Simulation of the effects of different substrates, temperature, and substrate roughness on the mechanical properties of Al₂O₃ coating as tritium penetration barrier

Simulation of the effects of different substrates, temperature, and substrate roughness on the mechanical properties of Al 2 O 3 coating as tritium penetration barrier 1 corresp first-author Corresponding author, liuze720@sina.com Corresponding author, liuze720@sina.com liuze720@sina.com 2 3 Key Laboratory for Radiation Physics and Technology of Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610064, China Key Laboratory for Radiation Physics and Technology of Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610064, China Chengdu Youfang Technology Co., Ltd, Chengdu 610041, China Chengdu Youfang Technology Co., Ltd, Chengdu 610041, China Southwestern Institute of Physics, Chengdu 610041, China Southwestern Institute of Physics, Chengdu 610041, China Residual thermal stress in the system is a serious problem that affects the application of tritium permeation barrier coatings in fusion reactors. The stress not only determines the adhesion between coating and substrate, but also changes the properties of the material. In this study, finite element analysis (FEA) was used to investigate the relationship between the residual thermal stress and the mechanical properties of Al 2 O 3 tritium penetration barrier systems. Moreover, the residual thermal stress influenced by factors such as different substrates, temperature, and substrate roughness was also analyzed. The calculation showed that the hardness and elastic modulus increased with increasing compressive stress. However, the hardness and elastic modulus decreased with increasing tensile stress. The systems composed of Al 2 O 3 coatings and different substrates exhibited different trends in mechanical properties. As the temperature increased, the hardness and the elastic modulus increased in an Al 2 O 3 /316L stainless steel system; the trend was opposite in an Al 2 O 3 /Si system. Apart from this, the roughness of the substrate surface in the system could magnify the change in hardness and elastic modulus of the coating. Results showed that all these factors led to variation in the mechanical properties of Al 2 O 3 tritium permeation barrier systems. Thus, the detailed reasons for the changes in mechanical properties of these materials need to be analyzed. Finite element analysis Thermal stress Mechanical properties Al 2 O 3 tritium penetration barrier systems Nanoindentation 1. Introduction 1 To safely solve radioactive tritium problems and to optimize the balance of tritium in a fusion reactor, a tritium permeation barrier (TPB) deposited on the surface of structural materials can be used effectively to suppress tritium permeation. Many researchers have investigated different kinds of tritium permeation barriers such as nitrides (TiN, Si 3 N 4 and Fe 2 N) and oxides (Er 2 O 3 , Al 2 O 3 , Y 2 O 3 and Cr 2 O 3 ). The results show that these kinds of coatings are beneficial in minimizing tritium permeation. Among these materials, an Al 2 O 3 coating is considered to be a promising candidate due to its good compatibility with liquid Pb-Li, excellent thermal stability, and high permeation reduction factor (PRF) [ 1 1 – 3 3 1–3 ]. Currently, several fabrication approaches [ 4 4 , 5 5 ] such as plasma spraying (PS), chemical vapor deposition (CVD), and physical vapor deposition (PVD) are used to deposit an Al 2 O 3 TPB coating. Among these methods, the PVD technique is a widely used method to prepare Al 2 O 3 coatings [ 6 6 ]. During the PVD process, the residual stress that exists in the coating can limit the growth of the coating thickness and influence the microstructure and morphology of the coating [ 7 7 ]. The magnitude of residual stress can be affected by various factors such as substrate bias [ 8 8 ], gas precursor [ 9 9 – 10 10 9–10 ], pressure [ 11 11 – 12 12 11–12 ], and power density [ 13 13 ]. A great deal of effort has been made to determine the relationship between the residual stress and the mechanical properties of the material. Mani et al. [ 14 14 ] obtained the residual stress of a TiC coating by measuring the radius of curvature. They also analyzed the hardness of this coating by using a nanoindentation technique. The results showed that the compressive residual stress in the coating has a dominant relationship with its hardness rather than with the grain size. Bai et al. [ 15 15 ] studied the mechanical properties of CN x coatings by nanoindentation experiments. They found that CN x coatings with compressive residual stress have greater hardness and elastic modulus than those without compressive stress. Karlsson et al. [ 16 16 ] measured the residual stress in TiC x N 1- x coatings using an X-ray diffraction method and obtained the elastic modulus of the coatings by nanoindentation. The results showed that the elastic modulus of the coating increases with the increase in negative stress in the coating. Chang et al. [ 17 17 ] studied a Ti coating that was deposited by radio frequency (RF) magnetron sputter, and found that as the tensile stress increases, the elastic modulus of the coating decreases. Mallik et al. [ 18 18 ] investigated the mechanical properties of a Cu coating by a curvature method and found that the hardness in the coating gradually increases with increasing compressive stress. These studies showed that residual stress can affect the mechanical properties of the coating. However, the work focused on the residual stress in the coating and neglected the existence of the substrate, which can lead to the substrate effect [ 19 19 , 20 20 ]. The substrate roughness, which affects the residual thermal stress distribution of the system, has also not been taken into consideration. Apart from this, few research studies explore the relationship between the residual thermal stress and the mechanical properties of the tritium permeation barrier. In this study, the commercial software ANSYS, which is widely employed for solving engineering problems [ 21 21 – 23 23 21–23 ], was used to investigate the relationships between the mechanical properties of an Al 2 O 3 tritium permeation barrier, residual thermal stress, temperature, and substrate roughness. We not only were concerned with the effect of residual thermal stress, but also paid attention to the substrate effect and its roughness. This process consisted of two steps. First, residual thermal stress was generated in the whole system by a change in temperature. Second, nanoindentation experiments were simulated by finite element analysis (FEA) to obtain the hardness and elastic modulus. Factors such as different substrates, temperature, and substrate roughness were then investigated. 2. Method 1 2.1 Theoretical background for nanoindentation 2 Nanoindentation is an efficient technique developed over the decades for measuring the hardness and the elastic modulus of thin coatings [ 24 24 – 27 27 24–27 ]. One of the advantages of this technique is that some of the mechanical properties can be obtained directly from a load-displacement curve. Another advantage is that the test can be performed on a very small scale. After the nanoindentation experiment, the imprint area can be found at the top surface of the specimen. The depth of the imprint is so extremely small that nanoindentation technology is considered to be non-destructive to the material. In addition, depth sensing technology, which replaces the measurement of the imprint area, is used in nanoindentation to measure the mechanical properties of the pressed material. Fischer et al. [ 28 28 ] proposed a polynomial to describe the relationship between the projected area A c and the contact depth h c of the Berkovich indentation. The relationship between A c and h c can be shown as follows: <math display="block" id="M1"><mrow><msub><mi>A</mi><mtext>c</mtext></msub><mo>≈</mo><mn>24.5</mn><msubsup><mi>h</mi><mtext>c</mtext><mtext>2</mtext></msubsup><mo>.</mo></mrow></math> The value of h c can be measured by load-displacement data during nanoindentation experiments, and h c is defined as <math display="block" id="M2"><mrow><msub><mi>h</mi><mtext>c</mtext></msub><mo>=</mo><msub><mi>h</mi><mrow><mi>max</mi></mrow></msub><mo>−</mo><mi>ε</mi><mfrac><mrow><msub><mi>P</mi><mrow><mi>max</mi></mrow></msub></mrow><mi>S</mi></mfrac><mo>,</mo></mrow></math> where S is the contact stiffness, h max is the maximum indentation depth, and ε is a geometry correction factor with a value of 0.75 for the Berkovich indenter. During the indenter unloading process, the relationship between the load P and the depth h can be determined as follows [ 29 29 ]: <math display="block" id="M3"><mrow><mi>P</mi><mo>=</mo><mi>A</mi><msup><mrow><mo stretchy="false">(</mo><mi>h</mi><mo>−</mo><msub><mi>h</mi><mtext>f</mtext></msub><mo stretchy="false">)</mo></mrow><mi>m</mi></msup><mo>,</mo></mrow></math> where A is an indent constant, <math id="M4"><mrow><msub><mi>h</mi><mtext>f</mtext></msub></mrow></math> is the final depth, and m depends on the geometry of the indenter. The elastic modulus of the sample can be derived from the initial unloading contact stiffness S , the formula for which is [ 30 30 ] <math display="block" id="M5"><mrow><mi>S</mi><mo>=</mo><mtext>d</mtext><mi>P</mi><mo>/</mo><mtext>d</mtext><mi>h</mi><mo stretchy="false">(</mo><msub><mi>h</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mi>m</mi><mi>A</mi><msup><mrow><mo stretchy="false">(</mo><msub><mi>h</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>−</mo><msub><mi>h</mi><mi>f</mi></msub><mo stretchy="false">)</mo></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>.</mo></mrow></math> The relationship between the reduced elastic modulus ( E r ), the contact stiffness ( S ), and the contact area ( A c ) was obtained from Sneddon’s work [ 31 31 ]; the formula is <math display="block" id="M6"><mrow><msub><mi>E</mi><mtext>r</mtext></msub><mtext>=</mtext><mfrac><mn>1</mn><mi>β</mi></mfrac><mfrac><mrow><msqrt><mi>π</mi></msqrt></mrow><mn>2</mn></mfrac><mfrac><mi>S</mi><mrow><msqrt><mrow><msub><mi>A</mi><mtext>c</mtext></msub></mrow></msqrt></mrow></mfrac><mo>,</mo></mrow></math> where the value of <math id="M7"><mi>β</mi></math> depends on the geometry of the indenter and is 1.034 for the Berkovich indenter. The reduced elastic modulus E r is expressed as follows: <math display="block" id="M8"><mrow><mfrac><mn>1</mn><mrow><msub><mi>E</mi><mtext>r</mtext></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>−</mo><msup><mi>ν</mi><mn>2</mn></msup></mrow><mi>E</mi></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn><mo>−</mo><msubsup><mi>ν</mi><mtext>i</mtext><mtext>2</mtext></msubsup></mrow><mrow><mi>E</mi><mrow/><mtext>i</mtext></mrow></mfrac></mrow></math> where <math id="M9"><mi>ν</mi></math> and E are the Poisson’s ratio and elastic modulus of the specimen, and ν i and E i are the Poisson’s ratio and elastic modulus of the indenter. King [ 32 32 ] provided a specific method for calculating the reduced elastic modulus E r in a layered system: <math display="block" id="M10"><mrow><mfrac><mn>1</mn><mrow><msub><mi>E</mi><mtext>r</mtext></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>−</mo><msubsup><mi>ν</mi><mtext>i</mtext><mtext>2</mtext></msubsup></mrow><mrow><msub><mi>E</mi><mtext>i</mtext></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn><mo>−</mo><msubsup><mi>ν</mi><mtext>f</mtext><mtext>2</mtext></msubsup></mrow><mrow><msub><mi>E</mi><mtext>f</mtext></msub></mrow></mfrac><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>exp</mi><mo stretchy="false">(</mo><mo>−</mo><mi>α</mi><mi>t</mi><mo>/</mo><msub><mi>h</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>+</mo><mfrac><mrow><mn>1</mn><mo>−</mo><msubsup><mi>ν</mi><mtext>s</mtext><mtext>2</mtext></msubsup></mrow><mrow><msub><mi>E</mi><mtext>s</mtext></msub></mrow></mfrac><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>e</mi><mi>x</mi><mi>p</mi><mo stretchy="false">(</mo><mo>−</mo><mi>α</mi><mi>t</mi><mo>/</mo><msub><mi>h</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo></mrow></math> where t is the coating thickness. The subscripts s and f represent substrate and coating, respectively. <math id="M11"><mi>α</mi></math> is a constant that equals 1.24 in this formula for the Berkovich indenter. 2.2 Analysis model 2 The residual thermal stress is generated from a heating or cooling process during deposition [ 33 33 ]. By using two steps in the FEA, we can investigate the relationship between residual thermal stress and the mechanical properties of an Al 2 O 3 coating. The coating and substrate parameters, such as coefficient of thermal expansion (CTE), Poisson’s ratio, and elastic modulus, affect the residual thermal stress significantly. The residual thermal stress formula is [ 34 34 ] <math display="block" id="M12"><mrow><msub><mi>σ</mi><mrow><mtext>th</mtext></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>E</mi><mtext>c</mtext></msub><mo stretchy="false">(</mo><msub><mi>α</mi><mtext>c</mtext></msub><mo>−</mo><msub><mi>α</mi><mtext>S</mtext></msub><mo stretchy="false">)</mo></mrow><mrow><mn>1</mn><mo>−</mo><msub><mi>ν</mi><mtext>C</mtext></msub></mrow></mfrac><mi>Δ</mi><mi>T</mi><mo>,</mo></mrow></math> where E c is the elastic modulus of the coating, and <math id="M13"><mrow><msub><mi>α</mi><mtext>c</mtext></msub></mrow></math> and <math id="M14"><mrow><msub><mi>α</mi><mi>s</mi></msub></mrow></math> are the coefficients of thermal expansion of coating and substrate, respectively. <math id="M15"><mrow><msub><mi>ν</mi><mtext>c</mtext></msub></mrow></math> is the Poisson’s ratio of the coating and Δ T is the temperature difference. Substrate materials consisting of 316L stainless steel (SS) and of silicon (Si) were used in the model to investigate the substrate effect. All calculations were performed by using two-dimension axisymmetric models. Furthermore, the roughness of substrate surface was described as a sinusoidal function [ 35 35 ]. The simplified axisymmetric coating/substrate model, which contained flat or rough substrates, is shown in Fig. 1 Fig. 1 . For the system with flat substrate, the coating thickness h was 2.2 μm and the substrate thickness H was 50 μm. For the rough substrate surface, the coating thickness h was defined as the distance from the top of the coating to the centerline of the wavy line. The coating and substrate thicknesses were the same in both smooth and rough substrate systems. The amplitude A of the substrate surface was 1.2 μm, and the half wavelength L was 12.5 μm. Lichinchi et al. [ 36 36 ] found that the sharpness of the Berkovich indenter has a great influence on the measurement of mechanical properties in a nanoindentation experiment. The ISO-14577 standard shows that the mean curvature radius of the Berkovich indenter ranges from 150 nm to 200 nm. Moreover, the elastic modulus and Poisson’s ratio of the Berkovich indenter are 1140 GPa and 0.07 respectively. Thus, in the simulation, the indenter was considered as a rigid body containing a cone tip with a 150 nm rounding radius. A Berkovich indenter with a half-angle of 70.3° was used in this axisymmetric model. The indenter was driven into the model in a negative direction along the Y axis to a depth of 0.22 μm and at a speed of 44 nm/s. When the tip of the indenter reached the final position in the coating, the indenter began the unloading process. The large deflection option and Newton-Raphson method were used in the simulation. Fig. 2 (a) Fig. 2 (a) shows the axisymmetric mesh and boundary condition. Due to the axial symmetry of the model, the PLAN182 elements in ANSYS were adopted for the calculation. To ensure the convergence of the calculation, a reasonable mesh was set for the whole system. Fig. 2 (b) Fig. 2 (b) shows that the most deformed region, which is under the indenter of the Al 2 O 3 coating, had the finest mesh. The smallest elements measured 0.03 by 0.03 μm near the contact area between the coating and the indenter. Away from the center of contact, bias elements were set along the axis. A total of 12,474 quadrilateral elements and 38,044 nodes were meshed in the whole system. Fixed constraints were imposed on the left and bottom of the system where the nodes cannot move in the horizontal or vertical direction. All the other nodes could move according to the degrees of freedom. Fig. 3 Fig. 3 shows the residual thermal stress distribution at different press-in positions (A, B, C) of the coating at 100 °C. The coating exhibits residual compressive stress while most of the substrate region shows residual tensile stress. The residual compressive stress, located near the edge region, gradually increases. Compared to positions B and C, the residual thermal stress at the center point A in the coating is relatively uniform. Therefore, to avoid the impact of non-uniform stress on the indenter tip, point A was selected as the nanoindentation press-in position. In this manner, we could obtain the load-displacement curve by FEA. The properties of Al 2 O 3 , Si, and 316L SS were assumed to be isotropic and homogeneous, and the materials were modeled as having perfect elastic-plastic behavior. The mechanical properties of these materials at room temperature (RT = 23 °C) are shown in Table 1 Table 1 . 1 1 Properties 2 1 Materials 1 1   1 1 Al 2 O 3 1 1 316L  SS  1 1 Si 1 1 Poisson’s ratio 1 1 0.22 1 1 0.28 1 1 0.224 1 1  Elastic modulus  (GPa) 1 1 375 1 1 198 1 1 164.4 1 1 Coefficient of thermal expansion (10 -6 ×℃ -1 ) 1 1 8.4 1 1 14.7 1 1 3.2 1 1 Yield strength (MPa) 1 1 15400 1 1 195 1 1 4410 3. Results and discussion 1 3.1 Effect of residual thermal stress on different substrates 2 Fig. 4 Fig. 4 shows the distribution of stress at ± 100 °C for the Al 2 O 3 /316L SS and Al 2 O 3 /Si systems. When the temperature of the Al 2 O 3 /316L SS system rises to 100 °C ( <math id="M16"><mrow><mi>Δ</mi><mi>T</mi><mo>></mo><mn>0</mn></mrow></math> ) from room temperature (RT), the Al 2 O 3 coating shows a negative shear stress. When the temperature drops from RT to -100 °C ( <math id="M17"><mrow><mi>Δ</mi><mi>T</mi><mo><</mo><mn>0</mn></mrow></math> ), the Al 2 O 3 coating shows a positive shear stress. Comparison of the Al 2 O 3 /316L SS system to the Al 2 O 3 /Si system at same temperature shows that the shear stress distribution of the Al 2 O 3 /316L SS system is significantly opposite to that of Al 2 O 3 /Si system, as illustrated in Fig. 3 (c) and (d) Fig. 3 (c) and (d) . The reason is that the CTE of the Al 2 O 3 coating is larger than that of the Si substrate but smaller than that of the 316L SS substrate, as shown in Eq. 8. For simplicity, only the simulation process of nanoindentation at RT is shown in Fig. 5 Fig. 5 . When the equivalent stress reaches the yield strength of the material, plastic deformation begins to occur. The formula for calculating the equivalent stress is <math display="block" id="M18"><mrow><mi>σ</mi><mo>=</mo><msqrt><mrow><mfrac><mrow><msup><mrow><mo stretchy="false">(</mo><msub><mi>σ</mi><mn>1</mn></msub><mo>−</mo><msub><mi>σ</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo stretchy="false">(</mo><msub><mi>σ</mi><mn>2</mn></msub><mo>−</mo><msub><mi>σ</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo stretchy="false">(</mo><msub><mi>σ</mi><mn>1</mn></msub><mo>−</mo><msub><mi>σ</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></mrow><mn>2</mn></mfrac></mrow></msqrt><mo>,</mo></mrow></math> where <math id="M19"><mrow><mi>σ</mi><mrow/><mn>1</mn></mrow></math> , <math id="M20"><mrow><msub><mi>σ</mi><mn>2</mn></msub></mrow></math> , and <math id="M21"><mrow><msub><mi>σ</mi><mn>3</mn></msub></mrow></math> represent the first, second, and third principal stress generated at each point in the sample. As shown in Fig. 5 (b) Fig. 5 (b) , the equivalent stress is nearly 75.61 GPa when the indenter is at the final depth of the loading process. Furthermore, the value of stress is greater than the yield strength of Al 2 O 3 (see Table 1 Table 1 ), which indicates that the stress beneath the tip of the indenter reached the yield limit of the Al 2 O 3 coating before the indenter stopped at the lowest position. As the indenter unloading progresses, the zone of elastic deformation in the coating gradually decreases to zero and plastic deformation results in an indentation footprint, as shown in Fig. 5 (c) Fig. 5 (c) . Fig. 6 Fig. 6 and Fig. 7 Fig. 7 show the effect of residual thermal stress on hardness and elastic modulus of the Al 2 O 3 /316L SS system and Al 2 O 3 /Si system. In both these systems, the changes in the residual thermal stress in the coatings are inversely proportional to their hardness and elastic modulus. For positive shear stress, hardness and elastic modulus decrease with increasing shear stress. The trend is reversed for negative shear stress. These results indicate that the compressive shear stress can improve both the hardness and elastic modulus of the coating. However, the tensile shear stress can reduce the hardness and elastic modulus of the coating. These analysis results are similar to results obtained previously by the present authors [ 15 15 , 16 16 , 42 42 ]. Shear stress can determine the adhesion between the coating and the substrate [ 43 43 ]. For example, compressive shear stress can help to increase the adhesive strength and tensile stress can prompt initiation and propagation of cracks. The properties of the substrate material determine the distribution of residual thermal stress in the coating, which influences to varying degrees the coating’s mechanical properties. From the aspect of residual thermal stress, this is another "substrate effect". As shown in Fig. 6 Fig. 6 and Fig. 7 Fig. 7 , for the 316L SS substrate system, when the coating is subjected to compressive stress, the slopes of hardness and elastic modulus are approximately -1.2×10 9 and -5.07×10 9 , respectively. When the coating is subjected to tensile stress, the slopes of hardness and elastic modulus are approximately -0.23×10 9 and -2.08×10 9 , respectively. For the Si substrate system, when the coating is subjected to compressive stress, the slopes of hardness and elastic modulus are approximately -0.9×10 9 and -1.27×10 9 , respectively. When the coating is subjected to tensile stress, the slopes of hardness and elastic modulus are approximately -0.1×10 8 and -7.3×10 8 , respectively. These data show that, for the same substrate material, the effect of residual thermal stress on the elastic modulus is greater than that on the hardness of the coating. Furthermore, the substrate material determines the varying degrees of hardness and elastic modulus of the coating. Fig. 8 Fig. 8 shows the load-displacement curves for the systems with 316L SS and with Si substrates at different temperatures. For the Al 2 O 3 /316L SS system, the load-displacement curve shifts to the left as the system temperature increases. The trend for the Al 2 O 3 /Si system is opposite. The reason is that the temperature determines the magnitude of the residual thermal stress, which is determined by the CTE between coating and substrate. As the temperature increases, the residual compressive stress in the coating gradually increases in the Al 2 O 3 /316L SS system. Meanwhile, the residual tensile stress in the coating increases in the Al 2 O 3 /Si system as the temperature increases. The residual thermal stress further influences the degree of curve drift. The trends of the load-displacement curves imply that, when the coating is subjected to compressive stress in either Al 2 O 3 /316L SS system or Al 2 O 3 /Si system, the curve shifts to the left (to smaller displacements) and vice versa. Similar observations have been reported by Wei and Yang [ 20 20 ]. The load stress of the Berkovich indenter increases with the increase in temperature to achieve the same displacement, as shown in Fig. 8 (a) Fig. 8 (a) . This result further indicates that the hardness of coating increases with the increase in temperature. The trend is opposite for the Al 2 O 3 /Si system as show in Fig. 8 (b) Fig. 8 (b) . Sarikaya [ 44 44 ] investigated the effect of temperature on an Al 2 O 3 coating deposited on a stainless-steel substrate. He found that, as the temperature increased from 25 °C to 500 °C in the coating/substrate system, the hardness of the coating increased. Thus, the trend obtained in the present study is consistent with the work by Sarikaya. 3.2 between substrate roughness and mechanical properties 2 The effect of residual thermal stress on hardness and elastic modulus is magnified by introducing roughness of the substrate. For simplicity, only the Al 2 O 3 /316L SS systems with different amplitudes at 100 °C are shown here. Fig. 9 Fig. 9 shows the effect of increasing substrate amplitude on residual thermal stress in the systems. In contrast to the Al 2 O 3 /316L SS system with smooth substrate, the existence of surface amplitude results in an increase in residual thermal stress. Furthermore, the residual thermal stress increases with increasing amplitude of the substrate. The region with a positive slope of the sinusoidal curve acts as a stress concentrator. The compressive stress in the edge region of the substrate gradually expands as substrate amplitude increases. Fig. 10 Fig. 10 demonstrates that the hardness and elastic modulus decrease with the increase in amplitude of the substrate. Furthermore, the amplitude of the substrate surface shows an approximately linear relationship with hardness and elastic modulus. The trend of Al 2 O 3 coating hardness change, obtained by FEA, is similar to that in previous work [ 44 44 ]. 4. Conclusion 1 To study the effect of factors such as different substrates, temperature, and substrate roughness on mechanical properties of Al 2 O 3 tritium permeation barrier systems, axisymmetric finite element models were used to simulate the distribution of residual thermal stress and the process of nanoindentation. The main results demonstrate the following: 1. The substrates of different materials, such as 316L SS and Si, influence the mechanical properties of the Al 2 O 3 coating. As the temperature changes, the substrate determines the rate of variability of the coating’s hardness and elastic modulus. 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