13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Λ= fN s N√2π exp,- 1 2 εe p q-εN SN 2. (3) Where: f N= volume fraction of void nucleating particles sN = standard deviation ε N = mean value ε eq P = equivalent plastic strain. An additional feature of the GTN model, introduced by Tvergaard and Needleman, was to take into consideration the initial void fraction f0, a critical void volume fraction for coalescence fc, and a critical void fraction that corresponds to the failure of the matrix, fF. f*=/ f for f ≤fc fcfu *- f c fF- fc ! f- fc$ for f >fc 3 (4) Where: fc = critical void volume fraction (typically fc = 0.15 for carbon steel) fF = actual void volume fraction at final fracture fu * = modified void volume fraction (typically f u * = 1/q1) The distribution of the initiating particles as well as their void volume fraction are key microstructural features that are needed to accurately calibrate the GTN model. These material specific parameters are usually calibrated using metallographic observations of the non-fractured material and the material volume around fractured test specimens from carefully controlled experiments. The fracture tests can be performed using a range of specimens introducing different levels of constraint and stress states. The highly constrained pre-cracked compact test (CT) specimen is frequently used to measure fracture toughness and will be used and discussed throughout this paper. Previous experiments have shown that void volume fractions (VVF) may vary by material but also by specimen types. Work by Kerry et al [7] on a high strength and low toughness aluminium alloy AL2024-T351 have shown that there is a difference in the distribution of the void volume fraction below the fracture surface for notched tensile specimens when compared with CT specimens. Using 3D X-ray tomography Taylor et al demonstrated that the CT specimens exhibited a higher concentration of voids close to the fracture surface when compared with that measured close to the fracture surface in notched tensile specimens. On the other hand, the voids extended further below the fracture surface in notched tensile specimens than was observed in CT specimens. Further work has recently been performed by Daly et al [8] with respect to an A508 Class 3 RPV ferritic steel to quantify the void volume fraction using 2D optical micrographs. Similar
RkJQdWJsaXNoZXIy MjM0NDE=