The effect of out-of-plane constraint in terms of the T-stress in connection with specimen thickness

• The effect of the non-singular terms is analyzed in connection with specimen thickness.
• There is strong effect of out-of-plane constraint on crack tip plastic zones.
• The theoretical results are compared with the results computed by FEM.
• The increase of specimen thickness leads to the increase of crack tip constraint.

The present study focuses on theoretical and numerical analysis of the joint effect of the non-singular TxxTxx and TzzTzz-stresses on sizes of the plastic zone in the vicinity of the crack tip under mode I loading conditions. The three-dimensional crack tip stresses including TxxTxx and TzzTzz stresses are incorporated into the von Mises yield criterion to develop an expression that models the crack tip plastic zone. The plastic zone size distribution is mapped for the middle plane of CT specimens. It is shown that the plastic zone size is affected by the TzzTzz-stress, i.e. there is strong effect of out-of-plane constraint (specimen thickness) on crack tip plastic zones. The theoretical results are compared with the results computed by finite element method.In addition, to study the effect of thickness and loading mode mixity (mode I and II) of the specimen on the singular (KI, KII) and the non-singular (TxxTxx, TzzTzz) terms along crack front, three-dimensional stress fields are analyzed by means of finite element analysis. The strong effect of specimen thickness and mixed mode loading conditions on the TzzTzz-stress is observed. At the same time, there is not the effect of specimen thickness on the non-singular TxxTxx-stress at same loading conditions.