NEW MODIFIED FORMULA OF RICHARD MODEL FOR CRACK GROWTH DIRECTION

This research proposed a modification of  Richard formula regarding crack growth direction via considering a particular case study concerning small bore copper pipes (12200) under mixed mode (I/II) conditions as a consequence to multiaxial cyclic loads effect on the proposed pipe where the geometry selected in such away  the real service conditions have been simulated with different crack inclination (from 00 to 900) to demonstrate the modified formula clearly , so the results have been justified and good agreement has been received to illustrate the durability of the new formula  to be applicable for different crack inclination.