A review of fracture toughness transferability with constraint and stress gradient

Abstract

A B S T R A C T In this review paper, only constraint and stress gradient approaches to transferability of fracture toughness are examined. The different constraint parameters are defined and discussed, and one example is given in each case. Factors that influence the constraint are studied. Special attention is given to the actual trends to use the plastic constraint in the material failure master curve and the material transition temperature master curve. The paper also deals on the influence of T stress on the crack path and out-of-plane constraint and on the influence of thickness on fracture toughness. The uses of plasticity with gradient and the relative stress gradient in local fracture approaches are also examined.A = constant A i = Williams' stress distribution parameterŝ A i = HRR stress distribution parameters A P = Constraint parameter A p,c = current plastic zone area A p,ssy = reference plastic zone area A εp,c = area surrounded by the equivalent plastic strain A εp,ref = reference area surrounded by the (ε p ) isolines B = thickness B 0 , B 1 , B 2 and B 3 = constants D = pipe diameter D 0 = length E = Young's modulus F = geometry correction factor G = shear modulus G c = fracture toughness I = complex function of eigenvalues I n = dimensionless integration constant J = path integral J c = fracture toughness J Ic = fracture toughness in plane strain conditions J ref = reference fracture toughness K Ic = fracture toughness for plane strain conditions K Jc = fracture toughness K Iz,c = three-dimensional fracture toughness in pure mode I K 0 = lower bound of the notch fracture toughness K ρ,c = notch fracture toughness K 0 ρ;c = fracture toughness corresponding to T ef,c = 0 L = plastic constraint factor N = strain hardening exponent

An η‐compliance method to estimate the J‐Δa curve for pipes with a circumferential surface crack

“…8c). Ruggierie and Cravero 21 have reported a similar load-level dependence of the η value for pin loaded and clamped SE(T) specimen. A typical FE model of the pipe includes approximately 50 000-60 000 nodes and (8)].…”

“…However, previous studies 8- 10 have demonstrated the over-conservatism in J-Δa curves from these standard fracture specimens, including the single-edge-notched bend, SE(B) specimen and the compact tension, C(T) specimen due to the significant crack-front constraint loss in the pipes. Pluvinage et al 21 have presented a comprehensive review on the constraint and stress gradient approaches for fracture toughness, based on four different constraint parameter, L , β, Q and T. Recent studies [22][23][24][25][26][27] advocate the use of single-edge-notched tension, SE(T), specimens to measure the J-Δa curve for surface-cracked pipes due to the closer constraint condition between an SE(T) specimen and a surfacecracked pipe than that between a deeply notched SE(B) or C(T) specimen and a surface-cracked pipe. 11 The geometry and plasticity-induced constraint loss can lead to significant differences in the near tip stress triaxiality between a surface crack front and a deeply cracked fracture specimen.…”

Characterisation of the surface damage of X38CrMoV5 (AISI H11) tool steel at room temperature and 600 °C

“…18 Strain energy density has been used to characterise the cycles to failure in the high cycle regime of a 40CrMoV13.9 steel from room temperature up to 650°C. [21][22][23]. 20 Threshold values of FCGR at 600°C are found to be excessive.…”

Two basic approaches in a search of the crack propagation angle

“…It should be noted that the one‐term asymptotic expansion is not enough for correct prediction of the crack‐tip stress field. In this case, additional parameters should be introduced in basic equations of fracture mechanics for better description of the crack‐tip stress field . One of these parameters is the second term (non‐singular T ‐stress) in a series expansion of the elastic stress components.…”