Harwood Engineering Company, Inc.

The Effect of Machining After Full Autofrettage

by Donald H. Newhall

An investigation of the effects of machining after autofrettage was made at Watertown Arsenal. For economy of time and material tests were made on many discs cut transversely from an autofrettaged gun tube rather than on many tubes, validity being established. It was found that thin slices of an autofrettaged tube when slit radially would open an amount dependent on the yield strength and modulus of elasticity yet reflecting alteration to the residual stress pattern by the Bauschinger effect and reverse yielding. The reverse yielding and the Bauschinger effect are clearly seen. Boring is shown to slightly increase the strength while turning has the opposite effects.

Introduction

The alteration of residual stress by machining, is of current interest to those concerned with the design, manufacture, and use of high pressure equipment now in common use in industrial processing and research, particularly since it is well known that the elastic strength and resistance to fatigue is increased by autofrettage. (11), (12), (13). It became an important consideration during World War II when autofrettage was first used in the production of large numbers of cannon by the U.S. Army. At that time the author, then an officer in the Ordnance Department was in charge of this phase of cannon tube manufacture at the Watertown Arsenal. While steps were taken to keep machining to a minimum, still an appreciable amount was necessary to finish the tube.

Background

In designing the gun tubes for the prior-to-autofrettage contour, care had to be taken that the taper was not so small that an inordinate amount of jack force was required to remove the guns from the containers because of the gripping, mentioned above, at the muzzle end. This consideration tended to leave considerable metal to be turned from the outside after autofrettage and was one of the major reasons for this study. If it could be proved that the residual stresses in a relatively thin disc cut from an autofrettaged tube retained essentially the same pattern and magnitude of residual stresses existing in the complete tube itself, the experimental procedure could be considerably shortened and simplified, for then, thin discs could be machined and tested instead of whole cylinders.

Theoretical Considerations

    Equation (1)

    Equation (2)

If a disc as described above is cut radially the residual tangential stresses, varying from comprehensive at the bore to tensile at the periphery cause the disc as a whole to dilate, with a tapered opening corresponding to the cut. If the disc is now treated mathematically as a curved beam, of constant curvature, it can be shown that upon evaluating the couple necessary to reclose it, the stresses developed will be the same as those relieved by the cut-through described by different constants, as follows:

    Equation (3)

    Equation (4)

One can visualize that a low value of Dd/2d on Figure 4 implies a relatively weak gun, for Dd is proportional to the locked-in favorable residual stress.

If the von Mises-Henchy (16) theory of yielding were used, Dd/2d would not be quite a constant since that theory is slightly sensitive to the wall ratio of the cylinder that is yielding.

Experiment

In the second experiment, a few discs were cut and ground on both faces to ½" thickness from two gun tubes, 155 mm and 90 mm, processed with 6 percent borg expansion and subsequently soaked at 575° K. A milling cut was made radially from the outside to the bore, releasing the residual stresses. The radial and tangential stresses are principal stresses the radial cut relieves them, and the disc opens to a larger diameter. If the autofrettage stresses developed in the long cylinder are retained in the thin slice, the increase in diameter provides a measure of them (see Appendix).

The discs increased in diameter, following the radial cut, an amount very close (within 5%) of that expected from the constant Dd/2d = S_y/E. The material in these discs had properties essentially the same as the material used to develop Figures 1 and 2. Thus it appears that the thin slices retain practically all of the autofrettage.

In view of the encouraging results of the preliminary experiments an 105 mm howitzer was diverted from production for conclusive tests. This was a centrifugally cast tube, number C-3615, and had been processed through autofrettage and subsequent routine soak at 575° K. It was reported to have the physical properties shown in the table:
 

Table 1

	Yield Strength	Tensile Strength	Elongation	Red.	Charpy Impact
Breech 6 o'clock	79,500 psi	104,000 psi	21.4	58.9	39.1 ft. lbs.
Breech 12 o'clock	80,500 psi	104,000 psi	19.3	50.2	37.4 ft. lbs.
Muzzle 6 o'clock	77,000 psi	99,500 psi	23.6	65.7	44.7 ft. lbs.
Muzzle 12 o'clock	76,500 psi	99,500 psi	23.6	62.0	47.5 ft. lbs.
The tube had the following chemical analysis and had received the tabulated heat treatment prior to autofrettage:  C Mn Si S P Cr Mo Cu V .255 .74 .195 .017 .011 .91 .49 .16 .095   Heated to: Hours Held: How Cooled: 1475° K 16 Air 1145° K 9 Furnace 1175° K 9 Water, 3½ mins. & 9 mins. 980° K 7 Furnace

After removing sufficient metal from each end to avoid extraneous effects, the weapon was cut traversely into 124 slices, ground on both sides to ½" thick and numbered consecutively from muzzle to breech 1 to 124 (some of the discs were reserved for another experiment). Before grinding, the slight taper of the outside diameter was trimmed off. The amount of this trimming was negligible. One series of discs was tested with no machining, while other series were machined with 2½, 5, 10, 15, 20, 25, or 30% of the outside diameter turned off. Other series were machined with similar percentages of bore increase. Still other services were tested without various combinations of boring and turning, After cutting radially and measuring the changes in diameter, the data in Table 1 were tabulated and shown in Figure 3.

Conclusion

1. Nearly all values of the stress factor, Dd/2d (excluding points for the muzzle end of the canon, to be discussed later), lie within a zone of variation of roughly ±10% from the theoretical based on the Tresca theory of yielding.
2. All the points for no machining lie below the theoretical level, the average difference being about 7%.
3. Four fifths of the points obtained after boring lie above the theoretical by about 6%
4. All but one of the points after turning are below the theoretical and their average exceeds the average of the points for no machining by about one percent, which is of doubtful significance.

Discussion

    Equation (5)

When it is assumed that the yield strength in tension and compression are equal, Turner (19) shows that for wall ratios in excess of 2.2 there will be reverse yielding. Actually, due to the Bauschinger effect, reverse yielding occurs in wall ratios less than 2.2. Bauschinger points out that overstraining  in one direction increases the yield strength in that direction while diminishing that in the other direction. Thus in the process of autofrettage, involving as it does overstrain in tension, the compressive yield strength is diminished, the maximum effect being at the bore. That there has been reversed yielding throughout the length of the tube is apparent from the boring operation which produces an improvement in the Dd/2d ratios whereas turning has the opposite effect. The boring removes metal in which reverse yielding has occurred while turning removes metal that has been overstrained in tension only and has thereby acquired a higher yield strength.

As a visual aid, the points for the condition of no machining have been plotted, Dd/2d against wall ratio, in Figure 4, line B. To better show a trend the mid-points have likewise been plotted, and they are connected with a solid line. The lines of least regression for the two sets of points are shown, ignoring the discs numbered 30 or lower for the reasons set forth above. As noted, all points fall below the theoretical constant value. The evident explanation for this, as suggested above, derives from the reverse yielding and Bauschinger effect in the tangential stresses as the ultimate autofrettage pressure is released. Moreover, for the higher wall ratios the range of elastic stress is greater and consequently there is a greater Bauschinger effect and a greater opportunity for reverse yielding. This adversely affects the residual stress distribution and the differential diameter reflects this.

It is interesting to note the apparent correlation of the amount of boring and the amount of turning. Figure 5 shows the effect of percentage boring or turning on the Dd/2d ratio. For the former it appears that the relative strength of the disc is increased by the removal of the material subject to reverse yielding. The point for 30 percent boring suggests that the process has gone too far. On the other hand, as metal on the outside (which has not been subjected to reverse yielding but has been strengthened by overstrain in tension) is turned off, the remainder of the tube, having a proportionally larger portion weakened by reverse yielding, has a diminishing Dd/2d ratio. The fact that in both cases linearity is apparent is interesting and suggestive, but quantitative discussion of the reverse yielding is not justified with this data.

As noted, equations (1) and (2) were developed on the basis of the Tresca theory of yielding, occurring first at the bore, when the maximum shear stress is equal to the half of the tensile yield stress of the material. Generally more accurate is the von Mises criterion based on the constant energy of distortion, but this is mathematically far more unwieldy and the differences between the two are small. According to Tresca the pressure for initial yield is:

    Equation (6)

    Equation (7)

This investigation was very beneficial in improving the efficiency of the autofrettage process, by showing that any extra machining resulting from a desired adjustment of wall ratio, particularly if the muzzle end were thickened to avoid the difficulties caused by excessive gripping there, would not materially impair the strength of the gun. It is to be noted that the technique of this experiment is very attractive on the score of economy, both of time and expense. Many gun tubes would have been required to attain the credence resulting from the present work. It is hoped that the method may be applied with respect to high strength materials and to only partially autofrettaged tubes.

Appendix

In Figure 6, which represents a radially cut disc,

    Equation (8)

    Equation (9)

    Equation (10)

    Equation (11)

The stress distribution in the beam is given by the following equation, all the residual stress having been relieved by the cut:

    Equation (12)

    Equation (13)

    Equation (14)

    Equation (15)

    Equation (16)

    Equation (17)

    Equation (18)

    Equation (19)

    Equation (20)

The moment M may also be evaluated by an alternate approach. Referring to Figure 7, which shows the distribution of residual tangential stresses after autofrettage, expressed algebraically by Equation (1). By taking the moment about 0 of the forces released when the disc is cut and noting that radial stresses produces no moment, the moment necessary to return the disc to its original size is:

    Equation (21)

    Equation (22)

    Equation (23)

    Equation (24)

    Equation (25)

Conversion Factors

References