Microsoft Word - numero_61_art_19_3516.docx L. Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 282 Identification of the anisotropic behavior of the laser welded Interstitial Free steels subjected to off-axis tensile tests Arfaoui Latifa University of Tunis El Manar, ENIT, LR-MAI-ENIT, Tunisia arfaoui_latifa@hotmail.fr, https://orcid.org/0000-0001-5019-7479 Samet Amel, Znaidi Amna University of Tunis El Manar, IPEIEM, LR-MAI-ENIT, Tunisia amel.samet@ipeiem.utm.tn, amna.znaidi@ipeiem.utm.tn ABSTRACT. The main purpose of this paper is to study the anisotropic behavior of laser welded interstitial free steel HC 260Y when it is subjected to monotonic tensile tests. The specimens were cut in different orientations according to the rolling direction, annealed and finally assembled by laser welding. The plastic behavior was modelled using an identification strategy based on a behavior law taking into account the anisotropy of this material, a hardening law describing the evolution of the hardening curves and an evolution law. The proposed identification strategy allowed for a good validation of the model. The model was afterwards used to predict the behavior of the welded material when it is subjected to various solicitations. Finally, the fracture surfaces of the specimens were examined using the scanning electron microscope (SEM) to determine the failure characteristics under the tensile loading. KEYWORDS. Interstitial Free steel; Laser welding; Off-axis tensile tests; anisotropy; Identification strategy; SEM. Citation: Arfaoui, L., Samet, A., Znaidi, A., Identification of the anisotropic behavior of the laser welded Interstitial Free steels subjected to off-axis tensile tests, Frattura ed Integrità Strutturale, 61 (2022) 282-293. Received: 18.03.2022 Accepted: 29.05.2022 Online first: 02.06.2022 Published: 01.07.2022 Copyright: © 2022 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION ith the advent of new generation automobiles, the demand of high formability steels especially Interstitial Free (IF) steels, has progressively accentuated. IF steels are mainly used in autobody fabrication. They are generally formed into intricate shapes at high production rates and manufactured by welding. The excellent formability of IF steels is achieved through the reduction of the amount of interstitial elements, carbon and nitrogen, to an extremely low level [1-3], mainly by the addition of stabilizing elements, such as Titanium and/or Niobium [4-6]. IF steels are cold-rolled into sheets first, in order to fabricate a variety of final product components. However, the cold rolling leads to a directional microstructural texture, and thus anisotropic mechanical properties in the processed steels [7]. W https://youtu.be/UbO_OnBMZho L Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 283 The Laser welding processes, of thin sheets assemblies or Tailored Welded Blanks (TWBs), have given many successful advantages in manufacturing engineering [8]. It surpasses traditional welding techniques with speed, thin welding, strength, easy integration, contactless process, and minimal maintenance costs [9]. The welded auto-components are exposed to static, impact or fatigue loading conditions because of sudden braking, vehicle crash, rough roads, etc. Numerical simulation tools are increasingly used in industry for the study of the failure of the welded joints as well as the optimization of the welding operation itself. The accuracy of all predictions made using numerical modelling strongly depends on the constitutive laws used to describe the plastic behavior of the welded material as well as the base material. For a proper mathematical modelling of its behavior at the macro-level, an accurate understanding of different effects related to the material; such as its initial anisotropy as well as its hardening is necessary. Many studies have focused in the welding of IF steels [9,29-31]. However, there is a need to develop models that can describe the behaviour of this laser welded material under a number of loading conditions. The main objective of this paper is therefore the development, through an identification strategy followed by its validation, of a constitutive model able to describe the elastoplastic behavior of the laser welded IF steel HC260Y when it is subjected to several stresses. The anisotropic yield function proposed by Barlat was used to model the elastoplastic behavior of the welded material. The parameters of the criterion were determined based on the off-axis tensile tests performed on three loading directions (00°, 45° and 90°). The Hollomon power law was used to describe the hardening behavior of the welded steel, under the isotropic hardening assumption. The proposed model was subsequently used to predict the evolution of the Lankford coefficient depending on the off-axis angle and to determine the load surfaces for several tests. The fracture surfaces were examined by the SEM in order to characterize the fracture mechanism in the welded specimens. EXPERIMENTAL PLATFORM Chemical composition n this work, cold-rolled IF steel sheets of thickness 1.2 mm have been used to prepare the tensile specimens. The chemical composition of the material is given in Tab. 1. C Mn P Si Ti Al Cr Ni Cu S Mo Sn B 0.003 0.541 0.072 0.071 0.062 0.052 0.030 0.013 0.012 0.010 0.002 0.001 0.0004 Table 1: Chemical composition of the IF-Ti steel (wt %). Preparation of the specimens of IF steel They were prepared by annealing and laser welding. They were firstly machined from the as-received parent metal by CO2 laser cutting in order to ensure that edge straightness and burr size are within the acceptable limits for laser welding. They were taken at different orientations at 0°, 45° and 90° in accordance with the rolling direction. Then, they were subjected to a recrystallization heat treatment conducted in a preheated air furnace, at 700°C for 4h 30min (Fig.1-a). The selected annealing conditions [10,13] resulted in a complete recrystallization of the specimens without development of abnormal growth of ferrite grains. The samples were laser welded in a protective Argon’s atmosphere with flow rate of 0.7 bar using a 4.6 kW capacity Nd-YAG laser (Fig.1-b). The welding was made in a butt joint square groove. Run-out plates of the same material and thickness were added to ensure a uniform heat input throughout the welded section. The welding parameters are summarized in Tab. 2. Pulse duration (ms) Pulse energy (J) Laser power (KW) Gas 4 11.5 4 Argon Table 2: Parameters of the laser welding. In order to determine the mechanical properties of welded specimens, the tensile specimens were prepared as per ISO 4136- 2013 specifications (Fig.2). The angle between the loading direction and the rolling direction will be subsequently noted . I L. Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 284 Figure 1: a) furnace and b) laser welding machine. Figure 2: Specimen drawing (dimensions in mm). Description of the tests The tensile specimens were tested on a 200 kN traction compression machine (MTS Insight 200) equipped with a 0.2% precision contact extensometer (MTS 634-12F-54) (Fig. 3-a) at a constant cross-head speed of 20mm/min. The weld line was oriented at 90° with respect to the loading direction. The examinations of the fracture surfaces were conducted by means of scanning electron microscopy (SEM), using a Thermo Scientific Q250 model (see Fig. 3-b). Figure 3: a) Tensile test machine and b) Scanning electron microscope. L Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 285 RESULTS AND DISCUSSION he stress-strain curves have been plotted for different loading directions (Fig. 4). The mechanical properties of the welded material have been summarized in Tab. 3 as follows: E - Young modulus of elasticity, A% - specimen maximum elongation, Rm – ultimate tensile strength, Re – yield strength (proof strength at 0.2% elongation). Figure 4: Stress-strain curves of the welded IF steel loaded in different orientations from the rolling direction. Direction Re (MPa) Rm(MPa) E (GPa) A% 00° 221 295.52 179.89 5.44 45° 208 307.54 149.82 4.73 90° 215 315.1 180.09 5.04 Table 3: Mechanical properties of the welded specimens. The considered steel exhibits an anisotropic behavior that is shown by the variation of the mechanical properties with the in-plane direction [14-16]. However, it is noticed that the hardening curves present extremely similar mechanical properties above 0.35 % in strain. The highest values of the maximum tensile strength and the percent of elongation were principally found in the transverse direction. In addition, the yield strength measured in this direction was less than that of the RD. Thus, the specimens cut parallel to the transverse direction exhibit the best characteristics in terms of ductility and formability. SEM OBSERVATIONS he fracture morphology of the welded specimens, illustrated in Fig. 5, consists mainly in a transgranular cleavage fracture, which explains the significant decrease in the mechanical characteristics of the welded material, particularly elongation percentage [7, 20]. In fact, the microstructural examination of the heat affected zone reveals the presence of coarse grains. The rapid growth of massive ferrite caused strain in the matrix, which was relieved by the production of dislocations. As a result, grains with irregular boundaries containing numerous dislocations appeared and became a typical feature of massive ferrite. The ferrite formed was subjected to tempering during the cooling phase. Therefore, the accumulated dislocations in massive ferrite subsequently formed cell structures [24,25]. The specimen is deformed plastically. The cleavage initiates, under the combined action of the dislocations and the applied stress, from the fracture of a brittle particle (a carbide or a non- metallic inclusion) located in the grain boundary [26-28]. The material fails along well defined crystallographic planes within the grain but the crack path is affected by grain boundaries and inclusions. The laser welding reduces the ductility and the formability of the material which leads to defects such as wrinkles, earing, and shearing in drawing, splits and wrinkles in stamping and thinning and buckling in bending. T T L. Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 286 Figure 5: SEM fractgraphs. CONSTITUTIVE MODEL his work is limited to the study of the plastic orthotropic behavior. The material is considered incompressible with negligible elastic deformation. The material is initially orthotropic and remains orthotropic; the isotropic hardening is represented by a single scalar hardening internal variable called P . The behavior model is defined by: Yield function The elastic range is considered to be evolving homothetically. The yield function can be written as follows: ( , ) ( ) - ( )   P P c sf q q (1) where f is the yield function,  s is the isotropic hardening function,  P is the equivalent plastic strain and  c is the equivalent stress given by the Barlat criterion [17] as below: 1 ( ) ( ) (| | | | | | )      m m m m c I II II III I IIIq q q q q q q (2) where m: parameter that defines the shape of the load surface; Iq , IIq and IIIq are the eigenvalues of the tensor q defined by the following equation: T L Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 287 : Dq A σ (3) A 4th order tensor of the linear transformation; Dσ the deviator of the Cauchy stress tensor Hardening law Due to its simplicity, the Hollomon power law is commonly used to characterize the isotropic hardening behavior of metals and alloys [18]. 1 1( ) ( ) P P n s ε k ε (4) where ( ) P s ε is the isotropic hardening function, Pε is the plastic strain, 1k is the strength coefficient and 1n is the strain hardening exponent. 1k and 1n are material parameters to be identified. Plastic flow law The associated flow rule is given by:       P D f ε (5) The direction of the plastic strain rate Pε is perpendicular to the yield surface. The plastic multiplier  defines its magnitude. It can be determined from the consistency condition 0f . Anisotropy coefficient The Lankford coefficient measures the variation of the plastic behavior with direction [19]. It is given by the following expression: 2 3      r (6) where 2 and 3 are the in-plane and through-the-thickness plastic strain rates, respectively. The subscript  specifies the angle between the specimen axis and the rolling direction. IDENTIFICATION PROCEDURE: he following assumptions were taken into account in order to simplify the identification process:  The condition of incompressibility was considered (the volume remains constant during the plastic deformation).  The plane stress assumption was adopted (thin steel sheet).  The material behavior was considered as rigid plastic (negligible elastic deformation).  The isotropic hardening assumption was adopted and the plasticity surface was considered to be evolving homothetically. Identification of the hardening curves The Hollomon hardening rule was curve-fitted to the stress-strain curves obtained from the uniaxial tensile tests (Fig. 6). The minimization of the quadratic error between the theoretical and experimental results allowed the identification of the hardening parameters corresponding to the mentioned law. Comparing the hardening exponent values, identified for different tests, it can be noticed that the T L. Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 288 exponent 1n is independent of the loading direction (Tab. 4). By convention, the value corresponding to the rolling direction, 1 0.143n , is considered as reference [20-23]. The hardening coefficients 1k , calculated for this value of 1n considering the Hollomon law, are summarised in Tab. 5.  00° 45° 90° 𝑘 464.9342 466.1388 471.5584 𝑛 0.1430 0.14785 0.1403 Table 4: Identification of the Hollomon law parameters for the welded specimens.  00° 45° 90° 𝑘 464.9342 457.1954 422.3050 Table 5: Identification of the parameter 1k for the fixed value of 1n =0.143. (a) (b) L Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 289 Figure 6: Identification of the hardening curve for (a) = 00°, (b) = 45° and (c) = 90°. Identification of the shape coefficient m and the anisotropy coefficients based on the hardening curves: The parameters of the Barlat criterion [20], in terms of anisotropy coefficients and shape coefficient, were identified through the minimization of an objective function (Eqn. 7) representing the square deviation between the theoretical and the experimental values of the parameter 1k , denoted 1( )k th and 1( )k exp respectively (Tab. 6). The optimisation algorithm was developed under Matlab. In the case of plane stresses, the number of plastic anisotropy parameters is reduced to four (f, g, h and n). 2 1 1( ( ) ( ))  i E k exp k th (7) Parameters f g h n m Values 0.2399 0.3947 0.3279 1.2425 5.7876 Table 6: identification of the anisotropic coefficients and the shape coefficient m. Figure 7: Evolution of the Lankford coefficient depending on the off-axis angle . Based on the identified parameters, the evolution of the Lankford coefficient according to the off-axis angle was represented in Fig. 7. The minimum Lankford coefficient value was measured at =45°. The highest values were related to the rolling and the transverse directions. (c) L. Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 290 The estimated Lankford coefficients values as well as well as the normal anisotropy nr and the planar anisotropy r ratios are presented in Tab. 7. The normal anisotropy ratio nr is lower than unity. This indicates that thinning is the preferential metal flow direction which increases the risk of failure in drawing operations. r r r r ∆r 1.19 0.57 1.18 0.87 0.3 Table 7: Estimated Lankford coefficients values for different loading directions. Validation: In order to validate the identification strategy, the experimental tensile curve in the transverse direction and the identified anisotropic parameters of the behavior model are used. The Fig. 8 shows a good agreement between the theoretical and the experimental curves. Figure 8: Validation of the hardening tensile curve for =90°. EVOLUTION OF THE YIELD SURFACE IN THE DEVIATORY PLANE  2 3,x x he mechanical behavior of this material subjected to a simple tensile test, a simple shear test and planar tension test is shown in Fig. 9, through the load surfaces determined based on the proposed model in the deviatory plane  2 3,x x : 2 | | 2   Dx sin cos (8) 3 | | 2   Dx sin sin (9) where  D is the deviator of the Cauchy stress tensor,  is the off-axis angle and  is the angle defining the type of the test. The welded specimens are resistant to simple shear much better than simple tension and planar tension. T L Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 291 Figure 9: Evolution of the yield surface in the deviatory plane  2 3,x x . L. Arfaoui et alii, Frattura ed Integrità Strutturale, 61 (2022) 282-293; DOI: 10.3221/IGF-ESIS.61.19 292 CONCLUSION he model presented in this manuscript focused on the plane orthotropy in the specific case of the isotropic hardening assumption. The analytical law of Hollomon was used to describe the hardening behavior of the welded material and the yield criterion proposed by Barlat was adopted to model its elastoplastic behavior. The proposed identification methodology, based on the hardening curves obtained from the off-axis tensile tests, allowed a good validation of the model. The constitutive model was subsequently used to predict the Lankford coefficient evolution depending on the off-axis angle and to present the load surfaces relating to different mechanical tests. The highest values of Rm and A% are related to the transverse direction. The maximum values for the Lankford coefficient correspond to the rolling direction as well as the transverse direction. The specimens cut parallel to the transverse direction exhibit the best characteristics in terms of ductility and formability. The proposed methodology gave satisfactory results for the identification of the hardening curves and the Lankford coefficients. However, it is less satisfying for the description of the evolution of the load surfaces. In fact, improvements of the model can be considered. It would be interesting to modify the assumption of isotropic hardening used to describe the plastic behavior. Hardening variables should be further investigated by performing cyclic tests or by adopting methodologies allowing their estimation from the monotonic properties. The examination of the fractographs corresponding to the welded specimens show a transgranular cleavage fracture. 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