A crack opening stress equation for in-phase and out-of-phase thermomechanical fatigue loading

• A new scaling relation to describe the crack opening stress under TMF loading.
• The scaling relation accounts for the constraint (plane stress and plane strain).
• The scaling relation accounts for the temperature dependent yield stress.
• Based on the scaling relation, Newman’s crack opening stress equation is modified.
• The crack opening stress under TMF loading can be predicted.

In this paper, a crack opening stress equation for in-phase and out-of-phase thermomechanical fatigue (TMF) loading is proposed. The equation is derived from systematic calculations of the crack opening stress with a temperature dependent strip yield model for both plane stress and plane strain, different load ratios and different ratios of the temperature dependent yield stress in compression and tension. Using a load ratio scaled by the ratio of the yield stress in compression and tension, the equation accounts for the effect of the temperature dependent yield stress and the constraint on the crack opening stress. Based on the scaling relation established in this paper, Newman’s crack opening stress equation for isothermal loading is enabled to predict the crack opening stress under TMF loading.