Abstract
Scale or size effects in fracture result from the interaction of some energies dependent upon volume and other energies dependent on area (cube-square scaling). The known scaling laws within the lefm and nlefm ranges and within the rigid-plastic range are highlighted along with applications. This paper derives for the first time the scaling laws for elastoplastic fracture based on linear power-law behaviour which span the different regimes from lefm at one end of the spectrum to extensive ductile fracture at the other. The existence of a master-curve of normalised load X vs normalised displacement ū is demonstrated on which fall all results from different size geometrically-similar testpieces up to first cracking. Crack propagation in larger bodies begins at smaller normalised loads and displacements than geometrically-similar small bodies. Large bodies behave as if their fracture toughness were given by (R/λ), where λ(>1) is the scaling factor, rather than by the material value R. Propagation behaviour is path-dependent and each size cracked body has its own X-ū propagation plot. This explains departures from ‘geometric’ (λ3) scaling well-known in the literature. Comparison is made with old and recent experimental results.
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Atkins, A. Scaling laws for elastoplastic fracture. International Journal of Fracture 95, 51–66 (1999). https://doi.org/10.1023/A:1018683830486
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DOI: https://doi.org/10.1023/A:1018683830486