Developed in this work is a methodology for assessing the fragmentation characteristics of a welded spherical titanium pressure vessel. The presentation is divided into two parts. Part I makes use of the incremental theory of plasticity such that the nonlinear constitutive behavior for each material element can be determined individually in accordance with the local strain and strain rate. This enables the coverage of a much wider range of the strain rate dependent deformation in contrast to the conventional approach where each material element is governed by a single constitutive relation. That is no limitation would be placed on the change in local strain rates. Details of the weldment and region near the vessel opening are analyzed as sites of potential failure initiation. Particular emphases are placed on an accurate evaluation of the volume energy density contours from which failure by fragmentation could be predicted in terms of location and critical pressure. Part II is concerned with determining the energy imparted to the fragments, which are characterized by size, velocity and distance traveled.

Based on the elastic-plastic stress and energy density results in Part I for a welded spherical titanium pressure vessel, Part II carries out a details analysis of failure where plastic deformation and fragmentation take place. The volume energy density criterion predicts failure to first initiate in the heat affected zone and bottle-neck section of the vessel at an internal pressure of approximately 8.5 ksi followed by failure of the weld material at 9.2 ksi. Total rupture of the vessel into two halves is estimated to occur between 9 to 10 ksi with a portion of the weld material and bottle-neck section ejected as debris at high velocities as they dislodge from the main vessel. The average velocity of the two large fragments is estimated to be approximately 600 ft/s; their travelled distance is approximately 18 feet within 30 ms. These predictions are in general agreement with the available experimental data. Increase of the average density in the vessel was found to be close to that estimated from the isentropic thermodynamic process at the terminal internal pressure of 10 ksi that was previously reported. Other details provide a more in-depth understanding of the bursting behavior of pneumatic pressure vessels.