single-fibre pull-out. To achieve analytical solutions, the radial dependences of the axial stresses in the fibre and the matrix are generally ignored in the shear-lag model. The present study considered these radial dependence in the shear-lag model. The differences between the predictions obtained by ignoring these radial dependences, considering the radial dependence of the axial stress in the fibre only, considering the radial dependence of the axial stress in the matrix only, and considering both radial dependences, have been addressed.

The relative residual fibre displacement after indentation loading and unloading of fibre-reinforced ceramic composites

The interfacial properties of fibre-reinforced ceramic composites have been evaluated by using the indentation technique. The ratio of the residual fibre displacement after complete unloading to the fibre displacement at peak loading is examined. Assuming a constant interfacial shear stress at an unbonded interface, this ratio is 0.5. However, deviation of this ratio from 0.5 is always obtained from experimental results. Both Poissons effect and the existence of the residual axial stress have been proposed to explain this deviation. A methodology is presented in this study to classify conditions for which either Poissons effect or the residual axial stress dominates this deviation. The application of this methodology to Nicalon fibre-reinforced lithium aluminosilicate glass-ceramic is also illustrated.

Residual stress and strain in pyrolytic boron nitride resulting from thermal anisotropy

Residual stresses in chemically deposited pyrolytic boron nitride (PBN) crucibles caused by thermal expansion anisotropy during cooling immediately following deposition are analysed. The calculations reveal that radial tension and combined tangential tension and compression exist in the crucible. The maximum stresses increase with an increase in the thickness of the crucible. Furthermore, while the outer wall of the crucible always shrinks upon cooling, the inner wall may expand, due to the residual stress states, resulting in a negative effective thermal expansion coefficient in the tangential direction. The influence of the PBN attachment to the mandrel on which it is deposited is also considered. Specifically, the radial tensile stress in the crucible is shown to increase due to this attachment, which in turn, enhances the delamination of the crucible.