Finite element analysis of effect of interfacial bubbles on performance of epoxy coatings under alternating hydrostatic pressure

Journal Pre-proof Finite element analysis of effect of interfacial bubbles on performance of epoxy coatings under alternating hydrostatic pressure Rui Liu, Li Liu, Wenliang Tian, Yu Cui, Fuhui Wang

PII:

S1005-0302(19)30451-7

DOI:

https://doi.org/10.1016/j.jmst.2019.10.008

Reference:

JMST 1848

To appear in:

Journal of Materials Science & Technology

Received Date:

29 June 2019

Revised Date:

21 August 2019

Accepted Date:

21 October 2019

Please cite this article as: Liu R, Liu L, Tian W, Cui Y, Wang F, Finite element analysis of effect of interfacial bubbles on performance of epoxy coatings under alternating hydrostatic pressure, Journal of Materials Science and amp; Technology (2019), doi: https://doi.org/10.1016/j.jmst.2019.10.008

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Article Research Finite element analysis of effect of interfacial bubbles on performance of epoxy coatings under alternating hydrostatic pressure Rui Liu1, 2, Li Liu1,3,*, Wenliang Tian1, Yu Cui1, Fuhui Wang1, 3 1

Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China

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Key Laboratory for Anisotropy and Texture of Materials (MoE), School of

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Materials Science and Engineering, Northeastern University, Shenyang 110819, China

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* Corresponding author. E-mail address: [email protected] (L. Liu).

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[Received 29 June 2019; Received in revised form 21 August 2019; Accepted 21 October 2019]

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The stresses around bubbles formed on a coating/substrate interface under hydrostatic pressure (HP) and alternating hydrostatic pressure (AHP) were calculated using the finite element method. The results reveal that HP

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promotes coating failure but does not mechanically destroy the interface, whereas AHP can provide tensile stress on bubbles formed at the interface

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and accelerate disbonding of the coating. Because of water resistance, a lag time exists for the coating that serves in an AHP environment. The coating can have a better protective performance if the lag time suits the AHP to minimize the impact of the AHP on the interface.

Key words: Finite element method; Organic coatings; Alternating 1

hydrostatic pressure; Interfacial bubbles; Adhesion

1. Introduction The deep ocean continues to attract attention because of the abundant marine

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resources. However, exploration in the deep-ocean environment is often restricted by the pronounced corrosion of structural materials in such environments [1-3]. Epoxy resin-based organic coatings have been effectively and widely used to protect metals from corrosion in marine environments [4-6].

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Unfortunately, coatings suffer dramatic deterioration and premature damage in the deep-sea environment, in sharp contrast to their good protective performance in

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typical marine environments, which is relatively well understood from several studies, including studies of the transport mechanism of water in organic coatings [7, 8], and

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the adhesion properties and corrosion performance at the coating/metal interface [9]. In the deep sea, one of the major factors is hydrostatic pressure (HP), which varies with ocean depth [10-12]. HP has a pronounced impact on coating performance

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compared with other factors such as oxygen level and pH. A series of studies on the failure behaviour of organic coatings in the deep-sea environment have been reported

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in the literatures [13-15]. Liu et al. [13] studied the failure behaviour of an epoxy coating under HP using electrochemical impedance spectroscopy (EIS) measurements.

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The high HP accelerates the failure of the organic coating by enhancing water diffusion rate and the electrochemical reactions. Liu et al. [14] observed that high HP did not degrade the mechanical properties of coatings but instead induced the loss of wet adhesion by forming blisters. The idea that loss of wet adhesion is the first step towards coating failure is controversial, with some researchers suggesting that the loss of adhesion results from the pressure-relief process in the experiment rather than from HP itself. Subsequent studies under an alternating hydrostatic pressure (AHP) 2

condition [16, 17] showed that AHP decreased the protective properties of coatings more rapidly than HP via a “push-and-pull” effect, which promotes bubble formation at the interface between the coatings and the base metal. However, the detailed mechanism of the AHP effect, as well as the possible roles of HP, is not yet clear. Compared with other simulation methods, the finite element method (FEM) is more capable of providing a multi-physical field to solve complex engineering problems such as materials processing more effectively. It has also been used extensively to develop solutions for corrosion and protection problems such as

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cathodic protection [18-21], corrosion behavior [22-28], and coating properties [29-32] in complex environments that are not easily monitored in situ. Legghe et al. [33] and Diodjo et al. [34] reported that a zone exists in which maximal internal stresses are

located at the epoxy/steel interface. Some researchers have observed that corrosion in

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the AHP environments often occurs after disbonding of the coating [16]. The interface is most susceptible to corrosion, and the coating failure can be affirmed when the

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corrosion products are visible on the interface. However, very few studies have attempted to establish a model to explicitly describe the failure originating from the

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blisters in the AHP environment. Fortunately, such FEM-based tools can be adapted to describe conditions in the deep-sea environment, which couples high hydraulic

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pressure and electrochemical reactions. In this work, we attempt to develop a model of the growth of a bubble and the change in the stress distribution at the coating/substrate interface under AHP by means of FEM. The blisters are apparently

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the main reason for the coating failure [14, 16], because their formation at the interface is inevitable and earlier than the failure. The calculations have been

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combined with experimental data to yield useful insights into the coating design suitable for deep-ocean environments. 2. Experimental 2.1. Sample preparation and adhesion tests

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The substrate material was a low-alloy, high-strength steel commonly used in the marine environment. Its composition was (in wt.%): 0.076 C, 0.29 Si, 0.54 Mn, 0.6 Cr, 4.67 Ni, 0.46 Mo, 0.065 V, balance Fe. All specimens were wet ground successively to 600 grit size using SiC paper to attain a required roughness and were then degreased and dewatered with commercial acetone and ethanol to meet the need for practical applications. The epoxy varnish coating consisted of E-44 epoxy resin (bisphenol A, Wuxi Resin Factory, China) as the binder, polyamide (TY-650, Tianjin Yanhai Chemical Co.,

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Ltd., China) as the curing agent and dimethylbenzene as the solvent; these components were combined in a weight proportion of 1:0.8:0.3 for the stoichiometric

reaction. They were mixed and stirred for 1.5 h using a commercial magnetic stirring machine to ensure sufficient mixing. The samples were prepared by brushing paints

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onto the substrate, followed by curing in an oven under the following conditions:

40 °C for 4 h, 60 °C for 20 h, and room temperature (25 V, 30% RH) for 7 d [17]. The

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coating thickness was measured by a hand-held electronic gauge (PosiTector 6000 of Defelsko, United States) at different points for each sample according to ISO

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2080-2007 [35] and an average thickness of 200 ± 10 μm was obtained. The adhesion tests were conducted using a PosiTest pull-off adhesion tester

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according to ASTM D4541-02 [36], to evaluate the strength of adhesion between a coating and substrate. The specimens were cut into plates (30 mm × 30 mm × 2 mm) and painted with the coating. Before immersion in the 3.5% NaCl solution, the edges

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of all the specimens were sealed with a mixture of wax-colophony (volume ratio 1:1) to prevent any possible influence on the test results. The tests were carried out for

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different immersion durations, and measured in air immediately after the specimens were moved from the solution to ensure that the state of the coating/metal interface is similar in measurement to that in solution. At least six parallel experiments were conducted, and the average values were taken as the results. The diameter of the test dolly was Φ20 mm. 2.2. Computational modelling 4

The failure of the coatings reflects the loss of the ability to protect metals from corrosion. In our previous work, we used EIS and adhesion tests to evaluate the protective performance of coatings [13, 14]. When the impedance modulus falls below 108 Ω cm2, the coating loses its protecting ability [37] and corrosion products are observed by the naked eye on the interface [38]. However, the failure of the coatings has already occurred before the fall of the impedance modulus, and we can imply that the coating begins to fail when the water arrives at the interface and the electrochemical reactions start on the metal surface.

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In this work, the failure analysis was focused mainly on the coating/metal interface. To discuss the impact of blisters on disbonding, we modified a formed bubble with a circular border of radius 5 μm at the coating/substrate interface

according to the average experimental size reported in Ref. [13]. Meanwhile, the

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angle between the bubble/coating interface and the bubble/substrate interface was

varied to account for differences in bubble sizes and shapes. Additionally, the epoxy

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(sufficiently mixed resin) was assumed to be homogeneous, isotropic and elastic; its characteristics are shown in Table 1. These properties are based on experiments and

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values reported in the literatures [39, 40].

Because of the manufacturing process, some formed bubbles are inevitably

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present at the interface between a coating and the base metal, even before being immersed into the solution. Additionally, some bubbles are formed during the process of immersion. Thus, two different types of bubbles were considered, as shown in Fig.

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1. The dry bubble with air was under HP, P0 = 10 MPa (HP equals to 1000 m depth in the ocean), and the air pressure variations in the bubble due to deformation were

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ignored. For the wet bubble filled with water, the AHP with the following sinusoidal-type pressure, Pout 

1  1 P0 cos t  P0 2 12 2

(1)

was applied outside the coating given the diving and surfacing of the submersible, where t is the immersion time of the coating. The formation of the higher pressure in 5

the coating is due to the presence of more water locally in the coating, which results from AHP applied on the coating surface. Because it takes time for the water to diffuse to coating/metal interface, the variation of the AHP on the interface always occurs later than the change in the AHP on the coating surface. To describe most of determinants of the water resistance of the coatings (e.g., thickness and diffusion coefficient) and value the lag phenomenon under AHP, a lag time is considered:

t  tdiff  Pout 

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(2)

where tdiff (Pout) is the diffusion time when the water just reaches to the coating/metal

interface from the coating surface referring to Fick’s law [41-43] under Pout, which is

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dependent on the coating thickness and diffusion coefficient. Then, the variation of the pressure applied on the bubble surface (Pin) in a cycle is:

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1) When Pout increases with the value larger than Pin, Pin will increase. 2) After Pout reaches the maximum value, and decreases to the value equal to Pin, Pin will still

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increase until the water content near the coating/metal interface is always higher than that near the coating surface. After that, Pin begins to decrease, and its value is higher than Pout. 3) After Pout reaches the minimum value, and increases to the value equal to

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Pin, Pin still decreases because there are still some areas between the coating/metal interface and the coating surface with the water content less than that at the interface.

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4) When the water content near the coating/metal interface is always less than that near the coating surface, Pin begins to increase with the value less than Pout.

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Accordingly, the AHP on the bubble surface was set as follow: Pin 

1  1 P0 cos  t  t   P0 2 12 2

(3)

COMSOL Multiphysics 5.2 was adapted to solve the problem of stress

distribution of the epoxy coating with a bubble under HP and AHP. Because the volume of the coating was infinitely large in contrast to the space with only one bubble, a periodic boundary was chosen for modelling the stress distribution on the 6

target region. To save the calculation time, the bubble was divided in half by a symmetric boundary. In addition, because only the stress distribution on the coating/metal interface was concerned, the thickness of the coating was set at 50 μm; the stress distribution would become more uniform far from the bubble and would not be changed at the interface with the same pressure when the thickness was greater than 50 μm.

   F  0

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In the elastic regime in this work [44], (4)

where σ is the stress tensor and F is the body force. For isotropic materials, Hooke’s law relates the stress tensor to the strain tensor:

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1

𝜀𝑥 = 𝐸 [𝜎𝑥 − 𝜐(𝜎𝑦 + 𝜎𝑧 )] 1

1

(5)

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𝜀𝑦 = 𝐸 [𝜎𝑦 − 𝜐(𝜎𝑧 + 𝜎𝑥 )]

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𝜀 = [𝜎 − 𝜐(𝜎𝑥 + 𝜎𝑦 )] { 𝑧 𝐸 𝑧

𝐸

𝛾𝑦𝑧 = 2(1+𝑣) 𝜏𝑦𝑧

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𝐸

𝛾𝑧𝑥 = 2(1+𝑣) 𝜏𝑧𝑥

(6)

𝐸

{𝛾𝑥𝑦 = 2(1+𝑣) 𝜏𝑥𝑦

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where E is Young’s modulus; υ is the Poisson’s ratio; σx, σy, and σz are the normal stress components; τxy, τxz, and τyz are the shear stress components; εx, εy, and εz are the

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normal strain components; and γxy, γxz, and γyz are the shear strain components. 3. Results and discussion 3.1. Adhesion tests The adhesion of the coating with respect to immersion time at atmospheric pressure (AP) is shown in Fig. 2. The average value of the dry adhesion was 7

approximately 5.2 MPa before immersion, which can reflect the original adhesion of the coating on the base metal. After the specimens were immersed into water, dry adhesion transformed into wet adhesion. The results demonstrate that the adhesion decreased rapidly at first, and then eventually reached a stable value of 2.3 MPa. Compared to the values reported in Refs. [14, 16, 17], the stable values of adhesion under different HPs are similar because the high HP only accelerates the loss of adhesion. Thus, the dry adhesion value and the stable value measured under the AP

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can be extended to the AHP environment for comparison with the simulation results. 3.2. Effect of hydrostatic pressure on bubbles

A bubble with a circular border of 5 μm radius was set up at the interface

between the epoxy resin and the base metal. Different angles between the

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substrate/bubble interface and the bubble/coating interface have been designed. Such

angle variations represent bubbles of different sizes. Three angles were designed: 30°,

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60° and 90°, depicted as a flat bubble, a middle-shape bubble and a full bubble, respectively. Under these conditions, only a dry bubble formed before immersion was

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considered because after water diffuses into it, the pressure will be balanced inside and outside. Thus, under HP, the stress concentration near the bubble can be observed

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only when it is dry. In addition to the pressure, the size of the bubble also influences the distribution of stress around the bubble. Fig. 3 shows the calculated stress distribution around the dry bubble under the HP of 10 MPa, where the various colours

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represent different stress values. The navy-blue region is the minimum stress zone, 0 MPa, and the dark-red area is the maximum zone with the value of 30 MPa at the

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border, which is the theoretical value calculated according to Ref. [45]:



P0 2

 a2 a4  2+  3  r2 r 4  

(7)

where a is the radius of the bubble, and r is the distance from the center of the bubble. When r = a, σ = 3P0. When the angle is 30° (Fig. 3(a1 and a2)), the stress is concentrated at the border 8

of the bubble, with the maximum stress being approximately 20 MPa, and the minimum stress being approximately 0 MPa on the top of the bubble and 3.58 μm above it. For the angle of 60° (Fig. 3(b1 and b2)), the bubble becomes much larger and higher in the vertical direction. The stress still concentrates at the bottom, reaching approximately 25 MPa, and decreases to 0 MPa at 2.78 μm above the bubble. At the angle of 90°, the bubble reaches the maximum height. The stress decreases slightly from the bottom to the top of the bubble, and the stress concentration is not as obvious as those at lower angles (Fig. 3(c1 and c2)). The maximum stress is

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approximately 18 MPa at the border, whereas the least stress is 0 MPa, which occurs at 2.26 μm above the bubble.

For different shapes of bubbles, the stress gradually decreases with increasing

distance from the bottom, and the maximum stress is always located at the border line,

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whereas the minimum stress is situated above the bubble. The distance from the

minimum stress zone to the top of the bubble decreases with increasing height.

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Meanwhile, the stress distribution varies with the bubble shape, which confirms that the geometrical shape strongly influences the stress concentration.

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Point A was selected on the border line of the bubble shown in Fig. 3(c2), whereas the z and y component stress tensors relative to the angle (θ) were calculated

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for the dry bubble, as shown in Fig. 4. Both the z and the y component fluctuate strongly with variation of the angles because the geometric discontinuities and the

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deformation lead to stress concentration near the bubble. However, the absolute value of the z stress tensor tends to increase with increasing angle, peaking at approximately

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20.7 MPa when θ = 65°, then decreasing to approximately 14.7 MPa at 90°. In addition, the absolute value for the y component stress tensor, which is parallel to the coating/substrate interface, decreases with increasing angle. The stress tensors for all the bubbles are negative, corresponding to the compressive stress resulting from HP. Moreover, the strength of the epoxy varnish coating was investigated when loads were applied to dry coatings [14]. The observation was unexpected that the reduction in strength under 35 atm was slower than the reduction in strength under 1 atm, which 9

implies that the mechanical properties of the epoxy coatings were better under mechanical pressure. Such behaviour has been attributed to a ‘closure effect’ at high pressures [46], which means that HP compresses the dry bubble only before the water diffuses into it. Corresponding to Refs. [47-49], HP can slightly improve the coating failure by pushing water into some hard diffusion areas to accelerate the water diffusion, which makes the aggressive solution reach the metal surface quickly. However, once the dry bubble becomes a wet bubble, the pressure inside and outside the bubble will be equal, similar to the conditions under AP, and the pressure inside

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the bubble can neither accelerate the damage to the bubble nor quickly mechanically destroy the coating/metal interface.

3.3. Effect of alternating hydrostatic pressure on bubble development

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Under the pressure-relief process, the coating is stripped much more easily from the base metal, resulting in the observed bubbles with different sizes and shapes at the

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coating/substrate interface. Diffusion of water into the coatings leads to pressure buildup inside the bubble. However, because of the water resistance, the pressure

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variation inside the bubble lags the change in the AHP outside the coating. The AHP (Eq. 1) was applied outside with P0 = 10 MPa and the period tp = 24 h.

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Meanwhile, another AHP (Eq. (3)) was applied in a wet bubble at the coating/substrate interface. The lag time, Δt, was described for the hysteresis effect of pressure variation. The different angles not only represent the sizes and shapes of

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bubbles but also display the development of a bubble. A representative lag time, Δt = 3 h, was chosen; at this lag time, the value of the

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stress tensor variation with immersion time was more moderate. The corresponding computation results in an immersion cycle are shown in Fig. 5. The stress tensor on the z component at point A varies in a sinusoidal manner repeatedly during the immersion cycles and periodically exhibits compressive and tensile stress, due to the AHPs on coating surface and the bubble repeat the changes in different cycles. The peak stress on the positive direction for the angles of 15°, 30°, 75° and 90° 10

corresponds to 2.5, 2.2, 3.5 and 3.2 MPa, respectively. These results show that the maximal stress tends to occur at larger angles. The time interval when the stress acts as a tensile stress for smaller angles is 7 h, less than 9 h for larger angles. Therefore, the stress concentration under AHP is more serious with a larger angle. The computational results for the relationship between the maximum z component stress and angle compared with experimental findings of adhesion tests are shown in Fig. 6. The maximum stress tensor fluctuates substantially with increasing angle when Δt = 3 h. However, the trend of the stress tensor increases from

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0° to 90°, which is indicative of an accelerated failure during the development of the bubble. From the adhesion tests, the values of adhesion are 5.2 MPa and 2.3 MPa before immersion and after immersion for 7 d. A comparison of the adhesion results

reveals that the maximum stress tensors with angles smaller than 30° are less than the

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stable adhesion value of 2.3 MPa. However, the maximum stress tensors with angles

greater than 30° are greater than 2.3 MPa but less than the dry adhesion value of 5.2

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MPa. Thus, there is a critical angle of 30° under these conditions, revealing that the AHP cannot accelerate disbonding of the coating when the angle is less than 30°.

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When θ = 90° and Δt = 3 h, the variations in the stress distribution and deformation within an AHP cycle around the bubble were calculated; the results are

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shown in Fig. 7. At 0 h (Fig. 7(a)), the bubble was compressed considerably, with the stress concentration localized on the top, middle and bottom of the bubble reaching approximately7 MPa. With increasing distance of the zone from the bubble, the stress

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dropped sharply to 3 MPa above the bubble. When t = 4 h (Fig. 7(b)), the bubble was still under compressive deformation. The stress concentrated on the top and bottom of

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the bubble, reaching 10 MPa and decreasing subsequently to 2 MPa on the side. When t = 8 h (Fig. 7(c)), the stress was still concentrated at the top and bottom of the bubble with a more pronounced value of 10 MPa at the bottom, which decreased slightly to 1 MPa from the bubble to the coating. At 12 h (Fig. 7(d)), the bubble appeared restored to the free state, with the stress distributed quite equally at the maximum value of only 4 MPa on the bottom, whereas the minimum stress is 0 MPa surrounding the bubble. 11

Moreover, in Fig. 7(e), at 16 h, the stress concentration was slightly greater than the stress concentration at 12 h, with a value of 4 MPa at the bottom of the bubble; the location of minimum stress shifted back to the zone above the bubble, where the stress was 0 MPa. Finally, when t = 20 h (Fig. 7(f)), compression of the bubble was obvious, and the stress concentrated on the middle of the compressing bubble, with a moderate value of 7 MPa. The minimum stress was 0 MPa on the top of and above the bubble. In summary, the stress distribution under AHP is considerably more complicated

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than the stress distribution under HP, because the pressure simultaneously loaded on the coating surface and the bubble surface. A wide variation in the stress distribution is observed within an immersion period. In addition to the maximum stress always

locating at the bottom, the stress is also concentrated on the top and middle of the

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bubble, unlike the stress under the HP. Liu et al. [50], from FTIR measurements,

observed that the chemical structures of epoxy coatings did not change under high HP,

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implying that water did not participate in a chemical reaction in the coating under these conditions. Again, our results indicate that the coating damage under AHP is

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much more severe than the coating damage resulting only from the water diffusion. In Fig. 6, the stress tensor on the z component located on the border line is

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relatively small at the initial stages of bubble growth; hence, the stress as a tension is unable to strip the coating from the base metal. The physical interactions between the water and the coating may be the main element at this stage. When the bubble grows

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large enough (the angle more than 30° in Fig. 6), the stress tensor on the border can strip of the coating from the substrate because the tensile force is greater than the

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stable value of the adhesion. AHP acts as the principal effective factor in the latter condition, inducing dramatic deterioration of the coatings. Tian et al. [51] measured the relative impedance modulus of coatings under AHP to illustrate the change in barrier properties over time and found a substantial decrease in the value of the relative impedance modulus from 36 h to 48 h. It indicates there is a critical size for bubbles under AHP, the coating will suddenly fail when most bubbles grow to the 12

critical size. 3.4. Design recommendations for organic coatings under AHP The water-resistance ability of different types of epoxy coatings differs widely, depending on the coating formulation. Such variations might be related to the lag time when different coatings are immersed under AHP. We assumed that for the same coating, the lag time was constant during its service life. Fig. 8 shows a distinct relationship between the maximum stress tensor and the lag time.

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As shown, the stress first increases with increasing lag time between 0 h and 12 h, and then decreases with increasing lag time from 12 h to 24 h. Compared with

experimental results for the adhesion values, the maximum stress is larger than the stable adhesion value and less than the dry value with the lag time between 2.3 h and

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4.5 h and from 19.5 h to 21.7 h. During these intervals, the interface between the coatings and substrate can be destroyed by the AHP after the samples have been

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immersed for a certain time. Within the interval from 4.5 h to 19.5 h, the maximum stress is much greater than the dry adhesion value, which results in serious breakup of

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the interface at the beginning of immersion. However, when the lag time is less than 2.3 h or greater than 21.7 h, the stress is always smaller than the stable adhesion value,

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and the destruction of the interface by the AHP is minimized. On the basis of the lag time, an optimum region, Δt > 21.7 h, is obtained when the coatings with a relatively higher water resistance are considered.

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Tian et al. conducted water absorption and adhesion tests on epoxy glass flake coatings [16] and on commercial pigmented coatings [17]. The water absorption was

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described by the relative mass uptake (Mt/M∞), where Mt is the mass of absorbed water at time t and M∞ is the mass of water absorbed at saturation under AP. Fig. 9(a and b) show the water absorption and the adhesion test results for the epoxy flake coating, respectively. Fig. 9(c and d) display the respective counterparts of the commercial coating. The epoxy glass flake coating with superior water resistance was found to exhibit poorer adhesion, which implies that the AHP environment adversely 13

affects the adhesion performance of a coating with excellent water resistance. On the basis of the foregoing discussion, the stability of coatings deployed in service under AHP is clearly a function of both water diffusion and AHP. Hence, coating design should not only consider the water resistance of the coatings but also focus on the pronounced effect of the AHP on the coating/metal interface. The lag time of a coating is reasonably considered more important when the protective performance is appraised under an AHP environment.

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4. Conclusions

The stress distribution at the interface between the metal and the epoxy coating was studied using the finite element method. The impacts of alternating hydrostatic

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pressure and hydrostatic pressure on the bubble formed at the interface were compared.

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(1) Hydrostatic pressure cannot mechanically destroy the coating/metal interface because it acts as a compressive stress on the dry bubbles.

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(2) Alternating hydrostatic pressure can provide tensile stress on the wet bubbles during every immersion period; consequently, alternating hydrostatic pressure accelerates disbonding of the coating. However, the maximum stress on the bottom of

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wet bubbles can be minimized to less than the stable adhesion value if the lag time is sufficiently large. In this case, alternating hydrostatic pressure can no longer

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accelerate disbonding. Acknowledgements

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This work was financially supported by the National Natural Science Foundation

of China (Nos. 51871049 and 51622106), the National Key R&D Program of China (No. 2017YFB0702303), and A-class pilot of the Chinese Academy of Sciences (No. XDA22010303).

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Fig. 1. Schematic of bubble formed on coating/metal interface under applied stress by

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(a) hydrostatic pressure (HP), and (b) alternating hydrostatic pressure (AHP). For the

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dry bubble (a) under HP, the internal pressure approaches atmospheric pressure.

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Fig. 2. Adhesion test results with immersion time from 0 to 10 d for epoxy glass flake coating/steel samples under atmospheric pressure.

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Fig. 3. Stationary calculated stress distribution around a dry bubble formed on coating/metal interface under a HP of 10 MPa by FEM. Overall views and larger versions around bubble of the angles (θ) between the bubble/coating interface and bubble/metal interface are: (a1) and (a2) with 30°, (b1) and (b2) with 60°, (c1) and (c2) with 90°, respectively.

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Fig. 4. Stationary calculated stress tensor of y and z component as a function of angle at point A (in Fig. 3(c2)) under 10 MPa HP.

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Fig. 5. Time-dependent calculated results of relationship between z component stress tensor and immersion time with 10 MPa AHP in a cycle (24 h) at point A (in Fig. 3(c2)) when Δt = 3 h.

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Fig. 6. Calculated results of relationship between the maximum z component stress tensor in one AHP cycle and angle under 10 MPa AHP at point A (in Fig. 3 (c2)) when Δt = 3 h.

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Fig. 7. Time-dependent stress distribution and deformation around a wet bubble formed on the coating/metal interface during one immersion cycle (24 h) under 10 MPa AHP when θ = 90° and Δt = 3 h: (a) beginning (0 h) of one AHP cycle, (b) within one AHP cycle for 4 h, (c) within one AHP cycle for 8 h, (d) within one AHP cycle for 12 h, (e) within one AHP cycle for 16 h, and (f) within one AHP cycle for 20 h.

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Fig. 8. Calculated results of maximum z component stress tensor in one AHP cycle as a function of the lag time, Δt, under 10 MPa AHP at point A (in Fig. 3(c2)) when θ = 90°.

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Fig. 9. (a) Water absorption (Mt/M∞)-t1/2 curves for epoxy glass flake coating measured in experiments under atmospheric pressure (AP) and AHP [16]. (b) Adhesion test results with immersion time of the epoxy flake coating under AP and AHP [16]. (c) Water absorption (Mt/M∞)-t1/2 curves for a commercial coating, as measured in experiments under AP and AHP [17]. (d) Adhesion test results as a function of immersion time for a commercial coating under AP and AHP [17].

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Table and Figure list: Table 1 Properties of epoxy coatings Young's modulus, E (Mpa)

Density, ρ (kg/m3)

0.33

1200

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1150

Poisson’s ratio, υ

25