Effect of elastic gradient along the crack front on the crack-tip fields for a propagating crack in a graded material

• Derived three-dimensional structure of crack-tip fields for propagating crack.
• The elastic properties are assumed to vary along the propagating crack front.
• Inverse square root behavior of stress field is not affected by elastic gradient.
• The field is affected due to (i) three-dimensionality and (ii) elastic gradient.
• The structure of terms r3/2r3/2 and above in the stress field is affected for mode-I.

The near-tip fields for a crack propagating in a graded material are derived assuming exponential variation of properties along the crack front. Using a three-dimensional framework, the expansion of the field is obtained through an asymptotic analysis. Though the structure of the first two terms in the expansion is found to be identical to that for a plane crack propagating in a homogeneous plate, the multipliers of the terms are functions of z, implying variation of stress intensity factor along the crack front. The structure of the higher order terms is affected by both three-dimensionality and elastic gradient.

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