# Optically Pumped Magnetometer Measuring Fatigue-Induced Damage in Steel
## 2 Experimental Procedures  
Several different types of OPMs are commercially available and they can be sorted into two main classes: zero-field OPMs and total-field OPMs. Zero-field OPMs achieve sensitivities below 50 fT/\(\sqrt{\mathrm{Hz}}\) but require a very low environmental magnetic field \(B\) (<50 nT) due to their limited measurement range. Total-field OPMs are less sensitive (<1 pT/\(\sqrt{\mathrm{Hz}}\)) but can operate in the Earths' magnetic field. In this work, we use a commercial OPM to measure the variation of the magnetic field \(B(t)\) of a ferromagnetic specimen, which is placed under a cyclic mechanical load controlled by a strain \(\varepsilon(t)\). The setup presented in Figure 1 uses a zero-field OPM, namely QZFM Gen2 from QuSpin (Louisville, US-CO). However, to exploit the full sensitivity of the OPM, ambient noise from various sources, such as piezoelectric sensors, actuators, or moving components close to the OPM, is suppressed to a level similar or lower than the sensitivity of the OPM. The main idea behind the setup is to mount the OPM and the mesoscopic specimen under test (SUT) in a magnetically shielded environment. The mechanical forces of the tensile testing setup are guided to the specimen by a construction employing only non-magnetic parts. For this setup, we redesigned a micro-mechanical tensile testing device in such a way that the SUT and the OPM are mounted in proximity to each other inside a magnetic shield (Twinleaf, MS-1L, Plainsboro, US-NJ) [22]. The magnetic shield comprises four concentric cylindrical layers of mu-metal to isolate the OPM and the SUT from external electromagnetic fields. Mu-metal is a nickel-iron alloy, which features a very high permeability (\(\mu_{r}\sim~{}10^{5}\)), which allows it to shield an environment from magnetic fields. An internal system of coils allows active compensation of residual magnetic fields to provide appropriate field strengths and homogeneity in the center of the mu-metal shield. A non-magnetic breadboard and sensor holder serve as a mount for the OPM. For uniaxial tensile  
Figure 1: Experimental (micro-magneto-mechanical) setup used in this work. On the left, a picture of the setup with the main components is shown. The specimen under test (SUT) is placed inside of a mu-metal shield and kept in position by means of ceramic rods and titanium mounts. The OPM, which measures the field emanating from the specimen, is placed right below the specimen. A digital image correlation (DIC) sensor is positioned outside of the shield and serves as a non-contact optical detector of the deformations of the SUT. On the right, a schematic representation of the same setup is drawn. It shows more details on the image formation of the DIC. A system of coils inside of the mu-metal shield allows adaption of the magnetic environment to the specific operating conditions of the OPM. The detailed specimen view shows the dimensions of the SUT gauge. To the left of it, an electron backscatter diffraction image of a cross-section of this ferritic steel conveys an impression of the texture, which features grain sizes of 10-15 \(\upmu\)m.  
testing, a piezoelectric actuator with a low stray field applies a cyclic mechanical load to the right end of the SUT. On the left, the resulting force \(F(t)\) is measured to calculate the engineering stress \(\sigma(t)=F(t)/A\) using the initial cross-sectional area \(A\) of the specimen. The tensile testing machine accommodates two actuators, a linear motor (Physik Instrumente, M-238.5 PL, Karlsruhe, Germany) and a piezo actuator (Physik Instrumente, P-216.90, Karlsruhe, Germany), imposing a tensile or compressive load on the SUT. Depending on the range of loading, displacements, and the necessary dynamics, either one of the loading modes can be employed. In the present work, load was applied solely with the piezo actuator. The load is conveyed to the SUT through load-carrying bars and dovetail camps, which hold the SUT in place.