We show that mechanical design can be conducted where consideration of polycrystalline microstructure as a continuous design variable is facilitated by use of a spectral representation space. Design of a compliant ÿxed-guided beam is used as a case study to illustrate the main tenets of the new approach, called microstructure-sensitive design (MSD). Selection of the mechanical framework for the design (e.g., mechanical constitutive model) dictates the dimensionality of the pertinent representation. Microstructure is considered to be comprised of basic elements that belong to the material set. For the compliant beam problem, these are uni-axial distribution functions. The universe of pertinent microstructures is found to be the convex hull of the material set, and is named the material hull. Design performance, in terms of speciÿed design objectives and constraints, is represented by one or more surfaces (often hyperplanes) of ÿnite dimension that intersect the material hull. Thus, the full range of microstructure, and concomitant design performance, can be exploited for any material class. Optimal placement of the salient iso-property surfaces within the material hull dictates the optimal set of microstructures for the problem. Extensions of MSD to highly constrained design problems of higher dimension is also described.

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A material placed in direct contact with a high explosive experiences a Taylor wave (triangular-shaped) shock loading profile. While a large number of studies have probed the structure, properties, and tensile response of materials subjected to square-topped shock loading pulses histories, few studies have systematically quantified the influence of shock-wave profile shape on material response. Samples of 316L stainless steel were shock loaded to peak stresses of 6.6, 10.2, and 14.5 GPa to examine the influence of square-topped and triangular (Taylor wave)-shaped pulse loading on the dynamic tensile behavior (spallation). The 316L SS samples were loaded with a square-topped pulse to each peak shock stress, using a pulse duration of 0.9 μs. They displayed increasing incipient spallation damage with increasing peak stress. Samples loaded to the peak shock stresses of 6.6 and 10.2 GPa with a Taylor-wave loading pulse (which immediately unloads the sample after the peak Hugoniot stress is achieved) exhibited no damage. Only the 14.5 GPa Taylor pulse shocked sample exhibited both a pull-back signal and incipient damage following tensile loading. The damage evolution in the square-topped shocked samples was found to be a mixture of void and strain localization damage, the void fraction increasing with peak shock amplitude. With the Taylor-wave loading profile of amplitude 14.5 GPa, a high incidence of shear localization and low incidence of void formation was observed. Detailed analysis of the damage evolution as a function of shock pulse shape revealed that a nominally equivalent level of incipient damage was obtained using a Taylor-wave or square-topped loading pulse when a similar rear sample surface stress-time total impulse was applied. In order to induce equivalent damage with the two pulse shapes, the impulse applied needed to be nominally matched. For this to occur, the Taylor-wave profile required twice the amplitude of the square one and the durations of each pulse needed to be appropriately scaled. Detailed metallographic, microtextural, and void shape and size analyses of the damage evolution are presented as a function of the inferred loading pulse shape and the peak Hugoniot stress.

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