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.
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