br Correlation Hardness and ultrasonic wave

Correlation Hardness and ultrasonic wave velocity measurements are performed before and after each annealing stage. Their variation in initial condition are investigated in terms of annealing temperature, and then the variations of hardness and ultrasonic wave velocity are correlated for each steel type. The initial hardnesses of steel samples are given in Table 2. The second-order polynomial function of these correlations are given in Eq. (3)where is variation of hardness; v0 is initial ultrasonic wave velocity; v is measured ultrasonic wave velocity; and a1, a2 and a3 are constants. The left column in Fig. 3 illustrates the variations of hardness and ultrasonic wave velocity related to annealing temperature. Results show that there is an inverse relation between the two data. The relation between hardness and ultrasonic wave velocity variation for each sample are proposed in the right column in Fig. 3. Careful observations showed that the relation of hardness and ultrasonic wave velocity has a regular order for each carbon content, but these cftr inhibitor do not fit the exponential, logarithmic or linear trends. On the other hand, the high order polynomial trends provide good regression analysis results, but provides unrealistic fluctuation. Investigations showed that the best fitting to hardness and ultrasonic wave velocity relation data is obtained with the second-order trends, and accordingly the trend of each data is determined in terms of the second-order polynomial function. Without heat treatment, no change occurs in the hardness of the material. At that point the variations of ultrasonic wave velocity and hardness are zero so that the upper and lower values of the third coefficient (a3) of the second-order polynomial are limited to zero. Investigations on the relation between ultrasonic wave velocity and hardness show that a convex function is obtained when the carbon content is zero. Increasing the carbon content replaces the function from convex to concave, because the ultrasonic wave velocity varies with a lower rate after the increase in carbon content. The hardness decreases with the increase in ultrasonic wave velocity in all cases. The second-order polynomial functions are given in Eqs. (4)–(6): Eq. (4) is used for carbon-free IF steel. Correlations for steels with 0.092 and 0.478 weight % of carbon contents are defined using Eqs. (5) and (6), respectively. Rockwell hardness measurements are compared with predictions of the correlations. The investigations are performed using the isotropic samples. It is accepted that the hardness within these samples is homogeneous. Accordingly, the results are plotted with a first-order trend line, as shown in Fig. 4. Trend line perfectly fits the data points with R2 value of 0.925. It can be stated that the correlations developed based on ultrasonic wave velocity variations have success on the determination of average hardness.
Hardness of welded steel Ultrasonic wave velocity measurements cannot be performed on weld beam because of the rough surface so that the ultrasonic and Rockwell hardness measurements are accomplished as close as possible to weld beam, which is at 10 mm away from weld center, as illustrated in Fig. 2. The measured results of all three samples are merged and analyzed in a single distribution. The welding process causes the formation of residual stresses within and around the weld beam. The relation between hardness and residual stress was investigated [24,25]. These studies showed that hardness is affected by residual stress in materials. The ultrasonic waves are also used to observe the bulk residual stresses in welded steel [26,27]. Similarly, the thickness average hardness is expected to be investigated for welded materials. Results show that the hardness of IF steel increases as a result of the welding process around weld beam, as illustrated in Fig. 5. Hardness increases around the weld beam. The increase in surface hardness starts in the measurement points at 40 mm away from the weld center, but taxis distance is around 20 mm for the thickness average hardness.