Prediction of cracking initiation in enamel coated ... - Springer Link

Journal of Mechanical Science and Technology 28 (4) (2014) 1481~1489 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-014-0134-2

Prediction of cracking initiation in enamel coated product and its verification by four-point bending test† Young-Ki Son1, Yu-Long Zhao1, Dae-Cheol Ko2 and Byung-Min Kim3,* 1

Precision Manufacturing System Division, Pusan National University, 30 Jangjeon-Dong, Geumjeong-Gu, Busan, 609-735, Korea 2 Industrial Liaison Innovation Center, Pusan National University, 30 Jangjeon-Dong, Geumjeong-Gu, Busan, 609-735, Korea 3 Department of Mechanical Engineering, Pusan National University, 30 Jangjeon-Dong, Geumjeong-Gu, Busan 609-735, Korea (Manuscript Received June 7, 2013; Revised September 24, 2013; Accepted November 12, 2013)

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Abstract The cracking of enamel coating often occurs because of excessive tensile stress under the product usage environment. The cracks loosen the enamel coating, leading to spalling and peeling and subsequent corrosion of the metal substrate. The cracking is also affected by the residual stress, which complicates the prediction of cracking initiation. The objective of this study is to predict the cracking initiation of the enamel coating by the FE-analysis. The brittle fracture properties of the enamel coating in the FE-analysis were determined by an experimental Vickers indentation fracture (VIF) test and a uniaxial tensile test. The effect of the residual stress of the enamel coating generated by the firing and cooling process on the cracking was considered and analyzed with a four-point bending model by the FEanalysis. To verify the predicted displacement up to the cracking initiation of the enamel from the FE-analysis, a four-point bending test was also performed using the same conditions as the simulation and the results were in agreement with those of the simulation. Keywords: Enamel coating, Brittle fracture; Residual stress; FE-analysis; Four-point bending ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction Enamel coating, which is a substantially vitreous inorganic coating, has excellent properties, including abrasion resistance, chemical resistance, excellent hardness, display of brilliant colors, and resistance to high temperatures [1, 2]. Therefore, this coating is widely applied in the manufacturing of home appliances such as refrigerators, stoves, washing machines, water silos or tanks, and other house-hold utilities. In spite of the large numbers of advantages, the use of enamel coated product has been limited by cracking of enamel coating. Cracking of the enamel is a serious defect that extends from the surface of the enamel to the metal, as shown in Fig. 1. The cracks loosen the enamel coating, which can lead to spalling and peeling of the enamel coating, as well as corrosion of the metal substrate. Therefore, in order to evaluate the service life of enamel coated product, it is important to predict the cracking initiation. In commercial practice, the enamel coated product is manufactured by a firing process in which the enamel frit is bonded to the metal substrate at a target temperature of approximately 830°C for 3 min. Next, the enamel coated product is cooled to *

Corresponding author. Tel.: +82 51 510 3074, Fax.: +82 51 581 3075 E-mail address: [email protected] † Recommended by Associate Editor Dae-Cheol Ko © KSME & Springer 2014

room temperature. During the cooling process, a residual stress is generated because of the mismatch between the coefficient of thermal expansion of the enamel and the metal substrate. In general, residual stress introduced by the manufacturing process plays an important role in stress state of the enamel coating. Thus, the cracking is also affected by the residual stress, which complicates the prediction of cracking initiation. In reviewing previous researches, Zheng and Tang studied the effect of enamel compositions on cracking by oxidation and corrosion [3, 4]. Wang and Shieu evaluated the effect of adherence strength between the enamel coating and the metal substrate on interface cracking [5, 6]. Kim and Yang investigated the cracking propagation according to heat treatment condition during the hot isostatic pressing [7, 8]. However, the prediction of enamel cracking under tensile stress has been rarely discussed. Thus, precise prediction method for crack initiation of enamel coating is required to manufacture the enamel coated product without crack. The aim of this study is to predict the cracking initiation of enamel coating by the FE-analysis. The crack initiation of enamel coating is described by brittle fracture model, which is a fracture criterion for the brittle material such as ceramic, glass, and concrete. The brittle fracture properties of the enamel coating such as failure stress, fracture energy release

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Y.-K. Son et al. / Journal of Mechanical Science and Technology 28 (4) (2014) 1481~1489

Table 1. Chemical composition of steel substrate. Composition wt%

Fe

C

Mn

Ti

Cu

S

P

N

99.675 0.008 0.13 0.110 0.033 0.031 0.011 0.0082

Table 2. Chemical composition of enamel coating. ComposiSiO2 B2O3 K2O Na2O Al2O3 TiO2 CoO CaO Li2O etc. tion wt%

45

15

5.8

7.4

3.5

3.2

1.5

3.2

15.4

Fig. 2. Stress-strain curves of steel at elevated temperatures.

(a) Surface view

(a) Shearing

(b) Washing

(c) Spaying

(d) Firing and cooling

(b) Cross section

Fig. 3. Enamel firing procedure with four-point bending specimen. Fig. 1. Cracking defects of enamel coated product.

rate are determined by an experimental Vickers indentation fracture (VIF) test and a uniaxial tensile test with the rule of mixture. As mentioned above, the residual stress is a very important factor in prediction of crack initiation. Therefore, in order to predict more precisely the cracking initiation of the enamel coating, the effect of the residual stress generated by the firing and cooling process is considered. The FE-analysis is applied to a four-point bending model where displacement up to the cracking initiation of the enamel coating is predicted. To verify the displacement predicted from the FE-analysis, a four-point bending test is also performed using the same condition as the simulation.

2. Properties of steel substrate and enamel coating A sheet of low carbon steel is used as the substrate for the enamel coating, of which the chemical compositions are summarized in Table 1. The stress-strain curves of the steel substrate are obtained from tensile tests at elevated temperatures, as shown in Fig. 2. The tensile strength is 320 MPa and

the elongation is 34% at the room temperature. The chemical compositions of the enamel coating are listed in Table 2, which is mainly composed of SiO2 and B2O3. The thickness of the enamel coating and the steel substrate used in this study are chosen to be 0.2 mm and 0.8 mm, respectively, on the basis of known commercial practices. An enameled steel sheet is prepared by the following procedures: (1) shearing, (2) industrial alcohol washing to remove the steel rust, (3) spraying a single layer of dried enamel powder on one side of the sheet, (4) firing at 830°C for 3min to promote the fusion process, and (5) cooling the sheet in open air. The enamel powders are sprayed to steel sheet by electrostatic spraying at high voltage (70 kV) resulting in an average thickness of 0.2 mm, and then enameled steel is transferred to the furnace for the firing stage. In the firing stage, the enamel powders are melted to a kind of fluid and is bonded to the steel substrate by the chemical reaction at a target temperature about 830°C for 3min. In the cooling stage, the enameled steel is cooled down to room temperature, and then enamel coating changes into the vitreous solid state, as shown in Fig. 3.


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Fig. 5. Stress-strain curves of steel specimens with and without enamel coating.

Fig. 4. Brittle fracture properties of enamel.

3. Brittle fracture criterion of enamel coating 3.1 Determination of failure stress The behavior of the enamel coating under tensile stress at room temperature is that of a brittle material. Therefore, the cracking initiation can be predicted by brittle fracture mechanics model of Hillerborg [9]. A linear relationship of stressdisplacement is determined, as shown in Fig. 4, to illuminate the brittle fracture behavior of the enamel coating. The brittle fracture criteria are composed of failure stress σf and fracture energy release rate G. The coating exhibits a linear elastic behavior with an elastic modulus E (from a to b in Fig. 4) under tensile stress until the stress reaches σf (point b). According to the brittle fracture criteria, the softening behavior after the damage initiation is assumed a linear loss of strength, which is determined by G. The fracture energy release rate required to form a crack initiation, G, can be calculated using Eq. (1): uc

G= ò σ edu uf

(a) Reuslt of uniaxial tensile test

(b) Enameled tensile specimen dimension

(1)

where, σe is the stress in enamel coating, uf and uc are displacement at the initiation of damage and occurrence of crack, respectively. The damage accumulates until the deformation is greater than the failure stress of the material. As the deformation accumulates, the damage also enlarges (from b to c in Fig. 4). Finally, when the stress value of enamel reaches 0, which is shown as point c in Fig. 4, the enamel coating fails and cracking occurs. The critical stress corresponding to the damage initiation is defined as the failure stress of the enamel coating, which can be determined by a uniaxial tensile test. A uniaxial tensile test based on the rule of mixtures is applied in this study to measure the failure stress of the enamel, which is necessary to determine the point of damage initiation in the enamel coating. This test is widely used in research to

Fig. 6. Enamel cracks generated by tensile test.

determine the properties of coating materials, because it is difficult to perform the tensile test with pure coating material specimens [10]. It is difficult to perform tensile tests with freestand enamel coating specimens that are brittle, specimens with enamel bonded to a steel substrate and steel specimens without enamel are both prepared. The dimensions of the specimens are 180 mm in total length with gauge sections of 50 mm and 12.5 mm in width. In the uniaxial tensile test of the enamel coated steel, the specimen is subjected to a uniaxial tensile stress until several cracks are generated in the enamel coating, while the substrate retains its mechanical properties. Stress-strain curves for two types of specimens are shown in Fig. 5, in which cracks in the enamel are visible at a displacement of approximately 0.4 mm, as shown in Fig. 6.

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Interfacial cracking does not occur during loading and unloading because the enamel coating is perfectly bonded to the steel substrate. The stress of the enamel coated steel specimen can be expressed by the rule of mixtures: σ sp =

σ s t s +σ e t e t s +t e

(2)

where, σsp, σs, and σe indicate the stress of the enamel coated steel, steel substrate, and enamel coating, respectively, and ts and te indicate the thickness of the steel substrate and the enamel, respectively. The stress of the enamel coating σe at failure can be calculated as 96.3 MPa from the results of the tensile test. 3.2 Determination of fracture energy release rate There are many methods, such as the single-edge precracked bending (SEPB) [11], single-edge notched bending (SENB) [12], single edge notched tensile (SENT) [13], double cantilever beam (DCB) [14], chevron notch bar (CNB) [15], single cantilever beam (SCB) [16], compact tension (CT) [17], and VIF [18] methods, to determine fracture energy release rate (G) under different conditions and materials. It is difficult to prepare specimens for the SENB, DCB, and SCB methods, and it is impossible to apply jigs or fixtures during the tests using the CT and SENT methods. Therefore, the VIF method is used in this study. The energy released per unit of new crack area for an infinitesimal crack extension is defined by Irwin [19]: G=

πσ 2c (N/mm) E

(3)

where, σ is the critical stress, c is the crack size, and E is the Young’s modulus. The fracture toughness factor, KIC describes the stress state at the crack tip and can be calculated using Eq. (3): K IC = πσ 2c ´ f ( c/w )

(4)

where, f(c/w) is a dimensionless parameter that depends on the geometries of the specimen and the crack. For an infinite plate with a central crack of length 2c, f(c/w) = 1 and thus KIC can be written as: K IC = πσ 2c .

(5)

Combining Eqs. (3) and (4) for G and KIC, respectively, the following relation is yielded: G=

K 2IC . E

(6)

In this study, the value of KIC is measured by the VIF method. 3.3 VIF method An MAT-X1 indentation tester (Japan) is used in this study to determine the value of KIC. For the experiments, a Vickers diamond pyramid indenter is applied to the surface of the enamel coating. After indentation, a diamond-shaped mark is formed with four cracks radiating from the corners. The KIC is calculated by the measurements of the length from the tip of one crack to the tip of the opposite crack and the diagonal length of the mark. Normal loads P of 4.9 N and 9.8 N are employed to obtain clear marks on the surface during the test. The dwell time for the formation of each mark is approximately 10s. The size of the indenter a and the length of radial crack c are measured by an optical microscope (OM), as shown in Fig. 7, in which each length is measured ten times to evaluate an average of KIC. K IC =α(

E 1/2 P ) 3/2 Hν c

(7)

where, α is the indenter geometrical factor, which is assumed to be 0.02 for a Vickers diamond indenter, HV is the Vickers hardness of the enamel (MPa), P is the indenter load (N), and c is the radial crack length (μm). The values of G for the enamel coatings are calculated and listed in Table 3.

4. Cracking initiation prediction by FE-analysis 4.1 FE-modeling of four-point bending Four-point bending tests are widely applied to substrate coating systems to evaluate the adhesive strength between two layers [20] or the mechanical properties of films [21]. In this study, the FE-model is designed based on the four-point bending test, which is simple and provides a region of uniform stress for the Mode I state of tension in order to predict the cracking initiation. Commercial finite element software, ABAQUS, is used as the simulation platform. Also, the firing and cooling processes of creating an enamel coating to obtain the residual stress state are analyzed by FE-analysis. Next, the four-point bending test is simulated to predict the cracking initiation due to deformation-induced tensile stress. The FE-model for the four-point bending simulation is shown in Fig. 8. The dimensions of the enameled specimen in the model are 150 mm × 35 mm, and the rollers are modeled as Φ10 mm × 70 mm. 3D hexahedral eight-node elements are used in this simulation. Because 3D hexahedral eight-node element is recommended for the suitable element type according to ABAQUS Verification Manual when brittle cracking constitutive model is used in ABAQUS. The steel and enamel layers compose two layers of elements. The boundary conditions are imposed on the nodes that are adjacent to the rollers, as shown in Fig. 8. An element deletion


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Table 3. Results of VIF test. Load

Crack length(μm)

KIC (MPa·mm1/2)

G (N/mm)

Case 1

4.9 N

57.6

22.7

0.063

Case 2

9.8 N

108

22.4

0.061

(a) Load = 4.9 N

Fig. 8. FE-model and dimensions of four-point bending.

(b) Load = 9.8 N Fig. 7. Indentation mark of the enamel from VIF test.

technique is used to simulate the cracking initiation of the enamel coating. As an enamel element fails according to the brittle fracture criterion during the simulation, the element loses its properties and the nodes lose their load-carrying capacity. Lastly, the element is removed from the mode I. 4.2 Cracking prediction of enamel coating The enamel coating is a brittle material and often fails under excessive tensile stress during deformation. Residual stress is inevitably generated in the enamel coating after the firing and cooling processes, which affect the deformation performance. Therefore, the residual stress should be considered in the prediction of cracking initiation in enamel coatings. The temperature profile of the process of firing the enamel coating on the substrate is shown in Fig. 9. From point a to point b, the steel substrate sprayed with enamel powder is

Fig. 9. Comparison of thermal expansion and stress state in enamel coating.

placed in the furnace and heated uniformly to the firing temperature. The enamel powder is melted to bisque, which does not generate perceptible stress or strain. Next, the enamel cools, which is represented by the line between point b and point c, as the specimen is removed from the furnace. Because the enamel contracts faster than the steel, it is under tensile stress and the specimen is bent towards the enamel. This condition is maintained until the enamel coating becomes more viscous. As it cools to the equivalent rate temperature, the contraction of the enamel equalizes the contraction of the steel at the peak stress of point c in this figure. As the contraction rate of the enamel decreases abruptly, the stress state drops to the no-strain curve and then to room temperature. This is represented by the line between point c and point d, where the enamel is under compression [22]. In this study, the firing and cooling processes that generate residual stress is analyzed and

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simulated to precisely predict cracking initiation. 4.3 FE-modeling of four-point bending Residual stress in enamel coatings generated during the firing and cooling processes is firstly calculated by FE-analysis. In the simulation, the dimensions of the FE-model are the same as those of the four-point bending model and no boundary constraints are imposed. The firing process is simulated by heating the specimen to a temperature of 830°C, at which the enamel is considered to be bisque. The deformation during the firing process is mainly caused by the thermal expansion of the steel substrate. Then the cooling process is simulated, and the specimen deformation during this process is demonstrated in Fig. 10. The specimen bends towards the steel substrate because of the mismatch between the coefficients of thermal expansion of the enamel and steel substrates. The deformations of five points on the specimen during the simulation are measured. At room temperature, the deformation is approximately 3.4 mm at the center. As mentioned in Sec. 3.2, the enamel coating retains a compressive residual stress after the Table 4. Enamel and steel properties for FE-analysis. Enamel

Steel

Density

2.6E-06 Kg/mm3

7.8E-06 Kg/mm3

Young’s modulus

7.06E+4 MPa

21.0E+4 MPa

Poisson’s ratio

0.23

0.3

Failure stress

96MPa

320 MPa

Energy release rate

0.06 N/mm

-

(a) Deformed shape Fig. 10. Deformation in FE-analysis and test specimen during cooling.

firing and cooling process, while the steel substrate retains a tensile residual stress. An enamel coated steel specimen is prepared under the same conditions as the FE-analysis. The deformation is measured and compared with the FE-analysis results. The deformation tendencies of real specimens are observed to match those in the simulation. The center of the specimen after the firing and cooling processes has a displacement of 3.5 mm, which is in good agreement with the simulation. The FE-model with residual stress after the firing and cooling processes is used for the simulation of the four-point bending model at room temperature, as shown in Fig. 8. The enamel coating elements in this model are located on the side of the fixed support rollers that are subjected to a Mode I stress. The concentration load of a 1 mm/min velocity is assumed to act on the centers of the loading rollers, which are assumed to be rigid. During the test, the effect of friction is ignored, so only compressive forces are transmitted across the interface between the rollers and the specimen. In this simulation, the steel properties do not change while the enamel coating undergoes brittle cracking, as shown in Table 4. The four-point bending simulation is applied to two models with the same dimensions. Case 1 is a model of the residual stress state by simulating the firing and cooling processes. In order to evaluate the effect of the residual stress state on the enamel coating performance, case 2 is a model designed without the residual stress after the same firing and cooling processes. Both cases are simulated under the same conditions to compare the prediction of enamel cracking initiation during bending. The results of the simulation and the maximum principle stress-displacement curves are shown in Fig. 11. The

(b) Displacement


(a) Case 1, displacement = 0.0 mm

(d) Case 2, displacement = 0.0 mm

(b) Case 1, displacement = 2.2 mm

(d) Case 2, displacement = 2.2 mm Crark initiation

(c) Case 1, displacement = 3.8 mm Crark initiation

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(f) Max. principle stress-displacement curve

Fig. 11. Results of FE-analysis for four-point bending model.

specimen in case 1 begins to deform under a compressive stress state, whereas the specimen in case 2 deforms without stress, as shown in Figs. 11(a) and (d). As the displacement of loading rollers reaches 2.2 mm, cracks are generated in the enamel coating for case 2, while no crack is observed for case 1. From the maximum principle stress-displacement curves in Fig. 11(f), the enameled specimen is required more deformation before cracking initiation because of the compressive residual stress generated during the firing and cooling processes. Therefore, the residual stress affects the enamel coating resistance against cracking and the simulation that considered the residual stress better reflects the real deformation behavior of enamel coatings.

5. Verification of FE-analysis by experiment To verify the effectiveness of the cracking prediction of enamel from the FE-analysis, a four-point bending test is performed under the same conditions as the simulation. The specimen is manufactured by the firing process and cooled in open

air. Since the enamel coating is made from enamel powder, it is difficult to control the uniform thickness of enamel coating. Therefore, enameled sheet used in this study is chosen by the measurement of real thickness. If thickness variation of each point is satisfied within 20 μm on the basis of thickness of 200 μm, this specimen is adopted as a test specimen in the verification experiment. After being removed from the furnace, the specimen bends towards the steel substrate because of the residual stress, as mentioned in the previous section. The fourpoint bending test is carried out using a material testing system (MTS) with a load extension program. The dimensions of the specimen and the rollers are equivalent to those in the simulation. The loading rollers move with a velocity of 1 mm/min. The test apparatus is shown in Fig. 12(a). It is difficult to visually detect or observe the micrometer-sized cracks that are initiated in the experiment with an OM. Therefore, in this test, an acoustic emission (AE) system is used to measure the crack occurrence times accurately. During the test, an AE sensor is attached to the enamel coating surface. When a crack occurs, the AE sensor detects the sound from the cracking and

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(b) Pulses on AE monitor

(a) Section 2, displacement = 3.5 mm (a) Test apparatus Fig. 12. Four-point bending test.

(c) Load-displacement curve at crack initiate

transfers the signal to a controller. The signal is calculated and displays as a pulse on a screen. Fig. 12(b) shows the pulses recorded by the AE system during the test. As the specimen deforms under the loading force, pulses are observed on the AE monitor. When the displacement reaches 3.7 mm, relatively large pulses are observed on the AE monitor, shown at pulse A in Fig. 12(b), which indicates that the enamel coating cracked. After initiation, the initial crack propagates while other cracks are initiated, represented by pulse B in Fig. 12(b). The load-displacement curve from the test is presented in Fig. 12(c). The enamel coating inner energy increases as the load increases. As the enamel coating fails, the load decreases. The inner energy at a displacement of 3.7 mm is released when cracks are initiated. To verify the results, the specimen is unloaded and observed with the OM, as shown in Fig. 13. During the test, the stress state of the enameled specimen can be divided into sections. In Sec. 1 and 3, the enamel coating is affected by the shear stress, and only Sec. 2 is under linear tensile stress where the crack is initiated. When the displacement is 3.5 mm in Fig. 13(a), there is no crack on the enamel coating surface. When the displacement reaches 3.7 mm, 2 or 3 cracks are observed. Therefore, a displacement of 3.7 mm is determined as the crack initiation displacement. Comparing the results of the FE-analysis with those obtained from the four-point bending test, the results of the simulation that considered residual stress agrees well with the test results, for both the displacement and the cracking phenomenon of the specimens. The FE-model in this study is roughmeshed to reduce the computational time. If the model were fine-meshed, the location of the cracks in the simulation would be better predicted. Therefore, the FE-analysis suggested in this study can be used for evaluating the brittle fracture properties of enamel and for predicting the occurrence of cracks under tensile stress.

(b) Section 2, displacement = 3.7 mm Fig. 13. Results of four-point bending test.

6. Conclusions An FE-analysis technique was presented to predict the cracking initiation of enamel coatings considering their residual stress history from the firing and cooling processes. From the simulation and the experiment of the four-point bending model, the following conclusions were drawn: (1) The brittle fracture properties of the enamel coating bonded on a low-carbon steel substrate, such as the failure stress σ and the energy release rate G were determined to be σ = 96 MPa and G = 0.06 N/mm by a uniaxial tensile test and a VIF test, respectively. (2) Residual stress is inevitably generated in an enamel coating after the firing and cooling processes. Therefore, it was found that residual stress affected the enamel coating resistance against cracking. The FE-analysis considering residual stress better reflected the real deformation behavior of enamel coatings. (3) The cracking initiation of the enamel coating was predicted at a displacement of 3.8 mm, from the suggested technique with a four-point bending model of the enamel coated steel. Similarly, 2 or 3 cracks were observed at a displacement of 3.7 mm in the four-point bending test. The simulation that considered residual stress was in good agreement with the test


results from the aspect of the displacement at cracking initiation and the cracking phenomenon of the enamel coated steel. (4) The deformation and the fracture behavior of enamel coatings can be predicted by the suggested technique under the consideration of brittle fracture criterion and the residual stress state of the enamel coating. Therefore, this technique can be used as a convenient way to evaluate and prevent crack occurrences, extending the service life of enamel coated products.

Acknowledgment This work was supported by a National Research Foundation of Korea (NRF) grant funded by Korea government (MSIP) (No. 2012R1A5A1048294).

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Young-Ki Son is currently a Ph.D. candidate at the Precision Manufacturing Systems Division at Pusan National University in Busan, South Korea. His current research interests include coated metal forming.

Byung-Min Kim received his B.S., M.S. degrees and Ph.D. from Pusan National University, South Korea, in 1979, 1984 and 1987, respectively. He is currently a professor at the School of Mechanical Engineering at Pusan National University in Busan, Korea.