*2.1. InSAR Phase Noise Principle*

The interferogram Γ is defined as the conjugate product of a pair of single-look complex SAR images.

$$\Gamma = \mathbf{z}\_1 \cdot \mathbf{z}\_2^\* = |\mathbf{z}\_1 \cdot \mathbf{z}\_2^\*| e^{j(\boldsymbol{\Phi})} \tag{1}$$

where **z**1 and **z**2 are the two complex SAR images; \* indicates the complex conjugate; and ϕ denotes the measured interferometric phase with noise. The phase noising model with additive noise is as follows.

$$
\mathfrak{q} = \mathfrak{q}\_{\mathfrak{c}} + \mathfrak{n}\_{\mathfrak{Y}} \tag{2}
$$

where ϕ**c** denotes the clear interferometric phase and **n**γ is the zero-mean additive Gaussian noise associated with the coherence coefficient *γ*, which is expressed as:

$$\gamma = \frac{E(\mathbf{z}\_1 \cdot \mathbf{z}\_2^\*)}{\sqrt{E\left(|\mathbf{z}\_1|^2\right) \cdot E\left(|\mathbf{z}\_2|^2\right)}}\tag{3}$$

The interferometric phase noise level is correlated with the coherence coefficient *γ*. The higher the coherence coefficient, the lower the noise level.

It is worth noting that the value range of the interferometric phase is distributed in (− π, π]. Hence, phase denoising is implemented in the complex field in for the subsequent phase unwrapping steps. Employing a mathematical manipulation on Equation (2), we obtain the following expression.

$$\mathbf{p} = \mathbf{e}^{j\mathbf{q}} = \mathbf{e}^{j(\mathbf{q}\_c + \mathbf{n}\_\gamma)} = \mathbf{q}\_{\bar{r}} + j\mathbf{q}\_{\bar{i}} \tag{4}$$

where **p** indicates the interferogram and ϕ*r* and ϕ*i* denote the real and imaginary parts of **p**, respectively. According to the analysis of [45], ϕ*r* and ϕ*i* can be given by.

$$\begin{aligned} \mathfrak{sp}\_{\mathcal{I}} &= \cos(\mathfrak{sp}\_{\mathcal{L}} + \mathfrak{n}\_{\mathcal{I}}) = \aleph\_{\mathcal{L}}\cos(\mathfrak{sp}\_{\mathcal{L}}) + \mathfrak{n}\_{\mathcal{I}\mathfrak{c}} \\ \mathfrak{sp}\_{i} &= \sin(\mathfrak{sp}\_{\mathcal{L}} + \mathfrak{n}\_{\mathcal{I}}) = \aleph\_{\mathcal{L}}\sin(\mathfrak{sp}\_{\mathcal{L}}) + \mathfrak{n}\_{\mathcal{I}\mathfrak{s}} \end{aligned} \tag{5}$$

where **n***γc* and **n***γs* are defined as the zero-mean additive noise, and *Nc* is a phase quality evaluation metric related to the coherent coefficient *γ*. Finally, combining Equations (4) and (5), the formulation of the interferometric phase is derived as follows.

$$\mathbf{p} = \mathbf{N}\_{\mathcal{E}} \cdot \mathbf{p}\_{\mathcal{E}} + \mathbf{n} \tag{6}$$

where **n** = **n***γc* + *j***n***γs* denotes the noise of the interferogram and **p***c* = *ej*ϕ*c* is the ideal interferogram.

### *2.2. InSAR Phase SR Filtering Model*

The conventional SR model for recovering a single from a measurement is as follows.

$$y = \Phi x + n\tag{7}$$

where *y* ∈ R*M* is the measurement; **Φ** ∈ R*M*×*N* is dubbed the measurement matrix; *x* ∈ R*N* is the recovered signal; and *n* ∈ R*M* is the noise.

According to Section 2.1, the InSAR phase filtering model can be modeled as.

$$\mathbf{p} = \Phi \mathbf{p}\_c + \mathbf{n} \tag{8}$$

Aiming to solve Equation (8), it is transformed into the following convex optimization problem.

$$\hat{\mathbf{p}}\_{\varepsilon} = \underset{\mathbf{p}\_{\varepsilon}}{\operatorname{argmin}} \frac{1}{2} \|\boldsymbol{\Phi}\mathbf{p}\_{\varepsilon} - \mathbf{p}\|\_{2}^{2} + \lambda \|\boldsymbol{\Psi}\mathbf{p}\_{\varepsilon}\|\_{1} \tag{9}$$

where ψ**p***c* is a sparse representation of **p***c*; ψ denotes a certain transform such as Wavelet, Fourier and so on; and *λ* is a tunable soft threshold parameter.

The main iterative steps of solving Equation (9) by the ISTA algorithm are as follows.

$$\mathbf{h}^{(k)} = \mathbf{p}\_{\varepsilon}^{\ (k-1)} - \kappa \boldsymbol{\Phi}^{\mathbf{H}} \left( \boldsymbol{\Phi} \mathbf{p}\_{\varepsilon}^{\ (k-1)} - \mathbf{p} \right) \tag{10}$$

$$\mathbf{p}\_c^{(k)} = \boldsymbol{\Psi}^{\mathbf{H}} \text{soft}\left(\boldsymbol{\Psi} \mathbf{h}^{(k)}, \boldsymbol{\lambda}\right) = \boldsymbol{\Psi}^{\mathbf{H}} \text{sign}(\boldsymbol{\Psi} \mathbf{h}^{(k)}) \text{max}\left\{ \left| \boldsymbol{\Psi} \mathbf{h}^{(k)} \right| - \boldsymbol{\lambda}, 0 \right\} \tag{11}$$

where *α* indicates the step size; sign(·) denotes a sign function; **ΦH** is the conjugate transpose of **Φ**; and **h**(*k*) is the residual error in iteration *k*. However, the sparse transform ψ and parameters such as *α* and *λ* are hand-crafted, which results in the algorithm being nonadaptive. Moreover, ISTA usually suffers from a huge calculative burden due to its large number of iterative steps.

We chose the identity matrix as the measurement matrix **Φ** by the formulation of the interferometric phase. It can be seen from the above analysis that the phase filtering is operated in the complex domain to achieve high-precision phase unwrapping. Therefore, taking advantage of the idea of separating real and imaginary parts, the noisy phase **p**, the ideal phase **p***c*, and the measurement matrix **Φ** are transformed as

$$\mathbf{p}\_{\mathbb{R}} = \left( \begin{array}{c} \mathfrak{q}\_{\mathbb{T}} \\ \mathfrak{q}\_{i} \end{array} \right) \mathbf{p}\_{\mathbb{c}\mathbb{R}} = \left( \begin{array}{c} \mathfrak{q}\_{\mathbb{c}\mathbb{T}} \\ \mathfrak{q}\_{\mathbb{c}i} \end{array} \right) \tag{12}$$

$$
\Phi\_{\mathbb{R}} = \begin{pmatrix} \Phi\_r & -\Phi\_i \\ \Phi\_i & \Phi\_r \end{pmatrix} \tag{13}
$$

where ϕ*cr* and ϕ*ci* are the real and imaginary parts of the ideal interferogram **p***c*, and **Φ***r* and **Φ***i* denote the real and imaginary parts of the measurement matrix **Φ**, respectively.

In the end, the filtered interferometric phase is obtained by the real part ϕ *r* and imaginary part ϕ *i*of the recovered interferometric phase as follows.

$$\mathbf{q}' = \angle(\mathbf{q}'\_r + j\mathbf{q}'\_i) \tag{14}$$


**Thermodynamic Aspects of CVD Crystallization of Refractory Metals and Their Alloys**

Yu. V. Lakhotkin

*Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Moscow, Russia*


**Author details**

Dhary Alewy Almashhadany1 \*, Zean F. Zefenkey1 , Sahar Hassannejad1 , Nyan Jasim Mohammed1 , Rzgar F. Rashid1 , Rawaz R. Hassan2 and Abdullah O. Hassan1

1 Department of Medical Laboratory Science, College of Science, Knowledge University, Erbil, Iraq

2 Department of Medical Microbiology, College of Science, Knowledge University, Erbil, Iraq

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


*Mitigating Diabetic Foot Ulcers: The Effect of Diet and Microbiome DOI: http://dx.doi.org/10.5772/intechopen.106629*

glycogen, or stimulated by incretins to be digested and absorbed into adipocytes and stored as fat (see **Figure 1**).

Incretins also stimulate the release of insulin as well and as incretin levels rise because of overeating, insulin levels rise as well. GLP-1 is released from L-cells of the small intestine [16]. One of the effects of increased secretion of insulin however can cause insulin receptors to desensitize and become nonresponsive and promoting insulin resistance. This leads to high blood glucose levels leading to diabetes. Increased amounts of insulin, incretin agonists, DTT inhibitors, and other drugs are

#### **Figure 1.**

*Represented above is a simplified diagram of blood glycemic control and fat deposition. Incretins are at the heart of control and not just involved in stimulating insulin release. Incretins can have direct effects on fat deposition. In the energy balance mode and carbohydrate – insulin model of obesity it appears the influence of diet and SCFAs are not emphasized enough on the impact of glycemic control and fat deposition. Microbiota and the production of SCFAs have a profound effect on insulin release. Although carbohydrates have a large effect on secretion of insulin, other nutrients also have an effect. Although insulin can stimulate the production fat in adipocytes, incretins and SCFAs can have a direct effect as well.*

designed to increase the amounts of insulin without fixing the underlying physiological causes. For TTDM and similar forms of diabetes, this is possible but for TT1 this is more difficult and in most cases impossible. So, depending on the cause, the diets and effects of microbiota are quite different.

GLP-1 and GIP both stimulate the secretion of insulin from the Beta cells of the Pancreas, yet they have different effects on obesity and fat deposition and different studies are making the functions unclear [17]. GLP-1 directly inhibits appetite and food intake and GLP-1 antagonists have been developed into drugs that can help glycemic control. GIP however lacks these functions and although some studies have used agonists to reduce weight gain, also antagonists have shown the same effect [17–20]. In addition, GIP receptor knockout mice fail to gain weight even when fed a high-fat diet [21]. GIP is released when glucose and proteins are absorbed which then promote additional absorption [22, 23].

Incretin control is what causes insulin release and increased amounts can lead to diabetes and eventually the complications that eventually lead to foot ulcers. Rises in incretins particularly GIP can contribute to weight gain by increasing absorption of nutrients and fat deposition (**Figure 1**). Control of incretin release could modulate and maintain controlled diabetes and less of a risk of ulcers. Even before one eats a meal, incretins such as GLP-1 and GIP are released in anticipation of glucose absorption. But the evidence is rather ambiguous [24]. Some studies show that even the sweet taste of food (even if it's an artificial sweetener) can trigger incretin release during the cephalic phase of digestion [1, 25]. Others have shown no release of insulin during the cephalic phase [26, 27].


Conflict of interest

1. Deinking of paper in paper recycling

an effective and successful flotation.

stronger the selectivity of collector.

well for reverse flotation process.

24

polymers to enhance their depressing action.

simple and customized reagent regimes for given ore deposits.

property along with their collecting capability.

• There is a trade-off between the pH of the slurry, surfactants and the mineral surface for maximum flotation performance. It can thus be concluded that the length of alkyl chain, arrangement of atoms, nature and type of bonds present within the surfactants and regulation of pH in the flotation pulp are solely for

• Mineral surface and collector chemistry interaction is the first and critical step in flotation. The larger the electronegativity of the group, the stronger is the acting solid intensity, and the larger the radical section of collector, the

• Surfactants containing alcohol group and amine group have inherent frothing

• Though the cost of hydroxamate is higher than fatty acids, its superiority over fatty acids in flotation of the fine-grained oxide ore deserves further attention for industrial application. Research is geared at (a) developing alternate cheaper reagents with similar performances as hydroxamates, (b) modifying the structure of fatty acids for similar or better results than hydroxamates, (c) application of other chelating agents for enhanced flotation response, (d) successfully using flotation of silicated ores and other minerals, and (e) using green surfactants and solvents given their advantage of biodegradability and sustainability. However their high cost at present continues to be a barrier preventing their use although their benefits have been well realized.

• For cationic surfactants, another cationic group can be inserted, which can be further upgraded to dicationic and tricationic surfactants, which will work out

• For the use of depressants, more kosmotropic ions can be added to existing

As discussed earlier, froth flotation has the ability to treat any mineral and thus reigns supreme as it is the most versatile concentration process for ore fines. A universal solution for all minerals is not possible but it depends on a case-by-case basis as each mineral ore has different compositions. The challenging aspect of the interaction of value and gangue minerals of any ore could be overcome by specifically improved reagents. A universal specific reagent recipe cannot be proposed for any ore flotation due to variation of mineralogical composition of different ores, tailings and slimes. The knowledge and research about surfactant chemistry have to be given due recognition and used judiciously through encouraging innovative,

2. Flotation of wastewater treatment

3. Processing of oil sands

Surfactants and Detergents

5. Conclusions

No potential conflict of interest was reported by the authors.


**1. Introduction**

Electromagnetic technology has a wide range of applications in various fields. Nasim (2019) proposed a metamaterial platform for solving integral equations using a monochromatic electromagnetic field [1]. The application of electromagnetic technology in medical diagnosis equipment realizes the measurement of blood glucose and the detection of cancer stage [2,3]. In addition, it is necessary to consider electromagnetic fields in plasma electronics [4,5].

Here, we apply electromagnetic technology to geophysics. Grounded electrical-source airborne transient electromagnetic (GREATEM) is a useful detection geophysical method where the transmitter is set on the ground and the receiver is installed on the aircraft [6]. Combining the ground and airborne electromagnetic systems, GREATEM has the advantages of large detection depth, high resolution, wide range, and fast speed. In particular, it has unique superiority in mountains, forest-covered areas, swamps, and other special areas [7,8]. Ji (2013) used an airship as the carrier and the two-dimensional finite difference method to calculate the time-domain GREATEM response with a long wire source [9]. Ren (2017) investigated a three-dimensional time-domain airborne electromagnetic model based on the finite volume method, and then used the strategy of separating the primary field from the secondary field, which significantly saved on calculation time [10]. For airborne transient electromagnetic measurement, a three-dimensional forward simulation method which considered attitude change was proposed, and the electromagnetic response of a shallow surface was analyzed in Reference [11]. Later, the spectral element method (SE) was used to carry out three-dimensional modeling of GREATEM, effectively improving the modeling accuracy [12].

To interpret GREATEM, researchers often make the assumption that the earth is just conductive or resistive. However, there is an induced polarization (IP)effect in the earth, which is usually reflected as a reverse signal. The existence of the IP effect has a great impact on the electromagnetic response [13,14]. The IP effect is related to conductivity and frequency, and its dispersion characteristics can be expressed by the Debye model and the Cole–Cole model [15,16]. At present, numerical simulations of the polarization effect are mainly conducted in the frequency domain. Most of the early studies simulated the IP effect by converting the electromagnetic field from the frequency domain to the time domain [17,18]. Unfortunately, when broadband frequency content is considered, the methods are not so efficient [19]. In order to simulate the IP effect in the time domain, Kang (2015) proposed a method to generate a three-dimensional pseudo charge distribution using airborne time-domain electromagnetic data and effectively extracted the polarization signal [20]. Wu (2017) used the FDTD (finite difference time-domain) method to simulate the IP effect with a small loop source [21]. Commer (2017) expanded the finite difference time-domain scheme, modeled and analyzed the IP effect, and developed a simple calculation of the Cole–Cole model [22].

However, three-dimensional (3D) numerical simulations of IP effects based on FDTD require a high computation load, when including the air layer. In addition, it is difficult to calculate the source in the FDTD method; thus, the upward continuation method is often used to avoid directly loading the emission source. Mittet (2010) put forward the theory of wave field transformation and successfully applied it to marine CSEM (controllable source electromagnetic method), increasing the calculation efficiency by nearly 10-fold [23]. Mittet (2018) used the least squares fitting method to calculate the IP response of sea water in the fictitious wave field [24]. Ji (2017) improved the emission source, applied the wave field transformation method to the ground transient electromagnetic simulation, and realized a three-dimensional transient electromagnetic numerical simulation including the air layer [25]. However, it did not consider the IP effect of the earth. Therefore, here, we perform the wave field transformation in GREATEM, and we realize a three-dimensional numerical simulation in polarizable media using the Cole–Cole model. In addition, the computing efficiency is also improved.

The wave field transformation method is proposed for the grounded electrical-source airborne transient electromagnetic system in this paper. The Maxwell equations in the real diffusion field are transformed into the fictitious wave field by using the transformation relationship between the diffusion field and fictitious wave field. The fractional order Cole–Cole model is introduced into the fictitious wave field, and the Maxwell equations with the Cole–Cole model are solved using the finite difference time-domain method. Finally, an integral transformation method is used to transform the calculation results back to the real diffusion field. In the case of including polarized media, the two-field numerical simulation of the induction field and polarization field is realized. In addition, the computing efficiency is also improved.


**3.7 Statistical analysis**

The results are expressed as means±SEM. An analysis was performed using the paired or unpaired Student's *t-*test to compare between before and after SVR, respectively. The criterion for statistical significance was set at a value of *P*<0.05.


**2.1.2 Diagnostic evaluation**

Hemangiomas demonstrate a typical pattern of enhancement on triple phase contrast enhanced CT. The lesion appears as a well circumscribed hypodense mass with peripheral enhancement in the arterial phase that will progress toward the center of the lesion. This pattern is typically known as centripetal enhancement. Sensitivity of triple phase CT has been reported from 75-85% with specificity of 75-100%(Trotter, JF & Everson, GT 2001). Even better results have been reported with the use of magnetic resonance imaging, with reported sensitivity and specificity of up to 95% and 100%, respectively (Semelka, RC et al 2001). Because of the highly vascular nature of these tumors, percutaneous biopsy of suspected hemangiomas is contraindicated.


*2.3. Oxidation of WPI*

The oxidation of WPI was performed according to Duan et al. [15] with some modifications. Briefly, dried WPI was dispersed in phosphate buffer (PB, 0.01 mol/L, pH 7.4) to prepare 25 mg/mL protein suspension, then mixed with various concentrations of AAPH (0, 0.04, 0.20, 1.00, 3.00, 5.00 and 10.00 mmol/L), followed by incubation for 24 h at 37 ◦C under light protection. The reaction solutions were centrifuged for 30 min at 1000× *g* and 4 ◦C. The supernatants were dialyzed (molecular weight cut-off 7 kDa) against distilled water for 72 h at 4 ◦C. Next, the dialysates were freeze-dried at −80 ◦C for 24 h to obtain AAPH oxidized WPI (APPH-WPI) and were stored frozen at −80 ◦C for spare use.

#### *2.4. Determination of Oxidation Degree of AAPH-Oxidized WPI (APPH-WPI)*

#### 2.4.1. Determination of Carbonyl Content

The carbonyl contents of WPI and APPH-WPI were measured by 2,4 dinitrophenylhydrazine (DNPH) assay. Briefly, 1.5 mL protein dispersion (10 mg/mL) was mixed with 1 mL DNPH solution (10 mmol/L, containing 2 mol/L HCl), after incubation in the dark for 1 h at room temperature, then 1 mL of trichloroacetic acid (TCA, 20%) was added and it was mixed well, followed by centrifugation at 8000× *g* for 15 min. The precipitate was washed with 1 mL of ethyl acetate-ethanol (1:1, *v/v*) three times, and then dissolved in 4 mL urea (6 mol/L) for 20 min at 37 ◦C. After centrifugation at 8000× *g* for 15 min, absorbance of the supernate was read at 370 nm by a microplate reader (Biotek, Winooski, VT, USA), and the carbonyl content of protein was expressed as nmol/mg protein using the molar extinction coefficient of 22,000 L·mol−1·cm−1 [16]. Measurement was repeated at least three times to calculate the carbonyl content of the samples.

#### 2.4.2. Determination of Sulfhydryl Group Content

The sulfhydryl group content of WPI and APPH-WPI was measured in triplicate and repeated three times by using the DTNB assay. A 4 mg/mL DTNB solution was first prepared in 0.086 M Tris-Gly buffer (containing 5 mM EDTA, pH 8.0), followed by a suspension of protein samples in Tris-Gly buffer (containing 2% (*w/w*) sodium dodecyl sulfate (SDS)) to obtain a concentration of 10 mg/mL. Then, 1 mL of the sample solution was reacted with 10 μL of DTNB solution for 1 h at room temperature, followed by centrifugation at 10,000× *g* for 10 min, the absorbance of supernate was then measured at 412 nm against the blank (without DTNB and sample). The free sulfhydryl group contents of protein samples were calculated using the extinction coefficient of 13,600 L·mol−1·cm−1, while the total sulfhydryl content was measured as a similar procedure, except that 8 M urea was added to the sample buffer [17,18].

#### 2.4.3. Determination of Free Amino Groups Content

The o-phthaldialdehyde (OPA) method was used to measure the free amino groups content of proteins samples. OPA was first dissolved in methanol solution (0.4 g/mL), followed by addition of 2.5 mL of SDS solution (200 g/L), 25 mL of boric acid solution (0.1 mol/L), and 100 μL of β-mercaptoethanol. The mixture was diluted to a certain volume with distilled water to obtain the OPA working solution for the subsequent analysis. Next, an amount of 200 μL of protein solution was mixed with 4 mL of OPA working solution, and then water bathed at 35 ◦C for 2 min. The absorbance at 340 nm was measured against distilled water as control. This trial was repeated three times to calculate the free amino group content [19].


**5. Economic criteria and cost‐benefit analysis**

Research and development in the field of electrical energy is not oriented to the production part only, but it should be achieved through management of transmission and distribution networks. Due to the volatility of renewable resources, their integration poses major stability problems in overall networks. It is important to emphasize that technological advances have certain inertia and uncertainties in the outcome. Compared to these two characteristics, it is highly useful to introduce an adequate method of cost/benefit analysis and the decision applicability following economic criteria in uncertain future.

Cost‐benefit analysis (CBA) incorporates many different aspects and interests of the involved parties in the decision of the investment strategy. In the traditional least cost planning method, the project with the lowest cost is selected. In that case, the overall cost involves operational, maintenance, and investment costs. However, this is only an economic criterion, and an energy production project might still not be able to provide satisfactory profit, as many parties are affected and during the project period the system configuration may change (e.g., increasing clean energy and decreasing fossil one, and vice versa). The proposed method will help select the project with a discounted benefit greater than its discounted cost, given as an indication of its profitability. It should be combined with the multi‐criteria analysis described earlier to provide satisfactory information for a confident solution. We propose a CBA that considers environmental, economic, and social benefits. The expression of these benefits turns around the rest of the difference between the revenues and the total costs. For economic criteria inspired from the game theory, there are a number of criteria for the analysis of game matrix and decision choice [17, 30].

In the Bayes‐Laplace criterion, a probability or a weight is associated with each scenario *i*. If the cost associated with scenario *i* for a strategy *j* is *Vij* and the probability of each scenario is *Qj* , then the selection is made as follows:

$$Z\_{BL} = \min\_{j} \sum\_{j} \mathcal{Q}\_{j} V\_{y} \tag{10}$$

In this economic criterion, each scenario is taken into account, and its importance is reflected through its probability of occurrence. The advantage of this criterion is that it leads to a risky decision.

In Laplace's criterion, the occurrence probabilities of scenarios are unknown, and the events are assumed equality probable. Laplace's criterion is processed as an optimal solution, minimizing the mathematical expectation of costs; its formulation is as follows:

**Figure 2.** An explicit hierarchy to determination of business electricity sustainability.

284 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

Research and development in the field of electrical energy is not oriented to the production part only, but it should be achieved through management of transmission and distribution networks. Due to the volatility of renewable resources, their integration poses major stability problems in overall networks. It is important to emphasize that technological advances have certain inertia and uncertainties in the outcome. Compared to these two characteristics, it is highly useful to introduce an adequate method of cost/benefit analysis and the decision

Cost‐benefit analysis (CBA) incorporates many different aspects and interests of the involved parties in the decision of the investment strategy. In the traditional least cost planning method, the project with the lowest cost is selected. In that case, the overall cost involves operational, maintenance, and investment costs. However, this is only an economic criterion, and an energy production project might still not be able to provide satisfactory profit, as many parties are affected and during the project period the system configuration may change (e.g., increasing clean energy and decreasing fossil one, and vice versa). The proposed method will help select the project with a discounted benefit greater than its discounted cost, given as an indication

**5. Economic criteria and cost‐benefit analysis**

applicability following economic criteria in uncertain future.

$$Z\_L = \min\_i \frac{1}{n} \sum\_j V\_y \tag{11}$$

The mini‐max decision rule is to seek decision makers' action, which minimize the maximum potential loss. A decision maker who uses the mini‐max criterion acts extremely conservative. He seeks the actions that achieve the best outcome under the worst scenario. The optimal solution is given as follows:

$$Z\_{mM} = \min\_{i} \max\_{j} \quad V\_{y} \tag{12}$$

The maxi‐min criterion, known as Wald one, describes a prudent attitude of a decision maker. Its objective involves the identification of a scenario leading to worse outcomes. A decision maker adopting this criterion tries to cover himself by providing the least bad possible result. This technique provides information that the evolution of the competition (scenarios) is detrimental to the company.

$$Z\_{Mm} = \max\_{i} \min\_{j} \ V\_{ij} \tag{13}$$

Adopting the Hurwitz criterion consists of the assessment for each strategy a weighted average of the worst and the best of its potential outcomes and choose the one for which the solution is the largest. According to this criterion, the solution is given as follows:

$$Z\_H = \min\_i \left[ \alpha. \max\_j (V\_{ij}) + (\mathbf{l} - \alpha). \min\_j (V\_{ij}) \right] \tag{14}$$

where 0≤*α* ≺1 is a parameter indicating planers' attitude toward risk. The value *α* =1 reduces Hurwitz' criterion to mini‐max criterion as described above and corresponds to an extremely pessimistic decision maker. The value *α* =0 corresponds to an extreme optimism.

### **6. Electricity sustainability development**

#### **6.1. Criteria and indicators**

This investigation was conducted to assist decision makers to understand the societal, economic, and environmental issues of the need for sustainable energy transition. The assumptions and models were summarized on the basis of existing data provided in the bibliographic references. They were submitted to experts to select those that meet the criteria of quality and relevance. The data used in this work are obtained from the statistical treatment and probabilistic modeling in the case where there are no archive data or a limited number available, with the help of expert judgments. Experts are energy service providers, politics oriented to research and development, specialists in the integration of renewable resources to networks, nuclear and nonrenewable energy scientists, researchers in risk analysis, and specialists in the management of energy‐related conflicts. Each expert group dealing with the issue of sustainable development can provide a range of economic, environmental, and social indicators. As noticed in the literature, economic and environmental indicators seem to be obvious and common to the overall society, but it is not the case for social ones. Certainly, the sources of conflicts and accidents in the energy field are not frequent looking to electricity, but the impact of nuclear component highlights the main concerns. They reside in the utilities dysfunction causing blackouts due to their high capacities of production and risk of contam‐ ination in the case of accidents (random or premeditated (sabotage)). As for sustainable development, electricity sustainability (ES) is based on the three known pillars such as social aspects, economic and environment criteria, and indicators noted (*Ci*) and their associated sub‐ criteria noted (*Cij*).

Environment (C1): Resources (C11; energy resources and mineral resources), Climate change (C12), Ecosystem damage (C13; impacts from normal operation and impacts from severe accidents), Waste (C14; chemical waste in underground depositories and radioactive waste in geological repositories).

#### **6.2 Case study application, simulation, and results**

Adopting the Hurwitz criterion consists of the assessment for each strategy a weighted average of the worst and the best of its potential outcomes and choose the one for which the solution

> a

ë û (14)

*H* min .max( ) (1 ).min( ) *ij ij i j j Z VV*

pessimistic decision maker. The value *α* =0 corresponds to an extreme optimism.

é ù = + - ê ú

where 0≤*α* ≺1 is a parameter indicating planers' attitude toward risk. The value *α* =1 reduces Hurwitz' criterion to mini‐max criterion as described above and corresponds to an extremely

This investigation was conducted to assist decision makers to understand the societal, economic, and environmental issues of the need for sustainable energy transition. The assumptions and models were summarized on the basis of existing data provided in the bibliographic references. They were submitted to experts to select those that meet the criteria of quality and relevance. The data used in this work are obtained from the statistical treatment and probabilistic modeling in the case where there are no archive data or a limited number available, with the help of expert judgments. Experts are energy service providers, politics oriented to research and development, specialists in the integration of renewable resources to networks, nuclear and nonrenewable energy scientists, researchers in risk analysis, and specialists in the management of energy‐related conflicts. Each expert group dealing with the issue of sustainable development can provide a range of economic, environmental, and social indicators. As noticed in the literature, economic and environmental indicators seem to be obvious and common to the overall society, but it is not the case for social ones. Certainly, the sources of conflicts and accidents in the energy field are not frequent looking to electricity, but the impact of nuclear component highlights the main concerns. They reside in the utilities dysfunction causing blackouts due to their high capacities of production and risk of contam‐ ination in the case of accidents (random or premeditated (sabotage)). As for sustainable development, electricity sustainability (ES) is based on the three known pillars such as social aspects, economic and environment criteria, and indicators noted (*Ci*) and their associated sub‐

Environment (C1): Resources (C11; energy resources and mineral resources), Climate change (C12), Ecosystem damage (C13; impacts from normal operation and impacts from severe accidents), Waste (C14; chemical waste in underground depositories and radioactive waste in

is the largest. According to this criterion, the solution is given as follows:

286 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

a

**6. Electricity sustainability development**

**6.1. Criteria and indicators**

criteria noted (*Cij*).

geological repositories).

To the hierarchy given in **Figure 1**, were associated the criteria and their sub‐criteria introduced in ‐Section 6.1 and using energy production resources as alternatives, we have determined a long‐run growth of a company in the context of electricity sustainability.

To highlight the great interest of AHP application in sustainability, particularly in the field of energy, we have applied this process with the objective to compare the obtained results with those outlined by other MCDA methods summarized by Hirschberg [3], investigating the development of sustainability assessment at PSI. The different steps of AHP applications were followed, and the pair‐wise comparison results between the indicators with respect to the goal are given in **Table 1**.

**Table 1.** Pair‐wise comparison matrix of the criteria with respect to the goal.

It appears clearly that the criteria are equally prioritized and shown in **Figure 3(a)**. In **Figure 3(b)** are given the proportions (in %) of each sub‐criterion against its main criterion (red color % represents the main criterion, black color % represents the sub‐criterion against the main criterion, and blue color % represents the sub‐criterion against the goal). Each value of a sub‐criterion can be found using the following operation: (sub‐criterion priority (in %) = the sub‐criterion priority (in %) against the goal/the main criterion priority (in %) against the goal). In this case, the advantage of the AHP method is that it is possible to change weights to have an appropriate priority. However in the case of MCDA proposed in reference [3], the results are obtained from a survey work. The results in **Table 2** show the priorities of alternatives are based on all sub‐criteria. The results have allowed us to do a synthesis in the case of equal priorities of main criteria, as given in **Table 3**. From decision makers' point of view, this consideration shows the prudent attitude. And the results show a high priority to renewable resources, followed by nuclear one, but the gap is not significant.

**Figure 3.** Syntheses of criteria and sub‐criteria priorities (case of a prudent decision maker): Main criteria with relative‐ ly equal priorities (a) and sub‐criteria weights (% in black) using AHP, to achieve the priorities (% in blue) compared to the goal (b).

Combining AHP Method with BOCR Merits to Analyze the Outcomes of Business Electricity Sustainability http://dx.doi.org/10.5772/64042 289

**Table 2.** Comparison matrices and local priorities.

**Figure 3.** Syntheses of criteria and sub‐criteria priorities (case of a prudent decision maker): Main criteria with relative‐ ly equal priorities (a) and sub‐criteria weights (% in black) using AHP, to achieve the priorities (% in blue) compared to

288 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

the goal (b).

**Table 3.** Final results using synthesis (equal importance of main criteria).

In the case where the decision maker is optimistic toward environment effects, a high priority is given to the environmental aspects as highlighted in **Table 4** and confirmed in **Figure 4**; it shows that the renewable resources won the highest priority with an important gap com‐ pared to the other alternatives.

**Figure 4.** Syntheses of criteria and sub‐criteria priorities (case of an optimistic decision maker toward environment): Main criteria with the main dominance of environment criterion (a) and sub‐criteria weights (% in black) using AHP, to achieve the priorities (% in blue) compared to the goal (b).

Combining AHP Method with BOCR Merits to Analyze the Outcomes of Business Electricity Sustainability http://dx.doi.org/10.5772/64042 291

**Table 4.** Final results using synthesis (with the dominance of environmental aspect).

**ENVIRONMENT (C1) ECONOMY (C2) SOCIETY (C3) Priorities**

*Weights* **0.343 0.343 0.314**

290 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

**Table 3.** Final results using synthesis (equal importance of main criteria).

pared to the other alternatives.

*Sub‐criteria* C11 C12 C13 C14 C21 C22 C23 C24 C31 C32 C33 C34 C35 C36 *Weights* 0.254 0.346 0.242 0.157 0.321 0.252 0.226 0.200 0.139 0.207 0.205 0.149 0.153 0.145 *Nuclear resource* 0.222 0.249 0.105 0.135 0.637 0.297 0.527 0.539 0.581 0.558 0.332 0.539 0.218 0.186 0.364 *Fossil resource* 0.112 0.097 0.256 0.235 0.258 0.539 0.332 0.163 0.309 0.319 0.527 0.297 0.151 0.126 0.266 *Renewable resources* 0.666 0.654 0.639 0.630 0.104 0.163 0.139 0.297 0.109 0.122 0.139 0.163 0.630 0.687 0.370

In the case where the decision maker is optimistic toward environment effects, a high priority is given to the environmental aspects as highlighted in **Table 4** and confirmed in **Figure 4**; it shows that the renewable resources won the highest priority with an important gap com‐

**Figure 4.** Syntheses of criteria and sub‐criteria priorities (case of an optimistic decision maker toward environment): Main criteria with the main dominance of environment criterion (a) and sub‐criteria weights (% in black) using AHP,

to achieve the priorities (% in blue) compared to the goal (b).

Based on the investigation of Doane and Mac Gillivray [4], where they have stated that the economic criterion should be of high interest compared to the other criteria, we have consid‐ ered that the decision maker is optimistic toward economy and relatively pessimistic toward social and environmental issues. The synthesis given in **Table 5** shows a high priority for nuclear resource with a nonsignificant gap compared to the other alternatives.

**Table 5.** Final results using synthesis (with the dominance of economic aspects) with a completed number of sub‐ criteria.

Through this simulation, we retain the interest of the environmental aspect in sustainable development, and the development of renewable resources is imperative. From decision makers' point of view, the AHP method allowed us to simulate attitudes of managers without difficulty.


**Carbozincation of Substituted 2-Alkynylamines, 1-Alkynylphosphines, 1-Alkynylphosphine Sulfides with Et 2Zn in the Presence of Catalytic System of Ti(O-***i***Pr) 4 and EtMgBr**

### **Rita N. Kadikova \*, Ilfir R. Ramazanov, Azat M. Gabdullin, Oleg S. Mozgovoi and Usein M. Dzhemilev**

Institute of Petrochemistry and Catalysis of Russian Academy of Sciences, 141 Prospekt Oktyabrya, 450075 Ufa, Russia<EMAIL_ADDRESS>(I.R.R<EMAIL_ADDRESS>(A.M.G<EMAIL_ADDRESS>(O.S.M<EMAIL_ADDRESS>(U.M.D.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +7-(347)-284-27-50

Received: 1 November 2019; Accepted: 28 November 2019; Published: 4 December 2019

**Abstract:** The EtMgBr and Ti(O-*i*Pr)4-catalyzed ethylzincation of 1-alkynylphosphine sulfides with Et2Zn in diethyl ether followed by hydrolysis and deuterolysis a ffords corresponding β,β-disubstituted 1-alkenylphosphine sulfides with high yield. The EtMgBr and Ti(O-*i*Pr)4-catalyzed reaction of 2-alkynylamines, 1-alkynylphosphines, and 1-alkenylphosphine sulfides with Et2Zn in various solvents was studied. It has been found that the reaction of 2-alkynylamines and 1-alkynylphosphines in methylene chloride, hexane, toluene, benzene, and anisole leads to the selective formation of 2-alkenylamines and 1-alkenylphosphine oxides after oxidation with H2O2.

**Keywords:** ethylzincation; 1-alkynylphosphine sulfides; 1-alkynylphosphines; 2-alkynylamines; 2-zincoethylzincation; titanium catalysis; diethylzinc


**2. Method**

#### **2.1 Microstructure image and mapping**

**Figure 1(a)** shows the workflow procedure of OOF2 analysis. The complete OOF2 simulation and analysis process consists of six steps. In the first step, a microstructure image is needed as input; for this purpose, materials scanning electron microscopy (SEM) or back-scattered electron (BSE) images can be used. A BSE microstructure image of NBT-6BT/ZnO composites contains 4% ZnO by volume is used for analysis, as shown in **Figure 1(b)**. The image consists of a length of 24 μm

#### **Figure 1.**

*(a) Outline of OOF2 analysis procedure (b) microstructural image of composites having NBT-6BT-4% ZnO, (c) single-phase material pixel selection, assign group and properties. (Reprint with permission from Ref. [2]. Copyright© 2020 Elsevier BV).*

and size of 645 484 pixels. In the BSE microstructure, contrast is used to differentiate NBT-6BT (matrix) and ZnO (inclusion or filler phase). The single-phase material pixels are selected by pixel selection and grouped to give each phase thermal and mechanical properties. **Figure 1(c)** illustrates that the red color pixel belongs to NBT-6BT and the gray color pixel represents the ZnO. It is to be noted that the composite is not fully dense; thus, pores (4%) are also obtained, as shown in **Figure 1(c)** in white color. Then selected single phase pixel materials are assigned with their thermal and mechanical properties, i.e., Poisson ratio, Y (GPa), λ (W/m-K) and α (K1 ).

Similar kinds of pixel selection and properties assignment are used by many researchers where two-phase materials or composites such as Ni-Al [37], Al-MgO [19], WC-Al2O3 [20] and AlN-TiN [21] for various applications. Moreover, a varying ZnO composition from 4–10% is also studied by Manish *et al.* [2] for NBT-6BT-ZnO composites. In the next step, microstructural finite element meshing is created by a skeleton, as shown in **Figure 2**. The geometry of the mesh explained the geometry of the skeleton. It does not cover the information about the finite element shape functions, equations, fields, etc. The skeleton represents the FE discretization of the microstructural. It is composed of quadrilateral and triangular elements, nodes, and segments. In the OOF2, the skeleton is refined by various tools, as discussed in Section 2.2.

#### **2.2 Skeleton modification and refinement**

**Figure 2(a)** and **(b)** show the nodes of a skeleton element where nodes are on the element's corner and edges. However, the other FEM tools generally do not consider the nodes along their edges or interiors. In the refinement process, nodes of the edge move along the edge only. Moreover, the interior nodes are free to move *Thermomechanical Analysis of Ceramic Composites Using Object Oriented Finite Element… DOI: http://dx.doi.org/10.5772/intechopen.100190*

#### **Figure 2.**

*(a) and (b) Microstructural meshing with node movement, (Reprint with permission from Ref. [2] Copyright © 2014 Wiley Publishing Ltd) (c) energy functional approach used during skeleton mesh refinement process [38], (d) final mesh with boundary conditions of NBT-6BT-4% ZnO (Reprint with permission from Ref. [21] Copyright© 2020 Elsevier BV).*

anywhere. These node's movement can also be restricted by the pin node tool. In the **Figure 2(a)**, an element (A, B, C) is shown, which can create an illegal element via movement, as shown in **Figure 2(b)**. The node 'B' motion (see **Figure 2(a)**) generates two illegal elements (**Figure 2b**). The illegal element refers to an element that breaks the ordering; three collinear nodes also create illegal elements (nonconvex quadrilaterals). The highlighted quadrilateral element represents the illegal element because its nodes (A, B, C) are not convex (**Figure 2b**).

This type of node movement and element creation depends on the mesh energy parameters. Further, the FE skeleton elements refinement process increases the mesh quality and reduces functional energy parameter (Ё) [36]. Two types of effective energy function maintain the mesh quality as shape energy (ЁS) and homogeneity energy (ЁH). The ЁH is given as [15]:

$$
\ddot{\mathbf{E}}\_H = \mathbf{1} - \ddot{\mathbf{E}}\_{HM} \tag{1}
$$

where ЁHM is microstructural components homogeneity energy. ЁH can be reduced when all components of the microstructure are encompassing a singlephase material. In the case of triangular element ЁS is defined as [13]:

$$
\ddot{\mathbf{E}}\_{\mathcal{S}} = \mathbf{1} - \mathbf{4}\sqrt{3} \, A\_T/l^2 \tag{2}
$$

where A*T* and *l* are triangle element area and side length, respectively. For the equilateral triangular component, *ЁS* is zero and equal to one when all the vertices are collinear (zero aspect ratio). It can also be estimated for quadrilateral elements using a quality factor *γi* for each corner *i* as [16]:

$$\gamma\_i = \frac{A\_{par}}{l\_0^2 + l\_1^2} \tag{3}$$

where *Apar* is, the area of the parallelogram formed by *l0* and *l*1 edge length element converges at node *i*. *γi* <1 at a corner where the two converging edges have different lengths or meet at an acute/obtuse angle. *γi* ¼ 0 when edges are collinear or the length of one edge is zero (degenerate cases). Shape energy for a quad element is estimated by weighted average from the *γS* at the corner with the minimum γ (*γM*) and the corner opposite to it (*γ*0). The weighted average method is utilized to make sure that each node movement affects the total energy and quadrilateral element ЁS can be defined as [13, 15]:

$$\ddot{\mathbf{E}}\_{\mathcal{S}} = \mathbf{1} - [(\mathbf{1} - \eta)\boldsymbol{\sigma}\_{m} + \eta \boldsymbol{\gamma}\_{0}],\tag{4}$$

where η = 10�5 is an arbitrary small parameter. It is needed to avoid pathologies that arise due to the shape energy has no dependence on the position of one of the nodes. The energy functional parameter (*Ё*) is expressed by [13, 16]:

$$
\ddot{\mathbf{E}} = \mathbf{6}\ddot{\mathbf{E}}\_H + (\mathbf{1} - \mathbf{6})\ddot{\mathbf{E}}\_S,\tag{5}
$$

For δ = 0, ЁS will note benefaction in Ё of the elements. There will be a trade-off between ЁS and ЁH when 0 < δ > 1. Some skeleton refinement processes are used to achieve the optimum homogeneity and shape of the element. These energy functions elements are depicted in **Figure 2(c)**.

The homogeneity energy (ЁH) of the elements is contributing the total Ё when δ = 1 and skeleton refining δ is several according to homogeneity index. For the mesh refinement, firstly, we focus on reduce ЁH of an element by assigning a higher value of δ. **Figure 2(c)** displays different types of ЁS and ЁH components. In the equilateral triangular element 1, as shown in **Figure 2(c)**, the contribution of ЁS is zero. Further, element 1 also contain single material; hence the ЁH value of the element is also zero. ЁS rise for elements 2 and 3 as the triangular shape deviates from that of an equilateral triangle. Similarly, element 2 also has ЁH as zero because of homogeneous phase content. Therefore, ЁS and ЁH of elements 2 and 3 contribute to the total energy function parameter (Ё).

Subsequently, the skeleton is generated and modified by various refinement tools, i.e., snap refine, anneal, snap node, merge triangle, refine, smooth, etc. In the snap anneal process, each node tries to move and turns to a pixel boundary. Snap refine skelton modifier tool combines the most likable refine and snap nodes features in a single method. It is subdivided into components along pixel boundaries. Snap refine introduces additional edges and new nodes that can be made to follow pixel category boundaries. So, it can also be more flexible than snap nodes in fitting a skeleton, as shown in **Figure 2(c)**. In a smooth tool, nodes move to the average positions of their nearby element. The node satisfied the acceptance criteria and the move is accepted. Smoothing of the skeleton requires several iterations. The merge triangle modifier tool is used to merge neighboring homogeneous triangles to form a quadrilateral element. Rationalize is used to fix an irregular-shaped component of a *Thermomechanical Analysis of Ceramic Composites Using Object Oriented Finite Element… DOI: http://dx.doi.org/10.5772/intechopen.100190*

microstructure skeleton by removing their immediate neighbors. Relax tool moves nodes and improves element shape and homogeneity. Thus, each refinement tool has its refinement process. The final skeleton explains only the mesh's geometry; it does not cover any information about the finite element shape functions, field, equations, etc. The skeleton creates FE mesh, and the final mesh generation is shown in **Figure 2(d)**. The accuracy of FE solutions be dependent on the homogeneity index and mesh quality. The FE mesh has a 0.98 homogeneity index with 6039 nodes and 8373 elements [38].

#### **2.3 Micro-scale fields and equations**

In the case of temperature and displacement applied on the image, the force balance equation and temperature field should be defined in-plane. Fields are defined on two and more graphically overlapping subproblems on a FE mesh. For each subproblem, the field's value is the same. These values are only stored on a FE mesh. OOF2 used 3D material but solved 2D problems. OOF2 has a generalized plane strain and plane stress approach, implemented by an in-plane elastic modulus. In this software, two types of equations are used plane-flux and divergence. It is activated and deactivated on subproblems. The static divergence equation is expressed as [39]:

$$\nabla \cdot f \mathbf{l} \omega \mathbf{x} + \text{force} = \mathbf{0} \tag{6}$$

where force is generalized force, i.e., heat equation (∇�J = �∂U/∂T, where -∂U/ ∂T is a change of energy density) and force balance equation (∇�σ = f, where f is actual force). The nonstatic equation is a general form of divergence equation ( time-dependent version) and given by [39]:

$$M\frac{\partial^2}{\partial t^2}\text{field} + \mathcal{C}\frac{\partial}{\partial t}\text{field} + \nabla \cdot f\text{flux} + \text{force} = \mathbf{0},\tag{7}$$

Heat equation for the first-order problem, M term will be zero. C is the second problem that may be zero. Plane flux equation is a generalization of plane stress and the out of plane component flux is zero and can be written as [39]:

$$(Fl\boldsymbol{u}\boldsymbol{\omega})\_x = \mathbf{0} \tag{8}$$

It can solve nonlinear Eqs. (6)-(8) if the nonlinearity is limited to force and flux terms.

#### **2.4 Boundary conditions**

OOF2 FE tool provides five boundary conditions: Dirichlet, floating, periodic, Navman, and generalized force. This work uses Dirichlet boundary conditions on the microstructure image, as shown in **Figure 2(d)**. The Dirichlet boundary condition has identified the value of one component of a field along with a boundary. In both cases, the temperature and displacement application force balance equation and temperature field are defined in-plane. However, when plane strain is used, then the displacement is defined, active, and in-plane. Similarly, for thermal stress force balance equation is used when the temperature is defined, active, and inplane. The periodic boundary conditions are applied on the left and right vertical edges. The microstructure edge is considered at a constant temperature and/or displacement. In the present work, boundary conditions are depicted in the

**Figure 2(d)**, where the left side edge is fixed or at zero displacements (i.e.*, U*|*left* = *U0* = 0). When a temperature gradient is used, the same edge is considered under a low temperature (*T*|*left* = TL). However, the right edge is kept as defined displacement (*U*|*right* = *U1*). When a temperature gradient is used, the same edge is considered for higher temperature (*T*|*right* = TR). Moreover, the governing equations are solved iteratively and the convergence criterion is fixed as 10�13. Finally, thermal or elastic stress/strain contours are plotted for the analysis (discussed in Section 4). It is to be mentioned that these steps are previously discussed in detail by several researchers [2, 13, 16, 19, 20, 40].

#### **2.5 Assumption**

The matrix and individual filler properties are considered isotropic, linear elastic and homogeneous. It is considered that matrix and filler interfaces have good bonding. The homogeneity index of mesh is obtained as 98% and the same is used for simulation. In the selected temperature range, material properties are assumed to be constant. In the simulation 2D microstructure is used; thus, the effect of thickness is not considered. The OOF2 software maintained vector (displacement), scalar (temperature) and tensor fields on two and more graphically overlapping sub-problems of a FE mesh. In the case of uniform temperature application, all the edges temperature fixed at the same temperature. The basic iterative matrix equation solver is applied to obtain the solution. The symmetric and asymmetric matrixes are solved using Conjugate Gradient and generalized minimum residual method, respectively. In both cases, a Bi-conjugate gradient with the incomplete lower upper (ILU) preconditioner is used for FE simulation. Once field equations achieve the solution, thermal and mechanical properties are obtained with the help of averaging the applied field.

#### **3. Comparison of analytical and simulation analysis**

#### **3.1 Young's modulus**

Young's modulus (Y) is predicated using OOF2 analysis and results are compared with the analytical method. It is well known that the NBT-6BT ceramics is brittle in nature and have lower fracture toughness. Therefore, ZnO addition can improve the *Y* and elevate other properties of the composite. The left edge (*d*j *left*) of microstructure is considered at zero displacement and right edge (*d*j *right*) is given a uniform displacement as:

$$d|\_{left} = d\_0(d\_\times = \mathbf{0})\tag{9}$$

$$d|\_{\rm right} = d\_1(d\_\mathbf{x} = \mathbf{0}.001) \tag{10}$$

A similar boundary condition is depicted in the **Figure 2(d)**. Y of composites is calculated by:

$$Y\_{\text{avg}} = \frac{\text{stress}}{\text{strain}} = \frac{\sigma\_{\text{avg}}}{\mathbf{\mathcal{E}}\_{\text{avg}}} \tag{11}$$

Where ɛavg is average strain and σavg is average stress. The small displacement is applied to the microstructure; hence, it can be assumed that only elastic deformation occurs. The calculated Y is given in the **Table 1**.

*Thermomechanical Analysis of Ceramic Composites Using Object Oriented Finite Element… DOI: http://dx.doi.org/10.5772/intechopen.100190*

The predicated Y is also compared with various theoretical models, i.e., Reuss rule of mixture [41], Voigt rule mixture [42] and Hashin and Shtrikman [43] are also given in **Table 1**. Many researchers considered these methods to estimate *Y* of composites and compared them with OOF2 results [2, 13, 19, 44, 45]. The estimated value by OOF2 is in close agreement with that of theoretical methods values. Similar studies are also considered with various compositions by variation of filler content [2, 13, 19, 44, 45]. As the filler volume increases, the effective Y of composites also increases in most cases. However, the composites Y variations depend on the difference between matrix and filler Y.

#### **3.2 Thermal expansion coefficient and thermal conductivity analysis**

In order to predict the thermal properties of NBT-6BT- ZnO composites, the α is estimated by OOF2 analysis. The α is predicted when the microstructure edges are at a 10°C temperature difference. The thermal boundary conditions are depicted in the **Figure 2(d)**, where the left side edge is kept at low temperature (*T*|*left* = TL = 30° C). However, the right edge is kept at a higher temperature (*T*|*right* = TR = 40°C). Moreover, the bottom and top edges are kept as adiabatic. The α is obtained by:

$$a = \frac{\mathfrak{E}\_{\text{avg}}}{\Delta t} \tag{12}$$

where ΔT is the temperature difference. The α predicted with the help of OOF2 analysis is given in **Table 1**. The α is also estimated with the help of different theoretical methods, i.e., Kerner's model [46], Rule of a mixture, Turner's model [47], and Schapey's model [48] and given in **Table 1**. It can be said that the OOF2 predicted value of α is in good agreement with different theoretical methods. A similar analysis is performed with different filler (ZnO) compositions based composited and found that as the filler content increases, α decreases [2]. This is because the filler's α is lower than the matrix α. A similar study is also performed to analyze the behavior of α in composites with different filler content by many researchers [1, 2, 12, 13, 49].

**Figure 3(a)** and **(b)** show the boundary conditions for WC-Al2O3 and AlN-TiN based composites to obtain the λ. In this case, the top and bottom edges are considered insulating to ensure heat transfer in one direction only.

The heat flux equation is solved by the conjugate gradient method with the help of a linear solver. The equivalent effective λ of composites is expressed by Fourier's law:

#### **Table 1.**

*Comparison of Young's modulus (GPa) and the effective α (*�*10*�*6 °C*�*1 ) obtained using OOF2 analysis and various theoretical methods [2].*

**Figure 3.**

*(a) Boundary condition for WC-Al2O3 (Reprint with permission from Ref. [20] Copyright© 2014 Imperial College Press) and (b) heat flux profile of AlN-5%TiN composites for thermal conductivity analysis. (Reprint with permission from Ref. [21] Copyright© 2014 Wiley Publishing Ltd).*

$$
\lambda = A \frac{Q\_{avgdx}}{dT} \tag{13}
$$

where Qavg is average heat flux, A is the cross-sectional area, dT is temperature difference and x is width of the microstructure.

The λ of both composites WC-Al2O3 and AlN-5%TiN is predicated by OOF2 and found that results agree with various theoretical methods/models (effectivemedium theory arithmetic and harmonic mean model, geometric mean model Lewis and Nielsen method, and Maxwell method) [20, 21]. A similar investigation is performed with various Al2O3 and TiN content and found that as the Al2O3 and TiN increase, λ of composites decreases and increases, respectively [20, 21].

Thus, the increase or decrease of composites λ is dependent on the filler's λ. The Y, α and λ analysis shows that OOF2 can effectively predict composites' thermal and mechanical properties. In order to look in-depth at the thermal and elastic stress/ strain behavior under uniform and gradient temperature conditions, various contour plots are discussed in Section 4.

#### **4. Microstructural stress-strain analysis**

#### **4.1 Stress-strain analysis under uniform temperature**

A homogenous temperature is applied to the microstructure and thermal stress distribution is analyzed in the composites. **Figure 4(a)** shows typical thermal stress (σxx) contour plots when a homogenous temperature of 500°C is applied on NBT-6BT-4%ZnO composite. It is found that the stresses are highest at the sharp edges/ interfaces of matrix and filler. At the interface, the stress distribution region is varied and nonuniformly distributed in the filler region. This is because the stress variation depends on the size of the filler particles/grains [50]. If the applied temperature is sufficiently large, local stress can reach above the yield strength, resulting in thermal cracking of the composite [17]. It is important to note that a critical radius is needed for the thermal or residual stress-based crack initiation in the composites. However, most of the case length of maximum stress is small compared to the critical length of crack initiation. Thus, the residual or thermal stress does not form a crack in the composites. Therefore, composites will not fail under such circumstances and can be utilized at higher temperatures. Moreover, when the composite is cool down to room temperature, the residual stresses play a

*Thermomechanical Analysis of Ceramic Composites Using Object Oriented Finite Element… DOI: http://dx.doi.org/10.5772/intechopen.100190*

#### **Figure 4.**

*Thermal stress (a) contour plots when a homogenous temperature of 500°C is applied on microstructure/image and (b) variation across the line scan as shown in (a), (c) thermal stress variation under different uniform temperature conditions, (d) thermal strain contours when a homogenous temperature of 500°C is applied. All plots are shown for the NBT-6BT-4%ZnO composite. (Reprint with permission from Ref. [2]. Copyright© 2020 Elsevier BV).*

vital role. The magnitude of the residual stress varies according to the applied temperature; however, the exact value of residual stress is hard to predict by OOF2. Further, the filler has more stress distribution compared to the matrix because filler/ZnO have lower α (4.3 106 °C1 ) compared to matrix/NBT-6BT (7 106 ° C1 ) [2]. However, if the matrix has lower α compared to filler, then vice versa stress distribution can be observed. This type of stress behavior is reported for AlN-TiN composites where filler (TiN) and matrix (AlN) has an α of 9.1 106 °C1 and 4.6 106 °C1 , respectively [21].

In order to look in-depth at stress distribution around the filler/matrix interface, a line scan is used (zoom part in the **Figure 4(a)**). The corresponding stress variation is depicted in **Figure 4(b)**. At the interface, stresses increase to 10 and 3 times of average stress in matrix and filler regions. Moreover, the filler region has 3 times higher stress distribution compared to the matrix region. This is because of the difference between Y and α of filler and matrix of composites. It is found that filler consists of tensile stress of 60 MPa, whereas matrix has a compressive stress of 20 MPa. The compressive and tensile stress distributions are observed in different regions of composites. When the temperature is applied, one material expands more than others because of a mismatch of α, which compresses the other materials in some regions. However, in NBT-6BT-ZnO composites, the compressive stress value is lower than tensile stress.

In the same way, the homogenous temperature is varied from 100 to 1100°C and contours are plotted at each temperature. It is found that stress distribution is similar to **Figure 4(a)**, whereas the magnitude of stress is varied according to applied temperature. **Figure 4(c)** shows the maximum stresses (tensile and

compressive) when a homogenous temperature of 100 to 1100°C is applied. As the applied temperature increases, both tensile and compressive stress increases. This is because of that at higher temperature large mismatched between α of filler and matrix is obtained. A similar trend is also observed in other ZnO content compositions. Moreover, it was found that as the filler content increases magnitude of the stress (tensile and compressive) also increases. It is because the higher volume content of filler increases the larger surface area for the mismatch of α. A similar stress–strain simulation is performed on various ceramics composites such as Al2O3- SiC [51], Ni-Al2O3 [10], WC-Al2O3 [20], AlN-TiN [21], etc. They found that with an increase in temperature and filler volume, stress distribution also increases. The detailed discussion on the interface stress variation due to mismatch of the α and Y in composites is also discussed by Chawla *et al.* [13, 14] and Wang *et al.* [45].

**Figure 4(d)** shows the thermal strain contour when a homogenous temperature of 500°C is applied on the NBT-6BT-4%ZnO composite. The matrix has a high strain compared to filler due to the mismatch of α. Further, strain looks homogenous in both filler and matrix, resulting in constant stress in NBT-6BT and ZnO. However, **Figure 4(a)** shows that the stresses are nonuniformly distributed in the composites. Moreover, **Figure 4(d)** shows positive strain only, whereas negative stress is also observed in **Figure 4(a)**. When a temperature is applied on the composites, each grain/interface regions of matrix/filler consist of different thermal strain distribution, which results in stress variation/distribution at the interface. At some point, the interface experiences large compressive stress that can be negligible or act on a small length compared to tensile stress. Further, it was found that as the applied temperature increases, the strain also increases. It is a result of an increase in α with temperature for both filler and matrix. The thermal strain variations also alter with an increase in ZnO/filler content in compositions. This is because the higher volume content of filler increases the larger surface area for the mismatch of α. In the same way, Al-MgO [19], WC-Al2O3 [20], Ni-Al2O3 [4, 10], AlN-TiN [21], etc., are also studied to look at the effect of uniform temperature and filler content. Apart from these, numerous other composites are also studied for better strain control via tailoring α of the filler/matrix [5, 10, 18, 19, 23, 41, 51]. Moreover, the effective α in composites analysis is potentially used in TBC and thermal resistancebased applications [7–9].

#### **4.2 Stress-strain behaviors under gradient temperature**

The OOF2 analysis is performed under a gradient temperature condition of 0– 800°C for composites (AlN-5%TiN). For this purpose left and right edge is applied with a temperature of 0°C and 800°C. However, the bottom and top edges are considered adiabatic, as depicted in **Figure 5(a)**. The resultant thermal stress contour under gradient temperature is shown in the **Figure 5(a)**. It is observed from **Figure 5(a)** as the temperature increases from left to right, corresponding stresses also increase. The stresses are found to be maximum at the interface of the filler/ matrix and nonuniformly distributed. Further, the stress distribution is localized at the filler region and increases composite failure/crack risk. As the filler content increases, the risk of failure is considerably higher due to clustering. The inclusion of the filler can decrease or increase the stress distribution in composites which again depends on the difference of Y and α of matrix/filler. Moreover, the possibility of crack generation depends on the length maximum stress distribution at the interface or critical length of the crack. The reason for the same is already discussed in Section 4.1 and the same is also valid here. Interestingly, it is found that the stress distribution largely varies according to the orientation of the filler grain. The inset of **Figure 5(a)** shows stress variation around two grains (i) and (ii). It can be seen

*Thermomechanical Analysis of Ceramic Composites Using Object Oriented Finite Element… DOI: http://dx.doi.org/10.5772/intechopen.100190*

#### **Figure 5.**

*(a) Thermal stress contour when a gradient temperature of 0–800°C is applied, (b) maximum upper (tensile) and lower (compressive) thermal stress and (c) thermal strain contours when a gradient temperature of 0–800° C is applied for AlN-5%TiN composites. (Reprint with permission from Ref. [21]. Copyright © 2014 Wiley Publishing Ltd).*

that in the region (i) (**Figure 5(a)**), filler/grain is aligned with the applied temperature consists of higher stress compared to grain (ii) which is almost perpendicular to applied temperature. However, both the grain (i) and (ii) regions have similar temperature zones. Alike behavior is also observed in entire composites. Similar behavior is also observed in numerous compositions of Al-MgO [19], WC-Al2O3 [20], NBT-6BT-ZnO [2], Ni-Al2O3 [4, 10], etc. Further, with an increase in filler compositions, the magnitude of the stress increases, whereas the grain orientation behavior remains the same. It can be said that the various strength of composites can be fabricated via preferred grain orientation. Moreover, a large amount of thermal/residual stress can be increased/decreased in composites according to the direction of the grain (transverse and longitudinal). Hence, if composite is synthesized by oriented grain, i.e., filler as platelets/nanorods instead of power can show better performance. Recently, BaTiO3:100xZnO composite ceramics are made with a micrometer and nanometer scaled power, supporting these observations [52].

Similar to Section 4.1, tensile and compressive stress is observed in the gradient temperature conditions, whereas the magnitude is lower than that of uniform temperature conditions. The tensile and compressive stress increases with applied temperature, as shown in the **Figure 5(b)**. The left side edge temperature is fixed as 0°C, whereas the right side temperature varies from 100 to 1100°C. The stresses linearly increase with the applied temperatures. Several researchers have reported alike trends in various composites. Thermal strain contour under a gradient temperature condition of 0–800°C for composites (AlN-5%TiN) is presented in **Figure 5(c)**. It is observed that as the temperature increases from left to right, the corresponding strain also increases. The filler has a higher strain than the matrix because of filler has higher α compared to the matrix. Further, a large number of

pores are observed in the AlN-TiN composites. When a temperature is applied, filler/matrix can easily expand at pores; hence, the variation in stress distribution is not observed. These types of strain contour and analysis are also discussed in the literature [2, 5, 13, 20]. It can be said the OOF2 can be an effective tool to see the effect of grain orientation or stress concentration at the interface.

## **4.3 Elastic stress-strain analysis**

The elastic stress-strain is studied in the composite by deforming microstructure, as presented in **Figure 6**. Thus, the left edge is kept as fixed *U*|*left* = 0 and the right edge *U*|right = 0.3 μm is deformed and resultant stress-strain contours are depicted in **Figure 6** for Al-10% MgO composites. **Figure 6(a)** shows that the matrix (Al) has lower stress as compared to filler (MgO). This is due to the fact that the matrix has lower Y than filler as 70 GPa and 294 GPa, respectively [19]. Further, maximum stresses are obtained at the interface of the filler and matrix in an entire composite. It gives crucial information about the composite that interfaces play a vital role in effective load transfer between filler and matrix. The sharp edges of the grain have enormous stress (stress intensification occurs) compared to smooth edges. These edges of filler act as stress concentration sites and are more pronounced when filler/grain is oriented in the direction of the applied load. Hence, if the uniform size of grain/filler is added to the matrix, then the strength of the composites can be improved. Similar behavior is also observed when the filler content is increased from 5–15%. However, the magnitude of stress increases with the inclusion of filler due to more frequent particle-to-particle contact. It is also observed that grain orientation also plays a vital role in stress distribution. The effect of filler orientation on elastic stress distribution is the same as discussed in Section 4.2.

The stress distribution can help to obtain the composite failure analysis. If the length of stress distribution (higher than yield stress) is more than the critical radius, crack generation will occur. Another software integration or analytical calculation is needed to find the exact failure stress analysis because OOF2 cannot provide direct failure analysis. The elastic behavior under various deformed conditions in different composites is previously studied [2, 5, 13, 20, 21]. They also found a similar type of stress–strain contour. However, the magnitude of the stress varies according to composite compositions. Effect of Y in matrix and filler interface, load transfer and orientation effect in composites are discussed by Chawla *et al.* [13] and

#### **Figure 6.**

*(a) Elastic stress (b) elastic strain contours for composites under μm displacement. Al-10%MgO composites. (Reprint with permission from Ref. [19]. Copyright © World Scientific Publishing Company).*

#### *Thermomechanical Analysis of Ceramic Composites Using Object Oriented Finite Element… DOI: http://dx.doi.org/10.5772/intechopen.100190*

Wang *et al.* [33], respectively [45]. They found that closely spaced filler encourages more deformation within the matrix. Moreover, the neighbor of weak filler zones evolves and, in the end, leads to mechanical failure. These low and high stresses can be calculated and used to forecast the composite's failure displacement and temperature. Additionally, **Figure 6(b)** depicts the contour of strain variation under the elastic displacement condition. The matrix has a higher strain compare to filler and is concentrated at interfaces. A higher strain is observed at closely placed filler because of a large degree of constraint region. Other researchers in different ceramic composites previously observe a similar effect. This region can lead to failure of the composites; in this direction, matrix, filler and filler-matrix interface failure criteria are provided by Ha *et al.* [53]. It can be said that the geometric inhomogeneity in composites produces the nonuniform strain/stresses due to mechanical or thermal loadings. Thus, failure can initiate at any point within the composite, filler, matrix, or filler-matrix interface and consists of different failure processes according to the initiation of critical points. Recently, a similar boundary condition (shown in **Figure 6**) is also applied for NBT-6BT/ZnO composite to obtain the elastic stress–strain response [2, 38]. It was found that the stresses are concentrated at the sharp edges or interface of the composites and increase with the ZnO concentration. However, strain is uniform throughout the composites for particular compositions and varied with ZnO content [2, 38]. Further, the predicated stress–strain are compared with experimental data, which shows good agreement and validates findings by OOF2 [2].

In summary, ceramics composites have a wide variety of applications in aerospace, defense, energy, medical and transport sectors due to higher strength, toughness or fracture, etc. [54]. They are also extensively used for the TBC [7–9] and nuclear fuel cell [6] applications due to high α [10–12], thermal shock resistance [3, 6] and better λ [1, 3, 5, 6, 11]. However, predicting precise ceramics composites' thermal and mechanical properties by numerical or simulation techniques has limited success so far. In this direction OOFEM based analysis only take care of the effect of size, shape, orientation, distribution and arrangement of individual matrix/filler phases during the analysis. Hence, considering these individual phases properties, it is used to predict ceramics composite λ, α, Y, σr, wear, cracking analysis and thermal/mechanical stress–strain contour on microstructure images. It can be said that OOF2 is an effective tool to obtain real microstructural analysis compared to other existing FE analysis techniques. Moreover, it provides the input meshing/parameter for various commercial software to achieve real-time thermal/ mechanical/electric analysis. Thus, ceramic composites' effective thermal/mechanical properties (λ, α, Y) should be analyzed with OOF2 to obtain the real interaction between filler/matrix or distribution of σr, wear and crack in individual phases.

#### **4.4 Integration of OOF2 with other software**

The OOF2 software is also integrated with other software where composite failure analysis is performed. In this direction, OOF2 is utilized for mesh generation because it uses the actual microstructure of composites. Then the mesh is imported into the other software such as ABAQUS for further analysis. In this direction, OOF2 is used for Al-Al2O3 composites, matrix, pores and particles selection in microstructure; then mesh is generated and converted to two dimensional-FE to analyze in ABAQUS [55]. Similarly, W/Cu composite is considered for preprocessing by OOF2; however, the commercial FEM code ABAQUS is used as a solver [11]. Moreover, SiC/SiC composite microstructure generates FE by OOF2 from simplified images of the composite cross-sections. The final FE mesh is exported directly into the ABAQUS to analyze effective material properties and

stress distributions [56]. OOF2 and ANSYS are used to obtain the λ based on 2D and 3D calculations, respectively [57]. They found that a power-law function can accurately define the relationship between 2D and 3D results [57]. Further, they concluded that various microstructure images with pores are also valid for λ and 2D image-based model is easy to implement [57]. The YSZ based TBC image is imported in OOF2 and a mesh is constructed; then, a nonlinear elastic–plastic simulation model of micro-indentation is used for further simulation performed by ABAQUS software [58]. Finally, a three-dimensional (3D) OOFEM is also developed by NIST USA to simulate materials' overall mechanical, dielectric, or thermal properties using actual or simulated micrographs [59]. In summary, it can be said that OOF2 can be used in varieties of microstructure mesh generation, which is further integrated into other software for detailed analysis.