Areal fatigue strength assessment of cast aluminium surface layers

Journal Pre-proofs Areal fatigue strength assessment of cast aluminium surface layers S. Pomberger, M. Stoschka, R. Aigner, M. Leitner, R. Ehart PII: DOI: Reference:

S0142-1123(19)30527-4 https://doi.org/10.1016/j.ijfatigue.2019.105423 JIJF 105423

To appear in:

International Journal of Fatigue

Received Date: Revised Date: Accepted Date:

21 October 2019 12 December 2019 15 December 2019

Please cite this article as: Pomberger, S., Stoschka, M., Aigner, R., Leitner, M., Ehart, R., Areal fatigue strength assessment of cast aluminium surface layers, International Journal of Fatigue (2019), doi: https://doi.org/ 10.1016/j.ijfatigue.2019.105423

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© 2019 Published by Elsevier Ltd.

Areal fatigue strength assessment of cast aluminium surface layers S. Pomberger1a , M. Stoschkaa , R. Aignera , M. Leitnera , R. Ehartb a

Christian Doppler Laboratory for Manufacturing Process based Component Design, Chair of Mechanical Engineering, Montanuniversit¨ at Leoben, Franz-Josef-Straße 18, 8700 Leoben, Austria b BMW Motoren GmbH, Hinterbergerstrasse 2, 4400 Steyr, Austria

Abstract The fatigue strength of cast aluminium surface layers is significantly affected by casting imperfections. Experimental work reveals crack initiation due to three failure modes; microporosity, cast surface texture as well as a combination of both. A novel local sub-area evaluation of notch factors for surface texture characterisation utilises areal surface texture by pit depth values Svlocal , ranging within several hundred microns, and related notch root radii ρ distributions. Additionally, the cast bulk strength is calculated by Murakamis approach. For all three failure cases, the presented holistic fatigue layer strength assessment methodology is well applicable for sand cast aluminium. Keywords: Cast aluminium surface layer, Fatigue strength, Areal roughness parameter, Sub-area analysis, Porosity

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Corresponding author; [email protected]

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Nomenclature α αmu κ κ1 κ2 ρ ψ ρ σa σF L,0 σF L σLLF,∗,app σLLF,0 σLLF,m σLLF,p σLLF,s σ √LLF area A a0,lc a1 ,a2 Asub C1 , C2 cval E emin , emax G H K k1 , k2 Kf Kt Kf,m

Pore elongation parameter Material depending coefficient of Murakamis approach Principal curvature Minimum principal curvature Maximum principal curvature Equivalent multi-axial notch root radius of a sub-area Asub Interaction coefficient Notch root radius Stress amplitude Unnotched high cycle fatigue strength Fatigue strength Approximated long life fatigue strength Near defect-free long life fatigue strength Local fatigue strength of mixed defect case Local porosity affected fatigue strength Local surface fatigue strength Long life fatigue strength Defect size Elongation at rupture Microstructural length of the long crack threshold Exponents in modified stress concentration factor Sub-area size Coefficients of Murakamis approach Data selection range Young’s modulus Pore location parameters Relative stress gradient Mean curvature Gaussian curvature Inverse slopes of the S/N-curve Fatigue notch factor Stress concentration factor Mixed fatigue strength reduction factor

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Kf,p Kf,s Kt,mod n NT nbm Nrupture p1 , p2 Rm,bm Rm RP 0.2 Ra Rt Rz Sa Sv Svlocal Svrev TS,1e7 vi HV DAS DOM FV R R2 SEM SGS tansig

Fatigue strength reduction factor Surface fatigue notch factor Modified stress concentration factor Notch sensitivity Transition knee-point Fracture mechanical notch sensitivity Number of load cycles at total rupture Power function variables Base material ultimate strength as given in FKM-guideline Ultimate strength 0.2 % offset yield strength Arithmetical mean deviation of the assessed profile Total height of profile Maximum height of profile Arithmetical mean height of the scale-limited surface Maximum pit height of the scale-limited surface Local maximum pit height of the sub-area Asub Mean value of crack initiating surface pits Fatigue scatter index at ten million load cycles Input variables of the neural network Vickers hardness Dendrite arm spacing Digital optical microscope Focus variation technique Load stress ratio Coefficient of determination Scanning electron microscope Surface geometrical structure Hyperbolic tangent sigmoid transfer function

1. Introduction Within the design process in mechanical engineering, a reliable local fatigue strength assessment is of utmost importance for lightweight applications, such as drivetrain or housing components in combustion engine or e-mobility 3

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applications. In order to accomplish such demanding lightweight construction goals, aluminium is an auspicious design material due to its low density combined with its satisfying mechanical properties [1]. Furthermore, the sound castability of Al-Si alloys allows the design of complex geometries by sand-cast technology, which facilitates a cost-efficient component design and sustainable resource management due to reduction of post-machined surfaces. This supports weight savings of parts up to 50 %, as exemplified for the automotive sector [2]. However, aside its support of utmost complex designs, cast aluminium components inevitably contain material inhomogeneities, such as shrinkage cavities as well as surface defect related stress concentration due to micro and macro notches. The later are driven by the surface geometrical structure (SGS), often simplified referenced as surface roughness. The shrinkage imperfections are basically caused by the manufacturing process. The local cooling rate affects the local microstructure and its mechanical properties [3, 4]. Hardness as well as dendrite arm spacing (DAS) are therefore commonly linked to microporosity formation [5–8] and affect the mechanical properties [9–13]. However, this effect on mechanical properties is significantly diminishing in the presence of notches or porosity inherited by the material as reported in [14]. Since microporosity plays a decisive role in terms of fatigue strength, various studies contributed to the impact of material inhomogeneities on fatigue strength [15–18]. Evolved probabilistic concepts, taking the statistical distribution of the defect population into account [19–24], and XCT-scan supported in-situ fatigue testing [25–27], enable a comprehensive defect assessment regarding shrinkage imperfections of cast components. Studies in [28, 29] utilise XCT-scans to gain detailed information about pore sizes, their shapes and locations within the bulk material. It is stated that the pore size as sole assessment parameter can only provide qualitative results. Not only the defect size, but also the location of material imperfections acts as a significant factor in fatigue strength, since crack growth rates are higher for surface near cracks, compared to internal ones within the bulk material. Serrano-Munoz [26] reasoned, that a three times larger internal defect than a surface related one is needed, to reach simultaneous crack nucleation life. This attests to the surface layer effect on the fatigue strength of cast components. Considering √ both, cavities within the bulk material and surface related defects, the area-approach by Murakami [30], given by equation (1), is frequently used due to its feasible applicability√for a wide range of metals. Murakamis approach is based on the defect size area, the Vickers hardness 4

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HV , as well as on the material and defect location dependent coefficients C1 and C2 . The location coefficient C1 therein is given as 1.43 for surface defects and 1.56 for subsurface defects, while C2 possesses a constant value of 120. (HV + C2 ) σ F L = C1 √ ( area)1/6

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(1)

Despite of broached cavities, respectively inhomogeneities close to, or within, the surface layer, surface notches affect the local fatigue strength additionally, as they raise the local stress concentration within the surrounding material. To calculate the stress peak within the notch root, the linear-elastic stress concentration factor Kt is commonly applied, extended to the fatigue notch factor Kf fractioned by the notch sensitivity n, which is material and load case dependent. To characterise both the stress concentration of single notches with varying shapes as well as multiple notches, numerous studies have contributed to this topic [31–33]. For imperfections, a unified model is proposed in [16], which extends Murakamis approach by the stress concentration factor, studying artificial surface defects located within artificial notch roots. Previous studies in [34, 35] investigated the reduction in fatigue strength of machined surfaces. Revised stress concentration factors have been presented in [36], which covered also machined surfaces. Those design concepts are based either on traditional roughness parameters like Ra, Rz or Rt [36–38] or on areal roughness parameters like Sa [39]. McKelvery [40] investigated the surface finish effect, utilising the guideline from the Forschungskuratorium Maschinenbau (FKM) [41] by means of the roughness parameter Rz. However, the authors proposed in [42] that in case of a holistic, three-dimensional characterisation of cast surface textures, the application of areal roughness parameters is preferable. Ahmed [43] recently showed, that two parallel to the load axis aligned surface defects do not interact regardless to the distance between them, but those aligned perpendicular do affect each other. This influence is also present in terms of cavities interacting within the surrounding area of surface notches within the SGS. Hence this paper contributes to a unified fatigue assessment methodology of cast aluminium surface layers, considering pores, cast surface roughness as well as a superimposed case of surface layer defects.

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2. Investigated material 75

The specimens are taken out of a characteristic position within aluminium sand cast crankcases in T6 heat treatment condition. The specification of the alloy is EN AC-46200 and its nominal chemical composition, in line with standard DIN EN 1706 [44], is given in Table 1. Table 1: Nominal chemical composition of the investigated material according to standard DIN EN 1706 [44]

Element

Al

Si

Cu

Fe

Mn

Mg

Ni

Zn

Weight (%) bal. 7.5-8.5 2.0-3.5 0.8 0.15-0.65 0.05-0.55 0.35 1.2

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85

Additionally, tested material properties such as vickers hardness HV 10 and quasi static properties are listed as mean values in Table 2. All tests where performed at room temperature. Vickers hardness HV 10 is evaluated by means of seventeen measurements on varying specimens at identical position, whereat a value of 123 ± 3 HV 10 is evaluated. The static material parameters such as the young’s modulus E, ultimate strength Rm , 0.2 % offset yield strength RP 0.2 and the elongation at rupture A are obtained from four tests at identical sampling position. Table 2: Tested material properties of the investigated material with T6 heat threatment

Alloy EN AC-46200 T6

90

95

HV 10 [-] E [MPa] Rm [MPa] RP 0.2 [MPa] A [%] 123

74300

300

285

0.51

As the specimen is taken out of real cast components, no round specimen geometry possessing cast surface structure is manufacturable. Therefore, a flat specimen geometry is chosen as depicted within Figure 1. This specimen geometry possesses a cast surface texture for determining the effect on fatigue strength, while all other surfaces of the specimen are machined, respectively polished. All sharp edges are removed in order to reduce the risk of crack initiation due to specimen geometry reasons. By the constant cross section over a length of about 15 mm, crack initiation is enabled to occur at critical surface pits independent of their axial location within this area. This specimen geometry also enables testing of machined and polished surface condition to evaluate the surface layer fatigue strength without the surface roughness 6

effect. Thus, only microstructural inhomogeneities within the surface layer, such as shrinkage pores, affect the fatigue strength. 0 0, ,0 02 2 A A

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cast surface Gussroh

cast surface

A A

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Gussroh

16

0 -0.1

8

±0.05

3

15 85

2

Figure 1: Specimen geometry possessing cast surface structures

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3. Fatigue assessment This section contributes to the stress-based fatigue assessment of either the surface texture, respectively surface roughness, or porosity within the surface layer, as well as a combination of both to assess the local fatigue strength of the cast surface layer holistically.

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3.1. Surface texture Since the surface topography can be considered as a stochastic agglomeration of micro and macro notches, it is important to evaluate the entire surface and not only a partial region. As reasoned in a preliminary work [42], a slight deviation in evaluation profile positioning for line based roughness calculation may result in significant varying roughness values. Therein, satisfying results have already been achieved by taking an area of about 240 mm2 for areal roughness evaluation of cast surfaces into account. But, global areal roughness values do not reflect distinctive roughness pits, respectively notches, by their local values and therefore, an areal characterisation is recommendable.

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3.1.1. Notch depth Within this study, areal roughness parameters are utilised, enabling the characterisation of the entire cast surface at once. Focusing on local topography characteristics, a more precise fatigue strength assessment is feasible by means of local roughness values and notch root radii at crack initiation points. Therefore, specimen surfaces with cast surface condition are scanned by means of a digital optical microscope (DOM) with focus variation technique (FV) at first. The evaluation area is about 240 mm2 in size for each specimen. The, by the measurement instrument extracted, 3D data is filtered, as proposed by [45], in order to receive representative surface roughness values inheriting targeted surface textures of interest. As suggested, a nesting index of 8 mm was used to remove low frequency components of the surface texture. Afterwards, the areal roughness values are calculated according to standard ISO 25178 [46] and evaluated for all 1 mm × 1 mm sized sub-areas, generating roughness maps inheriting local roughness values [45]. Figure 2 shows the Sv-roughness map of a representative specimen ”X”. Thereat, crack initiation arises at the notch root of a roughness pit, which is marked by a red cross within the figure. Beside the surface notch, no cavities or other kinds of defects within the crack initiation area are observed by fracture surface analysis utilising a scanning electron microscope (SEM).

80 60 3 mm

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Sv [µm]

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20 Figure 2: Sv-roughness map of 1 mm × 1 mm sub-areas of specimen ”X” with crack initiation at a distinct surface pit marked by a red cross 135

The notch depth at technical crack initiation is measured firstly by means of fracture surface analysis. Secondly, a comparison with local roughness parameters reveals that the maximal pit depth of the local sub-area Svlocal is valid for notch depth characterisation. This procedure is applicable for all investigated specimens, which possess cast surface structures, as no other 8

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areal roughness parameter features such a statistical link to the notch depth. Therefore, the local areal roughness parameter Svlocal according to the standard ISO 25178 [46], given by equation (2), is calculated for the related sub-area size Asub and further on used for fatigue strength assessment of cast surfaces in the following work. Svlocal = |minAsub z(x, y)|

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3.1.2. Notch root radius Besides the notch depth, surface curvature, respectively notch root radius, is the second essential parameter for notch factor description. As a notch becomes sharper, the local stress concentration increases and hence, the local fatigue strength is reduced, especially respective to high cycle fatigue design [47]. The notch root radius ρ is defined as the reciprocal of the principal curvature κ, see equation (3). 1 (3) κ For each point on a given geometrical surface within the three-dimensional euclidean space, two principal curvatures are evaluable, denoted as the minimum principal curvature κ1 and the maximum principal curvature κ2 . Those are the eigenvalues of the shape operator, acting as a measure how the surface spatially bends at a certain evaluation point. The tangential vectors, these principal curvatures are associated with, are always perpendicular to each other [48]. Exemplarily for a sphere, the principal curvatures are equal for each evaluation point. Taking both principal curvatures into account, two curvature definitions are used in engineering applications. The Gaussian curvature K, which is the product of κ1 and κ2 , and the mean curvature H, defined as the mean value of both principal curvatures [49]. By that, a multiaxial curvature assessment and a subsequent local fatigue strength assessment is facilitated. Both equations are listed in Table 3 and the application of only the maximum curvature, resulting in the smallest notch root radius, is also investigated for comparison purposes. The calculation of the curvature is executed according to [50]. Therefore, for curvature calculation at a specific data point of the surface fraction, data points within a given search radius are incorporated for radius fitting. To study the effect of varying search radii, values of 10 µm, 25 µm, 50 µm and 100 µm were investigated. The grid spacing of the evaluation points is ρ=

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(2)

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Table 3: Applied curvature formulations for radius calculation of the cast surface

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Maximum

Gaussian

κ = κ2

K = κ1 · κ2

Mean H=

1 2

· (κ1 + κ2 )

unaffected by the search radius, but the given radius defines the number of data points, which are evaluated in one step. Hence, the curvature computation time decreases with increasing search radius in the implemented evaluation routine. As the evaluation can be calculated independently for each cell, multiprocessing library is invoked to reduce overall computation time. For a synthetically representative surface of size 12 mm × 12 mm, covering about 8053 × 8053 data points by a chosen magnification of 150x [45], the curvature processing time changes from about 45 s for 0.1 mm search radius to about 670 s for 0.01 mm radius. Concluding, the implemented routine is suitable for curvature calculation of complexly shaped surfaces within a reasonable amount of time. Regarding the quality of notch radius evaluation, the application of search radii less than 25 µm results in significantly lowered notch root radii, increasingly characterising the micro-roughness rather than the notch root radius of the macroscopic texture, which is the driving force in terms of linear elastic stress concentration. In respect to the computational efficiency and evaluated macroscopic notch factors, the search radius of 50 µm revealed to be most suitable. Thereby, computed notch root radii values of the cast surface are also in line with manual notch root radii measurements of crack initiating surface pits by means of fracture surface analysis. Beside that, studies like [51] discuss the problematic of small notch root radii in fatigue notch factor Kf formulations. For improved prediction, therein the material constant a0 is used. Hence, the applied search radius of 50 µm may also be linked to the characteristic microstructural length of the long crack threshold a0,lc , which is about 46 µm for the investigated material. The application of a search radius of 100 µm also leads to adequate results, however, by taking such an extended area for radii calculation into account, the surface is additionally smoothed by the curvature calculation compared to the results of the 50 µm search radius. Concluding, the application of a search radius of 50 µm for notch root radius ρ calculation is well applicable, both in terms of computational efficiency and reproducible notch sharpness of the cast surface texture. 10

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Since the notch root radius is computed for every surface datapoint, linking the x-, y- and z-coordinate information with its notch root radius ρ, a huge data basis is retrieved. For fatigue strength assessment by means of a local stress concentration factor, a representative notch root radius has to be applied. Identical to the sub-area roughness values of the 1 mm × 1 mm area patterns, a representative notch root radius for each sub-area has to be calculated. This is derived by computing the mean value of the notch root radii within each sub-area. While neither the notch root radius nor the depth information, respectively height information (z-coordinate) of the datapoints, is suitable as sole assessment parameter, the combination of both is meaningful in terms of the notch effect. A notch which is both, deep and sharp, thus possessing a small notch root radius, is significantly more crucial for stress concentration than a notch with a comparably large root radius and shallow curvature. Hence, only the highest ratios of the notch depth zi and its associated notch root radius ρi for each datapoint within the sub-area are considered, utilising the variable cval as limiting evaluation range value. For example, by applying cval = 0.7 only datapoints possessing a value of at least 70 % of the maximum zi -ρi -ratio will be considered for calculation of the equivalent notch root radius of the sub-area. Investigating cval values of 0.7, 0.9 and 0.95, a difference of only 1.8 % in the final averaged result is revealed. This indicates that this variable is not significantly sensitive, however it facilitates to derive an sub-area based, averaged notch radius of interest, which is representative for crack initiation as observed by fracture surface analysis. Since the surface notches are already smoothed by the previous application of a search radius of 50 µm for principal curvature evaluation, a value of 0.95 for cval is applicable, thereby taking only the most critical ratios into account. Summing up, the calculation of the equivalent multi axial notch root radius of the sub-area ρ is mathematically defined by equation (4). Hence, the value of ρ is influenced by: ˆ The applied curvature formulation (κ, K, H), see Table 3. ˆ The search radius of curvature calculation for each datapoint of the surface texture.

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ˆ The selected value of cval, taking only a selected range of extremal sorted data values into account.

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For the investigated sand cast surface textures the best statistically matching results where achieved by means of the mean curvature H, an applied search radius of 50 µm and a cval value of 0.95. This leads to an equivalent multiaxial notch root radius for each sub-area which can be subsequently used to assess the local fatigue strength. j 1 X zi ρ = Svlocal · · j i=1 ρi

"

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#−1

zi ∀ ≥ cval · maxAsub ρi

z(x, y) ρ(x, y)

 (4)

3.1.3. Assessment methodology Roughness pits generally do not possess a distinctive geometry. They vary in size as well as in shape and therefore, many formulations for stress concentration factors have been developed [33]. However, since this study is about deriving an applicable method to describe sub-area based surface roughness notches, more generally applicable formulations of Kt are studied, revealing that the equation of Peterson show promising results. Modified by means of the local surface roughness parameter Svlocal and the equivalent multiaxial notch root radius ρ, equation (5) is introduced for a sub-area related stress concentration factor Kt,mod . It was found that, for the investigated cast surfaces, the stress concentration of distinct macroscopic notches possessing high values of Svlocal is overrated due to local stress relief effects of adjacent surface pits. Hence, Svlocal is additionally rated to the mean value Svrev of 150 µm of crack initiating surface pits as mean reference value, thereby leading to well matching fatigue strength assessment results. Furthermore, the exponents a1 = 0.6 and a2 = 2 are introduced for the modification of Peterson’s formulation.  Kt,mod = 1 + 2 

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Svlocal Svrev

a1 ρ

· Svrev

 a12 

(5)

Taking the fracture mechanical notch sensitivity factor nbm [41], see equation (6), into account, the surface fatigue notch factor Kf,s is calculated as given in equation (8). Thereby, the materials forming capacity factor nvm and the statistical supporting effect nst are set to one and the relative stress gradient G is calculated based on the equivalent multi-axial notch root radius ρ, see equation (7). Rm is the material ulitmate strength and Rm,bm a

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material depending constant, denoted in [41]. √ 5 + G · mm q nbm = √ 7.5+ √G·mm m 5 · nvm · nst + RR 1+0.2· G·mm m,bm

(6)

with G=

2 ρ

(7)

Kt,mod (8) nbm Following this procedure for each sub-area, a Kf,s -mapping can be computed, revealing areas of the sand cast surface, which are more likely to cause crack initiation due to stress concentration caused by sand cast surface texture, respectively notches. Figure 3 depicts the Kf,s -mapping of the previously investigated specimen ”X”, compare to the related surface pit depth in Figure 2. The crack initiation point is again marked with a red cross. Identical to Figure 2, Figure 3 indicates this marked sub-area to be most critical in terms of notch effect due to the local surface roughness pit. If nbm values below one are calculated, the fracture mechanical notch sensitivity is set to one, as proposed by [41]. In case no pronounced surface roughness texture is present, as for polished surfaces, Kf,s equals to one. Kf,s =

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2.72

2.10 3 mm

Kf,s [-]

2.41

1.78 1.47

Figure 3: Mapping of the surface fatigue notch factor Kf,s of specimen ”X”, calculated with mean curvature formulation H, search radius of 50 µm and cval = 0.95.

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3.2. Porosity To consider the effect of surface near porosity, the fatigue limit is calculated by Murakamis expanded approach, see equation (9), including the effect of 13

load mean stress by means of the load stress ratio R a material depended coefficient αmu , given by equation (10).  α (HV + C2 ) 1 − R mu σF L = C 1 √ · (9) 2 ( area)1/6 with

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αmu = 0.226 + HV · 10−4 (10) √ The crack initiating defect size area, determined by fracture surface analysis utilising a scanning electron microscope (SEM), is not measured in the by Murakami proposed way [30], but with more detail as presented in [52]. According to [15] the constant value C2 is not suitable for nonferrous metals, since estimation errors are obtained. Thus, a revised constant number was presented which is expanded by a ratio of the Young’s modulus, leading to a value of about 45. Concordant to that, the value for C2 was also revised by Aigner in [53], proposing C2 to be zero in case of more accurately measured defects of aluminium alloys. Hence, this study also sets C2 to zero as the same measurement methodology and aluminium alloy is invoked. Beside the fact, that equally sized surface defects are more critical than internal ones, as proposed by [25, 26], the application of tumescent bending testing intensifies crack initiation on defects located at, or near, the surface because of the localised stress peak. Both within this study investigated surface conditions, machined as well as cast surfaces, predominantly show crack initiation at broached pores or cavities within the surface layer, exemplary depicted for machined surfaces in Figure 4. Therefore, the value of C1 is defined as 1.43 according to Murakamis suggestion. As reference for an unnotched and defect free high cycle fatigue strength σF L,0 , the by Murakami [54] presented relationship between hardness and fatigue limit is used, see equation (11) .  α 1 − R mu σF L,0 = 1.6 · HV · (11) 2 Finally, the fatigue strength reduction factor Kf,p due to micropores within the surface layer is determined by equation (12). Kf,p =

σF L,0 σF L

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(12)

√

100 µm

area = 230 µm

Figure 4: Crack initiating pore for machined surface evaluated by SEM

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3.3. Cast surface layer As sand cast surface layers possess both, defects like cavities within the bulk material, and surface notches due to the cast surface texture, they need to be combinatorially considered in fatigue strength assessment. By means of fracture surface analysis it was found that shrinkage porosity increasingly occurred within the surface layer. The major part of crack initiating porosity is broaching the surface right beneath, or in immediate vicinity of cast surface pits, respectively notches. Since Ahmed [43] described the effect of interacting defects by means of artificial imperfections, the same is valid for the present combination of shrinkage porosity and cast surface notches. Thus, the fatigue notch factors for pore and surface assessment are multiplicatively combined, resulting in the mixed fatigue strength reduction factor Kf,m , see equation (13), and additionally, a dimensionless interaction coefficient ψ is introduced. Kf,s and Kf,p are calculated as described in section 3.1 and section 3.2. In case neither surface roughness nor micropores within the surface layer are present, the corresponding factor (Kf,s or Kf,p ) is set to a value of one. Kf,m = (Kf,s · Kf,p )ψ

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(13)

The interaction coefficient ψ is computed by means of a shallow neural network utilising the neural network training tool incorporated in Matlab® software. The network consists of two layers, one hidden layer with six neurons and an output layer. Currently, within this study the application of six hidden neurons, equalling the number of inputs, leads to reliable results. In general, the optimal number of neurons within a hidden layer can 15

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rarely be defined, however they must not√necessarily match the number of inputs [55]. Key input variables are the area of the defect, the roughness parameter Svlocal , describing the notch depth of the local surface pit, and ρ, representing the notch root radius of the local surface pit. Furthermore, the location and elongation parameters of the defect such as emin , emax and α are also acting as inputs, evaluated by means of fracture surface analysis as described in [56]. The input variables are weighted and then merged within the hidden layer by a hyperbolic tangent sigmoid transfer function (tansig), see equation (14), as this algorithm is commonly used in multilayer networks with backpropagation training [55, 57, 58]. For training of the neural network the Levenberg-Marquardt algorithm was used. It is well suited for neural networks whereat the performance index is the mean square error [55]. After weighting the neurons results, the output parameter as interaction coefficient is calculated. Thereby, for each of the twenty-five investigated specimen covering combinatoric defect cases, the interaction coefficient ψ is calculated and ranges from ψ = 0.54 to ψ = 0.69. The coefficient of determination for the training set was R2 = 0.976. The workflow of the neural network is schematically depicted in Figure 5 for input variables vi with i = 1...n, and n = 6 in this study. tansig(vin ) = Input

2 −1 1 + e−2·vin

(14)

Hidden layer Weights

v1 eig W s ht

v2

Output

ψ

vi Figure 5: Schematic depiction of a neural network with various neurons and input variables vi for evaluation of the interaction coefficient ψ as output variable.

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4. Experimental 350

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Fatigue tests were performed on aluminium specimens with T6 heat treatment, possessing sand cast surfaces as well as on specimens which are additionally machined and polished to evaluate only the influence of surface near porosity. The specimen geometry is given in Figure 1. The tests were performed under tumescent bending load (load stress ratio R = 0) at ambient temperature utilising a Rumul Cracktronic® testing machine. Therewith, the specimen is clamped on both sides and a bending moment M is applied, thus ensuring a constant load along the specimen axis. The loading principle as well as a picture of the specimen clamped within the test device is given in Figure 6.

(a) (b)

M

(c) M

cast surface

Figure 6: (a) Testing principal (b) Specimen with cast surface and machined clamping areas (c) Test device with clamped specimen 360

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As this study focuses on the cast surface layer fatigue strength, especially the effect of the cast surface texture, and the specimens do only possess a cast surface on the top side, the load stress ratio of R = 0 is chosen to intentionally concentrate the maximum stress within the cast surface layer. Thus, crack initiation occurs either at surface pits, respectively surface notches due to the cast surface texture, or at cavities close to the surface, as exemplary shown in Figure 4 in case of a machined sample, or as a combination of both. If a stress load ratio of R = -1 would be applied, crack initiation may be caused by microporosity located at the lower machined, respectively polished, surface and thus no information about the surface roughness effect can be evaluated as preliminary test indicated. The testing frequency was 70 Hz and the tests where stopped at ten million load cycles, whereat specimens are declared as runouts and statistically considered for the evaluation of the long life fatigue strength σLLF . If this criterion is not reached, the specimens 17

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are tested until the total rupture failure criterion occurs, represented by the number of load cycles at total rupture Nrupture . Aluminium does not show a distinctive fatigue resistance due to its microstructural imperfections, thus the slope k2 of the S/N-curve in the long life region is set to k2 equals five times the slope k1 of the finite life region, as proven applicable in prior studies [18, 23, 59], and originally proposed in [60]. The finite life evaluation is conducted by the pearl string method as given in standard DIN 50100:2016-12 [61], while the long life fatigue strength assessment was executed by means √ of the arcsin p method, see [62]. This results in two different stress scatter indices TS and leads in combination with the definition of the slopes k1 and k2 to slightly varying transition knee-point NT (Ps ) values dependent on the probability of survival. For statistically not well covered fatigue testing data within the long life region, Sonsino [63] proposes that the transition knee point ought to be set to a given value independent of the probability of survival. Furthermore, recommendations are given for the slope within the long life region k2 as well as for the stress scatter index TS , which is for cast aluminium TS = 1:1.4. Specimens declared as runouts are re-inserted at a higher load level to increase the sample size in the finite life region for statistical evaluation. Although Gnser [64] studied the effect of re-inserted runouts, observing a non-conservative prediction of the finite lifetime of about ten percent, within this study on surface-layer initiating cast aluminium samples no significant differences in lifetime between re-inserted runouts and new specimens was found. Hence, no further statistical correction of re-inserted runouts was performed and it is assumed, that a cyclic work hardening or pre-damaging of the base material due to re-insertion can be neglected as the crack initiates at dominant imperfections, respectively notches. Figure 7 depicts the S/N-curve of the sand cast surface testing series with T6 heat treatment under tumescent bending load. Therein, the evaluated S/N-curve is given with its 90 % and 10 % probability of survival lines. The stress scatter index given in Figure 7 and Figure 8 as well as in Table 4 was evaluated at ten million load cycles TS,1e7 and calculated according to [65] with its definition TS = 1:[σa (Ps = 10%)/σa (Ps = 90%)]. The stress amplitude σa is normalised by the materials near defect-free long life fatigue strength σLLF,0 under bending load condition with a load stress ratio of R = 0. Within the diagram, the cause of crack initiation is marked either by a blue circle for crack initiation at a surface pit (Cast-S), or by a red triangle in case of crack initiation due to a combination of broached pores and a surface pit (Cast-M). Those marked specimens are further on used for comparison of the assessment 18

415

methodology with the experimental data, see section 5.1. Additionally tested and for validation taken specimens of the S/N-curve are also added in the diagram, named ”Cast-n.d.”. The comparably high scatter of this test series results from the distinctly varying surface texture condition as well as from the change in surface layer porosity. The evaluated data of the cast surface S/N-curve is shown in Table 4.

N o r m a lis e d s t r e s s a m p lit u d e



a

[- ]

0 .8 R

0 .7

R u n C a s C a s C a s

= 0 , T 6 , c a s t s u r fa c e

P s = 9 0 %

P s = 5 0 %

P s = 1 0 %

0 .6 T

0 .5

o u t t t -



a ,P s 5 0



a ,P s 1 0



a ,P s 9 0

S ,1 e 7

t S M n .d .

= 1 : 1 .2 9

0 .4

1 0

5

1 0

6

C y c le s N

1 0 r u p tu r e

7

[- ]

Figure 7: Normalised S/N-curve of cast surface testing series, with marked crack initiation cause either due to a surface pit (Cast-S), or a combination of a broached pore and a surface pit (Cast-M)

420

425

The S/N-curve of the testing series with machined, respectively polished surface (Polished-P), is given in Figure 8 and the evaluated fatigue data is also listed in Table 4. Since no surface pits are present, crack initiation can be caused by porosity within the surface layer, respectively by broached pores, as investigated for all specimens of this series. The specimens, which are subsequently used for comparison of the presented fatigue assessment model with the experimental work, are marked within the diagram by a purple square, representing crack initiation at pores only. The application of the described SN-curve evaluation process revealed a reduced stress scatter index 19

430

435

440

445

450

455

460

within the long life region of TS,1e7 = 1:1.07 compared to the stress scatter index within the finite life region of TS = 1:1.15. This might be caused by the limited number of samples currently available for the machined series and due to non-existing surface roughness as additional influence factor. However, this stress scatter index reduction after the transition knee-point is physically not possible, thus the cycle number at NT of all probabilities of survival are set to the value of Ps = 50% and the stress scatter index of the finite life region is applied to the long life region as proposed by [63]. The slope within the long life region is set to k2 equals five times k1 and the mean long life fatigue √ strength σLLF (Ps = 50%) is statistically calculated by means of the arcsin p method. By that, also the tested fatigue data is covered more properly by the evaluated SN-curve, as given in Figure 8. Application of the normalisation process of woehler curves, according to [65], lead to a common stress scatter index of TS,1e7 = 1:1.25. This lies within the recommended value of TS = 1:1.4 for alumnium castings by Sonsino [63]. The evaluated SN-curve parameters of this experimental work on aluminium castings are given in Table 4 and match the proposed values in [63] quite well. Both S/N-curves show almost identical mean long life fatigue strengths σLLF , see Table 4. One might wrongly conclude that this indicates that the cast surface has no influence on the fatigue strength. This circumstance coincidentally arises, as the machined, respectively polished, specimens show crack initiation at larger pores than the cast surface specimens. The sampling position of the investigated specimens are identical and so does the pore size distribution. For the machined testing series some cast surface specimens are additionally machined, removing only the upper layer of the cast surface, in fact about 0.8 mm. Thus, pores located about 0.8 mm below the cast surface are getting closer to the highly stressed surface region, or are even broached due to the manufacturing process. The fact, that these crack initiating pores are by the factor of two times larger than the pores located directly beneath the cast surface indicates that porosity in a certain depth is more distinct. This can be confirmed by about one-hundred metallographic specimens, whereat the gradient of porosity is optically visible. A representative metallographic specimen is depicted in figure 9, clearly showing more distinct pores, respectively higher degree of porosity, within a certain layer depth of approximately one to two millimetres measured from the cast surface. Overall, a degree of porosity of about 0.5 % to 1 % was observed within the near surface layer of up to two millimetres thickness, whereat a decrease to 0.2 % to 0.5 % was measurable towards the bulk volume. 20

N o r m a lis e d s t r e s s a m p lit u d e



a

[- ]

0 .8 R

0 .7

R u n o u t P o lis h e d - P P o lis h e d - n .d .

= 0 , T 6 , p o lis h e d s u r fa c e

P s = 9 0 %

P s = 5 0 %

P s = 1 0 %

0 .6 T



a ,P s 5 0



a ,P s 1 0



a ,P s 9 0

S ,1 e 7

= 1 : 1 .1 5

0 .5

0 .4

1 0

5

1 0

6

C y c le s N

1 0 r u p tu r e

7

[- ]

Figure 8: Normalised S/N-curve of the testing series posessing a polished surface condition, with marked crack initiation due to shrinkage porosity

465

470

However, the initial statement about spacial pore size distribution can not clearly be proven, since the pore size is investigated only by means of fracture surface analysis and the crack initiation is also significantly influenced by the surface roughness in terms of cast surface specimens. Same sized porosity may also be present directly beneath the cast surface, however other regions with a combination of a smaller broached pore and the surface pit above are more crucial for crack initiation. To get detailed information about the pore size and statistical location distribution within the surface layer, XCT-scans will be conducted in further work. Table 4: Evaluated results of the fatigue tests of the two investigated testing series

Surface condition

k1 [-]

k2 [-]

σa,P s50 [-]

NT [-]

TS,1e7 [-]

Cast surface Polished surface

3.97 4.28

19.85 21.40

0.435 0.431

927.960 1,235.861

1:1.29 1:1.15

21

Metallographic specimen 2 mm

Detected Pores

Figure 9: Exemplary metallographic specimen highlighting porosity gradient within the cast surface layer, revealing varying pore sizes and degrees of porosity dependent on the distance to the surface

5. Model application and validation 475

480

485

490

For comparison the proposed fatigue assessment methodology of section 3 for rough cast surfaces is applied to the whole surface and subsequently linked against the experimental fatigue test results, summarised in section 4. Furthermore only Cast-n.d. specimens are taken for validation, since they have not been used for assessment methodology development. An overview of the available fatigue assessment results is given in Table 5. All data is normalised to the near defect-free long life fatigue strength σLLF,0 under bending load condition with a load stress ratio of R = 0, statistically evaluated at ten million load cycles. To compare the experimental data with the estimations of the presented assessment methodology, the stress amplitude at ten million load cycles is calculated for each specimen within the finite life region as well as within the long life region. This extrapolation is done by means of the slopes k1 and k2 of the corresponding S/N-curve. 5.1. Near-surface laxer fatigue assessment Firstly, the assessment methodology of specimens possessing a cast surface with crack initiation at surface pits (Cast-S), marked as blue circles within Figure 7, is discussed. Utilising the roughness information at the crack initiation point, generated as described in section 3.1, the surface fatigue notch factor Kf,s is calculated for each specimen. For Cast-S specimens, Svlocal values at crack initiation ranged from 120 µm up to 200 µm with a 22

495

500

505

510

mean value of about 150 µm. The notch root radius ρ thereby varies from 65 µm up to 220 µm with a mean value of about 130 µm. Next, starting from the materials near defect-free long life fatigue strength σLLF,0 , the local surface fatigue strength σLLF,s is calculated for each specimen by means of equation (15). Since this equation is identical for all specimens, the subscript placeholder * is replaced with index s,p or m, depended on the assessed specimen. Figure 10 depicts the thereby evaluated σLLF,s for each specimen, based on the local crack initiating surface pit. Subsequently, the mean value and the corresponding 90 % and 10 % scatter index is calculated, revealing a normalised mean value of σLLF,s,P s50 = 0.360 with a fatigue scatter index of TS,1e7 = 1:1.138. The black dashed line in Figure 10 represents the experimental long life fatigue strength σa,P s50 with a probability of survival of 50 %. Comparison of the mean value of the calculated local fatigue strength σLLF,s,P s50 , with the σa,P s50 value of the experiments reveals the assessment methodology to be about 7.5 % conservative. Furthermore, the evaluated σLLF,s,P s10 at ten percent probability of survival is 5.2 % conservative as well. σLLF,∗ =

515

520

525

σLLF,0 Kf,∗

(15)

Investigating the specimens possessing polished surfaces with crack initiation at broached pores (Polished-P), the derived Kf,p values are calculated √ utilising the procedure detailed in subsection 3.2. Average pore size area values of this investigated specimens, evaluated by fracture surface analysis, range from 160 µm up to 280 µm with a mean value of about 200 µm. The fatigue strength reduction factors are again leading to a conservative calculated mean value of σLLF,p,P s50 = 0.369, which is about 6.2 % conservative to the experimentally evaluated fatigue strength σa,P s50 with a probability of survival of 50 %, see Figure 11. Furthermore, a reduced fatigue scatter index of TS,1e7 = 1:1.087 is evaluated at ten million load cycles for the evaluated fatigue strength. The assessment methodology results for Cast-M specimens, with crack initiation at a combination of surface pits and beneath located porosity, are depicted in Figure 12. For the investigated Cast-M specimens, the local roughness parameter Svlocal ranges from 18 µm up to 190 µm with a mean value of about 90 µm. The notch root radius ρ ranges from 20 µm√up to 375 µm with a mean value of about 135 µm. For pore size parameter area, values of 40 µm up to 285 µm with a mean value of about 120 µm are measured. Utilising equation (13), the mixed fatigue strength reduction factor Kf,m is 23

[- ]  L L F

N o r m a lis e d lo n g life fa t ig u e s t r e n g t h

 L L F ,0

1 .0

0 .8

 a ,P s 5 0

( E x p .)

 L L F ,s

( M o d e l)

 L L F ,s ,P s 5 0  L L F ,s ,P s 9 0

7 .5 %

0 .6

5 .2 %

 L L F ,s ,P s 1 0

c o n s e r v a tiv e

T

c o n s e r v a tiv e

S ,1 e 7

= 1 :1 .1 3 8

0 .4

0 .2 0

A r e a o f c o n s e r v a tiv e fa tig u e s tr e n g th e s tim a tio n

1 0

2 0

S p e c im e n n u m b e r [- ] Figure 10: Fatigue assessment result of Cast-S specimens with cast surface condition and crack initiation only at surface pits

530

535

540

calculated for each specimen with a specific interaction coefficient ψ, evaluated √ by the neural network by means of the input variables area, Svlocal , ρ, emin , emax and α. The calculated Kf,m values are also conservative, leading to a mean value of σLLF,m,P s50 = 0.362 and a fatigue scatter index TS,1e7 = 1:1.028 at ten million load cycles. This reduced fatigue scatter is a result of the trained neural network, utilising Cast-M specimen input information, since the aim was to meet a specific long life fatigue strength. However, the mean conservativeness of this assessment methodology is again at about 7.3 % in order to create a unified fatigue strength assessment methodology. A holistic consideration of obtained results of the three assessed crack initiation cases leads to a unified fatigue scatter index of TS,1e7 = 1:1.093 at ten million load cycles, being overall 7.2 % conservative, see Table 5. It should be noted that with the presented assessment methodology not only the present cast surface structure of aluminium castings can be assessed, but more generally the cast surface layer itself, respectively considering

24

[- ]  L L F

N o r m a lis e d lo n g life fa t ig u e s t r e n g t h

 L L F ,0

1 .0

0 .8

 a ,P s 5 0

( E x p .)

 L L F ,p

( M o d e l)

 L L F ,p ,P s 5 0  L L F ,p ,P s 9 0

6 .2 %

0 .6

4 .7 %

 L L F ,p ,P s 1 0

c o n s e r v a tiv e

T

c o n s e r v a tiv e

S ,1 e 7

= 1 :1 .0 8 7

0 .4

0 .2

A r e a o f c o n s e r v a tiv e fa tig u e s tr e n g th e s tim a tio n

0

1 0

2 0

S p e c im e n n u m b e r [- ] Figure 11: Fatigue assessment result of Polished-P specimens with polished surface condition and crack initiation only due to surface layer porosity

545

microporosity distribution and surface roughness texture. Finally, the applied fatigue strength assessment of polished surfaces possessing only surface layer √ porosity, utilising the area approach of Murakami with a coefficient C2 = 0, also leads to sound fatigue strength assessment. Table 5: Long life fatigue assessment methodology results

Condition

Experiment σa,P s50 [-]

Model σLLF,∗,P s50 [-]

Difference ∆ [%]

Model TS,1e7 [-]

Cast-S Cast-M Polished-P

0.435 0.435 0.431

0.360 0.362 0.369

-7.5 -7.3 -6.2

1:1.138 1:1.028 1:1.087

0.435

0.363

-7.2

1:1.093

Unified ∗

Placeholder, replaced by s,p or m for the corresponding defect case

25

[- ]  L L F

N o r m a lis e d lo n g life fa t ig u e s t r e n g t h

 L L F ,0

1 .0

0 .8

0 .6

7 .3 %

c o n s e r v a tiv e

6 .8 %

c o n s e r v a tiv e

 a ,P s 5 0

( E x p .)

 L L F ,m

( M o d e l)

 L L F ,m

,P s 5 0

 L L F ,m

,P s 9 0

 L L F ,m

,P s 1 0

T

= 1 :1 .0 2 8

S ,1 e 7

0 .4

0 .2 0

A r e a o f c o n s e r v a tiv e fa tig u e s tr e n g th e s tim a tio n

1 0

2 0

3 0

S p e c im e n n u m b e r [- ] Figure 12: Fatigue assessment result of Cast-M specimens with cast surface condition and crack initiation at a combination of surface pits and surface layer porosity

550

555

560

5.2. Validation methodology In order to validate the fatigue strength assessment methodology by means of an independent data set, the specimens named Cast-n.d., see Figure 7, are used for this purpose. The mixed fatigue strength reduction factor is calculated depending on the present defect, which caused crack initiation as described in section 3. Fracture surface analysis reveals that only two of the fourteen usable validation specimens showed crack initiation due to a surface pit. The remaining twelve specimens showed crack initiation due to a combinatorial defect case, as described in section 3.3. The coefficient of determination of the validation data set was R2 = 0.887 for the calculation of the interaction coefficient √ ψ by means of the neural network. The related values of the parameters area, Svlocal , ρ are within the range of the Cast-M specimen values. The result of the fatigue assessment is depicted in Figure 13. Therein, the specimens with interacting defects are again marked in red, while the specimens showing crack initiation at a surface pit are marked in blue. 26

N o r m a lis e d lo n g life fa t ig u e s t r e n g t h

 L L F

[- ]

565

Overall, the fatigue strength assessment based on the validation specimens is again 7.1 % conservative. Since the neural network was not trained by this data, a slight increase of the fatigue scatter index at ten million load cycles to TS,1e7 = 1:1.066 is observed. However, the validation indicates a sound fatigue strength assessment by means of the introduced methodology.

 L L F ,0

1 .0

0 .8

 a ,P s 5 0

( E x p .)

 L L F ,m

( M o d e l)

 L L F ,s

( M o d e l)

 L L F ,* ,P s 5 0

0 .6

7 .1 %

c o n s e r v a tiv e

5 .9 %

c o n s e r v a tiv e

 L L F ,* ,P s 9 0  L L F ,* ,P s 1 0

T

S ,1 e 7

= 1 :1 .0 6 6

0 .4

0 .2 0

A r e a o f c o n s e r v a tiv e fa tig u e s tr e n g th e s tim a tio n

1 0

2 0

S p e c im e n n u m b e r [- ] Figure 13: Fatigue assessment result of validation specimens, revealing the assessment methodology to be valid in case of sand cast aluminium surface layers

6. Conclusion 570

575

This paper scientifically contributes to the development of a fatigue assessment methodology for cast aluminium surface layers by evaluating sub-area based notch stress factors. Cast aluminium surface layers possess either surface notches, or surface layer near porosity, or a combination of both within each local evaluation area. The assessment methodology is validated by the experimental work, whereat fatigue tests have been conducted under tumescent bending load utilising specimens with cast surface and machined, respectively polished, surface condition. Based on the results presented within this paper, the following conclusions can be drawn. 27

580

585

590

595

600

605

610

615

1. Crack initiation can arise due to three defect groups. The crack can initiate (I) due to stress concentration at surface pits, respectively surface notches, inherited by the surface geometrical structure, or (II) due to micropores within the surface layer, either predominantly broached by the surface itself or directly beneath the surface, or (III) due to a combination of both defect cases. 2. Assessing the effect of the cast surface texture on the fatigue strength, a local notch stress concept is adopted. The stress concentration factor of Peterson is modified, utilising the local areal roughness parameter Svlocal as well as a representative local notch root radius ρ. By means of the fracture mechanical notch sensitivity nbm , the surface fatigue notch factor Kf,s is subsequently calculated for each evaluated sub-region of the surface texture. The application of Kf,s lead to 7.5 % conservative results compared to the fatigue test result. 3. For the fatigue assessment of micropores within the surface layer, Mu√ rakamis area approach is suitable, if the coefficient C2 is set to zero, since the measurement methodology of the defect size has been revised. Subsequently, the fatigue strength reduction factor Kf,p is introduced to assess the microporosity effect on the fatigue strength. Comparison with the experimental results of additionally machined specimens reveals the introduced pore assessment methodology to be 6.2 % conservative. 4. Since about half of the specimens show crack initiation due to a combination of surface pits and directly beneath located, often broached, pores, a combinatoric approach is also presented, utilising a interaction coefficient ψ to link both defect cases. The interaction coefficient is computed with a compact neural network, utilising the input variables √ area, emin , emax and α of the pore, and Svlocal as well as ρ of the local surface pit. After training, computation of the interaction coefficient ψ by the neural network lead to a coefficient of determination of R2 = 0.976. This methodology leads to a 7.3 % conservative local fatigue strength assessment in respect to the experimental result. 5. The validation of the surface layer fatigue strength assessment reveals the introduced methodology to be valid for sand cast surfaces. The assessment methodology results are on average conservative by about 7.1 % of the base material strength. The neural network computed interaction coefficient ψ revealed a coefficient of determination value of R2 = 0.887 for the validation set. Taking this statistically derived assessment factor into account, the long life fatigue strength can be 28

evaluated more exactly, thus enabling an improved fatigue design of cast surface components by their surface structure and near-surface layer pore distribution. 620

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It needs to be explicitly mentioned, that this assessment procedure development is based on the investigated sand cast surface texture of aluminium castings. Continuing investigations about the applicability of this assessment methodology are ongoing for other surface conditions, as for example for additionally hot-isostatic-pressed post-treatments or additively manufactured surfaces. Furthermore, this assessment procedure depends on the sub-area based surface roughness methodology [45], which introduces the key aspects of areal surface texture characterisation which can be beneficially invoked in local fatigue assessment as exemplified. In addition, sub-area based analysis enables a statistical description of the cast surface texture parameters, such that an engineering feasible application for high series production components is featured. Acknowledgements

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The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged. Furthermore, the authors would like to thank the industrial partner Nemak Dillingen GmbH for the excellent mutual scientific cooperation within the CD-laboratory framework. [1] J. Campbell, Complete Casting Handbook: Metal Casting Processes, Techniques and Design, Elsevier Butterworth-Heinemann, Oxford, UK, 2011. [2] J. Hirsch, rgen, Aluminium in Innovative Light-Weight Car Design, Materials Transactions 52 (5) (2011) 818–824. doi:10.2320/matertrans. L-MZ201132.

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Highlights    

Fatigue strength assessment utilising areal roughness parameters Sub-area mapping of surface fatigue notch factors Assessment of cast surface texture and surface layer micropores Consideration of interacting failure modes by novel interaction coefficient