Erratum: “Plane-Strain Propagation of a Fluid-Driven Fracture: Small Toughness Solution” [Journal of Applied Mechanics, 2005, 72(6), pp. 916–928]

Equations ,,,, and expression for

Π_{1}

in Appendix D in the published paper contain typographical errors. The corrected equations are written as follows:

\hat{K} = {(\frac{2}{3})}^{- 1 ∕ 3} γ^{- 1 ∕ 2} K

28

\hat{ε} = \frac{E^{'} μ^{'} v_{tip}}{K^{' 2}}

35b

E (K) = B_{1} K^{b} = {(\frac{2}{3})}^{1 ∕ 3} β_{1} {\hat{K}}^{b}

47

{\hat{Ω}}_{0} (\hat{ξ}) = {\hat{ξ}}^{1 ∕ 2} + F_{00} (\hat{ξ}) + \frac{4}{π} \sum_{j = 1}^{n - 1} {[a_{i} F_{\ln} (\hat{ξ}, \hat{η}) + b_{i} δ F (\frac{2}{3}, \hat{ξ}, \hat{η})]}_{\hat{η} = {\hat{ξ}}_{j}}^{\hat{η} = {\hat{ξ}}_{j + 1}} + F_{0 \infty} (\hat{ξ})

C16

Π_{1} = b_{11} {}_{2}F_{1} (c_{11}, 1; \frac{1}{2}; ξ^{2}) + b_{12} {}_{2}F_{1} (c_{12}, 1; \frac{1}{2}; ξ^{2}) + b_{13} ξ^{2} {}_{2}F_{1} (c_{13}, 2; \frac{3}{2}; ξ^{2}) + b_{14} (2 - π ∣ ξ ∣) (Appendix D, p. 927)

We are grateful to Dr. Andrew Bunger for bringing to our attention the second error.

View Original Article

by American Society of Mechanical Engineers