Scaling of quasibrittle fracture: asymptotic analysis |
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Authors: | ZP BA?ANT |
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Affiliation: | (1) Civil Engineering and Materials Science, Northwestern University, Evanston, Illinois 60208, USA |
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Abstract: | Fracture of quasibrittle materials such as concrete, rock, ice, tough ceramics and various fibrous or particulate composites,
exhibits complex size effects. An asymptotic theory of scaling governing these size effects is presented, while its extension
to fractal cracks is left to a companion paper 1] which follows. The energy release from the structure is assumed to depend
on its size D, on the crack length, and on the material length c
f governing the fracture process zone size. Based on the condition of energy balance during fracture propagation and the condition
of stability limit under load control, the large-size and small-size asymptotic expansions of the size effect on the nominal
strength of structure containing large cracks or notches are derived. It is shown that the form of the approximate size effect
law previously deduced 2] by other arguments can be obtained from these expansions by asymptotic matching. This law represents
a smooth transition from the case of no size effect, corresponding to plasticity, to the power law size effect of linear elastic
fracture mechanics. The analysis is further extended to deduce the asymptotic expansion of the size effect for crack initiation
in the boundary layer from a smooth surface of structure. Finally, a universal size effect law which approximately describes
both failures at large cracks (or notches) and failures at crack initiation from a smooth surface is derived by matching the
aforementioned three asymptotic expansions.
Walter P. Murphy Professor of
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | Scaling Size effect Structural strength Load capacity Nonlinear fracture mechanics quasibrittle fracture asymptotic methods stable load growth crack initiation energy release |
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