Ductile tearing and discrete void effects on cleavage fracture under small-scale yielding conditions

Over the mid-to-upper region of the ductile-to-brittle transition region, transgranular cleavage and ductile tearing define two competing failure mechanisms in ferritic steel. At metallurgical scales ([50 lm), formation and growth of the voids driving ductile crack extension likely alter the local stress fields acting on the smaller inclusions that trigger cleavage fracture. Here we study the effects of void growth on cleavage fracture by modeling discrete cylindrical voids lying on the crack plane ahead of the crack tip within a small-scale yielding (SSY) boundary layer model. These discrete voids have a spacing, D, within a highly refined crack-front region. This enables identification of both single void growth and multiple void growth mechanisms that depend primarily on the initial void porosity, f0. The crack grows in this model by release of nodal reactions (enforcing zero displacement) along the ligament (symmetry plane) between the blunted crack tip and closest void when the void obtains a specified critical porosity. This process grows the crack in discrete increments of size equal to the length of an intervoid ligament. Continued external loading leads to subsequent void growth and crack extensions through additional node releases. The external loads at the point of each crack extension define the crack growth resistance (JR) curves. This enables comparison with conventional JR–Da curves obtained using computational cell (Gurson–Tvergaard) analyses. The Weibull stress model is then employed to quantify the stress concentration effects on the probability of cleavage fracture. We describe a non-dimensional function, hðbJ Þ, to represent stress concentration effects on the Weibull stress in a convenient framework (bJ ¼ J=Dr0 denotes a nondimensional loading for SSY analyses). These h-functions also reflect the increase in volume of material sampled as the crack grows from the original tip to the first void, the second void, etc. The h-functions vary with material flow properties, initial porosity (f0), critical porosity (fc), Weibull modulus (m), and T-stress (Tr) or constraint level.