## 2 Materials and Methods
### Micromagnetic Multiparameter, Microstructure and Stress Analysis (3 MA) Method  
Non-destructive methods for material characterization are based on physical principles and effects. Acoustic methods have been developed for the non-destructive detection of material damage caused by fatigue. Ultrasonic techniques are widely used for internal crack detection. Recent advances focus on nonlinear acoustic techniques, which are sensitive to microstructural changes before visible cracks form [17; 18]. Ultrasonic laminography is one way of determining the state of damage over different component depths [19]. Fatigue-induced crack growth can be detected using ultrasonic methods. Phase transformations and the Villari effect can be measured 'in situ' using non-destructive magnetic testing methods and are used for assessing the fatigue condition and for a reliable service life calculation [20]. Furthermore, the fatigue properties of austenitic steels could be characterized at elevated service-relevant temperatures under isothermal and thermo-mechanical stress using electromagnetic acoustic transducers [21; 22; 23]. Ultrasonic methods can be used to detect fatigue-induced crack growth, but microstructures, such as carbides M\({}_{23}\)C\({}_{6}\), Laves phases (Fe\({}_{2}\)Mo) and Z-phases, as they occur in the case of the materials analyzed in the current study, cannot be detected using such methods. The behavior of steels during fatigue testing can also be monitored by infrared thermography, an advanced, high-speed, high-sensitivity and non-destructive evaluation technique [24]. Micromagnetic techniques are used to study the properties of ferromagnetic steels. Based on the correlation between the magnetic and mechanical properties of the considered materials, both classes of properties depend on the microstructure. Hence, micromagnetic measurements allow for the estimation or prediction of mechanical properties [8; 9; 10; 25; 26]. Depending on the microstructure state, particularly on the size and distribution of the microstructural imperfections, different effects have an influence on the magnetic Bloch-wall movement: the foreign-body effect (in case of small precipitates), stress effect (in case of precipitates and dislocations) or stray field effect (in case of dislocations and big precipitates) [27]. The micromagnetic techniques detect a combination of these effects. For measuring magnetic hysteresis loops, the specimen must be rod-shaped and magnetized homogeneously at a low frequency, and the magnetic flux in the test specimen must be measured with a coil [8]. Due to the fact that the direct measurement of the hysteresis curve is not suitable for practical application with components, alternative magnetic techniques are applied for characterizing ferromagnetic materials. Frequently, micromagnetic effects in non-destructive testing are minor hysteresis loops, magnetic Barkhausen noise, harmonic analysis of the magnetic tangential field strength, eddy currents and incremental permeability [8; 9; 10; 25; 26; 27; 28; 29; 30; 31; 32]. Micromagnetic measuring devices comprise a magnetization unit, a probe and a unit for measurement control and data processing. The design and measurement parameters determine the depth and area of the materials that are analyzed. Micromagnetic methods can thus be used to measure a controllable fraction of the specimen volume. Fraunhofer IZFP developed the Micromagnetic Multiparameter, Microstructure and Stress Analysis (3 MA) technique, which indirectly and non-destructively predicts mechanical material properties using an on-site access micromagnetic sensor to measure the features derived from several magnetic methods [9]. The 3 MA method is a powerful technique that allows for the integral comprehensive recording of micromagnetic characteristics across the entire surface of a specimen. The 3 MA method has been applied in the characterization of various steel grades and types of damage over the last decades [28; 29; 30; 31; 32; 33].