Limit analysis based on GM criterion for defect-free pipe elbow under internal pressure

• With GM criterion, an analytical solution of limit load for pipe elbow considering strain hardening effect is obtained.
• The GM solution lies between Tresca and TSS solutions and is located close to Mises solution.
• The limit load decreases with the increase of strain hardening exponent.
• The limit load increases with the increase of ratio of thickness to radius and curvature influence factor.

Analytical solution of limit load for a defect-free pipe elbow is obtained under internal pressure using GM (geometric midline), in which the strain hardening effect has been taken into account. The limit load is a function of ratio of thickness to radius t0/r0, strain hardening exponent n, curvature influence factor m and ultimate tensile strength. Comparison with FE and analytical results of other investigators was performed. Although the limit loads calculated by GM criterion are little higher than the traditional analytical results, the GM results are in good agreement with FE results. Besides, the effect of different criteria, strain hardening exponent, ratio of thickness to radius, as well as curvature influence factor on the limit loads are also discussed systematically.