# Optically Pumped Magnetometer Measuring Fatigue-Induced Damage in Steel
## 2 Experimental Procedures
The load is measured by a load cell (TE connectivity, XFTC-300-500, Schaffhausen, Switzerland), which has a dynamic range of 500 N. The load can be applied either under force-, displacement- or strain-controlled mode. The measurement of strain on such a small specimen is a special challenge. Strain gauges are hardly applicable as they are large and produce magnetic fields through the resistance measurement of electric currents. Mechanical extensometers are too large as well and require significant pressure on the specimen surface to avoid slippage. Therefore, we used an optical real-time DIC system based on a Basler acA2040-180 km camera with 2040 \(\times\) 2040 pixel with a pixel pitch of 5.5 \(\upmu\)m, allowing up to 1200 integral strain measurements per second on 2 subsets per image due to GPU evaluation [23]. To avoid magnetic perturbations from the camera electronics and LED illumination on the OPM sensor, both, the camera and lens, were mounted outside of the mu-metal shield as shown in Figure 1. To use the full resolution of 2000 pixels per line, a telecentric lens with coaxial illumination, a magnification of 1:3, and a working distance of at least 150 mm would be ideal. However, such lenses are scarce, and we used one with a magnification of 1:2 (VS-THV2-150 CO/S), resulting in an object side resolution of 2.75 \(\upmu\)m/pixel. The 2 subsets with a size of 51 \(\times\) 51 pixel, i.e., the inner green squares in Figure 2a, measure integral strain. This is analogous to a mechanical extensometer placed at the beginning of the dovetails of the SUT at a distance of 469 pixels (1.3 mm). This gives the base length for integral strain measurement. The outer green squares in Figure 2a mark the search areas where path-independent correlation is possible. This allows for more robust strain-control. In combination with blue LED illumination (4W electrical power at 465 nm), a strain sampling rate of 600 Hz was achieved, which is sufficient for strain-controlled low-cycle fatigue tests (LCF) according to ASTM E606 [24]. In addition, the DIC system can be used to quantify effects, such as stress or strain concentrations, e.g., at crack tips, in full-field mode [25]. Furthermore, surface imaging facilitates the detection of surface protrusions and cracks with advanced computer vision techniques [26]. The ferritic steel specimen was extracted from cold-rolled sheets with the specimen axis pointing in the transversal direction. A strong crystallographic anisotropy is present because of this processing. The information on the alloy composition cannot be disclosed because of a confidentiality agreement. Static tensile tests on macroscopic specimen revealed a yield strength \(\text{Rp}_{-0.2}\) of 170 MPa. The mesoscale test specimens are fabricated with conventional wire erosion and micro wire erosion. Thus, specimen dimensions in the order of a few hundred micrometers can be obtained. At this scale, complementary characterizations by different techniques can be carried out for the whole volume of a specimen. Moreover, individual damage locations, such as early cracks, affect the load signal and the magnetic response in a pronounced manner, rendering the measurement more sensitive. In contrast to specimens with conventional macroscopic sizes, here the whole specimen volume can be monitored with the OPM without compromising the sensitivity. For full coverage of larger specimens, the specimen-sensor distance must be increased, which decreases the sensitivity of the magnetic measurement. The magnetic field variations in Figure 2 are on the level of only a few nT. This is significantly smaller than the magnetic fields produced by larger specimens [7; 12]. Our aim with this approach is to fully exploit the sensitivity of OPMs to measure more details of the stray field of the specimen. The workflow followed to operate this setup and to perform a full measurement on a specimen comprises the following steps:  
1. [label=(0)]
2. Placing the specimen in the dovetail clamps of the titanium mount inside of the mu-metal shield;
3.