G. Garmong

Attainment of full interfacial contact during diffusion bonding

The rate-limiting step in the diffusion bonding of materials such as Ti−6 A1−4V is the complete elimination of porosity from the bondline. Here a model for predicting the time to complete bonding based on the mechanisms of porosity removal is developed. Bonding is pictured as a two-stage process: in the first stage long-wavelength surface asperities are flattened by plastic flow, and in the second stage voids are reduced in size by a combination of plastic flow and vacancy diffusion. Both stages have been treated analytically, and the resulting predictions of bonding time are in general agreement with the times usually required for industrial diffusion-bonding operations. In addition, a limited number of experiments have been conducted to verify some basic predictions of the model. As expected, the calculations have shown that the bonding die must be carefully designed so that the local bonding pressure is never unreasonably low. The results also demonstrate that the presence of long-wavelength surface asperities—a result of most surface preparation procedures —can significantly lengthen the bonding times.

A Theory for the mechanical properties of metal-matrix composites at ultimate loading

A theory describing the strain, ultimate strength, and work during uniform strain to ultimate loading of metal-matrix composites deformed in tension parallel to the reinforcement is presented. These quantities may be calculated for composites of arbitrary volume fraction using only the component stress-strain curves. The theory is based on the systematic application of a macroscopic principle commonly used to predict the ultimate strength of ductile monolithic materials—namely, that necking occurs when the load borne by the material is maximized. For brittle reinforcing elements, the results are identical to those of previous workers. For ductile reinforcing elements, necking strains intermediate between those of the components and ultimate strengths increasing smoothly with volume fraction from that of the matrix to that of the reinforcement are predicted. The theory can be used to predict the variation of composite ultimate properties with any parameter of interest. In this paper the variation with volume fraction and yield strength of the matrix are studied, with both exact solutions and useful approximations being derived.

Matrix strengthening mechanisms of an iron fiber-copper matrix composite as a function of fiber size and spacing

Copper matrix-iron fiber composites of fiber diameters from 10 to 5 × 10−3 mils and volume fractions from 0.03 to 0.97 were fabricated in order to study the dependence of mechanical properties on these variables. Composite elastic moduli agreed well with the predictions of the rule of mixtures. However, matrix and composite yielding and plastic flow were quite dependent on fiber diameter and spacing, exhibiting positive deviations from the simple rule of mixtures by factors of more than five in some cases. Yielding behavior may be explained by a combination of dislocation extrusion and pileup models for low volume fractions of fiber. Triaxiality generated by the difference in Poisson coefficients of the phases inhibits matrix yielding in higher volume fraction composites, allowing matrix flow only when the fibers also yield.

Elastic-plastic analysis of deformation induced by thermal stress in eutectic composites: II. thermal Expansion

In part I a theory was developed to analyze the deformation produced in eutectic composites by temperature changes. Experimental determinations of the coefficient of expansion are used here to test the predictions of that theory. Measurements of length versus temperature in the absence of external stresses were made for Al-Al3Ni, Al-CuAl2, and Sb-Cu2Sb eutectic composites, and for monolithic 6061 Al. Hysteresis loops in the graph of composite coefficient of expansion vs temperature are seen when the expansion coefficients of the phases are different and plastic deformation occurs. The nature of the hysteresis is shown to depend upon heating and cooling rates, prior history and the relative values of the matrix and reinforcement expansion coefficients. The theory correctly predicts these qualitative effects. In Al-Al3Ni the available component data justify a quantitative comparison of calculated and experimentally determined coefficient of expansion-temperature curves. The values compare well, further verifying the analytical approach.

Crystallography and morphology of as-grown and coarsened Al-Al3Ni directionally solidified eutectic

The structure of the rodlike Al-Al3Ni eutectic directionally solidified vertically at rates ranging from 0.8 to 36.5 cm/h was studied in as-grown and coarsened conditions. The observed crystallographic relations are growth direction ∥ [010]A13Ni ∥ [011]A1or [21l]A1 and (111)A1 ∥ (102)A13Ni in the zone of the growth direction. The facet structure of as-grown rods is most pronounced at low growth rates. Elevated temperature exposure of the composite produces fiber coarsening and improved definition of the facets, both effects becoming more rapid with increasing growth rate. The facets themselves are, in many cases, of such crystallographic orientations that nearly equal atomic densities occur on both sides of the boundary. We conclude that, although faceting occurs to a marked degree, the related shape anisotropy is probably of second-order importance in calculations of coarsening rates. However, the presence of facets does preclude fiber foreshortening during coarsening.

Monotonic and fatigue deformation of Ni-W directionally solidified eutectic

Unlike many eutectic composites, the Ni-W eutectic exhibits extensive ductility by slip. Furthermore, its properties may be greatly varied by proper heat treatments. Here results of studies of deformation in both monotonic and fatigue loading are reported. During monotonie deformation the fiber /matrix interface acts as a source of dislocations at low strains and an obstacle to matrix slip at higher strains. Deforming the quenched-plus-aged eutectic causes planar matrix slip, with the result that matrix slip bands create stress concentrations in the fibers at low strains. The aged eutectic reaches generally higher stress levels for comparable strains than does the as-quenched eutectic, and the failure strains decrease with increasing aging times. For the composites tested in fatigue, the aged eutectic has better high-stress fatigue resistance than the as-quenched material, but for low-stress, high-cycle fatigue their cycles to failure are nearly the same. However, both crack initiation and crack propagation are different in the two conditions, so the coincidence in high-cycle fatigue is probably fortuitous. The effect of matrix strength on composite performance is not simple, since changes in strength may be accompanied by alterations in slip modes and failure processes.

The directional solidification of Al−Cu−Mg monovariant alloys

Alloys whose compositions lie along the ternary monovariant line between the binary Al−Cu and the ternary Al−Cu−Mg eutectics were directionally solidified at rates of 0.17 to 20 cm per hr. Both plane front and cellular or dendritic structures were obtained. A criterion for the breakdown of plane front growth based on constitutional supercooling was found to be valid at both ends of the monovariant line. It was found that the amount of ternary eutectic present at the boundaries of cellular or dendritic structures may be closely predicted by the nonequilibrium lever rule for freezing.

Structure and crystallography of curved Al-Al3Ni and Al-CuAl2 directionally solidified eutectic alloys

Curved ingots of Al, Al-6.1 pct Ni, and Al-33.2 pct Cu were grown by rotating a mold on a radius arm through an induction coil. The specimens were examined to determine their microstructural morphology and crystallography. In both eutectic alloys the minor phase (Al3Ni or CuAl2) curves to follow the shape of the mold. The lamellae in Al-CuAl2 and the fibers in Al-Al3Ni are morphologically identical to those in linearly grown samples. In both cases preferred orientations develop between the phases early in the growth process and remain nearly unchanged at various angular positions. In Al-CuAl2 rotations at sub-grain-like faults allow the crystallographic curvature, but no mechanism could be identified in Al-Al3Ni. Observations of the detailed crystallographic relations suggest that a boundary-coincidence model provides a useful description of the Al-CuAl2 interfaces.

Elastic-plastic analysis of deformation induced by thermal stress in eutectic composites: III. thermal-cycling damage

The analytical method of part I is used to calculate the dependence of composite deformation on cyclic, geometric, and constituent deformation parameters. The calculated hysteresis loop of matrix stress versus temperature caused by plastic deformation stabilizes after a few cycles so that a steady-state plastic compression-tension fatigue results when no external stress is present. In most cases plastic shakedown is thereby precluded. The calculated stresses can be much different from those predicted by existing elasticity analyses. Even when the matrix plasticity is fairly small, the elasticity approaches at best predict the range of, but not the extrema in, component stresses. Failure of a cycled eutectic composite may be due to any of several causes, and all must be considered in any evaluation.

The aging response of Al-Cu and Al-Cu-Mg directionally solidified eutectics

The microstructure and mechanical properties of directionally solidified Al-Cu eutectic and the microstructure of directionally solidified Al-Cu-Mg eutectic alloys have been studied in as-grown, quenched, and aged conditions. In both systems the microstructure of the aluminum-rich α phase responded to aging treatments in a manner like that of dilute alloys of comparable composition. The cooling rate of the alloys from the solutionizing temperature is important in determining final α-phase composition, since the diffusion path to the lamellar interphase boundaries is only on the order of 1 µ in length. Even when water quenched, the aged α lamellae contain precipitate-free zones along the interphase boundaries, probably due to the epitaxial precipitation of solute as CuAl2 or CuMgAl2 onto the corresponding bulk phases. Mechanical testing of the Al-Cu binary composite in tension and compression shows that the strength of properly aged specimens is twice that of as-grown material. The calculated α- phase yield strength is generally higher than expected, and there is a strength-differential effect whose magnitude varies with heat treatment.