A modification on Brook formula in calculating the misfit of Ni-based superalloys. (15th July 2017) - Long, Haibo; Mao, Shengcheng; Xiang, Sisi; Chen, Yanhui; Wei, Hua; Zhou, Yizhou; Liu, JinLai; Liu, Yinong
Abstract: The validity of the Brooke formula in estimating the lattice misfit based on dislocation network structure in Ni-based superalloys is investigated. The misfit value of a sample subjected to prolonged thermal exposure as derived from the popular Brooke formula is below that determined by X-ray diffraction (XRD) method, whereas the misfit estimated using the Brooke formula for a sample subjected to creep is greater than that determined by XRD method. These discrepancies imply the invalidity of the popular Brooke formula in two aspects: that a dislocation network is not always mature to fully relax the lattice misfit leading underestimate the misfit and that using the full magnitude of the Burgers vector overestimates the misfit. To overcome this problem, a modified Brook formula using the 100 projection of the edge component of a Burgers vector as the effective magnitude to relieve the misfit is proposed. The misfit derived from the modified Brook formula is in good agreement with the values determined by XRD method for a number of Ni-based superalloys studied. Graphical abstract: Highlights: Brooke formula is only valid for estimating the lattice misfit relaxed by the dislocation network. The two historical Brooke formulas overestimate the magnitude of the misfit. The modified Brooke formula can correctly estimate the misfit.