Fatigue Life Assessment of Corroded AlSi10MgMn Specimens

Abstract

This study investigates the influence of pre-corrosion damage on the fatigue behavior of AlSi10MgMn high-pressure die-cast specimens, using the statistical distribution of corrosion depths. The analysis is conducted on two different surface conditions: an unmachined rough surface ($R_a=5.05$ $\mathsf{\mu }\mathrm{m}$) and a machined, polished surface ($R_a=0.25$ $\mathsf{\mu }\mathrm{m}$). For the unmachined specimens, the corrosive damage manifests as homogeneously spread localized corrosion, whereas the polished specimens exhibit less uniform but deeper corrosion. The average corrosion depth of the polished specimens is found to be slightly higher (313 $\mathsf{\mu }\mathrm{m}$ compared to 267 $\mathsf{\mu }\mathrm{m}$) with a broader depth distribution. Specimens are tested under a constant bending load amplitude in laboratory conditions at a stress ratio of $R=0$ until fracture. A fracture mechanics-based methodology is developed to assess the remaining fatigue life of corroded specimens, utilizing short and long crack fracture mechanical parameters derived from SENB specimens. This model incorporates a thickness reduction of the critical specimen cross-section based on the corrosion depth distribution and combines it with a small initial crack of the intrinsic defect size ($a_{eff}=14$ $\mathsf{\mu }\mathrm{m}$). Regardless of the surface condition, using the most frequent corrosion depth for thickness reduction provides a good estimate of the long-life fatigue strength, while using the 90th percentile depth allows for a conservative assessment.

1. Introduction

Aluminum alloys are highly valued in the automotive industry for their blend of characteristics, including low density, relatively high strength, and excellent processability. These properties make them essential for achieving cost-effective and energy-efficient lightweight designs. Alloys like the investigated AlSi10MgMn high-pressure die-cast alloy are commonly used in the structural components of automotive vehicles, where they must endure both mechanical stresses and corrosive environments throughout their service life [1]. In particular, exposure to de-icing salts during winter operations can lead to significant corrosive damage.

High-pressure die-casting enables the rapid production of complex, thin-walled parts with relatively smooth surfaces, making it highly economical for mass production [2]. The corrosion resistance of aluminum casting alloys can be diminished by the presence of alloying elements, which are typically added to enhance mechanical properties or processability [3]. Casting alloys containing high levels of silicon can form a defective anodic layer, making them more susceptible to corrosion. In the case of the alloy AlSi10MgMn in saline solutions, corrosion primarily occurs through the eutectic areas rather than at the boundaries of the intermetallic compounds [4].

Structural parts are typically subjected to corrosive environments over many years during their service life. Corroding specimens prior to fatigue testing is a common and effective method to simulate the corrosive loading experienced by components under corrosion fatigue conditions [5,6,7,8,9,10]. Larrosa et al. [11] present in their review various approaches to quantify the reduction in fatigue strength caused by corrosion. Song et al. [12] developed a data-driven fatigue assessment model for pre-corroded aluminum alloy 2050-T8 that incorporates multiple factors correlating with the fatigue life, including maximum stresses, pit volume, pit surface area, and local roughness at the crack initiation region.

Corrosive damage is often linked to notches and is modeled using smooth semi-ellipsoids. XuangRui et al. [13] developed numerical models to examine the combined effects of corrosion pit length, width, and depth on the stress concentration factor. Based on their findings, they proposed an empirical model to assess the fatigue life of corroded 7075-T651 aluminum alloy specimens. Li et al. [14] analyzed the pit-induced stress concentration in 7005 aluminum alloy using smooth semi-ellipsoids. Their findings revealed that secondary pits located at the bottom of primary pits significantly increase stress concentration. Dobson et al. [15] simulated stress concentrations for real pit geometries and discovered that the stress concentration factor is 1.32–1.65 times higher than for smooth semi-ellipsoids.

Bauer-Troßmann et al. [5] investigated the influence of pre-corrosion on the fatigue behavior of the wrought alloy AlMg3.5Mn in different sensitization conditions. They found that the aggressive media used in screening tests to evaluate the probability of undesirable forms of corrosion under operational conditions often induce localized corrosion damage with a homogeneous lateral and depth distribution. This homogeneous form of corrosion, which results in a reduction of the stress-bearing cross-section, is expected to be less critical than isolated corrosion attacks, such as pitting.

Corrosive defects are frequently treated like cracks, and their fatigue life assessment is therefore often based on linear elastic fracture mechanics. Schönbauer et al. [16] investigated pitted 12% Cr martensitic steel specimens and concluded that such an assumption is valid. In another study, they utilized the El Haddad modification of the Kitagawa–Takahashi diagram to assess fatigue strength depending on the corrosion pit depth. They replaced the geometry factor with an empirically fitted constant ($Y^{\prime }=0.42$) for this purpose [17]. Fatoba et al. [18] conducted similar research on API 5L X65 steel, revealing a slightly lower constant ($Y^{\prime }=0.32$) when quantifying the reduction in fatigue strength due to corrosion pits assumed as semi-elliptical defects. Xu et al. [8] developed a fracture mechanical assessment approach for pre-corroded aluminum alloy (Al-Cu-Mg) by modeling corrosion pits as semi-elliptical surface cracks.

Fatoba et al. [18] observed crack propagation occurring below the threshold for long crack growth, highlighting the significance of considering short crack behavior. Malíková et al. [19] investigated the interaction between corrosion pits and fatigue cracks. Their findings demonstrate a notable influence of corrosion pits on the stress intensity range, particularly affecting short cracks. Elahi et al. [20] employed a short crack model, and Shamir et al. [21] employed a modified NASGRO equation to quantify the reduction in fatigue strength attributed to corrosion pits, which were assumed to be semi-elliptical defects, for the steel S355. Huang et al. [22] employed the NASGRO equation in combination with a semi-elliptical surface crack model to assess the fatigue life of pre-corroded aluminum alloy 7075-T6 based on an equivalent crack size model. Xiang et al. [23] proposed a model where they position the crack at the bottom of a pit assumed to be a semi-circular notch. Their model includes plastic correction and is validated using experimental data from both aluminum alloys and steels. Furthermore, they based their calculations on the equivalent initial flaw size (EIFS) as previously described by Liu et al. [24].

The objective of this study is to assess the impact of corrosion defects on the fatigue behavior of the high-pressure die-cast alloy AlSi10MgMn. This study aims to investigate whether the statistical distribution of corrosion depths can be correlated with fatigue reduction using stress-based and fracture mechanical methods. To validate the different models, S-N curves of pre-corroded specimens will be compared with the results of specimens without corrosive damage previously published in [25]. Two different surface conditions, namely unmachined and polished, are employed for the tests. The corrosion depth is analyzed automatically using the fracture surfaces. The obtained results will be utilized to demonstrate the capabilities and effectiveness of different fatigue life assessment approaches.

2. Materials and Methods

2.1. Material

The investigated aluminum alloy AlSi10MgMn is frequently utilized for manufacturing high-pressure die-cast automotive components. All the specimens used for investigation are taken from a high-pressure die-cast component. Figure 1 illustrates the microstructure of this alloy. Light gray regions represent $\alpha$-Al phases, which are surrounded by eutectic Si-rich phases. The elements Mn and Mg are predominantly incorporated within intermetallic phases, which are visible as larger, gray precipitates.

The measured hardness remains constant across various specimens, regardless of their location, with an average value of $82HBW1/10$ and a standard deviation of $1HBW1/10$ over all measurements.

Additionally, tensile tests were conducted to characterize the material. The specimen geometry for these tests is depicted in Figure 2.

The tensile tests were strain controlled with a constant strain rate of $2.5·{10}^{-4}$ s⁻¹ until fracture. Strain measurements were obtained using an extensometer with a gauge length of 25 mm. Seven specimens were tested with only four failing within the measuring length. These four tests are depicted in Figure 3.

The variation between the different tested specimens is minimal.

Table 1. Tensile test parameters for the investigated AlSi10MgMn alloy.

	E in GPa	A in %	At in %	Rp 0.2 in MPa	Rm in MPa
Mean value	73	6.3	6.7	122	258
Standard deviation	1	0.3	0.3	2	2

summarizes the tensile test results for the four valid tests.

2.2. Specimens

Small SENB (Single Edge-Notched Bending) specimens were utilized for the evaluation of fracture mechanical parameters. Figure 4 illustrates the geometry of these specimens. The size of the specimens was constrained by the geometry of the cast parts from which they were extracted.

The bending specimens were extracted from a section of the cast parts with a curved surface. Figure 5 illustrates the geometry of these specimens with the notch radius selected to concentrate the highest stresses at the apex in the center of the specimens. Consequently, cracks initiate at the investigated surface rather than at a machined edge in the notch root. Further details on the rationale behind this geometry choice are provided in [25].

Bending specimens with four different surface conditions were investigated. In addition to specimens with a cast and blast-cleaned surface (manufacturing condition), specimens with machined and polished surfaces were also tested both with and without pre-corrosion damage. During the machining process, approximately 0.5 mm of the surface material was removed, which is followed by a polishing process using abrasive paper.

Table 2. Surface roughnesses for the investigated bending specimens (Reprinted from Ref. [25]).

Values in $\mathsf{\mu }$m		Ra	Rz	Rt
unmachined	MV	5.05	25.08	33.88
	SD	1.10	4.94	8.01
polished	MV	0.25	2.07	3.00
	SD	0.14	1.02	1.56

compares the measured surface roughness (mean values/MV and standard deviation/SD) of the bending specimens with the cast and the polished surface.

Given a minimal variation in curvature, which is particularly noticeable in cast specimen surfaces, a 3D scan of each specimen is conducted prior to testing. Subsequently, the actual specimen geometry is reconstructed within a finite element model and subjected to a bending load. Utilizing the simulation results, a correlation between load and stress can be established. The comprehensive explanation of this process, from measurement to simulation results, is provided in detail in [25].

In a previous study, it was discovered that pores become exposed during surface removal. Figure 6 schematically depicts that process. Furthermore, it was found that the surface condition has no significant impact on the fatigue strength of the investigated material. This holds true not only for the tests conducted in air but also for the corrosion fatigue tests performed in a 5% NaCl solution [25].

2.3. Testing

A resonant testing machine (Rumul Cracktronic, Neuhausen am Rheinfall, Switzerland, Figure 7) was employed for both fatigue testing of the bending specimens and crack propagation testing of the SENB-specimens with adjustments made to the clamping to accommodate different specimen geometries. The machine applies a four-point bending load to the specimens with the testing frequency varying based on specimen stiffness, decreasing as crack length increases. All tests were performed at room temperature in air.

The notch of the SENB specimens (Figure 4) was sharpened using a razor blade and abrasive diamond paste. Additionally, the specimens were compression pre-cracked at a stress ratio of $R=20$. This methodology ensures that the pre-crack is fully open at the beginning of the fatigue crack growth measurements, so that crack closure effects at the beginning of the test can be neglected [26,27]. The pre-cracks had a length in the range of 100 $\mathsf{\mu }\mathrm{m}$. That specimen preparation with an initial crack can be seen in Figure 8.

The four-point bending crack propagation experiments are conducted at room temperature under laboratory conditions with a constant load ratio of $R=0$, which is consistent with the conditions for the bending specimens. Additionally, one specimen was tested at a load ratio of $R=0.8$ to estimate the effective threshold. It is assumed that crack closure effects are negligible under such high mean stresses. The resonant testing machine used in the experiments exhibits minimal frequency variation, typically dropping from approximately 85 Hz at the start of a test to approximately 75 Hz at the end due to the crack growth. Crack growth is measured using the direct current potential drop method (DCPD). To eliminate the influence of the Seebeck effect at bimaterial junctions, the electric current direction is periodically changed, and the different potentials for each direction are averaged. Crack arrest was defined as crack propagation falling below a value of 1 $\mathsf{\mu }\mathrm{m}$ per 100,000 load cycles. The experiments are conducted under step-wise increasing constant load levels as proposed by Pippan et al. [26]. The testing methodology, including the pre-cracking, is illustrated in Figure 9.

For load amplitudes smaller than the effective threshold ($▵K_{th,eff}$), no crack growth occurs. For amplitudes between the effective and the long crack threshold ($▵K_{th,lc}$), the crack propagates but stops due to the build-up of crack closure effects. This build-up of the threshold value depending on the crack length can be visualized using a cyclic R-curve, as depicted in Figure 9 (bottom right). The mathematical description of the threshold build-up is provided in Equation (1), where the parameters ${\nu }_i$ and $l_i$ are fitting parameters, and $▵a$ is the difference between the initial crack length (after pre-cracking) and the actual crack length [27]. We used four parameters for the description of the R-curve; therefore, $n=2$.

$$▵K_{th}=▵K_{th,eff}+\left(▵K_{th,lc}-▵K_{th,eff}\right)·\left[1-\sum _{i=0}^n{\nu }_i·e^{-▵a/l_i}\right],\sum _{i=0}^n{\nu }_i=1$$

(1)

Once the loading is increased to a level that induces stress intensity values surpassing the long crack threshold, crack growth becomes continuous. The load level is then maintained constant until the specimen fractures, causing the stress intensity to increase solely due to the growing crack length. The fatigue crack growth curve for long cracks can be measured, as depicted in Figure 9 (top right). A common model to assess the crack growth rate for a given stress intensity is the Paris–Erdogan model [28] expressed in Equation (2). In this equation, the parameters C and m describe the height and the slope of the approximated straight in the so-called Paris region.

$${\displaystyle \frac{da}{dN}}=C·▵K^m$$

(2)

Due to the high conservatism of the Paris–Erdogan model near threshold values, a modified NASGRO model, as proposed by Maierhofer et al. [27], was employed (Equations (3) and (4)). This model adjusts the crack velocity factor F to accommodate crack closure effects. The term for the description of the transition to unstable crack growth is omitted as the impact on fatigue life is negligible and no clear transition could be observed in the conducted crack propagation tests.

$${\displaystyle \frac{da}{dN}}=C·F·▵K^m·{\left(1-{\displaystyle \frac{\Delta K_{th}}{\Delta K}}\right)}^p$$

(3)

$$F=1-\left[1-{\left({\displaystyle \frac{1-f}{1-R}}\right)}^m\right]·\left[1-\sum _{i=0}^n{\nu }_i·e^{-▵a/l_i}\right]$$

(4)

The crack opening function ($f=K_{op}/K_{max}$) is the ratio between the crack opening stress and maximum applied stress. The calculation according to Newman [29] for the given stress ratio of $R=0$ is presented in Equation (5).

$$f=max(R;A_0),with{A}_0=\left(0.825-0.34\alpha +0.05{\alpha }^2\right)cos{\left({\displaystyle \frac{\pi {\sigma }_{max}}{2{\sigma }_F}}\right)}^{1/\alpha }$$

(5)

The parameters $\alpha =3$ and ${\sigma }_{max}/{\sigma }_F=0.3$ were chosen in accordance with [27] to account for approximately plane strain conditions and predominantly elastic crack behavior. Figure 7 depicts the test setup for the crack propagation tests.

The bending specimens were tested under a constant amplitude four-point bending load at a stress ratio of $R=0$ under laboratory conditions until fracture, consistent with the SENB tests and previous results, reported in [25]. The testing frequency was approximately 75 Hz, and the maximum number of load cycles was set at 5,000,000. Figure 10 and

Table 3. S-N results (50%) for the uncorroded surface conditions taken from [25].

Surface Condition	k	${\mathit{N}}_{\mathit{K}}$	${\mathit{L}}_{\mathbf{aL}}$ in MPa
unmachined	5.5	355,197	96.8
polished	6.7	805,325	94.3

present the results for the testing series without corrosion, as reported in [25]. In these and the following results, $L_{aL}$ represents the long-life fatigue strength at the knee-point $N_K$, and k denotes the first slope of the S-N curves.

3. Results and Discussion

3.1. Fatigue Testing

Consistent with previous investigations (see Table 3), all fatigue tests are evaluated according to the standard DIN 50100 [30]. The staircase method is applied for determining the long-life fatigue strength, and the pearl string method is used for the finite life regime. Run-outs, specimens that did not fail within 5,000,000 load cycles, are subjected to significantly higher load levels and tested again. The scatter range in the long-life regime has a major uncertainty due to the relatively small number of samples tested; therefore, a constant value ($T_L=L_{aL,90\%failureprob.}/L_{aL,10\%failureprob.}=1.18$) suggested by the standard is used for presenting the results.

Figure 11 depicts the S-N results for the pre-corroded specimens with the unmachined surface.

The fatigue strength is significantly reduced due to the corrosive damage, the 90% failure probability line of the corroded specimens is below the 10% failure probability line of the uncorroded specimens. A knee-point is clearly visible, and the scatter, particularly in the long-life regime, appears to be increased. A representative specimen failed at $63.6$ MPa after 637,700 load cycles, and the corresponding fracture surface is depicted in Figure 12.

The initial pre-corrosion damage is clearly distinguishable by the dark coloration of the affected areas. That corrosion damage of the unmachined specimens manifests as homogeneously spread corrosion occurring localized at the eutectic phase. The localized corrosive attack, which covers the whole specimen surface, is detailed in Figure 13. It is evident that cracks propagate from various corrosive defects across different crack planes; two advancing crack fronts are marked within Figure 12 (red and blue arrows). Areas where these planes converge at different heights appear as darker lines due to shadowing. The area of fatigue crack propagation appears smoother, and the residual fracture is marked by a green dashed line.

Figure 13 provides a detailed backscatter image of the corroded fracture surface, including a secondary electron detail (top right) that highlights the remaining eutectic, dendritic Al-Si structures. The corrosive attack predominantly targets the eutectic areas, as reported by Berlanga et al. [4].

Figure 14 depicts the S-N results for the pre-corroded specimens with the polished surface.

The fatigue strength is even more reduced due to the corrosive attack. Again, a knee-point is clearly visible, and the scatter, especially in the long-life regime, appears to be increased. While some specimens exhibit a similar corrosive attack, others in that series show a more inhomogeneous distribution of corrosion. A representative polished and pre-corroded specimen with an inhomogeneous distribution failed at 61.5 MPa after 752,100 load cycles, and the corresponding fracture surface is depicted in Figure 15.

Figure 16 compares all the S-N curves and reveals the significant reduction in fatigue strength due to pre-corrosion damage. While the surface condition has only a minor influence on the fatigue strength of the uncorroded state [25], this changes significantly with the applied corrosive damage. The fatigue strength of the polished and corroded specimens is significantly lower than that of the unmachined and corroded specimens.

Table 4. S-N results AlSi10MgMn, R = 0, comparison for different surface conditions.

Surface Condition	Pre-Corrosion	k	${\mathit{N}}_{\mathit{K}}$	${\mathit{L}}_{\mathbf{aL},\mathbf{rel}}$ in %
unmachined	no	5.5	355,197	100
	yes	6.2	583,532	65
polished	no	6.7	805,325	97
	yes	6.0	889,485	56

compares the fatigue results of the different test series. No significant influence on the slope as well as on the knee-point position could be found due to the pre-corrosion damage.

3.2. Corrosion Depth Evaluation

The high contrast between the corroded material and the base material in the images of the fractured surfaces (see Figure 12 and Figure 15) allows for a detailed analysis of the statistical distribution of the corrosion depth using a digital image processing routine. The edge of the specimen surface and the boundary between the initial corrosion damage and the base material were detected. The perpendicular distance from the surface to this boundary was defined and measured as the corrosion depth. The measurement is performed individually with a spacing of one horizontal pixel for all the images. Figure 17 shows a representative fracture surface with the detected edge of the specimen (blue) and the corrosion boundary (orange).

This evaluation was performed for all specimens, and the results are depicted in Figure 18, which compares the corrosion depths for the different surface conditions. The blue histogram represents the unmachined specimens and is displayed in the background, while the orange histogram for the polished specimens is shown transparently in the foreground. The frequency denotes the total number of measured points between the corresponding corrosion depth boundaries.

The depth distributions differ significantly. The corrosive attack on the unmachined specimens appears more uniform. Conversely, the polished and corroded specimens show substantial areas with minimal or no corrosive damage, but the overall distribution is much broader, with corrosion depths reaching up to 1 mm. Pores exposed by machining (see Figure 6) intensify the corrosive attack locally, resulting in increased corrosion depths.

Table 5. Characteristic corrosion depth values for both surface conditions.

Surface Condition	Corrosion Depth Values in $\mathsf{\mu }$m
	10%	50%	90%	Most Frequent 1
unmachined	69	267	436	300–325
polished	2	313	645	525–550

¹ Most frequent corrosion depth values above 100 $\mathsf{\mu }\mathrm{m}$, values below classified as “no corrosion”.

presents characteristic corrosion depth values for the two measured distributions.

3.3. Fracture Mechanical Testing

Four crack propagation tests at a stress ratio of $R=0$ were used to evaluate the Paris and NASGRO parameters (see Equations (2) and (3)). Additionally, one test at a stress ratio of $R=0.8$ was conducted to determine the effective threshold value. Figure 19 presents a representative test along with the evaluated model parameters.

Table 6. Fatigue crack growth models for AlSi10MgMn SENB-specimens at $R=0$, averaged parameters from all four conducted tests.

	NASGRO			Paris-Erdogan
$\Delta K_{th,lc}$	C	m	p	C	m
MPam1/2	nm/MPam1/2	-	-	nm/MPam1/2	-
2.24	0.139	3.636	0.304	0.030	3.951

summarizes the averaged NASGRO and Paris parameters derived from these tests. The effective threshold at $R=0.8$ was measured as 1.13 MPam^1/2, and the evaluated parameters for that test are given in

Table 7. Fatigue crack growth models for the one AlSi10MgMn SENB-specimen tested at $R=0.8$.

	NASGRO			Paris-Erdogan
$\Delta K_{th,eff}$	C	m	p	C	m
MPam1/2	nm/MPam1/2	-	-	nm/MPam1/2	-
1.13	0.271	3.657	0.606	0.086	4.560

. A cyclic R-curve (Figure 20) was generated by combining the results of all conducted tests.

3.4. Fatigue Life Assessment

Based on the results presented above, various approaches were used to quantify the effect of corrosive damage on the fatigue life of the tested specimens.

The first approach was stress-based. The corrosive attack, especially for the unmachined specimens, appeared relatively homogeneous. On the basis of the observations of Bauer-Troßmann et al. [5] for localized corrosion with homogeneous lateral and depth distribution, the specimen thickness was reduced to simulate the corrosive attack. In the FEM model, the thickness of the specimen was reduced in the critical, highly stressed area while keeping the thickness at the clamping sites constant. This thickness transition was carefully designed to avoid influencing the stress distribution within the highly stressed areas.

The thickness reduction simulation was performed in 10 $\mathsf{\mu }\mathrm{m}$ increments up to a maximum reduction of 1 mm. Using these results, a stress increase factor $K_S=\frac{S_{max,reducedthickness}}{S_{max,originalthickness}}$ was calculated. Figure 21 depicts those simulation results.

The pre-corrosion primarily affects the stress at the knee-point of the S-N curves rather than the slope in the finite life regime and the number of cycles at the knee-point. Therefore, the thickness reduction causing the difference in the S-N curves can be calculated by comparing the long-life fatigue strengths of uncorroded and pre-corroded specimens. For the unmachined and polished specimens, the long-life fatigue strength drops by a factor of 1.53 and 1.75, respectively, due to corrosive damage. This corresponds to a thickness reduction of 642 $\mathsf{\mu }\mathrm{m}$ for unmachined specimens and 809 $\mathsf{\mu }\mathrm{m}$ for polished specimens.

These derived values exceed the statistical corrosion depth distribution by 99.8% for the unmachined and 98.1% for the polished specimens (see Figure 18). Using mean values or even the 90th percentile would yield non-conservative results, and within a small sample size, no defects larger than these calculated values may be found. The non-uniformity of the corrosive damage depth distribution causes local stress concentrations, further reducing the fatigue strength. As anticipated, the polished specimens, which exhibit a more irregular depth distribution, experience a more significant reduction in fatigue strength, leading to a greater predicted thickness reduction. Therefore, this methodology was deemed unsuitable for fatigue life assessment in the context of the present corrosive damage and loading condition.

Since the stress-based approach is non-conservative and cracks begin to grow at multiple defects simultaneously, different fracture mechanical approaches, e.g., the EIFS-methodology (equivalent initial flaw size) presented in the introduction, were used for the fatigue assessment. The crack driving force, represented by the stress intensity factor $\Delta K$, is calculated according to Equation (6).

$$\Delta K=\Delta \sigma Y\left(a\right)\sqrt{\pi a}$$

(6)

Different crack geometries were analyzed, and the relating crack length-dependent geometry factor $Y\left(a\right)$ was calculated using a finite element model of the bending specimens with a defined initial crack, utilizing FRANC3D (Version 8.3.7). Subsequent calculations, incorporating Equations (1)–(6), were performed using MATLAB (Version R2022b). The crack propagation process is calculated incrementally with a step size of 1 $\mathsf{\mu }\mathrm{m}$ for these calculations. Since the maximum loading stresses of the pre-corroded specimens induce a certain amount of plastic deformation (see Table 1 and Figure 16), a plastic correction as proposed by Xiang et al. [23] was implemented (see Equations (7)–(9)), where the corrected crack size $a_{corr}$ substitutes a in the calculations presented above. The Dugdale model was applied to estimate the size of the plastic zone $\omega$.

$$a_{corr}=a+\omega$$

(7)

$$\omega ={\displaystyle \frac{\pi K_I^2}{8{\sigma }_y^2}}$$

(8)

$${\sigma }_y={\displaystyle \frac{R_m+R_{p0.2}}{2}}$$

(9)

The first fracture mechanical approach involved using a single semi-elliptical crack in the center of the bending specimen. The verification of that approach was performed via the EIFS (Equivalent Initial Flaw Size) method (see [23,24]). Given the relatively uniform corrosive damage, the aspect ratio of the ellipse was set at two ($c/a$ see Figure 22). This simplification is supported by the observed fracture surfaces; for the unmachined specimens, the aspect ratio of the initial defect appears to be slightly higher (Figure 12), whereas for the polished specimens, it seems to be slightly lower (Figure 15). Based on the S-N results, the size of an initial defect with the given shape was calculated for all conducted pre-corroded test specimens with an unmachined surface. The initial crack length versus the remaining load cycles until failure was calculated for a given stress level for different initial crack sizes. The calculation was performed starting from the initial growable crack to a final length of 3 mm, which marks the fracture of the specimen. By comparing the calculated remaining load cycles with the number of actual tested load cycles, the initial crack size (EIFS) was estimated (see Figure 22 top).

Figure 22 depicts the EIFS calculation and compares the results with the statistical distribution of the corrosion defects. Defect sizes below the the intrinsic defect size are excluded from the displayed corrosion depth distribution. The intrinsic defect size $a_{eff}=14$ $\mathsf{\mu }\mathrm{m}$ was calculated numerically based on the short crack threshold $\Delta K_{th,eff}$ and the long-life fatigue strength $L_{aL}$, according to Equation (10). The crack size was incremented by steps of 1 $\mathsf{\mu }\mathrm{m}$ to account for the influence of crack size on the geometry factor. For the long-life fatigue strength $L_{aL}$, the value for the unmachined specimens was used, as it is slightly higher than that of the polished specimens (see Table 3). However, the difference in using the long-life fatigue strength of the polished specimens is marginal and would only change the intrinsic defect size by 1 $\mathsf{\mu }\mathrm{m}$.

$$min\left(abs(2L_{aL}Y\left(a\right)\sqrt{\pi a}-\Delta K_{th,eff})\right)\to a_{eff}$$

(10)

The mean EIFS value (168 $\mathsf{\mu }\mathrm{m}$) for the unmachined specimens is smaller than 77% of all measured corrosion depths. The polished surface specimens yielded similar results with a slightly higher mean EIFS value of 288 $\mathsf{\mu }\mathrm{m}$, which is smaller than 53% of all measured corrosion depths, including significant uncorroded areas. It should be noted that specimens that failed at high load cycles, in the range of ${10}^6$, could not be evaluated within the EIFS approach due to the theoretical limitation that there is no initial crack small enough to grow to failure because the induced stress intensity is below the effective threshold. This limitation is particularly evident in the test series with polished specimens, which often fracture at high load cycles. Furthermore, the scatter of the estimated EIFS values is significant.

Using a single crack for the fatigue assessment of pre-corroded specimens, sized according to the mean or most frequent corrosion depth, would be conservative. This aligns with the findings of Schönbauer et al. [17] and Fatoba et al. [18], who employed an empirically fitted geometry factor significantly below the values for a single elliptical defect. The corrosive damage spreads in all three dimensions, while the simulation simplifies this to a two-dimensional defect, which is a significant limitation. This three-dimensional distribution could lead to local stress reductions due to interactions between various defects, which is an aspect that is not accounted for in the above evaluation.

A combination of the two methodologies presented above (stress-based and fracture mechanics) was found to deliver more accurate results. In this approach, the thickness within the highly stressed area is reduced to simulate the deloading effect of the relatively homogeneous three-dimensional corrosive damage. Additionally, a small elliptical initial crack is introduced at the center of the specimen to further represent the crack-like behavior of the corrosive damage (see Figure 23). For better comparison, the crack length is measured from the top of the original surface.

The thickness was reduced for different percentiles of the corrosion depth distribution (see Table 5). Additionally, the initial elliptical crack was set at the intrinsic defect size $a_{eff}$. The crack length versus load cycles was calculated iteratively, starting from the initial crack to a 3 mm long crack (which marks the specimen’s failure) for different load levels. By combining the load levels and the number of load cycles until fracture, fracture–mechanical assessed S-N curves were calculated. Figure 24 compares the evaluated S-N results to the assessed S-N curves based on the fracture mechanical approach for the unmachined specimens, while Figure 25 presents the same comparison for the polished specimens.

Using the most frequent corrosion depth as a parameter for thickness reduction yields excellent results in assessing the long-life fatigue strength for both surface conditions (polished/unmachined). Utilizing the 90th percentile of the measured corrosion depths allows for a conservative assessment of fatigue strength with only one test point from the unmachined series at the highest load level falling below this line. However, the assessed knee point and slope show some deviation from the measured test points.

Due to the uniformity of the corrosion depth distribution in the unmachined specimens, there is only a small difference between the most frequent and the mean corrosion depth. In contrast, the less uniform distribution in the polished specimens results in a significant difference between these values, leading to different assessment outcomes. The most frequent corrosion depth value is found to be more suitable for the applied model. Particularly for the non-uniform corrosion depth distribution, the 10th percentile is not a suitable measure for fatigue assessment.

It should be noted that the results are based on a simplified defect geometry, which is intentionally designed for easier applicability. For the tested samples under the specified test conditions, this approach demonstrated good agreement with experimental results. However, for other loading scenarios, complex components, or different types of corrosive damage, further validation of the methodology is required.

4. Conclusions

This study analyzed the impact of pre-corrosion damage on the fatigue behavior of AlSi10MgMn high-pressure die-cast specimens, using characteristic corrosion depths (see Table 5) derived from the corrosion depth distributions presented in Figure 18. Bending specimens with different surface conditions, cast and blast cleaned, and machined and polished, were pre-corroded. The damaging influence of the pre-corrosion on fatigue behavior (under laboratory conditions, $R=0$) was quantified.

The evaluation of corrosion depth was performed automatically using the fractured surfaces, revealing different depth distributions for the two surface conditions. For the unmachined specimens, the corrosive damage appeared as homogeneously spread localized corrosion, while the damage on the polished specimens was less homogeneously distributed. The corrosion depths of the polished specimens were, on average, higher than those of the unmachined specimens with a much broader distribution.

Both a stress-based approach and fracture mechanical calculations, based on evaluated cyclic fracture mechanical parameters, were used for fatigue life assessment. These investigations yielded the following outcomes:

• Irrespective of surface condition, no significant influence of pre-corrosion damage on the slope or the number of load cycles at the knee point is observed.
• The fatigue strength significantly decreases due to pre-corrosion damage, correlating with the corrosion depths. The fatigue strength drops by 35% for the unmachined specimens, with an average corrosion depth of 267 $\mathsf{\mu }\mathrm{m}$, and by 42% for the polished specimens with an average corrosion depth of 313 $\mathsf{\mu }\mathrm{m}$.
• Based on the corrosion depth distribution, a stress-based approach, where corrosion is modeled as thickness reduction, leads to a non-conservative fatigue assessment. This indicates that the damaging effect of the observed homogeneously spread localized corrosion exceeds the implications of a simple thickness reduction.
• In contrast, modeling the pre-corrosion damage as a single elliptical crack (with an aspect ratio of two) at the center of the specimen results in a highly conservative assessment.
• A combination of these two methodologies, thickness reduction based on the corrosion depth distribution in conjunction with a crack of the size of the intrinsic crack size ($a_{eff}=14$ $\mathsf{\mu }\mathrm{m}$), yields good agreement between test results and simulation.