Predicting Fracture Placement and Analyzing Fatigue Life in Exhaust Manifold Systems Using Finite Element Analysis

Many works are conducted to investigate and analyze the propagation of cracks [1-4]; this paper aims to evaluate fracture and propagation of crack analysis in this exhaust manifold; it’s solicited to thermos-mechanical loads. The propagation of the crack and its initiation is considered one of the most critical phenomena in the exhaust manifold, and the fracture toughness is analyzed. The crack propagates under applied stresses if the material’s fracture toughness (Ki) outreaches a critical fracture toughness (Kic). Martins et al. [5] depict the propagation of cracks in the exhaust system for naval gas turbines, usually occurring on the weld toes of butt and fillet weld joints positioned near the lower support ring of the structure, the Von Mises stress and the nominal principal stresses were calculated. The critical region's design and fatigue life is expected to increase to 6x10⁴ cycles. Hidayanti et al. [6] utilize Computational Fluid Dynamics (CFD) software to improve the performance of a racing exhaust system. Through CFD simulations, fluid flow patterns and thermal behavior were analyzed, leading to design modifications that optimize exhaust gas evacuation and minimize back pressure. The findings demonstrate CFD's potential as a valuable tool for developing high-performance racing exhaust systems, benefiting motorsport engineering and vehicle performance in competitive racing. Liu and Zhi [7] conducted a study on exhaust systems using Finite Element Analysis and optimization. Their research aimed to improve the efficiency and overall effectiveness of exhaust systems by examining their structural performance in various conditions. The study also provided valuable insights for developing better exhaust systems through advanced materials research.

Lee et al. [8] have developed a simulation program based on the FEM approach to forecasting the crack growth of structures.

Varun Ram et al. [9] have tried to analyze the exhaust system for an ultra-fuel-efficient vehicle; the CFD has been employed to make more accessible the study turbulent flow of the exhaust manifold to get a smooth flow. Accordingly, the design of the exhaust manifold has been optimized in terms of materials and geometry.

Sasikumar et al. [10] explained how to calculate the fatigue life for mounting brackets using CEA compared with physical testing; the exhaust system was meshed with 2D cells, using MSC/NASTRAN to specify the main reason for high stresses in critical placements and predominant mode causing failures. Ahmad et al. [11], the purpose of this paper is the thermo-mechanical analysis of tractor exhaust manifold; the material used is Austenitic Stainless steel-321. This study studied the response of exhaust manifold submitted to higher temperatures. The thermal effect was considered to evaluate the FEA simulation results. They found the fundamental frequencies by executing the free vibration-based modal analysis.

Salehnejada et al. [12] analyzed the crack failure based on the FEM approach; the exhaust manifold was submitted to a crack and a tensile test at a higher temperature; then, the critical fracture force was specified. As a result, the intensity factor was compared with the critical intensity factor, and the propagation of the fracture was discussed. Xie et al. [13] treat the propagation of cracks in pipelines combined with corrosion of the component. The FEM is developed to get the Stress Intensity Factors (SIF) for fatigue crack.

Based on this literature review, we can deduce that the Propagation of the crack and the fatigue life analysis was studied took into account the pre-existing location of the crack.

By bridging the gap between crack identification and fatigue life assessment, this article then aims to accurately identify the placement of crack in exhaust manifolds under thermos-mechanical loading and assessing the fatigue life of the exhaust manifold.

In mechanical fracture, it has three modes of classification; opening mode, sliding mode, and tearing mode, and SIF is used to reflect these modes; Opening mode is characterized by the creation of a crack that opens up in the material, with little or no sliding of the surfaces on either side of the crack. Sliding mode is characterized by the sliding of one surface over the other along the plane of the crack. Tearing mode is described as creating a crack along a plane that is not perpendicular to the material's surface. This fracture type is typically associated with layered materials, such as laminated composites.

According to the API579 criterion, the Stress Intensity Factors are determined as follows:

$\begin{gathered}K=\frac{p R_{i n}^2}{R_{0 u}^2-R_{i n}^2}\left[2 G_0+2 G_1\left(\frac{a}{R_{0 u}}\right)+3 G_2\left(\frac{a}{R_{0 u}}\right)^2+\right. \left.4 G_3\left(\frac{a}{R_{0 u}}\right)^3+5 G_4\left(\frac{a}{R_{0 u}}\right)^4\right] \sqrt{\frac{\pi a}{Q}}\end{gathered}$               (1)

where,

• R_in: the internal radius.
• R_ou: the outer radius.
• p: the internal pressure.
• a: the crack depth.

And is the parameter based on crack geometry

$Q=1.0+1.464\left(\frac{a}{c}\right)^{1.65}$, for $\frac{a}{c} \leq 1$               (2)

where,

• c: the half crack length;
• φ: the included angle;
• β: influence coefficients;
• K: the mode I SIF.

And

$\begin{gathered}G_0=A_{0,0}+A_{1,0} \beta+A_{1,0} \beta^2+A_{3,0} \beta^3+A_{4,0} \beta^4 +A_{5,0} \beta^5+A_{6,0} \beta^6 \,\,\,\,\,\,\,\,\,\,\, A_{i, j}(i \in\{0,1,2,3,4,5,6\},\{j \in 0,1\})\end{gathered}$               (3)

$\begin{aligned} G_1=A_{0,1}+A_{1,1} \beta & +A_{1,1} \beta^2+A_{3,1} \beta^3+A_{4,1} \beta^4+A_{5,1} \beta^5 +A_{6,1} \beta^6\end{aligned}$               (4)

$\beta=\frac{2 \varphi}{\pi}$               (5)

$\mathrm{G}_2=\frac{\sqrt{2 Q}}{\pi}\left(\frac{16}{15}+\frac{1}{3} M_1+\frac{1}{105} M_2+\frac{1}{12} M_3\right)$               (6)

$\mathrm{G}_3=\frac{\sqrt{2 Q}}{\pi}\left(\frac{32}{35}+\frac{1}{4} M_1+\frac{32}{315} M_2+\frac{1}{20} M_3\right)$               (7)

$\mathrm{G}_4=\frac{\sqrt{2 Q}}{\pi}\left(\frac{256}{315}+\frac{1}{5} M_1+\frac{256}{3465} M_2+\frac{1}{30} M_3\right)$               (8)

And

M₁= $\frac{2 \pi}{\sqrt{2 Q}}\left(3 G_1-G_0\right)-\frac{24}{5}$

M₂=3

M₃= $\frac{6 \pi}{\sqrt{2 Q}}\left(G_0-G_1\right)-\frac{8}{5}$

6.1 Von Mises’s stress analysis

As shown in Figure 7, The Max Avg. von Mises Stress observed around the crack is registered at 22052 MPa; this indicates regions of higher stress concentration, which may lead to the propagation of the crack and potential failure.

7.png

Figure 7. The von Misses stress around the crack

Upon comparing this result to the previous one obtained from the exhaust manifold without a crack, it is evident that the presence of a crack causes stress concentration in the area surrounding the crack tip. The von Mises stress values are expected to be significantly higher in the region surrounding the crack compared to the stress distribution in the product without a crack.

6.2 Strain’s von Mises analysis

In Figure 8, it was observed that the exhaust system had undergone a total deformation of approximately 0.176mm at the crack tip.

8.png

Figure 8. Total deformation of the exhaust manifold

The total deformation obtained from the cracked exhaust manifold under applied loads offers valuable insights into its displacement and distortion. This information aids in evaluating the structural integrity, pinpointing high-stress or strain concentration zones, and comprehending the crack’s influence on the overall deformation behavior.

6.3 Crack propagation and fracture analysis

Different indexes are deployed to determine the SIF for three modes. The SIF for mode I, II, and III are designated KI, KII, and KIII, respectively,

Mode I loading is a type of crack where the primary loading is perpendicular to the crack plane and parallel to the crack's leading edge. It's often called "opening mode" or "tensile mode" and is associated with tensile or bending stresses. It's common in materials subjected to these types of loads.

Mode II loading involves shear forces applied parallel to the crack plane, causing the surfaces to slide relative to each other. It's common in materials subjected to shearing forces, like torsional loading or in-plane shearing.

Mode III is a type of crack loading where the primary force is applied parallel to the crack plane. This mode is also known as "out-of-plane shear mode" or "tearing mode." It is less frequently encountered in practical applications compared to Modes I and II.

Figures 9, 10 and 11 represent the six contours of the KI, KII, and KIII stress intensity factors on the crack bottom when applying the nominal pressure (0.2MPa). These SIFs are displayed as in Figures.

Figures 9, 10, 11 and 12 illustrate the variation of $\frac{K_I}{\sigma(\pi a)^{0.5}}$, $\frac{K_{I I}}{\sigma(\pi a)^{0.5}}$ and $\frac{K_{I I I}}{\sigma(\pi a)^{0.5}}$.

9.png

Figure 9. SIFS (K1)

10.png

Figure 10. SIFS (K2)

11.png

Figure 11. SIFS (K3)

12.png

Figure 12. SIF Mode for KI, KII, and KIII

We notice that the exhaust manifold is subjected mainly to Mode I loading. In fact, KI has the maximum magnitude SIF ∆K₁, followed by KIII and KII (∆K₂, ∆K₃)

This simulation evaluates the SIFs on the exterior surface by internal pressure; then, the SIFs were much higher and dominant for circumferential cracks than the longitudinal cracks under thermo-mechanical loads.

6.4 Fatigue life

In this study, fatigue failure was estimated using the Goodman method. It is a stress-based approach commonly used for predicting fatigue life in engineering applications. It takes into account both the alternating stress (σ_a) and the mean stress (σ_m) acting on a material, The mathematical expression for it is as follows: The mathematical expression for it is as follows [14]:

$\frac{\sigma_a}{\sigma_e}+\frac{\sigma_m}{\sigma_u}=1$

where,

σ_m: mean stress

σ_e: is the endurance fatigue limit,

σ_u: is the ultimate tensile strength,

σ_a: Tensile yield stress

The Goodman method is adopted for calculating theoretical fatigue life. Fatigue load is obtained from the condition of the stability test. Based on the load (0.2MPa) applied in the structural analysis,

The results obtained from the fatigue analysis using Ansys Workbench provide insights into the fatigue life of the exhaust manifold. They can be used to optimize its design and material properties to improve its durability and reliability.

13.png

Figure 13. Fatigue life of the exhaust manifold without fracture

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Figure 14. Fatigue life of the exhaust manifold with fracture

Based on the illustration presented in Figure 13, it was observed that the exhaust manifold could last for a minimum of 11,686 cycles without any fractures, specifically in the exhaust bracket. However, the maximum lifecycle recorded is approximately 1 million cycles.

As shown in Figure 14, The exhaust manifold now has a reduced minimum fatigue life of 0 cycles, compared to its original minimum lifecycle without any cracks.

Table 3. Fatigue life

The presence of a crack in the product significantly reduces its fatigue strength compared to the exhaust manifold without a crack, as shown in Table 3. The crack acts as a stress concentration point, intensifying localized stress and promoting crack growth. As a result, the product with a crack is expected to have a shorter fatigue life.