A comparison between rapid expressions for evaluation of the critical J-integral in plates with U-notches under mode I loading

In this paper, some practical linear-elastic equations for evaluation of the critical value of the J-integral in plates with U-notches under mode I loading are presented and applied to brittle and quasi-brittle materials. The relationship between the J-integral and strain energy averaged over a well-defined control volume, depending on the static properties of the material, is applied, with the aim of obtaining the final expressions. It is found that these three proposed equations provide the same results, with any differences being negligible. By using one of these equations, one can evaluate J(cr) and then predict the critical fracture load by means of the J(cr) criterion. The results have shown that the critical value of the J-integral (J(cr)) is a function of the ratio of the material control radius to the notch-root radius (R(c)/rho), the ratio of specimen width to notch depth (w/a), the notch acuity (a/rho), and the loading condition (tensile or bending loadings) in U-notches under mode I loading. However, the effect of the loading condition, a/rho and w/a ratios may be negligible. Therefore only the R(c)/rho ratio (i.e. the material properties and the notch-root radius of the specimen) affects J(cr)