# Application of Laser-Ultrasonics for Evaluating Textures and Anisotropy
## Materials and Methods  
### Cold-Rolled 316  
To investigate different textures of rolled austenitic steel, 4 samples were produced from a piece of 316 stainless steel plate. The samples were then rolled with either 50% or 70% reduction at the in-house lab rolling mill at Swerm in Lulea. Two of the samples were annealed, prior to the rolling, to attain two samples with larger starting grain size. These parameters are listed in Table 1 together with the measured densities. The ultrasonic waves were generated in the ablation mode using a 20 Hz Q-switched Nd:YAG laser with 6 ns long pulses and up to 200 mJ of energy per pulse at a wavelength of 532 nm. The response was detected with an amplified single longitudinal mode laser at 1064 nm wavelength with a peak power of ~500 W and a pulse length of 100 \(\upmu\)s. The reflected detection laser light from the samples was collected and interfered in a GaAs crystal to convert the Doppler shifted, i.e., frequency modulated, light into amplitude modulated light and measured by photodiode. The crystal was pumped by ~1/6 of the light from the same amplified single longitudinal laser. The cold-rolled samples were prepared to achieve well-developed textures which were measured using EBSD patterns from many thousands of grains. Orientation distribution functions were derived according to Bunge's convention and method [21]. Textures were generally similar for all conditions, although sharper after the heavier rolling reductions. Examples of pole figures are shown in Figure 1 below. Figure 1a shows the 50% deformed sample and Figure 1b shows the 70% deformed sample. The principal components are major {110}<112> with minor {111}<112> and {110}<001> orientations, which are well known for rolled 316 steel from literature reports. These are all more fully developed after the 70% reduction, although the differences are not great. The resulting anisotropies should, therefore, be of a similar type, as was indeed found in subsequent LUS measurements. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Heat Treatment** & **Rolling Reduction** & **Start Grain Size** & **Thickness** & **Density** \\ \hline No treatment & 70\% & 20 \(\upmu\)m & 12 mm & 7938 kg/m\({}^{3}\) \\
1 h @ 1200 \({}^{\circ}\)C & 70\% & 60 \(\upmu\)m & 12 mm & 7933 kg/m\({}^{3}\) \\ No treatment & 50\% & 20 \(\upmu\)m & 12 mm & 7937 kg/m\({}^{3}\) \\
1 h @ 1200 \({}^{\circ}\)C & 50\% & 60 \(\upmu\)m & 12 mm & 7932 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of sample properties. The angular P-wave velocities were calculated using these orientation distribution functions with crystal stiffness coefficients obtained from the literature for 316 grade steel (c\({}_{11}\) = 205, c\({}_{12}\) = 138 and c\({}_{44}\) = 126 GPa) [26], together with its density, c.f., Table 1. The Voigt and Reuss limits applying to the stiffness tensors were first calculated and average values were then obtained using the approximations suggested by [PERSON] [19] as arithmetic averages or, alternatively, geometric averages of the limit values. Two different approaches were adopted for determining the wave velocities using LUS. In the first, cylinders were accurately turned co-axially with the rolling direction (RD) or the transverse direction (TD). An illustration of the cut-out, and a photograph of a sample after turning, are shown in Figure 2 below. The lasers were directed to opposite sides of the cylinder, and the longitudinal wave times of flight (ToFs) were measured while the specimen was rotated. The black line on the cylindrical sample in the photograph shows where the LUS measurements were performed. A typical B-scan is shown below for the polar scans with rotations around the TD and RD axes. The first horizontal line around 2.4 us is the first echo that has travelled through the cylindrical sample. This first echo exhibits double or quadruple symmetry as the polar angle is swept 360\({}^{\circ}\), Figure 3a,b, respectively.