Evaluate Fretting Fatigue Damage in Simple and Complex Geometries like Diesel Engine Head Gasket

The effect of wear on wear fatigue is investigated by Archard's progressive wear model and Ding's parameter, 𝐷𝑓𝑟𝑒𝑡2. Finally, the learning from 2D FEA is taken into account in the damage fatigue evaluation of the actual head gasket using 3D FEA.

Figure 106: Correlation between F1 parameter results and fretting fatigue life results obtained considering with deviatoric strain amplitude-based parameter corrected with Ding’s parameter for three engine platforms ((with area averaging) ...............

INTRODUCTION AND LITERATURE REVIEW

Introduction of Fretting Fatigue

Fretting defects are observed in various applications such as train axles [8⎼9], steel cables [10] and orthopedic implants [11].

Fretting Fatigue Damage in Engine Components

Fretting Fatigue Failure of Main Bearing Cap in Gasoline Engine
Fretting Fatigue Failure of Engine Block
Fretting Fatigue Failure of Connecting Rod
Fretting Fatigue Failure of Cylinder Head Gasket

Consequent cracks due to the crack damage can start at the contact surface of the MBC with respect to the engine block (see Figure 3). The combined effect of the relative slip between the connecting rod with the bearing and cyclic contact stresses leads to the fretting damage at the internal boring of the connecting rod.

Figure 1: Schematic diagram of internal combustion diesel engine

Basics of Metal Fatigue Analysis

Basic Fatigue Mechanism
Basic Classification of Fatigue Analysis: Stress Based and Strain Based Fatigue Analysis: 12
Fretting Fatigue

The resulting alternating stress due to the load reversal therefore causes the fatigue failure of the component. Stick area: is the area of the contact surface where relative displacement is zero/negligible.

Figure 10: Three modes of loading of crack tip

Different Fretting Fatigue Crack Initiation Methods

Critical Plane-Based Methods

Stress-Based Critical Plane Methods
Strain-based Critical Plane-Based Parameters
Strain Energy-Based Parameters
Stress-Strain Transformations

Stress Invariant-Based Approach
Continuum Damage Mechanics-Based Approach
Fretting Specific Parameter

❤ 𝑐 (14) where 𝜎𝑛𝑚𝑎𝑥 is the maximum normal stress at the critical level, ∆𝜀𝑛 is normal stress distance at the critical level, 𝜎𝑓′ is fatigue strength coefficient, 𝑁𝑖 is the cycle to crack initiation, 𝑏 is fatigue strength exponent in stress, 𝑐 is fatigue -extensibility exponent in stress and 𝜀𝑓′ is fatigue coefficient. 𝐶𝐿 = √𝐽2𝑎+ 𝜎𝐻,𝑚𝑎𝑥(3𝜏𝑓−1⁄𝜎𝑓 where 𝐽2,𝑎 is the amplitude of the second deviatoric stress tensor,𝥐 static stress tensor, 𝜎𝑥 is the normal stress in x direction, 𝜎𝑦 is the normal stress in Y-direction direction, 𝜏𝑓−1 is the fatigue limit in torsion, 𝜎𝑓−1 is fatigue limit in tension.

Figure 17: Generalized classification of fretting fatigue crack initiation criteria (Reproduced based on [52])

Important Parameters in Fretting Fatigue Evaluation

Operating Loads, Phase Difference and Frequency

Phase Difference
Operating Load Magnitude
Operating Load Frequency

Coefficient of Friction (COF)
Contact Geometry
Effect of Slip and Wear

Incremental Wear Modeling
Threshold Slip Magnitude

Stress-Strain Averaging Methods
Humidity, Temperature and Material Properties

For the general bolted joint assembly, the fatigue life is observed to decrease with increasing tightening torque, which corresponds to increasing normal force [107]. 108] have reported that the effect of normal strength value on boring fatigue life varies with different. As shown in Figure 31, the change in fatigue life is observed in relation to the change in contact size.

As discussed earlier, wear fatigue life initially decreases with the increase in slip size up to a certain threshold limit. Consequently, the effect of slip size on the results of friction fatigue can be considered as shown in Figure 33.

Figure 23: Different factors affecting fretting (Reproduced based on [103])

Motivation and Objective of The Thesis

Although the considered approach is suitable for both LCF and HCF, no estimation of the fatigue life has been done. Although the SWT parameter is suitable for LCF and HCF, no estimation of the fretting fatigue life has been done. Different methods for the initiation of fatigue are also effectively considered for the evaluation of the fretting fatigue life of basic, simple geometries.

If properly considered, these methods can also be effective in assessing actual engine fatigue damage. It must be combined with the corresponding FIP to obtain resultant fatigue life results of concern.

Table 5: Comparative assessment of different fretting fatigue crack initiation criterion considered for fretting fatigue life evaluation of basic, simple geometries

Structure of The Thesis

Therefore, the effect of resultant wear on wear fatigue life results is discussed in the following section. Further, the stress fatigue life results are corrected for the resulting Ding values of the parameter 𝐷𝑓𝑟𝑒𝑡2 and the corresponding experimental correlation is given in Figure 79. The stress fatigue life results for the head gaskets are extracted using the eI parameter in combination with the Ding parameter.

The resulting friction fatigue life results for the head gaskets of three engine platforms are shown in Figure 104. In this work, the deviator strain amplitude based parameter is taken into account for the evaluation of head gasket friction fatigue life.

FRETTING FATIGUE LIFE EVALUATION OF FLAT CONTACT PAIR USING TWO-

Details of Experimental Setup

Therefore, subsequent rubbing fatigue tests must be performed to create such conditions in the experimental setup. There are two additional configurations of the friction fatigue experimental setup: the first type is bridge type [4] which consists of two separate contact pads connected in the form of a bridge (as shown in Figure 38) and another configuration with the single contact pad which shown in Figure 39. In the considered reference work [58], friction fatigue tests are performed using a square indentation that creates the partial slip regime at the contact joint.

During the experimental tests in the reference problem, a uniaxial servo-hydraulic fatigue testing machine with a load capacity of +100 kN is assumed to perform the required friction fatigue tests. The initial surface roughness of the contact surface is maintained at 𝑅𝑎= 0.1 μm in transverse direction by means of the grinding operation.

Figure 37: Schematic representation of (A) flat contact pair fretting problem set-up and (B) head gasket assembly

Details of FEA Problem Setup in ANSYS

The contact pressure, 𝜎𝑃, is calculated as 𝜎𝑃 = P/2at, where 2a is the contact width and t is the thickness of the sample (as shown in Figure 40). Based on the mesh convergence study considering the contact pressure results (as shown in Figure 42), a mesh size of 15 μm is considered near the right end of the contact zone. The minimum contact pressure is achieved in the center and mathematically approaches infinity at the contact edge.

Initially, the non-linear model of 'Bi-linear kinematic hardening (BKIN)' is considered to capture the yielding stress-strain behaviour. These stabilized stress-strain results can be taken into account for the further calculations of FIP and consequent fatigue life by considering different crack initiation methods.

Table 6: Applied loads and experimentally obtained number of cycles to failure for the reference problem (P is the normal load, 𝜎 𝑃 is the contact pressure, 𝜎 𝐵𝑢𝑙𝑘 is the axial

Critical Plane Based Fatigue Life Evaluation

Stress-Strain Transformation Along Critical Plane
SWT Parameter-Based Fatigue Life Evaluation
FS Parameter-Based Fatigue Life Evaluation

The stress and strain values in different planes are calculated using the transformation equations as mentioned earlier (Equation 17-20). Once the stress and strain values are resolved, the resulting fatigue damage parameter is calculated on each plane and the plane with the maximum damage value is considered as the critical plane and the corresponding damage value is considered to estimate the resulting initial fatigue life. APDL-based macros are developed to perform the required stress-strain transformations (according to Eqs. 17-20) and for SWT damage and the resulting minimum fatigue life estimation (see Eq. 14).

Similar to SWT, for the FS parameter as well, APDL-based macros are written for performing subsequent stress-strain transformations, damage calculation, and minimum fatigue life estimation, according to Equation 12. It is similar to the flowchart of considered for the SWT parameter, except for considerations of appropriate stress/strain types.

Figure 45: Equivalent stress plot with linear material properties (for test#15) (unit: MPa)

Stress Invariant-Based Fatigue Life Evaluation

Therefore, a comparative assessment with other methods is considered in the current work. APDL-based macros are written to perform the appropriate fatigue damage calculation and minimum life estimation (see Equation 21). Here, unlike the previously discussed SWT and FS methods, the fatigue damage value is a scalar parameter calculated at each node and does not require stress-strain transformations along different planes passing through each node of the considered FEA domain.

Deviotoric Strain Amplitude-Based Method (eI) for Fatigue Life evaluation

According to this parameter, fatigue degradation results from a combination of load modes in mutually orthogonal directions in the deviatoric stress space. Similar to the voltage invariance based parameters such as the Crossland parameter (CL) [88], this parameter also produces scalar results at each node and the critical plane calculations are not required. APDL macros are written to perform resultant stress-strain transformations, damage calculation, and minimum life evaluation.

Figure 52: Flow-chart for CL parameter calculation

Initial Verification With Plain Fatigue Benchmark Problem

To verify the correct functionality of these macros, initial verification is performed by considering the benchmark problem of the 'SAE Keyhole Test Program' [145]. Thus, if a good correlation is obtained for this initial verification step, the developed macros can be considered suitable for further evaluation of wear fatigue life. The following details the loads and boundary conditions used in the "SAE Keyhole Test Program" benchmark problem.

Further, the predicted fatigue life results are compared with the experimental life values and the corresponding correlation results are given in Figure 55. Thus, it is observed that the developed APDL macros are able to correlate the experimental results well within the + 2N distribution band for simple fatigue state and therefore, can be further considered for fretting fatigue life assessment of the reference fretting fatigue problem [58].

Figure 53: Flow-chart for eI parameter calculation

Consideration of Stress Averaging Methods to Capture Resultant Stress Gradient

Fretting Fatigue Life Results for Different Considered Crack Initiation Methods

IDENTIFY CRITICAL PARAMETERS TOWARDS FRETTING FATIGUE DAMAGE

Effect of Material Nonlinearity on Fretting Fatigue Life Results

Resultant Stress-Strain Stabilization with Different Non-Linear Material Models

Effect of Coefficient of Friction (COF) on Fretting Fatigue Life Results
Effect of Wear Due to Relative Sliding

Effect of Wear using Archard’s Model
Effect of Slip using Fretting Specific Parameter of Ding’s Parameter (𝐷𝑓𝑟𝑒𝑡2)

Effect of Frictional Heat
Effect of Normal, Axial and Tangential Loads using 2D Axi-Symmetric Liner-Gasket-Block

Typical Head Gasket Joint of High Horse-Power Diesel Engine
Effect of Normal Load
Effect of Axial Load
Effect of Tangential Load

In this chapter, various parameters critical to boring fatigue results are evaluated based on 2D FEA of the considered flat contact pair. Parameters considered within the scope of the current job are based on their relationship to the current head-to-tail connection.

FRETTING FATIGUE ANALYSIS OF ACTUAL HEAD GASKET JOINT THROUGH

Fretting Fatigue Failure of Cylinder Head Gasket of High Horsepower Engine

Head Gasket Fretting Fatigue Analysis Procedure

FEA Model Details

Fretting Fatigue Damage Parameters

Results

Fretting Results Using Ruiz’s parameter F1
Fretting Life Results Using Deviatoric Strain Amplitude Based Parameter (eI) Corrected for

CONCLUSION

Summary

After the initial evaluation considering a simple flat complete contact pair, the approach based on combined consideration of deviatoric stress amplitude-based parameter and Ding's parameter is applied to the complex case study of the actual head gasket. These parameters are considered primarily based on their relevance to the head gasket case study considered. Based on the observed initial yield, various nonlinear material models such as BKIN, MKIN and Chaboche are considered in this work and subsequent fatigue life predicted results are obtained for each material model.

Relevant data required for AL7075-T6 are considered based on data available for another aluminum material, e.g., AL357 [148]. The resultant distress fatigue life results obtained considering the 'eI' and Ding parameters are compared with the current industry standard approach based on Ruiz's F1 parameter.

Conclusions

Fretting Fatigue Life Evaluation of Flat Contact Pair Using Two-Dimensional FEA
Critical Parameters Towards Fretting Fatigue Damage of Flat Contact Pair Through 2D

Therefore, APDL macros have been found to be capable of estimating the distressing fatigue life of the considered distressing fatigue problem [58]. However, it is observed that the distressed fatigue life results obtained considering Archard's wear model do not differ much compared to the previous results obtained without considering any wear correction (see Figure 76). 102] have performed the correlation of distress fatigue life by combining Ding's parameter, 𝐷𝑓𝑟𝑒𝑡2, with the SWT parameter.

In comparison, tangential loading is not observed to cause much variation in the resultant fatigue life results. 2D FEA is effective to quickly identify parameters important to fatigue life results of concern.

Scope for Future Work

Therefore, it is a promising and computationally effective approach for fatigue damage assessment of complex mechanical systems such as head gasket. To check for the resultant quantification in terms of fatigue damage and life results, actual 3D FEA can be performed in the future. Such a study can be effective for risk assessment and prioritization of critical parameters towards the evaluation of the dreaded fatigue damage of the head gasket.

Recently, 'Machine Learning' (ML) based fretting fatigue damage and life evaluation has been carried out. On a similar basis, ML-based approach can be considered in the fretting fatigue damage and life evaluation of real engine parts in terms of creating database that can be used for new product development as well as for field failure investigation.

Overall Analysis Approach for Liner Bite Ring Optimization

To minimize the risk of chafing damage to the steel packing, full factorial design of experiment (DOE) based on Ruiz parameter (F1) is performed to identify an optimized liner engagement ring geometry. DOE predicted results based on 2D axisymmetric FEA are further validated using full 3D FEA, with the boundary conditions consistent with the operating conditions known to accompany the chafing damage.

Full Factorial DOE Analysis and Verification Using 3D FEA

As the hierarchical requirement of the DOE model [180], it must therefore be kept within the DOE domain. Based on the observed value of R-sq of ~83%, it can be interpreted that the model is able to explain approximately 83% of the variation in the response, whereas with the R-sq(pred) value of ~68%, the model has a predictive power of approximately 68%. Considering these values in the regression equation, i.e. equation 51, F1 results are observed to be improved by 23.4% compared to baseline.

Therefore, to verify the actual improvement in friction damage results, a 3D FEA analysis should be performed. The cross-section of the baseline versus the modified geometry of the liner is shown in Figure 110 and the corresponding comparative assessment of the F1 parameter results, as observed in the 3D FEA models with the baseline and modified liner, is shown in Figure 111.