# Fatigue Assessment of Nodular Cast Iron with Material Imperfections.

INTRODUCTIONTo reduce the output of carbon dioxide and to preserve resources, the usage of more efficient thick-walled cast iron products has become increasingly important, especially for applications in wind energy and heavy industries, where solutions for a better material saturation for a lightweight design are needed. However, the machine's availability and safety are further crucial points that cannot be neglected.

To design such components properly, the cyclic material behavior of the nodular cast iron grade in a sound condition and in the presence of local material imperfections, such as shrinkages, needs to be known properly. Of similar importance is the detection of fatigue-relevant material imperfections, especially in thick-walled components. Therefore, measures for determining the influence of local material imperfections through non-destructive testing are desired, in order to prevent the rework or even the rejection of the heavy cast components. Presently, thick-walled cast iron components are assessed by certain severity levels e.g. [1, 2], indicating the influence of material imperfections on fatigue life depending on the results of NDT. However, these measures do not offer possibilities for an appropriate fatigue evaluation, since a correlation between the severity levels and the local fatigue strength is presently not given and the usage of the severity levels are statistically and experimentally not assured. Initial attempts to assess the local fatigue strength of material defects in thick-walled nodular cast iron grade GGG-40 were pursued by [3] by determining S-N curves for the shrinkages classes according to [4]. However, the results are not proven for other nodular cast iron grades and cannot be used if an X-ray analysis cannot be performed on the thick-walled components. Further investigations on shrinkages in steel castings [5, 6, 7, 8] were performed to determine a local fatigue notch factor [K.sub.f] for the shrinkages by using FEM and X-ray analysis, leading to large scatter bands for assessing [K.sub.f]. Furthermore, the results are not transferable to thick-walled cast iron components due to a demand for a high resolution of the local shrinkage of only a few 10 [micro]m, which cannot be offered by X-ray and ultrasonic tests on cast components having a wall thickness of several 100 mm.

Nevertheless, new methods of non-destructive testing, such as the ultrasonic technique, Sampling Phased Array, provide new possibilities for involvement in the design process enabling the determination of a local density and a three dimensional view of the shrinkages in the components [9, 10]. To investigate the fatigue strength of thick-walled nodular cast iron and to find a method for an assessment of thick-walled components made of nodular cast iron based on NDT methods, four different nodular cast iron materials, EN-GJS-400-18U-LT, EN-GJS-450-18, EN-GJS-700-2 and ADI-800, were investigated based on strain- and stress-controlled fatigue tests.

Through ultrasonic investigations with the measurement technique Sampling Phased Array, a design concept is discussed linking the local component's density measured by Sampling Phased Array and the fatigue life of the sound material with the local fatigue strength of the shrinkage-affected material.

MATERIALS AND FATIGUE SPECIMEN

The investigations were performed on cast blocks of ferritic EN-GJS-400-18U-LT, ferritic, solid solution strengthened EN-GJS-450-18, pearlitic EN-GJS-700-2 and ausferritic ADI-800. To achieve micro-structures comparable to those of thick-walled cast components, the blocks were cast with wall thicknesses d between 120 and 250 mm. In the case of EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2, large shrinkage volumes were generated inside the cast blocks by means of a controlled solidification. For ADI-800, only macroscopically sound material was investigated. Examples of the cast block of EN-GJS-400-18U-LT with 230 mm thickness and the Y-cast block for ADI-800 are shown in Figure 1. The chemical compositions of the materials and the mean results of three tensile tests performed on specimens removed in the rim zone of the cast blocks are shown in Table 1 and Table 2. Compared to the other materials, EN-GJS-450-18 has, at 3.18 %, the highest silicon content to achieve a solid solution strengthened matrix. The results of the tensile tests show high values for the breaking strain [A.sub.5] of the solid solution strengthened EN-GJS-450-18 compared to EN-GJS-400-18U-LT. This can be related back to the much higher wall thickness of the cast block of EN-GJS-400-18U-LT and, thus, to the better material parameters of EN-GJS-450-18U-LT, having only half of the wall thickness.

Additionally, the parameters of the microstructure were determined for all materials on polished sections. The results for graphite form, graphite size and nodularity, according to [11], are given in Table 3, as well as an example of an etched section for each material. Further investigations concerning the microstructure for specimens removed from the shrinkage volume in the cast blocks of EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2 are discussed in [12].

NON-DESTRUCTIVE TESTING

X-Ray and Ultrasonic Testing

All cast blocks were investigated non-destructively by ultrasonic measurement techniques, especially by Sampling Phased Array, and the blocks of EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2 were additionally X-ray analyzed [9, 10, 12]. The ultrasonic technique Sampling Phased Array was particularly used and further developed to detect the shrinkages in the cast blocks, to determine the three dimensional geometry of the shrinkages present and their density according to [9, 10]. Shrinkages were found only in the cast blocks of the ferritic and the pearlitic materials. The block of the ADI-800 was completely sound, according to the ultrasonic inspection. As an example, Figure 2 shows the result of the shrinkage volume detected in the cast block of EN-GJS-700-2. The resolutions of the detectable structures are dependent on test frequency and material and are in the range between 0.3 and 6.0 mm [9, 10].

Also the specimens, being removed from the cast blocks, were X-ray analyzed, according to the German standards for X-ray analysis [13, 14] and the shrinkages were categorized in the classes Cc-1 to Cc-5 according to [4]. The parameters for the X-ray testing are exemplified in [15].

DETERMINATION OF THE VIRTUAL YOUNG'S MODULUS

From investigations on steel castings [5, 6, 7, 8, 16] that measured the stiffness of the specimens with shrinkages by an extensometer during stress-controlled fatigue tests [5, 6, 7, 8] or tensile tests [16], it is known that the material's stiffness is influenced by the shrinkages present. According to these prior investigations, the so-called virtual Young's modulus [E.sub.f] was also determined for the specimens with shrinkages for EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2 that were removed from the cast blocks. The measurement was performed on servo-hydraulic test rigs, Figure 3. The specimens were loaded with a force and the resulting strain [epsilon] was measured by means of an extensometer. The extensometer had a gauge length of 1 = 25 mm and covered the complete length of the test volume. The measurement was repeated four times for each specimen, moving the extensometer by an angle of 90[degrees] around the specimen. Based on the measurement of the strain [epsilon] and the applied load, the evaluation of the so-called virtual Young's modulus [E.sub.f] was performed according to [17], who compared different methods of determining the Young's modulus E and finally suggested a hyperbolic approach. The determined Young's modulus is subsequently referred to as the so-called virtual Young's modulus [E.sub.f], since the expression Young's modulus is normally reserved only for the sound material condition. During the evaluation, the shrinkages in the specimens were neglected and the load was related to the nominal cross section. Thus, the resulting stresses are nominal stresses.

For metallic materials, it is known that a higher density p is generally accompanied by a higher Young's modulus E. To see whether this is also valid for the specimens with shrinkages, the test volumes of all specimens were cut off after the fatigue test, Figure 4. Both remaining pieces were weighed and the density [p.sub.W] determined. The correlation between the measured density [p.sub.W] and the measured virtual Young's modulus [E.sub.f] is shown in Figure 5 for the materials with detected shrinkages. Moreover, the correlation shows that this is valid for the investigated densities [[rho].sub.W] between 5.7 g/[cm.sub.3] and the nominal densities of around 7.2 g/[cm.sub.3] for a comprehensive range of materials, when taking EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2 into account.

SPECIMENS

From all cast blocks, fatigue specimens were removed. To differentiate between specimens with and without shrinkages for the cast blocks of EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2, removal plans were set up, based on the results of the Sampling Phased Array measurements. This makes a retracing of the results gathered for each single specimen to the positions in the cast block, where the specimens were taken from, possible. The removal plan for the cast block of EN-GJS-700-2 is shown in Figure 2. Different specimen geometries were considered in the plan, especially for the fatigue tests to determine the cyclic material behavior of the sound material condition [12]. For the fatigue tests, a specimen geometry with a highly stressed volume, according to Kuguel [19], of 6122 [mm.sub.3] and a test diameter of d = 15 mm was chosen. The highly stressed volume [19] defines a measure to include both the geometrical and the statistical size effects in describing the load hot-spot in a structure. The specimen geometry is depicted in Figure 6. The same specimen geometry was removed from the sound and the shrinkage-affected material volumes to directly compare the fatigue results of the specimens with shrinkages to those for the sound condition. A specimen with shrinkages in the test diameter is shown in Figure 7.

FATIGUE TESTS AND LOADING CONDITIONS

Fatigue tests were performed under stress and strain control for the sound material condition and under stress control for the specimens with shrinkages.

Strain-Controlled

For a basic material characterization and to check the elastic-plastic material behavior of the four investigated materials, strain-based fatigue tests were performed on servo-hydraulic tests rigs. The tests were conducted at room temperature and at test frequencies f between 0.05 and 25 Hz, depending on the maximum strain. The evaluation of the strain controlled fatigue tests was carried out according to Coffin, Manson, Basquin and Morrow [20, 21, 22, 23] defining the elastic strain-life curve [22], the plastic strain-life curve [20, 21] and the summation of both fractions to the total elastic-plastic strain-life curve [23]. Furthermore, for each material, the cyclic stress-strain curve according to Ramberg-Osgood [24] was determined. In comparison to the approaches in [20, 21, 22, 23, 24], investigations in [12, 26] for nodular cast iron show that a trilinear approach for the elastic strain-life curve, which was first discussed for aluminum in [25], leads to a much more precise description of the material behavior. With this method, the elastic strain-life curve according to [22] is divided into three different parts describing the single fatigue tests and thus the material behavior in the low-cycle, the high-cycle and the very high-cycle fatigue regimes much better. As a further result of the trilinear approach, the cyclic stress-strain curve according to [24] also fits the fatigue test data much better.

The servo-hydraulic fatigue test rig with the fatigue specimen and the extensometer measuring the strain [epsilon] is shown in Figure 3.

Stress-Controlled

The stress-controlled fatigue tests were performed on electric resonance test rigs with maximum load capacity of 100 and 150 kN under axial, alternating loading, [R.sub.[sigma]] = -1, at room temperature and at test frequencies f between 130 and 190 Hz. For the specimens with shrinkages, the test frequencies f varied during testing depending on the magnitude of shrinkages in the specimens, due to a reduction in the specimen's stiffness as demonstrated in Figure 5. The fatigue tests were performed until fracture of the specimens or until the ultimate lifetime [N.sub.lim] of 1*[10.sub.7] cycles was reached.

The parameters of the S-N curve were determined based on the test results, according to [27], defining a method to calculate the parameters including run-outs and run-out specimens re-tested at higher load levels. Due to the absence of a fatigue limit, a further slope k* = 44.9 of the S-N curve, according to [28], was assumed after the knee point [N.sub.k] for the results of the sound and shrinkage-affected material. The fatigue test rig with a specimen is shown in Figure 8.

RESULTS OF THE FATIGUE TESTS

Strain-Controlled

The determined stress-strain curves and the strain-life curves, according to [20, 21, 22, 23, 24], are shown in Figure 9 for the four investigated materials in comparison and in Figure 10 for ADI-800. The results show, for all four investigated materials, a cyclic hardening effect at higher strains. Thus, the materials tested are becoming stronger during usage, due to an accumulation of dislocations in the material and, in the case of ADI-800, possibly also because of a changing microstructure of the matrix due to a transformation of the ausferrite into martensite.

As an example, Figure 10 shows in detail the single fatigue tests determined in the stress-strain and the strain-life regime. By evaluating these results, according to [20, 21, 22, 23, 24], it can be stated that the stress-strain curve does not capture the single fatigue tests properly. Furthermore, it can be shown. for all the tested materials [12, 26], that the assumptions of compatibility, according to [29], for the stress-strain [24] and the strain-life curves [20, 21, 22, 23] are not fulfilled [12, 26].

The capturing of the single fatigue results and thus the description of the stress-strain curves for the nodular cast iron grades EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2 can be improved by applying a trilinear approach for the elastic strain-life curves, according to [26], which is based on investigations on aluminum wrought alloys [25]. The results of this trilinear approach are shown in Figure 10 for ADI-800 and in Figure 9 for all of the investigated materials. The trilinear approach shows, that now the single fatigue results are captured much more precisely. The parameters for the stress-strain and the strain-life curves for ADI-800, both for the conventional [20, 21, 22, 23, 24] and the trilinear approach [25, 12, 26], are given in Figure 10. The according stress-strain curves for the other three materials investigated are given in Figure 9 and the corresponding material data in [12].

Stress-controlled

The parameters determined for the cyclic stress-strain curves for alternating loading, [R.sub.[sigma]] = -1, of the investigated materials are given in Table 4.

The results for the investigated ADI-800 were determined from the strain-controlled fatigue tests based on the procedure discussed in [30], converting all fatigue results from strain-controlled fatigue tests with only linear-elastic material behavior into stresses. The results show that the investigated ADI-800 has the highest fatigue strength at the ultimate number of cycles [N.sub.lim] with a stress amplitude [[sigma].sub.a,n,Nlim,50%] = 198 MPa, followed by EN-GJS-700-2 with [[sigma].sub.a,n,Nlim,50%] = 174 MPa, the high silicon grade EN-GJS-450-18 with [[sigma].sub.a,n,Nlim,50%] = 160 MPa and EN-GJS-400-18U-LT with [[sigma].sub.a,n,Nlim,50%] = 136 MPa. The determined scatter bands [T.sub.[sigma]] reached values between 1:1.21 and 1:1.27 and were in good agreement with scatter bands achieved in other investigations on nodular cast iron [3, 31]. For ADI-800, no scatter band was determined, due to only 8 specimens being available to determine the S-N curve. In agreement with [3], it can be stated that a scatter band of [T.sub.[sigma]] = 1:1.30 is appropriate for the four investigated nodular cast iron materials. The S-N curves determined under stress control will later be denoted as reference S-N curves for the specimens with shrinkages. The reference S-N curve for EN-GJS-450-18 is shown in Figure 11.

FATIGUE STRENGTH OF THE MATERIALS WITH SHRINKAGES BASED ON DENSITY AND VIRTUAL YOUNG'S MODULUS

The results of the stress-controlled fatigue tests on the specimens with shrinkages, according to the shrinkages classification, is shown in Figure 12 with reference to the sound material S-N curve for EN-GJS-450-18.

To evaluate the fatigue strength of the specimens with shrinkages, a method was proposed by [3] based on the evaluation of the shrinkage classification according to [4]. This procedure was also adopted for the present materials investigated [12]. However, the evaluation showed that the scatter bands of the S-N curves derived are large. Additionally this method cannot be used if facilities for the X-ray analysis are not present in foundries. In these cases, ultrasonic investigations will be applied to determine shrinkages in thick-walled castings based on a locally measured density. The derivation of density by ultrasonic Sampling Phased Array has been shown in [9, 10].

It was already stated, in Figure 5, that the locally measured density of a component can be related to the so-called virtual Young's modulus [E.sub.f]. In this case, a link is given between a quasi-static material parameter and a parameter that can be measured by ultrasonic Sampling Phased Array after the casting of the component. Hence, the designer of a component made of nodular cast iron is able to recalculate the local stresses with a reduced stiffness to assess the real fatigue strength of a component affected with shrinkages. However, even in this case, it would be helpful to receive not only a local stiffness or Young's modulus, but also a local fatigue notch factor [K.sub.f]. Since the fatigue notch factor is not related to a single notch but to a shrinkage consisting of multiple more or less sharp notches, [K.sub.f] will later be indicated with an additional "s" for shrinkages, [K.sub.fs]. To derive [K.sub.fs]. for each tested specimen, the experimentally determined fatigue strengths for the specimens with shrinkages are referred to the sound condition material for EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2. To calculate the values for [K.sub.fs] corresponding to each single specimen, all nominal stress amplitudes [[sigma].sub.a,n,shrinkage] are transformed to the knee point [N.sub.k] of the reference S-N curve by applying the slopes k and k* of the reference S-N curves for alternating loading, [R.sub.[sigma]] = -1. [K.sub.fs] is then calculated using Equation 1. An example of this transformation is shown in Figure 13 for EN-GJS-450-18.

[K.sub.fs] = [[sigma].sub.a,n,k](sound)/[[sigma].sub.a,n,k,shrinkage](with slope k and k* from sound material) (1)

With investigations in [12], it could be shown that the determined values for [K.sub.fs] correlate with the virtual Young's modulus [E.sub.f] for each specimen, if the density [rho] and the virtual Young's modulus are determined for a volume equivalent to a distance of [+ or -] 3 mm around the position of fracture. The result of this correlation is shown in Figure 14 for all investigated materials with shrinkages. Arising from a determination of the local component density p by means of ultrasonic Sampling Phased Array with a possible resolution of about 6 mm, it is thus possible to derive a virtual Young's modulus [E.sub.f] and a fatigue notch factor [K.sub.fs] for the shrinkages to estimate the local fatigue strength arithmetically.

FATIGUE DESIGN CONCEPT

To perform a proper local fatigue estimation for cast components, safety factors are required, as becomes obvious when looking at the S-N diagram shown in Figure 15 for EN-GJS-450-18.

Determining the nominal stress amplitude and thus the fatigue strength of the specimens with shrinkages tested under stress control, [[sigma].sub.a,n,shrinkage,50%], based on the specimen-specific [K.sub.fs] and the reference S-N curve for [P.sub.S] = 50 %, will partially lead to an overestimation of the effective nominal stress amplitude due to a scatter in fatigue strength. This is indicated in Figure 15 by two examples, one leading to an overestimate and one leading to an underestimate of the effective fatigue strength. Because of this, a safety factor [S.sub.Sh] is introduced, whose value needs to be determined based on a specific design code. To obtain a convenient value for [S.sub.Sh], it is, for example, assumed that the local fatigue strength of a wind energy component needs to be assessed. According to such a design code [1], the component's fatigue strength needs to be determined for a probability of survival of [P.sub.S] = 97.7 %. To achieve the related value for [S.sub.Sh], the experimentally derived fatigue strength amplitudes for the specimens with shrinkages, [[sigma].sub.a,n,shrinkage], are transformed to [P.sub.S] = 97.7 %, using Equation (2), assuming that the experimentally determined fatigue strength [[sigma].sub.a,n,shrinkage] is, for each specimen, equivalent to a probability of survival of [P.sub.S] = 50 % and that the scatter band for these specimens is [T.sub.[sigma]] = 1:1.30 and thus corresponding to the scatter band of the sound material.

[mathematical expression not reproducible] (2)

This scatter band seems to be quite small compared to scatter bands determined in [12] for S-N curves, based on shrinkages classifications. However, assuming that an S-N curve will be determined only for specimens with the same shrinkage in each specimen, the scatter band would obviously be reduced to that of the sound material or lower. The resulting transformation by Equation (2) is shown again for EN-GJS-450-18 in Figure 16, indicated by the triangles.

By considering a safety factor of [S.sub.Sh] = 2.0 and the reference S-N curve for [P.sub.S] = 50 %, the arithmetically determined fatigue strengths are now able to cover all experimentally determined (and transformed to [P.sub.S] = 97.7 %) fatigue strengths for the specimens with shrinkages, [[sigma].sub.a,n,shrinkage,97.7%], Figure 16. In relation to the numbers given in Table 5, this is equivalent to dividing [[sigma].sub.a,n,shrinkage,97.7%] by a safety number [j.sub.[sigma],c] of 1.14, leading, for each single result, to a probability of confidence [P.sub.C] of 90 %, equation (3). The safety factor of [S.sub.Sh] = 2.0 is determined to be valid for all three materials investigated.

[[sigma].sub.a,n,50%]/[K.sub.fs]*[S.sub.sh] [less than or equal to] [[sigma].sub.a,n,shrinkage,97.7%]/[j.sub.[sigma]] (3)

Based on the results determined so far for the fatigue strength of the sound material and the specimens with shrinkages as well as on the correlation between virtual Young's modulus [E.sub.f], density [rho] and the fatigue notch factor of the shrinkages [K.sub.fs], a fatigue design concept was developed, depicted in Figure 17 as a flow chart including also results based on X-ray analysis and shrinkage classification [12].

Based on a measurement of the density by ultrasonic Sampling Phased Array, a local density [rho] and, from this, a local virtual Young's modulus [E.sub.f] is determined. Based on the density measurement, a load simulation with the sound Young's modulus E, a determination of the fatigue notch factor for the shrinkages [K.sub.fs] and a final assessment of the fatigue strength are performed, based upon on the safety factor [S.sub.Sh] and the reference S-N curve for [P.sub.S] = 50 %.

SUMMARY AND OUTLOOK

During the investigation, the strain- and stress-based cyclic fatigue behavior of the four thick-walled nodular cast iron grades EN-GJS-400-18U-LT, EN-GJS-450-18, EN-GJS-700-2 and ADI-800 were determined. It could be demonstrated that all four materials show a more or less strong cyclic strengthening leading to a higher material resistance against, for example, extreme loads during usage.

Based on stress-controlled fatigue tests on specimens with shrinkages taken from cast blocks made of EN-GJS-400-18U-LT, EN-GJS-450-18 and EN-GJS-700-2, a method was derived, enabling an assessment of the cast component's local fatigue strength by using local density information. The density is hereby determined by ultrasonic Sampling Phased Array and correlated with a so-called virtual Young's modulus determined on the fatigue specimens taken from the cast blocks in the shrinkage volume. It could be shown that a material invariant correlation exists between density p and the virtual Young's modulus [E.sub.f] determined for the specimen test volumes for the three investigated materials.

In the developed fatigue design concept, local density information, determined by ultrasonic Sampling Phased Array, the virtual Young's modulus Ef and the fatigue notch factor of the shrinkages [K.sub.fs] were combined with a safety factor [S.sub.Sh] to estimate the local component fatigue strength arithmetically. On the basis of a local and repeatable density measurement by ultrasonic Sampling Phased Array, this method enables a local fatigue assessment for thick-walled nodular cast iron components based on a reproducible process.

The validity of the process has been demonstrated only for alternating loading, [R.sub.[sigma]] = -1, and for constant amplitude loading for ferritic and pearlitic materials. In further work, this needs to be extended to variable amplitudes, also including mean loads, and to, for example, ausferritic materials. Since many thick-walled components, especially in wind energy and heavy industry applications, are subjected to multi-axial loading, this point also needs to be considered for further work.

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CONTACT INFORMATION

Christoph Bleicher, Dr.-Ing.

Fraunhofer Institute for Structural Durability and System Reliability

LBF

Work Phone: +49 (0) 6151 705 8359

christoph.bleicher@lbf.fraunhofer.de

ACKNOWLEDGMENTS

The results presented in this paper were derived mainly during the research projects "Lunkerfest" [1], "Ga[ss]nerWind" [2] and "unverDROSSen". For the funding of this project, sincere thanks are given to the German Federal Ministry of Economic Affairs and Energy (BMWi). Furthermore, all project partners are thanked for their participation and support to complete the projects successfully.

NOMENCLATURE

[A.sub.5] - breaking strain

b - fatigue strength exponent

c - fatigue ductility exponent

C - Carbon

d - thickness

E - Young's modulus

[E.sub.f] - virtual Young's modulus

f - frequency

k - slope bevor the knee point [N.sub.k]

k* - slope after the knee point [N.sub.k]

K' - cyclic hardening coefficient

[K.sub.f] - fatigue notch factor

[K.sub.fs] - fatigue notch factor of the shrinkages

[j.sub.[sigma]c] - safety number

Mg - Magnesium

Mn - Manganese

NDT - Non-destructive Testing

[N.sub.k] - cycles at the knee point

[N.sub.lim] - ultimate number of cycles

n' - cyclic hardening exponent

[P.sub.C] - probability of confidence

[P.sub.S] - probability of survival

[R.sub.m] - Tensile strength

[R.sub.p0.2] - yield strength

[R.sub.p0.2]' - cyclic yield strength

[R.sub.[sigma]] - load ratio

Si - Silicon

[S.sub.Sh] - safety factor

[T.sub.[sigma]] - scatter band in stress direction

[epsilon] - strain

[[epsilon].sub.f]' - fatigue ductility coefficient

[rho] - density

[[rho].sub.w] - density determined for the specimens test volume by weighing

[[sigma].sub.f]' - fatigue strength coefficient

[[sigma].sub.a,n,Nk] - nominal stress amplitude at [N.sub.k]

[[sigma].sub.a,n,Nlim] - nominal stress amplitude at [N.sub.lim]

[[sigma].sub.a,n,50%] - nominal stress amplitude for [P.sub.S] = 50 %

[[sigma].sub.a,n,shrinkage] - nominal stress amplitude of the specimens with shrinkages

[[sigma].sub.a,n,shrinkage,50%] - nominal stress amplitude of the specimens with shrinkages for [P.sub.S] = 50 %

[[sigma].sub.a,n,shrinkage,97.7%] - nominal stress amplitude of the specimens with shrinkages for [P.sub.S] = 97.7 %

Christoph Bleicher, Rainer wagener, Heinz Kaufmann, and Tobias Melz

Fraunhofer Institute LBF

doi:10.4271/2017-01-0344

Table 1. Chemical composition of the tested materials Material Chemical Composition (in %-weight) C Si Mn S Mg EN-GJS-400-18U-LT 3410 2.200 0.172 0.006 0.049 EN-GJS-450-18 3.320 3.180 0.160 0.008 0.051 EN-GJS-700-2 3.700 2.410 0.500 0.006 0.051 ADI-800 3.540 2.120 0.283 0.007 0.053 Table 2. Quasi-static material data of the tested materials Temperature EN-GJS-400-18U-LT EN-GJS-450-18 Tensile strength [RT.sub.1)] 351 443 [R.sub.m] [MPa] Yield strength [RT.sub.1)] 235 325 [R.sub.p0.2] [MPa] Breaking strain [RT.sub.1)] 13.6 20.4 [A.sub.5] [%] Wall thickness d [mm] 230 120 [RT.sub.1)] - room temperature EN-GJS-700-2 ADI-800 Tensile strength 713 782 [R.sub.m] [MPa] Yield strength 537 614 [R.sub.p0.2] [MPa] Breaking strain 1.9 2.5 [A.sub.5] [%] Wall thickness d [mm] 200 250 [RT.sub.1)] - room temperature Table 4. Parameters of the sound S-N curves Material Parameters of S-N curves for the sound material condition Knee Slope Nominal stress point amplitude at [N.sub.k] and [P.sub.s] = 50 % [MPa] [N.sub.k] k [[sigma].sub.a,n,NK] EN-GJS-400-18U-LT 1.58*[10.sup.6] 6.52 142 EN-GJS-450-18 2.00*[10.sub.6] 7.03 166 EN-GJS-700-2 1.00*[10.sup.6] 4.94 183 ADI-800 1.00*[10.sup.6] 5.87 208 Material Parameters of S-N curves for the sound material condition Nominal stress Scatter amplitude at [N.sub.lim] = 1*[10.sup.7] and [P.sub.s] = 50 % [MPa] [[sigma].sub.a,n,Nlim] 1/[T.sub.[sigma]] EN-GJS-400-18U-LT 136 1.21 EN-GJS-450-18 160 1.23 EN-GJS-700-2 174 1.27 ADI-800 198 - Table 5. Scatter bands, probabilities of confidence [P.sub.S] and safety numbers [j.sub.[sigma],c] based on values given in [32] Scatter band 1:1.50 1:1.30 1:1.30 1:1.30 [T.sub.[sigma]] [-] Probability of 97.7 90.0 97.7 99.996 confidence [P.sub.C] [%] Safety number 1.37 1.14 1.23 1.50 [j.sub.[sigma],c] [-]