Creep crack growth tests, conducted on contoured double cantilever beam (DCB) specimens are described for aluminium alloy RR58 and a chromium-molybdenum-vanadium steel. The results are analyzed in terms of ˙J, the rate equivalent of the J contour integral, which is a nonlinear fracture mechanics parameter. Direct proportionality is found between crack growth rate, ˙a and ˙J. The treatment is shown to reveal a unification of the linear elastic fracture mechanics and net section or reference stress descriptions of creep cracking.

Possible methods for evaluating J for a three-point bend specimen are reviewed and the effects of slow crack growth, experimental limit load, and lateral constraint noted. A procedure, compatible with linear elastic fracture mechanics (LEFM) and crack opening displacement (COD) testing, is suggested for finding Jc.

The dependence of J-R curves on size of test piece is examined for fully plastic deep notch bend (DNB) tests on H Y 130 steel, taken to large amounts of ductile crack growth (60 per cent of the ligament) for a range of initial widths at 20 mm thick and one geometrically similar size, 50 mm thick. The object is to understand the cause of the widely different patterns of behaviour that have been reported in the literature, even within the DNB type of configuration. In the present tests, the proportion of shear lip is the same for the geometrically similar pair but the J-R curve for the 50 mm thick piece is much lower than for the similar piece, 20 mm thick.The rate of change of displacement, dqldn, is analysed using the factor, r*, that defines the instantaneous centre of rotation at each step of growth, to give a measure of crack tip opening angle (CTOA), a s . After an initial transient regime of small growth, ag and r* remain constant. The normalized load, L, rises due to work hardening during crack growth by amounts that depend on size while a8 and r* vary mildly with initial width to give an appreciable variation of the combined term La&*, which is the factor that controls the behaviour of the J , curves. It is speculated that CTOA and its variation with configuration (as seen in the literature) may, for large growth, assume the role of the two parameters suggested in recent literature as controlling the variation of toughness with constraint. K e y words: deep notch bend tests, ductile tearing, J-R curves, crack opening displacement, fracture, energy dissipation rate

No abstract

The equations for the energy dissipation rate, D per unit area of crack growth, for plasticity and fracture combined, are presented for equilibrium crack extension in a real elastic-plastic material.These relationships are a necessary condition for stable growth. The term D is identical to G for lefm and to the rate at which work is done for the rigid-plastic limit. Crack growth is seen at both micro-and macro-levels as a two stage process of damage accumulation in a process zone followed by actual separation as a micro-instability at the crack tip. Some examples of the behaviour of ductile metals are cited in support at both micro-and macro-level. For the fully plastic case, D reduces strongly with growth. Relationships with conventional rising R-curves are stated for contained and uncontained yield. NOMENCLATUREThe main symbols, abbreviations and suffices are listed here but all terms with special meanings are defined in the text when first used. a = crack length b = ligament, W-a B = thickness C = energy rate available for dissipation, per unit area of crack growth da = an increment in crack length (here not implying the limit da-0) D = energy rate dissipated by the material, per unit area of crack growth E' =the effective modulus according to the degree of plane stress or strain G =the classical energy release rate I =the elastic exchange rate in the presence of plasticity J = the classical J-contour integral (though often evaluated from the area under a loading diagram) K =the classical stress intensity factor L = a normalised load (the classical constraint factor when at limit load) q = load-point displacement Q = load rp = plastic zone size (according to lefm) R = resistance to crack growth after initiation U = work done MI = internal energy (not necessarily recoverable)tip opening angle S = crack opening displacement y = surface energy per unit crack area r = surface energy q = a geometric factor relating J to work per unit area 0 = stress Aa = the accumulated crack growth Sufjices, abbreviations and particular meanings dis = dissipated nle = non-linear elastic el = elastic (linear) 1089 1090C . E. TURNER and 0. KOLEDNIK o = an initial or reference value pl = plastic rep = real elastic-plastic material behaviour (with incremental laws of plasticity and linear elastic unloading) rpl = rigid-ideally plastic "strict lefm" denotes the case where linear elastic fracture mechanics is applied to ideally brittle materials; "engineering lefm" is the regime where lefm is conventionally applied with a plastic zone important physically but sufficiently small to be neglected in the algebra.