# Application of Laser-Ultrasonics for Evaluating Textures and Anisotropy
## 1 Introduction  
This manuscript describes two new procedures for determining texture-related anisotropy from ultrasonic measurements using lasers. Textures in materials are usually measured by diffraction methods using X-rays, neutrons and more recently with electron back-scattering (EBSD). Less complete but still useful information about textures can be obtained from ultrasonics (US). US methods have the advantage of rapidity and do not necessitate special sample preparation to offer the potential for making measurements directly during materials processing. Electromagnetic acoustic transducers (EMATs) have been applied in many cases, although their applications are restricted to near room temperature conditions and by the need for small stand-off distances. Most other acoustic methods require physical contact. These limitations can be overcome when lasers are used instead for both generating and detecting US signals, which greatly enhances the freedom of operation [1]. For example, stand-off distance can be increased to a metre or even more and difficult environmental conditions such as atmospheres and high temperatures are not restricting. Even rapidly moving surfaces are not a problem for such measurements. This laser-ultrasonics (LUS) approach is, in fact, the only means by which textures can be assessed on-line in steel and metal production, including during hot-rolling operations. Knowledge of texture is often valuable in itself since it relates to plastic anisotropy and to the formability of rolled products so is a measure of sheet quality. In addition, however, textures vary depending on whether the microstructure is in a deformed or recrystallised state during hot working, which is important, for example in cold-rolled steels. It can also be added that other microstructural information, such as grain size, may be determined simultaneously; hence, LUS is a very powerful approach for the non-destructive characterisation of materials. The principal aim of our work has been to introduce LUS into industrial applications. The attenuation of sound waves depends on grain size and is now being used to measuregrain sizes continuously in connection with the hot-rolling of steels. Here, we demonstrate how additional data can be gathered simultaneously to obtain information about their textures, thus giving a very comprehensive characterisation of the austenite microstructure from on-line measurements. However, the LUS method has also been further developed to provide very precise and accurate measurements of texture in the laboratory environment. We demonstrate this with examinations of martensite in as-quenched and tempered conditions. From these measurements, it has been possible to draw conclusions about the elastic anisotropy of the constituent martensite crystals. Numerous investigations have been reported on how texture information can be obtained from ultrasonic measurements and in many cases, these have been integrated with predictions based on conventional texture determinations. Examples of these applications are described in [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. Calculation of relationships between elasticity and texture in cubic systems requires knowledge of the material's crystal elastic coefficients (\(c_{11}\), \(c_{12}\), \(c_{44}\)) which are, in most cases, available in the literature. Several models have been proposed to take into account the interactions between grains in a polycrystal [8] for this situation. The models of [PERSON] [17] and [PERSON] [18] were shown to give limiting upper and lower bounds for these interactions by [PERSON] [19] who also proposed that arithmetic or geometric means of the limits should be a good approximation to the actual behaviour. [PERSON]'s arithmetic mean construction has been widely used by later workers and generally found, e.g., [8], to work well, e.g., [20].