## 1 Introduction  
Low-alloyed steels are frequently employed in the construction of bridges and civil structures, in the automotive industry, and in other applications. Their mechanical properties strongly depend on the microstructure and the corresponding thermomechanical treatment [1; 2; 3; 4]. Low-alloyed steels with higher yield and ultimate strength are mostly due to grain refinement and/or phase transformation, mostly developed after hot rolling. The yield strength of low-alloyed steels up to 700 MPa can be obtained via grain refinement, and these steels are mostly composed of ferritic grains of reduced size [1; 2]. The further growth of yield strength can be produced via accelerated cooling rates and the corresponding bainite or martensite microstructure (or their mixture). Their alloying is quite limited, and a certain fraction of Ti or/and Nb is added to strengthen the matrix (this contributes to grain refinement as well as matrix precipitation hardening) [1; 2]. The high-strengthlow-alloyed steels are considered cheap materials. Obtaining good mechanical properties despite increasing strength is at the expense of decreased toughness [2; 3]. The functionality of components made of these steels can be negatively affected by corrosion, which can remarkably damage surface properties and/or reduce the bearing capacity with respect to decreasing the effective cross-section. Furthermore, increasing the true stress in components as a result of corrosion can redistribute stress to neighboring regions [5; 6]. Yielding components develop unacceptable deformations of construction, whereas plastic instability can initiate premature failures and collapse [5; 6; 7; 8]. To reveal the critical state through visual observation can be a risky approach since many defects are hidden and cannot be found by the naked eye. For these reasons, many non-destructive techniques have been developed in order to monitor the extent of corrosion and its influence on construction stability. These techniques are based on a diversity of physical phenomena such as acoustic emission [9] (cluster analysis applied for post-processing), ultrasonic tomography [10], gamma rays [11], or electromagnetic signals [12]. These techniques have found industrial relevance in some particular cases and can be employed for reliable inspections of bodies subjected to environmental damage (especially corrosion). In addition, magnetic methods, especially those based on magnetic inductive testing [13], can be applied for the aforementioned purpose. Moreover, Barkhausen noise emission (MBN--magnetic Barkhausen noise) was reported as a potential technique for the assessment of corrosion extent in wires [14] or conventional flat bodies [15; 16]. The origin of MBN can be found in electromagnetic pulses produced by magnetic domain walls (DWs) during their irreversible and discontinuous motion under an altering magnetic field [17; 18; 19]. MBN is strongly affected by three aspects: microstructure, surface topography, and stress state. All lattice imperfections (dislocations, grain boundaries, precipitates, hard and non-ferromagnetic phases, etc.) pin DWs in their position and/or interfere with DWs in motion [20; 21; 22; 23]. This aspect contributes to decreasing MBN. Increasing surface irregularities make the propagation of MBN pulses toward a sensing coil more difficult, which also attenuates MBN. With respect to the stress state, it should be distinguished between external stresses and the residual state. It is well known that tensile stresses tend to align DWs in the direction of this stress, whereas compressive stresses align DWs perpendicularly against the compressive stress (valid for Fe alloys). Therefore, tensile stress usually increases MBN, whereas compressive stress lowers MBN [24; 25; 26]. The influence of residual stress is less pronounced, especially in Fe alloys with a complicated microstructure [19; 27]. On the other hand, the relationship between external stress and MBN is much closer [24; 28].