Notes

Chapter 8: Implications for Everyday Systems

Section 3: The Breaking of Materials


Phenomenology of microscopic fracture

Different materials show rather different characteristics depending on how ductile or brittle they are. Ductile materials—such as taffy or mild steel—bend and smoothly neck before breaking. Brittle materials—such as chalk or glass—do not deform significantly before catastrophic failure. Ductile materials in effect flow slightly before breaking, and as a result their fracture surfaces tend to be less jagged. In addition, in response to stresses in the material, small voids often form—perhaps nucleating around imperfections—yielding a pock-marked surface. In brittle materials, the beginning of the fracture surface typically looks quite mirror-like, then it starts to look misty, and finally, often at a sharply defined point, it begins to look complex and hackled. (This sequence is qualitatively not unlike the initiation of randomness in turbulent fluid flow and many other systems.) Cracks in brittle materials typically seem to start slowly, then accelerate to about half the Rayleigh speed at which small deformation waves on the surface would propagate. Brittle fracture involves violent breaking of atomic bonds; it usually leaves a jagged surface, and can lead to emission of both high-frequency sound as well as light. Directly around a crack complex patterns of stress are typically produced, though away from the crack they resolve quickly to a fairly smooth and simple form. It is known that ultrasound can affect the course of cracks, suggesting that crack propagation is affected by local stresses. There are many different detailed geometries for fracture, associated with snapping, tearing, shattering, pulling apart, and so on. In many situations, individual cracks will split into multiple cracks as they propagate, sometimes producing elaborate tree-like structures. The statistical properties of fracture surfaces have been studied fairly extensively. There is reasonable evidence of self-similarity, typically associated with a fractal dimension around 0.8 or slightly smaller.


From Stephen Wolfram: A New Kind of Science [citation]