Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron

Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron

Engineering Fracture Mechanics xxx (2016) xxx–xxx Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.els...

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Engineering Fracture Mechanics xxx (2016) xxx–xxx

Contents lists available at ScienceDirect

Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech

Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron Francesco Iacoviello ⇑, Vittorio Di Cocco Università di Cassino e del Lazio Meridionale, DiCeM, via G. Di Biasio 43, 03043 Cassino, FR, Italy

a r t i c l e

i n f o

Article history: Received 7 January 2016 Received in revised form 15 February 2016 Accepted 14 March 2016 Available online xxxx Keywords: Ferritic ductile cast irons Fatigue crack propagation Degenerated graphite elements

a b s t r a c t Ductile cast irons (DCIs) are commonly considered as really interesting materials, due to their interesting combination of mechanical properties and technological peculiarities. Characterized by the high castability that is a cast irons technological peculiarity, DCIs are characterized by a very interesting combination of good mechanical properties (e.g., tensile strength and fatigue resistance). These properties are strongly influenced by the DCIs microstructure, that is defined both by the matrix (considering the morphological peculiarities like phases distribution, grain dimension, etc.) and by the graphite nodules elements, that are characterized by shape, dimension and distribution. In addition, the presence of defects (like pores, both micro and macro) can strongly affect the DCIs mechanical behaviour (e.g., considering large castings). In this work, a ferritic DCI with degenerated nodules was obtained and the fatigue crack propagation resistance was investigated by means of fatigue crack propagation tests and compared with the behaviour of a commercial ferritic DCIs. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Due to the interesting combination of mechanical and technological properties, ductile cast irons (DCIs) are widely used for different applications. Heavy section wind turbine components, railway brake discs, crankshaft, wheels, gears, pumps, valves, pipes are only a few examples of DCIs industrial applications [1–3]. Although the DCIs were discovered in 1948 with the aim to obtain a sort of ‘‘malleable iron” avoiding the necessary long (and expensive) heat treatments that characterize the malleable grades, in the last decades different chemical compositions and heat treatments have been optimized in order to obtain different matrix microstructures and to control the graphite nodules morphological peculiarities. The highest performances are obtained by means of a ‘‘austempering” heat treatment which involves the nucleation and growth of acicular ferrite within austenite, where carbon is rejected into the austenite. The resulting microstructure of acicular ferrite in carbon-enriched austenite is called ‘‘ausferrite” and it allows to obtain yield strength, toughness and impact resistance values that are comparable to many cast/forged steels, vibration dampening and heat transfer superior to other ferrous/non-ferrous alloys and an increased fracture and fatigue strength. On the other hand, the risk to obtain a degeneration of the graphite nodules shape during the heat treatment, with the consequent influence on the mechanical properties, is not negligible. In addition, many other defects can be observed in DCIs. Here follows a non standardized list [4] and some examples focused on graphite elements are shown in Figs. 1–5: ⇑ Corresponding author. E-mail addresses: [email protected] (F. Iacoviello), [email protected] (V.D. Cocco). http://dx.doi.org/10.1016/j.engfracmech.2016.03.041 0013-7944/Ó 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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Nomenclature DCI COD DK Pmax Pmin R

ductile cast irons crack opening displacement stress intensity factor variation maximum load minimum load load ratio

– Carbides, due to different causes, with a key role played by the presence of carbide promoting elements such as Mn, Cr, V, Mo, and by a rapid cooling rate, Fig. 1. – Chunky graphite, due to an excess of rare earth additions, Fig. 2. – Compacted graphite, mainly due to low residual magnesium and/or rare earth (high temperatures or long holding time), Fig. 3. – Exploded graphite, mainly due to an excess of rare earth additions, Figs. 2 and 4. – Gas holes, that can be due to many causes (e.g., melting procedures). – Graphite flotation, which potential causes can be high carbon equivalent, excess of pouring temperature, slow cooling rate in thicker sections or an insufficient inoculation. – Irregular graphite, due to high holding and/or long holding temperature or to a poor inoculation.

Fig. 1. Carbides in DCIs (500).

Fig. 2. Chunky and exploded graphite (100).

Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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Fig. 3. Compacted and flake graphite (100).

Fig. 4. Exploded graphite (1000).

Fig. 5. Ferritic DCI. Scanning Electron Microscope observation of the specimen lateral surface during a tensile test: ‘‘onion-like” mechanism.

Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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– – – – –

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Nodule alignment, due to the presence of large dendrites, with nodules aligned between arms of dendrite. Shrinkage, due to inadequate feed of available metal, excess of magnesium, under or over inoculation. Slag inclusions, that can be due to different causes (e.g., inadequate slag control from pouring system). Spiky graphite, due to very small amounts of lead which have not been neutralized by rare earth. Surface structure, due to a sulphur excess in molding sand.

All these defects can influence the DCIs mechanical properties, considering both static, quasi static, cyclic and dynamic loading conditions, but the importance of their contribution to the decrease of DCIs mechanical properties still needs to be deeper investigated [5–8]. Considering the ferritic DCIs, maybe the DCIs grades with the ‘‘simplest” microstructure (graphite elements embedded in a ductile matrix), different damaging micromechanisms have been identified depending on the loading conditions. Considering an increasing uniform stress state (tensile test), some authors identified the ferritic matrix–graphite nodules as the main damaging micromechanisms [9–11]. Some of these authors [9,10] suggested that the graphite nodules could be considered as analogous to micropores embedded in a ductile matrix; other authors [11] proposed that the graphite nodules should play a more complex role, due to the graphite mechanical properties and to the local stress state. Recently [12–14], on the basis of nanoindentation tests results and wearing behaviour analysis, considering that the more frequently observed damaging mechanisms corresponding to graphite nodules was not the graphite but was a sort of internal debonding (so called, ‘‘onion-like” mechanism, Fig. 5) and identifying the interface where this internal debonding mechanism nucleates and propagates with the transition in the graphite nodules growth mechanism (the core is obtained directly from the melt and the shield is the result of carbon solid diffusion, respectively), a more complex role in the damaging micromechanisms in DCIs played by the graphite nodules was proposed, being the graphite nodules–matrix only one of the observed damaging mechanism (in addition, not the most frequent one). Considering notched specimens and performing tensile tests, ‘‘onion-like” is still really important, and fracture surface Scanning Electron Microscope (SEM) observations confirmed the influence of triaxiality on nodules damaging micromechanisms, with notched specimens that are characterized by larger voids around the graphite nodules (if compared to smooth specimens) [15]. Fatigue crack propagation in ferritic DCIs is characterized by the presence of ductile striations and by an evident cleavage on the fracture surface (not depending on R, stress ratio, and applied DK values), [16]. Graphite nodules–matrix debonding is observed both for lower and for higher R and DK values: this debonding does not imply automatically a complete nodules removal from the fracture surfaces. Also nodules with less than half of their surface in contact with the ferritic matrix do not lose their grip to the fracture surface, although the debonding process implies a plastic deformation around the graphite nodule [17]. For lower R and DK values, it is worth to note that DCIs cannot be considered as homogeneous materials, being characterized by graphite nodules diameters that are comparable with the main fracture mechanics geometrical parameters (e.g., the reversed plastic zone [18]). The consequent stress redistribution ahead the crack tip (near the graphite nodules) decreases the stress intensity factor usefulness as a fracture mechanics parameter and it can be used only considering an ‘‘homogenized” microstructure that is able to take into account both the graphite nodules and the ferritic matrix. Finally, the application of overloads on fatigue cracks in ferritic DCIs implies a really reduced stable crack propagation. The increase of the applied overload implies a more and more evident crack tip plastic/damaged zone, with a more and more evident ferritic matrix–graphite nodules debonding and the initiation and growth of secondary cracks [18]. The aim of this work is the characterization of the influence of ‘‘degenerated” graphite nodules on the fatigue crack propagation in a ferritic DCI. A long annealing heat treatment was performed on a pearlitic DCI in order to activate the carbon atom solid diffusion process and increase the thickness of the outer graphite shield, obtaining a decrease of the graphite elements nodularity. Both fatigue crack propagation and overload conditions were investigated.

2. Investigated material and experimental procedure In order to obtain a fully ferritic DCIs with degenerated graphite nodules, an annealing heat treatment was performed on a fully pearlitic DCI with a good nodularization (Table 1 shows the chemical composition) according to the following procedure: – 170 h at 850 °C. – Cooling in furnace to lab temperature. Heat treatment was performed under vacuum (in order to avoid surface decarburation) on 10 mm thick Compact Type (CT) specimens. As a result of this heat treatment, a ferritic matrix with degenerated graphite nodules embedded was Table 1 Investigated pearlitic DCI chemical composition (5%F + 95%P, before heat treatment). C

Si

Mn

S

P

Cu

Mo

Ni

Cr

Mg

Sn

3.59

2.65

0.19

0.012

0.028

0.04

0.004

0.029

0.061

0.060

0.098

Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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Fig. 6. Ferritized DCI and ‘‘degenerated” graphite nodules.

obtained (Fig. 6). Nodules were characterized by a surface with a higher roughness (‘‘degenerated nodules”), if compared to the nodules embedded in the DCI before the heat treatment: the long term annealing activated a carbon solid diffusion process, with a consequent increase of the nodules diameters and an evident modification of their shape: the outer shield obtained during the long annealing treatment is characterized by an increased roughness and by the presence of some small embedded metal matrix particles. Fig. 6 is obtained with a Light Optical Microscope after a metallographic preparation: focusing on the graphite nodule in the center of the image, differences between the graphite nodule before the heat treatment, and the shield obtained during the annealing treatment are quite evident. Five ferritized CT specimens were submitted to a metallographic preparation procedure and, after, fatigue crack propagation tests were performed according to ASTM E647 standard [19], with a stress ratio of R = Pmin/Pmax = 0.1. Tests were performed using a computer controlled servohydraulic machine in constant load controlled conditions, considering a 20 Hz loading frequency, a sinusoidal loading waveform and laboratory conditions. Crack length measurements were performed by means of a compliance method using a double cantilever mouth gage and controlled using an optical microscope (40). These tests conditions are analogous to those used in former experimental activities. [17,18]. During the fatigue crack propagation tests, SEM crack path observations of the specimens lateral surfaces were performed according to a step by step procedure. Furthermore, fracture surfaces were analyzed by means of a SEM, focusing both the graphite elements and the metal matrix (in all the obtained photos, crack propagates from left to right). Results were compared with the behaviour of a ferritic DCI with ‘‘normal” graphite nodules (commercial DCI [17,18]). Always considering the fracture surfaces, a 3D fracture surface reconstruction procedure was performed. Corresponding to the same specimen position, a stereoscopic image was obtained performing an eucentric tilting around the vertical axis and capturing two different images, with a tilting angle equal to 6° (tilting results in a static center point in the image). 3D surface reconstruction was performed using the Alicona MeX software and profile evolution was analyzed corresponding to graphite nodules. Finally, static overloads were applied according to the following step-by-step procedure: (1) Applied KI increase was obtained by means of a servohydraulic machine under load control conditions. Corresponding p to each overload, COD was measured. Applied KI values were: 10, 20, 30, 40 MPa m, respectively. (2) The load was decreased to zero and the specimen was removed from the grips. Using the ‘‘screw loading machine” in Fig. 7, the specimen was loaded again up to the same COD value obtained in step 1. This ‘‘screw loading machine” allowed to observe the specimen lateral surface by means of a SEM under overloading conditions. 3. Experimental results and comments 3.1. Microstructure modification From the point of view of the graphite nodules morphology, this seems strongly modified to be modified by the long annealing treatment. Considering the results formerly obtained, this morphology can be summarized as follows: – A nodule core obtained directly from the melt during the solidification process (characterized by low nanohardness values and wearing resistance). – A (first) shield obtained during the cooling process by means of carbon solid diffusion through the austenitic shield (characterized by higher nanohardness values and wearing resistance compared to the nodule core).

Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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Fig. 7. Screw loading machine.

Fig. 8. Degenerated graphite nodule in ferritized DCI. Outer shield obtained during the annealing treatment.

– A (second) shield obtained during the annealing heat treatment by means of carbon solid diffusion process and due to the negligible carbon solubility in the ferritic grains that are obtained at high temperature (nanoindentation tests were not performed; anyway, considering the metallographic preparation process, it is possible to suggest that this outer shield is characterized by a lower wearing resistance compared to the first shield). In addition, the interface with the ferritic matrix is characterized by a very high roughness and many matrix microparticles are embedded in the graphite (Fig. 8).

3.2. Fatigue crack propagation Considering ferritic–pearlitic DCIs, corresponding to lower R values, da/dN  DK results are not influenced by the microstructure (Fig. 9) and they are characterized by a good repeatability [17,18]. Although the annealing heat treatment implies a strong microstructural modification (metal matrix changes from fully pearlitic to fully ferritic and graphite nodules modify their shape), the fatigue crack propagation results are still characterized by a good repeatability. As a consequence, only one crack propagation curve da/dN  DK will be considered for comparison with a commercial ferritic DCI (Fig. 10). Differences can be pointed out as follows: – Although threshold tests have not been performed, ferritized DCI with degenerated nodules seems to be characterized by a worse behaviour corresponding to the lower DK values. – In the Paris stage, ferritized DCI with degenerated nodules is characterized by higher ‘‘m” values if compared to the commercial ferritic DCI (but the difference is quite low, Fig. 10). – In the III stage, final rupture is obtained corresponding to lower values of the applied DK. From Fig. 9, it is evident that the degeneration of the graphite nodules implies a decrease of the fatigue crack propagation resistance, although the differences are not so important, especially in the Paris stage. Considering a commercial ferritic DCI [17,18], the presence of a graphite nodules internal damage is evident for lower DK values; matrix–nodules debonding seem to be the main fatigue crack propagation micromechanism for all the conditions Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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Fig. 9. Microstructure influence on fatigue crack propagation in ferritic–pearlitic DCIs (R = 0.1; [16]).

Fig. 10. Fatigue crack propagation in ferritic DCIs (R = 0.1): Influence of the graphite nodules shape.

Fig. 11. Ferritized DCI. Crack path (DK = 12 MPa

p

m).

that allow to obtain a larger reversed plastic zone (e.g., for higher R values) and/or a larger crack tip plastic zone (e.g., during an overload). In ferritized DCIs with degenerated graphite nodules, it is possible to observe that the path tortuosity is analogous to the one observed in a commercial ferritic DCI; fatigue crack mainly propagates through the graphite nodules and it doesn’t find a low energy propagation path corresponding to the matrix–nodules interfaces, for all the investigated fatigue loading conditions (Fig. 11). Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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Fig. 12. Commercial ferritic DCI. SEM fracture surface analysis (DK = 14 MPa

p

m).

Fig. 13. Ferritized DCI with degenerated nodules. SEM fracture surface analysis (DK = 14 MPa

p

m).

In Fig. 12 it is possible to observe the fracture surface due to fatigue propagation in a ferritic commercial DCI [17,18]. Matrix–nodules debonding is already observed in the stage II of III (Paris stage) and around the graphite nodules it is possible to observe cleavage. Some graphite residuals can be observed corresponding to the ‘‘lost” graphite nodules, but they are less evident with the increase of the applied DK. In the ferritized DCI with degenerated nodules, fracture surface is characterized by a peculiar morphology, due to the presence of the ‘‘second” shield obtained during the annealing treatment. Fatigue crack propagates through the second shield (lower mechanical properties), probably following the interfaces graphite–matrix particles embedded in the second shield (Fig. 13). When the fatigue crack meets the first shield (the one with the highest mechanical properties), the lowest energy propagation path is the interface first–second graphite shield. In addition, short secondary cracks are observed inside the second shield. It is worth to note that the cleavage around graphite nodules is less important for all the applied DK values. 3D reconstructed images analysis allows to underline that the fatigue crack propagation inside the second shield implies a deviation from the crack plane of less than 30° (Fig. 14). Crack avoids to propagate inside the graphite nodule: the result on the fracture surface can be a nodule embedded in the ferritic matrix or a void, depending on the crack propagation plane with respect to the nodule position. 3.3. Overloads Ahead the crack tip, increasing overloads in ferritic–pearlitic DCIs imply a more and more evident plastic-damaged zone due to the presence of graphite nodules. In addition: Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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Fig. 14. Ferritized DCI. SEM fracture surface analysis: 3D reconstruction (DK = 14 MPa

Fig. 15. Overload influence on the stable crack propagation (a: KI = 10 MPa

p

p

m).

m; b: KI = 40 MPa

p

m).

– Ferritic matrix [17]: crack stable propagation is negligible and the crack tip blunting is more and more evident with the increase of the applied KI value [20]. – Pearlitic matrix [21]: crack branching and a stable crack propagation are observed; crack path after the overload is more tortuous than the path obtained during the fatigue crack propagation; crack tip blunting seems to be almost negligible. – Ferritic–pearlitic matrix [22]: a reduced crack stable propagation is observed, with secondary cracks that nucleate and propagate ahead the main crack. Crack propagation with the increase of the applied KI seems to be due to the connection of the main crack with the secondary cracks ahead the crack tip rather than to a direct main crack propagation. Focusing the ferritized DCI with degenerated graphite nodules, overloads applied on fatigue crack imply always the presence of a crack tip plastic-damaged zone, with secondary cracks that mainly nucleates corresponding to the graphite element (Fig. 15). The increase of the applied KI values implies a crack propagation with a mechanism that is more similar to commercial ferritic–pearlitic DCI, rather than to a commercial ferritic DCI, with the connection of the main crack with the cracks that nucleates ahead the crack tip. Slip bands generation in the crack tip plastic-damaged zone are always really evident. Fracture surface corresponding to the instable crack propagation confirms the differences in the propagation mechanisms between the commercial ferritic DCI and the ferritized one with degenerated nodules. The first one (Fig. 16) is characterized Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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Fig. 16. Commercial ferritic DCI. SEM fracture surface analysis (instable crack propagation zone).

Fig. 17. Ferritized DCI with degenerated graphite elements. SEM fracture surface analysis (instable crack propagation zone).

by a virtual absence of graphite residuals corresponding to the voids formerly ‘‘filled” by nodules (the graphite nodules–matrix debonding mechanism is fully developed in these loading conditions). The second one (Fig. 17) is characterized by the presence of graphite residuals that correspond to the second graphite shield (the one obtained during the annealing treatment and due to the carbon solid diffusion). 4. Conclusions Ductile cast irons are versatile alloys thanks to the possibility to obtain different combinations of mechanical and technological properties by means of the chemical composition and/or heat treatment control. High temperature heat treatments (e.g. austempering) can imply a modification of the graphite nodules shape due to carbon solid diffusion mechanism. The aim of this work was to investigate the contribution of the degeneration of the graphite nodules shape to the modification of both the fatigue crack propagation resistance and the crack propagation micromechanisms, considering both the fatigue and the static overload loading conditions. Results were compared with the behaviour of commercial ferritic–pearlitic DCIs (mainly ferritic ones). On the basis of the obtained experimental results, the following conclusions can be summarized: – Long duration annealing treatments (170 h at 850 °C) allow to modify the matrix microstructure from fully pearlitic to fully ferritic but it activate the carbon atoms solid diffusion mechanism: the result is the presence of graphite elements with an increased diameter and a modified morphology (‘‘degenerated” nodules). The outer graphite shield obtained during the heat treatment is characterized by a peculiar morphology (higher roughness with embedded small metal matrix particles) and by low mechanical properties (at least, wear resistance).

Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041

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– The presence of ‘‘degenerated” nodules does not seem to affect the repeatability of the fatigue crack propagation results (but further tests are necessary to confirm this point); ‘‘degenerated” nodules decrease the fatigue crack propagation resistance (probably threshold values and lower toughness), but, considering the Paris stage, the differences between the commercial ferritic DCI and the investigated grade with degenerated nodules seem to be quite low; other defects like porosities and shrinkages seem to have a deeper influence on the fatigue crack resistance od DCI components [7]. – The lower mechanical behaviour that characterizes the graphite shield obtained during the heat treatment implies a low fatigue crack propagation resistance; fatigue crack finds a low energy crack path corresponding to the interface between the graphite shield obtained during the heat treatment and the ‘‘original” graphite nodule. – Overloads applied on the fatigue crack implies a plastic-damage zone ahead the crack tip that is more and more evident with the increase of the applied KI; ferritized DCI with degenerated nodules shows both the crack tip blunting (analogously to ferritic DCIs) and a stable crack propagation due to the connection between the main crack and the secondary cracks that nucleate ahead the crack tip (as in ferritic–pearlitic DCIs). Summarizing, in DCI with a ferritic matrix, the presence of degenerated graphite influences the crack propagation micromechanisms (considering both the fatigue crack propagation and the stable crack propagation due to overload), but mechanical properties do not seem to be subjected to an excessive reduction. Acknowledgement Figs. 1–4 are courtesy of Zanardi Fonderie S.p.A. Franco Zanardi is warmly acknowledged for his help. References [1] Shirani M, Härkegård G. Large scale axial fatigue testing of ductile cast iron for heavy section wind turbine components. Engng Fail Anal 2011;18:1496–510. http://dx.doi.org/10.1016/j.engfailanal.2011.05.005. [2] Šamec B, Potrcˇ I, Šraml M. Low cycle fatigue of nodular cast iron used for railway brake discs. Engng Fail Anal 2011;18:1424–34. http://dx.doi.org/ 10.1016/j.engfailanal.2011.04.002. [3] Asi O. Failure analysis of a crankshaft made from ductile cast iron. Engng Fail Anal 2006;13:1260–7. http://dx.doi.org/10.1016/j. engfailanal.2005.11.005. 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Please cite this article in press as: Iacoviello F, Cocco VD. Influence of the graphite elements morphology on the fatigue crack propagation mechanisms in a ferritic ductile cast iron. Engng Fract Mech (2016), http://dx.doi.org/10.1016/j.engfracmech.2016.03.041