Theoretical assessment of the errors involved in ultrasonic location and sizing of molten weld pools

Ultrasonic transit times may be used to locate the interface between molten weld metal and parent plate as a weld is formed. These transit times will lead to errors in interpretation of the location of the weld interface if account is not taken of the variation of ultrasonic velocity with temperature. We assess the magnitude of these errors using a theoretical model based on the Green's function to obtain the temperature distribution at any time and then convert the temperatures into elastic constants through empirical fits to high temperature data. A ray tracing method and a semi-analytical approach are used to estimate the effects of the changes in elastic constants on the ray paths and transit times. From these theoretical predictions we conclude that the location errors incurred by assuming ultrasonic velocities appropriate to cold metal are less than 0.5 mm for a 3.5 mm radius weld in austenitic steel or in iron. Experimental values tend to be larger than this, possibly suggesting that the solid-liquid interface is not as perfect as in the theoretical model. Under all of the conditions investigated, predicted errors are smaller with compression waves than with shear waves.