George Jefferson

The elastic response of a cohesive aggregate—a discrete element model with coupled particle interaction

Abstract A model is presented for the deformation of a cohesive aggregate of elastic particles that incorporates two important effects of large-sized inter-particle junctions. A finite element model is used to derive a particle response rule, for both normal and tangential relative deformations between pairs of particles. This model agrees with the Hertzian contact theory for small junctions, and is valid for junctions as large as half the nominal particle size. Further, the aggregate model uses elastic superposition to account for the coupled force–displacement response due to the simultaneous displacement of all of the neighbors of each particle in the aggregate. A particle stiffness matrix is developed, relating the forces at each junction to the three displacement degrees of freedom at all of the neighboring-particle junctions. The particle response satisfies force and moment equilibrium, so that the model is properly posed to allow for rigid rotation of the particle without introducing rotational degrees of freedom. A computer-simulated sintering algorithm is used to generate a random particle packing, and the stiffness matrix is derived for each particle. The effective elastic response is then estimated using a mean field or affine displacement calculation, and is also found exactly by a discrete element model, solving for the equilibrium response of the aggregate to uniform-strain boundary conditions. Both the estimate and the exact solution compare favorably with experimental data for the bulk modulus of sintered alumina, whereas Hertzian contact-based models underestimate the modulus significantly. Poissons ratio is, however, accurately determined only by the full equilibrium discrete element solution, and shown to depend significantly on whether or not rigid particle rotation is permitted in the model. Moreover, this discrete element model is sufficiently robust, so it can be applied to problems involving non-homogeneous deformations in such cohesive aggregates.

Modeling of crack density in ceramic matrix composites

The feasibility of utilizing the shear lag theory to estimate crack density in fabric reinforced composites was investigated. A geometric model was constructed for the fabric and meshed using a hybrid finite element approach. The small segment of the yarn and the surrounding matrix enclosed within each element were treated as a unidirectional composite and the shear lag theory was used to estimate the crack density. Model results were compared to experimental data for a 5-harness satin melt-infiltrated SiC/SiC composite under tension and showed a pattern similar to experimental data with the model starting to accumulate cracks at a stress corresponding to the point of departure from linearity in the stress–strain curve while cracks were experimentally observed around 60 MPa higher. The model and experimental data had a similar value for the crack density at the saturation level. Sensitivity analysis showed that the crack density was highly sensitive to the fiber volume fraction in the load direction followed by the weave angle of the crimped segments of the yarns and the interfacial shear strength between the fibers and the matrix.

Simultaneous Fatigue and Combustion Exposure of a SiC/SiC Ceramic Matrix Composite

A melt-infiltrated (MI) woven ceramic matrix composite consisting of a silicon carbide matrix reinforced by boron nitride coated Hi-Nicalon type STM SiC fiber, Hi-Nic-S/BN/SiC, was tested under tension-tension fatigue loading in combination with combustion conditions representative of those experienced by hot-section components such as turbine blades and vanes in modern gas turbine engines. The burner rig fatigue data and fracture surfaces were analyzed for the effects of oxidation on life, failure, and damage mechanisms. These test results were then compared with those obtained from similar fatigue tests performed in a standard furnace under laboratory air environment. Fatigue life in the combustion condition was lower by an order of magnitude in comparison to the isothermal furnace results across the range of applied stress, and so demonstrates the importance of representative combined environment testing in conjunction with fundamental load testing. The observed difference in fatigue performance is attributed to the thermal gradient stress and increased rate of oxidation due to a high moisture level in the combustion rig test condition. The former was verified using finite element analysis and the latter from microscopic analysis of the fracture surfaces.