Anthony P. Parker

A Comparison of Methods for Predicting Residual Stresses in Strain-Hardening, Autofrettaged Thick Cylinders, Including the Bauschinger Effect

High-pressure vessels, such as gun barrels, are autofrettaged in order to increase their operating pressure and fatigue life. Autofrettage causes plastic expansion of the inner section of the cylinder, setting up residual compressive stresses at the bore after relaxation. Subsequent application of pressure has to overcome these compressive stresses before tensile stresses can be developed, thereby increasing its fatigue lifetime and safe working pressure. This paper presents the results from a series of finite element models that have been developed to predict the magnitude of these stresses for a range of end conditions: plane stress and several plane-strain states (open and closed ended, plus true plane strain). The material model is currently bilinear and allows consideration of strain hardening and the Bauschinger effect. Results are compared to an alternative numerical model and a recent analytical model (developed by Huang), and show close agreement. This demonstrates that general purpose finite element analysis software may be used to simulate high-pressure vessels, justifying further refining of the models.

Mechanisms and modeling comparing HB7 and A723 high strength pressure vessel steels

HB7, an ultra-clean, high strength pressure vessel steel manufactured in France, is compared to A723 steel. This steel, suggested as an improved pressure vessel material is currently being proposed for critical applications, and will likely be used more frequently as design engineers discover its capabilities. This paper includes comparisons of strength, fracture toughness, fatigue properties and composition of the two steels, followed by an in-depth comparison and modeling of environmental cracking resistance, Bauschinger-modified residual stresses and fatigue lives. Results indicate that in all critical areas, with the exception of Bauschinger-reduced residual stress, the HB7 is superior to the A723 steel. Particularly for small amounts of autofrettage, near-bore residual stresses are reduced for HB7 steel compared to those for A723 steel at the same strength level. The greatest improvement of the HB7 over the A723 is in environmental cracking resistance. The HB7, when tested in concentrated sulfuric acid, exhibits five orders of magnitude longer crack incubation times and three orders of magnitude slower crack growth rates, when compared to A723 steel at the same strength level.

Mechanisms and Modeling Comparing HB7 and A723 High Strength Pressure Vessel Steels

HB7, an ultra-clean, high strength pressure vessel steel manufactured in France, is compared to A723 steel. This steel, suggested as an improved pressure vessel material is currently being proposed for critical applications, and will likely be used more frequently as design engineers discover its capabilities. This paper includes comparisons of strength, fracture toughness, fatigue properties and composition of the two steels, followed by an in-depth comparison and modeling of environmental cracking resistance, Bauschinger-modified residual stresses and fatigue lives. Results indicate that in all critical areas, with the exception of Bauschinger-reduced residual stress, the HB7 is superior to the A723 steel. Particularly for small amounts of autofrettage, near-bore residual stresses are reduced for HB7 steel compared to those for A723 steel at the same strength level. The greatest improvement of the HB7 over the A723 is in environmental cracking resistance. The BH7, when tested in concentrated sulfuric acid, exhibits five orders of magnitude longer crack incubation times and three orders of magnitude slower crack growth rates, when compared to A723 steel at the same strength level.Copyright

A Re-Autofrettage Procedure for Mitigation of Bauschinger Effect in Thick Cylinders

A manufacturing procedure for enhancing residual stresses and thereby improving fatigue lifetime and fracture resistance of pressure vessels is proposed. The procedure involves initial autofrettage; one or more ‘heat soak plus autofrettage’ sequences and an optional final heat soak. Stresses are calculated numerically for traditional, single autofrettage and compared with those created by the new procedure. The loss of bore compressive hoop stress due to Bauschinger effect is predicted to be significantly reduced. Associated fatigue lifetime calculations indicate that life may be improved by a factor of between 2 and 30, depending upon tube geometry and the ratio of cyclic pressure to yield strength. Repeated overload plus heat soak cycles may also be of benefit in other engineering design scenarios.Copyright

Autofrettage of a Spherical Pressure Vessel

There is a numerical procedure for modeling autofrettage of thick-walled cylinders that incorporates Bauschinger effect as a function of prior plastic strain and Von Mises’ yield criterion. In this paper the numerical procedure is extended to solve the analogous problem of a spherical, thick walled steel vessel. An equivalent new analytical solution for the case of a spherical vessel is also formulated. The analytical and numerical solutions are shown to be in close agreement. It is demonstrated numerically that a re-autofrettage procedure, previously proposed for cylindrical vessels, may be extremely beneficial for spherical vessels. Additional commentary is provided on the limitations of certain analytic solutions.Copyright

Compound and Monobloc Cylinders Incorporating Reverse-Autofrettage to Reduce External Hoop Stresses

Reverse autofrettage involves the application of pressure to the OD of a tube which in turn produces bore yielding and a residual stress profile equal in magnitude but opposite in sign to conventional autofrettage.The analyses within this paper identify two potential new manufacturing procedures involving reverse autofrettage. The procedures are predicted to reduce external tensile hoop stress in an autofrettaged gun tube. This reduction should increase lifetime of tubes that are prone to OD fatigue or corrosion-related failure from manufacturing defects or notches.The first procedure involves traditional autofrettage of an inner tube and reverse autofrettage of a larger outer tube. The outer tube is then compounded with the inner tube by thermal shrink-fitting or some equivalent process. The second procedure employs a monobloc tube which is subjected to reverse autofrettage followed by conventional internal autofrettage. Both procedures significantly reduce OD residual hoop stress but in the case of the monobloc tube there is an associated loss of compressive residual bore hoop stress.Copyright

Post-Autofrettage Thermal Treatment and Its Effect on Reyielding of High Strength Pressure Vessel Steels

The autofrettage process of a thick walled pressure vessel involves applying tensile plastic strain at the bore of the vessel, which reverses during unloading and results in favorable compressive residual stresses at the bore and prolongs the fatigue life of the component. In thick walled pressure vessels this process can be accomplished with either a hydraulic or mechanical overloading in process. The Bauschinger effect, which is observed in many of the materials used in thick walled pressure vessels, is a phenomenon, which results in lower compressive residual stresses than those predicted with classic ideal isotropic hardening. The phenomenon is a strong function of the amount of prior tensile plastic strain. A novel idea, which involves a multiple autofrettage processes, has been proposed by the present authors. This process requires a low temperature postautofrettage thermal treatment, which effectively returns the material to its original yield conditions with minimal effect on its residual stress state. Details of this low temperature thermal treatment are proprietary. A subsequent second autofrettage process generates a significantly lower amount of plastic strain during the tensile reloading and results in higher compressive residual stresses. This paper reports the details of the exploratory tests involving tensile and compressive loading of a test coupon, followed by a low temperature post-plastic straining thermal treatment, and subsequent reloading in tension and compression. Finally results of a full scale safe maximum pressure (SMP) test of pressure vessels are presented; these tests indicate a significant increase (11 %) in SMP.

Hydraulic Re-Autofrettage of a Swage Autofrettaged Tube

An earlier paper presented a non-linear analysis of hydraulic re-autofrettage following initial hydraulic autofrettage and low temperature heat soak. The benefits from such a sequence derive almost exclusively from the mitigation of Bauschinger effect. As a result yielding during re-autofrettage occurs in the near-bore region. In this paper hydraulic re-autofrettage following initial swage autofrettage and heat soak is analyzed. The benefits in this case derive mainly from the adjustment of stress fields within the wall of the tube, close to the original elastic-plastic interface created during the swage process. Bauschinger effect mitigation is a second order effect. This procedure is the subject of a recently-submitted patent application. The procedure can produce significant improvements in initial re-yield pressure and in safe maximum pressure as defined by additional permanent strain. An increase in fatigue crack growth lifetime is also predicted. At higher re-autofrettage pressures OD residual hoop stresses increase significantly.Copyright

Custom Material Modeling Within FEA for Use in Autofrettage Simulation

Finite Element Analysis (FEA) has been widely adopted. For autofrettage analysis, in order to represent real conditions and materials, it is necessary to properly model end conditions and material behavior, in particular the loss of compressive strength following prior tensile plastic strain, termed the ‘Bauschinger Effect’. The latter is a strong function of prior plastic strain and therefore of location; this implies the need to model a different material unloading behavior at each location in the tube. Two possible methods of implementing such a behavior within FEA are examined. These are an ‘elastic modulus and Poisson’s ratio adjustment procedure’ (EMPRAP) and a ‘user programmable feature’ (UPF). Finally the results are compared to an independent, non-FEA, EMPRAP numerical solution. Close agreement between all three methods is demonstrated. The UPF approach, validated here, is applicable in more complex loading scenarios.Copyright

An Improved Method for Recovering Residual Stress From Strain Measurements in Cylinders and Rings

The traditional method for determining the residual stress from experimental strain readings in axisymmetric configurations can produce large discrepancies in stress predictions, particularly radial stress. By numerical calculation of autofrettage residual stress in a long thick cylinder and subsequent numerical modeling of release of axial stress during the cutting of a short ring sample, a potential preexisting radial and hoop residual stress field is calculated. These stress values are converted to radial and hoop strains at a number of discrete radial locations. Numerical strain values are then randomized to enforce a standard deviation some 25% higher than that for a typical experimental procedure. Pairs of randomized, discrete strain values are used to predict associated residual stresses using the traditional method. This produces wide scattering of predicted stress values, particularly radial stress, and showed high sensitivity to assumed Poisson’s ratio. A simple, alternative strain-stress analysis procedure (ASSAP) is proposed. ASSAP enforces equilibrium requirements and essential stress free boundary conditions at the bore. ASSAP is shown to improve prediction of radial residual stress by around an order of magnitude in the near-bore region, and to effectively eliminate the sensitivity to Poisson’s ratio. The predicted radial stress profile is of sufficient quality to define the associated hoop stress profile. The predicted radial and hoop stress profiles are in close agreement with the original numerical solutions for the ring. Numerical and ‘recovered’ bore hoop stresses are within 1.4%. This work also demonstrates a significant limitation of methods that involve the cutting of axially short ring samples from a long, autofrettaged cylinder. Release of axial stress during cutting creates a reduction in compressive bore hoop stress. Such a discrepancy would be very significant if ring, rather than long-cylinder, values were used in fatigue lifetime calculations.Copyright