Application of an elastic-plastic model to the use of small specimen strength ratio for measuring fracture toughness

Data reported by Server and Wullaert correlating specimen strength ratio with fracture toughness were analyzed with the D-BCS-HSW model. This model is based on the Dugdale model, elaborated by Bilby, Cottrell, and Swinden, and extended by Heald, Spink and Worthington. The data included instrumented pre-cracked Charpy results on HSST plate 02, as well as static, intermediate, and dynamic tests of I-T compact and bend specimens of SA 533B-1 steel. The model relates the fracture toughness to the crack length, specimen shape and size, applied failure stress, and effective flow strength. The only parameter not provided by the data is the constraint factor (M), the ratio of the effective flow strength to the yield strength. The model was fitted to the data by non-linear least squares methods by which M was determined to be approximately 2.5 for the Charpy data, and from 2.1 to 2.6 for the other specimen data. The fit is considered to be reasonably good throughout the range from linear-elastic fracture mechanics through to plastic collapse. The result for the Charpy data is considered to be as good as that for the other specimens. The determination of only one parameter is needed to establish the relationship between specimen strength ratio and fracture toughness. This relationship then applies to the entire range of fracture regimes