Contact deformation regimes in sharp and spherical indentation experiments : mechanical property extractions

Pressure vessels, mostly cylindrical, are widely used in many industries. However, due to their optimal specific strength (strength/weight) and their ease of packaging, spherical pressure vessels are commonly used for example as: propellant/oxidizer/pneumatic tanks on spacecrafts and aircrafts, gas tanks on LNG (liquefied natural gas) carriers, pressurized storage tanks for chemical substances, cookers for the food industry, and as metal or concrete containment structures in nuclear plants. Furthermore, whenever extremely high pressure occurs, such as in high explosion containment tanks or in the apparatus used to manufacture artificial diamonds, spherical pressure vessels are the only feasible solution. In order to further increase the load capacity of such pressure vessels as well as to prolong their fatigue life, a favorable compressive residual stress field is introduced to the inner portion of the vessel's wall by the autofrettage process. Although there are many studies that investigated the autofrettage problem for cylindrical vessels, only a few solutions were recently proposed for spherical vessels. The purpose of this research is to extend the existing experimental-numerical model of the autofrettaged cylinder [1], in order to offer a more realistic solution for the residual stress field in an autofrettaged spherical pressure vessel, incorporating the Bauschinger effect. Two main processes are used to autofrettage cylindrical pressure vessels: hydrostatic autofrettage and the autofrettage. The hydrostatic autofrettage is modeled as an axisymetric, two-dimensional problem solved in terms of the radial displacement solely, while the three-dimensional swage autofrettage is solved in terms of the radial and the axial displacements. Due to it symmetries, spherical autofrettage is to be treated as a twodimensional problem and solved in terms of the radial displacement only, as the case is for hydrostatic autofrettage in a cylinder. The two-dimensional mathematical model is based on the idea of solving the elastic-plastic autofrettage problem using the form of the elastic solution [1]. The elastic strains are replaced in Hooke's law by the difference between the total and plastic strains. Substituting these new Hooke's equations into the equilibrium equation and using the strain-displacement relations, yields a differential equation of the radial displacements in terms of plastic strains: ) ; ( 2 2 2 2 2 p p r F u r dr du r dr u d