The Mechanics of Fractal Damage
Final rept. 30 Sep 1990-Jan 1992
TEXAS A AND M UNIV COLLEGE STATION DEPT OF MECHANICAL ENGINEERING
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This report describes a preliminary investigation of the applicability of fractal geometry to damage modeling. Microstructural heterogeneity, both the size distribution and spatial distribution of microstructural features, can be modeled simply and compactly with a fractal dimension. The ultimate goal of this research is the development of an alternative to continuum damage and micromechanics models. The scaling nature of fractal geometry may aid the development of models that connect microscale damage with global mechanical response. An assumed fractal size distribution of microcracks in a brittle solid was used to derive the Weibull distribution for strength, and a relationship between the Weibull shape parameter and the fractal dimension of the flaw distribution was obtained. Published data on the strength of glass fibers were consistent with a fractal flaw distribution. Stable damage evolution in tougher materials with fractal microstructures was also considered. Although preliminary results are promising, further work is necessary to develop the concepts of fractal damage more fully. Damage Mechanics, Micromechanics, Composite Materials, Fractal Geometry.
- Laminates and Composite Materials