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

Document Type: Research Paper


1 School of Mechanical Engineering, Shiraz university, Shiraz, Iran

2 School of Mechanical Engineering, Shiraz university, Shiraz, Irany


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.


[1] G. J. Franklin, J. L. M. Morrison, Autofrettage of Cylinders: Prediction of Pressure, External Expansion Curves and Calculation of Residual Stresses, Proceeding of Institute of Mechanical Engineers, 174 (1960) 947–74.
[2] P. C. T. Chen, Stress and Deformation Analysis of Autofrettaged High Pressure Vessels, ASME special publication PVP New York ASME United Engineering Center, (1986) 61–70.
[3] Stacey, G. A. Webster, Determination of Residual Stress Distributions in Autofrettaged Tubing, International Journal of Pressure Vessels and Piping 31 (1988) 205–220.
[4] D. W. A. Rees, Autofrettage of thick-walled pipe bends, International Journal of Mechanical Sciences 46 (2004) 1675–1696.
[5] P. Parker, Autofrettage of Open-End Tubes-Pressures, Stresses, Strains, and Code Comparisons, Journal of Pressure Vessel Technology 123 (2001) 271–281.
[6] P. Livieri, P. Lazzarin, Autofrettaged Cylindrical Vessels and Bauschinger Effect: an Analytical Frame for Evaluating Residual Stress Distributions, Transaction ASME Journal of Pressure Vessel Technology 124 (2002) 38–45.
[7] H. Jahed, G. Ghanbari, Actual Unloading Behavior and Its Significance on Residual Stress in Machined Autofrettaged Tube, ASME J. Pressure Vessel Technol. 125 (2003) 321–325.
[8] M. Grujicic, Y. Zhang, Determination of effective elastic properties of Functionally Graded Materials using Voroni Cell Finite Element Method, Materials Science and Engineering A 251 (1998) 64-76.
[9] J. Aboudi, M. Pindera, S. M. Arnold, Higher-order theory for Functionally Graded Materials, Composites: Part B 30 (1999) 777-832.
[10] Y. Bayat, H. Ekhteraei Toussi, Elastoplastic torsion of hollow FGM circular shaft, Journal of Computational and Applied Research in Mechanical Engineering 4 (2015) 165-180.
[11] G. H. Majzoobi, G. H. Farrahi, A. H. Mahmoudi, A finite element simulation and an experimental study of Autofrettage for strain hardened thick-walled cylinders, Materials Science and Engineering A359 (2003) 326-331.
[12] M. Moulick, S. Kumar, Comparative stress analysis of elliptical and cylindrical pressure vessel with and without Autofrettage consideration using finite element method, International Journal of Advanced Engineering Research and Studies, (2015) E-ISSN2249–8974.
[13] E. P. Popov, T. A. Balan, Engineering Mechanics of Solids, Pearson Education Inc. (2004).
[14] M. L. Wilkins, Use of artificial viscosity in multi-dimensional fluid dynamic calculations, Journal of Computational Physics 36 (1980) 281-303.
[15] T. Kalali, S. Hadidi-Moud, A Semi-analytical Approach to Elastic-plastic Stress Analysis of FGM Pressure Vessels, Journal of Solid Mechanics 5 (2013) 63-73.
[16] D. Benson, Computational methods in Lagrangian and Eulerian hydrocodes, Computer Methods in Applied Mechanics and Engineering 19 (1992) 235-394.
[17] S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, MacGraw-Hill, New York, (2010).
[18] M. L. Wilkins, J. E. Reaugh, Plasticity Under Combied Stress Loading, American Society of Mechanical Engineers Publication, (1980) 80-C2/PVP-106.
[19] E. J. Caramana, M. J. Shashko, Elimination of artificial grid distortion and hourglass-type motion by means of lagrangian subzonal masses and pressure, Journal of Computational Physics 142 (1998) 521-561.
[20] O. R. Abdelsalam, R. Sedaghati, Design Optimization of Compound Cylinders Subjected to Autofrettage and Shrink-Fitting Processes, Pressure Vessel Technology 135 (2013) 1-11.
[21] ABAQUS 6.14 user manual. Dassault Systemes (2014).