# Optically Pumped Magnetometer Measuring Fatigue-Induced Damage in Steel
## 4 Test Results and Discussion  
Figure 2 shows piezomagnetic signals together with optical DIC images from a strain-controlled low-cycle fatigue (LCF) experiment. A specimen made of ferritic steel was chosen since it produces a large magnetic signal. It has a cross-section of 0.22 mm\({}^{2}\) and the straight part of the target gauge is 400 \(\upmu\)m long (detailed in Figure 1). The strain amplitude of \(\pm\)1.5% results in a lifetime of 108 cycles. The magnetic time series in Figure 2 looks less smooth and less stable than the force time series. First, controlling the magnetic environment at an nT level becomes a challenge even with a multilayer mu-metal shield. Then, the magnetic time series contains richer information, which becomes clearer when represented as hysteresis curves in Figure 3. However, the general trend, where the signal becomes smaller as the specimen reaches failure, is clearly visible on both traces. The magnetic time series shows a significant shift around the zero crossing. This could be due to the fact that the specimen was not demagnetized before this measurement. Figure 3 shows the hysteresis curves corresponding to the data displayed in Figure 2. These curves represent the main observables of the setup, which can be measured with our apparatus. The complete set of curves over cycles 1 to 106 is drawn in light grey and some of the curves are highlighted with colors. Cycle 6 corresponds to Figure 2a, cycle 51 to macroscopic crack initiation (Figure 2b), and cycle 96 to rapid crack growth (Figure 2c). At  
Figure 3: The two observables, mechanical (\(F-\varepsilon\)) and piezomagnetic (\(B-\varepsilon\)) hysteresis curves, for the SUT. Six different cycles are highlighted to show the evolution of the hysteresis with an increasing cycle count. The most pronounced change in the observables is the emergence of “Villari reversals” on the (\(B-\varepsilon\)) hysteresis (marked by arrows). Another prominent difference is the evolution of the surface areas. An inflection of the hysteresis curve is visible between cycles 96 and 103 just before failure of the specimen. cycle 84, the force amplitude dropped by 5%, which is a common indicator for end-of-life. Cycle 103 is the last cycle before complete rupture. Until macroscopic crack initiation at cycle 51, the damage is assumed to be somewhat homogenous throughout the gauge section of the SUT. However, significant stress and defect concentrations occur near the crack tips during crack growth at cycle 96. The shape and the area of the hysteresis curves evolve as the SUT undergoes fatigue. The mechanical (\(F\)\(-\)\(\epsilon\)) hysteresis is used more widely than the piezomagnetic (\(B-\epsilon\)) hysteresis. The mechanical hysteresis curves overlap until cycle 51 and remain fairly constant in size and shape until cycle 84, where rapid crack growth starts as shown in Figure 2c. This drop is presumably due to the fatigue-induced reduction of the specimens' cross-section. The area delimited by the mechanical hysteresis curve is related to the energy for plastic deformation of the specimen. The rest of the energy is dissipated in the form of heat [29]. In contrast to the mechanical hysteresis, where almost all cycles have overlapping curves up to macroscopic crack initiation, the piezomagnetic curves clearly change their shape and size upon cycling. They reach the maximum area at cycle 12 and shrink continuously afterwards. In addition, the piezomagnetic curves exhibit distinct \"dent\" features near the zero-transitions of the force \(F\) (marked by the arrows in Figure 3). These \"dent\" features may be referred to as \"Villari reversals\", where the subsequent slight decrease in the magnetic field is potentially associated with a change in the sign of the magnetostrictive constant. Under tensile stresses, domains magnetized parallel to the tensile direction grow, whereas compressive stress favors the growth of domains with perpendicular magnetization directions [4].