International Journal of Fatigue 145 (2021) 106112

Available online 26 December 20200142-1123/© 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

On the correlation between microstructural parameters and the thermo-mechanical fatigue performance of cast iron

E. Kihlberg a,*, V. Norman a, P. Skoglund b,a, P. Schmidt c, J. Moverare a

a Division of Engineering Materials, Department of Management and Engineering, Linkoping University, SE-58183 Linkoping, Sweden b Scania CV AB, Materials Technology, Sodertalje, Sweden c Volvo Group Trucks Technology, Gothenburg, Sweden

A R T I C L E I N F O

Keywords: Cast iron Thermo-mechanical fatigue Graphite morphology Microhardness Microstructure

A B S T R A C T

Strain-controlled out-of-phase thermo-mechanical fatigue tests at 100–500 ◦C and various strain ranges were conducted on five cast iron grades, including one lamellar, three compacted and one spheroidal graphite iron. Investigations of graphite morphology and matrix characteristics were performed to associate parameters, such as geometrical features of graphite inclusions and the matrix microhardness, to the thermo-mechanical fatigue performance of each grade. From this, thermo-mechanical fatigue life as a function of maximum stress at half- life, is found to decrease consistently with increasing average graphite inclusion length irrespective of the graphite content. In contrast, no evident correlation between the fatigue life and the matrix microhardness is observed.

1. Introduction

Heavy-vehicle engine components, such as cylinder heads, are sub-jected to rough working conditions during operation, namely high temperatures and mechanical loads. Additionally, the demands of en-gine components are increasing due to higher combustion temperature and pressure as an increase of power efficiency is desired to reduce the emissions [1].

The temperature and mechanical loads are typically varying due to the non-continuous operation of the engine, often referred to as the start-operate-stop cycle [2], which have detrimental effects on the ser-vice life of the engine components. Regarding the cylinder head for instance, compressive loads are generated by thermal expansion as the engine heats up, leading to plastic deformation, creep and stress relax-ation. Due to the compressive inelastic strain accumulated at the high temperature, tensile stresses typically develop as the engine cools down [3]. This repetitive cycle of time-dependent temperature and mechani-cal load conditions, typically referred to as out-of-phase thermo-me-chanical fatigue (OP-TMF), contributes to crack formation at the valve bridge in the cylinder head [3–5]. Other engine components may experiencing in-phase (IP) TMF, even high cycle fatigue (HCF) may be present parallel to TMF loads, and all these fatigue conditions are limiting the components’ lives [2]. Managing fatigue properties is hence

of importance when the engine components are being developed. Thermo-mechanical fatigue of cast iron has been experimentally

investigated in the past and associated damage processes have been closely related to the microstructure [6–11], which consists of graphite inclusions embedded in a steel-like matrix. Generally, at low tensile loading, debonding between the graphite and matrix [12,8] or graphite cleavage [12,8] occur and it is therefore well motivated to consider graphite inclusions as pre-existing microcracks. For instance, many in-vestigators argue that graphite inclusions are not capable to support tensile load during uniaxial mechanical experiments [13,14]. Accord-ingly, previous studies have also found that microcracks typically initiate in the matrix starting from fractured or debonded graphite in-clusions under cyclic loading at temperatures between room tempera-ture and 500 ◦C [6,7,10,15,17]. For spheroidal graphite iron, there has also been observations of crack initiation occurring at casting defects [18,19,10]. Regardless, it is well established that crack growth rate is strongly related to crack length via different fracture mechanics con-cepts such as the stress-intensity factor [20], the cyclic J-integral [21–23] and the crack-tip-opening displacement [24,25]. Thus, based on the observation that graphite inclusions act as pre-existing cracks in lamellar and compacted graphite iron from which fatigue growth in the matrix follows, it is reasonable to suggest that more elongated graphite inclusions will promote higher crack growth rate.

* Corresponding author. E-mail address: ebba.kihlberg@liu.se (E. Kihlberg).

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International Journal of Fatigue

journal homepage: www.elsevier.com/locate/ijfatigue

https://doi.org/10.1016/j.ijfatigue.2020.106112 Received 13 October 2020; Received in revised form 18 December 2020; Accepted 20 December 2020

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Several attempts to correlate macroscopic mechanical and thermal properties with microstructural parameters of cast iron have been done previously [9,26–39]. It has been seen that parameters such as matrix phase, microhardness, graphite content and graphite shape may influ-ence the properties. For instance, the elastic modulus of wide variations of cast iron grades is strongly associated with the shape of the graphite inclusions [26–28], whereas yield and tensile strength are affected by both graphite morphology and matrix characteristics [29,30]. Notably, Fragassa et al. [31] used machine learning to derive mechanical prop-erties from microstructural parameters and had promising results regarding ultimate tensile strength and yield strength. Regarding ther-mal properties, the thermal conductivity has also been observed to relate to the graphite morphology [30,32,33]. There are also numerous in-vestigations which have addressed fatigue properties such as fatigue strength at room temperature [34,35], macroscopic crack growth properties [9,36] and even TMF properties [37–39]. However, more investigations are needed in order to fully understand the correlation between microstructure and TMF life and no previous studies have investigated the influence of microstructural parameters on TMF per-formance in cast iron as systematically as presented in this paper.

The objective with this investigation is to correlate microstructural parameters with thermo-mechanical fatigue performance. In this study, different cast iron grades used in heavy-vehicle automotive industry, namely lamellar graphite iron (LGI), compacted graphite iron (CGI) and spheroidal graphite iron (SGI), have been investigated in terms of TMF performance and microstructural assessment, in order to correlate these properties. With a better understanding of this correlation, the life prediction and engine material development will be easier, faster and cheaper thanks to less need of long and expensive TMF testing. The findings will not only support material selection, manufacture and development processes of heavy-vehicle components, but also gain in-sights in how to control the process parameters in order to optimise the material used in cylinder head.

2. Materials and methods

2.1. Materials

Five cast iron grades of high relevance for different heavy-vehicle engine components have been investigated in this paper. One pearlitic Cr-Mo-alloyed lamellar graphite iron typically used in cylinder heads, denoted pearlitic LGI290, from a cast staircase with different thickness to obtain different solidification and cooling conditions where the specimens for this paper was manufactured from the same thickness. Three of the grades were compacted graphite iron including a fully ferritic CGI alloy denoted ferritic CGI400, which was silicon solid- solution-strengthened and manufactured from a cast plate with geom-etry and cast procedure adjusted to obtain solidification and cooling conditions similar to the combustion plane of the cylinder head; a partly ferritic EN-GJV-350, denoted ferritic/pearlitic CGI350, manufactured from valve bridge in cylinder heads which was cast in green sand with cold-box cores; and EN-GJV-400, denoted pearlitic CGI400 intended for cylinder heads, manufactured from a cast plate [10]. There was also a fully ferritic spheroidal graphite iron EN-GJS-SiMo5-1 included, deno-ted ferritic SiMo51, manufactured from a cast plate with high content of

silicon and molybdenum which is commercially available and commonly used in engine components such as the exhaust manifolds [10]. The chemical composition measured using optical emission spec-troscopy of each grade is found in Table 1. Light optical microscopic images, described in Section 2.3, of the microstructure for all five grades can be seen in Fig. 1. Due to the well-controlled cooling conditions in the casting of plates and staircases, the amount of porosities was negligibly small in the lamellar and compacted grades, as verified by light optical microscopy including the CGI350 specimen taken from cast cylinder heads. However, despite the well-regulated cooling, SiMo51 manifested finely dispersed microshrinkage porosity, an average size with standard deviation of 27.5±22.9 μm and density of 2.1 pores per mm2, measured over one specimen cross section, 31.1 mm2.

Static data was obtained in accordance to the ISO standard 6892- 1:2009 [40] and is presented in Table 2. The elastic modulus was ob-tained with a linear regression between approximately 10 and 40% of an estimated proof strength. Due to the non-linear behaviour of lamellar graphite iron, the elastic modulus is difficult to determine and the offset proof strength, Rp0.2, is consequently not measured and therefore not included for pearlitic LGI290. Brinell hardness data are also presented in Table 2.

2.2. Thermo-mechanical fatigue

2.2.1. Test set-up and test procedure To simulate the start-operate-stop cycle, an idealised and simplified

combination of thermal and mechanical loads in a repeating cycle was tested on uniaxial specimens. This is a standardised test called thermo- mechanical fatigue (TMF) and was conducted according to the ISO standard 12111:2011 [41] using an Instron 8801 servo hydraulic test machine, see Fig. 2a. Induction heating and convection cooling through compressed air was used to control the temperature which was measured with a thermocouple spot welded perpendicular to the loading direction in the middle of the gauge length of the specimen. Thermal profiling was performed before each test series with thermocouples placed evenly over extensometer gauge length of the specimen, three on each side, to confirm that the temperature gradient was within ±10 ◦C from the expected value at any time during the cycle in accordance with the ISO standard. The temperature was ramped up and down between 100 ◦C and 500 ◦C for 200 s respectively with a dwell time of 25 s be-tween each turning point, as seen in Fig. 2b, giving a total cycle time of 450 s. The temperature cycle is a highly accelerated test selected to simulate component testing regularly performed on cylinder heads, which is also the reason for having dwell times at both maximum and minimum temperature. At the beginning of each test, temperature sta-bilisation was performed by running the temperature cycle ten times without mechanical load followed by another two temperature cycles to measure the thermal strain. An Instron extensometer with a gauge length of 12.5 mm measured the total strain, ε, which can be decom-posed as

ε = εth + εmech (1)

where εth is the thermal strain measured under zero load conditions and εmech is the selected mechanical strain to be applied. The mechanical strain was controlled in the Instron TMF software in such way that it was

Table 1 Measured chemical composition in weight percent of pearlitic LGI290, ferritic CGI400 silicon solid-solution-strengthened, ferritic/pearlitic CGI350, pearlitic CGI400 [10] and ferritic SiMo51 [10], the iron content is balanced.

C Si Mn P S Cr Mo Cu Sn

LGI290 P 3.09 1.8 0.56 0.03 0.08 0.12 0.21 0.89 0.047 CGI400 F 3.21 4.12 0.14 0.033 0.012 0.010 - - 0.007 CGI350 F/P 3.59 1.82 0.4 0.027 0.007 0.04 - 0.89 0.012 CGI400 P 3.38 1.9 0.37 0.019 0.01 0.025 - 0.97 0.09 SiMo51 F 3.16 4.33 0.41 0.014 0.008 - 0.91 0.073 <0.010

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ramped up and down between the minimum and maximum mechanical strain in an cycle out-of-phase to the temperature cycle, i.e. a 180◦ shift between the temperature and mechanical strain cycles, see Fig. 2b.

Various mechanical strain ranges were used where the maximum mechanical strain for each cycle was set to 0% at the minimum

temperature for all five materials. Cylindrical test specimens were used with geometries set to 7 mm diameter, 14 mm transition radius, 16 mm parallel length, 144 mm total length and smooth 10 mm diameter in the ends for hydraulic grips, see Fig. 2c, all allowed by the ISO standard.

Fig. 1. Microstructure of the five cast iron grades. Images to the left are unetched where the graphite inclusions are black and the matrix is light grey, and images to the right are etched where the pearlitic matrix appear as shifting dark grey intensities while the ferritic matrix remain light grey.

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2.2.2. Data analysis To determine the number of cycles to failure, Nf , a tangent to the

range of zero curvature was drawn in the stress range versus number of cycles plot with a 2% drop in stress range as the failure criterion. Maximum stress at half-life, σmax, and mechanical strain range, Δεmech, were each plotted versus number of cycles to failure in log–log scale. Relating the lifetime to the mechanical strain range is a common pro-cedure as suggested by the TMF standard [41], whereas the selection of maximum stress at half-life is based on the expected relation between stress and the rate of microcrack propagation, as motivated in the introduction and elsewhere [10,11,16,17,37]. A straight line was fitted to the data points of each material by using the least-square method [42]. The fitted line can be described with Eq. (2) in logarithmic scale and with Eq. (3) in linear scale:

log(y) = n⋅log(Nf )+ log(C) (2)

y = CNnf (3)

where y is either σmax or Δεmech, Nf is the number of cycles to failure, C is introduced as the TMF coefficient and n as the TMF exponent. The same

procedure was done for the mechanical strain range versus number of cycles to failure. It should be emphasised that the aim of the fitting procedure is not to make predictions, but rather to characterise the TMF behaviour of the materials in term of a few representative parameters in order to be able to relate them to microstructural parameters, see the next section. Thus, even though the data range in lifetime spans less than two orders of magnitudes, the fitted TMF coefficient and exponent are expected to characterise the TMF behaviour well within the studied interval.

To evaluate possible uncertainties of each fitted curve, an error measure was defined as the range between the lowest and highest possible value for C and n respectively when removing one data point at the time from the calculation. It is argued that if an additional experi-mental data point is added, the values of C and n would most likely stay within its error range.

2.3. Microstructural characterisation

Microstructural characterisation and graphite analysis were per-formed with a Leica DM6 M light optical microscope (LOM) for all five grades, more precisely in the same LOM with the same settings and no under- or over exposure.

Graphite image analysis, i.e. a method to analyse the two- dimensional features of graphite inclusions, was run according to the standards ISO 945-2:2012 and ISO 16112:2017 with metallographic surface area of approximately 18 mm2 per measurement using a Leica Las X software [43,44]. Measurement errors and uncertainties of image analysis results have been observed by Trejo-Navas et al. in a study of image segmentation methods [45]. To minimise the measurement er-rors, a newly developed method where a histogram representing the

Table 2 Static and hardness data of pearlitic LGI290, ferritic CGI400, ferritic/pearlitic CGI350, pearlitic CGI400 [10] and ferritic SiMo51 [10].

E [GPa] Rp0.2 [MPa] Rm [MPa] A [%] HB [MPa]

LGI290 P - - 292 0.38 220 CGI400 F 148 381 428 4.20 193 CGI350 F/P 162 289 361 2.30 176 CGI400 P 154 341 476 2.50 234 SiMo51 F 168 494 587 5.26 233

Fig. 2. Illustration of the (a) Instron 8801 servo hydraulic test machine used for TMF testing, (b) the temperature and mechanical strain in an out-of-phase TMF cycle and (c) the TMF specimen geometry.

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distribution of pixel intensity, i.e. the magnitude on a greyscale, was used to choose the threshold value, in other words the limit for which the darker pixels are considered as graphite. The threshold, X, was chosen in the middle of the two intensity peaks representing the graphite, G, and matrix, M, as seen in Fig. 3 and described by Eq. (4):

X = 0.5⋅(M − G)+G (4)

The parameters obtained from the graphite analysis was area, A, and length, a, i.e. the longest distance between two points on the graphite circumference also known as maximum feret, for each graphite inclu-sion. Additionally, the aspect ratio, a

c, was calculated as the length-to- width ratio were the width c was derived from the area and length by representing each graphite inclusion as an ellipse having the same area and major axis equal to the graphite length, see Fig. 4. An area-weighted average, x, was calculated for the graphite length and aspect ratio ac-cording to Eq. (5):

x =

∑k

i=1Ai⋅xi

∑k

i=1Ai

(5)

where Ai is the area for graphite inclusion i and xi is the parameter for graphite inclusion i. To estimate the uncertainty of each area-weighted average parameter, a standard deviation was calculated between the area-weighted average values of four measurements.

At this point, it must be emphazised that interpretating the graphite inclusions as ellipsoids when considering the three-dimensional struc-ture is incorrect. Rather, using focused ion beam nanotomography, it has been established that the graphite structure in lamellar and compacted graphite iron grades manifest much higher interconnnectiviety than what is indicated by looking at two-dimensional cross sections [46]. However, assessing shape parameters based on cross sections is a stan-dard procedure and the parameters are still considered to be a repre-sentative measures of the graphite morphology. As mentioned earlier, the elastic modulus of cast iron have been well correlated with the ellipsoidal aspect ratio assessed from metallographic cross sections [26–28].

The matrix microhardness was measured with HV 0.05 indents, which did not touch visible graphite inclusions, along four straight lines with a minimum of 40 indents per line. An average matrix microhard-ness was calculated for the indents in all four lines and an error was estimated by calculating the standard deviation for the average values of each line of indents respectively.

Ferrite content was determined by etching the microscopic sample in Nital 2% for approximately 20 s to enhance the pearlitic structure in the matrix. It then followed by analysis in LOM similarly to the graphite analysis but with a threshold value chosen manually so that the bright ferritic matrix was covered visually in the software.

3. Results and discussion

3.1. TMF performance

The maximum stress and stress range for TMF specimens of ferritic CGI400 is displayed in Fig. 5a showing increasing stress with increasing mechanical strain range, and the same trend was observed for the other four grades. Thus, higher mechanical strain range causes higher stresses in the TMF specimen. Furthermore, the stress is also correlated to the number of cycles to failure, i.e. high stress correlate to shorter TMF life. Fig. 5c compares the hysteresis loop of each material at half-life for the mechanical strain range 0.55% for pearlitic LGI290, ferritic CGI400 and ferritic/pearlitic CGI350 and the mechanical strain range 0.58% for pearlitic CGI400 and ferritic SiMo51 [10].

In Fig. 5b, the maximum stress is plotted for all materials at the mechanical strain range 0.55% for pearlitic LGI290, ferritic CGI400 and ferritic/pearlitic CGI350 and the mechanical strain range 0.58% for pearlitic CGI400 and ferritic SiMo51 [10]. The spheroidal graphite iron, ferritic SiMo51, had the highest maximum stress while the lamellar graphite iron, pearlitic LGI290, had the lowest maximum stress.

The logarithmic trend for the number of cycles to failure as a function of maximum stress at half the fatigue life can be seen in Fig. 6a for all five grades. All five fitted lines have similar slope but different intersection of the stress-axis, i.e. relatively similar TMF exponent, n, but different TMF coefficient, C. The number of cycles to failure are also plotted as a function of mechanical strain range in Fig. 6b which show more varia-tions for both the exponent and coefficient in the logarithmic trends.

Since there are less variations in the TMF exponents between the five grades in Fig. 6a than in Fig. 6b, it allows easier comparison of their coefficients. However, it must be remembered that the maximum stress at half-life is a representative measure of the stress level and that the cyclic maximum stress is generally not constant when the mechanical strain cycle is prescribed, see Fig. 5b. As previously argued, the crack growth rate can be strongly related to fracture mechanics parameters, which are known to depend on the globally applied stress [20–22,24]. Therefore, it is motivated to compare the TMF performance of materials based on maximum stress at half-life rather than mechanical strain range, since the stress is expected to have a more explicit influence on the microcrack growth rate.

3.2. Microstructural parameters

Graphite morphology and matrix parameters for the five cast iron grades investigated in this paper are displayed in Tables 3 and 4. The high amount of pearlite, seen in pearlitic LGI290 and pearlitic CGI400, appears to correlate with higher matrix microhardness. But due to shifting contrast between different pearlitic grains in the etched sam-ples, as seen in the etched images of pearlitic LGI290, ferritic/pearlitic CGI350 and pearlitic CGI400 in Fig. 1, the uncertainty is higher for the ferrite-pearlite ratio than the other parameters. Thus, any correlation to the ferrite-pearlite ratio is hard to find. Moreover, it is interesting to note that both CGI400 F and SiMo51 F have a ferritic matrix, their micro-hardness value differ in contrast to the purely pearlitic grades. This is expected to be due to the comparatively high molybdenum content in SiMo51, which is known to enhance strength, hardness and toughness in cast iron and steel [47].

Large graphite inclusions are expected to have a stronger influence Fig. 3. Schematic illustration of the histogram showing the intensity peaks for graphite, G, and matrix, M, and the calculated threshold value, X.

Fig. 4. A simplified graphite inclusion with its area, A, length, a, and width, c.

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on the macroscopic properties than small inclusions. Parameters repre-senting the graphite morphology are hence area-weighted so that large graphite inclusions have stronger influence on the average value than small inclusions. Accordingly, the area-weighted average graphite length, a, and area-weighted average aspect ratio, ac, represent the shape of an average graphite inclusion for each grade. It can be seen that grades with longer graphite also have higher aspect ratio, as well as shorter graphite have lower aspect ratio, which correspond well to the classification of each grade, i.e. lamellar, compacted or spheroidal

graphite.

3.3. Comparison of microstructural parameters and TMF properties

A correlation between microstructural parameters and TMF proper-ties as a function of maximum stress at half-life, i.e. TMF coefficient, C, and TMF exponent, n, both defined in Section 2.2, is found. However, there are no correlation for the microstructural parameters when comparing with TMF properties as a function of mechanical strain range.

Fig. 5. (a) Maximum stress and stress range versus number of cycles for ferritic CGI400, (b) Maximum stress versus number of cycles, and (c) Hysteresis loop at half- life for each material with the mechanical strain range 0.55%. Note that data for pearlitic CGI400 and ferritic SiMo51 is from Norman et al. [10] and their mechanical strain range in (b) and (c) is 0.58%.

Fig. 6. TMF results with 100–500 ◦C thermal cycle fitted with least square method. Maximum stress at half-life in (a) and mechanical strain range in (b) versus number of cycles to failure. Note that data for pearlitic CGI400 and ferritic SiMo51 is taken from Norman et al. [10].

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The comparisons are thus only presented between the TMF properties as a function of maximum stress at half-life and microstructure. As mentioned earlier, it is legitimate to focus on stress since crack growth rate is more correlated to stress rather than strain in a fracture me-chanics perspective.

3.3.1. Influence of graphite morphology on TMF performance A linear correlation between the area-weighted average graphite

length, a, and the TMF coefficient, C which is defined in Section 2.2, is shown in Fig. 7a. In view of the TMF exponent being fairly constant for the investigated materials, see Figs. 6a and 7b, the TMF performance in the studied range is strongly related to the TMF coefficient since a higher coefficient implies longer TMF lives for a given maximum stress. Thus, the experimental observations of the damage mechanisms in lamellar and compacted graphite iron when subjected to TMF load conditions [10,11,17] together with the trend seen in Fig. 7a support the

proposition that graphite influences TMF properties and that the graphite inclusions can be seen as fatigue crack initiation sites. How-ever, it must be emphasised that the microcrack initiation mechanism is different in the investigated SiMo51 compared to the lamellar and compacted graphite iron grades under TMF load conditions with 100–500 ◦C [10]. Under these conditions, microcracks were preferably initiated in microshrinkage porosities rather than graphite nodules, which must be kept in mind when comparing the materials in terms of graphite morphology. On the other hand, the average maximum diam-eter of microshrickage pores having initiated microcracks at half the fatigue life in this particular SiMo51 casting was measured by Norman et al. [10] to 63.0 μm, which is larger but still in the vicinity of the average graphite inclusion length, see Table 3. Furthermore, for a different kind of spheroidal graphite iron investigated by Hammers et al. [48], namely a EN-GJS-700 with significantly better TMF performance for similar TMF conditions, microcracks were only reported to be initi-ated at graphite nodules, presumably due to a lesser extent of casting defects. Thus, it seems as if a shorter graphite inclusion length is bene-ficial, but only up to a point where other sources of microcrack initia-tion, i.e. other defects, take over.

When comparing the area-weighted average aspect ratio, ac, and the TMF coefficient, C as defined in Section 2.2, a logarithmic correlation is observed in Fig. 8a. Since the aspect ratio describes the proportional relationship between length and width of graphite inclusions the graphite length will have an indirect influence in this comparison. But the width of the graphite inclusion should influence the stress concen-tration around it, i.e. a thinner graphite should cause higher stress concentration and hence increase the risk for crack propagation. Higher stress is thus needed for cracks to initiate at wider graphite inclusions, i. e. low aspect ratio, resulting in a higher measured stress at a given number of cycles to failure. The TMF coefficient is accordingly higher for the grades with lower aspect ratio, Fig. 8a.

By intuition, a higher graphite content is expected to result in worse TMF performance as more graphite inclusions implies more crack initiation sites. However, comparing the material with respect to graphite content, see Fig. 9a, it is seen that cast iron grades with high TMF coefficient contradictorily have more graphite phase. It is though much unlikely that a high graphite content would promote a high TMF coefficient, in view of the observed connection between graphite and fatigue damage in lamellar and compacted graphite iron [10,11,17]. Rather, the most likely explanation is that the graphite morphology, i.e. length and aspect ratio, have a dominant influence over the variation in graphite content between the studied materials.

In contrast to the TMF coefficient, there are no distinct trends when plotting the TMF exponent n against the average graphite length, aspect ratio or graphite content, see Figs. 7b, 8b and 8b. Evidently, the un-certainty in the exponent of each cast iron grade is high compared to the difference in the exponent between grades. Looking back at Fig. 6a, this

Table 3 Graphite morphology of pearlitic LGI290, ferritic CGI400, ferritic/pearlitic CGI350, pearlitic CGI400 and ferritic SiMo51. cG is the area fraction of graphite, ac

is the area-weighted aspect ratio, and a is the area-weighted graphite length.

The error for ac

and a represents the standard deviation between the area-

weighted average values of four measurements.

cG [%] ac

[-] a [μm]

LGI290 P 8.96 13.88 ± 0.85 119.6 ± 1.9 CGI400 F 12.11 4.83 ± 0.32 78.7 ± 4.6 CGI350 F/P 11.37 4.12 ± 0.13 82.3 ± 3.8 CGI400 P 10.09 4.94 ± 0.29 84.0 ± 5.7 SiMo51 F 12.04 1.85 ± 0.16 48.1 ± 1.4

Table 4 Matrix parameters of pearlitic LGI290, ferritic CGI400, ferritic/pearlitic CGI350, pearlitic CGI400 and ferritic SiMo51. cF is the matrix area fraction of ferrite, cP is the matrix area fraction of pearlite, and HV 0.05 is the average matrix micro-hardness of four lines with the minimum of 40 indents each with an estimated error as the standard deviation of the average values for each line of indents respectively.

cF [%] cP [%] HV 0.05

LGI290 P 0 100 291 ± 0.9 CGI400 F 100 0 234 ± 4.5 CGI350 F/P 25 75 252 ± 3.0 CGI400 P 0 100 283 ± 5.8 SiMo51 F 100 0 264 ± 1.3

Fig. 7. The area-weighted average graphite length, a, versus (a) the TMF coefficient, C, fitted with least-square method and (b) the TMF exponent, n. The vertical error bars represent the range of values obtained for C or n when removing one data point at the time and the horizontal error bars represent standard deviation for a of four analyses. Note that the TMF data, from which the TMF coefficient and exponent are calcu-lated, for pearlitic CGI400 and ferritic SiMo51 is taken from Norman et al. [10].

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is related to the fitted lines being fairly parallel, except for CGI400 P which has a significantly less steep slope. Consequently, despite SiMo51 F and LGI290 having a difference more than a factor of two in the graphite length and aspect ratio, the TMF exponent is almost unaffected. Thus, in view of this observation and the apparent absence of a clear trend, a strong connection between the graphite morphology and the TMF exponent is not considered likely.

3.3.2. Influence of matrix microhardness on TMF performance The matrix microhardness in cast iron can be expected to play a

significant role for crack initiation just as it does for steels [49,50]. But opposed to this argument, a comparison of ferritic/pearlitic CGI350 and pearlitic CGI400, which have negligible difference in area-weighted average graphite length, a, and TMF coefficient, C, observed in Fig. 7a, shows no different in matrix microhardness, see Fig. 10a. Thus,

Fig. 8. The area-weighted average aspect ratio, ac, versus (a) TMF coefficient, C, fitted with least-square method and (b) TMF exponent, n. The error bars represent the range of values obtained for C or n when removing one data point at the time vertically and the standard deviation of ac for four graphite analysis. Note that the TMF data, from which the TMF coefficient and exponent are calculated, for pearlitic CGI400 and ferritic SiMo51 is taken from Norman et al. [10].

Fig. 9. The area fraction of graphite, cG, versus (a) the TMF coefficient, C, fitted with least-square method and (b) the TMF exponent, n. The vertical error bars represent the range of values obtained for C or n when removing one data point at the time. Note that the TMF data, from which the TMF coefficient and exponent are calculated, for pearlitic CGI400 and ferritic SiMo51 is taken from Norman et al. [10].

Fig. 10. The matrix microhardness versus (a) the TMF coefficient, C, and (b) the TMF exponent, n. The vertical error bars repre-sent the range of values obtained for C or n when removing one data point at the time and the horizontal error bars represent the standard deviation of the mean values of four measurements with minimum 40 in-dents each. Note that the TMF data, from which the TMF coefficient and exponent are calculated, for pearlitic CGI400 and ferritic SiMo51 is taken from Norman et al. [10].

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the matrix microhardness seems to have an insignificant influence on the TMF properties. On the other hand, the TMF exponent, n, of pearlitic CGI400 is slightly different from the other grades, including ferritic/ pearlitic CGI350. It might be possible to find the influence of matrix microhardness on TMF performance in the TMF exponent. More studies are thus needed to understand how other microstructural parameters, such as matrix microhardness, may affect the TMF performance.

Furthermore, the ferrite-pearlite ratio might also have an influence on the TMF properties in combination with the graphite shape. This was however not seen in this paper, more studies is thus needed to under-stand how other microstructural parameters may affect the TMF performance.

4. Conclusions

This paper aims to correlate TMF performance with microstructure parameters, such as graphite length and matrix microhardness, by comparing TMF results with microstructural investigations for five cast iron grades including lamellar, compacted and spheroidal graphite iron. The following conclusions are drawn:

• Correlations between microstructural parameters and TMF proper-ties as a function of maximum stress at half-life are found. In particular, the graphite morphology was found to have a strong in-fluence on the TMF performance, especially the area-weighted average graphite length, a, which had a linear correlation with the TMF coefficient, C. Thus, shorter graphite inclusion increases the maximum stress at half-life without decreasing the number of cycles to failure.

• The TMF properties as a function of mechanical strain range showed no correlation with any of the microstructural parameters.

• An influence on TMF performance from the cast iron matrix, i.e. microhardness and ferrite-pearlite ratio, could not be confirmed.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This study was financed by Scania, Volvo and the Swedish agency for Innovation Systems (FFI-2017-05491). Special thanks to Patrik Harnman for his support on the TMF-machine, Rodger Romero Ramirez for his guidance with the metallographic investigations and the project group members at Scania and Volvo for their inputs and feedback.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijfatigue.2020.106112.

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