**Abstract**

This chapter discussed the object oriented finite element (OOF2)-based studies for ceramic composites. OOF2 is an effective method that uses an actual microstructure image of the material/composites for simulation. The effect of filler inclusions on the thermomechanical properties (coefficient of thermal expansion, thermal conductivity, Young's modulus, stress and strain) is discussed. For this purpose, various ceramics composites (thermal barrier coating and ferroelectric based) are considered at homogeneous and heterogeneous temperature/stress conditions. The maximum stress is found at the interface of the filler/matrix due to their mismatch of thermal expansion coefficient. Further, residual and localized interface stress distributions are evaluated to analyze the composite's failure behavior. The possible integration of OOF2 with other simulation techniques is also explored.

**Keywords:** OOF2, Ceramics composite, Object Oriented Finite Element, Thermal stress/strain, Thermomechanical analysis

## **1. Introduction**

Ceramics composites are a significant field of research for the industrialist and researcher [1–6]. This is because of their wide variety of applications and better mechanical properties such as higher strength, toughness or fracture, etc. Apart from the superior mechanical properties, ceramic composites are extensively used for the thermal barrier coating (TBC) [7–9] and nuclear fuel cell [6] applications due to high thermal expansion coefficient (α) [10–12], thermal shock resistance [3, 6] and thermal conductivity (λ) [1, 3, 5, 6, 11]. Many researchers have studied ceramics composites' effective thermal and mechanical properties with changes in compositions using different modeling approaches [4, 5, 13, 14]. However, the prediction of precise thermal and mechanical properties by various numerical or simulation techniques has limited success so far [4]. Several modeling methods are used to obtain ceramics composites' thermal and mechanical properties [4, 5, 13, 14]. These methods are categorized in two ways (i) macroscopic and (ii) microscopic. The macroscopic approach is easy to implement and predicts the average or global response of composites. Thus, it considers the volumetric effect of individual phases in the composites. However, the effect of size, shape, orientation, and arrangement of individual phases related to microstructure is wholly ignored.

This parameter plays a vital role in the effective thermal and mechanical properties of composites. Therefore, many finite element methods (FEM) are widely applied to predict/analyze and improve the thermomechanical properties of composite materials [4, 5, 13, 14]. FEM can easily integrate the microstructural details of composites and are also computationally intensive [4].

In this direction, the Object-oriented finite element method (OOFEM) can be an effective method in the FEM analysis. This method takes care of complexities of microstructure such as the effect of size, shape, orientation, and arrangement of individual phase, particularly in multiple component microstructure [2]. OOFEM is considered the actual microstructure of the materials compared to conventional FEM, where a "unit cell" model is used to predict material properties [2]. Moreover, the microstructure boundary conditions can be easy to implement. In this context, various researchers have used open-source software OOF2 2D version [1, 3, 4, 7, 15, 16]. The OOF2 software is developed by the National Institute of Standard and Technology (NIST) USA, an open-source tool [http://www.ctems. nist.govt./oof/oof2/index:html#download]. The OOF2 modeling uses microstructural images as input and considered individual phase grain size, shape, local orientation and distribution, etc., with their mechanical and physical properties for analysis [4, 5, 10, 15, 16]. It is used to predict composite thermal and mechanical properties such as λ, α, Young's modulus (Y) and thermal/mechanical stress– strain contour on microstructure images. Similarly, the residual thermal stresses (σr), the effect of thickness, λ and cracking in TBC due to stress relaxation are also investigated [3, 8, 9, 11, 17]. Additionally, these (σr, Y, λ and α) properties of composite with respect to filler content and operating conditions are analyzed. In this direction, numerous composites, i.e., 0.94Na1/2Bi1/2TiO3–0.06BaTiO3/ZnO (NBT-6BT-ZnO), Ni-Al2O3, Al/B4C, Al-TiB2 Al-MgO, WC-Al2O3, AlN-TiN, and Al-TiO2 are investigated and results are supported by various other techniques [2, 4, 10, 12, 18–21].

S. Patel *et al.* [2, 19–21] predicted the mechanical and thermal properties of NBT-6BT-ZnO, Al-MgO, WC-Al2O3 and AlN-TiN composites by the OOF2 method. The simulation results are validated with different analytical models. They show that an increase in the filler content increases the local stress concentration, which can be the start point of failure in the material. S. Patel *et al*. [2, 19–21] also studied filler orientation, gradient and uniform temperature environment effect on the thermomechanical properties. Neeraj *et al.* [4, 10] obtained Y of Ni-Al2O3 composite by OOF2 and compared it with the ultrasonic measurement with the possibility of crack initiation due to stress distribution. Andrew *et al.* [16, 22] studied the complex microstructure using the OOF2 FE tool and reported that the quality of the results depends on the quality of the generated mesh. The set of generics is modified, which results in improve the quality of the 2D mesh. Elomari *et al.* [23] have analyzed thermal expansion behavior between matrix and reinforcement in terms of silica layer formed during oxidation, size, and thermal stress. Chawla *et al.* [13, 14] performed a microstructure-based simulation to predict the thermomechanical behavior of composite. Plasma-sprayed Y2O3-stabilized ZrO2 analysis was carried out to measure Y of the actual coating and compared with experimentally observed values [24]. The magnitudes of σ<sup>r</sup> in textured and untextured Al2O3 are obtained concerning grain orientations with the help of OOF2 [17]. Thermal shock resistance and λ of yttria-stabilized zirconia (YSZ)-Al2O3 and 3Al2O32SiO2 are computed and compared by analytical methods [3]. Further, λ is analyzed for 4 phase and 3-phase composite of Y2O3 stabilized ZrO2-Al2O3-MgAl2O4-LaPO4 and CeO2-MgAl2O4- CeMgAl11O19, respectively to use them with nuclear fuel [6]. Moreover, porous W/CuCrZr composites micrographs with OOF2 are simulated for tensile deformation and thermal conduction behavior [7].

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

Recently, OOF2 was used to obtain the stress distribution and Young's modulus in the thermally treated Mg-9 wt.%Li-7 wt.%Al-1 wt.%Sn alloy to enhance the wear resistance [24–26]. Further, continuously reinforced concrete pavement α correlation with spalling, performance and mechanical behavior is also studied with OOF2 and results are compared with commercial FE software [27]. Furthermore, the λ and thermal effusivity are simulated for the different regions of TBCs as synthesized by thermal spray processes and suspension plasma spray for gas turbine applications [28]. It was found that modeling provides good results [28]. Moreover, Si3N4 welding with 316L stainless steel is designed using Mo/Ag composite as interlayer and the residual tensile stress in the interlayer is performed [29]. It can be said that the OOF2 provides a better transition between the mechanical/thermal behavior of a heterogeneous material at the macro-scale and the mechanical/thermal response of its constituent phases. It provides adequate information about microstructures/ phases (volume fraction, distribution, orientation) to ensure a realistic assessment of thermo-mechanical properties [30–32]. More recently, a study was performed on ferritic-pearlitic based steel and found that the predicted results was in good agreement with the experimental results [31]. They found that the microstructural morphology plays a vital role in strain partitioning, strain localization and formability of the ferritic-pearlitic steels [31].

Recently, OOF2 is also used for meshing and FE solutions are obtained by integrating meshing with ABAQUS or MATLAB. In this direction, many researchers have used OOF2-ABAQUS to get the shear stress distribution [26, 33], elastic modulus, crack distribution in the materials/composites [32, 34], residual stresses [29], and thermal properties [28]. Devi lal *et al.* [24, 26] fabricated 7 wt.% Y2O3 stabilized ZrO2 beam to study the presence of microcracks/pores during bending by OOF2 with ABAQUS. Similarly, crack analysis of duplex stainless steel (ferrite + austenite phases) strength and hydrogen diffusion characteristics are investigated at the microstructure scale [30, 32]. Most recently, the space charge distribution between two-grain boundaries or interface in bulk is also studied [35]. Moreover, to generate input data sets for machine learning, an OOF2 based simulation is performed with a variety and radii of pores for brittle porous materials failure analysis [36]. As discussed above, OOF2 is used by various researchers for numerous applications and integration with other software. Hence, this work focused on the ceramic composites' thermal/mechanical properties prediction.

This chapter discussed the detailed OOF2 analysis procedure with boundary conditions and assumptions for ceramics composites. The thermal (λ and α) and mechanical (Y) properties are predicted and compared with other analytical methods. In FE analysis, thermal stress–strain contour and heat flux are used to indicate the different temperature conditions on microstructure images. The local stress and σ<sup>r</sup> distribution interpenetrating phase and particle-reinforced structure are also studied.
