**3. Factors influencing reliability of ceramic-metal joint**

as well as to obtain the same aerodynamic characteristics as in the metal rotor. All applica‐ tions have depended upon improved mechanical and thermal properties, such as strength, and

Achieving high integrity joints between ceramics and metals, however, is a challenge. The properties of ceramics that make them attractive may pose major handicaps for joint fabrica‐ tion. Due to the chemical inertness of ceramics, conventional joining methods for metals cannot be used. To obtain adequate bond quality, high temperature and pressure are often required [3] and bonding media with reactive elements have been used [4]. The chemical phenomena occurring at interfaces determine the structure of the interface and hence, its properties. The chemical reaction between the ceramic and the metal may easily initiate bond formation; however, thick brittle reaction layers or intermetallics formed at the interface often cause

Even successful joint formation does not guarantee mechanical soundness of the joint. The inherent differences in physical properties between the ceramic and the metal make it very difficult to find an effective process to join that keeps detailed and comprehensive strength and flexibility. There are two primary factors that cause the reliability issue of joint such as the coefficient of thermal expansion (CTE) mismatch and the difference in the nature of the interface bond. The thermal residual stresses are induced in a joint during cooling due to the CTE mismatch and differing mechanical responses of ceramic and metal. This may lead to a

The aim of this chapter deals with problems of various studies in recent years on the joining between two dissimilar materials. The focus is on the general problems, solutions and factors

There exist many problems between ceramic and metal materials, such as the atom bond configuration, chemical and physical properties, etc. These problems make the joining of ceramics to metals difficult. The following main problems such as ionic bonds and covalent bonds are characteristic atomic bond configurations of ceramic materials. The peripheral electrons are extremely stable. Using the general joining method of fusion welding to join ceramics with metals is almost impossible, and the molten metal does not generally wet on

When joining ceramics to metals with the brazing method, for example, metallization on the ceramic surface is necessary with general inactive brazing filler metal or the use of active brazing alloys in order to get a reliable joint. The thermal expansion coefficients of ceramics are generally much lower than metals. Stress will be generated in the ceramic/metal joint due to the thermal expansion mismatch and will degrade the mechanical properties of the joint and can cause joint cracking immediate after the joining process. The thermal stress in the joint due to the thermal expansion mismatch should be carefully considered when joining ceramic

influencing reliability with different ceramic-metal joining processes.

resistance to fatigue, creep and oxidation.

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premature failure at very low stresses [5].

detrimental influence on joint strength [5, 6].

ceramic surfaces [7].

**2. General problems in ceramic-metal joint**

Joining ceramics to metallic materials is not so easy to be carried out without considerations of several problems originating from the differences in physical and chemical natures between ceramics and metals to be joined [8, 9]. **Figure 1** summarizes the several points, which may cause large scatter in the strength directly. From the microscopic view, interface contact formed by wetting, chemical and physical reaction at interfaces should be of concern in the first place [10]. The cracking in the layer frequently reduces joint strength. Thermal or residual stress in a joint becomes the other important factor. Large thermal stress both in joining process and in services induces flaws into joints. These factors will reflect the distribution of unbonded or weakly bonded is a land like defects on interfaces resulting in substantial reduction in joint strength [11, 12].

**Figure 1.** Schematics of factors influencing on reliability of ceramic/metal joint [1, 12].

The development of residual stresses is one of the major problems in the ceramic/metal joining at the interface when the material is cooled down from the bonding temperature to room temperature [13]. These residual stresses reduce the strength of the bonded material and in some cases lead to catastrophic failure at or near an interface, during the joining process. The mechanical analysis of a joint metal to ceramic is a very complex problem. There are many different characteristics to look at ceramic/metal joints. Depending on the detailed application, some characteristics are more important than others [14]. Therefore, in the following sections, we will focus in the joining problems researches for factors influencing on reliability of ceramic/ metal joint.

stresses caused by a difference in CTE mismatch between two materials joined together. For these stresses to arise from a difference in coefficients of thermal expansion, the temperature may be changing or it may have stabilized. Third, thermal stresses caused by a thermal stresses caused by a temperature gradient resulting in the thermal differential rates within the volume of the material or within the structure and potentially lead to cracking. For these stresses to arise from differential rates of expansion or contraction, the temperature must change and produce a gradient, which may or may not persist. Whether the temperature gradient persists

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Ceramic-metal joints represent an important class of components because of their applications in hostile environments. Examples can be found in different application such as automotive, microelectronics, the aerospace industry or biomedical applications. Generally, a ceramicmetal joint develops a residual stress field, which has its origin in the thermomechanical fabrication process and is due to the difference in CTE between the ceramic and metal (**Figure 2**). Residual stresses have significant effects on the mechanical stability of the interface, since they may cause plastic deformations on the metal side and cracking in the ceramic, thus

or not, the thermally induced stresses from this source persist [17].

compromising the adhesion or even inducing failure of the joint.

**Figure 2.** Comparison of thermal expansion coefficients of metals and ceramics [18].

conditions according to this equation [7]:

The residual stresses produced in the ceramic metal joint could be estimated for full elastic

### **3.1. Material reliability**

The ceramic, because of its inherent brittleness, is the most critical material for obtaining reliable joints [15]. The base properties of the bulk ceramic member are essential. When the properties of the bulk ceramic are not sufficient, the thermal stress simply fractures the ceramic member. Furthermore, the surface condition of the ceramic is also very important for the joint reliability. The ceramics are produced by the different forming methods and a subsequent densification during sintering at high temperatures. Due to high hardness and brittleness of ceramic, any shaping complicated treatment often needs diamond cutting tools and abrasives. Whereas it should avoid sharp edges and corners that may cause the concentration of tensile stress [16]. Moreover, when the ceramic material is ground by a metal bonded diamond wheel, microcracks are introduced at the surface of the ceramic. The size of the microcracks depends on the diamond grit size of the wheel and also on the rate of material removal. The surface damage can initiate major cracks in the ceramic by the thermal stress and, hence, result in an unreliable joint. Therefore, the ceramic surface should be free of damage to obtain high reliability joints. This condition can be met simply by using sintered ceramic materials. However, nearly all sintered ceramic parts over about 2 cm in size should be grounded, because distortion of the parts during the sintering requires grinding for dimensional control. Ground ceramic materials should be treated further to obtain a defect free surface condition. This can be performed by a resintering or lapping process. In the resintering process, the damaged layer is healed through sintering. In the case of the lapping process, the damaged layer is physically removed. It should be mentioned that the thickness removed by the lapping must completely eliminate the surface damages [15].

#### **3.2. Thermal expansion and residual stress**

Residual stresses are stresses that remain in the materials joining after the original cause of the stresses have been removed. Thermal residual stresses play the key role in the mechanical behaviour of various joint materials. Thermal stresses may occur in a heated structure which is rigidly constrained, and also in a structure with temperature gradients. Thermal residual stresses in the ceramic/metal joints can be classified into three groups in accordance with the mechanism that produces them. First, thermal stresses caused by a volumetric change, either expansion or shrinkage, associated with phase transformation. For these stresses arise from a phase change, the temperature must change to cause the phase change. Second, thermal stresses caused by a difference in CTE mismatch between two materials joined together. For these stresses to arise from a difference in coefficients of thermal expansion, the temperature may be changing or it may have stabilized. Third, thermal stresses caused by a thermal stresses caused by a temperature gradient resulting in the thermal differential rates within the volume of the material or within the structure and potentially lead to cracking. For these stresses to arise from differential rates of expansion or contraction, the temperature must change and produce a gradient, which may or may not persist. Whether the temperature gradient persists or not, the thermally induced stresses from this source persist [17].

The development of residual stresses is one of the major problems in the ceramic/metal joining at the interface when the material is cooled down from the bonding temperature to room temperature [13]. These residual stresses reduce the strength of the bonded material and in some cases lead to catastrophic failure at or near an interface, during the joining process. The mechanical analysis of a joint metal to ceramic is a very complex problem. There are many different characteristics to look at ceramic/metal joints. Depending on the detailed application, some characteristics are more important than others [14]. Therefore, in the following sections, we will focus in the joining problems researches for factors influencing on reliability of ceramic/

The ceramic, because of its inherent brittleness, is the most critical material for obtaining reliable joints [15]. The base properties of the bulk ceramic member are essential. When the properties of the bulk ceramic are not sufficient, the thermal stress simply fractures the ceramic member. Furthermore, the surface condition of the ceramic is also very important for the joint reliability. The ceramics are produced by the different forming methods and a subsequent densification during sintering at high temperatures. Due to high hardness and brittleness of ceramic, any shaping complicated treatment often needs diamond cutting tools and abrasives. Whereas it should avoid sharp edges and corners that may cause the concentration of tensile stress [16]. Moreover, when the ceramic material is ground by a metal bonded diamond wheel, microcracks are introduced at the surface of the ceramic. The size of the microcracks depends on the diamond grit size of the wheel and also on the rate of material removal. The surface damage can initiate major cracks in the ceramic by the thermal stress and, hence, result in an unreliable joint. Therefore, the ceramic surface should be free of damage to obtain high reliability joints. This condition can be met simply by using sintered ceramic materials. However, nearly all sintered ceramic parts over about 2 cm in size should be grounded, because distortion of the parts during the sintering requires grinding for dimensional control. Ground ceramic materials should be treated further to obtain a defect free surface condition. This can be performed by a resintering or lapping process. In the resintering process, the damaged layer is healed through sintering. In the case of the lapping process, the damaged layer is physically removed. It should be mentioned that the thickness removed by the lapping must completely

Residual stresses are stresses that remain in the materials joining after the original cause of the stresses have been removed. Thermal residual stresses play the key role in the mechanical behaviour of various joint materials. Thermal stresses may occur in a heated structure which is rigidly constrained, and also in a structure with temperature gradients. Thermal residual stresses in the ceramic/metal joints can be classified into three groups in accordance with the mechanism that produces them. First, thermal stresses caused by a volumetric change, either expansion or shrinkage, associated with phase transformation. For these stresses arise from a phase change, the temperature must change to cause the phase change. Second, thermal

metal joint.

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**3.1. Material reliability**

eliminate the surface damages [15].

**3.2. Thermal expansion and residual stress**

Ceramic-metal joints represent an important class of components because of their applications in hostile environments. Examples can be found in different application such as automotive, microelectronics, the aerospace industry or biomedical applications. Generally, a ceramicmetal joint develops a residual stress field, which has its origin in the thermomechanical fabrication process and is due to the difference in CTE between the ceramic and metal (**Figure 2**). Residual stresses have significant effects on the mechanical stability of the interface, since they may cause plastic deformations on the metal side and cracking in the ceramic, thus compromising the adhesion or even inducing failure of the joint.

**Figure 2.** Comparison of thermal expansion coefficients of metals and ceramics [18].

The residual stresses produced in the ceramic metal joint could be estimated for full elastic conditions according to this equation [7]:

$$
\sigma\_{\text{C}} = \frac{\Delta\alpha \times \Delta T \times E\_{\text{m}} \times E\_{\text{C}}}{(E\_{\text{m}} + E\_{\text{C}})} \tag{1}
$$

mismatch. However, it occasionally happens that some specimen will be strong but the other will be weak even if they are the same kind [20]. This depends on the presence and distribution of internal flaws induced by residual stress during joining. The strengths of the Si3N4/invar (iron-nickel alloy) and Si3N4/kovar (iron-nickel-cobalt alloy) joints, which are differing in the

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The thermal stress may be relieved by two different methods according to Lemus-Ruiz's thesis [23]. One method inserts a metal with approximately the same thermal expansion coefficient as that of the ceramic to decrease the magnitude of thermal stress generated, while the other method involves thermal stress relief by using a ductile metal that easily develops plastic deformation under thermal stress. These two methods may also be employed in combination. **Figure 4** shows a schematic illustration of thermal stress at a joint interface and the mode of cracking due to difference of thermal expansion coefficient [24]. When the thermal expansion coefficient, *α*<sup>C</sup> of the ceramic is smaller than that of the metal, *α*M, the ceramic is subjected to tension stress and cracks at the edges, as schematically illustrated in **Figure 4a**, on the other hand, when the thermal expansion coefficient, *α*M, of the metal is smaller than that of the ceramic, *α*C; tensile stress acts on the core of the ceramic and cracks the ceramic, not at the

**Figure 4.** Schematic illustration of thermal stress in joint interface and mode of cracking due to difference of thermal

To overcome for reducing the residual stress mentioned above, induced by the mismatch of the thermal expansion coefficient between the materials to be joined, the following methods can be used as reported by Zhou [7]: (1) Using soft filler metals, the soft filler metals have low yield strength and could release the residual stress. (2) Using soft interlayer, the residual stress could be reduced by the elastic and plastic deformation of an interlayer, e.g. when using Al or Cu as interlayer, the residual stress is decreased. According to Eq. (1), the residual stress will decrease with Young's model *E*m decreasing. (3) Using hard metals of which the thermal

amplitude of thermal stress, were examined statistically [21].

edges, but transversely at the core, as shown in **Figure 4b**.

expansion coefficient [23, 24].

where *σ*<sup>C</sup> is the residual stress after the joint cools to room temperature, Δ*α* is the difference of thermal expansion coefficient between materials, Δ*T* is the difference between joining tem‐ perature and room temperature, *E*m is a Young's model of metal, *E*C is a Young's model of ceramic. If the thermal stresses in the metal exceed its yield strength, the residual stresses in the joint could be determined by [7]:

$$
\sigma\_{\rm C} = \sigma\_{\rm my} + \Delta\alpha\Delta T.E\_{\rm mp} \tag{2}
$$

where *E*mp is the linear strain hardening coefficient and *σ*my is the yield strength of the metal (linear elastic-linear plastic conditions are assumed).

The distribution of thermal residual stress is not uniform in the joint and even along the interface between these different materials. The concentration of thermal stress becomes more intense with the proximity of the interface [19]. The most harmful effect of thermal stress is caused by the tensile stress at the interface or in the ceramic. The direction of the maximum tensile stresses is mainly perpendicular to the interface and the free surface direction, causing the crack opening and failure occurs. The breadth of thermal residual stress depends on the shape and dimension of the ceramic/metal interface [20]. For example, the diameter depend‐ ence of the thermal stress of the Si3N4/invar alloy joint measured on the surface near the interface as shown in **Figure 3**. The larger diameter leads to generate more thermal residual stress. It is also noteworthy that stress concentration at the corner of the rectangular bond face joint is more serious. The joint strength tends to decrease with increasing thermal expansion

**Figure 3.** Effect of size and shape of bond face of residual stress on Si3N4/invar alloy joints. The residual stress was vertical to the interface on the Si3N4 surface [22].

mismatch. However, it occasionally happens that some specimen will be strong but the other will be weak even if they are the same kind [20]. This depends on the presence and distribution of internal flaws induced by residual stress during joining. The strengths of the Si3N4/invar (iron-nickel alloy) and Si3N4/kovar (iron-nickel-cobalt alloy) joints, which are differing in the amplitude of thermal stress, were examined statistically [21].

m C

*E E* (1)

C my = + Δ .Δ . *T E*mp (2)

m C

where *σ*<sup>C</sup> is the residual stress after the joint cools to room temperature, Δ*α* is the difference of thermal expansion coefficient between materials, Δ*T* is the difference between joining tem‐ perature and room temperature, *E*m is a Young's model of metal, *E*C is a Young's model of ceramic. If the thermal stresses in the metal exceed its yield strength, the residual stresses in

> a

where *E*mp is the linear strain hardening coefficient and *σ*my is the yield strength of the metal

The distribution of thermal residual stress is not uniform in the joint and even along the interface between these different materials. The concentration of thermal stress becomes more intense with the proximity of the interface [19]. The most harmful effect of thermal stress is caused by the tensile stress at the interface or in the ceramic. The direction of the maximum tensile stresses is mainly perpendicular to the interface and the free surface direction, causing the crack opening and failure occurs. The breadth of thermal residual stress depends on the shape and dimension of the ceramic/metal interface [20]. For example, the diameter depend‐ ence of the thermal stress of the Si3N4/invar alloy joint measured on the surface near the interface as shown in **Figure 3**. The larger diameter leads to generate more thermal residual stress. It is also noteworthy that stress concentration at the corner of the rectangular bond face joint is more serious. The joint strength tends to decrease with increasing thermal expansion

**Figure 3.** Effect of size and shape of bond face of residual stress on Si3N4/invar alloy joints. The residual stress was

*TE E*

( )

Δ Δ

´´´ <sup>=</sup> <sup>+</sup>

a

C

ss

s

the joint could be determined by [7]:

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vertical to the interface on the Si3N4 surface [22].

(linear elastic-linear plastic conditions are assumed).

The thermal stress may be relieved by two different methods according to Lemus-Ruiz's thesis [23]. One method inserts a metal with approximately the same thermal expansion coefficient as that of the ceramic to decrease the magnitude of thermal stress generated, while the other method involves thermal stress relief by using a ductile metal that easily develops plastic deformation under thermal stress. These two methods may also be employed in combination. **Figure 4** shows a schematic illustration of thermal stress at a joint interface and the mode of cracking due to difference of thermal expansion coefficient [24]. When the thermal expansion coefficient, *α*<sup>C</sup> of the ceramic is smaller than that of the metal, *α*M, the ceramic is subjected to tension stress and cracks at the edges, as schematically illustrated in **Figure 4a**, on the other hand, when the thermal expansion coefficient, *α*M, of the metal is smaller than that of the ceramic, *α*C; tensile stress acts on the core of the ceramic and cracks the ceramic, not at the edges, but transversely at the core, as shown in **Figure 4b**.

**Figure 4.** Schematic illustration of thermal stress in joint interface and mode of cracking due to difference of thermal expansion coefficient [23, 24].

To overcome for reducing the residual stress mentioned above, induced by the mismatch of the thermal expansion coefficient between the materials to be joined, the following methods can be used as reported by Zhou [7]: (1) Using soft filler metals, the soft filler metals have low yield strength and could release the residual stress. (2) Using soft interlayer, the residual stress could be reduced by the elastic and plastic deformation of an interlayer, e.g. when using Al or Cu as interlayer, the residual stress is decreased. According to Eq. (1), the residual stress will decrease with Young's model *E*m decreasing. (3) Using hard metals of which the thermal expansion coefficient is close to ceramics as the interlayer. Using hard metals such as W, Mo or invar as the interlayer, could reduce the residual stress. Their validity is not obvious when hard metals with high yield strength are the interlayer. (4) Using composite interlayer where the composite interlayers often constitute hard metals and soft metals, like Cu/Mo-Cu/Nb, have a noticeable effect on reducing residual stress, with a combination of merits of those two kinds of metals. (5) Joining under low temperature where the joining ceramic to metal at a low temperature is good for reducing the joint deformation and effectively decreasing the residual stresses. (6) Heat treatment after joining because the proper heat treatment post joining sometimes releases the stress and the strength will vary based on the heat treatment. (7) Appropriate configuration of the joint could decrease the stress concentration extent and reduce the residual stress.

where *γ*M and *γ*C are the surface energies of the metal and ceramic, respectively, and *γ*MC is the metal/ceramic interfacial energy (**Figure 5**). When the bonding is chemical bonding and interfacial separation occurs without plastic deformation of the metal and the ceramic, Δ*G* is identical to the work of adhesion, *W*ad, which is the work required to separate a unit area of interface into the two original surfaces. Combined with the Young's equation [28], Eq. (3) can

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**Figure 5.** Liquid metal drop shape depending on the contact time: (a) initial contact or rigid solid surface, (b) formation

 g

where *θ* is the measured contact angle between the liquid or the solid and in equilibrium with a solid substrate. From Eq. (4), it is clear that the interfacial energy of the ceramic/metal, *γ*MC,

From **Table 1** it can be seen that, in general, *γ*MC for Al2O3-metal systems tends to increase with the cohesive energy of the metal, which is directly related to its melting temperature (*T*m). On the other hand, if the ceramic-metal is a solid-solid system, *W*ad can be estimated by measuring the dihedral angle, *Ø*, associated with residual voids on diffusion bonded interfaces [23].

 q

(1 cos ) (4)

of a ridge (vertical scale exaggerated) and (c) final equilibrium configuration on deformable solid [29].

*W*ad M C MC M = +- = +

g gg

decreases as *W*ad increases.

be expressed as [26]:

## **3.3. Interface reliability of the joints**

Interfaces play critical roles in properties of many material systems such as composites, coatings and joints. Particularly in ceramic to metal joints, the properties of interfaces have a significant effect on the mechanical reliability of the joints. The mechanism of bond formation at the interface determines the interface structure, which depends strongly on processing conditions as well as materials. The bonding mechanisms can be categorized in terms of mass transfer across the interface. When there is only charge transfer without mass transfer across the interface, the bonding is called chemical bonding. In some literature, it is also called physical bonding or adhesive bonding. When there is mass transfer across the interface such as chemical reaction and diffusion, the bonding mechanism is called chemical reaction bonding [5].

#### *3.3.1. Chemical bonding*

While atoms are the smallest units for solid-state physicists, interfaces are the smallest building units for material scientists. Heterogeneous interfaces between two different types of materials change the chemical bonding and new properties are formed [25]. Thus, the chemical bonding holds a significant position as a joining technique in this case and includes a chemical bond being created between both parts of the work through utilization of chemical reactions occurring at the ceramic/metal interface. The chemical bonding problem in that joints can be widely produced by chemical bonding at the interface between ceramics (ionic bonding, covalent bonding) and metals (metal bonding), which basically have different bonding modes [26].

The driving force for formation of ceramic-metal interfaces is the decrease in free energy (Δ*G*) that occurs when intimate contact is established between the ceramic and metal surfaces [27]. The free energy change per unit area of interface formed is given by the Dupré equation [5]:

$$
\Delta G = \left. \boldsymbol{\gamma}\_{\text{M}} + \boldsymbol{\gamma}\_{\text{C}} + \boldsymbol{\gamma}\_{\text{MC}} \right. \tag{3}
$$

where *γ*M and *γ*C are the surface energies of the metal and ceramic, respectively, and *γ*MC is the metal/ceramic interfacial energy (**Figure 5**). When the bonding is chemical bonding and interfacial separation occurs without plastic deformation of the metal and the ceramic, Δ*G* is identical to the work of adhesion, *W*ad, which is the work required to separate a unit area of interface into the two original surfaces. Combined with the Young's equation [28], Eq. (3) can be expressed as [26]:

expansion coefficient is close to ceramics as the interlayer. Using hard metals such as W, Mo or invar as the interlayer, could reduce the residual stress. Their validity is not obvious when hard metals with high yield strength are the interlayer. (4) Using composite interlayer where the composite interlayers often constitute hard metals and soft metals, like Cu/Mo-Cu/Nb, have a noticeable effect on reducing residual stress, with a combination of merits of those two kinds of metals. (5) Joining under low temperature where the joining ceramic to metal at a low temperature is good for reducing the joint deformation and effectively decreasing the residual stresses. (6) Heat treatment after joining because the proper heat treatment post joining sometimes releases the stress and the strength will vary based on the heat treatment. (7) Appropriate configuration of the joint could decrease the stress concentration extent and

Interfaces play critical roles in properties of many material systems such as composites, coatings and joints. Particularly in ceramic to metal joints, the properties of interfaces have a significant effect on the mechanical reliability of the joints. The mechanism of bond formation at the interface determines the interface structure, which depends strongly on processing conditions as well as materials. The bonding mechanisms can be categorized in terms of mass transfer across the interface. When there is only charge transfer without mass transfer across the interface, the bonding is called chemical bonding. In some literature, it is also called physical bonding or adhesive bonding. When there is mass transfer across the interface such as chemical reaction and diffusion, the bonding mechanism is called chemical reaction bonding

While atoms are the smallest units for solid-state physicists, interfaces are the smallest building units for material scientists. Heterogeneous interfaces between two different types of materials change the chemical bonding and new properties are formed [25]. Thus, the chemical bonding holds a significant position as a joining technique in this case and includes a chemical bond being created between both parts of the work through utilization of chemical reactions occurring at the ceramic/metal interface. The chemical bonding problem in that joints can be widely produced by chemical bonding at the interface between ceramics (ionic bonding, covalent bonding) and metals (metal bonding), which basically have different bonding modes

The driving force for formation of ceramic-metal interfaces is the decrease in free energy (Δ*G*) that occurs when intimate contact is established between the ceramic and metal surfaces [27]. The free energy change per unit area of interface formed is given by the Dupré equation [5]:

(3)

Δ M C MC *G* = ++ g gg

reduce the residual stress.

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[5].

[26].

*3.3.1. Chemical bonding*

**3.3. Interface reliability of the joints**

**Figure 5.** Liquid metal drop shape depending on the contact time: (a) initial contact or rigid solid surface, (b) formation of a ridge (vertical scale exaggerated) and (c) final equilibrium configuration on deformable solid [29].

$$\mathcal{W}\_{\rm ad} = \mathcal{\gamma}\_{\rm M} + \mathcal{\gamma}\_{\rm C} - \mathcal{\gamma}\_{\rm MC} = \mathcal{\gamma}\_{\rm M} \left( 1 + \cos \theta \right) \tag{4}$$

where *θ* is the measured contact angle between the liquid or the solid and in equilibrium with a solid substrate. From Eq. (4), it is clear that the interfacial energy of the ceramic/metal, *γ*MC, decreases as *W*ad increases.

From **Table 1** it can be seen that, in general, *γ*MC for Al2O3-metal systems tends to increase with the cohesive energy of the metal, which is directly related to its melting temperature (*T*m). On the other hand, if the ceramic-metal is a solid-solid system, *W*ad can be estimated by measuring the dihedral angle, *Ø*, associated with residual voids on diffusion bonded interfaces [23].


**Table 1.** Interfacial energies of solid-solid Al2O3-metal systems [23].

If the interface ruptures in a brittle fashion, *Ø* can be measured using an atomic force micro‐ scope and *W*ad is then obtained from [23]:

$$W\_{\rm ad} = \mathcal{V}\_{\rm m} (\text{l} - \cos \mathcal{Q}') \tag{5}$$

phase diagram is nearly impossible. In addition, the extent and possibility of the reaction are limited by kinetics for which data is not readily available for ceramic-metal interfaces [30].

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Reaction phases such as brittle intermetallics and solid solutions often cause interfacial failure at very low stress [5]. An increase in bonding temperature and excessive time generally enhance chemical reactions and lead to thick reaction layer formation, which may decrease the joint strength. At interfaces where planar reaction layers form the thickness of the layer is often optimized by controlling bonding conditions to prevent interfacial debonding or brittle interfacial fracture along the reaction layer. In many ceramic-metal systems, it is observed that the growth of the reaction layer follows a parabolic rate law. It is found that the reaction

Unjoined area is frequently formed at the edge of a joint. This edge defect weakens the joint extremely as it works as a notch induced on the interface and one must control the formation of an edge unjoined band. The inhomogeneity in deformation of the metal layer will also reflect the strength. In the case of the reaction gas releasing system, the reaction in the outer region may be promoted by continuous evacuation. This will cause excess thinning of the ceramic at

If the interface reaction emission gas as the reaction product, the pores loaded with the gas might be left on the interface bringing about the hindrance of contact. The Si3N4/Ni interface is one of the cases. This interface is feeble because of the nearness of pores along the interface.

product tends to be bonded to the ceramic with a coherent interface.

**Figure 6.** Chemical bonding of ceramics and metals [26].

*3.3.3. Pores and unbonded areas on interface*

the edge region.

Another important consequence of Eq. (3) is that a stable interface requires a positive Δ*G* (or *W*ad). For a number of ceramic-metal systems, *W*ad varies with the temperature, which provides an explanation for the minimum temperature requirements to achieve bonding.

#### *3.3.2. Chemical reaction bonding*

When there is mass transfer across the interface, bonding is formed by diffusion or chemical reactions. Chemical reactions at the interface lead to the formation of interfacial reaction layers with properties that differ from both the ceramic and the metal [5]. This can have favourable effects on joint quality by increasing the initial wettability of the metal on ceramic surfaces; however, thick reaction layers increase volume mismatch stresses and thermal residual stresses that detrimental to joint strength. **Figure 6** shows a schematic illustration of the chemical bonding methods and processes. Brazing for instance is a joining technique including the anomalies and gaps which happen on the surfaces of the work being brought into a condition of close cohesion by means of a liquid phase. It is also generally known that solidphase joining including good adherence which accomplished through heating, pressurization, also distortion that occurs through the surfaces at work and also the interdependence of natural temperature where it seemed direct contact for a period ranging between work surfaces through the settlement and activation. It involves normal temperature tension threads that are being made to produce a full-contact interface between these materials by an energy supply from a source other than the thermal one and to create a joint in the interface in proximity to its normal temperature.

The driving force for a chemical reaction is the chemical potential of the atomic species involved. In many systems, chemical reaction is not expected if only the interaction of the metal with non-metallic elements of the ceramic is considered. However, when all the possible reaction potentials are considered, a net negative free energy can result, which indicates that a chemical reaction is thermodynamically favourable. Equilibrium thermodynamics can use to predict possible reactions at the interface. However, when there are more than three elements in a ceramic-metal system, the prediction of all the possible reactions based on the phase diagram is nearly impossible. In addition, the extent and possibility of the reaction are limited by kinetics for which data is not readily available for ceramic-metal interfaces [30].

**Figure 6.** Chemical bonding of ceramics and metals [26].

**System** *γ***MC (J/m2**

1.57 at 700°C 1.80 at 1000°C 2.21 at 900°C 2.20 at 1000°C 2.73 at 1000°C

**Table 1.** Interfacial energies of solid-solid Al2O3-metal systems [23].

scope and *W*ad is then obtained from [23]:

*3.3.2. Chemical reaction bonding*

its normal temperature.

Al2O3-Ag Al2O3-Au Al2O3-Cu Al2O3-Ni Al2O3-Fe

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**)** *T***m of metal (°C)**

If the interface ruptures in a brittle fashion, *Ø* can be measured using an atomic force micro‐

Another important consequence of Eq. (3) is that a stable interface requires a positive Δ*G* (or *W*ad). For a number of ceramic-metal systems, *W*ad varies with the temperature, which provides

When there is mass transfer across the interface, bonding is formed by diffusion or chemical reactions. Chemical reactions at the interface lead to the formation of interfacial reaction layers with properties that differ from both the ceramic and the metal [5]. This can have favourable effects on joint quality by increasing the initial wettability of the metal on ceramic surfaces; however, thick reaction layers increase volume mismatch stresses and thermal residual stresses that detrimental to joint strength. **Figure 6** shows a schematic illustration of the chemical bonding methods and processes. Brazing for instance is a joining technique including the anomalies and gaps which happen on the surfaces of the work being brought into a condition of close cohesion by means of a liquid phase. It is also generally known that solidphase joining including good adherence which accomplished through heating, pressurization, also distortion that occurs through the surfaces at work and also the interdependence of natural temperature where it seemed direct contact for a period ranging between work surfaces through the settlement and activation. It involves normal temperature tension threads that are being made to produce a full-contact interface between these materials by an energy supply from a source other than the thermal one and to create a joint in the interface in proximity to

The driving force for a chemical reaction is the chemical potential of the atomic species involved. In many systems, chemical reaction is not expected if only the interaction of the metal with non-metallic elements of the ceramic is considered. However, when all the possible reaction potentials are considered, a net negative free energy can result, which indicates that a chemical reaction is thermodynamically favourable. Equilibrium thermodynamics can use to predict possible reactions at the interface. However, when there are more than three elements in a ceramic-metal system, the prediction of all the possible reactions based on the

 Æ

ad m *W* = g

an explanation for the minimum temperature requirements to achieve bonding.

(1 cos ) (5)

Reaction phases such as brittle intermetallics and solid solutions often cause interfacial failure at very low stress [5]. An increase in bonding temperature and excessive time generally enhance chemical reactions and lead to thick reaction layer formation, which may decrease the joint strength. At interfaces where planar reaction layers form the thickness of the layer is often optimized by controlling bonding conditions to prevent interfacial debonding or brittle interfacial fracture along the reaction layer. In many ceramic-metal systems, it is observed that the growth of the reaction layer follows a parabolic rate law. It is found that the reaction product tends to be bonded to the ceramic with a coherent interface.

#### *3.3.3. Pores and unbonded areas on interface*

Unjoined area is frequently formed at the edge of a joint. This edge defect weakens the joint extremely as it works as a notch induced on the interface and one must control the formation of an edge unjoined band. The inhomogeneity in deformation of the metal layer will also reflect the strength. In the case of the reaction gas releasing system, the reaction in the outer region may be promoted by continuous evacuation. This will cause excess thinning of the ceramic at the edge region.

If the interface reaction emission gas as the reaction product, the pores loaded with the gas might be left on the interface bringing about the hindrance of contact. The Si3N4/Ni interface is one of the cases. This interface is feeble because of the nearness of pores along the interface. At the point when nickel contains nitride forming elements, for example, chromium, no pore is formed at an interface and the strength is improved.

( ) <sup>0</sup>

=- - -

s

tionally, *σu* is set to be zero.

1 exp( (( ) / ) d ))

where *σu* , *σ*0 and *m* are the zero probability strength (location parameter), the scale parameter and the flaw density exponent (shape parameter). Below *σu*, the stress becomes zero; conven‐

**Figure 8** illustrates the sample geometry and test configuration used in the mechanical characterization of ceramic/metal joints. This characterization of the interfacial strength by pull-off or shear-off tests has several limitations. The first one relates to the variety of techni‐ ques used by different research groups, making it difficult to establish a mutual comparison of results. The shear test provides an alternative way to assess the mechanical strength of interfaces. Samples are easily produced, but the results are generally lower than those obtained for bend and tensile tests. The selection of an appropriate method for measuring the bond strength is dictated by the purpose of testing, but the bonding process and parameters affecting the mechanical quality of the bond can be monitored by both fracture mechanics and conven‐ tional testing methods. The bond strength values obtained also depend on the testing technique chosen. Bend test values are generally higher than tensile test values for joints and for brittle ceramic materials. The shear stress test is one of the simplest techniques. However, the shear stress at the interface is not simple shear and it always contains a component of tensile stress that originates from a bending moment, which cannot be neglected. The influence of a slight change of the push position and the fixing condition on the stress distribution is very impor‐ tant. Therefore, the shear test is not recommended for the common evaluation method. Bending and tensile test has almost the same stress distributions as those derived from

**Figure 8.** Sample geometry for mechanical tests of joining specimens: (a) tensile; (b) three-point bending, (c) four-point

bending, (d) plain shear and (e) shear on ring/cylinder [1, 30].

 s

ò *<sup>m</sup> F V u O* (6)

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ss

g

In the actual joining sequences, a perfect interface connection over the whole interface is hardly achieved within a certain joining period and temperature limited by the progress of interface reaction. Whereas the base surface roughness and applied pressure with a couple of critical features, which significantly affect the accomplishment of interfacial contact in the solid state bonding as well as in welding [31]. In solid-state joining, and advanced interfacial contact that plastic deformation in the next early stage that creep deformation and diffusion at a later stage. Basic effects pressure to achieve contact by plastic deformation at the elementary stage. Unjoined islands are formed inevitably on the interface joints under limited pressure. It will depend on the breadth of pressure, time, temperature and different material factors such as stress flow [32]. The relationship between the fracture stress and the unjoined area of the solidstate bonded Al2O3/Nb joint are shown in **Figure 7**. Apparently, the increase in unjoined area decreases the strength of the specimen [33].

**Figure 7.** Bending strength of individual Al2O3/Nb joints as a function of unjoined area formed on interface [32].

#### **3.4. Mechanical reliability of the joints**

The important factor in mechanical reliability is a deviation in the mechanical strength. Knowing the distribution mode of the strength of ceramic/metal joints is significant for the evaluation of reliability. Ceramic materials have a strength distribution obeying the Weibull theory in general. Several researchers suggested the possibility of adopting the Weibull theory to the distribution of the strength of ceramic/metal joints [19].

In the Weibull theory, the cumulative distribution function of fracture, *F*(*σ*), is written as [19, 34]

$$F\left(\sigma\right) = \mathbf{l} - \exp(-\int\_{\gamma}^{0} (\left(\sigma - \sigma\_u\right) / \left.\sigma\_o\right) \overset{\text{\textquotedblleft}}{\left.\mathbf{d}\right|} V\right) \tag{6}$$

where *σu* , *σ*0 and *m* are the zero probability strength (location parameter), the scale parameter and the flaw density exponent (shape parameter). Below *σu*, the stress becomes zero; conven‐ tionally, *σu* is set to be zero.

At the point when nickel contains nitride forming elements, for example, chromium, no pore

In the actual joining sequences, a perfect interface connection over the whole interface is hardly achieved within a certain joining period and temperature limited by the progress of interface reaction. Whereas the base surface roughness and applied pressure with a couple of critical features, which significantly affect the accomplishment of interfacial contact in the solid state bonding as well as in welding [31]. In solid-state joining, and advanced interfacial contact that plastic deformation in the next early stage that creep deformation and diffusion at a later stage. Basic effects pressure to achieve contact by plastic deformation at the elementary stage. Unjoined islands are formed inevitably on the interface joints under limited pressure. It will depend on the breadth of pressure, time, temperature and different material factors such as stress flow [32]. The relationship between the fracture stress and the unjoined area of the solidstate bonded Al2O3/Nb joint are shown in **Figure 7**. Apparently, the increase in unjoined area

**Figure 7.** Bending strength of individual Al2O3/Nb joints as a function of unjoined area formed on interface [32].

The important factor in mechanical reliability is a deviation in the mechanical strength. Knowing the distribution mode of the strength of ceramic/metal joints is significant for the evaluation of reliability. Ceramic materials have a strength distribution obeying the Weibull theory in general. Several researchers suggested the possibility of adopting the Weibull theory

In the Weibull theory, the cumulative distribution function of fracture, *F*(*σ*), is written as [19, 34]

is formed at an interface and the strength is improved.

170 Joining Technologies

decreases the strength of the specimen [33].

**3.4. Mechanical reliability of the joints**

to the distribution of the strength of ceramic/metal joints [19].

**Figure 8** illustrates the sample geometry and test configuration used in the mechanical characterization of ceramic/metal joints. This characterization of the interfacial strength by pull-off or shear-off tests has several limitations. The first one relates to the variety of techni‐ ques used by different research groups, making it difficult to establish a mutual comparison of results. The shear test provides an alternative way to assess the mechanical strength of interfaces. Samples are easily produced, but the results are generally lower than those obtained for bend and tensile tests. The selection of an appropriate method for measuring the bond strength is dictated by the purpose of testing, but the bonding process and parameters affecting the mechanical quality of the bond can be monitored by both fracture mechanics and conven‐ tional testing methods. The bond strength values obtained also depend on the testing technique chosen. Bend test values are generally higher than tensile test values for joints and for brittle ceramic materials. The shear stress test is one of the simplest techniques. However, the shear stress at the interface is not simple shear and it always contains a component of tensile stress that originates from a bending moment, which cannot be neglected. The influence of a slight change of the push position and the fixing condition on the stress distribution is very impor‐ tant. Therefore, the shear test is not recommended for the common evaluation method. Bending and tensile test has almost the same stress distributions as those derived from

**Figure 8.** Sample geometry for mechanical tests of joining specimens: (a) tensile; (b) three-point bending, (c) four-point bending, (d) plain shear and (e) shear on ring/cylinder [1, 30].

analytical equations. However, the elastic constant mismatch between ceramics and metal induces inhomogeneity in stress distribution [23].

The strength of metal/ceramic joint materials is generally characterized by bending tests, also referred to as flexure testing. The test specimen can have a circular, square or rectangular cross section and is uniform along the complete length. As shown in **Figure 10**, the test specimen is supported near the ends and the load is applied either at the centre, for three-point loading,

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**Figure 10.** Derivation of the modulus of rupture equation for three-point and four-point bending [23].

The bend strength is defined as the maximum tensile stress at failure and is often referred to as the MOR. The bending strength of a rectangular test specimen can be calculated using the

where *M* is the moment, *C* is the distance from the neutral axis to the tensile surface and *I* is

*S MC I* = . / (7)

<sup>3</sup> *I ab* = . / 12 (8)

*C b* = / 2 (9)

or at two positions for four-point loading.

general flexure stress formula:

For a rectangular test specimen [23]:

the moment of inertia.

and

In the case of three-point bending, the peak stress occurs only along a single line on the surface of the test bar opposite the point of loading. The tensile stress decreases linearly along the length of the bar into the thickness of the bar, reaching zero at each bottom support and at the neutral axis, respectively. The probability of the largest flaw in the specimen being at the surface along the line of peak tensile stress is very low. Therefore, the specimen will fracture at either a flaw smaller than the largest flaw or a region of lower stress. Four-point bend testing results in lower strength values for a given ceramic material than does three-point bending. The peak of the stress distribution in a four-point bend specimen is present over the area of the tensile face between the load points. The tensile stress decreases linearly from the surface to zero at the neutral axis and from the load point to zero at the bottom supports. The area and volume under peak tensile stress or near peak tensile stress is much greater for four-point bending than for three-point bending, and thus the probability of a larger flaw being exposed to high stress is increased. As a result, the modulus of rupture (MOR) or bend strength measured in four-point is lower than that measured in three-point. Uniaxial tensile strength results in lower strength values for a given ceramic than does bend testing. **Figure 9** illustrates that in the case of uniaxial tension the complete volume of the gauge section of a tensile test specimen is exposed to the peak tensile stress. Therefore, the largest flaw in this volume will be the critical flaw and will result in fracture.

**Figure 9.** Comparison of the tensile stress distributions for three-point, four-point and uniaxial tensile test specimens [23].

The strength of metal/ceramic joint materials is generally characterized by bending tests, also referred to as flexure testing. The test specimen can have a circular, square or rectangular cross section and is uniform along the complete length. As shown in **Figure 10**, the test specimen is supported near the ends and the load is applied either at the centre, for three-point loading, or at two positions for four-point loading.

**Figure 10.** Derivation of the modulus of rupture equation for three-point and four-point bending [23].

The bend strength is defined as the maximum tensile stress at failure and is often referred to as the MOR. The bending strength of a rectangular test specimen can be calculated using the general flexure stress formula:

$$\mathbf{S} = M\_{\cdot}\mathbf{C} / I \tag{7}$$

where *M* is the moment, *C* is the distance from the neutral axis to the tensile surface and *I* is the moment of inertia.

For a rectangular test specimen [23]:

$$I = a.b^3 / 12\tag{8}$$

and

analytical equations. However, the elastic constant mismatch between ceramics and metal

In the case of three-point bending, the peak stress occurs only along a single line on the surface of the test bar opposite the point of loading. The tensile stress decreases linearly along the length of the bar into the thickness of the bar, reaching zero at each bottom support and at the neutral axis, respectively. The probability of the largest flaw in the specimen being at the surface along the line of peak tensile stress is very low. Therefore, the specimen will fracture at either a flaw smaller than the largest flaw or a region of lower stress. Four-point bend testing results in lower strength values for a given ceramic material than does three-point bending. The peak of the stress distribution in a four-point bend specimen is present over the area of the tensile face between the load points. The tensile stress decreases linearly from the surface to zero at the neutral axis and from the load point to zero at the bottom supports. The area and volume under peak tensile stress or near peak tensile stress is much greater for four-point bending than for three-point bending, and thus the probability of a larger flaw being exposed to high stress is increased. As a result, the modulus of rupture (MOR) or bend strength measured in four-point is lower than that measured in three-point. Uniaxial tensile strength results in lower strength values for a given ceramic than does bend testing. **Figure 9** illustrates that in the case of uniaxial tension the complete volume of the gauge section of a tensile test specimen is exposed to the peak tensile stress. Therefore, the largest flaw in this volume will

**Figure 9.** Comparison of the tensile stress distributions for three-point, four-point and uniaxial tensile test specimens

induces inhomogeneity in stress distribution [23].

172 Joining Technologies

be the critical flaw and will result in fracture.

[23].

$$C = b \mid \mathcal{D} \tag{9}$$

where *b* is the thickness and *a* is the width of the specimen.

From **Figure 10**, it is possible to illustrate the derivation of the three-point and four-point flexure formulas for rectangular bars. We can observe that: *M* = (*L*/2)⋅(*F*/2) in the case of threepoint and *M* = (*F*/2)⋅*d* for four-point test.

Therefore, for three-point bending:

$$S = \sigma\_{\text{3p}} = \frac{\text{3.F.L}}{2.a.b^2} \tag{10}$$

And for four-point bending test:

$$S = \sigma\_{4\text{Pt}} = \frac{3.F.d}{a.b^2} \tag{11}$$

**Figure 11.** Brazing schematic [38].

Brazing has numerous focal points over other metal-joining methods, for example, welding [39]. Since brazing does not fuse the base metal of the joint, it permits much more tightly control over resilience and produces a perfect join without the requirement for optional wrapping up. Furthermore, dissimilar metals and ceramic can be brazed. When all is said in done, brazing likewise creates less thermal deformation than welding because of the uniform heating of a brazed piece [39]. Complex and multi-part assemblies can be brazed cost-effective. Another feature is that the brazing can be covered or clad for defensive purposes. Finally, brazing is effectively adjusted for large scale manufacturing and it is anything but difficult to mechanize on the grounds that the individual procedure parameters are less delicate to variety [40].

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One of the major disadvantages is the absence of joint strength when contrasted with a welded joint because of the softer filler metals utilized. The strength of the brazed joint is liable to be not as much as base metals but more than the filler metal [41]. Another disadvantage is that brazed joints can be damaged under high temperatures. The brazed material joints require a high purity when done in an industrial environment. Also some applications for brazing require the utilization of satisfactory fluxing agents to control cleanliness. The colour of joint is frequently not quite the same as that of the base metal, making a stylish disadvantage.

The two major problems when the joining these materials by brazing process are firstly the differences in physical properties between ceramics and metals, and secondly the poor wettability of ceramics by most metals and alloys [42, 43]. The first problem in joining ceramics to metals for high-temperature results from the huge contrasts in thermal expansion behav‐ iour. At the point when the thermal expansion of these materials get together is modified, these differences in the thermal expansion behaviour can prompt high stresses [42]. This condition is regularly subsequently heightened by thermal inclinations that rise as a result of thermal

For most ceramic materials, the apparent strength will decrease when going from three-point to four-point to tensile testing and as specimen size increases.

Whatever joining processes are used, the successful formation of the joint depends on ach‐ ievement of intimate contact between the base materials, conversion of the intimate contact into an atomic bonding/reaction, accommodation of residual stresses induced by different thermal and mechanical properties between the base materials undergoing temperature change. Each joining process is characterized by the methods and conditions employed to achieve intimate contact and to promote bond formation between the work pieces.
