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Spallation analysis of oxide scale on low carbon steel
Materials Science & Engineering A 676 (2016) 385–394
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Spallation analysis of oxide scale on low carbon steel Jae-min Lee a, Wooram Noh a, Deuk-Jung Kim b, Myoung-Gyu Lee a,n a b
Department of Materials Science and Engineering, Korea University, Seongbuk-Gu, Seoul 136-701, Republic of Korea POSCO R&D Center, Pohang, Gyeongbuk, Republic of Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 24 July 2016 Received in revised form 30 August 2016 Accepted 1 September 2016 Available online 3 September 2016
Failure at the interface between a steel substrate and the oxide scale was analyzed by finite element simulations. Two major stress components along the interface, i.e., tensile normal stress at the peak and shear stress at the inflection point of the undulated interface geometry, were calculated and used for the analysis. The mechanical properties of the oxide scale and steel substrate were experimentally measured by indentation and by uniaxial tensile tests, respectively. The simulations consist of cooling from 1000 °C to room temperature to predict residual stresses accumulated during cooling, followed by additional four-point bending to represent the uncoiling process. The two major stress components were amplified by the roughness of the interface and by the residual stress generated by thermal mismatch between the oxide and the steel substrate during cooling. In addition, the shear stress was proved to be a significant factor for the spallation behavior; this fact had not been well recognized in the previous literature. The finite element simulation showed that the severity of the fracture-inducing stress components increases as the oxide thickness and the period of the idealized undulation decrease; the severity also increases as the amplitude of the roughness increases. & 2016 Elsevier B.V. All rights reserved.
Keywords: Oxide scale Spallation Finite element simulation Stress Interfacial failure
1. Introduction In the hot rolling process, oxide scale is inevitably grown on the material surface because of the nature of its high temperature deformation. Therefore, so-called descaling processes have been used to remove the unnecessary oxide scale. One of the typical ways for the descaling of oxide scale is the high-pressure water jet. In general, the hot rolling process consists of several regions, i.e., a primary descaling box, roughing mills, a secondary descaling box, finishing mills and a run-out table (ROT) for cooling the rolled material. During the ROT, the material is rapidly cooled down to 500–700 °C, followed by coiling and cooling to room temperature in the air for 2 or 3 days [1–4]. The oxide scale grows on the surface of the sheet during its passage through the rolls. The oxide scale grown on the low carbon steel substrate consists of multiple layers of hematite (Fe2O3), magnetite (Fe3O4) and wüstite (FeO) phases [2]. The three constituents of the oxide scale have different properties, and the fraction varies with heat-treatment time, cooling rate, and the ambient atmosphere [2,4,5]. To remove the primary scale formed at the outlet of the furnace, a slab passes through the descaling box before entering the roughing mills. Then, secondary oxide scale grows between continuous rolling passes, which should be removed by high-pressure n
Corresponding author. E-mail address: [email protected] (M.-G. Lee).
http://dx.doi.org/10.1016/j.msea.2016.09.012 0921-5093/& 2016 Elsevier B.V. All rights reserved.
water jets in the descaling box before entering the finishing mills. Despite the descaling process, however, additional oxide scale forms during the passage through successive finishing mills. This oxide scale remains after coiling, and—although it is minor compared to the thickness of the primary oxide scale removed in the prior rolling processes—it should remain firmly attached to the final product to prevent corrosion and to maintain the surface quality. However, as a result of external loading such as uncoiling of the sheet for metal forming operation, unexpected spallation (or interface debonding between the metal substrate and the oxide scale) has been frequently reported. The usual thickness of the primary oxide scales ranges from 20 to 100 mm before passing into the descaling box, and decreases down to 20 mm after the ROT [4]. The spallation or decohesion of the oxide scale in steels has been mainly regarded as a result of interfacial fracture at the interface between the oxide scale and the metal substrate. In addition, the interfacial fracture was accelerated by the microstructural-level destruction of the oxide scale due to prior existing porosities or initial cracks [5–9]. Previous investigations of the mechanism of spallation at the interface usually focused on the normal stress development at the interface by simple deformation such as bending of the sheet. That is, when the traction along the interfacial normal direction is beyond the fracture limit of the interface, spallation is assumed to occur. There are several factors influencing the fracture of the oxide scale at the interface; these include bending curvature during uncoiling, volume fraction and size of the porosity in the
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Fig. 1. Geometrical dimensions of the interface between the oxide scale and the steel substrate: (a) interface fracture along the interface, (b) simplified interfacial geometry and definitions for the three locations of interest.
oxide scale, initial crack size at the interface, residual stress developed during the hot rolling process, scale thickness, and the geometry of the interface. The present study aims to examine the mechanism of oxide scale spallation during simple bending deformation. The analysis was motivated by the fact that the spallation is initiated by the interfacial stresses induced by the geometrical features of the interface between the oxide scale and the low carbon steel substrate. This is a reasonable presumption because the interfacial normal stress is very low in the case of a flat interface without any undulation during bending. However, in this study—unlike the previous researches—the general stress distribution including the shear component acting on the interface is also considered as a potential mechanism of the spallation. The role of shear stress component is particularly investigated considering the classical brittle failure model as a function of both normal and shear stress components on the fracture plane. For this purpose, finite element (FE) modeling was used by considering the variation of the interfacial dimensions such as roughness (or undulation) of the interface, and the scale thickness. For efficient analysis, the realistic interfacial geometry shown in Fig. 1(a) will be simplified as an undulation with constant amplitude and period as schematically drawn in Fig. 1(b). In the figure, three regions at the interface; i.e., the peak, valley, and inflection regions, represent critical spots for the potential fracture regions from the stress components developed during bending. Moreover, the effect of residual stress developed at the interface because of the mismatch of thermal expansions between the oxide scale and the metal substrate will be also investigated because this also influences the magnitude of major traction components at the interface [10]. An intensive numerical sensitivity study is provided by applying the cohesive zone brittle fracture model in ABAQUS finite element software [9,11,12]. To simplify the realistic uncoiling process, a four-point bending configuration is used for all the simulations.
Table 1 Composition of the oxide scale as a function of thickness after hot rolling. Scale thickness (μm)
FeO (%)
Fe3O4 (%)
Fe2O3 (%)
10.3 16.5 18.0
– 10.7 10.3
94.6 89.3 89.4
5.4 – –
Table 2 The flow stress curves of the low carbon steel fitted to combined Swift-Voce model. Plastic property, S-V model Temperature (°C) 25 100 200 300 400 500 600 700 800 900
A (MPa) 559.6 552.6 288.5 406.9 463.6 349.9 162.6 88.2 52.6 66.2
ε¯0 4
5.5e 7.9e 3 1.8e 1 3.3e 2 3.2e 3 4.8 e 3 9.7e 4 4.2e 3 4.5 e 1 5.0e 3
n
B (MPa)
p
0.21 0.23 0.20 0.27 0.20 0.16 0.05 0.04 0.27 0.07
22 44 286 221 90 25 21 6 4 8
32.0 17.9 21.0 30.1 34.2 68.7 33.5 742 777 39.7
* Poisson’s ratio was assumed as 0.3 for whole temperature range
of magnetite (Fe3O4) with a small fraction of hematite (Fe2O3) and wüstite (FeO) layers, depending on the thickness of the scale. Because the steel was slowly cooled down to room temperature in air, the majority of the magnetite layer was observed in the scale [2]. Examples of the oxide scale composition are shown in Table 1. The structure of the oxide scale was measured by X-ray diffraction. 2.2. Mechanical properties of steel substrate and oxide scale
2. Experiments 2.1. Model material The material considered in this study is a low carbon steel sheet, on which an oxide scale was grown with a thickness of approximately 10–18 mm. The chemical composition of the low carbon steel substrate is 0.05C-0.7Mn-0.04Al-0.01Si-0.01P in weight %, and the average grain size was about 10 mm. The thickness of the substrate was 5 mm. The oxide scale mainly consisted
In this study, the oxide scale was assumed to behave as an elastic material, while the substrate exhibits elastic-plastic behavior. Both elastic and plastic properties were assumed as rate insensitive. These mechanical properties will be applied to the finite-element analysis described in the next section. The elastic and plastic properties of the low carbon steel substrate were measured by a uniaxial tensile test from room temperature to 900 °C with a crosshead speed of 1 mm/min, and are listed in Table 2. The plastic properties of the substrate were fitted by the Swift-Voce (S-V) combined type hardening law as follows:
J.-m. Lee et al. / Materials Science & Engineering A 676 (2016) 385–394
σ¯ = A( ε¯ + ε¯0)n + B⎡⎣ 1 − exp( −pε¯)⎤⎦
(1)
where A, ε¯0 , and n are material parameters for the Swift part, while B and p are for the Voce hardening part. The flow stress curves were linearly interpolated from room temperature to 900 °C at intervals of 100 °C. For simplicity, the effect of strain rate is ignored in this study. The elastic properties of the oxide scale were measured by an indentation experiment, from which the Young’s modulus could be obtained by fitting the measured indentation displacementload curve. The indentation test was load controlled with a loading rate of 20000.0 μN/min until the specific depth of 500 nm was reached. The unloading rate was the same as the loading rate. The use of the indentation technique was a practical alternative to direct tensile testing because the oxide scale in this study was too brittle and thin to conduct the standard tensile-based experiment. Note that the indentation of the scale was performed on the crosssectioned surface through the thickness so that the effect of substrate deformation is efficiently ignored. The Young’s modulus could be calculated from the following well-accepted equations [13,14]
Er =
1 π S ⋅ γ 2 Ac
(2)
1 − νi2 1 − νs2 1 = + Er Ei Es
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a Berkovich indenter was assumed in this study. For details of the identification procedure for the Young’s modulus identification can be referred to Oliver and Pharr [13] and Xu and Li [14]. Once the Young’s modulus at room temperature was obtained, its values at higher temperatures were estimated by referring to the similar work [5], where a linear decrease of the elastic modulus with temperature was assumed as follows:
E = ERT ⎡⎣ 1 + n(T − 25)⎤⎦
(4)
where ERT is the elastic modulus at room temperature, n is a constant factor, and T is the temperature in degree Celsius. In this study, because of the difficulty in measuring the modulus at high temperatures, n ¼ 4.7 10 4 /°C was assumed, following the previous result for similar oxide scales [5]. The measured Young’s modulus at room temperature, or ERT is 151.2 GPa. In Fig. 3, the Young’s moduli used for the oxide scale and steel substrate are shown as functions of temperature. 2.3. Thermal properties To investigate the effect of the residual stress by cooling on the spallation, the thermal properties of the steel substrate and the oxide scale need to be identified. The thermal properties necessary
(3)
where Er is the reduced modulus, and S is the slope of the unloading part of the load-indentation depth curve as shown in the Fig. 2(a). Es, Ei, νs , and νi are the elastic moduli of the scale and the indenter, and the Poisson’s ratios of the scale and indenter, respectively. γ is a correction factor that depends on the shape of the indenter tip, and Ac is the projected contact area as illustrated in Fig. 2(b) [13]. The elastic modulus and Poisson’s ratio for the indenter were usually used to be the same as those for diamond: Ei = 1141 GPa and νi = 0.07 [14]; and the Poisson’s ratio of the oxide scale was used νs = 0.29 as in the reference [15]. The contact area is defined as Ac = αhc2 with a correction factor α and a geometrical contact depth hc . For the Berkovich indenter tip used in this study, α was assumed to be 24.5, based on the previous literature [16]. The depth hc was obtained from the relationship hc = hmax − hs where the sink-in depth hs could be related to P
the equation hs = ε⋅ max in which Pmax is the load at the maxS imum depth and ε is a geometrical factor. The value of ε = 0.76 for
Fig. 3. Young’s moduli of both substrate and oxide scale as functions of temperature. The Young’s moduli of the substrate were measured over the temperature range; while Young’s modulus at room temperature only was measured for the oxide scale, and the slope was inferred from the data presented in Ref. [5].
Fig. 2. Schematic views of (a) the load-penetration depth curve and (b) parameters before and after indentation by the Berkovich indenter.
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for the simulation include the coefficient of thermal expansion (CTE), specific heat, and thermal conductivity. In this study, these were obtained from either direct measurement or relevant literature [17,18]. Two types of specimen—with and without oxide scale —were prepared for the measurement of the CTE of oxide scale. The scale was grown by holding the samples for 5 min at 1000 °C in a 500 cc/min argon gas flow in the furnace. The heating rate was 10 °C/min. While the specimen was heated, the difference in the increased lengths of the steels between the samples with and without the oxide scale was measured at prescribed temperatures. Then, the CTE of the oxide scale was calculated from the following equation:
αox =
ΔL − αsL 0ΔT L 0, oxΔT
(5)
where αox, αs, L 0, L 0, ox, ΔL and ΔT are the CTEs of the oxide scale and substrate, the initial lengths of the substrate and oxide scale, the total elongation of the sample, and the temperature change, respectively. Note that the CTE of the substrate is known a priori from an independent test without any oxide scale. Even though the CTE is a function of temperature, for simplicity of analysis, averaged CTEs in two temperature regions are used in this study. The values are listed in Table 3. Note that the temperature range was divided into two at about 850 °C, which is the temperature where a phase transformation occurs. Other thermal properties such as the thermal conductivity and specific heat of the mild steel were obtained from the ASM handbook [18], while those of the oxide scale were measured using a transient hot bridge instrument by assuming 100% Fe3O4 content [20]. The thermal properties are shown in Fig. 4, where the specific heat and thermal conductivity of the low carbon steel and the oxide scale are displayed as functions of temperature. The measured CTE of the steel substrate was higher than that of the oxide scale for the temperature range under consideration, from room temperature to 1000 °C. Therefore, when the sample with the oxide scale is cooled down to room temperature, a compressive stress along the longitudinal direction will be developed at the oxide scale, while a tensile stress occurs in Table 3 The coefficient of thermal expansion (CTE) of the low carbon steel and oxide scale. Temperature (°C)
Low carbon steel
Oxide scale
25–850 850–1000
6.64 μm/m⋅K 13.0 μm/m⋅K
3.19 μm/m⋅K 3.0 μm/m⋅K
the substrate. This is illustrated in Fig. 5(a) and (b) by simple finite element simulation using the measured elastic properties of the substrate and oxide scale. In fact, this mismatch in CTE between the steel substrate and the oxide scale has been regarded as one of the origins of the weakened interface [10,19].
2.4. Finite element modeling To examine the effect of oxide scale-substrate interfacial geometry on the spallation behavior during plastic deformation, a four-point bending simulation was performed by the finite element method. The four-point bending simulation was chosen because this particular deformation mode is associated with a constant pure bending at the center of the specimen. Also, this bending deformation can be regarded as being equivalent to the uncoiling process, during which the spallation of the oxide scale is frequently observed in real applications. The commercial finite element software ABAQUS/Standard version 6.12 was used. The plane strain element with a reduced integration CPE4R was used for both the oxide scale and the metal substrate. To estimate the interfacial fracture between the oxide scale and the metal substrate, a cohesive zone element in ABAQUS, COH2D4, was applied at the interface, from which the stress state can be analyzed [11,21]. This is because the previous experimental studies frequently observed fractures at this region. In the next section, the normal and shear stress components are analyzed from the cohesive elements along the interface, as illustrated in Fig. 6. The total number of element was 232,800 for each condition and a very dense mesh was used near the interface at the center region of the bending specimen as shown in Fig. 6. A displacement of the upper tool by 0.25 mm was prescribed to simulate pure bending of the specimen; this is equivalent to a radius of curvature of 550 mm. The friction between the indenter and the scale was ignored, and hard contact was assumed to be the normal behavior. The simulation model and associated boundary conditions are shown in Fig. 7. In the first step, cooling is applied which induces stress distributions because of thermal expansion mismatch between the oxide scale and the substrate. Then, pure bending is applied with the transferred stress and strain after the cooling. Only half of the model is used for the bending with proper boundary conditions.
Fig. 4. (a) The specific heat and (b) the thermal conductivity of the low carbon steel and the oxide scale as functions of temperature.
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Fig. 5. (a) Longitudinal stress components at both scale and substrate after cooling, and (b) the stress evolution as a function of temperature during the cooling.
Fig. 6. Schematic illustration of the cohesive element at the interface with a local coordinate system.
Fig. 7. Schematic view of the cooling and bending simulation process using the finite element simulations. The upper figures show the cooling process, while the lower figures represent the four-point bending step.
3. Results and discussion Stress distribution at the oxide scale-metal substrate interface after the four-point bending was analyzed. The general observations from the FE simulation can be summarized as follows:
1. The current study confirmed that the stress component normal to the interface was caused by the undulated geometry of the interface, just as the previous experimental work had concluded [6,9]. Fig. 8 shows that almost negligible normal and shear
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Fig. 8. Comparison of stress development between the flat interface and the undulated interface. Normal stress at the peak region and shear stress at the inflection points are compared. The interface parameters are relative to the reference condition.
stresses were calculated for the interface with a flat geometry (i.e., without any undulation at the interface). On the other hand, considerable stresses evolve because of the undulated geometry of the interface. 2. The tensile normal traction appeared at the “peak” region of the undulated interface. In this study, only tensile normal stress was considered as a potential fracture-induced stress component, and compressive normal stress was pre-excluded. 3. The shear traction was maximum at a region between a “peak” and a “valley” of the undulated interface. This region will be called an “inflection” region in this study. Therefore, the analyses in this study will be focused on the stress state in these two regions. In the following, the sensitivity analysis that was conducted on the effects of scale thickness and interfacial roughness (or geometry) will be described and discussed. Moreover, the effect of cooling history before pure bending deformation is also considered. For this purpose, the “reference” condition was set as follows: the scale thickness and the amplitude of the scale were both 20 mm, and the period was 200 mm. For the sensitivity simulations, each parameter is varied from the reference condition.
3.1. Effect of scale thickness Fig. 9(a) and (b) show the normal and shear tractions at the peak and inflection regions, respectively, for three different scale thicknesses: 10, 20, and 30 mm. Both the normal traction at the peak and the absolute value of shear stress at the inflection point decrease as the thickness increases. Note that the shear stress is very small at the peak, and the normal stress is compressive at the inflection region. From this figure, it is estimated that the peak and inflection points are potential spallation regions because of the normal tensile stress and shear stress, respectively; and the likelihood of spallation might increase as the thickness decreases. The smaller tensile normal stress for thicker scale is due to the reduced longitudinal stress from bending because the location of the interface becomes closer to the neutral line where the longitudinal strain vanishes.
3.2. Effect of interfacial roughness The effect of the interfacial roughness parameters on the spallation-inducing stress components was evaluated. The parameters are three amplitudes of 10, 20, and 40 mm, and three periods of 100, 200, and 400 mm of the idealized roughness as defined in Fig. 1. The normal and shear tractions were analyzed at the peak and inflection point for each case. As Fig. 10 shows, both the tensile normal stress at the peak and the absolute value of shear traction at the inflection point increase as the amplitude increases. Again, the shear stress at the peak and the normal stress at the inflection point are ignorable for the spallation. Therefore, the interfacial failure increases as the amplitude of the undulated interface increases. Fig. 11 shows the normal and shear stress components at the interface for different periods. The figure shows that tensile normal stress at the peak increases, but the absolute value of shear stress at the inflection decreases, as the period of the interface increases. The tensile normal stress is saturated when the period is larger than 200 mm, while the magnitude of shear stress is significantly reduced as the period increases to 400 mm. Therefore, the shear stress at the inflection region at smaller period dominates against the normal traction at the peak, while for large period the normal traction at the peak becomes dominant for the spallation. Note that the exact evaluation of the interface failure depends on the fracture criterion based on the stress state, but here the analysis is purely based on the magnitude of the stress components. 3.3. Effect of cooling from high temperature on the stress development along the interface In this section, the effect on the spallation-inducing stress component of residual stress development after cooling is analyzed. For this purpose, the stress components at the peak and inflection point were examined after cooling from 1000 °C to room temperature followed by the bending. The stress states at the interface just after cooling are shown in Fig. 12. The normal stresses at the peak and valley have similar values, although the signs are different. Moreover, the shear stress at the inflection point is larger than the normal component. It is interesting that the cooling itself
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Fig. 9. Normal and shear traction (a) at the “peak” and (b) at the “inflection” regions as functions of scale thickness.
Fig. 10. Normal and shear traction (a) at the “peak” and (b) at the “inflection” region for different amplitudes of interfacial roughness.
Fig. 11. Normal and shear traction (a) at the “peak” and (b) at the “inflection” region for different periods of interfacial roughness.
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Fig. 12. (a) Normal and (b) shear stress components at the peak and inflection point, respectively, after cooling from 1000 °C to room temperature. The interface geometry refers to the reference condition (scale thickness 20 mm, amplitude 20 mm, and period 200 mm).
Fig. 13. (a) Normal and (b) shear stress components at the peak and inflection point, respectively, after cooling and bending. The interface geometry refers to the reference condition (scale thickness 20 mm, amplitude 20 mm, and period 200 mm).
induces considerable stress development at the interface because of the difference in the CTE between the oxide scale and the metal substrate. Fig. 13 shows the stress after cooling and subsequent four-point bending for the reference condition. As a result of the subsequent bending, the magnitudes of the stresses are amplified compared to the cooling-only case. However, the stresses at the peak and valley become significantly asymmetric because of the additional bending after cooling. The same parameters—thickness of oxide scale, amplitude, and period of the undulated interface—were used for the sensitivity analysis. Fig. 14 shows the change of stress components caused by the residual stress after cooling for three different thicknesses. It is notable that the tensile normal traction at the peak and the absolute shear traction at the inflection point increase when the cooling simulation is included, while the trend is the same as the pure bending case. Also, it is observed that the cooling (or prior residual stress) did not influence the shear stress at the peak or the compressive normal stress at the inflection region. Similar trends were observed for the other parameters in Fig. 15; i.e., the amplitude and period of the undulated interface, in terms of the effect of cooling. Therefore, the simulation demonstrates that the prior residual stress after cooling will increase the premature failure at the interface because the stress components dominating the interfacial fracture were increased by the cooling.
3.4. Discussion As results of the sensitivity simulations, it was concluded that the scale thickness, geometrical interface roughness, and thermal residual stress after cooling are factors that influence oxide spallation. A common observation is that the cooling of sheet metal amplifies the development of both normal and shear tractions. Regarding the effect of thickness: The normal tensile traction at the peak and the absolute value of shear traction at the inflection region decrease as the thickness increases. In these simulations, the effect of thickness on the spallation seems to depend on the properties of the scale. This might be so because the results depend on the prior state of the oxide scale where the pre-existing cracks through the thickness enhance the spallation, which usually increases as the thickness increases. However, in the present analysis, it was assumed that there were no pre-existing defects on the oxide scale surface. In terms of bending theory, as the position of the interface approaches the neutral surface, the magnitude of longitudinal stress decreases; this also decreases the normal and shear stress components. Regarding the roughness of the oxide scale: As the roughness increases, the interfacial stresses at the peak and inflection point increase, which might accelerate the decohesion of the oxide scale. In fact, Hiroshi et al. [22,23] reported that the reduction rate affects the roughness of the interface, which might help to prevent the premature oxide scale failure at the interface by reducing the normal and shear stresses. Mougin
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Fig. 14. Comparison of normal and shear traction values at the (a) “peak” and (b) “inflection” regions, respectively, with respect to the scale thickness between with and without consideration of thermal residual stress induced by cooling.
Fig. 15. Comparison of normal and shear traction values at the (a) “peak” and (b) “inflection” regions, respectively, with respect to the scale amplitude of the interface between with and without consideration of thermal residual stress induced by cooling. (c) and (d) present the same comparison of tractions at the same regions, but with respect to the period of the interface.
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et al. experimentally investigated the effect of interface roughness on the spallation of chromia scales thermally grown on pure chromium [7]. However, they only investigated the effect of the normal component of stress along the thickness. On the other hand, according to the present analysis, the shear stress component at the inflection point also will play a significant role in the interfacial failure, and this might compete with the normal stress component. Therefore, further studies should be performed to clarify the dependence of the critical failure stresses on the normal and shear deformation. Then, more advanced simulations predicting the failure at the interface can be conducted by applying appropriate brittle fracture criteria such as the cohesive zone fracture model.
4. Conclusions Finite element simulation was carried out to study the effects of the interface geometry and oxide thickness on the spallation behavior during a bending test. For this purpose, the mechanical properties of the oxide scale and the low carbon steel substrate were considered as elastic and elastic-plastic, respectively. To determine the elastic properties of the oxide scale, an indentation experiment was performed to calculate the Young’s modulus. To determine the plastic properties of the steel substrate, tensile tests were performed at various temperatures. The FE simulations consisted of cooling from 1000 °C to room temperature to predict the residual stress accumulated during cooling, followed by additional four-point bending to mimic the uncoiling process. The stress analysis along the interface showed that both tensile normal and shear components developed as a result of the roughness of the interface (or the undulated shape of the interface), and the residual stress produced by the thermal expansion mismatch between the oxide scale and the steel substrate during cooling amplified the magnitude of the stress components. It is notable that the magnitude of the shear stress might be a significant factor contributing to the spallation. The severity of the fracture-inducing stress components increases as the thickness and period of an idealized undulation decrease, and as the amplitude of the roughness increases. More quantitative analysis to predict the
fracture behavior at the interface might be possible if an accurate determination of the critical fracture stress at the interface can be made; this is in progress as a future work.
Acknowledgement This work was supported by POSCO. MGL appreciates the partial support by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No.2012R1A5A1048294) and (NRF-2014R1A2A1A11052889).
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Spallation analysis of oxide scale on low carbon steel Jae-min Lee a, Wooram Noh a, Deuk-Jung Kim b, Myoung-Gyu Lee a,n a b
Department of Materials Science and Engineering, Korea University, Seongbuk-Gu, Seoul 136-701, Republic of Korea POSCO R&D Center, Pohang, Gyeongbuk, Republic of Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 24 July 2016 Received in revised form 30 August 2016 Accepted 1 September 2016 Available online 3 September 2016
Failure at the interface between a steel substrate and the oxide scale was analyzed by finite element simulations. Two major stress components along the interface, i.e., tensile normal stress at the peak and shear stress at the inflection point of the undulated interface geometry, were calculated and used for the analysis. The mechanical properties of the oxide scale and steel substrate were experimentally measured by indentation and by uniaxial tensile tests, respectively. The simulations consist of cooling from 1000 °C to room temperature to predict residual stresses accumulated during cooling, followed by additional four-point bending to represent the uncoiling process. The two major stress components were amplified by the roughness of the interface and by the residual stress generated by thermal mismatch between the oxide and the steel substrate during cooling. In addition, the shear stress was proved to be a significant factor for the spallation behavior; this fact had not been well recognized in the previous literature. The finite element simulation showed that the severity of the fracture-inducing stress components increases as the oxide thickness and the period of the idealized undulation decrease; the severity also increases as the amplitude of the roughness increases. & 2016 Elsevier B.V. All rights reserved.
Keywords: Oxide scale Spallation Finite element simulation Stress Interfacial failure
1. Introduction In the hot rolling process, oxide scale is inevitably grown on the material surface because of the nature of its high temperature deformation. Therefore, so-called descaling processes have been used to remove the unnecessary oxide scale. One of the typical ways for the descaling of oxide scale is the high-pressure water jet. In general, the hot rolling process consists of several regions, i.e., a primary descaling box, roughing mills, a secondary descaling box, finishing mills and a run-out table (ROT) for cooling the rolled material. During the ROT, the material is rapidly cooled down to 500–700 °C, followed by coiling and cooling to room temperature in the air for 2 or 3 days [1–4]. The oxide scale grows on the surface of the sheet during its passage through the rolls. The oxide scale grown on the low carbon steel substrate consists of multiple layers of hematite (Fe2O3), magnetite (Fe3O4) and wüstite (FeO) phases [2]. The three constituents of the oxide scale have different properties, and the fraction varies with heat-treatment time, cooling rate, and the ambient atmosphere [2,4,5]. To remove the primary scale formed at the outlet of the furnace, a slab passes through the descaling box before entering the roughing mills. Then, secondary oxide scale grows between continuous rolling passes, which should be removed by high-pressure n
Corresponding author. E-mail address: [email protected] (M.-G. Lee).
http://dx.doi.org/10.1016/j.msea.2016.09.012 0921-5093/& 2016 Elsevier B.V. All rights reserved.
water jets in the descaling box before entering the finishing mills. Despite the descaling process, however, additional oxide scale forms during the passage through successive finishing mills. This oxide scale remains after coiling, and—although it is minor compared to the thickness of the primary oxide scale removed in the prior rolling processes—it should remain firmly attached to the final product to prevent corrosion and to maintain the surface quality. However, as a result of external loading such as uncoiling of the sheet for metal forming operation, unexpected spallation (or interface debonding between the metal substrate and the oxide scale) has been frequently reported. The usual thickness of the primary oxide scales ranges from 20 to 100 mm before passing into the descaling box, and decreases down to 20 mm after the ROT [4]. The spallation or decohesion of the oxide scale in steels has been mainly regarded as a result of interfacial fracture at the interface between the oxide scale and the metal substrate. In addition, the interfacial fracture was accelerated by the microstructural-level destruction of the oxide scale due to prior existing porosities or initial cracks [5–9]. Previous investigations of the mechanism of spallation at the interface usually focused on the normal stress development at the interface by simple deformation such as bending of the sheet. That is, when the traction along the interfacial normal direction is beyond the fracture limit of the interface, spallation is assumed to occur. There are several factors influencing the fracture of the oxide scale at the interface; these include bending curvature during uncoiling, volume fraction and size of the porosity in the
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Fig. 1. Geometrical dimensions of the interface between the oxide scale and the steel substrate: (a) interface fracture along the interface, (b) simplified interfacial geometry and definitions for the three locations of interest.
oxide scale, initial crack size at the interface, residual stress developed during the hot rolling process, scale thickness, and the geometry of the interface. The present study aims to examine the mechanism of oxide scale spallation during simple bending deformation. The analysis was motivated by the fact that the spallation is initiated by the interfacial stresses induced by the geometrical features of the interface between the oxide scale and the low carbon steel substrate. This is a reasonable presumption because the interfacial normal stress is very low in the case of a flat interface without any undulation during bending. However, in this study—unlike the previous researches—the general stress distribution including the shear component acting on the interface is also considered as a potential mechanism of the spallation. The role of shear stress component is particularly investigated considering the classical brittle failure model as a function of both normal and shear stress components on the fracture plane. For this purpose, finite element (FE) modeling was used by considering the variation of the interfacial dimensions such as roughness (or undulation) of the interface, and the scale thickness. For efficient analysis, the realistic interfacial geometry shown in Fig. 1(a) will be simplified as an undulation with constant amplitude and period as schematically drawn in Fig. 1(b). In the figure, three regions at the interface; i.e., the peak, valley, and inflection regions, represent critical spots for the potential fracture regions from the stress components developed during bending. Moreover, the effect of residual stress developed at the interface because of the mismatch of thermal expansions between the oxide scale and the metal substrate will be also investigated because this also influences the magnitude of major traction components at the interface [10]. An intensive numerical sensitivity study is provided by applying the cohesive zone brittle fracture model in ABAQUS finite element software [9,11,12]. To simplify the realistic uncoiling process, a four-point bending configuration is used for all the simulations.
Table 1 Composition of the oxide scale as a function of thickness after hot rolling. Scale thickness (μm)
FeO (%)
Fe3O4 (%)
Fe2O3 (%)
10.3 16.5 18.0
– 10.7 10.3
94.6 89.3 89.4
5.4 – –
Table 2 The flow stress curves of the low carbon steel fitted to combined Swift-Voce model. Plastic property, S-V model Temperature (°C) 25 100 200 300 400 500 600 700 800 900
A (MPa) 559.6 552.6 288.5 406.9 463.6 349.9 162.6 88.2 52.6 66.2
ε¯0 4
5.5e 7.9e 3 1.8e 1 3.3e 2 3.2e 3 4.8 e 3 9.7e 4 4.2e 3 4.5 e 1 5.0e 3
n
B (MPa)
p
0.21 0.23 0.20 0.27 0.20 0.16 0.05 0.04 0.27 0.07
22 44 286 221 90 25 21 6 4 8
32.0 17.9 21.0 30.1 34.2 68.7 33.5 742 777 39.7
* Poisson’s ratio was assumed as 0.3 for whole temperature range
of magnetite (Fe3O4) with a small fraction of hematite (Fe2O3) and wüstite (FeO) layers, depending on the thickness of the scale. Because the steel was slowly cooled down to room temperature in air, the majority of the magnetite layer was observed in the scale [2]. Examples of the oxide scale composition are shown in Table 1. The structure of the oxide scale was measured by X-ray diffraction. 2.2. Mechanical properties of steel substrate and oxide scale
2. Experiments 2.1. Model material The material considered in this study is a low carbon steel sheet, on which an oxide scale was grown with a thickness of approximately 10–18 mm. The chemical composition of the low carbon steel substrate is 0.05C-0.7Mn-0.04Al-0.01Si-0.01P in weight %, and the average grain size was about 10 mm. The thickness of the substrate was 5 mm. The oxide scale mainly consisted
In this study, the oxide scale was assumed to behave as an elastic material, while the substrate exhibits elastic-plastic behavior. Both elastic and plastic properties were assumed as rate insensitive. These mechanical properties will be applied to the finite-element analysis described in the next section. The elastic and plastic properties of the low carbon steel substrate were measured by a uniaxial tensile test from room temperature to 900 °C with a crosshead speed of 1 mm/min, and are listed in Table 2. The plastic properties of the substrate were fitted by the Swift-Voce (S-V) combined type hardening law as follows:
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σ¯ = A( ε¯ + ε¯0)n + B⎡⎣ 1 − exp( −pε¯)⎤⎦
(1)
where A, ε¯0 , and n are material parameters for the Swift part, while B and p are for the Voce hardening part. The flow stress curves were linearly interpolated from room temperature to 900 °C at intervals of 100 °C. For simplicity, the effect of strain rate is ignored in this study. The elastic properties of the oxide scale were measured by an indentation experiment, from which the Young’s modulus could be obtained by fitting the measured indentation displacementload curve. The indentation test was load controlled with a loading rate of 20000.0 μN/min until the specific depth of 500 nm was reached. The unloading rate was the same as the loading rate. The use of the indentation technique was a practical alternative to direct tensile testing because the oxide scale in this study was too brittle and thin to conduct the standard tensile-based experiment. Note that the indentation of the scale was performed on the crosssectioned surface through the thickness so that the effect of substrate deformation is efficiently ignored. The Young’s modulus could be calculated from the following well-accepted equations [13,14]
Er =
1 π S ⋅ γ 2 Ac
(2)
1 − νi2 1 − νs2 1 = + Er Ei Es
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a Berkovich indenter was assumed in this study. For details of the identification procedure for the Young’s modulus identification can be referred to Oliver and Pharr [13] and Xu and Li [14]. Once the Young’s modulus at room temperature was obtained, its values at higher temperatures were estimated by referring to the similar work [5], where a linear decrease of the elastic modulus with temperature was assumed as follows:
E = ERT ⎡⎣ 1 + n(T − 25)⎤⎦
(4)
where ERT is the elastic modulus at room temperature, n is a constant factor, and T is the temperature in degree Celsius. In this study, because of the difficulty in measuring the modulus at high temperatures, n ¼ 4.7 10 4 /°C was assumed, following the previous result for similar oxide scales [5]. The measured Young’s modulus at room temperature, or ERT is 151.2 GPa. In Fig. 3, the Young’s moduli used for the oxide scale and steel substrate are shown as functions of temperature. 2.3. Thermal properties To investigate the effect of the residual stress by cooling on the spallation, the thermal properties of the steel substrate and the oxide scale need to be identified. The thermal properties necessary
(3)
where Er is the reduced modulus, and S is the slope of the unloading part of the load-indentation depth curve as shown in the Fig. 2(a). Es, Ei, νs , and νi are the elastic moduli of the scale and the indenter, and the Poisson’s ratios of the scale and indenter, respectively. γ is a correction factor that depends on the shape of the indenter tip, and Ac is the projected contact area as illustrated in Fig. 2(b) [13]. The elastic modulus and Poisson’s ratio for the indenter were usually used to be the same as those for diamond: Ei = 1141 GPa and νi = 0.07 [14]; and the Poisson’s ratio of the oxide scale was used νs = 0.29 as in the reference [15]. The contact area is defined as Ac = αhc2 with a correction factor α and a geometrical contact depth hc . For the Berkovich indenter tip used in this study, α was assumed to be 24.5, based on the previous literature [16]. The depth hc was obtained from the relationship hc = hmax − hs where the sink-in depth hs could be related to P
the equation hs = ε⋅ max in which Pmax is the load at the maxS imum depth and ε is a geometrical factor. The value of ε = 0.76 for
Fig. 3. Young’s moduli of both substrate and oxide scale as functions of temperature. The Young’s moduli of the substrate were measured over the temperature range; while Young’s modulus at room temperature only was measured for the oxide scale, and the slope was inferred from the data presented in Ref. [5].
Fig. 2. Schematic views of (a) the load-penetration depth curve and (b) parameters before and after indentation by the Berkovich indenter.
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for the simulation include the coefficient of thermal expansion (CTE), specific heat, and thermal conductivity. In this study, these were obtained from either direct measurement or relevant literature [17,18]. Two types of specimen—with and without oxide scale —were prepared for the measurement of the CTE of oxide scale. The scale was grown by holding the samples for 5 min at 1000 °C in a 500 cc/min argon gas flow in the furnace. The heating rate was 10 °C/min. While the specimen was heated, the difference in the increased lengths of the steels between the samples with and without the oxide scale was measured at prescribed temperatures. Then, the CTE of the oxide scale was calculated from the following equation:
αox =
ΔL − αsL 0ΔT L 0, oxΔT
(5)
where αox, αs, L 0, L 0, ox, ΔL and ΔT are the CTEs of the oxide scale and substrate, the initial lengths of the substrate and oxide scale, the total elongation of the sample, and the temperature change, respectively. Note that the CTE of the substrate is known a priori from an independent test without any oxide scale. Even though the CTE is a function of temperature, for simplicity of analysis, averaged CTEs in two temperature regions are used in this study. The values are listed in Table 3. Note that the temperature range was divided into two at about 850 °C, which is the temperature where a phase transformation occurs. Other thermal properties such as the thermal conductivity and specific heat of the mild steel were obtained from the ASM handbook [18], while those of the oxide scale were measured using a transient hot bridge instrument by assuming 100% Fe3O4 content [20]. The thermal properties are shown in Fig. 4, where the specific heat and thermal conductivity of the low carbon steel and the oxide scale are displayed as functions of temperature. The measured CTE of the steel substrate was higher than that of the oxide scale for the temperature range under consideration, from room temperature to 1000 °C. Therefore, when the sample with the oxide scale is cooled down to room temperature, a compressive stress along the longitudinal direction will be developed at the oxide scale, while a tensile stress occurs in Table 3 The coefficient of thermal expansion (CTE) of the low carbon steel and oxide scale. Temperature (°C)
Low carbon steel
Oxide scale
25–850 850–1000
6.64 μm/m⋅K 13.0 μm/m⋅K
3.19 μm/m⋅K 3.0 μm/m⋅K
the substrate. This is illustrated in Fig. 5(a) and (b) by simple finite element simulation using the measured elastic properties of the substrate and oxide scale. In fact, this mismatch in CTE between the steel substrate and the oxide scale has been regarded as one of the origins of the weakened interface [10,19].
2.4. Finite element modeling To examine the effect of oxide scale-substrate interfacial geometry on the spallation behavior during plastic deformation, a four-point bending simulation was performed by the finite element method. The four-point bending simulation was chosen because this particular deformation mode is associated with a constant pure bending at the center of the specimen. Also, this bending deformation can be regarded as being equivalent to the uncoiling process, during which the spallation of the oxide scale is frequently observed in real applications. The commercial finite element software ABAQUS/Standard version 6.12 was used. The plane strain element with a reduced integration CPE4R was used for both the oxide scale and the metal substrate. To estimate the interfacial fracture between the oxide scale and the metal substrate, a cohesive zone element in ABAQUS, COH2D4, was applied at the interface, from which the stress state can be analyzed [11,21]. This is because the previous experimental studies frequently observed fractures at this region. In the next section, the normal and shear stress components are analyzed from the cohesive elements along the interface, as illustrated in Fig. 6. The total number of element was 232,800 for each condition and a very dense mesh was used near the interface at the center region of the bending specimen as shown in Fig. 6. A displacement of the upper tool by 0.25 mm was prescribed to simulate pure bending of the specimen; this is equivalent to a radius of curvature of 550 mm. The friction between the indenter and the scale was ignored, and hard contact was assumed to be the normal behavior. The simulation model and associated boundary conditions are shown in Fig. 7. In the first step, cooling is applied which induces stress distributions because of thermal expansion mismatch between the oxide scale and the substrate. Then, pure bending is applied with the transferred stress and strain after the cooling. Only half of the model is used for the bending with proper boundary conditions.
Fig. 4. (a) The specific heat and (b) the thermal conductivity of the low carbon steel and the oxide scale as functions of temperature.
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Fig. 5. (a) Longitudinal stress components at both scale and substrate after cooling, and (b) the stress evolution as a function of temperature during the cooling.
Fig. 6. Schematic illustration of the cohesive element at the interface with a local coordinate system.
Fig. 7. Schematic view of the cooling and bending simulation process using the finite element simulations. The upper figures show the cooling process, while the lower figures represent the four-point bending step.
3. Results and discussion Stress distribution at the oxide scale-metal substrate interface after the four-point bending was analyzed. The general observations from the FE simulation can be summarized as follows:
1. The current study confirmed that the stress component normal to the interface was caused by the undulated geometry of the interface, just as the previous experimental work had concluded [6,9]. Fig. 8 shows that almost negligible normal and shear
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Fig. 8. Comparison of stress development between the flat interface and the undulated interface. Normal stress at the peak region and shear stress at the inflection points are compared. The interface parameters are relative to the reference condition.
stresses were calculated for the interface with a flat geometry (i.e., without any undulation at the interface). On the other hand, considerable stresses evolve because of the undulated geometry of the interface. 2. The tensile normal traction appeared at the “peak” region of the undulated interface. In this study, only tensile normal stress was considered as a potential fracture-induced stress component, and compressive normal stress was pre-excluded. 3. The shear traction was maximum at a region between a “peak” and a “valley” of the undulated interface. This region will be called an “inflection” region in this study. Therefore, the analyses in this study will be focused on the stress state in these two regions. In the following, the sensitivity analysis that was conducted on the effects of scale thickness and interfacial roughness (or geometry) will be described and discussed. Moreover, the effect of cooling history before pure bending deformation is also considered. For this purpose, the “reference” condition was set as follows: the scale thickness and the amplitude of the scale were both 20 mm, and the period was 200 mm. For the sensitivity simulations, each parameter is varied from the reference condition.
3.1. Effect of scale thickness Fig. 9(a) and (b) show the normal and shear tractions at the peak and inflection regions, respectively, for three different scale thicknesses: 10, 20, and 30 mm. Both the normal traction at the peak and the absolute value of shear stress at the inflection point decrease as the thickness increases. Note that the shear stress is very small at the peak, and the normal stress is compressive at the inflection region. From this figure, it is estimated that the peak and inflection points are potential spallation regions because of the normal tensile stress and shear stress, respectively; and the likelihood of spallation might increase as the thickness decreases. The smaller tensile normal stress for thicker scale is due to the reduced longitudinal stress from bending because the location of the interface becomes closer to the neutral line where the longitudinal strain vanishes.
3.2. Effect of interfacial roughness The effect of the interfacial roughness parameters on the spallation-inducing stress components was evaluated. The parameters are three amplitudes of 10, 20, and 40 mm, and three periods of 100, 200, and 400 mm of the idealized roughness as defined in Fig. 1. The normal and shear tractions were analyzed at the peak and inflection point for each case. As Fig. 10 shows, both the tensile normal stress at the peak and the absolute value of shear traction at the inflection point increase as the amplitude increases. Again, the shear stress at the peak and the normal stress at the inflection point are ignorable for the spallation. Therefore, the interfacial failure increases as the amplitude of the undulated interface increases. Fig. 11 shows the normal and shear stress components at the interface for different periods. The figure shows that tensile normal stress at the peak increases, but the absolute value of shear stress at the inflection decreases, as the period of the interface increases. The tensile normal stress is saturated when the period is larger than 200 mm, while the magnitude of shear stress is significantly reduced as the period increases to 400 mm. Therefore, the shear stress at the inflection region at smaller period dominates against the normal traction at the peak, while for large period the normal traction at the peak becomes dominant for the spallation. Note that the exact evaluation of the interface failure depends on the fracture criterion based on the stress state, but here the analysis is purely based on the magnitude of the stress components. 3.3. Effect of cooling from high temperature on the stress development along the interface In this section, the effect on the spallation-inducing stress component of residual stress development after cooling is analyzed. For this purpose, the stress components at the peak and inflection point were examined after cooling from 1000 °C to room temperature followed by the bending. The stress states at the interface just after cooling are shown in Fig. 12. The normal stresses at the peak and valley have similar values, although the signs are different. Moreover, the shear stress at the inflection point is larger than the normal component. It is interesting that the cooling itself
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Fig. 9. Normal and shear traction (a) at the “peak” and (b) at the “inflection” regions as functions of scale thickness.
Fig. 10. Normal and shear traction (a) at the “peak” and (b) at the “inflection” region for different amplitudes of interfacial roughness.
Fig. 11. Normal and shear traction (a) at the “peak” and (b) at the “inflection” region for different periods of interfacial roughness.
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Fig. 12. (a) Normal and (b) shear stress components at the peak and inflection point, respectively, after cooling from 1000 °C to room temperature. The interface geometry refers to the reference condition (scale thickness 20 mm, amplitude 20 mm, and period 200 mm).
Fig. 13. (a) Normal and (b) shear stress components at the peak and inflection point, respectively, after cooling and bending. The interface geometry refers to the reference condition (scale thickness 20 mm, amplitude 20 mm, and period 200 mm).
induces considerable stress development at the interface because of the difference in the CTE between the oxide scale and the metal substrate. Fig. 13 shows the stress after cooling and subsequent four-point bending for the reference condition. As a result of the subsequent bending, the magnitudes of the stresses are amplified compared to the cooling-only case. However, the stresses at the peak and valley become significantly asymmetric because of the additional bending after cooling. The same parameters—thickness of oxide scale, amplitude, and period of the undulated interface—were used for the sensitivity analysis. Fig. 14 shows the change of stress components caused by the residual stress after cooling for three different thicknesses. It is notable that the tensile normal traction at the peak and the absolute shear traction at the inflection point increase when the cooling simulation is included, while the trend is the same as the pure bending case. Also, it is observed that the cooling (or prior residual stress) did not influence the shear stress at the peak or the compressive normal stress at the inflection region. Similar trends were observed for the other parameters in Fig. 15; i.e., the amplitude and period of the undulated interface, in terms of the effect of cooling. Therefore, the simulation demonstrates that the prior residual stress after cooling will increase the premature failure at the interface because the stress components dominating the interfacial fracture were increased by the cooling.
3.4. Discussion As results of the sensitivity simulations, it was concluded that the scale thickness, geometrical interface roughness, and thermal residual stress after cooling are factors that influence oxide spallation. A common observation is that the cooling of sheet metal amplifies the development of both normal and shear tractions. Regarding the effect of thickness: The normal tensile traction at the peak and the absolute value of shear traction at the inflection region decrease as the thickness increases. In these simulations, the effect of thickness on the spallation seems to depend on the properties of the scale. This might be so because the results depend on the prior state of the oxide scale where the pre-existing cracks through the thickness enhance the spallation, which usually increases as the thickness increases. However, in the present analysis, it was assumed that there were no pre-existing defects on the oxide scale surface. In terms of bending theory, as the position of the interface approaches the neutral surface, the magnitude of longitudinal stress decreases; this also decreases the normal and shear stress components. Regarding the roughness of the oxide scale: As the roughness increases, the interfacial stresses at the peak and inflection point increase, which might accelerate the decohesion of the oxide scale. In fact, Hiroshi et al. [22,23] reported that the reduction rate affects the roughness of the interface, which might help to prevent the premature oxide scale failure at the interface by reducing the normal and shear stresses. Mougin
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Fig. 14. Comparison of normal and shear traction values at the (a) “peak” and (b) “inflection” regions, respectively, with respect to the scale thickness between with and without consideration of thermal residual stress induced by cooling.
Fig. 15. Comparison of normal and shear traction values at the (a) “peak” and (b) “inflection” regions, respectively, with respect to the scale amplitude of the interface between with and without consideration of thermal residual stress induced by cooling. (c) and (d) present the same comparison of tractions at the same regions, but with respect to the period of the interface.
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et al. experimentally investigated the effect of interface roughness on the spallation of chromia scales thermally grown on pure chromium [7]. However, they only investigated the effect of the normal component of stress along the thickness. On the other hand, according to the present analysis, the shear stress component at the inflection point also will play a significant role in the interfacial failure, and this might compete with the normal stress component. Therefore, further studies should be performed to clarify the dependence of the critical failure stresses on the normal and shear deformation. Then, more advanced simulations predicting the failure at the interface can be conducted by applying appropriate brittle fracture criteria such as the cohesive zone fracture model.
4. Conclusions Finite element simulation was carried out to study the effects of the interface geometry and oxide thickness on the spallation behavior during a bending test. For this purpose, the mechanical properties of the oxide scale and the low carbon steel substrate were considered as elastic and elastic-plastic, respectively. To determine the elastic properties of the oxide scale, an indentation experiment was performed to calculate the Young’s modulus. To determine the plastic properties of the steel substrate, tensile tests were performed at various temperatures. The FE simulations consisted of cooling from 1000 °C to room temperature to predict the residual stress accumulated during cooling, followed by additional four-point bending to mimic the uncoiling process. The stress analysis along the interface showed that both tensile normal and shear components developed as a result of the roughness of the interface (or the undulated shape of the interface), and the residual stress produced by the thermal expansion mismatch between the oxide scale and the steel substrate during cooling amplified the magnitude of the stress components. It is notable that the magnitude of the shear stress might be a significant factor contributing to the spallation. The severity of the fracture-inducing stress components increases as the thickness and period of an idealized undulation decrease, and as the amplitude of the roughness increases. More quantitative analysis to predict the
fracture behavior at the interface might be possible if an accurate determination of the critical fracture stress at the interface can be made; this is in progress as a future work.
Acknowledgement This work was supported by POSCO. MGL appreciates the partial support by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No.2012R1A5A1048294) and (NRF-2014R1A2A1A11052889).
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