Autofrettage Pressure Research Articles

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.

Thermally induced stress analysis of composite/aluminum ring specimens at cryogenic temperature

In this study, the characteristics of filament wound composite/aluminum ring specimens were investigated at cryogenic temperature. Ring specimens were manufactured using carbon fiber and Type B epoxy resin which had been developed for cryogenic use. By measuring the thermal strain at −150 °C, it was found that compressive thermal stress was induced in the composite part, while the tensile thermal stress in aluminum part, which was about 32% of yield stress, in turn caused aluminum to yield at a lower load level. In addition, the thermal strain from a finite element analysis showed good agreement with this measure in an experiment. After six mechanical loading cycles were applied to the ring specimen at −150 °C, tensile tests were performed at −150 °C using split disk fixtures. The results of these tests showed that the composite strength in a liner-composite tank structure for use in a cryogenic propellant tank is decreased by the applied auto-frettage pressure.

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.

Stress intensity factor calculation of steel-lined hoop-wrapped cylinders with internal semi-elliptical circumferential crack

The purpose of this paper is to present mode I stress intensity factor for a circumferential semi-elliptical crack on the inner surface of a hoop-wrapped steel-lined CNG cylinder. The stress intensity factors along the crack front are directly computed by 3D finite element method for a wide range of variations of the crack geometry. Also influence of many parameters such as cylinder internal pressure, composite layer thickness, composite material properties and undertaking Auto-Frettage pressure are studied on the stress intensity factor of the crack and some conclusive results are drawn. For the sake of validation of the results and because of lack of the results for a circumferential semi-elliptical crack in the literature, a semi-elliptical axial crack in a composite hoop-wrapped cylinder has been modeled and the results have been compared with those in the literature showing a good agreement.

Residual Stress Evaluation and Its Effects on the Fatigue Life of an Autofrettaged Tube

The theoretical residual stresses in the autofrettaged tube were calculated, considering Bauschinger effect caused by the reverse yielding while removing autofrettage pressure. Actual residual stresses were measured by using X-ray diffraction analysis, and compared with the theoretical calculations. From the tension-compression tests, however, the tube steel showed a significant Bauschinger effect, depending on the plastic strain prior to unloading. Fatigue crack growth life of the tube was evaluated by integrating the crack growth rate equation. Stress intensity factor of an inside crack at the tube due to pressure and residual stresses was determined from finite element analysis and superposition principle. Compared to the unautofrettaged tube, the extended fatigue life of the autofrettaged thick-walled tube was obtained depending on the autofrettage level and the Bauschinger effect.

복합재/알루미늄 링 시편의 극저온 특성 평가

본 연구에서는 필라멘트 와인딩하여 제작된 복합재/알루미늄 링 시편의 극저온 특성을 고찰하였다. 링 시편은 탄소섬유와 극저온용으로 개발된 Type B 에폭시 수지를 사용하여 제작되었다. 상온으로부터 -150℃까지 링 시편의 열변형률 측정 결과, 극저온 영향에 의해 복합재 내에는 압축 열응력이 발생하였으나 알루미늄 내에는 항복응력의 약 32% 크기의 인장 열응력이 발생하였다. 그리고 이는 극저온에서 알루미늄의 소성하중을 낮추는 결과를 가져왔다. 또한, 실험으로부터 얻어진 극저온 물성을 사용하여 유한요소해석을 수행한 결과, 링 시편 실험을 통해 얻어진 열변형률과 잘 일치함을 보였다. -150℃에서 split disk 치구에 장착된 복합재/알루미늄 링 시편에 6회 하중 사이클을 수행한 후, -150℃에서 인장시험을 수행하였다. 그 결과, 라이너-복합재 탱크 구조물에 대하여 자긴압력 등이 가해질 때, 극저온에서는 자긴압력에 의해 복합재 강도가 상온 보다 더 크게 저하될 수 있음을 보였다. In this study, the characteristics of filament wound composite/aluminum ring specimens were investigated at cryogenic temperature. The ring specimens were manufactured using carbon fibre and Type B epoxy resin which had been developed for cryogenic use. As a result of measuring thermal strains at -150℃, it was found that compressive thermal stress was induced in composite part on the contrary, tensile thermal stress in aluminum part which was about 32% of yield stress and in turn, caused aluminum to be yielded at lower load level. In addition, Thermal strains which resulted from finite element analysis showed good agreement with those of the experiment. After 6 mechanical loading cycles had been applied to the ring specimen at -150℃, tensile tests were performed at -150℃ using a split disk fixture. As a result, it was shown that composite strength in a liner-composite tank structure which is for the use of cryogenic propellant tank would be decreased by auto-frettage pressure which is applied to it.

Evaluation of the optimum pre-stressing pressure and wall thickness determination of thick-walled spherical vessels under internal pressure

In the present study, in the first part for a spherical vessel with known dimensions and working pressure, two methods of hoop and equivalent stress optimization across the wall thickness are employed to determine the best autofrettage pressure. In the next part for a predefined working pressure the minimum wall thickness of the vessel is calculated using two other design criteria i.e. (A) optimizing the hoop stress, and (B) assuming a suitable percent for the penetration of yielding within the wall thickness. Finally, the optimum thickness and the necessary strengthening pressure are extracted and different plots are introduced for different types of structural materials under different internal pressures.

Re-Autofrettage

Loading, unloading, and reloading behavior of high-strength steel AISI 4340 (with yield strength of 1080MPa) has been measured using the round bar specimen and method described in (Jahad, H., and Ghanbari, G., 2003, ASME J. Pressure Vessel Technol., 125, pp. 321–325). Tests were conducted at plastic strains up to 3.4% for unloading and reloading. Re-autofrettage is the process of reapplication of overload pressure on an already autofrettaged tube. The question of whether reautofrettage results in a more beneficial compressive stress distribution and, therefore, in extension of life is examined in this study. Because of the profound influence of the Bauschinger effect on the unloading and reloading behavior of high-strength steel, the actual behavior of 4340 steel is used in calculations. It has been shown that with different combinations of first and second overload pressure, higher compressive stress is obtained as compared to a single autofrettage. Using a range of first and second autofrettage pressure, the compressive stress resulted by re-autofrettage is given.

Endurance limit of autofrettaged Diesel-engine injection tubes with defects

The endurance limit of cold drawn tubes under cyclic internal pressure has been investigated experimentally and numerically. Multiple specimen configurations regarding material state, defect depth and autofrettage pressures have been covered. The endurance limit can be increased considerably by autofrettage. Basic items of the proposed simulation method are the application of a plasticity model which is able to accurately describe all relevant deformation characteristics and a finite element based crack propagation calculation. Crack opening pressures and effective ranges of the stress intensity factor are calculated. The corresponding threshold condition yields the endurance limits. They are in good agreement with the experimental values.

A General Autofrettage Model of a Thick-Walled Cylinder Based on Tensile-Compressive Stress-Strain Curve of a Material

The basic autofrettage theory assumes elastic-perfectly plastic behaviour. Because of the Bauschinger effect and strain-hardening, most materials do not display elastic-perfectly plastic properties and consequently various autofrettage models are based on different simplified material strain-hardening models, which assume linear strain-hardening or power strain-hardening or a combination of these strain-hardening models. This approach gives a more accurate prediction than the elastic-perfectly plastic model and is suitable for different strain-hardening materials. In this paper, a general autofrettage model that incorporates the material strain-hardening relationship and the Bauschinger effect, based upon the actual tensile-compressive stress-strain curve of a material is proposed. The model incorporates the von Mises yield criterion, an incompressible material, and the plane strain condition. Analytic expressions for the residual stress distribution have been derived. Experimental results show that the present model has a stronger curve-fitting ability and gives a more accurate prediction. Several other models are shown to be special cases of the general model presented in this paper. The parameters needed in the model are determined by fitting the actual tensile-compressive curve of the material, and the maximum strain of this curve should closely represent the maximum equivalent strain at the inner surface of the cylinder under maximum autofrettage pressure.

Determination of Residual Stress Distribution in Autofrettaged Tube Based on Modified Yielding Criterion and Tensile-Compressive Curve of Material

An autofrettage model considering the material strain-hardening behavior and the Bauschinger effect, based on the actual tensile–compressive curve of material and modified yield criterion, has been proposed. The analytic expressions of residual stress distribution and the autofrettage pressure have been obtained. This model has stronger curve fitting ability, nearly all of the strain-stress curves of materials used in making autoefrettage tubes can be fitted well by this model, and each of those models based on the simplified strain hardening relationship of material is a special case of the model. It was used to predict the residual stress distributions of an autofrettaged tube. The results show that the residual stress distributions predicted by the present model are in good agreement with the experimental data.

A Study of the Residual Stress Distribution in an Autofrettaged, Thick-Walled Cylinder With Cross-Bore

It may be necessary to provide a radial opening such as gas evacuator holes, or an opening to operate the unlocking of the bolt mechanism by means of exhaust gases, in a gun barrel, which is a thick walled cylinder. A three dimensional finite element analysis has been performed to evaluate the effect of introducing a radial cross-bore in an autofrettaged thick-walled cylinder. From the analysis of the cross-bored autofrettaged cylinder, it was observed that there is a severe localized change in the residual stress profile in the vicinity of the cross-bore. The residual circumferential stress increases in compression at the bore. Similarly it increases in tension at the outer diameter, thus making the outer diameter more vulnerable to fatigue failure or crack initiation under stresses arising as a result of firing. Analyses were also performed by varying the cross-bore diameter and it was observed that, by increasing the diameter of the radial hole, the residual circumferential stress at the bore reduces, while it increases at the outer diameter, with an increase in the cross bore diameter. The re-pressurization pressure of an autofrettaged cylinder with radial cross-bore was found to be approximately 65 percent less than the actual autofrettage pressure in a particular case discussed in this paper. A comparison is also made with the residual stress field which would result if the cross-bore was machined before autofrettage.

Experimental and finite element prediction of bursting pressure in compound cylinders

Aluminium cylinders with a constant ratio of outer to inner radii, k=2.2, with different diametral interferences and various shrinkage radii were subjected to bursting and autofrettage pressures. Numerical simulations of the compound cylinders were also performed using the finite element code, NISA. The results can predict the optimum shrinkage radius to a reasonable accuracy with the use of finite element analysis. This radius corresponds to the situation when the maximum von-Mises stress at the internal radii of both the inner and outer cylinders become equal. It was shown that the maximum von-Mises stress across the wall of the cylinder is at the minimum at this shrinkage radius. The optimum diametral interference was found to be that which sufficiently brought the contact surface of the inner and outer cylinders to the point of yielding. Should the shrinkage pressure exceed the elastic limit, the pressure capacity of the cylinder will not be improved. The numerical and experimental results show that autofrettage had no effect on the bursting pressure of the thick-walled compound cylinder for the material tested.

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.

Yield Pressure Measurements and Analysis for Autofrettaged Cannons

Yield pressure corresponding to a small permanent OD strain was measured in quasi-static laboratory tests of autofrettaged ASTM A723 steel cannon pressure vessels. Yield pressure was found to be a consistent ratio of the yield strength measured from specimens located in close proximity to the area of observed yielding. Yield pressure measurements for dynamic cannon firing with typically a 5-ms pressure pulse duration gave 14% higher yield pressures, attributed to strain rate effects on plastic deformation. Calculated Von Mises yield pressure for the laboratory test conditions, including the Bauschinger-modified ID residual stress and open-end vessel conditions, agreed with measured yield pressure within 3–5%. Calculated yield pressure was found to be insensitive to the value of axial residual stress, since axial stress is the intermediate value in the Von Mises yield criterion. A description of yield pressure normalized by yield strength was given for autofrettaged A723 open-end pressure vessels over a range of wall ratio and degree of autofrettage, including effects of Bauschinger-modified residual stress. This description of yield pressure is proposed as a design procedure for cannons and other pressure vessels.

Fatigue investigations of autofrettaged steel cylinders based on neutron-diffraction measurements

A series of cyclic internal pressurization fatigue experiments was conducted on partially autofrettaged cylinders with multiple internal radial elliptic shaped cracks covering a wide range of possible configurations. A theoretical model was developed to predict the theoretical fatigue life using as input data the actual measured position of the plastic boundary from neutron-diffraction measurements on the failed specimens, as well as a position calculated analytically from the autofrettage pressure. The theoretical fatigue-life predictions based on the neutron-diffraction results were found to give the best correlation with experimental fatigue results.

The Influence of Multiple Axial Erosions on a Three-Dimensional Crack in Determining the Fatigue Life of Autofrettaged Pressurized Cylinders

Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from an erosion’s deepest point in a multiply eroded, autofrettaged, pressurized, thick-walled cylinder are investigated. The problem is solved via the finite element method (FEM). Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs are evaluated for a variety of relative crack depths, a0/t=0.01-0.40, and crack ellipticities, a0/c=0.5-1.5, emanating from the tip of erosions of different geometry, namely: (a) semi-circular erosions of relative depths of 1–10 percent of the cylinder’s wall thickness, t; (b) arc erosions for several dimensionless radii of curvature, r′/t=0.05-0.4; and (c) semi-elliptical erosions with ellipticities of d/h=0.3-2.0. The erosion separation angle, α, is taken from 7 to 360 deg. Deep cracks are found to be almost unaffected by the erosion. The effective SIF for relatively short cracks is enhanced by the presence, separation distance and geometry of the erosion, as well as the crack geometry, and may result in a significant decrease in the vessel’s fatigue life of up to an order of magnitude.

The Influence of Multiple Axial Erosions on the Fatigue Life of Autofrettaged Pressurized Cylinders

Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from an erosion’s deepest point in a multiply eroded, autofrettaged, pressurized, thick-walled cylinder are investigated. The problem is simulated as a two-dimensional problem and is solved via the finite element method. Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs are evaluated for a variety of relative crack lengths, a0/t=0.01-0.45 emanating from the tip of erosions of different geometries, namely, (a) semi-circular erosions of relative depths of 1–10 percent of the cylinder’s wall thickness, t; (b) arc erosions for several dimensionless radii of curvature, r′/t=0.05-0.4; and (c) semi-elliptical erosions with ellipticities of d/h=0.5-1.5, and erosion span angle, α, from 6 deg to 360 deg. The effective SIF for relatively short cracks is found to be increased by the presence of the erosion, which in turn may result in a significant decrease in the vessel’s fatigue life of up to an order of magnitude. Deep cracks are found to be almost unaffected by the erosion.

Autofrettage of Open-End Tubes—Pressures, Stresses, Strains, and Code Comparisons

Autofrettage is used to introduce advantageous residual stresses into pressure vessels. The Bauschinger effect can produce less compressive residual hoop stresses near the bore than are predicted by “ideal” autofrettage solutions. A recently developed numerical analysis procedure is adopted and extended. The ratio of calculated autofrettage pressure (numerical)/ideal autofrettage pressure (Tresca criterion and plane stress) is calculated and verified against available solutions. The case of open-end conditions based upon von Mises and engineering plane strain (constant axial strain with zero net axial force) is examined in detail. The ratio in this case varies between unity and 2/3, but exhibits very significant variations from the plane stress case when the diameter ratio of the tube exceeds 1.8. Results are within 0.5 percent of available analytical, numerical, and experimental results. A simple numerical fit allows all autofrettage pressures to be replicated to within 0.5 percent. The true plane strain pressure ratio is examined and shown to be inappropriate in modeling engineering plane strain. A number of residual hoop and axial stress profiles is presented for radius ratio 2.0. Calculated pressures are used to determine residual hoop stress values for tube diameter ratios from 1.1 to 3.0 for the full range of percentage overstrain levels. These comparisons indicate that Bauschinger effect is evident when the ratio autofrettage radius/bore radius exceeds 1.2, irrespective of diameter ratio. To assist designers the important values of residual hoop stress at the bore are summarized in a composite plot and a numerical fit is provided. The accuracy of the current ASME code using pressure criteria is assessed. The code is shown to be generally and modestly conservative. A design procedure is proposed which appears capable of extending code validity beyond 40 percent overstrain (the limit of the current code) and of eliminating the small nonconservatism at very low overstrain. Hoop strain values are calculated at both the bore and outside diameter of a tube of radius ratio 2 at the peak of the autofrettage cycle using von Mises criterion with open-end, closed-end, and plane strain conditions. These are compared with available solutions; general agreement is demonstrated, with agreement within 2 percent with an accepted simple formula in the case of open ends. ASME code predictions of percentage overstrain based upon strains at the peak of the autofrettage cycle are generally within 6 percent of numerical predictions. This is in turn produces an agreement within approximately 3 percent in residual bore hoop stress calculation. This discrepancy is generally conservative, becoming non-conservative only at overstrain levels exceeding 80 percent. Strain during removal of autofrettage pressure, in the presence of Bauschinger effect, is also calculated. This shows that the difference in strain during the unloading phase is up to 8 percent (ID) and 6.3 percent (OD) compared with the predictions of elastic unloading. These latter results show similar agreement with the ASME code as in the peak-strain analysis and permit correction of estimates of percentage overstrain based upon permanent bore enlargement.

An analytical procedure for estimating residual stresses in blocks containing crossbores

Intersecting bore geometries are used in a number of industrial applications such as the fluid ends of reciprocating pumps and have regions with high stress concentration. To increase the fatigue life of a fluid end, a reduction in the operating mean stress is helpful. This can be achieved with the introduction of compressive residual stresses in these critical regions by means of proof loading or autofrettage. Accurate estimation of fluid end fatigue lives necessitates accurate evaluation of the residual stresses induced by autofrettage. In this paper, finite element models were used to obtain hoop stress to pressure ratios, at the most highly stressed plane, in blocks of different sizes and bore ratios. The hoop stress to pressure ratios were used along with Neuber's rule and kinematic hardening to select an autofrettage pressure and to estimate the elastoplastic residual stresses on this plane. The suggested method estimates residual stress magnitudes close to finite element solutions, and eliminates the need for a lengthy and costly elastoplastic finite element analysis.