Using simple assumed deformation fields, approximate solutions have been obtained for tension and bending specimens containing welds for both limit loads and for fully plastic proportionality coefficients between the singular field amplitude J and the strain energy. The solutions allow for the degree of over or undermatch in the material tensile properties of the weld metal relative to the parent steel, and for the size of the weld region relative to the remaining ligament ahead of the crack.Detailed finite-element analyses have been performed for particular values of under/over-match and size of weld region. These refine the approximate analytical solutions for the particular cases examined, and show broad agreement with the trends predicted by the analytical models.The results have been used to provide guidance for testing weldments using standard, bend-type geometries. For small-specimen testing, cracks should be sufficiently deep for the remaining ligament ahead of a centrally located crack to be less than the total width of the weld. For large specimens, the weld region should be less than 20% of the size of the remaining ligament. If these guidelines are followed then standard relationships may be used to derive J from the area under the load-displacement curve.Common advice that the tensile properties of the weaker material in a weldment should be used in J-estimation techniques has been shown to be appropriate in many cases. However, the advice is likely to be overconservative when plastic deformation is predominantly in the weld even for overmatched weld properties, or predominantly in base metal even for undermatched weld properties. The results in the paper enable such cases to be identified. NOMENCLATURE a = crack length A = integration area b = thickness of the plastic mechanism c = semi-width of the punch loading of the 3PB specimen C = elastic compliance D = measure of contour dependence G = virtual extension function h = semi-width of the weld material J = crack tip integral fracture parameter k = uy/2 or 0,,/,/3 for Tresca and von-Mises effective stresses, respectively k, = k for the weld material K = stress intensity factor I = ligament length I,,, = length of the plastic mechanism l,, = reference length M = bending moment B, = thickness of the specimen 1061 1062 J. JOCH et al. nJ = component of the outward unit vector normal to contour r P = load per unit thickness P, = limit load PLr = limit load normalised by single base material limit load r = radius of the postulated plastic mechanism in bending u, = component of displacement vector u , ,~ = derivative of u, with respect of xJ U,, = strain energy U; = strain energy of elastic specimen Up, = dissipated energy Ut0 = area under the load-displacement curve ti = velocity of sliding along the plastic mechanism W = width of the studied specimen x, = component of the Cartesian coordinate system (x, is parallel to crack direction) b = angle describing the postulated plastic mechanism 8, = angle p which minimises the dissipated energy y = shear strai...

The development of singular fields for defects in steadily loaded creeping structures is examined as a function of geometry and crack size using finite-element analyses and results from the literature. Approximations for estimating the time-development of the amplitude of the fields are examined and it is shown that simple approximations are expected to apply for a wide range of geometries. It is shown both theoretically and numerically that plasticity on initial loading produces crack tip fields closer to the steady state condition than those produced elastically. NOMENCLATURE a = crack size B = constant in creep law of equation (3) b = normalising dimension in equations (2) and (4) C(t ) = non-steady creep characterising parameter C* = steady state creep characterising parameter D =constant in plasticity law of equation (1) E = Young's modulus h, = dimensionless function in equations (2) and (4) Z , = dimensionless function of n in equations (18) and (19) J, J,, = plasticity characterising parameter, value of J at t = 0 K = elastic stress intensity factor m = plasticity stress index in equation (1) n = creep stress index in equation (3) P, Po, PL = applied load, normalising load, collapse load R = length in equations (6) and (7) r, r,, P = distance from crack tip, maximum extent of creep zone, normalised creep zone size t, t,, = time, transition time of equation (14) w = section width fi = function of time in equation (9) L,,, E,J = strain tensor, dimensionless function in equation (19) ic, iLf = creep strain rate, value at reference stress level LP, egf = plastic strain, value at reference stress level 0 =polar angle K = 1 in plane stress, K = 1 -v 2 in plane strain v = Poisson's ratio u ,~, 8, = stress tensor, dimensionless function in equation (18) q,, ud, u,, = normalising stress, reference stress in equation (5), yield stress z = dimensionless time of equation (1 1) ?Present address: Nuclear Research Institute, 25068 Rez u Prahy, Czechoslovakia. 229 230 J. JOCH and R. A. AINSWORTH

3D atomistic simulations via molecular dynamics (MD) at temperature of 0 K and 295 K (22°C) with a high quasi-static loading rate dP/dt of 2.92 kN/s show that cleavage fracture is supported by surface emission of oblique dislocations < 111 >{011} and by their subsequent cross slip to {112} planes, which increases separation of the (001) cleavage planes inside the crystal. Under the slower loading rate by a factor 5, the crack growth is hindered by twin generation on oblique planes {112} and the fracture is ductile. The MD results explain the contribution of the crack itself to the ductile-brittle transition observed in our fracture experiments on Fe-3wt%Si single crystals of the same orientation and geometry, loaded at the same rates dP/dt as in MD. The loading rates are equivalent to the cross head speed of 5 mm/min and 1 mm/min used in the experiment. The MD results also agree with the stress analysis performed by the anisotropic LFM and comply with experimental observations.

This paper provides an initial examination of the development of singular fields for defects in creeping structures for combined mechanical and thermal loading. Finite-element analyses are reported for cylindrical and plate geometries with different ratios of mechanical and thermal loading. It is shown that approximations for estimating the time-development of the amplitude of the singular fields are given by formulae developed previously for mechanical loading, provided a normalised timescale is defined appropriately. NOMENCLATURE a, d = crack size, effective crack size of equation (15) C(t ) = non-steady creep characterising parameter B = constant in creep law of equation (1) C* = steady state creep characterising parameter D = constant in plasticity law E = Young's modulus J, J, = plasticity characterising parameter, value of J at t = 0 K, KM, KT = total elastic stress intensity factor, for mechanical loads, for thermal loads n = creep stress index in equation (1) r, r, = radius, outer radius of cylinder r,,, P = maximum extent of creep zone, normalised creep zone size of equation (5) r M , rM+T = values of P for mechanical and combined loading related by equation (1 1) --T, To, AT = temperature, constant temperature, temperature difference t , t, = time, transition time of equation (3) w = section width x = distance from centre-line of centre-cracked plate B = function of time in equation (2) 1' = creep strain rate L P =plastic strain IE = 1 in plane stress, K = 1 -v z in plane strain v = Poisson's ratio umf = reference stress r = dimensionless time of equation (7)