‘When can we apply LEFM principles to elastic softening materials?’
✍ Scribed by E. Smith
- Book ID
- 104614433
- Publisher
- Springer Netherlands
- Year
- 1993
- Tongue
- English
- Weight
- 618 KB
- Volume
- 64
- Category
- Article
- ISSN
- 1573-2673
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✦ Synopsis
The paper focusses on the determination of R, the size of the fully developed softening zone associated with a semi-infinite crack in a remotely loaded infinite elastic softening solid. R is a characteristic length for a material, and is important in that if R is less than an appropriate characteristic dimension of a structure, then LEFM principles can be used to describe the structure's failure. With Pc and 6c being respectively the maximum stress and displacement within the softening zone, then provided the softening is not particularly pronounced, i.e. the area under the stress (p)-displacement (v) curve is ~ 0.25pc5c, it is shown that R ~ 0.4Eohc/pc and R is relatively insensitive to the precise p-v softening behaviour (E0 = E/(1 -v z) where E is Young's modulus and v is Poisson's ratio). However, when the area under the curve is ~ 0.25pc6c, then R increases above this 0.4Eof~/pc value. For this case, and provided most of the area under the p-v curve is not associated with the tail in the softening law, a more appropriate expression for R is 2 2 2 ' 2 R ~ O.1Eofo/K~, with K~/Eo being the area under the/~v curve and K® being the stress intensity associated with the full development of a softening zone.