microstructural features, such as grain size and dislocation densities, of the matrix and interphase, that differ from monolithic features by virtue of the fabrication and consolidation process. The objective of this work is to develop in-situ constitutive laws for the matrix and the interface region. Both single and multiple fiber micromechanical composite models for stress distributions around fiber fracture(s) employ various mathematical forms for the matrix or interface, ranging from rigid plastic to strain hardening, for instance. The simplest model, developed by Kelly and Tyson [1], assumes the matrix or interface deform only in shear and are rigid plastic with a constant shear stress τ0. The fiber remains elastic and sustains only axial strains. Due to the high shear stress generated in the matrix next to the fracture site, inelastic matrix or interface deformation is assumed to initiate at the fiber fracture site and propagate axially away from the break. The axial length of this inelastic zone is commonly referred to as the slip length, Ls. For an MMC system, perhaps a less reasonable assumption is that axial deformation of the matrix is prohibited. According to [1], slip length Ls is (1) where, D is the fiber diameter, Ef is the Young’s modulus of the fiber and ε is the far-field applied strain. The fiber axial coordinate z originates at the fiber fracture. For z < Ls the fiber axial strain is simply ε, but for z > Ls the fiber axial strain εf is (2) This article describes a general approach to quantifying the in-situ deformation parameters by linking micromechanical modeling to neutron diffraction measurements of fiber and matrix strain around a fiber fracture. The model fiber composite studied consists of an Al matrix and a single Al2O3 fiber. The propagation and relaxation of matrix plasticity induced by the fiber fracture upon loading and unloading is also examined. To illustrate the approach we apply the Kelly-Tyson model [1] to the data. Matching the fiber axial stress distribution predicted from this model in Equation 2 to the neutron measured fiber strains under small applied load increments results in an estimate of the typically nonlinear stress-strain behavior of the matrix. EXPERIMENTAL PROCEDURE A model composite comprised of a single, polycrystalline Al2O3 (alumina) fiber (4.75mm diameter, from Coors Ceramics, Golden, CO) and an Al alloy (6061, ESPI Metals, Agoura Hills, CA) matrix prepared by casting was used in this study. In order to engineer fiber fracture at the center of the gage section a 0.7 mm thick notch was cut around the circumference of the fiber to a depth of 1 mm using a diamond saw. Prior to casting, the 6061 Al was machined to fit loosely in the mold around the fiber. The sample was cast in a stainless steel mold under vacuum after purging the mold with argon gas. The mold was machined to hold the alumina fiber vertically in a tube furnace while the Al melted around the fiber. Following 30 minutes at 800°C, the entire mold was quenched to room temperature in water. Cylindrical tensile samples were then machined from the cast. The final dimensions of the sample gave a 30 mm long gage length with an 8.23 mm total diameter. X-ray radiography images revealed a continuous matrix with no voids after casting. Reference samples (nominally free of thermal residual stresses) of the matrix and fiber were also prepared using the same technique. For the reference fiber sample, the Al matrix was polished away from the fiber along a 14 mm gage section in order to relieve the thermal residual stresses. The mechanical behavior of the monolithic Al matrix was determined in tension using a screw-driven Instron load frame at a constant applied strain rate of 0.1 mm/min. The yield stress obtained by finding Ls = DEf ε 4τ0 f f DE z0 4τ ε =
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