The first step in a widely used destructive procedure for measuring through-thickness residual stresses in pipes is a parting-out step in which a coupon is cut from the wall of the pipe. Strain gages provide information on the stress changes that take place at the two surfaces of the coupon when the coupon is removed. Back-computation methods are applied to the laboratory data to provide estimates of the residual stresses that were in the pipe before the coupon was parted-out. The laboratory data needed for the back-computation method are the residual stress distribution in the parted-out coupon, and the stress changes that occured at the surfaces of the coupon when it was parted-out. A simple back-computation method for the parting-out step assumes that the changes that occur in the through-thickness stress distribution of the coupon when it is parted out can be described by a straight line, the end points of the line being determined by the stress changes at the surfaces of the coupon. However, if the width of the coupon in the circumferential direction is small (which is often the case for coupons cut from pipes), this straight line back-computation method can lead to errors in the circumferential residual stress distribution estimate it provides. This paper presents an alternative back-computation procedure based on the Fourier series. Example problems presented in the paper show the Fourier series back-computation method to be accurate, even for narrow coupons, and to be quick and easy to apply.

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