Determination of Residual Stress for Single and Double Autofrettage of Thick-walled FG Cylinders Subjected to Dynamic Loading

In the present article a numerical procedure is developed for dynamic analysis of single and double autofrettage of thick–walled FG cylinders under transient loading. The governing differential equations are discretized and presented in explicit Lagrangian formalism. The explicit transient solution of discrete equations are obtained on the meshed region and results for stress and strain distribution for relevant problems under inner and/or outer boundary conditions are established. The autofrettage behavior is subsequently analyzed through the application of time dependent pressure at boundary regions of the axisymmetric domain. Dynamic results, in particular in transient loading, are different in comparison with static ones due to the presence of plastic deformation and wave propagation. The residual stress resulting from internal pressure changes structural load bearing capacity of the cylinder in so far as the tensile stress of the outer layers might reduce while compressive stress of the inner layers increase. For functionally graded materials whose material properties change continuously, dynamic analysis yields results which are entirely different as compared with their static counterparts due to the change in wavelength and acoustic impedance. In the static analysis, the dimensionless forms of equations can be developed from the onset, while in the dynamic analysis the physical dimensions and material properties gain importance due to inherent properties of the stress waves. Residual stresses in the inner and outer parts of the cylinder are also studied for various volume fractions of FG material under single or double autofrettage.