Autofrettage Process Research Articles

A 3-D Model for Evaluating the Residual Stress Field Due to Swage Autofrettage

In order to maximize the performance of modern gun barrels in terms of strength-to-weight ratio and total fatigue life, favorable compressive residual stresses are introduced to the inner portion of the barrel, commonly by the autofrettage process. There are two major autofrettage processes for overstraining the tube: the hydrostatic and the swage. There are several theoretical solutions for hydrostatic autofrettage based on Lamé’s solution and the von Mises or Tresca yield criteria. The residual stress field due to hydraulic autofrettage is treated as an axisymmetric two-dimensional problem solved in terms of the radial displacement solely. Once the Bauschinger effect was included in these models they yield very realistic results. Unlike in the case of hydraulic autofrettage, swage autofrettage needs to be modeled by a three-dimensional model. The present analysis suggests a new 3-D axisymmetric model for solving the residual stress field due to swage autofrettage in terms of both the radial and the axial displacements. The axisymmetric equilibrium equations are approximated by finite differences and solved then by Gauss–Seidel method. Using the new computer code the stresses, the strains, the displacements, and the forces are determined. A full-scale instrumented swage autofrettage test was conducted and the numerical results were validated against the experimental findings. The calculated strains, the permanent bore enlargement, and the mandrel pushing force were found to be in very good agreement with the measured values.

General Variable Material Property Formulation for the Solution of Autofrettaged Thick-Walled Tubes With Constant Axial Strains

In this paper a general variable material property (VMP) formulation for the solution of thick-walled tubes with constant axial strains was developed and compared with the alternative VMP method that is called the Hencky program. The VMP method was initially developed for the analysis of plane stress and plane strain states. However, the actual autofrettage process is under constant axial strain, i.e., open-end and closed-end conditions. Results indicate very good agreement with the Hencky program. Our method is simple, accurate, and very efficient, so that the number of iterations for convergence reduces approximately to one-tenth of Hencky program iterations. The solution algorithm for plane strain, open-end, and closed-end conditions is the same.

Machining effect of the autofrettaged compound cylinder under varying overstrain levels

The autofrettage process is used for the internal forming and sizing of cylinders designed to withstand high internal pressures. Once a tube is autofrettaged, it needs to be machined to its final dimensions on the bore and also on its outer surface. This paper presents an analytical and numerical study of a machined compound cylinder by using the finite element code, ANSYS10.0. An analytical model for predicting the level of autofrettage, either inner, outer, or combined machining of the compound cylinder is developed as the autofrettage residual stress field is simulated by an autofrettaged pressure. The autofrettaged pressures are obtained by using a trial and error method. When autofrettage is at 20%, the numerical results are found to be close in accordance to the analytical results. However, as the autofrettage is raised to 60%, the numerical results differ slightly to the analytical results.

자긴가공된 복합실린더의 기계가공해석

Autofrettage process is used for internal forming and sizing of cylinder designed to withstand high internal pressures. Once the tube is autofrettaged, it needs to be machined to its final dimensions both at the bore and its outer surface. This paper presents an analytical analysis and numerical analysis of machined compound cylinder using finite element code, ANSYS10.0. An analytical model for predicting the level of autofrettage following either inner, outer, or combined machining of the compound cylinder is developed for the autofrettage residual stress field is simulated by an autofrettaged pressure. The autofrettaged pressures are obtained by using trying-error method. As autofrettage percentage is 20 % and 40 %, the numerical results are found to be in almost agreement with the analytical ones. However, as autofrettage percentage is 60 %, the numerical results have a little difference with the analytical ones.

P-20 Fatigue crack propagation life of the autofrettaged compound cylinder

The autofrettage process is commonly used to produce compressive tangential residual stresses near the bore of high-pressure compound cylinder. The multi-layered cylinders can be manufactured with combining autofrettage and shrink fit process to extend fatigue lifetimes. And compressive stresses improve the fatigue life of the vessel during the loading-unloading high-pressure cycles. This paper presents the fatigue design of an autofrettaged compound cylinder for gun barrel which working at high internal pressure(707 MPa). To ensure the structural integrity of the autofrettaged compound cylinder subjected to cyclic internal pressure loading, the fatigue crack propagation life of the cylinder was evaluated. Stress intensity factors of the external cracked compound cylinder due to internal pressure and autofrettage loadings were calculated using the finite element method. The fatigue crack propagation life of the compound cylinder based on the fracture mechanics concepts were predicted and compared to the fatigue crack propagation life of the single cylinder. For FE simulations, the material has been modeled considering an elasto-plastic behaviour for the loading phase. As a result, predicted fatigue crack propagation life of the compound cylinder was about 1.3〜3.3 times more than those of the single cylinder depending on the level of autofrettage.

A numerical study of swage autofrettage of thick-walled tubes

Swage autofrettage process is used for internal forming and sizing of thick-walled tubes designed to withstand high internal pressures. In this process, a mandrel with a diameter slightly larger than that of the tube is pressed inside the tube and in so doing, creates the internal profile. This paper presents an experimental and numerical study of this process. Two dimensional axi-symmetric and three dimensional finite element analyses are used to investigate the effects of workpiece and mandrel geometry on the forming load and part quality. Experiments are carried out to validate the numerical results.

Theoretical and finite-element modeling of autofrettage process in strain-hardening thick-walled cylinders

The optimum autofrettage pressure and the optimum radius of the elastic–plastic boundary of strain-hardening cylinders in plane strain and plane stress have been studied theoretically and by finite-element modeling. Equivalent von-Mises stress is used as yield criterion. Comparison of the results of the two methods shows good agreement. Although there is no explicit expression for the optimum autofrettage pressure in plane stress, the equation for plane strain can be used with good accuracy. It has also been observed that the optimum autofrettage pressure is not a constant value but depends on working pressure.

An Experimental-Numerical Determination of the Three-Dimensional Autofrettage Residual Stress Field Incorporating Bauschinger Effects

Autofrettage of large-caliber gun barrels is used to increase the elastic strength of the tube and is based on the permanent expansion of the cylinder bore, using either hydraulic pressure or an oversized swage mandrel. The theoretical solution of the autofrettage problem involves different yield criteria, the Bauschinger effect, and the recalculation of the residual stress field post barrel’s machining. Accurate stress-strain data and their appropriate numerical representations are needed as input for the numerical analysis of the residual stress field due to autofrettage. The purpose of the present work is to develop a three-dimensional (3D) numerical solution for both the hydraulic and the swage autofrettage processes incorporating the Bauschinger effect, using an accurate numerical representation of the experimentally measured material behavior. The new 3D computer code that was developed is capable of determining the stresses, strains, displacements, and forces throughout the entire autofrettage process. The numerical results were validated by an instrumented standard swage autofrettage process. The numerical model was found to excellently reproduce the experimentally measured pushing force as well as the permanent bore enlargement of the barrel. The calculated tangential stresses and the measured ones follow a similar pattern, but their numerical magnitude differs considerably. A wide discrepancy in both pattern and magnitude was found between the calculated and the measured axial stresses. These discrepancies seem to stem from the exact details of the mandrel’s insertion into the tube and are now under further investigation. However, in order to further validate the numerical code an hydraulic autofrettage experiment will be performed, which will hopefully eliminate the swage autofrettage discrepancies.

Stress concentration factor and minimum hub length predictions for hollow tubes with internal and external flanges subjected to axial loading

This paper presents equations for estimating the elastic stress concentration factor Kt and minimum hub length δ in hollow tubes with internal and external flanges subjected to symmetrical axial pressure over the flat section of the flanges. Results from an extensive finite element study are supported by a limited number of experimental tests. The experimental Kt values are compared with data obtained numerically by the present authors and very good agreement was found between the two methods. Minimum hub lengths, which are an important parameter for fabrication, have been derived on the basis of Saint Venant's principle. It is seen that Kt and δ follow similar trends, being functions of several geometric parameters. Kt and δ values for the internal and external flange-tube intersections contained in this paper cover the most common practical range of geometries. The effect of tube wall radial pre-load (which can result from the compressive radial interface pressure established in the shrink-fitting process, compressive radial residual stress due to the autofrettage process or any other reinforcing process) on Kt and δ has also been studied. Furthermore, the effect of eccentric loading has been studied, using an experimental approach with one geometry. The extensive range of Kt and δ values obtained from the analyses is used to obtain useful prediction equations, using a statistical multiple non-linear regression model and a high level of accuracy is demonstrated. Finally, a direct relationship between elastic stress concentration factor, which is readily available, and minimum hub length, which usually requires a complex numerical analysis, is provided.

An integrated CAD/CAM system for CNG pressure vessel manufactured by deep drawing and ironing operation

The Tiber reinforced composite material is widely used in the multi-industrial field because of their high specific modulus and specific strength. It has two main merits which are to cut down energy by reducing weight and to prevent explosive damage proceeding to the sudden bursting which is generated by the pressure leakage condition. Therefore, Pressure vessels using this composite material can be applied in the field such as defence industry and aerospace industry. In this paper, for nonlinear finite element analysis of E-glass/epoxy filament winding of composite vessel subjected to internal pressure, the standard interpretation model is developed by using the ANSYS with AutoLISP and ANSYS APDL languages, general commercial software, which is verified as useful characteristic of the solution. Among the modules of the system, both the process planning module for carrying out the process planning of filament wound composite pressure vessel and the autofrettage process module for obtaining higher residual stress will minimize trial and error and reduce the period for developing new products. The system can serve as a valuable system for experts and as a dependable training aid for beginners.

Actual Unloading Behavior and Its Significance on Residual Stress in Machined Autofrettaged Tubes

A simple method for obtaining actual unloading behavior of high strength steels is proposed. Based on this method loading-unloading stress-strain curves for NiCrMoV125 steel is obtained. It is shown that the actual unloading behavior tends to be nonlinear as soon as unloading occurs. Using the variable material properties (VMP) method, residual stresses induced by autofrettage process of a tube made of this type of steel are calculated. Significance of employing actual unloading behavior is demonstrated by comparing the results with ideal models such as isotropic hardening and bilinear models. There is at least 30% over estimation of compressive residual stress at the bore if ideal models are used. Also, the process of material removal is simulated by using commercial FEM software to evaluate the recommended scenarios of removal on redistribution of residual stresses at the bore. Resulting stresses after machining are also calculated by the VMP method using actual behavior. It is shown that the final residual stress field differs significantly if actual unloading behavior is used.

A finite element simulation and an experimental study of autofrettage for strain hardened thick-walled cylinders

The effect of the autofrettage process on high pressure cylinders has been investigated. Both numerical and experimental techniques have been used for the investigation. It was observed that the best autofrettage pressure for raising the pressure capacity of the cylinder was the pressure P y2 which is just sufficient to bring the outer surface of the cylinder to yielding. Pressures higher than P y2 will have the inverse effect. It was found that the number of autofrettage stages has no effect on pressure capacity. It was also shown that to reduce the flow stress within the wall of the cylinder, the autofrettage pressure must be greater than the working pressure. For pressures lower than working pressure, the flow stress remains unchanged. A close agreement was found between the P y2 calculated from the Xioying and Gangling relation and with those obtained from experiments and numerical simulations.

The overstrain of Thick-Walled cylinders considering the bauschinger effect factor (BEF)

An independent kinematic hardening material model in which the reverse yielding point is defined by the Bauschinger effect factor (BEF), has been defined for stainless steel SUS 304. The material model and the BEF are obtained experimentally and represented mathematically as continuous functions of effective plastic strain. The material model has been incorporated in a non-linear stress analysis for the prediction of reverse yielding in thick-walled cylinders during the autofrettage process of these vessels. Residual stress distributions of the independent kinematic hardening material model at the onset of reverse yielding are compared with residual stresses of an isotropic hardening model showing the significant effect of the BEF on reverse yielding predictions. Critical pressures of direct and reverse yielding are obtained for the most commonly used cylinders and a range of permissible internal pressures for an efficient autofrettaged process is recommended.

Residual stress effects on the fatigue life of an externally grooved thick-walled pressure vessel

To ensure the structural integrity of a thick-walled pressure vessel containing residual stresses induced by the autofrettage process, a fatigue life evaluation of the pressure vessel was performed based on the local strain approach. Residual stress distributions due to autofrettage loading were calculated using an elastic–plastic finite element stress analysis. The tangential residual stress varied from compression at the inside radius to tension near the outside radius, showing a high stress concentration at the groove root. The local stresses and local strains calculated by the elastic–plastic analysis were applied to the fatigue life evaluation of the pressure vessel. Reasonable agreement was found between the predicted and the experimental fatigue lives of the pressure vessel within factors of 3–4, depending on autofrettage level and the fatigue damage parameter.

Experimental verification of the autofrettage process for thick-walled tubes

The success of the autofrettage process applied to thick-walled tubes is determined in industry via a control chart representing the measured permanent diametral expansions versus the yield stress of the material. The widely used acceptance limits are due to Hill's analysis of the problem. An experimental investigation showed that the above limits might lead to refusal of a substantial number of autofrettaged tubes. By considering the separate effects of hardening, the Bauschinger factor, reverse yielding, anisotropy and geometrical eccentricity, the need for a more realistic material model is demonstrated. A model incorporating the first three factors, found in the literature, is used to suggest new acceptance limits. Autofrettage experiments on a relatively large number of tubes indicated that the new control limits might render refusals acceptable.

Fatigue analysis of autofrettaged pressure vessels with radial holes

Fatigue analysis has been performed to predict the fatigue life of an autofrettaged pressure vessel containing radial holes subjected to cyclic internal pressure of 200 MPa. Finite element analyses were used to calculate the residual and operating stress distributions of the pressure vessel due to the autofrettage process and pulsating internal pressure, respectively. Numerical stress concentration factors at the hole of the autofrettaged pressure vessel subjected to internal pressure were approximately 3. Fatigue damages, including the mean stress effects, were evaluated using the local stresses and local strains determined from the elastic–plastic finite element analysis. An increase in the amount of overstrain by the autofrettage process moved the fatigue cracking location from the inner radius towards a mid-wall, and extended the fatigue life. Predicted fatigue life of a 50% autofrettaged pressure vessel with radial holes increased by 45%, compared to that of the unautofrettaged pressure vessel. The level of autofrettage did not significantly influence the failure location and fatigue life of the pressure vessel for more than 50% autofrettage level.

Elastic-plastic stress analysis and fatigue lifetime prediction of cross-bores in autofrettaged pressure vessels

Elastic-plastic stress analysis has been performed to evaluate the fatigue life of an autofrettaged pressure vessel containing cross-bores subjected to pulsating internal pressure of 200 MPa. Finite element analyses were used to calculate the residual and operating stress distributions of the pressure vessel due to the autofrettage process and pulsating internal pressure, respectively. Theoretical stress concentration factors of 3.06, 2.58, and 2.64 were obtained at the cross-bore of the pressure vessel due to internal pressure, 50%, and 100% autofrettage loadings, respectively. Local stresses and local strains determined from the elastic-plastic finite element analysis were employed to calculate the failure location and fatigue life of the pressure vessel with radial cross-bores, incorporating the low-cycle fatigue properties of the pressure vessel steel and fatigue damage parameters. Increase in the amount of overstrain by autofrettage process moved the crack initiation location from the inner radius toward a mid-wall, and extended the crack initiation life, Predicted fatigue life of the fully autofrettaged pressure vessel with cross-bores increased about 50%, compared to the unautofrettaged pressure vessel. At the autofrettage level higher than 50%, the failure location and fatigue life of the pressure vessel were not significantly influenced by the autofrettage level.

Evaluation of the Autofrettage Effect on Fatigue Lives of Steel Blocks with Crossbores Using a Statistical and a Strain-Based Method

Abstract A problem of fundamental and industrial interest is the effect of autofrettage on fatigue lives and the structural integrity of engineering components. The component considered is a steel block containing crossbores, a situation found in many industrial applications such as the fluid ends of positive displacement pumps. Twenty-one steel blocks containing intersecting perpendicular crossbores were autofrettaged with pressures ranging from 79 to 172 MPa. The specimens were subsequently fatigue tested on a specially designed test facility under 53 and 69-MPa pressures. Statistical procedures based on analysis of variance were used to analyze the effect of the different autofrettage pressure levels on fatigue lives of specimens. The reverse plasticity criterion was also used to investigate the fatigue enhancement limit of the autofrettage process. Results of the statistical methodology correlated with results of the reverse plasticity criterion showed the existence of an “optimal” autofrettage pressure.

A Short History of High Pressure Technology From Bridgman to Division 3

This paper will briefly review the development of high pressure technology from the early basic science through the major applications that have driven the technology. These include gun barrel development, the polyethylene process, and isostatic pressing and crystal growth. A parallel effort on the development of man-made diamonds will be mentioned. More recently, jet cutting and food sterilization are driving the technology in new directions. The paper will discuss the differences in design approach between thin-walled and thick-walled cylinders, including the use of favorable residual stresses. The author’s experiences with the development of the autofrettage process for gun barrels, including the “swage” method, will be reviewed. The history of the development of the new Division 3 of Section VIII of the Boiler and Pressure Vessel Code will be described, including some of the controversies and compromises that arose during the process. [S0094-9930(00)01403-7]

Residual Stress Estimation in Crossbores With Bauschinger Effect Inclusion Using FEM and Strain Energy Density

Crossbore intersections in liquid ends of positive displacement pumps (PDPs) have regions with high stress concentration. Due to the cyclic loading that occurs in most PDPs, these stress concentration points are susceptible to fatigue cracking. In order to prolong their life, the liquid ends are often overpressurized (autofrettaged), thus inducing beneficial compressive hoop stresses in these critical regions upon removal of the autofrettage pressure. This autofrettage process drives the region of high stress concentration beyond the elastic limit and well into the elastic-plastic region. Elastic-plastic stresses and strains due to loading and unloading were analyzed in crossbore geometries, with Bauschinger effect included, using 3-D finite element analysis of the liquid end. For comparison, an analytical approach was developed, based on the strain energy density criterion first proposed by Glinka. The approach was modified to include the Bauschinger effect for precise estimation of such stresses and strains. Good correlation was observed between elastic-plastic crossbore stresses and strains predicted by the analytical approach and the finite element analysis.