- Email: [email protected]
Residual-stress evolution of cold-rolled DC04 steel sheets for different initial stress states
Finite Elements in Analysis and Design xxx (2017) 1–6
Contents lists available at ScienceDirect
Finite Elements in Analysis and Design j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fi n e l
Residual-stress evolution of cold-rolled DC04 steel sheets for different initial stress states Thomas Mehner a, *, Alexander Bauer b, Sebastian H€ artel b, Birgit Awiszus b, Thomas Lampke a a b
Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09125 Chemnitz, Germany Virtual Production Engineering Group, Institute for Machine Tools and Production Processes, Chemnitz University of Technology, D-09125 Chemnitz, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Cold rolling Initial state Residual stress Finite-element analysis DC04 steel
Cold-rolling processes are commonly used in industrial production. Rolling-induced residual stresses influence the behavior of the material significantly. Thus, the prediction of this state is of high importance. In this study, the influence of the initial residual-stress state on the final state after cold rolling is investigated by means of finiteelement analysis simulations and X-ray diffraction. It is shown that the initial residual-stress state of DC04 is eliminated after two cold-rolling passes even for comparably low plastic strains.
1. Introduction Residual stresses play a major role for the fabrication of various products, especially in the metal forming industries. A large part of research topics deals with thermally induced residual stresses but also cold-forming processes are well-known for causing these kinds of stresses. Such residual stresses can lead to a widespread influence of the product characteristics, for example towards their life cycle or the resistance against loads, abrasion and corrosion as well as fatigue or wear, and tear [1–3]. In general, a lot of research topics focus on eliminating or reducing residual stresses, and characterizing the influence of residual stresses on failure [4–6]. This results from the fact that tensile residual stresses are responsible for a wide range of failures or for the reduction of the product resistance against external influences. Some researchers also address the topic of a focused application of compressive residual stresses to strengthen products against external influences like abrasion or loads. Therefore, shot peening is a widely used application to induce those compressive residual stresses into the workpiece surfaces [2,7]. Furthermore, also other manufacturing processes were analyzed in relation to their influence on the residual stress state before and after processing the work pieces [8–11]. Especially during cold-rolling operations, residual stresses are induced into the sheet metal. Research on residual stresses, which occur in cold-rolling processes, are not that common because, normally, annealing is the process following the rolling process. Within this annealing process, most of the induced stresses were relieved from the sheet metals. Nevertheless, a few research topics also deal with the development and the targeted use of residual stresses from
the cold-rolling processes and how they can influence the following process steps [12–16]. From that point of view, it is also useful to understand how it is possible to use the residual stresses from the coldrolling processes as advantageous characteristics for the following process steps. Therefore, it is necessary to know, how residual stresses develop within the cold flat-rolling processes and the separate rolling passes, and how initial stresses exert influence on the following process steps. In this paper, the influence of different initial residual-stress states on the resulting stress states after cold rolling will be investigated by means of finite-element analysis (FEA) simulations and X-ray diffraction (XRD). 2. Materials and methods Samples were prepared from a commercial DC04 sheet with the composition (mass fraction): 0.042% C, 0.242% Mn, 0.035% Al, 0.011% Si, 0.013% S, 0.010% P, balance Fe and with initial thicknesses of 2.0 mm or 1.5 mm. To gain an understanding of the basic processes without phase transformations or similar micromechanical issues, it is very important to choose a carbon steel type with only a small proportion of alloying elements. Prior to rolling, the metal sheets were cut into small samples with the dimensions of 100 mm 14 mm or 100 mm 40 mm by water-jet cutting. Water-jet cutting was applied to minimize the influence on residual stresses and to avoid additional shear or tensile stresses caused by the cutting process. Different samples were prepared by cold rolling. The samples were rolled on a Duo/Quarto EW 105 100 strip rolling mill (Bühler und Co
* Corresponding author. E-mail address: [email protected] (T. Mehner). https://doi.org/10.1016/j.finel.2017.11.006 Received 21 June 2017; Received in revised form 15 November 2017; Accepted 16 November 2017 Available online xxxx 0168-874X/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: T. Mehner, et al., Residual-stress evolution of cold-rolled DC04 steel sheets for different initial stress states, Finite Elements in Analysis and Design (2017), https://doi.org/10.1016/j.finel.2017.11.006
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
GmbH). A roll speed of 12.12 rpm was used. The maximum rolling force is stated with 100 kN while using the duo mode with two working rolls. The two processing routes (1) and (2) were selected in such a way so that (1) similar v. Mises equivalent plastic strains (φ) after different processing steps or (2) different plastic strains for an identical sample thickness were reached. Thus, the influence of carefully prepared initial states of the residual stresses on further forming processes and the resulting residual stresses can be investigated by using the processing routes: (1) Rolling of 2.0 mm thick hot-rolled sheets with two different sample widths (14 mm and 40 mm) down to a thickness of 1.7 mm, afterwards reducing of the width to 14 mm by water-jet cutting, and further rolling passes, (2) Comparison of 2.0 mm → 1.5 mm cold-rolled sheets with 1.5 mm cold rolled and annealed samples and following rolling passes. The samples prepared are summarized in Table 1. To exclude influences by different rolling directions, the samples were processed using always the same rolling direction. The samples were even and no visible bends occurred. The cutting of the samples with 40 mm width was also performed by water-jet cutting after the first rolling pass (1.7 mm), thereby providing a homogeneous sample (width: 14 mm) from the center of the 40 mm sheet to gain a comparable sample geometry with a different stress state than in the samples which were cut before the first rolling pass. Numerical analyses of the cold-rolling process were performed using the FEA program simufact. forming (SF) 13.0. The numerical model was generated with 8-node hexahedral elements with the size of 1.5 mm 1.5 mm 0.5 mm. A 3D coupled simulation was used. The flow curves used in the simulation were generated by flat compression tests of the used DC04 at a QUASAR 50 kN (Galdabini) compression tension testing machine at 20 C room temperature for a φ_ of 0.1 s1, even though the DC04 is hardly affected by small variations of the strain rate. The measured values were corrected to an ideal flow curve without friction effects and thermal influences. Thermal effects were kept low by a slow forming motion. Afterwards the data points were implemented into the simulative tool as flow curve for the corresponding rolling model. The tools in the numerical setup (Fig. 1) were defined as rigid bodies. Between the working rolls and the sample, a combined friction coefficient (Coulomb and shear friction) of μ ¼ 0.15 and m ¼ 0.3 was used. The required mechanical force to overcome the rolls feed was applied by a pusher. Furthermore, for the inhibition of sample’s bending, additional surfaces (fences) were used within the FEA model. Similar to the real process, the numerical analysis of cold flat rolling is very susceptible to bending and therefore, it is necessary to integrate those fences. Their
Fig. 1. Setup used in the numerical FEA simulation.
friction coefficient is zero so there is no further influence within the numerical simulation. No initial residual stress state (i.e., all stresses equal 0) was applied for sheets with the initial thickness (2.0 mm or 1.5 mm). Thus, the numerical results of the first rolling pass correspond to the different initial stress states considered within the further investigations. X-ray residual-stress measurements were carried out using a D8 Discover (Bruker AXS) diffractometer with Co Kα radiation (tube parameters: 40 kV, 40 mA, point focus), polycap optics for beam focusing, a 0.5 mm pinhole collimator, and a 1D detector Lynxeye XE with 2.1 aperture angle. The sin2ψ method [17] was used with tilt angles corresponding to sin2 ψ ¼ 0.0, 0.1, …, 0.8 both in positive and negative tilt direction. For rotation around the sample normal, the angles 0 , 45 , and 90 were used. The {211} lattice planes of α-Fe were measured in the diffraction angle (2θ) range of 97.0 –102.5 with a step size of 0.015 and 0.8 s measurement time per step, which corresponds to 153.6 s/step due to the use of the 1D detector. The evaluation of the residual-stress measurements was carried out using the program Leptos (Bruker AXS) with the corresponding Young’s modulus E{211} ¼ 220 GPa and Poisson ratio V{211} ¼ 0.28 for α-Fe [18]. Fig. 2 shows the positions of the residual-stress measurements schematically. The positions were 7.0 mm (“center”) or 3.5 mm (“edge”) away from the edges of the samples. After rolling, a local difference is expected for samples with an initial width of 14 mm. 3. Results and discussion
Table 1 Samples prepared for the determination of the influence of the initial residual-stress state. Numbers in bold print represent the final thickness of the samples. Processing route
Initial thickness in mm
Initial width in mm
Rolling passes: thicknesses in mm
(1) (1) (1) (1)
2.0 2.0 2.0 2.0
1.7 1.7 → 1.5 1.7 → 1.5 → 1.3 1.7
(1)
2.0
(1)
2.0
(2) (2) (2) (2) (2) (2)
2.0 2.0 2.0 1.5 1.5 1.5
14 14 14 40 (14 after cutting) 40 (14 after cutting) 40 (14 after cutting) 14 14 14 14 14 14
The processing route (1) was implemented as numerical analyses and was investigated experimentally. By using two different initial sheet widths, varying initial stress states were produced (2.0 mm → 1.7 mm, Fig. 3 red bars). This results of the fact that a different initial width includes a different geometry in the rolling gap and therefore leads to a variating material flow, which causes the different stress states between 40 mm and 14 mm specimen. Furthermore, the effect of expansion in width is smaller for the specimen with 40 mm width because the effect of expansion is decreasing with an increasing ratio of width to the compressed length under the working rolls. Additionally it is known that a ratio between width to height of 10 or bigger leads to a rolling process without expansion in width. Similar to the numerical results, which were evaluated below, the experimental residual stresses within the samples were superimposed by the stresses of the following rolling passes. Depending on the plastic strain (calculated by FEA), which is almost identical for the same sheet thicknesses (increased by about 0.2 in each
1.7 → 1.5 1.7 → 1.5 → 1.3 1.5 1.5 → 1.3 1.5 → 1.3 → 1.1 – 1.3 1.3 → 1.1
2
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
Fig. 2. Example of the location of three measured points within the center of the sheets (widths 14 mm) and 3.5 mm away from the edge.
Fig. 3. Experimental evolution of the residual stresses in (σ xx) and perpendicular (σ yy) to the rolling direction of DC04 sheets produced using processing route (1) for the center of the sheets (left) and for positions 3.5 mm away from the edges of the samples (right).
tensile stresses for the 40 mm sheets, whereas σ xx are tensile and σ yy compressive stresses for the 14 mm sheets. After performing the first rolling pass (1.7 mm → 1.5 mm), there is one tensile and one compressive stress component for both sets of samples. Again, the stress orientations are almost identical. The maximum differences of the stresses are below 15 MPa or 10 MPa for the two rolling passes shown. The resulting residual-stress states for the same plastic strain prove that the initial state of the residual stress prior to rolling is only of minor relevance. The experimental results were supported by FEA calculations made in accordance with the real processes (Fig. 4). The FEA was used to calculate
rolling pass), the initial stresses were eliminated directly in the first rolling pass (Fig. 3, green bars). The residual stress state in the center of the 14 mm sheets with a thickness of 1.7 mm is almost uniaxial. In comparison, the sheets with an initial width of 40 mm show about 50 MPa lower tensile stresses in rolling direction (σ xx) and 40 MPa higher tensile stresses perpendicular to the rolling direction (σ yy). These differences in the stresses are reduced to 16 MPa or 12 MPa in the next two rolling passes. The stress orientations also align almost exactly. Comparing the residual stresses close to the edges of the samples, this effect is even more pronounced: Both residual-stress components are
Fig. 4. Evolution of σ xx stress of an exemplary sheet section (33 mm 14 mm) after different rolling passes within the FEA (processing route (1)). 3
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
additional rolling passes and complex stress states, which cannot be generated within the real rolling process. The residual stress σ xx within a sheet section is shown for the samples with the initial widths of 14 mm or 40 mm and three rolling passes. Therefore the processing route was given as follows: 2 mm → 1.7 mm, 1.7 mm → 1.5 mm, and 1.5 mm → 1.3 mm. The sample with 14 mm initial width is illustrated on the left side. On the right side, the one with an initial width of 40 mm is shown, which was cut to a width of 14 mm after the first rolling pass. The cutting process was used to gain a second stress states, which differs from the one with 14 mm initial width. So both samples with different stress states can be proceeded within further rolling passes for a comparison of their behavior. The post-processor value and the scale show the residual stress in rolling direction. For a better understanding and illustration, a section of the full geometry was selected. In the third rolling pass, the average numerical difference between the two sets of samples reaches almost zero in the center of the samples, and the local different distribution of σ xx, which is clearly visible in pass 1 (1.7 mm), disappears. Table 2 shows the comparison between experiment and simulation. With regard to the fact that the FEA is an approximation method, which discretizes the ideal geometries, there is a good agreement with the experimental results. The maximum deviation of the residual stress components between experiment and simulation is 28 MPa. The differences arise from the idealization of the geometry with its sharp, ideal edges and an optimal even surface. In addition, the XRD results possess an uncertainty of typically ±10 MPa. Both the experimental and the numerical analyses prove that the characteristics of the initial state do not influence the final stress state significantly. It is important to note that the resulting residual stresses depend on the processing route. Thus, the two processing routes (1) and (2) lead to different residual stresses for similar plastic strains, which is described below. Processing route (2) was only studied experimentally because it is quite difficult to generate an accurate 3D initial stress state (tensor) with proper stress orientation for the initial material thickness without previous rolling passes. The results of the residual-stress measurements after rolling in accordance with processing route (2) are shown in Fig. 5. The initial residual-stress states of the 1.5 mm sheets differ significantly (Fig. 5, green). There are two compressive residual-stress components with low absolute values for the sheet with an initial thickness of 1.5 mm and an almost uniaxial residual-stress state with about 130 MPa tensile stress in rolling direction for the sheet 2.0 mm → 1.5 mm. Rolling to 1.3 mm changes the stress state causing tensile stresses for rather low φ of 0.19. Reaching a plastic strain of about 0.40 … 0.50, the stress states of the two sheets become almost identical (compressive stresses) with a maximum difference of 12 MPa. This means that the initial stress states do not influence the final stress state after rolling after two rolling passes were performed. Further rolling does almost not change the principal stresses for the considered forming steps. This could be caused by the flow curve, which reaches an area of very low increase within higher plastic strains. Furthermore, selected residual-stress states were only tested within
Fig. 5. Experimental evolution of the residual stresses in (σ xx) and perpendicular (σ yy) to the rolling direction of differently produced DC04 sheets in the center of the samples using processing route (2).
the FEA with the aim to show the influence of further rolling passes on the final stress state. A sample was taken from the edge region of a sheet with 42 mm initial width rolled down from 2.0 mm to 1.7 mm (pass 1): The sheet is separated into three parts of the width 14 mm (Fig. 6). This was used to gain an extreme stress state. The upper part was used for further rolling passes and is shown in Fig. 7. The local residual stresses of the sample differ between 200 MPa and 100 MPa up to 4 mm distance from the upper edge and 50 MPa–100 MPa from approx. 4 mm away from the upper edge to the lower edge of the specimen. Further rolling passes were simulated (1.7 mm → 1.5 mm, 1.5 mm → 1.3 mm). The residual stresses converge within rolling pass 2 to values similar to the ones shown above for processing route (1). For the following rolling pass 3 (1.5 mm → 1.3 mm), the sample shows the same stress state like all of the other ones, manufactured with processing route (1). In Fig. 8, the simulated residual stresses σ xx, and σ yy, in the center of the samples, are shown for the rolling passes of processing route (1) using different initial states: “40 mm” and “14 mm” correspond to the states shown in Table 2, “inhomogeneous” is the state shown in Fig. 7, and “1.7 mm zero” means that the initial residual stresses of a 1.7 mm thick sheet were set to zero for all elements in the FEA. The initial stress state was generated by different rolling processes 2.0 mm → 1.7 mm (as described above), and thus, an initial plastic strain of about 0.2 is present. A similar plastic strain was assigned to the sample “1.7 mm zero”. The plastic strain itself is distributed in a characteristic way over and inside the specimen but the maximum deviation from the surface to the inside or from the edges to the center of the sample is 5/100 for the example of the rolling pass from 2 mm → 1.7 mm.
Table 2 Comparison of residual stresses between experiment and FEA for processing route (1). The sample with a thickness of 1.7 mm is considered as the initial state. Sample (center)
σ xx in MPa (experiment/FEA/ deviation)
Initial width: 40 mm 1.7 135/147/12 1.7 → 1.5 68/42/26 1.7 → 1.5 → 1.3 29/34/5 Initial width: 14 mm 1.7 179/180/1 1.7 → 1.5 84/89/5 1.7 → 1.5 → 1.3 41/40/1
σ yy in MPa (experiment/FEA/ deviation) 48/37/11 24/21/3 57/37/20 8/15/7 25/17/8 52/24/28
Fig. 6. Exemplary cut out of a 14 mm sample from a 42 mm sheet (2 mm → 1.7 mm) within the FEA. 4
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
Fig. 7. Evolution of σ xx stress through the rolling passes for an inhomogeneous initial stress state.
Fig. 8. FEA results of the development of the residual stresses in the center of the samples in (σ xx, left) and perpendicular (σ yy, right) to the rolling direction of DC04 sheets using four different initial states and processing route (1).
All different initial stress states converge quickly (marked by the brown bars in Fig. 8), and the residual stresses reach a similar value at a change of the plastic strain of about 0.3 (i.e., φ 0.5). This behavior correlates with the change of the microstructure as described below.
The results prove that no careful adjustment of the initial residualstress state is necessary because the initial state is eliminated even for low plastic strains. This is valid for both simulations and industrial rolling processes.
4. Summary and conclusion
Acknowledgements
It was shown that the residual stresses of the FEA simulations and the experimental values are in very good agreement for cold-rolled DC04. This is also valid for the local distribution and orientation of the residualstress tensors. It was found that there is a good correlation between the forming and the resulting residual stresses for cold-rolled DC04: Only the used material, rolling-pass sequence and the plastic strain will influence the residual stresses, but the initial residual-stress state has no significant influence on the residual-stress state after the deformation. Based on the results presented above, it can be concluded that the first rolling pass after the hot-rolling completely replaces the initial stress state, replacing it with a characteristic one. This state is characterized by high tensile stresses in rolling direction of more than 130 MPa. The tensile stress increase with decreasing sample width because the major deformation takes place in length direction but the total amount of material stays the same due to the constant volume during the forming process. Perpendicular to the rolling direction, there are low tensile stresses < 50 MPa because the increase in width is less dominant. Using other processing routes (not shown here), this characteristic state is also formed and thus a correlation to the change of the microstructure of the samples due to the strong compressive stress during the rolling process is assumed: The first rolling pass leads to significant changes of the initial microstructure. The dislocation density, grain size, crystallite size, roughness, and texture quickly approach their maximum values (published in detail in Ref. [19]). Already for φ 0.5, the major changes have occurred. Related to these changes, the characteristic stress state is formed. Starting from this state, further rolling passes result in residuals stress states that are specific for the rolling-pass sequence.
The authors gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG) for funding this work (grant numbers LA 1274/27-1 and AW 6/27-1) and thank Vanessa Drexler for providing language help. References [1] A. Abvabi, B. Rolfe, P.D. Hodgson, M. Weiss, The influence of residual stress on a roll forming process, Int. J. Mechan. Sci. 101–102 (2015) 124–136. [2] A.H. Mahmoudi, A. Ghasemi, G.H. Farrahi, K. Sherafatnia, A comprehensive experimental and numerical study on redistribution of residual stresses by shot peening, Mater. Des. 90 (2016) 478–487. [3] D. Shang, X. Liu, Y. Shan, E. Jiang, Research on the stamping residual stress of steel wheel disc and its effect on the fatigue life of wheel, Int. J. Fatigue 93 (2016) 173–183. [4] V.F. Skvortsov, A.O. Boznak, A.B. Kim, A.Y. Arlyapov, A.I. Dmitriev, Reduction of the residual stresses in cold expanded thick-walled cylinders by plastic compression, Def. Technol. 12 (2016) 473–479. [5] M.R. Nejad, Using three-dimensional finite element analysis for simulation of residual stresses in railway wheels, Eng. Fail. Anal. 45 (2014) 449–455. [6] P.J. Withers, Residual stress and its role in failure, Rep. Prog. Phys. 70 (2007) 2211–2264. [7] K. Sherafatina, G.H. Farrahi, A.H. Mahmoudi, A. Ghasemi, Experimental measurement and analystic determination of shot peening stresses considering friction and real unloading behavior, Mater. Sci. Eng. A 657 (2016) 309–321. [8] C.D. Moen, T. Igusa, B.W. Schafer, Prediction of residual stresses and strains in coldformed steel members, Thin-Walled Struct. 46 (2008) 1274–1289. [9] S.M. Hassani-Gangaraj, M. Carboni, M. Guagliano, Finite element approach toward an advanced understanding of deep rolling induced residual stresses and an application to railway axles, Mater. Des. 83 (2015) 689–703. [10] K.J. Kang, J.H. Song, Y.Y. Earmme, Fatigue crack growth and closure behavior through a compressive residual stress field, Fatigue Fract. Eng. Mater. Struct. 13 (1990) 1–13.
5
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
[11] D. Tsivoulas, J. Quinta da Fonseca, M. Tuffs, M. Preuss, Effects of flow forming parameters on the development of residual stresses in Cr-Mo-V steel tubes, Mater. Sci. Eng. A 624 (2015) 193–202. [12] P. Parikin, P. Killen, A. Rafterry, Measurements of residual stresses in cold-rolled 304 stainless steel plates using X-ray diffraction with rietveld refinement method, Atom Indones. 35 (2009) 19–36. [13] M. Giorgi, Residual stress evolution in cold-rolled steels, Int. J. Fatigue 33 (2011) 507–512. [14] N. Hattori, R. Matsumoto, H. Utsunomiya, Residual stress distribution through thickness in cold-rolled aluminum sheet, Key Eng. Mater. 622 (2014) 1000–1007. [15] M. Sedighi, M. Honarpisheh, Investigation of cold rolling influence on near surface residual stresses distribution in explosive welded multilayer, Strength Mater. 44 (2012) 693–698.
[16] M. Weiss, B. Rolfe, P.D. Hodgson, C. Yang, Effect of residual stress on the bending of aluminium, J. Mater. Process. Technol. 212 (2012) 877–883. [17] E. Macherauch, P. Müller, Das sin2ψ-Verfahren der r€ ontgenographischen Spannungsermittlung, Z. angew. Physik 13 (1961) 305–312 (in German). [18] B. Eigenmann, E. Macherauch, R€ ontgenographische Untersuchung von Spannungszust€anden in Werkstoffen Teil III, Mat.-wiss. u. Werkstofftech 27 (1996) 426–437 (in German). [19] T. Mehner, A. Bauer, B. Awiszus, T. Lampke, Macromechanical finite-element simulations for predicting microstructures by experimental calibration, IOP Conf. Ser. Mater. Sci. Eng. 181 (2017), 012036.
6
Contents lists available at ScienceDirect
Finite Elements in Analysis and Design j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fi n e l
Residual-stress evolution of cold-rolled DC04 steel sheets for different initial stress states Thomas Mehner a, *, Alexander Bauer b, Sebastian H€ artel b, Birgit Awiszus b, Thomas Lampke a a b
Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09125 Chemnitz, Germany Virtual Production Engineering Group, Institute for Machine Tools and Production Processes, Chemnitz University of Technology, D-09125 Chemnitz, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Cold rolling Initial state Residual stress Finite-element analysis DC04 steel
Cold-rolling processes are commonly used in industrial production. Rolling-induced residual stresses influence the behavior of the material significantly. Thus, the prediction of this state is of high importance. In this study, the influence of the initial residual-stress state on the final state after cold rolling is investigated by means of finiteelement analysis simulations and X-ray diffraction. It is shown that the initial residual-stress state of DC04 is eliminated after two cold-rolling passes even for comparably low plastic strains.
1. Introduction Residual stresses play a major role for the fabrication of various products, especially in the metal forming industries. A large part of research topics deals with thermally induced residual stresses but also cold-forming processes are well-known for causing these kinds of stresses. Such residual stresses can lead to a widespread influence of the product characteristics, for example towards their life cycle or the resistance against loads, abrasion and corrosion as well as fatigue or wear, and tear [1–3]. In general, a lot of research topics focus on eliminating or reducing residual stresses, and characterizing the influence of residual stresses on failure [4–6]. This results from the fact that tensile residual stresses are responsible for a wide range of failures or for the reduction of the product resistance against external influences. Some researchers also address the topic of a focused application of compressive residual stresses to strengthen products against external influences like abrasion or loads. Therefore, shot peening is a widely used application to induce those compressive residual stresses into the workpiece surfaces [2,7]. Furthermore, also other manufacturing processes were analyzed in relation to their influence on the residual stress state before and after processing the work pieces [8–11]. Especially during cold-rolling operations, residual stresses are induced into the sheet metal. Research on residual stresses, which occur in cold-rolling processes, are not that common because, normally, annealing is the process following the rolling process. Within this annealing process, most of the induced stresses were relieved from the sheet metals. Nevertheless, a few research topics also deal with the development and the targeted use of residual stresses from
the cold-rolling processes and how they can influence the following process steps [12–16]. From that point of view, it is also useful to understand how it is possible to use the residual stresses from the coldrolling processes as advantageous characteristics for the following process steps. Therefore, it is necessary to know, how residual stresses develop within the cold flat-rolling processes and the separate rolling passes, and how initial stresses exert influence on the following process steps. In this paper, the influence of different initial residual-stress states on the resulting stress states after cold rolling will be investigated by means of finite-element analysis (FEA) simulations and X-ray diffraction (XRD). 2. Materials and methods Samples were prepared from a commercial DC04 sheet with the composition (mass fraction): 0.042% C, 0.242% Mn, 0.035% Al, 0.011% Si, 0.013% S, 0.010% P, balance Fe and with initial thicknesses of 2.0 mm or 1.5 mm. To gain an understanding of the basic processes without phase transformations or similar micromechanical issues, it is very important to choose a carbon steel type with only a small proportion of alloying elements. Prior to rolling, the metal sheets were cut into small samples with the dimensions of 100 mm 14 mm or 100 mm 40 mm by water-jet cutting. Water-jet cutting was applied to minimize the influence on residual stresses and to avoid additional shear or tensile stresses caused by the cutting process. Different samples were prepared by cold rolling. The samples were rolled on a Duo/Quarto EW 105 100 strip rolling mill (Bühler und Co
* Corresponding author. E-mail address: [email protected] (T. Mehner). https://doi.org/10.1016/j.finel.2017.11.006 Received 21 June 2017; Received in revised form 15 November 2017; Accepted 16 November 2017 Available online xxxx 0168-874X/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: T. Mehner, et al., Residual-stress evolution of cold-rolled DC04 steel sheets for different initial stress states, Finite Elements in Analysis and Design (2017), https://doi.org/10.1016/j.finel.2017.11.006
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
GmbH). A roll speed of 12.12 rpm was used. The maximum rolling force is stated with 100 kN while using the duo mode with two working rolls. The two processing routes (1) and (2) were selected in such a way so that (1) similar v. Mises equivalent plastic strains (φ) after different processing steps or (2) different plastic strains for an identical sample thickness were reached. Thus, the influence of carefully prepared initial states of the residual stresses on further forming processes and the resulting residual stresses can be investigated by using the processing routes: (1) Rolling of 2.0 mm thick hot-rolled sheets with two different sample widths (14 mm and 40 mm) down to a thickness of 1.7 mm, afterwards reducing of the width to 14 mm by water-jet cutting, and further rolling passes, (2) Comparison of 2.0 mm → 1.5 mm cold-rolled sheets with 1.5 mm cold rolled and annealed samples and following rolling passes. The samples prepared are summarized in Table 1. To exclude influences by different rolling directions, the samples were processed using always the same rolling direction. The samples were even and no visible bends occurred. The cutting of the samples with 40 mm width was also performed by water-jet cutting after the first rolling pass (1.7 mm), thereby providing a homogeneous sample (width: 14 mm) from the center of the 40 mm sheet to gain a comparable sample geometry with a different stress state than in the samples which were cut before the first rolling pass. Numerical analyses of the cold-rolling process were performed using the FEA program simufact. forming (SF) 13.0. The numerical model was generated with 8-node hexahedral elements with the size of 1.5 mm 1.5 mm 0.5 mm. A 3D coupled simulation was used. The flow curves used in the simulation were generated by flat compression tests of the used DC04 at a QUASAR 50 kN (Galdabini) compression tension testing machine at 20 C room temperature for a φ_ of 0.1 s1, even though the DC04 is hardly affected by small variations of the strain rate. The measured values were corrected to an ideal flow curve without friction effects and thermal influences. Thermal effects were kept low by a slow forming motion. Afterwards the data points were implemented into the simulative tool as flow curve for the corresponding rolling model. The tools in the numerical setup (Fig. 1) were defined as rigid bodies. Between the working rolls and the sample, a combined friction coefficient (Coulomb and shear friction) of μ ¼ 0.15 and m ¼ 0.3 was used. The required mechanical force to overcome the rolls feed was applied by a pusher. Furthermore, for the inhibition of sample’s bending, additional surfaces (fences) were used within the FEA model. Similar to the real process, the numerical analysis of cold flat rolling is very susceptible to bending and therefore, it is necessary to integrate those fences. Their
Fig. 1. Setup used in the numerical FEA simulation.
friction coefficient is zero so there is no further influence within the numerical simulation. No initial residual stress state (i.e., all stresses equal 0) was applied for sheets with the initial thickness (2.0 mm or 1.5 mm). Thus, the numerical results of the first rolling pass correspond to the different initial stress states considered within the further investigations. X-ray residual-stress measurements were carried out using a D8 Discover (Bruker AXS) diffractometer with Co Kα radiation (tube parameters: 40 kV, 40 mA, point focus), polycap optics for beam focusing, a 0.5 mm pinhole collimator, and a 1D detector Lynxeye XE with 2.1 aperture angle. The sin2ψ method [17] was used with tilt angles corresponding to sin2 ψ ¼ 0.0, 0.1, …, 0.8 both in positive and negative tilt direction. For rotation around the sample normal, the angles 0 , 45 , and 90 were used. The {211} lattice planes of α-Fe were measured in the diffraction angle (2θ) range of 97.0 –102.5 with a step size of 0.015 and 0.8 s measurement time per step, which corresponds to 153.6 s/step due to the use of the 1D detector. The evaluation of the residual-stress measurements was carried out using the program Leptos (Bruker AXS) with the corresponding Young’s modulus E{211} ¼ 220 GPa and Poisson ratio V{211} ¼ 0.28 for α-Fe [18]. Fig. 2 shows the positions of the residual-stress measurements schematically. The positions were 7.0 mm (“center”) or 3.5 mm (“edge”) away from the edges of the samples. After rolling, a local difference is expected for samples with an initial width of 14 mm. 3. Results and discussion
Table 1 Samples prepared for the determination of the influence of the initial residual-stress state. Numbers in bold print represent the final thickness of the samples. Processing route
Initial thickness in mm
Initial width in mm
Rolling passes: thicknesses in mm
(1) (1) (1) (1)
2.0 2.0 2.0 2.0
1.7 1.7 → 1.5 1.7 → 1.5 → 1.3 1.7
(1)
2.0
(1)
2.0
(2) (2) (2) (2) (2) (2)
2.0 2.0 2.0 1.5 1.5 1.5
14 14 14 40 (14 after cutting) 40 (14 after cutting) 40 (14 after cutting) 14 14 14 14 14 14
The processing route (1) was implemented as numerical analyses and was investigated experimentally. By using two different initial sheet widths, varying initial stress states were produced (2.0 mm → 1.7 mm, Fig. 3 red bars). This results of the fact that a different initial width includes a different geometry in the rolling gap and therefore leads to a variating material flow, which causes the different stress states between 40 mm and 14 mm specimen. Furthermore, the effect of expansion in width is smaller for the specimen with 40 mm width because the effect of expansion is decreasing with an increasing ratio of width to the compressed length under the working rolls. Additionally it is known that a ratio between width to height of 10 or bigger leads to a rolling process without expansion in width. Similar to the numerical results, which were evaluated below, the experimental residual stresses within the samples were superimposed by the stresses of the following rolling passes. Depending on the plastic strain (calculated by FEA), which is almost identical for the same sheet thicknesses (increased by about 0.2 in each
1.7 → 1.5 1.7 → 1.5 → 1.3 1.5 1.5 → 1.3 1.5 → 1.3 → 1.1 – 1.3 1.3 → 1.1
2
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
Fig. 2. Example of the location of three measured points within the center of the sheets (widths 14 mm) and 3.5 mm away from the edge.
Fig. 3. Experimental evolution of the residual stresses in (σ xx) and perpendicular (σ yy) to the rolling direction of DC04 sheets produced using processing route (1) for the center of the sheets (left) and for positions 3.5 mm away from the edges of the samples (right).
tensile stresses for the 40 mm sheets, whereas σ xx are tensile and σ yy compressive stresses for the 14 mm sheets. After performing the first rolling pass (1.7 mm → 1.5 mm), there is one tensile and one compressive stress component for both sets of samples. Again, the stress orientations are almost identical. The maximum differences of the stresses are below 15 MPa or 10 MPa for the two rolling passes shown. The resulting residual-stress states for the same plastic strain prove that the initial state of the residual stress prior to rolling is only of minor relevance. The experimental results were supported by FEA calculations made in accordance with the real processes (Fig. 4). The FEA was used to calculate
rolling pass), the initial stresses were eliminated directly in the first rolling pass (Fig. 3, green bars). The residual stress state in the center of the 14 mm sheets with a thickness of 1.7 mm is almost uniaxial. In comparison, the sheets with an initial width of 40 mm show about 50 MPa lower tensile stresses in rolling direction (σ xx) and 40 MPa higher tensile stresses perpendicular to the rolling direction (σ yy). These differences in the stresses are reduced to 16 MPa or 12 MPa in the next two rolling passes. The stress orientations also align almost exactly. Comparing the residual stresses close to the edges of the samples, this effect is even more pronounced: Both residual-stress components are
Fig. 4. Evolution of σ xx stress of an exemplary sheet section (33 mm 14 mm) after different rolling passes within the FEA (processing route (1)). 3
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
additional rolling passes and complex stress states, which cannot be generated within the real rolling process. The residual stress σ xx within a sheet section is shown for the samples with the initial widths of 14 mm or 40 mm and three rolling passes. Therefore the processing route was given as follows: 2 mm → 1.7 mm, 1.7 mm → 1.5 mm, and 1.5 mm → 1.3 mm. The sample with 14 mm initial width is illustrated on the left side. On the right side, the one with an initial width of 40 mm is shown, which was cut to a width of 14 mm after the first rolling pass. The cutting process was used to gain a second stress states, which differs from the one with 14 mm initial width. So both samples with different stress states can be proceeded within further rolling passes for a comparison of their behavior. The post-processor value and the scale show the residual stress in rolling direction. For a better understanding and illustration, a section of the full geometry was selected. In the third rolling pass, the average numerical difference between the two sets of samples reaches almost zero in the center of the samples, and the local different distribution of σ xx, which is clearly visible in pass 1 (1.7 mm), disappears. Table 2 shows the comparison between experiment and simulation. With regard to the fact that the FEA is an approximation method, which discretizes the ideal geometries, there is a good agreement with the experimental results. The maximum deviation of the residual stress components between experiment and simulation is 28 MPa. The differences arise from the idealization of the geometry with its sharp, ideal edges and an optimal even surface. In addition, the XRD results possess an uncertainty of typically ±10 MPa. Both the experimental and the numerical analyses prove that the characteristics of the initial state do not influence the final stress state significantly. It is important to note that the resulting residual stresses depend on the processing route. Thus, the two processing routes (1) and (2) lead to different residual stresses for similar plastic strains, which is described below. Processing route (2) was only studied experimentally because it is quite difficult to generate an accurate 3D initial stress state (tensor) with proper stress orientation for the initial material thickness without previous rolling passes. The results of the residual-stress measurements after rolling in accordance with processing route (2) are shown in Fig. 5. The initial residual-stress states of the 1.5 mm sheets differ significantly (Fig. 5, green). There are two compressive residual-stress components with low absolute values for the sheet with an initial thickness of 1.5 mm and an almost uniaxial residual-stress state with about 130 MPa tensile stress in rolling direction for the sheet 2.0 mm → 1.5 mm. Rolling to 1.3 mm changes the stress state causing tensile stresses for rather low φ of 0.19. Reaching a plastic strain of about 0.40 … 0.50, the stress states of the two sheets become almost identical (compressive stresses) with a maximum difference of 12 MPa. This means that the initial stress states do not influence the final stress state after rolling after two rolling passes were performed. Further rolling does almost not change the principal stresses for the considered forming steps. This could be caused by the flow curve, which reaches an area of very low increase within higher plastic strains. Furthermore, selected residual-stress states were only tested within
Fig. 5. Experimental evolution of the residual stresses in (σ xx) and perpendicular (σ yy) to the rolling direction of differently produced DC04 sheets in the center of the samples using processing route (2).
the FEA with the aim to show the influence of further rolling passes on the final stress state. A sample was taken from the edge region of a sheet with 42 mm initial width rolled down from 2.0 mm to 1.7 mm (pass 1): The sheet is separated into three parts of the width 14 mm (Fig. 6). This was used to gain an extreme stress state. The upper part was used for further rolling passes and is shown in Fig. 7. The local residual stresses of the sample differ between 200 MPa and 100 MPa up to 4 mm distance from the upper edge and 50 MPa–100 MPa from approx. 4 mm away from the upper edge to the lower edge of the specimen. Further rolling passes were simulated (1.7 mm → 1.5 mm, 1.5 mm → 1.3 mm). The residual stresses converge within rolling pass 2 to values similar to the ones shown above for processing route (1). For the following rolling pass 3 (1.5 mm → 1.3 mm), the sample shows the same stress state like all of the other ones, manufactured with processing route (1). In Fig. 8, the simulated residual stresses σ xx, and σ yy, in the center of the samples, are shown for the rolling passes of processing route (1) using different initial states: “40 mm” and “14 mm” correspond to the states shown in Table 2, “inhomogeneous” is the state shown in Fig. 7, and “1.7 mm zero” means that the initial residual stresses of a 1.7 mm thick sheet were set to zero for all elements in the FEA. The initial stress state was generated by different rolling processes 2.0 mm → 1.7 mm (as described above), and thus, an initial plastic strain of about 0.2 is present. A similar plastic strain was assigned to the sample “1.7 mm zero”. The plastic strain itself is distributed in a characteristic way over and inside the specimen but the maximum deviation from the surface to the inside or from the edges to the center of the sample is 5/100 for the example of the rolling pass from 2 mm → 1.7 mm.
Table 2 Comparison of residual stresses between experiment and FEA for processing route (1). The sample with a thickness of 1.7 mm is considered as the initial state. Sample (center)
σ xx in MPa (experiment/FEA/ deviation)
Initial width: 40 mm 1.7 135/147/12 1.7 → 1.5 68/42/26 1.7 → 1.5 → 1.3 29/34/5 Initial width: 14 mm 1.7 179/180/1 1.7 → 1.5 84/89/5 1.7 → 1.5 → 1.3 41/40/1
σ yy in MPa (experiment/FEA/ deviation) 48/37/11 24/21/3 57/37/20 8/15/7 25/17/8 52/24/28
Fig. 6. Exemplary cut out of a 14 mm sample from a 42 mm sheet (2 mm → 1.7 mm) within the FEA. 4
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
Fig. 7. Evolution of σ xx stress through the rolling passes for an inhomogeneous initial stress state.
Fig. 8. FEA results of the development of the residual stresses in the center of the samples in (σ xx, left) and perpendicular (σ yy, right) to the rolling direction of DC04 sheets using four different initial states and processing route (1).
All different initial stress states converge quickly (marked by the brown bars in Fig. 8), and the residual stresses reach a similar value at a change of the plastic strain of about 0.3 (i.e., φ 0.5). This behavior correlates with the change of the microstructure as described below.
The results prove that no careful adjustment of the initial residualstress state is necessary because the initial state is eliminated even for low plastic strains. This is valid for both simulations and industrial rolling processes.
4. Summary and conclusion
Acknowledgements
It was shown that the residual stresses of the FEA simulations and the experimental values are in very good agreement for cold-rolled DC04. This is also valid for the local distribution and orientation of the residualstress tensors. It was found that there is a good correlation between the forming and the resulting residual stresses for cold-rolled DC04: Only the used material, rolling-pass sequence and the plastic strain will influence the residual stresses, but the initial residual-stress state has no significant influence on the residual-stress state after the deformation. Based on the results presented above, it can be concluded that the first rolling pass after the hot-rolling completely replaces the initial stress state, replacing it with a characteristic one. This state is characterized by high tensile stresses in rolling direction of more than 130 MPa. The tensile stress increase with decreasing sample width because the major deformation takes place in length direction but the total amount of material stays the same due to the constant volume during the forming process. Perpendicular to the rolling direction, there are low tensile stresses < 50 MPa because the increase in width is less dominant. Using other processing routes (not shown here), this characteristic state is also formed and thus a correlation to the change of the microstructure of the samples due to the strong compressive stress during the rolling process is assumed: The first rolling pass leads to significant changes of the initial microstructure. The dislocation density, grain size, crystallite size, roughness, and texture quickly approach their maximum values (published in detail in Ref. [19]). Already for φ 0.5, the major changes have occurred. Related to these changes, the characteristic stress state is formed. Starting from this state, further rolling passes result in residuals stress states that are specific for the rolling-pass sequence.
The authors gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG) for funding this work (grant numbers LA 1274/27-1 and AW 6/27-1) and thank Vanessa Drexler for providing language help. References [1] A. Abvabi, B. Rolfe, P.D. Hodgson, M. Weiss, The influence of residual stress on a roll forming process, Int. J. Mechan. Sci. 101–102 (2015) 124–136. [2] A.H. Mahmoudi, A. Ghasemi, G.H. Farrahi, K. Sherafatnia, A comprehensive experimental and numerical study on redistribution of residual stresses by shot peening, Mater. Des. 90 (2016) 478–487. [3] D. Shang, X. Liu, Y. Shan, E. Jiang, Research on the stamping residual stress of steel wheel disc and its effect on the fatigue life of wheel, Int. J. Fatigue 93 (2016) 173–183. [4] V.F. Skvortsov, A.O. Boznak, A.B. Kim, A.Y. Arlyapov, A.I. Dmitriev, Reduction of the residual stresses in cold expanded thick-walled cylinders by plastic compression, Def. Technol. 12 (2016) 473–479. [5] M.R. Nejad, Using three-dimensional finite element analysis for simulation of residual stresses in railway wheels, Eng. Fail. Anal. 45 (2014) 449–455. [6] P.J. Withers, Residual stress and its role in failure, Rep. Prog. Phys. 70 (2007) 2211–2264. [7] K. Sherafatina, G.H. Farrahi, A.H. Mahmoudi, A. Ghasemi, Experimental measurement and analystic determination of shot peening stresses considering friction and real unloading behavior, Mater. Sci. Eng. A 657 (2016) 309–321. [8] C.D. Moen, T. Igusa, B.W. Schafer, Prediction of residual stresses and strains in coldformed steel members, Thin-Walled Struct. 46 (2008) 1274–1289. [9] S.M. Hassani-Gangaraj, M. Carboni, M. Guagliano, Finite element approach toward an advanced understanding of deep rolling induced residual stresses and an application to railway axles, Mater. Des. 83 (2015) 689–703. [10] K.J. Kang, J.H. Song, Y.Y. Earmme, Fatigue crack growth and closure behavior through a compressive residual stress field, Fatigue Fract. Eng. Mater. Struct. 13 (1990) 1–13.
5
T. Mehner et al.
Finite Elements in Analysis and Design xxx (2017) 1–6
[11] D. Tsivoulas, J. Quinta da Fonseca, M. Tuffs, M. Preuss, Effects of flow forming parameters on the development of residual stresses in Cr-Mo-V steel tubes, Mater. Sci. Eng. A 624 (2015) 193–202. [12] P. Parikin, P. Killen, A. Rafterry, Measurements of residual stresses in cold-rolled 304 stainless steel plates using X-ray diffraction with rietveld refinement method, Atom Indones. 35 (2009) 19–36. [13] M. Giorgi, Residual stress evolution in cold-rolled steels, Int. J. Fatigue 33 (2011) 507–512. [14] N. Hattori, R. Matsumoto, H. Utsunomiya, Residual stress distribution through thickness in cold-rolled aluminum sheet, Key Eng. Mater. 622 (2014) 1000–1007. [15] M. Sedighi, M. Honarpisheh, Investigation of cold rolling influence on near surface residual stresses distribution in explosive welded multilayer, Strength Mater. 44 (2012) 693–698.
[16] M. Weiss, B. Rolfe, P.D. Hodgson, C. Yang, Effect of residual stress on the bending of aluminium, J. Mater. Process. Technol. 212 (2012) 877–883. [17] E. Macherauch, P. Müller, Das sin2ψ-Verfahren der r€ ontgenographischen Spannungsermittlung, Z. angew. Physik 13 (1961) 305–312 (in German). [18] B. Eigenmann, E. Macherauch, R€ ontgenographische Untersuchung von Spannungszust€anden in Werkstoffen Teil III, Mat.-wiss. u. Werkstofftech 27 (1996) 426–437 (in German). [19] T. Mehner, A. Bauer, B. Awiszus, T. Lampke, Macromechanical finite-element simulations for predicting microstructures by experimental calibration, IOP Conf. Ser. Mater. Sci. Eng. 181 (2017), 012036.
6