PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 90 NR 12/2014 161 Maciej SULIGA, Lech BOROWIK, Krzysztof CHWASTEK, Piotr PAWLIK Częstochowa University of Technology A non-destructive method to determine residual stress in drawn wires based on magnetic measurements Abstract. Estimation of residual stress in drawn wires is an important issue in contemporary metallurgy. The present paper considers the possibility to use a non-destructive method based on magnetic measurements for this purpose. The Jiles-Atherton-Sablik model is used for the description of hysteresis loop. Streszczenie. Oszacowanie poziomu naprężeń szczątkowych w drutach podczas procesu ich wytwarzania jest istotnym zagadnieniem we współczesnej metalurgii. W niniejszej pracy rozważono możliwość wykorzystania do tego celu metody nieniszczącej, opartej na pomiarach magnetycznych. Model Jilesa-Athertona-Sablika wykorzystano do opisu pętli histerezy magnetycznej. Nieniszczące magnetyczne badanie naprężeń w drutach Keywords: hysteresis loop, residual stress, Jiles-Atherton-Sablik model. Słowa kluczowe: pętla histerezy magnetycznej, naprężenia szczątkowe, model Jilesa-Athertona-Sablika. doi:10.12915/pe.2014.12.39 Introduction Diagnostics of devices plays an ever increasing role in contemporary industry, as it allows one to eliminate the possible sources of their faults and may lead to substantial economic savings [1-5]. The present paper focuses on a non-destructive method to determine the level of residual stress in drawn wires. Controlling the level of deformation and residual stress during steel-forming processes remains one of the most important problems for metallurgists [6,7]. At present much attention is paid to magnetic methods as useful non-destructive testing and evaluation techniques [8]. The examination of the variation in shape of hysteresis loop for the sample subject to stress may provide information on the stress level [9]. By analogy, hysteresis loop may be an indicator of residual stress level. The effective field and the Jiles-Atherton model In order to describe qualitatively how residual stress affects the shape of hysteresis loop, it is expedient to avail of the concept of ,,effective field’’. The effective field is the field, which indeed exists within the ferromagnetic sample. It is different from the externally applied magnetic field, as it includes at least one additional term related to the cooperative action between the magnetic moments in the material. The effective field may also include other terms related to some relevant physical phenomena, e.g. stress, viscosity, eddy currents etc. The concept of effective field is extensively used in a number of hysteresis models, but the generic macroscopic example is the formalism developed by Jiles and Atherton [10,11]. The Jiles-Atherton (JA) model is based on the assumption that the process responsible for formation of hysteresis loop is the irreversible translation of domain walls through the imperfections of crystalline lattice, inclusions etc. Jiles and Atherton have proposed a set of equations including an ordinary differential equation and some supplementary relationships to describe the branches of hysteresis loop. In the existing literature there exist a number of different formulations of the JA model equations. The model equations have evolved in time and some researchers have modified them to improve the model capabilities to describe more accurately e.g. minor hysteresis loops [12-16] or to take into account the effects of texture and anisotropy [16, 17] and temperature [18, 19] on the modelled curves. The problems with the apparently simple description and its numerical implementation have been noticed [20-22] and a number of sophisticated procedures for model identification have been devised [12, 16, 23-27]. In the present paper we have decided to focus on a simplified version of model equations, as presented in Ref. [10]. In that version there is no decomposition of total magnetization into the irreversible and reversible components and the rate-dependent effects are considered negligible. The JA model is applied to major loops only and the sole mechanism responsible for a change of loop shape under the applied stress is due to the modification of the relationship for the effective field in accordance with the Sablik’s model extension. Sablik et al. [28, 29] have suggested the possibility to extend the JA theory to take into account the effect of stress by the introduction of an additional term in the definition of the effective field (1)        dM d H     0 2 3 where  denotes the stress,  is the magnetostriction, whereas 0  is the free space permeability. The full set of model equations and the derivation of the formula for differential susceptibility are given in the Appendix. The study of interactions of stress with magnetostriction has been the subject of intensive research worldwide [30, 31]. The present paper focuses on the possibility to estimate the level of residual stress in real-life metallurgical products (drawn wires made of high carbon steel) on the basis of measurements of their hysteresis loops. Experiment Major hysteresis loops for wires drawn at selected drawing speeds and in the annealed state have been determined with the use of a vibrating sample magnetometer VSM 7301 from Lakeshore. The chemical composition in weight% of the steel C78DP used for production of the wires is given in Table 1. Before drawing the wires had been patented, itched and phospored. The drawing process of 5.5 mm wires down to the final diameter 1.7 mm was carried out in industrial conditions in 12 passes using a modern multi-step drawing machine Koch KGT 25/12. The value of speed in subsequent part of the text denotes the speed at the final drawing die. The sodium- based compound TRAXIT C4540 was used as the lubricant during the drawing process. Table 1. Chemical composition of C78DP steel Fe C Mn Si P S Cr Ni Cu Al N 98.241 0.790 0.610 0.200 0.010 0.013 0.060 0.020 0.050 0.003 0.003