A welding procedure does introduce different material properties in terms of anisotropy and grain size enlargement. This will cause backscattered ultrasonic grain noise superposed to the defect signal in a real inspection situation. A simple model is introduced which consists of modeling the grains by a random distribution of elastic spherical inclusions in a weld geometry. The radius of the inclusions are calculated from a one dimensional model relating welding conditions and grain size in weld heat-affected zone (HAZ). The backscattered field is then calculated as a superposition of direct scattering from each defect, no multiple scattering effects are considered in the noise signal. The grain size varies with the distance from the fusion line. It is well known that the rate of grain growth can be expressed by a one-dimensional equation relating the mean grain size to the temperature and the activation energy. Together with a simple solution of the heat conduction equation for an instantaneous plane heat source, the grain growth can be calculated over a thermal cycle. The HAZ is divided into n subparts with equal thickness and the HAZ boundary is calculated as a function of the input electrical energy. The grain growth model is implemented in such a way that the radius is calculated at each boundary of the subparts of the HAZ. The radius of the inclusions inside every subpart is randomly distributed between these boundary values. The positions of the inclusions, modeling the grains, are given by a uniform random distribution in the weld and HAZ and the number of inclusions inside the subparts is given by the condition of constant volume fraction. Numerical simulations will show some examples of backscattered grain noise superposed to a defect signal when a defect is placed inside the weld.
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