Application of image processing for simulation of mechanical response of multi-length scale microstructures of engineeri
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INTRODUCTION
MICROSTRUCTURES often contain features at length scales ranging from nanometers to millimeters. These features have complex geometry, their locations and orientations are usually nonuniform, and strong spatial correlation often exists among different types of features. In such complex microstructures, deformation and fracture processes are usually governed by several types of microstructural features that may be present at widely different length scales. Further, damage evolution and local fracture processes at lower length scales are affected by the amount, size distribution, and spatial arrangement of features at higher length scales, and vice versa. The “coupling effect” of the microstructural features at widely different length scales, and their complex geometry, creates serious difficulties in modeling the mechanical response of real multi–length scale microstructures. For example, consider a typical microstructure of A356 cast alloy (an Al-Si-Mg base alloy containing 7 wt pct Si and 0.3 wt pct Mg) shown at different magnifications in Figure 1 to illustrate the presence of microstructural features at widely different length scales. Figure 1(a) shows a very low magnification macrograph that depicts nonuniformly distributed micropores, which is typical in cast microstructure. Figure 1(b) shows the microstructure at somewhat higher magnification, illustrating that the micropore sizes are on the order of 50 to 300 mm and interpore distances are on the order of 300 to 500 mm (,half a millimeter). The microstructural space between micropores contains features at lower length scales. Figure 1(c) is a higher magnification micrograph depicting the presence of aluminum-rich dendrite cells whose sizes are on the order of 20 to 70 mm and silicon-rich interdendrite regions. Figure 1(d) is a high ARUN M. GOKHALE, Professor, and SHICHEN YANG, Graduate Student, are with the Department of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245. Manuscript submitted November 3, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
magnification micrograph (500X) which shows the silicon particles in the interdendritic regions. The Si particles have sizes on the order of 1 to 4 mm, and the interparticle distances between the Si particles are on the order of 3 to 5 mm. Therefore, the length scales of the micropores and Si particles differ by about two orders of magnitudes. In this alloy, microstructural features such as Mg2Si precipitates are present at the submicron and lower length scale regimes. An important damage mechanism in A356 cast alloy is gradual fracture and debonding of silicon particles.[1–4] Such damage evolution is typical of many alloys containing particulate phases. Fracture and debonding of Si particles (Figure 2(a)) initiates at stresses slightly above the yield stress.[1] The extent of this damage increases with the applied stress.[1–4] At sufficiently high stresses, microcracks link the fractured/ debonded Si particles in the interdendritic regions, and ultimately l
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