Analytical Solution of Aluminum Alloy Plates with Holes Subjected to Cold Expansion with Reverse Yielding

The expansion induced by cold working is a common process that generates residual stresses. It is used when fatigue damage accumulation and life reduction of aluminum alloy perforated plates is an issue in the aeronautics industry. This process is an attractive solution to extend the fatigue lifetime of these structures. It aims at generating residual stresses and increases thereby the strength of hollow parts including aluminum alloy plates with holes commonly used in the manufacture of airplane fuselage. Unfortunately, the life predictions require a good prediction of the residual stresses and in particular when reverse yielding takes place. An analytical model to predict the residual stresses induced during the expansion process due to the cold strain hardening is developed. The proposed analytical model is based on an elasto-plastic behavior, with a power law material behavior and relies on the theory of autofrettaged thick wall cylinders in plane strain state to which reverse yielding is incorporated. The application of Hencky theory of plastic deformation is used in the analytical calculations of the stresses and strains. Finite-element numerical simulation is used to validate the developed analytical model by comparison of the radial, Hoop, longitudinal and equivalent stresses for both the loading and unloading phases. The obtained results show clearly that the level of residual stresses depends mainly on the interference and strain hardening while reverse yielding reduce the stresses near the hole.

Analytical and Numerical Modelling of Sheet Plate Cold Expanded Hole Subjected to Reverse Yielding

Predicting and mitigating the effect of expansion induced by cold working on damage fatigue accumulation and life assessment of aluminum alloy is a common process in the aeronautics industry, especially to extend the fatigue lifetime of their structures. This process aims at generating residual stresses and increases thereby the strength of hollow parts including aluminum alloy plate holes that are employed in manufacturing the airplane fuselage. An analytical model to predict the residual stresses induced during the expansion process due to the cold strain hardening is developed. The proposed model is based on an elasto-plastic behavior, with a power law material behaviour and relies on the theory of autofrettaged thick wall cylinders in plane strain state to which reverse yielding is incorporated. The application of Hencky theory of plastic deformation is used in the analytical calculations of the stresses and strains. Finite-element numerical simulation is used to validate the developed analytical model by comparison of the radial, Hoop, longitudinal and equivalent stresses for both the loading and unloading phases. The obtained results show clearly that the level of residual stresses depends mainly on the interference and strain hardening while reverse yielding reduce the stresses near the hole.

Effect of Reverse Yielding on the Residual Contact Pressure in Tube-to-Tubesheet Joints

The analytical prediction of the contact stress in tube-to-tubesheet joints subjected to hydraulic expansion is conducted without any consideration to reverse yielding that can occur inside the tube. Most existing models consider the tube and tubesheet to unload elastically when the expansion pressure is released. These models are therefore less conservative as they overestimate the contact pressure. An analytical model that considers strain-hardening material behavior of the tube and tubesheet and accounts for reverse yielding has been developed. The model is based on Henckey deformation theory and the Von Mises yield criteria. The paper shows that reverse yielding that is present in tubes during hydraulic expansion unloading makes the joint less rigid and causes a decrease in the contact pressure depending on the gap clearance and the materials used. A good correlation between the analytical and finite elements results is obtained on different treated cases which gives confidence on the developed model.

Effect of Reverse Yielding on the Residual Contact Stresses of Tube-to-Tubesheet Joints Subjected to Hydraulic Expansion

The analytical prediction of the contact stress in tube-to-tubesheet joints subjected to hydraulic expansion is conducted without any consideration to reverse yielding that can occur inside the tube. Most existing models consider the tube and tubesheet to unload elastically when the expansion pressure is released. These models are therefore less conservative as the overestimate the contact pressure. An analytical model that considers strain-hardening material behavior of the tube and tubesheet and accounts for reverse yielding has been developed. The model is based on Henckey deformation theory and the Von Mises yield criteria. The paper shows that reverse yielding that is present in tubes during hydraulic expansion unloading makes the joint less rigid and causes a decrease in the contact pressure depending on the gap clearance and the materials used. A good correlation between the analytical and FEM results is obtained on different treated cases which gives confidence on the developed model.

Investigation of Residual Stress Development During Swage Autofrettage, Using Finite Element Analysis

Swaging is one method of autofrettage, a means of prestressing high-pressure vessels to increase their fatigue lives and load bearing capacity. Swaging achieves the required deformation through physical interference between an oversized mandrel and the bore diameter of the tube, as it is pushed through the tube. A finite element model of the swaging process was developed, in ansys, and systematically refined, to investigate the mechanism of deformation and subsequent development of residual stresses. A parametric study was undertaken, of various properties such as mandrel slope angle, parallel section length, and friction coefficient. It is observed that the axial stress plays a crucial role in the determination of the residual hoop stress and reverse yielding. The model, and results obtained from it, provides a means of understanding the swaging process and how it responds to different parameters. This understanding, coupled with future improvements to the model, potentially allows the swaging process to be refined, in terms of residual stresses development and mandrel driving force.

Theoretical Analysis and Finite Element Simulation of Autofrettage for Extrusion Die

The design of extrusion die has been investigated by autofrettage technique considering the characteristics of the extrusion die. Ideal elastoplastic autofrettage model was established and the stress formulae of three loading procedures were derived and the theoretical calculation method of the maximum autofrettage pressure and working load was put forward. The simulations of stress distribution and the inwall displacement of the autofrettaged extrusion die were performed using MARC finite element software, and the results coincided well with the theoretical derivations. It was observed that the autofrettaged extrusion die can raise the elastic loading capacity under the inner displacement limit , without the appearance of reverse yielding and reyielding under the working load. The results show that the autofrettage technique is appropriate for the design of extrusion die.

Residual Stress Measurements of Explosively Clad Cylindrical Pressure Vessels

Tantalum refractory liners were explosively clad into cylindrical pressure vessels, some of which had been previously autofrettaged. Using explosive cladding, the refractory liner formed a metallurgical bond with the steel of the pressure vessel at a cost of induced strain. Two techniques were employed to determine the residual stress state of the clad steel cylinders: neutron diffraction and mechanical slitting. Neutron diffraction is typically nondestructive; however, due to attenuation along the beam path, the cylinders had to be sectioned into rings that were nominally 25 mm thick. Slitting is a destructive method, requiring the sectioning of the cylindrical samples. Both techniques provided triaxial stress data and useful information on the effects of explosive cladding. The stress profiles in the hoop and radial directions were similar for an autofrettaged, nonclad vessel and a clad, nonautofrettaged vessel. The stress profiles in the axial direction appeared to be different. Further, the data suggested that residual stresses from the autofrettage and explosive cladding processes were not additive, in part due to evidence of reverse yielding. The residual stress data are presented, compared and discussed.