Simplified micromechanical equations for thermal residual stress analysis of coated fiber composites

The fabrication of metal matrix composites poses unique problems to the materials engineer. The large thermal expansion coefficient (CTE) mismatch between the fiber and matrix leads to high tensile residual stresses at the fiber/matrix (F/M) interface which could lead to premature matrix cracking during cooldown. Fiber coatings could be used to reduce thermal residual stresses. A simple closed form analysis, based on a three phase composite cylinder model, was developed to calculate thermal residual stresses in a fiber/interphase/matrix system. Parametric studies showed that the tensile thermal residual stresses at the F/M interface were very sensitive to the CTE and thickness of the interphase layer. The modulus of the layer had only a moderate effect on tensile residual stresses. For a silicon carbide titanium aluminide composite, the tangential stresses were 20 to 30 pct. larger than the axial stresses, over a wide range of interphase layer properties, indicating a tendency to form radial matrix cracks during cooldown. Guidelines for the selection of appropriate material properties of the fiber coating were also derived in order to minimize thermal residual stresses in the matrix during fabrication

Micromechanical combined stress analysis: MICSTRAN, a user manual

Composite materials are currently being used in aerospace and other applications. The ability to tailor the composite properties by the appropriate selection of its constituents, the fiber and matrix, is a major advantage of composite materials. The Micromechanical Combined Stress Analysis (MICSTRAN) code provides the materials engineer with a user-friendly personal computer (PC) based tool to calculate overall composite properties given the constituent fiber and matrix properties. To assess the ability of the composite to carry structural loads, the materials engineer also needs to calculate the internal stresses in the composite material. MICSTRAN is a simple tool to calculate such internal stresses with a composite ply under combined thermomechanical loading. It assumes that the fibers have a circular cross-section and are arranged either in a repeating square or diamond array pattern within a ply. It uses a classical elasticity solution technique that has been demonstrated to calculate accurate stress results. Input to the program consists of transversely isotropic fiber properties and isotropic matrix properties such as moduli, Poisson's ratios, coefficients of thermal expansion, and volume fraction. Output consists of overall thermoelastic constants and stresses. Stresses can be computed under the combined action of thermal, transverse, longitudinal, transverse shear, and longitudinal shear loadings. Stress output can be requested along the fiber-matrix interface, the model boundaries, circular arcs, or at user-specified points located anywhere in the model. The MICSTRAN program is Windows compatible and takes advantage of the Microsoft Windows graphical user interface which facilitates multitasking and extends memory access far beyond the limits imposed by the DOS operating system

A macro-micromechanics analysis of a notched metal matrix composite

A macro-micromechanics analysis was formulated to determine the matrix and fiber behavior near the notch tip in a center-notched metal matrix composite. Results are presented for a boron/aluminum monolayer. The macro-level analysis models the entire notched specimen using a three dimensional finite element program which uses the vanishing-fiber-diameter model to model the elastic-plastic behavior of the matrix and the elastic behavior of the fiber. The micro-behavior is analyzed using a Discrete Fiber-Matrix (DFM) model containing one fabric and the surrounding matrix. The dimensions of the DFM model were determined by the ply thickness and the fiber volume fraction and corresponded to the size of the notch-tip element in the macro-level analysis. The boundary conditions applied to the DFM model were determined from the macro-level analysis. Stress components within the DFM model were calculated and stress distributions are presented along selected planes and surfaces within the DFM model, including the fiber-matrix interface. Yielding in the matrix was examined at the notch tip in both the macro- and micro-level analyses. The DFM model predicted higher stresses (24 percent) in the fiber compared to the global analysis. In the notch-tip element, the interface stresses indicated that a multi-axial criterion may be required to predict interfacial failure. The DFM analysis predicted yielding to initiate in the notch-tip element at a stress level 28 percent lower than predicted by the global analysis

Class Transitions and Two Component Accretion Flow in GRS 1915+105

The light curve of the galactic micro-quasar GRS 1915+105 changes in at least thirteen different ways which are called classes. We present examples of the transitions from one class to another as observed by the IXAE instrument aboard the Indian Satellite IRS-P3. We find that the transitions are associated with changes in photon counts over a time-scale of only a few hours and they take place through unknown classes. Assuming that the transitions are caused by variation of the accretion rates, this implies that a significant fraction of the matter must be nearly freely falling in order to have such dramatic changes in such a short time.Comment: 9 pages, 6 figures, Astronomy and Astrophys. (in press

A large magnetoinductance effect in La0.67Ba0.33MnO3

We report four probe impedance of La0.67Ba0.33MnO3 at f = 100 kHz under different dc bias magnetic fields. The ac resistance (R) exhibits a peak around Tp = 325 K which is accompanied by a rapid increase and a peak in the reactance (X) in a zero field. The magnetoreactance exhibits a sharp peak close to Tp and its magnitude (= 60% in H = 1 kG) exceeds that of the ac magnetoresistance (= 5 % inH = 1 kG). It is suggested that the magnetoreactance arises from changes in the self inductance of the sample rather than the capacitance.Comment: 13 pages, 3 figures. accepted in Appl. Phys. Let

Fracture mechanics analysis for various fiber/matrix interface loadings

Fiber/matrix (F/M) cracking was analyzed to provide better understanding and guidance in developing F/M interface fracture toughness tests. Two configurations, corresponding to F/M cracking at a broken fiber and at the free edge, were investigated. The effects of mechanical loading, thermal cooldown, and friction were investigated. Each configuration was analyzed for two loadings: longitudinal and normal to the fiber. A nonlinear finite element analysis was performed to model friction and slip at the F/M interface. A new procedure for fitting a square-root singularity to calculated stresses was developed to determine stress intensity factors (K sub I and K sub II) for a bimaterial interface crack. For the case of F/M cracking at a broken fiber with longitudinal loading, crack tip conditions were strongly influenced by interface friction. As a result, an F/M interface toughness test based on this case was not recommended because nonlinear data analysis methods would be required. For the free edge crack configuration, both mechanical and thermal loading caused crack opening, thereby avoiding frictional effects. A F/M interface toughness test based on this configuration would provide data for K(sub I)/K(sub II) ratios of about 0.7 and 1.6 for fiber and radial normal loading, respectively. However, thermal effects must be accounted for in the data analysis

Heterogeneous Response Functions in Advertising

De Fleur (1956) provides the earliest evidence of diminishing returns. He finds a common logarithmic pattern for leaflets dropped and message recalled in field experiment. Since then, many researchers have applied logarithmic or square root patterns to capture the effect of diminishing returns with their advertising response modeling across different media. But discussions with managers support the notion that the diminishing returns to incremental dollars spent on one medium (say, television) are not likely to be the same as those for equivalent dollars spent on other media (e.g., Print). But if diminishing returns indeed vary across media, how does that change the resulting allocation recommendation? To address this issue, we derive a dynamic model that captures the notion of differential diminishing returns and disentangles it from closely related notions of differential carryovers and differential ad effectiveness. Second, we develop a systematic method to estimate the model's parameters using market data and illustrate empirically that all three effects, diminishing returns, carryover and ad effectiveness vary across the four media employed. Finally, we investigate the normative implications for managerial decision-making. Here, we additionally account for varying media buying efficiencies across media. Taken together, the approach and its illustration should provide managers with a better toolkit to allocate their multimedia budgets. --

Effects of bolt-hole contact on bearing-bypass damage-onset strength

A combined experimental and analytical study was conducted to investigate the effects of bolt-hole contact on the bearing bypass strength of a graphite-epoxy laminate. Tests were conducted on specimens consisting of 16-ply quasi-isotropic T300/5208 laminates with a centrally located hole. Bearing loads were applied through a clearance-fit steel bolt. Damage onset strength and damage mode were determined for each test case. A finite element procedure was used to calculate the bolt-hole stresses and bolt contact for each test case. A finite element procedure was used to calculate the bolt-hole stresses and bolt contact for each measured damage-onset strength. For the tension bearing-bypass cases tested, the bolt contact half-angle was approximately 60 degrees at damage onset. For compression, the contact angle was 20 degrees as the bypass load increased. A corresponding decrease in the bearing damage onset strength was attributed to the decrease in contact angle which made the bearing loads more severe. Hole boundary stresses were also computed by superimposing stresses for separate bearing and bypass loading. Stresses at the specimen net section were accurately approximated by the superposition procedure. However, the peak bearing stresses had large errors because the bolt contact angles were not represented correctly. For compression, peak bearing stress errors of nearly 50 percent were calculated