Mapping Residual Stress Fields by Ultrasonic Tomography

It is well known that the velocity of sound in a solid is affected by stress. This phenomenon is a third order effect, and has been used primarily as a research tool to determine the Lame and Murnaghan elastic constants for various materials. A few preliminary attempts to use it for stress analysis have also been made. In this paper we describe the first attempt to combine this effect with the newly revived mathematical technique known as Computerized Axial Tomography (CAT) to provide quantitative maps of velocity within thick metal sections. From these maps , it is possible to infer the state of residual stress within the material. The technique requires that time-of-flight profiles through a section of the solid be made in a number of angular directions. This is equivalent to measuring the velocity through the solid from many different directions in a single plane. The computer takes the set of data so gathered and inverts it to produce a cross-sectional plot of velocity versus position. We have succeeded in mapping velocity anomalies as low as 0.21% and estimate that 0.5% is technically feasible. This kind of sensitivity should allow us to map stress anomalies as low as 1000 psi/inch in steel. We will also describe an experiment with a mild steel section in which we inserted an oversized pin by shrink fitting. The reconstruction clearly shows the high compressive stress within the pin, and the tensile .stress in the metal surrounding the pin