A Study of the Thermo-Mechanical Behavior of a Gas Turbine Blade in Composite Materials Reinforced with Mast

Nowadays, the improvement of modern turbo machines efficiency, especially gas turbines, is achieved mainly by increasing their temperature level in the combustion chamber. The maximum temperature at the inlet of the turbine is currently limited by the resistance of the materials used for the impeller blades. The deterioration of the thermal barrier systems occurs by peeling the ceramic layer. The bared metal is then exposed to dangerously hot gases from the combustion chamber. So far, numerous studies have been conducted on the materials of gas turbine blades [1]. Uses ANSYS 16 for static, thermal and modal analysis of the distribution of thermal stress and temperature in the gas turbine blade of different titanium alloy, stainless steel and aluminum 2024 materials [2]. A study was carried out by other authors [3] on thermo-mechanical fatigue behavior for material Inconel 738. The work is mainly focused on the resistance of solid turbine blades to investigate the balanced thermal and structural performance of the blade for Inconel 738 materials and Inconel U500. A coupled thermo-mechanical simulation of a coated vane is used to model the flaking of the thermal barrier that occurs under the service conditions of the blade [4]. Another work [5] An attempt to analyze the gas turbine blade by comparing the Hastelloy X material to Nimonic alloy 80A and Inconel 625. Alain KÖSTER [6] has carried out a work on Modeling of Super was paloy damage in thermal fatigue. Whereas M. Pierre-Yvan THERY [7] has conducted a work on the experimental and modeling scaling realized on two particular thermal barrier systems and a comparison was proposed. Then Antoine MILLECAMPS [8] has carried out numerical simulations for the study of blades dynamics and the influence of the contact, the wear and the thermo-mechanical forces on the vibratory behavior [9]. A study was carried out by other authors [10] on thermo-mechanical fatigue behavior for two different materials (Inconel 718 and titanium T6). The work is mainly focused on the resistance of solid turbine blades to investigate the balanced thermal and structural performance of the blade for N 155 materials, X nickel base super alloy and Inconel 625. Finally [11] has studied a new thermal insulation ceramic that can operate at higher temperatures and based on partially stabilized zirconia with uterus. This is a logical continuation of the work conducted for several years at ONERA on the search for new ceramic compositions. It is from these considerations that the study of thermo-mechanical behavior on a composite material is initiated. The objective of optimizing such a composite material is to design a fin which supports the bulk of the thermo-mechanical loading. The objective of this work is to evaluate the thermo-mechanical behavior of fins in composite materials with reinforcement in short fiber (mast) high modulus carbon.

3.1 Mechanical characteristics

All equations of mechanical characteristics are given by Gay [12] and are recalled here for more clearness.

Longitudinal modulus of elasticity E_L is given by the following equation:

$\mathrm{E}_{\mathrm{L}}=\mathrm{E}_{\mathrm{f}} V_{\mathrm{f}}+\mathrm{E}_{\mathrm{m}}\left(1-\mathrm{V}_{\mathrm{f}}\right)$     (1)

Transverse modulus of elasticity E_T is expressed as follows:

$\mathrm{E}_{\mathrm{T}}=\frac{\mathrm{E}_{\mathrm{m}} \mathrm{E}_{\mathrm{f}}}{\mathrm{E}_{\mathrm{f}} \mathrm{V}_{\mathrm{m}}+\mathrm{E}_{\mathrm{m}} \mathrm{V}_{\mathrm{f}}}$     (2)

Then Poisson’s ratio ν_L and $v_{\mathrm{T}}$ is written as:

$\mu_{\mathrm{L}}=v_{\mathrm{f}} V_{\mathrm{m}}+v_{\mathrm{m}}\left(1-V_{\mathrm{f}}\right)$     (3)

$\mu_{\mathrm{T}}=\mu_{\mathrm{L}} \frac{\mathrm{E}_{\mathrm{T}}}{\mathrm{E}_{\mathrm{L}}}$     (4)

Finally the Longitudinal shear modulus G_L and Transverse shear modulus G_T expressed as follows:

$\mathrm{G}_{\mathrm{L}}=\frac{\mathrm{G}_{\mathrm{m}} \mathrm{G}_{\mathrm{f}}}{\mathrm{G}_{\mathrm{f}} \mathrm{V}_{\mathrm{m}}+\mathrm{G}_{\mathrm{m}} \mathrm{V}_{\mathrm{f}}}$   (5)

$G_{T}=\frac{E_{T}}{2\left(1+v_{T}\right)}$     (6)

3.2 Thermal characteristics

Thermal characteristics are explained and resumed by Mallick [13].

The longitudinal thermal expansion $\alpha_{\mathrm{L}} \text { and }$ Transverse thermal expansion are written as:

$\alpha_{\mathrm{L}}=\frac{\left(1-\mathrm{V}_{\mathrm{f}}\right) \alpha_{\mathrm{m}} \mathrm{E}_{\mathrm{m}}+\mathrm{V}_{\mathrm{f}} \alpha_{\mathrm{f}} \mathrm{E}_{\mathrm{f}}}{\left(1-\mathrm{V}_{\mathrm{f}}\right) \mathrm{E}_{\mathrm{m}}+\mathrm{V}_{\mathrm{f}} \mathrm{E}_{\mathrm{f}}}$     (7)

$\alpha_{\mathrm{T}}=\left(1-\mathrm{V}_{\mathrm{f}}\right) \alpha_{\mathrm{m}}+\mathrm{V}_{\mathrm{f}} \alpha_{\mathrm{f}}+\left(\alpha_{\mathrm{f}}-\alpha_{\mathrm{m}}\right) \frac{\mathrm{v}_{\mathrm{f}} \mathrm{E}_{\mathrm{m}}-\mathrm{v}_{\mathrm{m}} \mathrm{E}_{\mathrm{f}}}{\frac{\mathrm{E}_{\mathrm{m}}}{\mathrm{V}_{\mathrm{f}}}+\frac{\mathrm{E}_{\mathrm{f}}}{1-\mathrm{V}_{\mathrm{f}}}}$    (8)

3.3 Mechanical properties of the composite with mast reinforcement [14]

In this case the corresponding transformed reduced rigidity will be examined by:

$\widetilde{Q}_{i j}=\frac{\int_{0}^{2 \pi}\left(\bar{Q}_{i j}\right) \partial \theta}{\int_{0}^{2 \pi} \partial \theta}$    (9)

And the elastic modules of the mast layer are:

$\mathrm{E}_{\mathrm{mât}}=\frac{\left(\mathrm{V}_{1}-\mathrm{V}_{4}\right)\left(\mathrm{V}_{1}+\mathrm{V}_{4}\right)}{\mathrm{V}_{1}}$

$v_{\text {mât }}=\frac{V_{4}}{V_{1}}$     (10)

$G_{\text {mât }}=\frac{V_{1}-V_{4}}{2}$

With the expressions of $\mathrm{V}_{\mathrm{i}}$ are:

$V_{1}=\frac{1}{8}\left(3 Q_{11}+3 Q_{22}+3 Q_{12}+4 Q_{66}\right)$;

$V_{2}=\frac{1}{2}\left(Q_{11}-Q_{22}\right)$;     (11)

$V_{3}=\frac{1}{8}\left(Q_{11}+Q_{22}-2 Q_{12}\right)$;

$\mathrm{V}_{4}=\frac{1}{8}\left(\mathrm{Q}_{11}+\mathrm{Q}_{22}+6 \mathrm{Q}_{12}-4 \mathrm{Q}_{66}\right)$

5.1 By the law of mixtures

The characteristics of composite material studied are presented below in Tables 3 and 4, respectively.

Table 3. Mechanical and thermal characteristics of the material studied

5.2 By the law of the behavior of the composite with reinforcement mast

Table 4. Mechanical properties of the mast reinforced composite

Due to the absence of the experimental study for that is why we compared the results obtained with the results obtained by Ahmed [1]. Structural analysis was carried out by applying the same limit conditions and mechanical forces selected materials for blade for validation. The desired comparison was made on the materials such as Aluminum 2024 Alloy, Stainless Steel Alloy and Titanium Alloy.

Figure 3 Show the displacement of the blade in the Titanium Alloy. the maximum displacement with a magnitude of 0.3915 mm.

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Figure 3. Resultant displacements of titanium alloy

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Figure 4. Resultant displacements of stainless steel alloy

Figure 4 shows the displacement of the blade in the Stainless-Steel Alloy. The maximum displacement with a magnitude of 0.40188 mm.

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Figure 5. Resultant displacements of aluminum 2024 alloy

Figure 5 Show the displacement of the blade in the Aluminum 2024 Alloy. the maximum displacement with a magnitude of 1.0994 mm.

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Figure 6. Turbine blade materials as a function of displacements

To confirm the reliability of our numerical study, we compared the results of our attempt with the previous results.

The results obtained and published by Ahmed [1] are used to illustrate the validity of the attempt. Figure 6 Show the comparison between the displacements results for the (present numerical study and numerical studied by Ahmed [1]. The results of displacement allowed us to note the conformity of the results given by the present numerical study and those obtained by Ahmed [1]. It should be noted that the precision of the numerical study gives very acceptable results.

The choice of optimized composite material, significantly reduces the deformations along the fin and therefore locally reduces micro cracking causing wear flaking. In order to achieve the desired results, we completed the establishment of a research protocol in a predefined order:

1. A critical study on thermo-mechanical behavior in relation to the wear by flaking of gas turbine blades (problematic) for different materials.
2. A broad literature review on new materials (composites) and technical means to integrate them into the design and manufacture of turbine blades in general. The choice of a couple (reinforcement /matrix) is Carbon / ceramic after an optimization study to choose the optimum composition (fiber volume fraction v_f=0.4).
3. Successive studies of simulations carried out on a real geometrical model (blade) of composite materials compared with the same model in super alloys to define essentially the displacements of the same point for the different materials and the local deformations.
4. The obtained results have showed a clear improvement of the fin stiffness and a reduction of the displacement of the extreme point of the blade. The local deformations are reduced. These results allow us to conclude that the cracking by scaling will be reduced significantly.
5. The optimization of a composite material (carbon/ceramic) in the design of turbojet blades has confirmed that the carbon/ceramic torque is very well adapted to an optimum thermo-mechanical operation. Increased stiffness, local reduction of deformations, reduction of micro cracking, and reduction of flaking and therefore increased life time can be achieved.