Crack tip higher order stress fields for functionally graded materials with generalized form of gradation |
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Authors: | Xiu-fa Yan Qi-hu Qian Hong-biao Lu Wei Wang and Ao Sun |
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Affiliation: | (1) University of Rhode Island, Kingston, RI, USA;(2) University of Massachusetts, Dartmouth, MA, USA;(3) Auburn University, Auburn, AL, USA |
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Abstract: | A generalized form of material gradation applicable to a more broad range of functionally graded materials (FGMs) was presented.
With the material model, analytical expressions of crack tip higher order stress fields in a series form for opening mode
and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis. Then, a numerical
experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and
their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite
element analysis by local collocation and then comparing the estimations with the existing solution. The expressions show
that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and
at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects
on crack tip stress fields in the case of FGMs. The numerical experiment further confirms that the addition of the nonhomogeneity
specific terms in the expressions not only improves estimates of stress intensity factor, but also gives consistent estimates
as the distance away from the crack tip increases. Hence, the analytical expressions are suitable for the representation of
crack tip stress fields and the analysis of full field data. |
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