Hill Stress Calculations for Autofrettaged Tubes Compared With Neutron Diffraction Residual Stresses and Measured Yield Pressure and Fatigue Life

Abstract

Calculations of Bauschinger-modified residual stress in autofrettaged tubes using a simple elastic-plastic model based on the Hill method are compared with neutron diffraction measurements of hoop residual stresses in sections from a swage-autofrettage cannon tube. These residual stresses combined with pressurization stresses are used to describe tube yield pressure and fatigue lives, for comparison with laboratory measurements from cannon tubes from recent publications and new results. Gun steels in the yield strength range from 1000 to 1400 MPa are considered. Results from neutron diffraction measurements show a significantly shallower depth of overstrain in a swage autofrettaged tube compared with that predicted from earlier work with hydraulic pressure autofrettaged tubes, for the same amount of total bore hoop strain. This difference between depth of overstrain for swage and hydraulic autofrettage is incorporated into calculations of yield pressure corresponding to a small amount of permanent strain on the tube outer diameter. Comparison is made with measurements of yield pressure at the same amount of permanent strain. Comparison between calculated and measured yield pressure is good, suggesting a simple design method. Calculations of fatigue life using the classic Paris method compare well with measurements from cannon tests, once Bauschinger-modifications are made in near-bore hoop residual stresses and the difference in overstrain between swage and hydraulic autofrettage is incorporated in the model calculations.

Use of the Contour Method to Determine Autofrettage Residual Stresses: A Proposed Experimental Procedure

“…One convincing and consistent series of results for gun tubes consists of a set of X-ray and neutron diffraction (ND) experiments commissioned by Benet Laboratories' Fatigue and Fracture Analysis facility. These are reported in reference [1], Underwood et al…”

Kendall Analysis of Cannon Pressure Vessels

“…Pressure vessel results are shown in Table 1 for breech sections of four ASTM A723 steel cannon tubes that were pressurized in small increments, with strain gages used to monitor permanent OD hoop strain after each increment [5]. The measured yield pressure, P m , is that corresponding to a small but measurable permanent OD hoop strain of 0.01%.…”

“…This was easily done here with spread sheet calculations, followed by a slight shift in the limited curve to insure equal areas above and below the zero stress axis, as required for equilibrium. The resulting plots of Equations (3) and (4) are shown as Figure 2, compared with neutron diffraction measurements of hoop residual stress from two sections of an autofrettaged tube [5]. See also Table 3 Table 3.…”

“…The classic Paris approach to fatigue life determination has been well described in the technical literature; a summary [6] for the purpose here is shown in Equations (5) and (6). Equation 5is the usual Paris law for crack growth per cycle, da/dN, in terms of stress intensity factor range, ∆K and Paris constants C and m. Equation 6is the final integrated form of Equation (5) where the cycles to failure, N, depends on: the preexisting initial crack length, a i ; the final crack length [for a vessel], (b-a); the Paris constants C and m; the crack shape factor, f varying between 1.12 for a straight-fronted edge crack and 0.66 for a semicircular edge crack [7]; the applied and residual stresses, S applied and S residual combined with any stress concentration, k t that applies; and vessel internal pressure, p.…”

Design of two-pass swage autofrettage processes of thick-walled cylinders by computer modeling

“…Experimental evaluation methods include the destructive Sachs boring method, the positionsensitive X-ray diffraction method, the strain gage method (also applied to measure the mandrel's axial load), the neutron diffraction method, the compliance method, and the deep-hole method, among others. 19,[27][28][29][30][31][32] All these methods have certain disadvantages. Real-time measurements can only be taken on the surface of the cylinders, and an accurate threedimensional measurement is impossible.…”