Three-dimensional T-stresses for three-point-bend specimens with large thickness variation

• 3PB specimens’ T-stress solutions with various crack depths and thicknesses were obtained.
• Mid-plane T11 and T33 were reported for 3 PB specimens with a/W = 0.2–0.8 and B/W = 0.1–40.
• T11 showed 3D effect, and approached 2D plane strain solutions for large thickness.
• T33 increased with thickness, and saturated to νT11 for B/W ⩾ 2.

Three-point-bend (3 PB) test specimens are useful for the systematic investigation of the influence of statistical and constraint loss size effects on the cleavage fracture toughness of a material in the ductile-to-brittle transition temperature range. Because the in- and out-of-plane elastic T-stresses (T11 and T33) are a measure of the crack-tip constraint and even the in-plane T11 exhibits three-dimensional (3D) effects, the 3D T-stresses solutions were obtained by running finite element analyses (FEA) for 3 PB specimens with wide ranges of the crack depth-to-width ratio (a/W = 0.2–0.8) and the specimen thickness-to-width ratio (B/W = 0.1–40). The results show that the 3D T11 at the specimen mid-plane tended to deviate from the 2D T11 as B/W increased, with the deviation saturating for B/W ⩾ 2. The mid-plane T33 increased with B/W and was close to the plane strain value νT11 for B/W ⩾ 2.