Linking the microstructure with strain-life curves for improved utilization of the lightweight potential of thick-walled nodular cast iron

The assessment of the fatigue life of critical, highly stressed component areas is an important aspect in the design of thick-walled components for wind turbines made of nodular cast iron. With the demand for resource efficiency through lightweight design combined with a certain capability to withstand extreme loads and special events, this issue is becoming increasingly important. However, there are still gaps in the description of local strain-based material behaviour. For the design and local strain-based fatigue assessment of large cast components, possibilities to determine the fatigue life as accurately as possible must be provided by standards and guidelines. The paper aims to provide a wide range of material and fatigue data from one common source for general design interests. During research projects at Fraunhofer LBF, material properties for the PRAM-based fatigue life assessment and the elastic-plastic material behaviour have been derived from 9 nodular cast iron grades with 44 microstructural variations. To describe the influence of the technological size effect on cyclic stress-strain and PRAM-N curves the quasi-static parameters (tensile strength and elongation at break) and the microstructure (nodularity and graphite particle density) are considered. In addition, suggestions for scatter bands in the strain-based design approach are given to the designers of thick-walled GJS components.


Symbol directory
Parameter for determining the slope of the PRAM-N curve in the LCF range -A Elongation at break % ρgraphite Graphite particle density mm -² ngraphite Nodularity of the graphite particles % AZ,0; AZ,1; AZ,2; AZ,3 Parameters for determining the first KP of the PRAM-N curve MPa AD,0; AD,1; AD,2; AD,3 Parameters for determining the second KP of the PRAM-N curve MPa Nexperimental Experimentally determined number of cycles -Ncalculated Calculated number of cycles -

Introduction
The assessment of the fatigue life of critical, highly stressed component areas is an important aspect in the design of thick-walled components for wind turbines made of nodular cast iron.With the demand for resource efficiency through lightweight design combined with a certain capability to withstand extreme loads and special events, this issue is becoming increasingly important.The material class "nodular cast iron" (GJS) represents a wide range of different grades from ferritic microstructures, offering low tensile strength but therefore high elongation at break, to ausferritic microstructures (ADI) with inversed strength-ductility-ratio.Due to the casting process, the material further offers the possibility of producing components with a high freedom in design adopted to the specific load case.The fatigue life assessment gains importance when notches or deviations in the local microstructure are present.However, there are still gaps in the description of local strain-based material behavior.New cast iron grades such as ADI have been little studied.However, they do offer the potential for lightweight design or increasing the maximum allowable load on the component.For the design and local strainbased fatigue assessment of large cast components, possibilities to determine the service life as accurately as possible must be provided by standards and guidelines [1,2,3].While [3] and [2] only offer a stress-based fatigue assessment concept, [1] gives a guideline for a strain-based fatigue assessment concept using the damage parameter P RAM, at least for smaller components and other groups of materials.
Recent investigations on thick-walled GJS have shown the influences on the fatigue strength resulting from changing microstructure for stress-based design purposes [4,5,6,7,8,9].In these works, mainly wind energy related ferritic GJS have been investigated based on stress-controlled fatigue tests while defects and size effects according to [10] were considered.In further works from the literature [11,12,13,14,15] and works performed at LBF [7,8,16,17], the focus is also on strain-based approaches to better understand the cyclic deformation behavior as well as the strain-based fatigue behavior.The influence of locally different microstructures is not significant on the cyclic stress-strain behavior for large castings made of EN-GJS-400-18LT as well as on the material cyclic hardening [11,12].A cyclical hardening effect can be observed for all grades of nodular cast iron [7,13,16].However, there is a lack of available strain-life curves that allow an evaluation for the fatigue life, which takes the local microstructure into account.
Based on the previous work at LBF and in the literature, the paper aims to provide an extension of the FKM guideline "Non-linear" [1].The intention is to present the user of this guideline all the required parameters for the design of components made of thick-walled nodular cast iron.For the strain-based fatigue life assessment, material-specific PRAM-N curves are essential.To derive these material-specific PRAM-N curves and correlate them with the tensile strength, the damage parameter PRAM-N curves of 9 different grades and different wall thicknesses have been summarized from several research projects at LBF.This leads to a fatigue assessment concept that follows the FKM "Non-linear" very closely and allows to derive PRAM-N curves based only on the tensile strength.
The next step in the design of components using the FKM "Non-linear" is to determine the strain under plastic deformation at the highest stress area of the component.Therefore, the parameters of the deformation curve according to Ramberg-Osgood K' and n' are derived as a function of the tensile strength Rm, these correlations could be further confirmed with parameters from literature.This enables the designer of structural cast components to compute the local plastic deformations using an FE calculation with an elastic-plastic material model or to use the notch root approximation according to Neuber, as recommended by [1].
To obtain the design PRAM-N curves from the material-specific PRAM-N curves, the use of statistically verified safety factors is mandatory.A detailed safety assessment has shown that all available fatigue tests can be safely modelled using the in this paper specified factor for conversion to 2.5 % probability of failure f2.5%.
In addition, a second approach to the fatigue life assessment concept is presented based on more information.To describe the influence of the technological size effect more accurately, the characteristics of the microstructure in terms of graphite morphology and elongation at break A are also considered in the latter concept.A multiple linear regression is used to link the quasi-static and microstructural parameters with the parameters of the PRAM-N curves and to statistically secure them.

Determination of PRAM-N curves and cyclic stress-strain curves according to FKM19
The aim of this paper is to provide an extension of the FKM guideline "Non-linear" for components made out of thick-walled nodular cast iron based on previous work at LBF and in the literature.All the necessary parameters for the design of nodular cast iron components are presented to the user of this guideline.Material-specific damage parameter PRAM-N curves are the main element of the strain-based fatigue life assessment according to [1].The fatigue data of 9 different grades and wall thicknesses from several research projects at LBF were investigated to derive experimental PRAM-N curves and cyclic stress-strain curves.

Definition of the damage parameter PRAM
The damage parameter PRAM is a modification of the damage parameter PSWT according to Smith, Watson and Topper [18] with consideration of the influence of mean stress according to Bergmann [19].The damage parameter PRAM is used in the FKM guideline [1] "Rechnerischer Festigkeitsnachweis für Maschinenbauteile unter expliziter Erfassung nichtlinearen Werkstoffverformungsverhaltens" (engl., "Computational strength assessment for structural components with explicit consideration of non-linear material deformation behavior").Equation (1) shows the formula for the damage parameter as a function of the mean stress σm and the nominal stress amplitude σa,n.
If there is a mean stress σm present on the component that has to be assessed, the factor k must be determined.The factor k is then obtained from the mean stress sensitivity Mσ, which according to [2] results in a mean stress sensitivity Mσ = 0.4 independent of the tensile strength of the material which is assumed to be valid for all nodular cast iron grades.The factor k is therefore only dependent on the mean stress sensitivity and is thus calculated according to equation (2).

Determination of PRAM-N curve from strain-controlled and stress-controlled fatigue tests
The present series of experiments include ferritic, pearlitic, solid solution strengthened [20] and ausferritic [21] nodular cast iron grades.The materials investigated were thick-walled castings with wall thicknesses of over 75 mm and differing microstructures.The strain-controlled fatigue tests were performed under constant amplitude loading with a strain ratio of Rε = -1 on servo-hydraulic test rigs with an applied extensometer, which measures the strain as a controlled variable.The strain-controlled fatigue tests were performed until crack initiation (a force reduction of 10 % related to the stabilized hysteresis) or until the limit number of cycles Nlim = 1•10 7 .Specimens were tested in the frequency range of f = 0.1 and 25.0 Hz.
The stress-controlled fatigue tests were performed under constant amplitude loading with a stress ratio of Rσ = -1 on electric-resonance test rigs until crack initiation (a reduction in the frequency of 4 Hz) or until the limit number of cycles Nlim = 1•10 7 .These specimens were tested with a higher frequency and were mainly in the range of f = 100 to 200 Hz.A more detailed overview of the specimen geometries used in the research projects [7,22,23,24,25,26,27], the geometry of the casted Y-blocks and casted components, sampling, the chemical composition, images of the microstructure and the test procedure can be found in the open source [28].
The experimental determination of the damage parameter PRAM is performed for strain-controlled tests with a strain ratio of Rε = 1 by evaluating the nominal stress amplitude σa,n and the total strain amplitudes εa,tl from the hysteresis at half the number of cycles to crack initiation and is calculated according to equation (3).
For the force-controlled fatigue tests, with a stress ratio of Rσ = -1, the damage parameter PRAM is calculated using the nominal stress amplitude σa,n.The strain amplitude εa,tl is also calculated from the stress amplitude using Hook's law and the average Young's modulus E under the assumption of strictly linear-elastic loading.
In the FKM guideline "Non-linear" [1], a bilinear approach with a knee point at N = 10 3 cycles is used to describe the PRAM-N curves.The main benefit of this approach is that the entire curve can be described using 3 parameters, a stress value for the knee point PRAM,Z,WS cycles as well as the slope of the LCF range d1 and the MCF range d2.For the analysis of the experimental fatigue data, an extended approach, adding an additional knee point to separate the LCF range, is used.This implies that two more parameters are required, the stress value of the second knee point PRAM,D,WS and the number of cycles of the second knee point Nk,2.
To determine the damage parameter PRAM-N curve according to equation ( 4), a combined evaluation of the strain-controlled and the force-controlled tests is needed.This evaluation is carried out using maximum likelihood, including iterative definition of the second knee point Nk,2 for the maximum probability of occurrence of the fatigue tests with consideration of runouts.The evaluation results in the two knee points PRAM,Z,WS and PRAM,D,WS as well as the slope of the low cycle fatigue (LCF) range d1 and the slope of the medium cycle fatigue (MCF) range d2 , Figure 1.The first knee point Nk,1 is defined as Nk,1 = 10 3 according to [1].
The approach for evaluating the damage parameter PRAM-N curve is based on the approach for evaluating stress-life curves from force-controlled test series according to [29].The slope of the high cycle fatigue (HCF) range d3 is set to 1/d3 = 44.89according to [30] for nodular cast iron.This is equal to a reduction of the damage parameter of 5 % per decade.In addition, the scatter band TPRAM is determined from the standard deviation of the fatigue tests in relation to the 50 % PRAM-N curve.Figure 1 shows an exemplary PRAM-N curve.
,    <  , (4) Figure 1.Combined evaluation of straincontrolled and force-controlled test series to determine the trilinear PRAM-N curve.The PRAM-N curve is shown for a probability of survival PS = 50 % and PS = 90 %, considering the scatter band TPRAM.

Assessment of the fatigue life using the damage parameters
To obtain the design PRAM-N curves required for the numerical fatigue assessment, the material-specific PRAM-N curves must be shifted by considering the statistical size effect [10] and converted from a 50% to a 97.5 % probability of survival using a safety factor.For the fatigue life assessment according to [1] the factor for conversion to 2.5 % probability of failure f2.5% is used.This factor can be calculated from the scatter band of the damage parameter curve TPRAM according to equation (5).Furthermore, the elementary approach with a continuous slope after the second knee point d3 = d2 is applied to calculate the number of cycles in the HCF range according to [1], Figure 2.
If the highly stressed surface of the critical component area is not the same as the highly stressed reference surface Aref of the FKM guideline [1], the statistical size effect has to be considered.To compensate for the statistical size effect the factor nst is used to adjust the experimental damage parameter PRAM-N curves according to equation (6).For this approach, the Weibull coefficient kst is set to kst = 10 according to [2].
Figure 2. PRAM-N curve diagram using the elementary approach in the HCF range.The PRAM-N curve is shown for a survival probability of PS = 50 % and PS = 97.5 %, considering the factor for conversion to 2.5% probability of failure f2.5%.

Determination of the parameters of the cyclic stress-strain curve
Above, the relationship between damage parameter and fatigue life was described using design PRAM-N curves.Next, the relationship between an external load leading to plastic deformations in the highly stressed area on a component and the damage parameter is required.The value of the damage parameter has to be determined according to equation ( 1) considering the plastic strain amplitude εa,pl.The plastic strain amplitude εa,pl has to be calculated either from FE simulation using a linear elastic material model and the notch root approximation by Neuber or by applying an elastic-plastic material model in the FE simulation.In both cases the relationship between an external load and the damage parameter is described by the cyclic stress-strain curve.
As recommended in [1], the Ramberg-Osgood approach [31] is applied for the definition of the cyclic stress-strain curve, equation (7).As described in [28], the cyclic stress-strain curve is defined with scatter bands to include variations in the hardening behavior and stress-strain curve of the investigated materials.
The Young's modulus E is calculated for each series of experiments as an average of all straincontrolled fatigue tests in the considered test series.The Young's modulus of each fatigue test is evaluated from the initial loading curve by linear regression in the range from 10 % to 40 % of the yield strength.The Young's modulus for the present test series is within a range of E = 155 -172 GPa.
The evaluation of the Ramberg-Osgood parameters K' and n' is performed using linear regression in the double-logarithmic diagram of the stress amplitude σa,n versus the plastic strain amplitude εa,pl according to [1] and only the strain-controlled tests are considered.The stress amplitude σa,n and the plastic strain amplitude εa,pl are derived from the hysteresis at half the cycles of crack initiation.The plastic strain amplitude εa,pl results from the difference of the total strain amplitude εa,tl and the elastic strain amplitude εa,el.The elastic strain amplitude εa,el itself is calculated from the stress amplitude σa,n using Hook's law and the average Young's modulus.Furthermore, the scatter band of the cyclic stress-strain curve Tσ is also determined using the standard deviations of the linear regression.Figure 3 shows an exemplary cyclic stress-strain curve.

Present experimental PRAM-N curves and experimental cyclic stress-strain curves
Figure 4 shows exemplary the diagram of all test series of the EN-GJS-400-18LT.It shows that the damage parameter PRAM at 1•10 7 cycles and a probability of survival PS = 50 % are within the range of 133 MPa to 238 MPa.This equals to a difference of 63 % within this nodular cast iron grade, which is widely used in many industrial sectors.This is presumably due to the different wall thicknesses and solidification times, which results in varying microstructures and therefore material properties.The damage parameter PRAM-N curve from [24] has a significantly lower slope in the MCF range with 1/d2 = 16.7 while all other PRAM-N curves have a slope in the range of 1/d2 = 5.4 -8.4.This is most likely because the cast component from which the specimens for the test series of [24] were taken was cast using the permanent mold casting process, whereas the other test series were cast using the sand molded casting process which results in a different pronounced local microstructure.
Figure 5 shows the lognormal probability plot of the scatter bands of the damage parameter PRAM-N curves and the cyclic stress-strain curves of the 44 analyzed test series.It appears that the two parameters mostly follow the lognormal distribution.From this graph, it is possible to determine that for a 90 % probability of occurrence, P = 90 %, the factor for conversion to 2.5 % probability of failure, f2.5%, can be set to f2.5% = 0.803.A factor for conversion to 2.5 % probability of failure, f2.5% = 0.803, corresponds to a scatter band TPRAM for a probability of survival PS = 90% of TPRAM = 1:1.33,following equation (5).
Applying the same approach on cyclic stress-strain curves for a 90 % probability of occurrence in the lognormal probability plot, the scattering band for the cyclic stress-strain curve can be determined to Tσ = 1:1.12.These characteristics provide a reference for the use on experimentally determined damage parameter PRAM-N curves and cyclic stress-strain curves if experimental data is used for a numerical fatigue assessment.

Derivation of the fatigue assessment concept depending on the tensile strength
The FKM guideline "Non-linear" [1] provides a fatigue assessment concept for the materials steel, cast steel and wrought aluminium alloys.The required parameters for the PRAM-N curves and cyclic stressstrain curves of those materials are determined in the guidelines using only the tensile strength Rm.The exponential relationships used in the guideline are adopted and the required parameters are specified with updated values for nodular cast iron.
To enable the application of the above discussed approaches, it is necessary to show that all parameters required for the fatigue assessment of nodular cast iron components according to [1] can be determined with a statistical certainty using the tensile strength Rm.Furthermore, a safety concept is presented that follows closely the approach in [1] so that all available fatigue tests can be summarized.

Defining the parameters K' und n' for the determination of stress-strain curves.
To determine the parameters of the cyclic stress-strain curve in Figure 6 and Figure 7, the cyclic hardening coefficient K' and the cyclic hardening exponent n', literature data [13,14,15,32,33,34] is included in the evaluation alongside to the 44 present series of tests.This correlation has already been shown very similarly in [28] for nodular cast iron.The correlation between the parameters of the cyclic stress-strain curve and the tensile strength Rm can be derived from equation ( 8) and equation ( 9).Additionally, a threshold was set for the cyclic hardening exponents n' so that it is constant for a tensile strength of Rm > 1000 MPa.The resulting parameters of this correlation can be found in Table 1.
Table 1.Parameters for determining the cyclic hardening coefficients and cyclic hardening exponents from the tensile strength.

Defining the parameters for the determination of PRAM-N curves.
To determine the PRAM-N curves based on the tensile strength Rm, the two knee points are the most important parameters for generating the design PRAM-N curves.The correlation between the knee points of the damage parameter curve PRAM,Z,WS and PRAM,Z,WS and the tensile strength Rm can be derived from equation (10) and equation (11).
The resulting parameters of this correlation can be found in Table 2.
Furthermore, in contrast to the other material groups in [1], no constant value is assumed for the slope of the LCF range d1, but instead this parameter is described as a function of the tensile strength Rm for this approach, equation (12).The slope of the MCF range d2 results from the two knee points of the damage parameter curve PRAM,Z,WS and PRAM,Z,WS and is therefore also dependent on the tensile strength Rm, equation (13).To shift all the experimental PRAM-N curves with different specimen geometries used for the fatigue tests to a same level, the factor for statistical size effect nst has to be considered according to equation (6).In this case, the aim is to compensate for the statistical size effect [10] so that all experimental PRAM-N curves are related to the same highly stressed reference surface Aref = 500 mm².Therefore, the reciprocal of the factor for statistical size effect nst is used and multiplied with the knee points PRAM,Z,WS and PRAM,Z,WS.The relationship between the product of the experimentally determined knee points PRAM,Z,WS and PRAM,D,WS, the inverse factor for the statistical size effect 1/nst and the tensile strength Rm is shown in Figure 8.Moreover, the dependency of the resulting slope of the MCF range d2 according to equation ( 13) is depicted.Furthermore, the factor for conversion to 2.5% probability of failure f2.5% is applied to the regression line.The factor for conversion to 2.5% probability of failure f2.5% is determined below and must be selected so that a safe design based on the tensile strength is achieved.

Defining the factor for the conversion of material-specific PRAM-N curves to design PRAM-N curves with a 2.5 % probability of failure.
To determine the factor for conversion to 2.5 % probability of failure f2.5% for this fatigue assessment concept, the experimentally determined cycles Nexperimental of all fatigue tests are compared with the calculated cycles to crack initiation Ncalculated in a scatterplot, Figure 9.Moreover, the logarithmic ratio of the calculated to the experimental fatigue strength log(Nexperimental/Ncalculated) is displayed in a normal probability plot with 95 % confidence bounds, Figure 10.
The logarithmic ratio of experimental to calculated fatigue strength log(Nexperimental/Ncalculated) is equal to 0 if the experimental fatigue strength is equal to the calculated fatigue strength.The factor for conversion to 2.5 % probability of failure f2.5% is hereby chosen so that in the normal probability plot for log(Nexperimental/Ncalculated) = 0 a 2.5 % probability of occurrence, P = 2.5 %, with the use of the lower percentile of the confidence bounds is achieved.This approach leads to the factor for conversion to 2.5 % probability of failure f2.5% = 0.71 and secures a robust and conservative design using the parameters derived from the experimental fatigue data.

Improvement of the fatigue strength assessment concept with consideration of the tensile strength, the elongation at break and the microstructure
Since a low factor for conversion to 2.5 % probability of failure f2.5% must be chosen if the damage parameter PRAM-N curve is only determined from the tensile strength, another fatigue life assessment concept is presented in the following based on two more variables.In this case the knee points of the damage parameter curve at the two knee points PRAM,Z,WS and PRAM,Z,WS are determined using not only the tensile strength Rm but also the elongation at break A and the graphite particle density ρgraphite to account for the microstructure.The latter parameter is to be determined according to [35].
The relationship between the experimental parameters is determined with a multiple linear regression (MLR).The statistical significance of the parameters on the model is evaluated using the t-value and the statistical significance of the entire model is evaluated using the F-value.Furthermore, the adjusted coefficient of determination R 2 adj, which considers how many independent variables are added, is also taken as a measure of the performance of the MLR.The experimental knee points of the damage parameter PRAM,Z,WS and PRAM,Z,WS are shown in Figure 11 and Figure 12 in comparison to the calculated knee points of the damage parameter using the MLR.The resulting relationship between the knee points of the damage parameter curve and the tensile strength Rm, elongation at break A, graphite particle density ρgraphite can be found in equation (14) and equation (15).The resulting parameters of this correlation can be found in Table 3 The factor for conversion to 2.5% probability of failure f2.5% is likewise chosen so that in the normal probability plot, Figure 14 for log(Nexperimental/Ncalculated) = 0 a 2.5 % probability of occurrence P = 2.5 % with the use of the lower percentile of the confidence bounds is achieved.This approach leads to the factor for conversion to 2.5% probability of failure f2.5% = 0.74.

Discussion and Conclusion
The work presented gives the designer of thick-walled GJS components an overview of the strain-life material behaviour and provides methods and results for the assessment of components under cyclic loading.In the present paper, the material properties for the damage parameter PRAM-N curves and the elastic-plastic material behaviour of 9 different GJS grades, EN-GJS-400-18LT, EN-GJS-450-18, EN-GJS-500-14, EN-GJS-600-3, EN-GJS-700-2 and ADI were summarised.The materials investigated differ in their chemical composition, the specimen geometry, the relevant wall thickness as well as the casting process.From these process parameters, 44 different microstructures with different quasi-static properties and graphite morphologies were obtained.The tensile strengths of the materials investigated were in the range of 351 MPa to 966 MPa with elongations at break in the range of 1 % to 27 %.The damage parameter PRAM-N curves in the LCF range at N = 1⸱10 7 cycles were between 133 MPa to 362 MPa.The microstructures were ferritic, pearlitic, solid solution strengthened and ausferritic and showed a nodularity in the range of 31 % to 94 % and graphite particle density in the range of 30 mm² to 663 mm².Furthermore, suggestions for scatter bands in the strain-based design approach are given to the designers of thick-walled GJS components, if experimental fatigue data is used for the design process.For a 90 % probability of occurrence, the factor for conversion to 2.5 % probability of failure f2.5% can be set to f2.5% = 0.803 and the scatter band of the cyclic stress-strain curve to Tσ = 1.12.However, it should be noted that the factor for conversion to 2.5 % probability of failure f2.5% of the experimental damage parameter curves was at least f2.5% = 0.74 and the maximum scatter band of the cyclic stressstrain curve was Tσ = 1.16.
Based on the approach in [1], which does not provide a fatigue assessment concept for nodular cast iron, a corresponding solution was determined from the present fatigue data.This fatigue assessment concept determines all required parameters of the cyclic stress-strain curve according to Ramberg Osgood and the PRAM-N curve from the tensile strength Rm.The parameters of the cyclic stress-strain curves according to Ramberg-Osgood K' and n' enables the designer of a cast component to calculate the local plastic strain εa,pl using an FE simulation with an elastic-plastic material model or to use the notch root approximation according to Neuber, as explicitly recommended in [1].This fatigue assessment concept, which only requires the tensile strength Rm as an input variable, can be used very conveniently for the design process.Furthermore, the reduced tensile strengths from standardization [20,21] for thick-walled nodular cast irons can be used as input variable for the fatigue assessment concept since most of the material data used meet these standards.
The design concept including tensile strength Rm, elongation at break A and graphite particle density ρgraphite allows a more precise assessment compared to the simpler approach.This is accomplished with a statistically equally secured assessment.Considering the microstructure in the use of strain-based concepts has not yet been applied in industry, as no practical approaches for nodular cast iron have been found in research in this area either.
A direct comparison of the two design concepts presented in the scatterplot of the experimental versus the calculated fatigue strength, Figure 15, shows that the calculated cycles of the fatigue assessment concept depending on the tensile strength and the microstructure are closer to the line for Nexperimental = Ncalculated.From this it can be summarized that a more precise determination of the damage parameter curve can be achieved by considering multiple parameters.
A less conservative design concept is obtained due to the better assessment of the damage parameter curve compared to the approach that only considers the tensile strength.By reducing conservativity in the design process, the relevant wall thickness and thus the total component weight could be reduced.The advantage of the proposed approach offers potential in terms of lightweight construction and resource efficiency.The reduction of conservativity in the design process combined with a statistically validated safety concept allows the component weight to be reduced, while simultaneously considering extreme loads and special events with elastic-plastic loadings based on a calculated damage parameter curve.Considering the immense challenges in the production of components with unit weights of several tonnes and the associated costs for transport and assembly, cost and energy savings can be achieved along the entire life cycle of wind turbines through better design methods.

Funding and Acknowledgement
The results presented in this paper were derived during the research project "GaßnerWind" (Grant number 0325707) [23], "Lunkerfest" (Grant number 0325239) [22], "Gusswelle" (Grant number 0324329) [24], "Gusszahnrad" (Grant number 03ET1555) [27], "SiGuphit-B³" (Grant number 03EE2007) [26], "DNAguss³" (Grant number 033EE3018) [25].For the funding of this project, sincere thanks are given to the German Federal Ministry of Economic Affairs and Climate Action (BMWK).All project partners are thanked for their participation and support to complete this project successfully.Abbreviation of the material without the terminator "EN-GJS-" according to [20] and [21]  Abbreviation of the material without the terminator "EN-GJS-" according to [20] and [21] b Excluded from the evaluation of the scattering bands, as some fatigue tests showed a very high hardening effect.

Table-A3.
Summary of the results of the evaluation of the damage parameter PRAM-N curve with scatter bands.

Figure 3 .
Figure 3. Determination of the cyclic stress-strain curve.

Figure 4 .
Figure 4. Diagram of the PRAM-N curves of the EN-GJS-400-18LT test series.

Figure 5 .
Figure 5. Lognormal probability plot of the scatter bands of the damage parameter PRAM-N curves and the cyclic stress-strain curves.

Figure 8 .
Figure 8. Knee points of the damage parameter PRAM versus the tensile strength Rm.

Figure 9 .
Figure 9. Scatterplot of the calculated cycles to crack initiation, Nexperimental, versus the experimental cycles to crack initiation, Ncalculated, of all fatigue tests.

Figure 10 .
Figure 10.Logarithmic ratio of the calculated to the experimental cycles to crack initiation in a normal probability plot.

Figure 11 .
Figure 11.Calculated knee point at Nk,1 of the damage parameter curve nst • PRAM,Z,WS versus the experimentally determined knee point of the damage parameter curve.

Figure 12 .
Figure 12.Calculated knee point at Nk,2 of the damage parameter curve nst • PRAM,D,WS versus the experimentally determined knee point of the damage parameter curve.

Figure 13 .
Figure 13.Scatterplot of the calculated Nexperimental versus the experimental cycles to crack initiation Ncalculated of all fatigue tests.

Figure 14 .
Figure 14.Logarithmic ratio of the calculated to the experimental cycles to crack initiation in a normal probability plot.

Figure 15 .
Figure 15.Comparison of the scatterplots of the fatigue assessment concept depending on the tensile strength with the fatigue assessment concept depending on the tensile strength and the microstructure.

Table 2 .
Parameters for determining the knee points of the damage parameter curve and the slope of the LCF range from the tensile strength.

Table 3 .
Parameters for determining the knee points of the damage parameter curve and the slope of the LCF range from the quasi-static parameters and the microstructure

Table -
A1. Summary of the results of the quasi-static tensile tests, metallography and highly stressed specimen surface.

Table -
A2. Summary of the results of the evaluation of the Young's modulus and the Ramberg-Osgood parameters.