A Revised Procedure for the Construction of a 3-Parameter $J_R$ Resistance Curve and the Determination of Initiation Toughness $J_{0.2}$
Wardle G
(Received 24 February 2006; accepted 5 March 2007)

Abstract

Fracture toughness testing procedures often advocate the use of a 3-parameter offset power law fit to define a resistance curve, and subsequently an estimate of initiation toughness (e.g., $J_{\mathrm{0.2}}$). $J_R=A+\alpha {\left(\mathrm{\Delta }a\right)}^{\beta }.$ Experience has indicated that the fit coefficients A, α, and β are highly variable. What is required is a consistent method of estimating A and thus α and β to reflect physical sense. In this paper it is proposed that the offset A is defined using a J-elastic term $J_e$ given by $A=J_e=W/2({\sigma }_y^2∕E^{\prime })f(a_o∕W)$. Experimental data are provided in support of the use of $J_e$ for a well characterized A533B-1 steel. Tests were made at ambient temperature using geometrically scaled plain-sided and side-grooved compact C(T) specimens of sizes $20<W<200\mathrm{mm}$. The fixing of A through the use of $J_e$ provides less variable α and β parameters. The exponent β is found to be independent of W, noting that ${\beta }_{\mathrm{SG}}<{\beta }_{\mathrm{plain}}$, as is the α coefficient for side-grooved specimens $\left({\alpha }_{\mathrm{SG}}\right)$. The α coefficient for plain-sided specimens $\left({\alpha }_{\mathrm{plain}}\right)$ may be related to specimen width and thus thickness (B) for geometrically-scaled specimens, noting that ${\alpha }_{\infty }$ approximates to ${\alpha }_{\mathrm{SG}}$. ${\alpha }_{\mathrm{plain}}={\alpha }_{\infty }(1+1∕\sqrt{B})$. The results indicate that the $J_R$ curves and thus $J_{0.2}$ vary with specimen width W. For conventional laboratory-sized C(T) specimens (i.e., $25<W<100\mathrm{mm}$) the variation in $J_{0.2}$ with a size over this range is of the same order as the general level of scatter observed in the $J_{0.2}$ measurement. However, for specimen sizes outside of this range size effects may be predicted.

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Author Wardle G Title A Revised Procedure for the Construction of a 3-Parameter $J_R$ Resistance Curve and the Determination of Initiation Toughness $J_{0.2}$ Symposium , Committee: on