This section focuses on the upper main bearing wall of an HT300 cast iron diesel engine cylinder block, with its material parameters detailed in Table 1. Due to the large size, complex structure, and variable loading conditions of the upper main bearing wall, data acquisition is relatively challenging. To facilitate fatigue crack propagation (FCP) testing on the upper main bearing wall, this study first conducts a scaling analysis to ensure identical stress fields before and after scaling (Petrović et al., 2021). Considering the dimensions of the fatigue testing machine, a scaling ratio of 1:7 was adopted, reducing the large-scale main bearing wall (Figure 1a) to a scaled model (Figure 1b) suitable for mounting on the testing machine. To validate the accuracy of the FCP data obtained from the scaled model, a SENB specimen was introduced as a control, with its dimensions specified in Figure 1c. To minimize the potential influence of material microstructure on the test results, 16 scaled models and SENB specimens were fabricated using wire cutting from the upper main bearing wall. From these, six specimens with the most similar microstructural distributions were selected for repeated FCP testing to enhance the reliability of the experimental results (Wei et al., 2023).

The accurate establishment of the da/dN model for the upper main bearing wall hinges on the precise determination of FCP data, which comprises the da/dN curve and the threshold stress intensity factor range (ΔK _th). To enhance the accuracy of FCP data measurement, this section employs a scaled model of the upper main bearing wall that incorporates structural factors. Specifically, da/dN tests (Section 2.2.1) and ΔK _th tests (Section 2.2.2) are conducted using the scaled model. Additionally, SENB specimens are introduced for comparative analysis to validate the accuracy of the scaled model. This approach ensures a robust evaluation of the model’s precision and reliability.

This section presents fatigue tests conducted on the main bearing wall of the diesel engine cylinder block under three typical working conditions (WC). The tests employed a sinusoidal loading waveform with a frequency set at 30 Hz (Figure 3a). The experiments were performed in accordance with the relvant standards of the “Fatigue Testing Method for Diesel Engine Cylinder Blocks” (National Technical Committee for Standardization of Internal Combustion Engines, 2018) and were carried out on a hydraulic pulse-type block fatigue testing rig developed by the Institute of Power Machinery and Vehicle Engineering at Zhejiang University (Figure 3b). After the test, the fatigue life of the component (N _f) is recorded, as explained below. N _f is a key parameter in fatigue life prediction and represents the number of load cycles that a material or component can endure under specified loading conditions before failure occurs, such as crack initiation or complete fracture. It serves as an important indicator in structural degradation models, providing a quantitative measure of the durability of the component under cyclic loading.

To minimize random and systematic errors during the experiments, the fatigue test results of the main bearing wall under each working condition were averaged. This approach not only enhanced the representativeness and reliability of the data but also effectively smoothed out potential random fluctuations in individual tests, providing more robust experimental evidence for subsequent structural degradation predictions and engineering applications.

It is critically important to investigate the microscopic failure mechanisms of the main bearing wall in diesel engine blocks, as this can lay a solid foundation for accurate monitoring of its structural degradation. This section presents a systematic microstructural characterization study. The experimental procedure was conducted as follows:

To ensure that the scaled model can accurately reflect the microscopic failure mechanism of the upper main bearing wall, this study adopts an experimental verification method. The effectiveness of the scaled model is evaluated by comparing the stress fields and da/dN curves at key failure locations between the prototype of the upper main bearing wall and its scaled model. Specifically, if the stress fields and da/dN curves of the prototype and the scaled model show good consistency in key parameters and curve trends, it proves that the scaled model can effectively simulate the fatigue crack propagation behavior of the prototype, thereby validating its effectiveness.

To improve the prediction accuracy of the structural degradation model for the upper main bearing wall, this study develops a structural degradation model that comprehensively considers the effects of structural features and loading conditions, based on da/dN data obtained from scaled model tests. To verify the reliability of the scaled test results, a comparative analysis was also conducted using standard SENB specimens. In engineering practice, structural degradation of a component is characterized by a gradual decline in key mechanical properties such as strength, stiffness, and toughness as service time or loading cycles increase. The physical essence of this degradation process lies in the continuous accumulation of micro-damage caused by cyclic loading, environmental corrosion, thermo-mechanical coupling, and wear during long-term operation. This accumulation eventually leads to a progressive deterioration of macroscopic mechanical performance until the component reaches its critical fatigue life N _f. In summary, from the perspective of damage mechanics, N _f quantitatively represents the accumulated degradation reaching the failure threshold. This relationship can be clearly described by Miner’s linear cumulative damage theory, with its mathematical expression given as Equation 9: D = ∑ i = 1 n n i N i  and  D ≥ 1 (9)

In this equation, D represents the accumulated damage value, n _i is the number of cycles experienced under the ith stress amplitude, and N _i is the number of cycles required to cause fatigue failure at that stress amplitude. This formula indicates that the reduction of remaining life is closely related to the cumulative load and service time. Therefore, structural degradation is essentially a process in which the material state evolves over time. In this section, the relationship between the component’s fatigue life N _f and time t is used to represent the structural degradation process.

The establishment procedure of the structural degradation model is illustrated in Figure 6. First, the Wiener process, one of the most commonly used stochastic process models for structural degradation, is selected as the basic model (Jing et al., 2023). The core concept of this model is to treat the structural degradation process as a continuous process with random fluctuations, assuming that the change in degradation over time follows a stochastic process with increments that are normally distributed and independent. Therefore, the Wiener process can effectively describe degradation processes that exhibit a linear trend accompanied by random variability, providing high modeling flexibility. The mathematical expression of the Wiener model is given as Equation 10: X t = x 0 + μ Λ t + σ B t (10)

In this equation, X(t) represents the actual degradation level of the component at time t, and x ₀ denotes the initial degradation state. The term Λ(t) is a deterministic function of time that characterizes the drift component in the stochastic process. It is typically used to describe the trend effect accumulated over time due to external conditions or internal mechanisms. When Λ(t) takes a linear form (e.g., Λ(t) = t), it indicates that the system’s drift grows at a constant rate over time. If it adopts a nonlinear or integral form, it can capture more complex time-dependent evolution patterns. Unlike the random perturbation term B(t), the value of Λ(t) is fixed and predictable at any given time, reflecting the deterministic part of the system’s evolution. Here, μ is the drift coefficient, σ is the diffusion coefficient, and B(t) represents standard Brownian motion. Furthermore, based on the two upper main bearing wall da/dN models derived from the scaled model and the SENB specimens presented in Section 3, we use the da/dN data to predict the structural degradation behavior of the component and assume the Equation 11: a = a 1 a 2 ⋮ a n , N = N 1 N 2 ⋮ N n (11)

Substituting the a and N data obtained from the component test into the Wiener model, the likelihood function and the log-likelihood function of the component’s nonlinear function are respectively as Equations 12, 13: f θ ∣ a = 1 2 π n Ξ exp − a − μ N T Ξ − 1 a − μ N 2 (12) ln ⁡ f θ ∣ a = − n 2 ln 2 π − ln Ξ − a − μ N T Ξ − 1 a − μ N 2 (13)

In the formula, Ξ = σ 2 Q , Q = t 1 t 1 ⋯ t 1 t 1 t 2 ⋯ t 2 ⋮ ⋮ ⋱ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ t 1 t 2 ⋯ t n , T = Λ t 1 Λ t 2 ⋮ Λ t n . By taking the derivative of the likelihood function and finding the extremum, we obtain as Equation 14: μ ^ = T T Ξ − 1 X T T Ξ − 1 T = T T Q − 1 X T T Q − 1 T σ ^ 2 = X − μ T T Q − 1 X − μ T n (14)

Therefore, the probability density function expression f(l) of the Wiener model reaching the threshold and the reliability function (P _s) are respectively as Equations 15, 16: f l = D − x k − Λ t k + l − Λ t k − l d Λ t k + l − Λ t k d l 2 π σ 2 l 3 exp − D − x k − μ l 2 2 σ 2 l (15) P s = P Z > 0 = P y t k + Δ t ⩽ a cr y , y 1 : m ⩽ a cr P y t k + Δ t ⩽ a cr y , y 1 : m ⩽ a cr ∫ Θ ∫ Ω g θ 1 , θ 2 , σ ε , t k , Δ t , a cr d σ ε d θ (16)

In the formula, D is the failure threshold corresponding to the fracture failure of the component. Based on the obtained f(l) of the component, the expected (E) of the component at different times can be obtained, and its formula is as Equation 17: E p ( θ 1 , θ 2 , σ ε | V 1 : m ) g θ 1 , θ 2 , σ ε , t k , Δ t , a cr = ∫ Θ ∫ Ω g θ 1 , θ 2 , σ ε , t k , Δ t , a or p θ 1 , θ 2 , σ ε ∣ y 1 : m d σ ε d θ = 1 N − M ∑ n = M + 1 N g θ 1 n , θ 2 n , σ ε n , t k , Δ t , a cr (17)

In this equation, E represents the expected lifetime of the component, which quantifies the remaining service life from the current state to the failure state. By calculating the expected lifetime, the time-dependent relationship of the remaining life can be determined. Visualizing this relationship enables the construction of the structural structural degradation curve. This curve clearly illustrates the decreasing trend of structural performance over time during service, providing a theoretical basis and quantitative support for remaining life prediction and maintenance decision-making. Finally, based on the predicted N _f at different time points, two structural degradation models of the upper main bearing wall, derived from the scaled model and the SENB specimens, are plotted and designated as D _scale and D _SENB, respectively.

To validate the accuracy of the structural degradation model for the main bearing wall established in this study based on the scaled model, an accuracy verification study was conducted as follows. First, evaluation criteria were determined. This section employs the root mean square error (RMSE), coefficient of determination (R ²), mean absolute relative error (MARE), and mean absolute error (MAE) as evaluation metrics for the structural degradation model. The formulas for these metrics are as Equations 18–21: RMSE = 1 N ∑ i = 1 n y i − y ^ i 2 (18) R 2 = ∑ i = 1 n y i − y ^ i 2 / ∑ i = 1 n y i − y ¯ 2 (19) MAE = 1 n ∑ i = 1 n y i − y ^ i (20) MARE = 1 n ∑ i = 1 n y i − y ^ i y i (21)

Second, structural degradation evaluation was conducted. The accuracy of the scaled model was verified by comparing the structural degradation models D _scale and D _SENB—derived from the scaled model and the SENB specimen, respectively—with the actual structural degradation behavior of the main bearing wall obtained in Section 2.3.

Accurate determination of the actual FCP mode in the upper main bearing wall of diesel engine cylinders is of critical importance for enhancing the precision of structural degradation monitoring. Accordingly, this section presents a comprehensive microstructural characterization study of the upper main bearing wall following the experimental procedures detailed in Section 2.4.

Figures 7a–d respectively illustrate the fracture surface morphology and microstructural characteristics of the upper main bearing wall. Initial macroscopic examination (Figure 7a) reveals that the fracture surface exhibits characteristically flat morphology. Quantitative analysis indicates significant grain coarsening at the fracture zone. Furthermore, pronounced flake graphite segregation and markedly increased pearlite interlamellar spacing are observed, both of which are typical morphological features associated with instantaneous fracture. Microscopic analysis (Figures 7b–d) of three distinct regions located 3 mm, 6 mm, and 18 mm from the crack initiation site demonstrates consistent plastic deformation within the matrix material. The fracture surfaces in these regions predominantly exhibit dimple rupture features, indicative of ductile fracture mechanisms.

Based on the combined macro- and microstructural evidence, we conclusively identify the fracture mode of the upper main bearing wall as primarily ductile fracture characterized by dimple rupture. These findings provide crucial experimental evidence for understanding the failure mechanisms of the upper main bearing wall and significantly contribute to improving the accuracy of structural degradation monitoring.

The accuracy of the ΔK _th and da/dN curves of the upper main bearing wall directly determines the precision of its da/dN model, thereby influencing the prediction accuracy of its structural degradation. Therefore, this section employs a scaled model that comprehensively considers the structural and loading factors of the upper main bearing wall to conduct three sets of repeated FCP tests, thereby obtaining accurate ΔK _th and da/dN curves. Additionally, SENB specimens are introduced for comparison to elucidate the influence of structural and loading factors on FCP results (Carpiuc-Prisacari et al., 2017; Erdogan and Sih, 1963; Irwin, 1957; Leung and Su, 1995; Zhu et al., 2021).

Figure 8 sequentially presents the da/dN curves and ΔK _th of the three scaled models and SENB specimens in the full FCP stage and near-threshold region. As shown in Figure 8, the da/dN curves of the three scaled models are significantly lower than those of the SENB specimens in both the full FCP and near-threshold regions. Moreover, the ΔK _th values of the scaled models are notably higher than those of the standard SENB specimens. This indicates that, under the same testing conditions, the scaled models exhibit stronger resistance to crack propagation. The primary reason for this is that the FCP path in the scaled models is influenced by their geometric shape and load distribution, resulting in a more tortuous crack path. This tortuous FCP path significantly increases the energy consumption of crack propagation, thereby slowing the crack growth rate in the scaled models (Harris and Patel, 2017). Furthermore, Kim and Park (2018) and Zhang and Lee (2015) have pointed out that the local strengthening effects of complex structures and the discontinuities in material microstructure can significantly enhance the crack propagation resistance of components under actual loading conditions by influencing crack growth behavior. This further underscores the necessity of fully considering the actual geometric features and loading conditions of components during FCP experiments to improve the accuracy of da/dN and ΔK _th measurements.

To ensure the accuracy of the micro-failure mechanism results for the upper main bearing wall obtained using the scaled model, this section follows the procedures described in Section 2.5 to validate the accuracy of the equivalent model by assessing the consistency between the test results of the upper main bearing wall and its equivalent component. In addition, the results from standard SENB specimens, which consider only material properties, are compared with the actual characteristics of the upper main bearing wall to highlight the limitations of conventional ISO specimen testing methods.

Figures 8a–f shows the da/dN curves of the upper main bearing wall and its equivalent parts, as well as the SENB specimens. The calculated da/dN curves of the upper main bearing wall and its equivalent parts have small errors, while the SENB specimens show the opposite. Figure 8g displays the stress field of the upper main bearing wall and its equivalent parts. As can be seen from Figure 8, the stress fields of both are highly consistent. Therefore, the scaled model has high equivalence and can be used to study the microscopic failure mechanisms.

The accuracy of the da/dN model for the upper main bearing wall is crucial for the precise prediction of its structural degradation. Additionally, the structural and loading factors of the upper main bearing wall significantly influence its FCP behavior. Therefore, to enhance the prediction accuracy of the structural degradation of the upper main bearing wall, this section establishes a more accurate da/dN model based on the FCP data obtained from the scaled model in Section 5.2. For comparison, SENB specimens, which consider only material factors, are introduced to further elucidate the impact of structural and loading factors on the da/dN model. The formulas for the da/dN models of the three SENB specimens and the scaled model are as Table 2:

By comparing the C, n, and ΔK _th values from the three da/dN models derived from the two types of specimens, it is evident that, under the same precision, the C and n values of the three SENB specimens are greater than those of the scaled model, while their ΔK _th values are smaller. This indicates that the da/dN rate of the scaled model is slower, suggesting stronger fatigue resistance of the material (Yang et al., 2024a; Wang et al., 2023; Teng et al., 2023; Li et al., 2024). This finding aligns with the results obtained in Section 5.2 (Barter et al., 2016; Ciavarella and Papangelo, 2018; Zhang et al., 2023; Oh, 2023). Additionally, to facilitate subsequent analysis of the structural degradation model, this section calculates the average values of the da/dN model formulas for the three SENB specimens and the scaled model. The resulting da/dN model formulas for the upper main bearing wall, derived from the scaled model and SENB specimens, are presented in Table 3.

Since the scaled model incorporates the structural factors of the upper main bearing wall in the cylinder block, this section utilizes the da/dN model developed from the scaled model in Section 5.4 to predict the structural degradation of the upper main bearing wall, aiming to enhance prediction accuracy. For comparison, SENB specimens are introduced, and the structural degradation models derived from the D _Scale and D _SENB are evaluated against D _Experiment using metrics such as RMSE, R ², MARE, and MAE. This comparative study validates the accuracy of the D _Scale based on the scaled model.

Figures 9a–c compares the structural degradation predictions of the scaled model and SENB specimens for three different types of upper main bearing walls. As shown in Figures 8a–c, the D _Scale model derived from the scaled model exhibits closer agreement with the D _Experiment than the D _SENB model derived from SENB specimens. To further assess the accuracy of D _Scale, Table 4 presents the RMSE, R ², MARE, and MAE metrics for D _SENB and D _Scale, based on the results from Figures 9a–c. The comparison of these four metrics demonstrates that D _Scale outperforms D _SENB overall. This superiority is primarily attributed to the fact that D _Scale is constructed based on a scaled model that accounts for structural and loading effects. The modeling process not only considers the material properties of the upper main bearing wall but also fully incorporates the complexity of its structural and loading conditions (Wang and Zhang, 2016; Huang et al., 2022; Hosseini and Mahmoud, 1985). Consequently, the scaled model can more accurately simulate the stress distribution and local strengthening effects of the upper main bearing wall, thereby more precisely reflecting its structural degradation behavior under actual operating conditions (Jing et al., 2023; Shakeri et al., 2022). In contrast, D _SENB only considers the material characteristics of the upper main bearing wall and fails to fully capture geometric discontinuities and local stress concentration effects (Yang et al., 2024b). As a result, D _Scale demonstrates higher precision in predicting the structural degradation of the upper main bearing wall, aligning more closely with experimental values and providing more reliable fatigue data for engineering applications.