In-plane and out-of-plane constraint effects under pressurized thermal shocks

• Crack ligament and loading plays an important role for in-plane constraint.
• Hardening behavior of the material has a significant role on the constraint effect.
• Thickness has a more important impact than the loading on out-of-plane constraint.
• K–T11–T33 provides a consistent method for the constraint analysis.
• Safety margin of the RPV is increased based on the K–T approach.

Transferability of fracture toughness data obtained on small scale specimens to a full-scale cracked structure is one of the key issues in integrity assessment of engineering structures. In order to transfer fracture toughness under different constraints, both in-plane and out-of-plane constraint effect should be considered for the specimens and structures. In this paper both in-plane and out-of-plane constraint effects of a crack in a reference reactor pressure vessel (RPV) subjected to pressurized thermal shocks (PTSs) are analyzed by two-parameter and three-parameter methods. The comparison between elastic and elastic–plastic analysis shows that the constraint effect varies with the material property. T11 (the second term of William’s extension acting parallel to the crack plane) generally displays a reversed relation to the stress intensity factor (SIF) with the transient time, which indicates that the loading (SIF) plays an important role on the in-plane constraint effect. The thickness at the crack tip contributes more than the loading to the out-of-plane constraint, such that T33 (the second term of William’s extension acting along the thickness) displays a similar relation to ε33 (strain along the thickness direction) and a different relation to T11 during the transient. The results demonstrate that both in-plane and out-of-plane constraint effect should be analyzed separately in order to describe precisely the stress distribution ahead of the crack tip.