John G. Hetherington

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.

Hydrocode Simulation with Modified Johnson-Cook Model and Experimental Analysis of Explosively Formed Projectiles

The formation of mild steel (MS) and copper (Cu) explosively formed projectiles (EFPs) was simulated in AUTODYN using both the Johnson-Cook (JC) and modified Johnson-Cook (JCM) constitutive models. The JC model was modified by increasing the hardening constant by 10%. The previously established semi-empirical equations for diameter, length, velocity, and depth of penetration were used to verify the design of the EFP. The length-to-diameter (L/D) ratio of the warhead used in the simulation varied between 1 < L/D < 2. To avoid projectile distortion or breakup for large standoff applications, the design of the EFP warhead was modified to obtain a lower L/D ratio. Simulations from the JC model underestimated the EFP diameter, resulting in an unrealistically elongated projectile. This shortcoming was resolved by employing the JCM model, giving good agreement with the experimental results. The projectile velocity and hole characteristics in 10-mm-thick aluminum target plates were studied for both models. The semi-empirical equations and the JC model overestimated the projectile velocity, whereas the JCM model underestimated the velocity slightly when compared to the experimental results. The depths of penetration calculated by the semi-empirical equations in the aluminum (Al) target plate were 55 and 52 mm for Cu and MS EFPs, respectively.

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.

Numerical Analysis of the Effect of Machining on the Depth of Yield, Maximum Firing Pressure and Residual Stress Profile in an Autofrettaged Gun Tube

A multi-linear kinematic, two dimensional finite element model incorporating Bauschinger effect, developed using ANSYS commercial software is used to determine the effect of machining both at the bore and at the outside diameter, on the depth of yield, maximum firing pressure and final residual stress field present in an autofrettaged gun tube. The model, which is in good agreement with experimental findings, clearly shows that the reduction in maximum compressive circumferential stress is more sensitive to internal machining than to external machining; the depth of yield remains stable and there is no movement of the elastic-plastic interface, relative to its location before material removal. If the internal machining removes material in which reverse yield has occurred, the maximum firing pressure is not affected. The finite element analysis supported by experimental evidence thus leads to an optimization technique for gun tube design.

Investigation of Driving Force Variation 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 along and through the bore of the tube. A finite element (FE) model of the swaging process, developed previously by the author in ANSYS , was configured for comparison with an earlier model; this allowed the accuracy of further properties of the ANSYS model to be investigated. Driving force was the main property of interest, specifically how it varied with mandrel slopes and parallel midsection, to allow direct comparison with the earlier model. The variation of driving force with respect to coefficient of friction was investigated; driving force increased in near proportion, but a subtle trend indicated a further study of stress component be made. This was followed by a two-pass swage process. Close agreement was found with empirical data and the discrepancies observed between the two models are explained by the relatively coarse mesh used by the earlier model. This further verifies the sensitivity of the model described here.

Material Modeling for Autofrettage Stress Analysis Including the “Single Effective Material”

Analytical and numerical stress analysis of the autofrettage process has made great strides in the last few years. The major challenge is no longer the stress analysis process but the incorporation of ‘real’ material behavior, including Bauschinger effect. This means that material properties may vary at every radial location within the tube. In this paper it is demonstrated that Finite Element Analysis (FEA) may be accomplished using a ‘user programmable feature’ within a non-linear FEA or, more simply using an elastic modulus and Poisson’s ratio adjustment procedure within a linear-elastic FEA. The results of these two methods are shown to be in agreement with each other and with an independent numerical analysis. It is further demonstrated that numerical solutions may be obtained using a single ‘fictitious’ material. This is called a ‘single equivalent material’ (SEMAT). Whilst this requires a very small number of iterations for accurate convergence, it dramatically reduces the material-modeling challenges. Furthermore, SEMAT may be implemented into an analytical procedure thereby permitting highly accurate modeling of a real material whose unloading behavior varies with radius. Comparisons indicate that this is a robust, accurate procedure.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

The Explosively Formed Projectile (EFP) as a Standoff Sea Mine Neutralization Device

There are many methods that can be used for the clearance of underwater ammunition; for example, sea mines. In all such techniques, the primary aim is to defuse underwater ammunition without detonation. Explosively formed projectiles (EFPs) have great potential to cleanly and safely defuse underwater ammunition. Underwater simulations and experiments were conducted to highlight the use of EFPs for safe destruction of sea mines. The copper liner configuration was used to study the penetration performance of the EFPs in water. ANSYS AUTODYN-2D hydrocode was used to simulate copper EFP penetration, passage, and impact with a target immersed in water. Simulation results were obtained by making use of Lagrangian and Euler formulations. The results indicated that the velocity of an EFP reduces sharply as it enters the water. However, the velocity of an EFP is stable in the later part of its flight through the water. The results further indicated that after covering five cone diameters (CDs) in water, the velocity of the EFP was reduced below critical and it failed to perforate an aluminum target plate of 5 mm thickness. Nevertheless, it perforated the target plate at 4 CDs in water. A known quantity of high explosive sandwiched between two plates, just like explosive reactive armor (ERA), was used as a target to simulate the sea mine. Flash X-ray was also used to record the flight and penetration of the EFP through the target plate. Simulation results matched reasonably well with the experimental results.

Numerical Simulations as a Reliable Alternative for Landmine Explosion Studies: The AUTODYN Approach

In order to validate the numerical procedure, the explosion of a mine was recreated within the non-linear dynamics software, AUTODYN. Two models were created and analysed for the purposes of this study — buried and flush HE charge in sand. The explosion parameters — time of arrival, maximum overpressure and specific impulse were recorded at two stand-off distances above the ground surface. These parameters are then compared with LS-DYNA models and published experimental data. The results, presented in table format, are in reasonable agreement.Copyright

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

Swaging is one method of autofrettage, a means of pre-stressing 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.Copyright