*Article* **Tube Expansion by Single Point Incremental Forming: An Experimental and Numerical Investigation**

**Carlos Suntaxi 1,2 , Gabriel Centeno 2, \* , M. Beatriz Silva 3 , Carpóforo Vallellano <sup>2</sup> and Paulo A. F. Martins 3**


**Abstract:** In this paper, we revisit the formability of tube expansion by single point incremental forming to account for the material strain hardening and the non-proportional loading paths that were not taken into consideration in a previously published analytical model of the process built upon a rigid perfectly plastic material. The objective is to provide a new insight on the reason why the critical strains at failure of tube expansion by single point incremental forming are far superior to those of conventional tube expansion by rigid tapered conical punches. For this purpose, we replaced the stress triaxiality ratio that is responsible for the accumulation of damage and cracking by tension in monotonic, proportional loading paths, by integral forms of the stress triaxiality ratio that are more adequate for the non-proportional paths resulting from the loading and unloading cycles of incremental tube expansion. Experimental and numerical simulation results plotted in the effective strain vs. stress triaxiality space confirm the validity of the new damage accumulation approach for handling the non-proportional loading paths that oscillate cyclically from shearing to biaxial stretching, as the single point hemispherical tool approaches, contacts and moves away from a specific location of the incrementally expanded tube surface.

**Keywords:** single point incremental forming; tube expansion; formability; fracture; stress-triaxiality
