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Influence of microstructure on the thermo-mechanical fatigue behavior and life of vermicular graphite cast irons
Materials Science & Engineering A 771 (2020) 138617
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Materials Science & Engineering A journal homepage: http://www.elsevier.com/locate/msea
Influence of microstructure on the thermo-mechanical fatigue behavior and life of vermicular graphite cast irons M.X. Zhang, J.C. Pang *, Y. Qiu, S.X. Li, M. Wang, Z.F. Zhang ** Materials Fatigue and Fracture Laboratory, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang, 110016, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Thermo-mechanical fatigue Vermicular graphite cast iron Microstructures Life prediction Fracture mechanism
Cylinder head is subjected to the combination changes of temperature and mechanical loads in service. In such harsh condition, thermo-mechanical fatigue (TMF) failure is a main problem. In this study, two kinds of vermicular graphite cast irons were selected to reveal the TMF properties and life prediction. Vermicular graphite casts with different microstructures have different ferrite cluster morphologies, which result in different fracture mechanisms. The hysteresis loops of both materials display obvious asymmetry. Hysteresis energy and me chanical strain amplitude were selected as damage parameters to determine the fatigue life. It is found that the TMF performance of vermicular graphite cast iron with higher pearlite content is better; meanwhile, the life of TMF at different constraint ratios was also studied. Hysteretic energy related to constrain ratio is in a parabolic form, and the life of TMF decreases with the absolute value of constraint ratio increasing. Finally, the quanti tative relationship between constraint ratio and TMF life was also discussed.
1. Introduction Vermicular graphite cast iron is a widely used structural material because of its excellent mechanical properties and thermal conductivity [1–3]. One of the typical applications is the engine cylinder head [4]. Its service conditions usually include simultaneous changes of temperature and load, so thermo-mechanical fatigue (TMF) is a common failure mode [5]. These changes will lead to severe fatigue damage than the conventional fatigue; it may cause economic losses and even heavy ca sualties. Therefore, selecting the cast iron as a model material to study the thermal mechanical fatigue performance is definitely necessary, and the life prediction is indispensable [6–8]. Not only the temperature and load changes,but also there are some other complex factors such as phase condition and constraint ratio. So, the complexity of TMF operating conditions determines that TMF research needs a lot of time and money. Zieher et al. [9] proposed a life simulation process. Based on the continuous damage mechanics method, they discussed different life prediction models and gave suggestions for design improvement. Neu and Sehitoglu [10,11] considered that for TMF there are three main aspects: fatigue, creep damage and environ mental oxidation. Those factors, such as maximum (or minimum) tem perature, mechanical strain amplitude, phase angle between
temperature and mechanical strain, service time and environment, can act independently or be combined with service conditions and material types. The TMF behaviors must be very complicated due to so many influencing factors involved. Although intensive studies have been conducted, the dependence between microstructure and TMF life has not been well understood. Skoglund et al. [12] chose gray cast iron for TMF test, they found that if the solidification time is longer, the prop erties may be completely controlled by large graphite sheets, and the alloying elements do not affect the properties much. On the contrary, different alloying elements, such as molybdenum can improve the life of TMF. Recently, Neu-Sehitoglu TMF model was widely and successfully used to evaluate TMF damage [13–15], however, the ferrite cast iron cannot fully meet the requirements of this model due to intergranular embrittlement at 400 � C, low ductility at low temperature and phase transformation at high temperature. By the way, too many parameters to be determined by pre-TMF test are time and money consuming; there fore, it is necessary to explore the concise method for TMF evaluation in the materials improvement process. In a previous work [16], the rela tionship between low-cycle fatigue and TMF has been established, and the effect of temperature on TMF has also been analyzed. To some extent, these studies can explain some TMF behaviors [17–20]; however for vermicular graphite cast iron, the relationship between matrix
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (J.C. Pang), [email protected] (Z.F. Zhang). https://doi.org/10.1016/j.msea.2019.138617 Received 3 July 2019; Received in revised form 17 September 2019; Accepted 30 October 2019 Available online 7 November 2019 0921-5093/© 2019 Elsevier B.V. All rights reserved.
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microstructure and TMF is still not clear, and the related fracture mechanisms are not clear either. For simplicity, two vermicular graphite cast irons (cast with high area fraction of pearlite (high pearlite iron) and cast with high area fraction of ferrite (high ferriet cast)) with approximate equal vermicular rate but different microstructures were employed in this study. The relationship between the TMF life and constraint ratio was also studied. Finally, the influencing factors and fracture mechanisms of TMF life for the vermicular graphite casts were analyzed.
3. Experimental results 3.1. Microstructure As shown in Fig. 2, both high ferrite iron and high pearlite iron vermicular graphite casts consist of ferrite, pearlite and vermicular graphite, in which the gray zone is equiaxed ferrite, the white zone is laminar pearlite and the graphite is black. But their proportions in the two vermicular graphite casts are different. For high ferrite iron, the area fractions are 69.6%, 19.6% and 10.7%, respectively. The corre sponding values in high pearlite iron are 36.1%, 55.8% and 8.1%. The mean grain sizes of ferrite were measured by intercept method to be about 9.6 μm and 12.6 μm for high ferrite iron and high pearlite iron, respectively. For high ferrite iron, the ferrite zone can be divided into many clusters with different sizes (see Fig. 2a marked by red dash oval) by pearlite. The mean area of ellipse-like clusters is 3.89 mm2. And for high pearlite iron, the chrysanthemum pattern (eutectic cell) of ferrite can be found (see Fig. 2c marked by red dash cycle), the average area of those chrysanthemum cells (regard as circles) is 1.13 mm2. The ferrite zone is surrounded by pearlite zone, but for high ferrite iron, there is almost no pearlite in the ferrite cluster, the ferrite is a massive bulk; for high pearlite iron, some fine and dispersed pearlite can be seen in the pattern. The tensile strength, yield strength of the two materials at room and 500 � C temperatures are listed in Table 2.
2. Experimental materials and procedures In the present study, two kinds of vermicular graphite cast samples were cut from the flame deck of the cylinder head. The chemical com positions are shown in Table 1. As shown in Fig. 1, TMF specimens with a total length of 160 mm and a gauge section ofϕ8 mm � 30 mm were machined by using finish turning and followed by grinding. To avoid the negative effect of surface roughness, all specimens were polished with emery papers (#400, #800, #1200 and 2000# in order) along the axial direction. Cast iron specimens were cyclically deformed in air under the control of the axial strain range, and measured by a 25 mm gauge length extensometer on a hydraulic servo testing machine MTS 810. The samples were inductively heated with 5 kW generator, cooled by com pressed air in two directions and the mechanical chucks were cooled by circulating water. The spiral induction coil was used to reduce the temperature gradient of the sample gauge section. Temperature was controlled and measured by a ribbon Ni–CrNi thermocouple element, positioned in the middle of the standard distance by spot welding. The heating and cooling times are both 60 s (120s for one cycle). The defined TMF cycles were repeated until fracture of the specimen or until the maximum stress in a cycle falls below 60% of stable cycles. The run-out cycle number is 2500. Before TMF test, two or three cycles of thermal fatigue (without mechanical strain load) were needed. This was used to measure the relationship between temperature and thermal strain of the materials. The thermal strain can be calculated by the formula below [15]:
3.2. Thermo-mechanical fatigue behavior The half-life hysteresis loops of high ferrite iron and high pearlite iron in out-of-phase TMF at 125–500 � C are shown in Fig. 3a and b. The temperature of tensile semi-cycle is lower than that of compress semicycle, the resistance to deformation is higher, of the maximum of ten sile stress is higher than the mean is stress is tensile stress. For the two materials at the same mechanical strain amplitude, the compressive stress is almost identical, but the tensile stress of high pearlite iron is significantly higher. This can be attribute to the difference of hardness and tensile strength. The hardness and tensile strength for pearlite are 100 HB and 750 MPa, for ferrite are 80 HB and 230 MPa [24],respec tively. And for high ferrite iron, the difference between loading modulus and unloading modulus is almost invariable in different strain ampli tude; but for high pearlite iron, the difference at lower strain amplitude is higher than that at higher strain amplitude, and the asymmetry of those loops at lower strain amplitude is very obvious. The change stress amplitude during the TMF is investigated. For high ferrite iron (Fig. 3c), the phenomenon is cyclic stability or extremely unobvious hardening, but for high pearlite iron, obvious cyclic hard ening is obvious (Fig. 3d). Usually, the cyclic stability should be regar ded as the combined effects of the dislocation strengthening and the grain-boundary weakening. In general, at high temperature, the slip deformation may be restricted by the diffusion of carbon atoms into dislocations. But based on the previous studies [22,23], it is known that for high ferrite iron, the grain boundary weakening of ferrite in 400–500 � C plays the leading role in the cyclic hardening. So, it can be regard as that pearlite is hardening, but the ferrite is not hardening during the TMF circles. For high ferrite iron, the pearlite is only 19.6%, so the high pearlite iron as a whole is not clearly cyclic hardening. For high pearlite iron, more pearlite provides cyclic hardening capability. This can be also used to explain the asymmetry of loops in Fig. 3b. The area of each loops in Fig. 3 indicated the damage of specimen in one cycle of fatigue process. Fig. 4 established the relationship between mechanical strain amplitude and area of half-life hysteresis loops (Wa). It can be seen that for identical strain amplitude, the dissipation energy of high pearlite iron is always higher than that of high ferrite iron. It can be attributed to the better strength of pearlite. The dissipation energy increases with the mechanical strain amplitude increasing. The gap between high ferrite iron and high pearlite iron trends to increasing
(1)
dεth ¼ αðTÞ dT
where εth is thermal strain and α is thermal expansion coefficient at temperature T. The total strain is the linear superposition of thermal strain and mechanical strain and can be expressed as below [15]: (2)
εt ¼ εmech þ εth
where εt is total strain and εmech is mechanical strain. The εmech is calculated by the difference between εt (real-time measured by the extensometer) and εth (calculated by the temperature tests). Since the out-of-phase condition (thermal and mechanical cycles have the same period, but the peak value of temperatue corroponding to the valley value of mechanical strain) is critical for the cylinder head in the service, the out-of-phase TMF tests of two materials with different mechanical strain amplitudes from 0.1% to 0.3% for 125–500 � C were conducted. Meanwhile, the high pearlite iron material was employed to study the influence of different constraint ratio conditions, different ratios from 1.25 to þ1 were used. The constraint ratio (γ) can be calculated by the formula: (3)
γ ¼ εmech =εth Table 1 The chemical compositions (wt%) of vermicular graphite cast irons. Material
C
Si
Mn
S
P
high ferrite iron high pearlite iron [21]
3.5 3.5
2.6 1.5
0.5 0.13
0.04 0.015
0.03 0.03
2
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Materials Science & Engineering A 771 (2020) 138617
Fig. 1. Dimensions of the thermomechanical fatigue test specimen.
It reflects that no mechanical strain loading, no hysteresis loop. So c ¼ 0, and corresponding fitted values of a and b are 59.44 and 14.96, respectively. The maximum and minimum stresses under different constraint ratio are shown in Fig. 5c, difference between maximum and minimum stress decreases with the decrease of absolute value of constraint ratios. The means stress of condition with negative constraint ratio is always tensile stress and vice versa, this is also due to the change of mechanical properties of materials with temperature, deformation resistance in high temperature is lower. 3.3. Thermo-mechanical fatigue fracture morphology The fracture surface and lateral section morphologies out-of-phase TMF samples are shown in Fig. 6. For high ferrite iron, it can be seen that there is no obvious fatigue source in the view, but some separated arcs which consist of pearlite (see Fig. 6a and b). Based on the previous work [16], it can be known that this appearance should be caused by the different ΔKth of pearlite and ferrite, at higher temperature the rapid decrease of ΔKth of pearlite will promote the crack to pass through the phase boundary and avoid the formation of full ellipse-like pattern. For high pearlite iron, it also reveals the feature of multi-source cracking (see Fig. 6e and f). Around the edge of specimen, a clear circular flat area shows the fatigue crack initiation and slow propagation region, and in the interior the rough area shows the transient broken region (see Fig. 6e). Comparing the crack propagation paths from figures Fig. 6c and g, high pearlite iron has a smoother path. The cracks do not propagate along clusters for both materials. Comparing Fig. 6d with 6 h, the micro-cracks formed by bridge connection of vermicular graphite in ferrite zone can be found, which means that at high temperature, the micro-cracks preferentially initiats at ferrite cluster of high ferrite iron and at the ferrite in the chrysanthemum pattern of high pearlite iron. Typical TMF fractographies and lateral section appearance with the constraint ratios of 1 and þ1 are shown in Fig. 7. The mechanical strain is always negative (or positive). Similar to Fig. 6e, the a clear circular flat area shows the fatigue crack initiation and slow propagation region. But for different constraint ratios, the thickness is obviously different (see the red arrows). When the material bear tensile stress in high temperature (γ ¼ þ1 condition), the less thickness means smaller crack propagation zone and shorter fatigue life. No obvious feature of multi-source cracking in Fig. 7a and e, the reason can be attributed to the samll propagation zone. Crack propagation paths are smooth (Fig. 7c and g) and the crack formed by bridge connection of vermicular graphite in the ferrite zone can also be found in Fig. 7d and h. Besides, there is no obvious difference between the TMF fractographies under γ ¼ 1 and γ ¼ þ1 conditions.
Fig. 2. The microstructures of (a), (b)high ferrite iron and (c), (d) high pearlite iron.
along with the strain amplitude increased. It can also be attributed to the cyclic hardening capability of pearlite. In addition, high pearlite iron material was employed to reveal the influence of constraint ratio, based on the thermal strain test, the ther mal strain of high pearlite iron is from 0.12% to 0.66% under 125–500 � C. The shapes of half-life hysteresis loops are shown in Fig. 5a. The area of loop increases with the absolute value of ratio. This phe nomenon may be controlled by the cyclic deformation capacity and tension-compression asymmetry, and further study is necessary. Theo retically, if the constraint ratio is 0, there should be no hysteresis loops, because no mechanical strain loads in the specimens, and the fatigue life equals to the life of thermal fatigue (may be infinite life). For same ab solute value, the negative ratio means larger loops, and the mean stress is tensile stress. But for positive ratio, the temperature of tensile semicycle is higher, so the mean stress is compressive stress. The upward parabola style can be found in Fig. 5b. The points in Fig. 5a can be fitted by the formula below: (4)
Wa ¼ aγ2 þ bγ þ c:
The a, b and c are fitted parameters, and are considered as the boundary condition, the point (0,0) which is shown in Fig. 5b should be calculated.
Table 2 The microstructures and mechanical properties of high ferrite iron and high pearlite iron. Material
Ferrite (%)
Pearlite (%)
Graphite (%)
Vermicular rate (%)
Tensile strength of (MPa)
Yield strength (MPa)
500 � C tensile strength (MPa)
high ferrite iron high pearlite iron
69.6 36.1
19.6 55.8
10.7 8.1
87.4 77.4
293 431
225 314
228 323
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Fig. 3. Half-life hysteresis loops of out-of-phase TMF at 125–500� C for (a) high ferrite iron and (b) high pearlite iron; the variation trends of stress amplitude with cyclic number for (c) high ferrite iron and (d) high pearlite iron.
will fracture preferentially, so no ellipse, but arcs formed. For high pearlite iron, there is no obvious arc or ellipse trace (Fig. 6e), but the fatigue crack propagation area (surface layer) and transient cracking area (inner) can be found. The process of micro-crack initiation is similar to high ferrite iron, the micro-cracks initiated at the interface between graphite and ferrite in the chrysanthemum patterns. But even at 500 � C, the fatigue crack growth threshold of pearlite is still higher than that of ferrite. Cracks prefers to propagate in the chrysanthemum-like eutectic cells, rather than through the pearlite zones. So, many micro-cracks initiats and propagats in the chrysanthemum-like eutectic cells which are located in the edge of specimens, this is the cause of formation of propagation area at out layer and the transient broken area at the central section. The schematic di agram of fracture mechanism for high ferrite iron and high pearlite iron is shown in Fig. 8. The red line represents the micro-cracks and the pink zone represents the crack propagation zone.
Fig. 4. Relationship between mechanical strain amplitude and area of half-life hysteresis loops.
4.2. Fatigue life prediction method
4. Discussion
For industrial applications, to predict fatigue life is necessary. Two Fatigue life prediction methods were studied in this work. First, strain as a very important factor is easy to test or control, but under some service conditions, the factor which can reflect the combined effect of strain and stress is preferential, so, to study the hysteresis energy is very useful. Usually, the Manson-Coffin equation is widely used to calculate the relationship between strain and fatigue life [25], it can be expressed as follows: �c εe ¼ ε’f 2Nf (5)
4.1. Thermo-mechanical fatigue fracture mechanism The high ferrite iron and high pearlite iron show two different fracture mechanisms under the same TMF load. For high ferrite iron, the fractographies reveal many arcs (not full ellipse, see Fig. 6a), apparently, this can be attributed to the crack propagation. Combining with the SEM observation in Fig. 6d, it can be known that the micro-cracks initiates at the interface between graphite and ferrite, followed by propagation along the ferrite grain boundaries. Cracks initiate from the ferrite clus ters and slow down at the pearlite due to its higher fatigue threshold. During TMF loading, the phenomena appear in many clusters. When the cracks exist in many clusters, the actual stress of pearlite is much higher than the nominal stress applied. Because of the thickness of pearlite which around the cluster is not uniform (see Fig. 2a). The thinner section
Where: Nf——number of cycles to failure
ε0 f——fatigue ductility coefficient c——fatigue ductility exponent
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Materials Science & Engineering A 771 (2020) 138617
Fig. 5. (a) The half-life hysteresis loops under different constraint ratios, (b) the area of loops vs. constraint ratio, (c) maximum and minimum stresses vs. the constraint ratio.
The fitted curves are shown in Fig. 9a. For high ferrite iron, ε0 f ¼ 1.14 and c ¼ 0.26; for high pearlite iron ε0 f ¼ 0.83 and c ¼ 0.22, respec tively. At higher strain amplitude, the TMF life of high pearlite iron is higher; but at lower strain amplitude, the TMF life of high ferrite iron is close to that of high pearlite iron. The reason can be attributed to the follows. As shown in Fig. 3d, at lower strain amplitude, the relatively longer life provided more intensive work hardening, material will be continually strengthened during the TMF loadings. However, large fraction of ferrite of high ferrite iron cannot be strengthened too much due to the weakening effect of grain boundary at high temperature. But for high pearlite iron, the effect of ferrite grain boundary is substantially limited due to low fraction of ferrite. Meanwhile, lots of chucks of pearlite embed in the ferrite eutectic cell; they provide the positive effect which may be similar to the dispersion reinforcing. Similar to the strain-fatigue life curves, the relationship between hysteresis energy and fatigue life is linear in log-log coordinates [26–28]. The fatigue life can be calculated as below:
of external damage, but does not consider the damage tolerance of the material itself [29]. This phenomenon can attribute to the mechanism of crack propa gation. Combining with Fig. 8, different from the high pearlite iron, the propagation zone of high ferrite iron is located within the cluster; it is not easy to form multiple stress concentration points. However, the annular propagation zone is beneficial to eliminate more stress con centration points, this reduces the probability of simultaneous propa gation of multiple cracks. It can increase the loss tolerance (by the way of reduce crack growth rate). The relationship between constraint ratio and TMF life is shown in Fig. 10a. With the increase of the absolute value of constraint ratio, the TMF life decreases; and in logarithmic coordinates, the relationship between them is linear. Therefore, the constraint ratio and TMF life satisfy the exponential equation as follow:
W0 2Nf ¼ ð Þβ Wa
2Nf ¼ Að γÞK
2Nf ¼ AðγÞK
(6)
For constraint ratio greater than 0
(7)
For constraint ratio less than 0
(8)
similar to the Manson-Coffin equation, where A and K are material constants. In this study, we define A and K as fatigue constraint coeffi cient and fatigue constraint exponent, respectively. For the high pearlite iron, the corresponding specific values are A ¼ 85.6, K ¼ 5.52 of Eq. (7) and A ¼ 470.9, K ¼ 2.73 of Eq. (8), respectively. Fatigue constraint exponent reflects the sensitivity of the material to the constraint ratio; while fatigue constraint coefficient is controlled by the thermal fatigue property of material. The two parameters can be obtained by fitting, but how to obtain them through other tests such as thermal fatigue still needs further study. Based on the studies in section 4.2, the hysteresis energy method can characterize the TMF lifetime of materials (Fig. 10b). When the constraint ratio is positive or negative, the curves are obviously different. When the constraint ratio is negative, the TMF life change is very close to that of out-of-phase (red and green lines in Fig. 10b). This
Where: Wa——the hysteresis energy β ——external damage parameter W 0——intrinsic fatigue toughness of materials It is noted that the curves shown in Fig. 9b are slightly different from the strain-fatigue life curves shown in Fig. 9a. For high ferrite iron, β ¼ 4689 and W 0 ¼ 0.77; for high pearlite iron, β ¼ 4225 and W0 ¼ 0.69, respectively. When the hysteresis energy is a constant value; the TMF life of high pearlite iron is always longer than that of high ferrite iron. In other words, under same TMF load, if the damage of each cycle is identical, the damage tolerant of high pearlite iron should be higher. Eq. (5) takes strain as a variable, which only represents the effect 5
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Fig. 6. Typical thermo-mechanical fatigue fractographies and their lateral section appearances for different materials under the same loading condition (out-of-phase, 125–500 � C,�0.3): (a)~(d) high ferrite iron; (e)~(h) high pearlite iron.
Fig. 7. Typical thermo-mechanical fatigue fractographies and lateral section appearances for different constraint ratios: (a)~(d) 1; (e)~(h) þ1.
phenomenon can be attributed to the influence of average stress. When the constraint ratio is negative, the direction of the average stress is the same as that of out-of-phase. When the constraint ratio is positive, the material bears the maximum tensile stress at high temperature, and the crack is easier to propagate. So when the hysteresis energy is the same, the lifetime of in-phase TMF is lower. The linear relationship between life and hysteretic energy is very accurate even if the constraints are different, which further illustrates the rationality of using hysteretic energy to characterize TMF life. In summary, under logarithmic (or double logarithmic) coordinates, TMF life is linearly correlated with restraint ratio (or energy), which also provides an idea for predicting TMF life. 5. Conclusions The TMF behaviors of vermicular graphite casts with different mi crostructures, fatigue fracture morphologies and failure mechanisms were studied in this work. The influence of constraint ratio was also discussed. The main conclusions were summarized as follows:
Fig. 8. Schematic diagram of fracture mechanism for high ferrite iron and high pearlite iron.
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Fig. 9. The fatigue life curves predicted by different methods for high ferrite iron and high pearlite iron: (a) Manson-Coffin equation; (b) hysteresis energy method.
Fig. 10. (a) Variation of constraint ratio with number of cycles (2Nf) for high area fraction pearlite versus number of cycles for high area fraction pearlite under 125–500 � C; (b) Variation of hysteresis energy with fatigue life (2Nf) for different constrain ratios.
1) Elliptical ferrite clusters can be seen in microstructure of high ferrite cast iron, and ferrite clusters in high pearlite cast iron are chrysanthemum-like. Differences in the proportion of pearlite and ferrite lead to the difference of TMF properties. 2) Muti-source fatigues fracture is the main form of TMF failure. For high ferrite cast iron, the propagation zone locats within the cluster; for high pearlite cast iron, the propagation zone locats around the specimen. 3) By choosing mechanical strain amplitude and hysteretic energy as variables, high pearlite cast iron and high ferrite cast iron show different TMF life trends. In the hysteresis energy-TMF life curves, high pearlite cast iron has longer TMF life than high ferrite cast iron has. The different propagate zones lead to the different TMF life. 4) In logarithmic coordinates, the relationship between TMF life and constraint ratio is linear. Constraint coefficient and constraint exponent are proposed to measure the TMF life of materials. Constraint exponent reflects the sensitivity of materials to constraint ratio under TMF condition, while constraint coefficient reflects the thermal fatigue performance of materials.
References [1] Z.J. Ma, D. Tao, Z. Yang, et al., The effect of vermicularity on the thermal conductivity of vermicular graphite cast iron, Mater. Des. 93 (2016) 418–422. [2] R. O’Bourke, Cast iron: the engineered metal, Adv. Mater. Process. 159 (2001) 65–68. [3] M. Holtzer, M. G� orny, R. Da� nko, Microstructure and Properties of Ductile Iron and Compacted Graphite Iron Castings: the Effects of Mold Sand/metal Interface Phenomena, Springer, Berlin, 2015. [4] C.D. Rakopoulos, G.C. Mavropoulos, Experimental instantaneous heat fluxes in the cylinder head and exhaust manifold of an air-cooled diesel engine, Energy Convers. Manag. 10 (2000) 1265–1281. [5] C. Çetinkaya, An investigation of the wear behaviors of white cast irons under different compositions, Mater. Des. 6 (2006) 437–445. [6] K. H€ oschler, J. Bischof, W. Koschel, Thermo-mechanical analysis of an automotive diesel engine exhaust manifold, Struct. Integrity Soc. 29 (2002) 299–308. [7] A. Nitta, K. Kuwabara, Thermal-mechanical Fatigue Failure and Life Prediction, Elsevier Applied Science Publishers, High Temperature Creep-Fatigue, 1988, pp. 203–222. [8] M. Metzger, B. Nieweg, C. Schweizer, et al., Lifetime prediction of cast iron materials under combined thermomechanical fatigue and high cycle fatigue loading using a mechanism-based model, Int. J. Fatigue 53 (2013) 58–66. [9] F. Zieher, F. Langmayr, A. Jelatancev, et al., Thermal Mechanical Fatigue Simulation of Cast Iron Cylinder Heads, SAE Technical Paper, 2005. [10] R.W. Neu, H. Sehitoglu, Thermomechanical fatigue, oxidation, and creep: Part I. Damage mechanisms, Metall. Tran. A 20 (1989) 1755–1767. [11] R.W. Neu, H. Sehitoglu, Thermomechanical fatigue, oxidation, and creep: Part II. Life prediction, Metall. Tran. A 20 (1989) 1769–1783. [12] P. Skoglund, J. Elfsberg, N. Ipek, et al., Thermo-mechanical fatigue of grey cast iron for cylinder heads-effect of niobium, molybdenum and solidification time// materials science forum, Trans. Tech. Publ. 925 (2018) 377–384. [13] Y. Liu, Y.H. Chen, N. Sawkar, et al., A Thermo-Mechanical Fatigue Analysis on a Ductile Cast Iron Exhaust Manifold, SAE Technical Paper, 2018. [14] A.O. Abu, S. Eshati, P. Laskaridis, et al., Aero-engine turbine blade life assessment using the Neu/Sehitoglu damage model, Int. J. Fatigue 61 (2014) 160–169. [15] H. Sehitoglu, Thermo-mechanical Fatigue Life Prediction Methods. Advances in Fatigue Lifetime Predictive Techniques, ASTM International, 1992. [16] M.X. Zhang, J.C. Pang, Y. Qiu, S.X. Li, M. Wang, Z.F. Zhang, Thermo-mechanical fatigue property and life prediction of vermicular graphite iron, Mater. Sci. Eng. A 698 (2017) 63–72.
Acknowledgments The authors would like to thank Mr. Jing Long Wen and Dr. Cui Hong Li, Prof. Zhong Yang and Prof. Jian Ping Li for their helps of the fatigue experiments, SEM observations and specimen preparation. This work is supported by National Natural Science Foundation of China (NSFC) under Grant No. 51871224.
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Materials Science & Engineering A 771 (2020) 138617 [23] Y. Qiu, J.C. Pang, M.X. Zhang, et al., Influence of temperature on the high-cycle fatigue properties of compacted graphite iron, Int. J. Fatigue 112 (2018) 84–93. [24] M.T. Shi, Metal Materials and Heat Treatment, Shanghai Scientific and Technical Publishers, 2005. [25] S.S. Manson, Fatigue: a complex subject some simple approximation, Exp. Mech. 5 (1965) 193–226. [26] J. Park, D. Nelson, Evaluation of an energy-based approach and a critical plane approach for predicting constant amplitude multi-axial fatigue life, Int. J. Fatigue 22 (2000) 23–39. [27] R. Liu, Z.J. Zhang, P. Zhang, et al., Extremely-low-cycle fatigue behaviors of Cu and Cu–Al alloys: damage mechanisms and life prediction, Acta Mater. 83 (2015) 341–356. [28] S. Suresh, Fatigue of Materials, Cambridge University Press, Cambridge, 1998. [29] Z.F. Zhang, H.C. Gu, Plastic work model for fatigue damage and life prediction, Struct. Env. Eng. 3 (1998) 55–59.
[17] F. Bagnoli, F. Dolce, M. Bernabei, Thermal fatigue cracks of fire fighting vehicles gray iron brake discs, Eng. Fail. Anal. 16 (2009) 152–163. [18] X. Wu, G. Quan, R. MacNeil, et al., Thermomechanical fatigue of ductile cast iron and its life prediction, Metall. Mater. Trans. A 6 (2015) 2530–2543. [19] H. Zhang, Y.C. Wang, F. Liu, et al., Thermal-mechanical fatigue behavior and life analysis of cast Ni-base superalloy K417, J. Mater. Sci. Technol. 18 (2009) 176–180. [20] V.L. Diaconu, T. Sj€ ogren, P. Skoglund, et al., Influence of molybdenum alloying on thermomechanical fatigue life of compacted graphite irons, Int. J. Cast Metals Res. 25 (2012) 277–286. [21] C.L. Zou, J.C. Pang, M.X. Zhang, et al., The high cycle fatigue, deformation and fracture of compacted graphite iron: influence of temperature, Mater. Sci. Eng. A 724 (2018) 606–615. [22] Y. Qiu, J.C. Pang, C.L. Zou, et al., Fatigue strength model based on microstructures and damage mechanism of compacted graphite iron, Mater. Sci. Eng. A 724 (2018) 324–329.
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Materials Science & Engineering A journal homepage: http://www.elsevier.com/locate/msea
Influence of microstructure on the thermo-mechanical fatigue behavior and life of vermicular graphite cast irons M.X. Zhang, J.C. Pang *, Y. Qiu, S.X. Li, M. Wang, Z.F. Zhang ** Materials Fatigue and Fracture Laboratory, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang, 110016, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Thermo-mechanical fatigue Vermicular graphite cast iron Microstructures Life prediction Fracture mechanism
Cylinder head is subjected to the combination changes of temperature and mechanical loads in service. In such harsh condition, thermo-mechanical fatigue (TMF) failure is a main problem. In this study, two kinds of vermicular graphite cast irons were selected to reveal the TMF properties and life prediction. Vermicular graphite casts with different microstructures have different ferrite cluster morphologies, which result in different fracture mechanisms. The hysteresis loops of both materials display obvious asymmetry. Hysteresis energy and me chanical strain amplitude were selected as damage parameters to determine the fatigue life. It is found that the TMF performance of vermicular graphite cast iron with higher pearlite content is better; meanwhile, the life of TMF at different constraint ratios was also studied. Hysteretic energy related to constrain ratio is in a parabolic form, and the life of TMF decreases with the absolute value of constraint ratio increasing. Finally, the quanti tative relationship between constraint ratio and TMF life was also discussed.
1. Introduction Vermicular graphite cast iron is a widely used structural material because of its excellent mechanical properties and thermal conductivity [1–3]. One of the typical applications is the engine cylinder head [4]. Its service conditions usually include simultaneous changes of temperature and load, so thermo-mechanical fatigue (TMF) is a common failure mode [5]. These changes will lead to severe fatigue damage than the conventional fatigue; it may cause economic losses and even heavy ca sualties. Therefore, selecting the cast iron as a model material to study the thermal mechanical fatigue performance is definitely necessary, and the life prediction is indispensable [6–8]. Not only the temperature and load changes,but also there are some other complex factors such as phase condition and constraint ratio. So, the complexity of TMF operating conditions determines that TMF research needs a lot of time and money. Zieher et al. [9] proposed a life simulation process. Based on the continuous damage mechanics method, they discussed different life prediction models and gave suggestions for design improvement. Neu and Sehitoglu [10,11] considered that for TMF there are three main aspects: fatigue, creep damage and environ mental oxidation. Those factors, such as maximum (or minimum) tem perature, mechanical strain amplitude, phase angle between
temperature and mechanical strain, service time and environment, can act independently or be combined with service conditions and material types. The TMF behaviors must be very complicated due to so many influencing factors involved. Although intensive studies have been conducted, the dependence between microstructure and TMF life has not been well understood. Skoglund et al. [12] chose gray cast iron for TMF test, they found that if the solidification time is longer, the prop erties may be completely controlled by large graphite sheets, and the alloying elements do not affect the properties much. On the contrary, different alloying elements, such as molybdenum can improve the life of TMF. Recently, Neu-Sehitoglu TMF model was widely and successfully used to evaluate TMF damage [13–15], however, the ferrite cast iron cannot fully meet the requirements of this model due to intergranular embrittlement at 400 � C, low ductility at low temperature and phase transformation at high temperature. By the way, too many parameters to be determined by pre-TMF test are time and money consuming; there fore, it is necessary to explore the concise method for TMF evaluation in the materials improvement process. In a previous work [16], the rela tionship between low-cycle fatigue and TMF has been established, and the effect of temperature on TMF has also been analyzed. To some extent, these studies can explain some TMF behaviors [17–20]; however for vermicular graphite cast iron, the relationship between matrix
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (J.C. Pang), [email protected] (Z.F. Zhang). https://doi.org/10.1016/j.msea.2019.138617 Received 3 July 2019; Received in revised form 17 September 2019; Accepted 30 October 2019 Available online 7 November 2019 0921-5093/© 2019 Elsevier B.V. All rights reserved.
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microstructure and TMF is still not clear, and the related fracture mechanisms are not clear either. For simplicity, two vermicular graphite cast irons (cast with high area fraction of pearlite (high pearlite iron) and cast with high area fraction of ferrite (high ferriet cast)) with approximate equal vermicular rate but different microstructures were employed in this study. The relationship between the TMF life and constraint ratio was also studied. Finally, the influencing factors and fracture mechanisms of TMF life for the vermicular graphite casts were analyzed.
3. Experimental results 3.1. Microstructure As shown in Fig. 2, both high ferrite iron and high pearlite iron vermicular graphite casts consist of ferrite, pearlite and vermicular graphite, in which the gray zone is equiaxed ferrite, the white zone is laminar pearlite and the graphite is black. But their proportions in the two vermicular graphite casts are different. For high ferrite iron, the area fractions are 69.6%, 19.6% and 10.7%, respectively. The corre sponding values in high pearlite iron are 36.1%, 55.8% and 8.1%. The mean grain sizes of ferrite were measured by intercept method to be about 9.6 μm and 12.6 μm for high ferrite iron and high pearlite iron, respectively. For high ferrite iron, the ferrite zone can be divided into many clusters with different sizes (see Fig. 2a marked by red dash oval) by pearlite. The mean area of ellipse-like clusters is 3.89 mm2. And for high pearlite iron, the chrysanthemum pattern (eutectic cell) of ferrite can be found (see Fig. 2c marked by red dash cycle), the average area of those chrysanthemum cells (regard as circles) is 1.13 mm2. The ferrite zone is surrounded by pearlite zone, but for high ferrite iron, there is almost no pearlite in the ferrite cluster, the ferrite is a massive bulk; for high pearlite iron, some fine and dispersed pearlite can be seen in the pattern. The tensile strength, yield strength of the two materials at room and 500 � C temperatures are listed in Table 2.
2. Experimental materials and procedures In the present study, two kinds of vermicular graphite cast samples were cut from the flame deck of the cylinder head. The chemical com positions are shown in Table 1. As shown in Fig. 1, TMF specimens with a total length of 160 mm and a gauge section ofϕ8 mm � 30 mm were machined by using finish turning and followed by grinding. To avoid the negative effect of surface roughness, all specimens were polished with emery papers (#400, #800, #1200 and 2000# in order) along the axial direction. Cast iron specimens were cyclically deformed in air under the control of the axial strain range, and measured by a 25 mm gauge length extensometer on a hydraulic servo testing machine MTS 810. The samples were inductively heated with 5 kW generator, cooled by com pressed air in two directions and the mechanical chucks were cooled by circulating water. The spiral induction coil was used to reduce the temperature gradient of the sample gauge section. Temperature was controlled and measured by a ribbon Ni–CrNi thermocouple element, positioned in the middle of the standard distance by spot welding. The heating and cooling times are both 60 s (120s for one cycle). The defined TMF cycles were repeated until fracture of the specimen or until the maximum stress in a cycle falls below 60% of stable cycles. The run-out cycle number is 2500. Before TMF test, two or three cycles of thermal fatigue (without mechanical strain load) were needed. This was used to measure the relationship between temperature and thermal strain of the materials. The thermal strain can be calculated by the formula below [15]:
3.2. Thermo-mechanical fatigue behavior The half-life hysteresis loops of high ferrite iron and high pearlite iron in out-of-phase TMF at 125–500 � C are shown in Fig. 3a and b. The temperature of tensile semi-cycle is lower than that of compress semicycle, the resistance to deformation is higher, of the maximum of ten sile stress is higher than the mean is stress is tensile stress. For the two materials at the same mechanical strain amplitude, the compressive stress is almost identical, but the tensile stress of high pearlite iron is significantly higher. This can be attribute to the difference of hardness and tensile strength. The hardness and tensile strength for pearlite are 100 HB and 750 MPa, for ferrite are 80 HB and 230 MPa [24],respec tively. And for high ferrite iron, the difference between loading modulus and unloading modulus is almost invariable in different strain ampli tude; but for high pearlite iron, the difference at lower strain amplitude is higher than that at higher strain amplitude, and the asymmetry of those loops at lower strain amplitude is very obvious. The change stress amplitude during the TMF is investigated. For high ferrite iron (Fig. 3c), the phenomenon is cyclic stability or extremely unobvious hardening, but for high pearlite iron, obvious cyclic hard ening is obvious (Fig. 3d). Usually, the cyclic stability should be regar ded as the combined effects of the dislocation strengthening and the grain-boundary weakening. In general, at high temperature, the slip deformation may be restricted by the diffusion of carbon atoms into dislocations. But based on the previous studies [22,23], it is known that for high ferrite iron, the grain boundary weakening of ferrite in 400–500 � C plays the leading role in the cyclic hardening. So, it can be regard as that pearlite is hardening, but the ferrite is not hardening during the TMF circles. For high ferrite iron, the pearlite is only 19.6%, so the high pearlite iron as a whole is not clearly cyclic hardening. For high pearlite iron, more pearlite provides cyclic hardening capability. This can be also used to explain the asymmetry of loops in Fig. 3b. The area of each loops in Fig. 3 indicated the damage of specimen in one cycle of fatigue process. Fig. 4 established the relationship between mechanical strain amplitude and area of half-life hysteresis loops (Wa). It can be seen that for identical strain amplitude, the dissipation energy of high pearlite iron is always higher than that of high ferrite iron. It can be attributed to the better strength of pearlite. The dissipation energy increases with the mechanical strain amplitude increasing. The gap between high ferrite iron and high pearlite iron trends to increasing
(1)
dεth ¼ αðTÞ dT
where εth is thermal strain and α is thermal expansion coefficient at temperature T. The total strain is the linear superposition of thermal strain and mechanical strain and can be expressed as below [15]: (2)
εt ¼ εmech þ εth
where εt is total strain and εmech is mechanical strain. The εmech is calculated by the difference between εt (real-time measured by the extensometer) and εth (calculated by the temperature tests). Since the out-of-phase condition (thermal and mechanical cycles have the same period, but the peak value of temperatue corroponding to the valley value of mechanical strain) is critical for the cylinder head in the service, the out-of-phase TMF tests of two materials with different mechanical strain amplitudes from 0.1% to 0.3% for 125–500 � C were conducted. Meanwhile, the high pearlite iron material was employed to study the influence of different constraint ratio conditions, different ratios from 1.25 to þ1 were used. The constraint ratio (γ) can be calculated by the formula: (3)
γ ¼ εmech =εth Table 1 The chemical compositions (wt%) of vermicular graphite cast irons. Material
C
Si
Mn
S
P
high ferrite iron high pearlite iron [21]
3.5 3.5
2.6 1.5
0.5 0.13
0.04 0.015
0.03 0.03
2
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Fig. 1. Dimensions of the thermomechanical fatigue test specimen.
It reflects that no mechanical strain loading, no hysteresis loop. So c ¼ 0, and corresponding fitted values of a and b are 59.44 and 14.96, respectively. The maximum and minimum stresses under different constraint ratio are shown in Fig. 5c, difference between maximum and minimum stress decreases with the decrease of absolute value of constraint ratios. The means stress of condition with negative constraint ratio is always tensile stress and vice versa, this is also due to the change of mechanical properties of materials with temperature, deformation resistance in high temperature is lower. 3.3. Thermo-mechanical fatigue fracture morphology The fracture surface and lateral section morphologies out-of-phase TMF samples are shown in Fig. 6. For high ferrite iron, it can be seen that there is no obvious fatigue source in the view, but some separated arcs which consist of pearlite (see Fig. 6a and b). Based on the previous work [16], it can be known that this appearance should be caused by the different ΔKth of pearlite and ferrite, at higher temperature the rapid decrease of ΔKth of pearlite will promote the crack to pass through the phase boundary and avoid the formation of full ellipse-like pattern. For high pearlite iron, it also reveals the feature of multi-source cracking (see Fig. 6e and f). Around the edge of specimen, a clear circular flat area shows the fatigue crack initiation and slow propagation region, and in the interior the rough area shows the transient broken region (see Fig. 6e). Comparing the crack propagation paths from figures Fig. 6c and g, high pearlite iron has a smoother path. The cracks do not propagate along clusters for both materials. Comparing Fig. 6d with 6 h, the micro-cracks formed by bridge connection of vermicular graphite in ferrite zone can be found, which means that at high temperature, the micro-cracks preferentially initiats at ferrite cluster of high ferrite iron and at the ferrite in the chrysanthemum pattern of high pearlite iron. Typical TMF fractographies and lateral section appearance with the constraint ratios of 1 and þ1 are shown in Fig. 7. The mechanical strain is always negative (or positive). Similar to Fig. 6e, the a clear circular flat area shows the fatigue crack initiation and slow propagation region. But for different constraint ratios, the thickness is obviously different (see the red arrows). When the material bear tensile stress in high temperature (γ ¼ þ1 condition), the less thickness means smaller crack propagation zone and shorter fatigue life. No obvious feature of multi-source cracking in Fig. 7a and e, the reason can be attributed to the samll propagation zone. Crack propagation paths are smooth (Fig. 7c and g) and the crack formed by bridge connection of vermicular graphite in the ferrite zone can also be found in Fig. 7d and h. Besides, there is no obvious difference between the TMF fractographies under γ ¼ 1 and γ ¼ þ1 conditions.
Fig. 2. The microstructures of (a), (b)high ferrite iron and (c), (d) high pearlite iron.
along with the strain amplitude increased. It can also be attributed to the cyclic hardening capability of pearlite. In addition, high pearlite iron material was employed to reveal the influence of constraint ratio, based on the thermal strain test, the ther mal strain of high pearlite iron is from 0.12% to 0.66% under 125–500 � C. The shapes of half-life hysteresis loops are shown in Fig. 5a. The area of loop increases with the absolute value of ratio. This phe nomenon may be controlled by the cyclic deformation capacity and tension-compression asymmetry, and further study is necessary. Theo retically, if the constraint ratio is 0, there should be no hysteresis loops, because no mechanical strain loads in the specimens, and the fatigue life equals to the life of thermal fatigue (may be infinite life). For same ab solute value, the negative ratio means larger loops, and the mean stress is tensile stress. But for positive ratio, the temperature of tensile semicycle is higher, so the mean stress is compressive stress. The upward parabola style can be found in Fig. 5b. The points in Fig. 5a can be fitted by the formula below: (4)
Wa ¼ aγ2 þ bγ þ c:
The a, b and c are fitted parameters, and are considered as the boundary condition, the point (0,0) which is shown in Fig. 5b should be calculated.
Table 2 The microstructures and mechanical properties of high ferrite iron and high pearlite iron. Material
Ferrite (%)
Pearlite (%)
Graphite (%)
Vermicular rate (%)
Tensile strength of (MPa)
Yield strength (MPa)
500 � C tensile strength (MPa)
high ferrite iron high pearlite iron
69.6 36.1
19.6 55.8
10.7 8.1
87.4 77.4
293 431
225 314
228 323
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Fig. 3. Half-life hysteresis loops of out-of-phase TMF at 125–500� C for (a) high ferrite iron and (b) high pearlite iron; the variation trends of stress amplitude with cyclic number for (c) high ferrite iron and (d) high pearlite iron.
will fracture preferentially, so no ellipse, but arcs formed. For high pearlite iron, there is no obvious arc or ellipse trace (Fig. 6e), but the fatigue crack propagation area (surface layer) and transient cracking area (inner) can be found. The process of micro-crack initiation is similar to high ferrite iron, the micro-cracks initiated at the interface between graphite and ferrite in the chrysanthemum patterns. But even at 500 � C, the fatigue crack growth threshold of pearlite is still higher than that of ferrite. Cracks prefers to propagate in the chrysanthemum-like eutectic cells, rather than through the pearlite zones. So, many micro-cracks initiats and propagats in the chrysanthemum-like eutectic cells which are located in the edge of specimens, this is the cause of formation of propagation area at out layer and the transient broken area at the central section. The schematic di agram of fracture mechanism for high ferrite iron and high pearlite iron is shown in Fig. 8. The red line represents the micro-cracks and the pink zone represents the crack propagation zone.
Fig. 4. Relationship between mechanical strain amplitude and area of half-life hysteresis loops.
4.2. Fatigue life prediction method
4. Discussion
For industrial applications, to predict fatigue life is necessary. Two Fatigue life prediction methods were studied in this work. First, strain as a very important factor is easy to test or control, but under some service conditions, the factor which can reflect the combined effect of strain and stress is preferential, so, to study the hysteresis energy is very useful. Usually, the Manson-Coffin equation is widely used to calculate the relationship between strain and fatigue life [25], it can be expressed as follows: �c εe ¼ ε’f 2Nf (5)
4.1. Thermo-mechanical fatigue fracture mechanism The high ferrite iron and high pearlite iron show two different fracture mechanisms under the same TMF load. For high ferrite iron, the fractographies reveal many arcs (not full ellipse, see Fig. 6a), apparently, this can be attributed to the crack propagation. Combining with the SEM observation in Fig. 6d, it can be known that the micro-cracks initiates at the interface between graphite and ferrite, followed by propagation along the ferrite grain boundaries. Cracks initiate from the ferrite clus ters and slow down at the pearlite due to its higher fatigue threshold. During TMF loading, the phenomena appear in many clusters. When the cracks exist in many clusters, the actual stress of pearlite is much higher than the nominal stress applied. Because of the thickness of pearlite which around the cluster is not uniform (see Fig. 2a). The thinner section
Where: Nf——number of cycles to failure
ε0 f——fatigue ductility coefficient c——fatigue ductility exponent
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Fig. 5. (a) The half-life hysteresis loops under different constraint ratios, (b) the area of loops vs. constraint ratio, (c) maximum and minimum stresses vs. the constraint ratio.
The fitted curves are shown in Fig. 9a. For high ferrite iron, ε0 f ¼ 1.14 and c ¼ 0.26; for high pearlite iron ε0 f ¼ 0.83 and c ¼ 0.22, respec tively. At higher strain amplitude, the TMF life of high pearlite iron is higher; but at lower strain amplitude, the TMF life of high ferrite iron is close to that of high pearlite iron. The reason can be attributed to the follows. As shown in Fig. 3d, at lower strain amplitude, the relatively longer life provided more intensive work hardening, material will be continually strengthened during the TMF loadings. However, large fraction of ferrite of high ferrite iron cannot be strengthened too much due to the weakening effect of grain boundary at high temperature. But for high pearlite iron, the effect of ferrite grain boundary is substantially limited due to low fraction of ferrite. Meanwhile, lots of chucks of pearlite embed in the ferrite eutectic cell; they provide the positive effect which may be similar to the dispersion reinforcing. Similar to the strain-fatigue life curves, the relationship between hysteresis energy and fatigue life is linear in log-log coordinates [26–28]. The fatigue life can be calculated as below:
of external damage, but does not consider the damage tolerance of the material itself [29]. This phenomenon can attribute to the mechanism of crack propa gation. Combining with Fig. 8, different from the high pearlite iron, the propagation zone of high ferrite iron is located within the cluster; it is not easy to form multiple stress concentration points. However, the annular propagation zone is beneficial to eliminate more stress con centration points, this reduces the probability of simultaneous propa gation of multiple cracks. It can increase the loss tolerance (by the way of reduce crack growth rate). The relationship between constraint ratio and TMF life is shown in Fig. 10a. With the increase of the absolute value of constraint ratio, the TMF life decreases; and in logarithmic coordinates, the relationship between them is linear. Therefore, the constraint ratio and TMF life satisfy the exponential equation as follow:
W0 2Nf ¼ ð Þβ Wa
2Nf ¼ Að γÞK
2Nf ¼ AðγÞK
(6)
For constraint ratio greater than 0
(7)
For constraint ratio less than 0
(8)
similar to the Manson-Coffin equation, where A and K are material constants. In this study, we define A and K as fatigue constraint coeffi cient and fatigue constraint exponent, respectively. For the high pearlite iron, the corresponding specific values are A ¼ 85.6, K ¼ 5.52 of Eq. (7) and A ¼ 470.9, K ¼ 2.73 of Eq. (8), respectively. Fatigue constraint exponent reflects the sensitivity of the material to the constraint ratio; while fatigue constraint coefficient is controlled by the thermal fatigue property of material. The two parameters can be obtained by fitting, but how to obtain them through other tests such as thermal fatigue still needs further study. Based on the studies in section 4.2, the hysteresis energy method can characterize the TMF lifetime of materials (Fig. 10b). When the constraint ratio is positive or negative, the curves are obviously different. When the constraint ratio is negative, the TMF life change is very close to that of out-of-phase (red and green lines in Fig. 10b). This
Where: Wa——the hysteresis energy β ——external damage parameter W 0——intrinsic fatigue toughness of materials It is noted that the curves shown in Fig. 9b are slightly different from the strain-fatigue life curves shown in Fig. 9a. For high ferrite iron, β ¼ 4689 and W 0 ¼ 0.77; for high pearlite iron, β ¼ 4225 and W0 ¼ 0.69, respectively. When the hysteresis energy is a constant value; the TMF life of high pearlite iron is always longer than that of high ferrite iron. In other words, under same TMF load, if the damage of each cycle is identical, the damage tolerant of high pearlite iron should be higher. Eq. (5) takes strain as a variable, which only represents the effect 5
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Fig. 6. Typical thermo-mechanical fatigue fractographies and their lateral section appearances for different materials under the same loading condition (out-of-phase, 125–500 � C,�0.3): (a)~(d) high ferrite iron; (e)~(h) high pearlite iron.
Fig. 7. Typical thermo-mechanical fatigue fractographies and lateral section appearances for different constraint ratios: (a)~(d) 1; (e)~(h) þ1.
phenomenon can be attributed to the influence of average stress. When the constraint ratio is negative, the direction of the average stress is the same as that of out-of-phase. When the constraint ratio is positive, the material bears the maximum tensile stress at high temperature, and the crack is easier to propagate. So when the hysteresis energy is the same, the lifetime of in-phase TMF is lower. The linear relationship between life and hysteretic energy is very accurate even if the constraints are different, which further illustrates the rationality of using hysteretic energy to characterize TMF life. In summary, under logarithmic (or double logarithmic) coordinates, TMF life is linearly correlated with restraint ratio (or energy), which also provides an idea for predicting TMF life. 5. Conclusions The TMF behaviors of vermicular graphite casts with different mi crostructures, fatigue fracture morphologies and failure mechanisms were studied in this work. The influence of constraint ratio was also discussed. The main conclusions were summarized as follows:
Fig. 8. Schematic diagram of fracture mechanism for high ferrite iron and high pearlite iron.
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Fig. 9. The fatigue life curves predicted by different methods for high ferrite iron and high pearlite iron: (a) Manson-Coffin equation; (b) hysteresis energy method.
Fig. 10. (a) Variation of constraint ratio with number of cycles (2Nf) for high area fraction pearlite versus number of cycles for high area fraction pearlite under 125–500 � C; (b) Variation of hysteresis energy with fatigue life (2Nf) for different constrain ratios.
1) Elliptical ferrite clusters can be seen in microstructure of high ferrite cast iron, and ferrite clusters in high pearlite cast iron are chrysanthemum-like. Differences in the proportion of pearlite and ferrite lead to the difference of TMF properties. 2) Muti-source fatigues fracture is the main form of TMF failure. For high ferrite cast iron, the propagation zone locats within the cluster; for high pearlite cast iron, the propagation zone locats around the specimen. 3) By choosing mechanical strain amplitude and hysteretic energy as variables, high pearlite cast iron and high ferrite cast iron show different TMF life trends. In the hysteresis energy-TMF life curves, high pearlite cast iron has longer TMF life than high ferrite cast iron has. The different propagate zones lead to the different TMF life. 4) In logarithmic coordinates, the relationship between TMF life and constraint ratio is linear. Constraint coefficient and constraint exponent are proposed to measure the TMF life of materials. Constraint exponent reflects the sensitivity of materials to constraint ratio under TMF condition, while constraint coefficient reflects the thermal fatigue performance of materials.
References [1] Z.J. Ma, D. Tao, Z. Yang, et al., The effect of vermicularity on the thermal conductivity of vermicular graphite cast iron, Mater. Des. 93 (2016) 418–422. [2] R. O’Bourke, Cast iron: the engineered metal, Adv. Mater. Process. 159 (2001) 65–68. [3] M. Holtzer, M. G� orny, R. Da� nko, Microstructure and Properties of Ductile Iron and Compacted Graphite Iron Castings: the Effects of Mold Sand/metal Interface Phenomena, Springer, Berlin, 2015. [4] C.D. Rakopoulos, G.C. Mavropoulos, Experimental instantaneous heat fluxes in the cylinder head and exhaust manifold of an air-cooled diesel engine, Energy Convers. Manag. 10 (2000) 1265–1281. [5] C. Çetinkaya, An investigation of the wear behaviors of white cast irons under different compositions, Mater. Des. 6 (2006) 437–445. [6] K. H€ oschler, J. Bischof, W. Koschel, Thermo-mechanical analysis of an automotive diesel engine exhaust manifold, Struct. Integrity Soc. 29 (2002) 299–308. [7] A. Nitta, K. Kuwabara, Thermal-mechanical Fatigue Failure and Life Prediction, Elsevier Applied Science Publishers, High Temperature Creep-Fatigue, 1988, pp. 203–222. [8] M. Metzger, B. Nieweg, C. Schweizer, et al., Lifetime prediction of cast iron materials under combined thermomechanical fatigue and high cycle fatigue loading using a mechanism-based model, Int. J. Fatigue 53 (2013) 58–66. [9] F. Zieher, F. Langmayr, A. Jelatancev, et al., Thermal Mechanical Fatigue Simulation of Cast Iron Cylinder Heads, SAE Technical Paper, 2005. [10] R.W. Neu, H. Sehitoglu, Thermomechanical fatigue, oxidation, and creep: Part I. Damage mechanisms, Metall. Tran. A 20 (1989) 1755–1767. [11] R.W. Neu, H. Sehitoglu, Thermomechanical fatigue, oxidation, and creep: Part II. Life prediction, Metall. Tran. A 20 (1989) 1769–1783. [12] P. Skoglund, J. Elfsberg, N. Ipek, et al., Thermo-mechanical fatigue of grey cast iron for cylinder heads-effect of niobium, molybdenum and solidification time// materials science forum, Trans. Tech. Publ. 925 (2018) 377–384. [13] Y. Liu, Y.H. Chen, N. Sawkar, et al., A Thermo-Mechanical Fatigue Analysis on a Ductile Cast Iron Exhaust Manifold, SAE Technical Paper, 2018. [14] A.O. Abu, S. Eshati, P. Laskaridis, et al., Aero-engine turbine blade life assessment using the Neu/Sehitoglu damage model, Int. J. Fatigue 61 (2014) 160–169. [15] H. Sehitoglu, Thermo-mechanical Fatigue Life Prediction Methods. Advances in Fatigue Lifetime Predictive Techniques, ASTM International, 1992. [16] M.X. Zhang, J.C. Pang, Y. Qiu, S.X. Li, M. Wang, Z.F. Zhang, Thermo-mechanical fatigue property and life prediction of vermicular graphite iron, Mater. Sci. Eng. A 698 (2017) 63–72.
Acknowledgments The authors would like to thank Mr. Jing Long Wen and Dr. Cui Hong Li, Prof. Zhong Yang and Prof. Jian Ping Li for their helps of the fatigue experiments, SEM observations and specimen preparation. This work is supported by National Natural Science Foundation of China (NSFC) under Grant No. 51871224.
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Materials Science & Engineering A 771 (2020) 138617 [23] Y. Qiu, J.C. Pang, M.X. Zhang, et al., Influence of temperature on the high-cycle fatigue properties of compacted graphite iron, Int. J. Fatigue 112 (2018) 84–93. [24] M.T. Shi, Metal Materials and Heat Treatment, Shanghai Scientific and Technical Publishers, 2005. [25] S.S. Manson, Fatigue: a complex subject some simple approximation, Exp. Mech. 5 (1965) 193–226. [26] J. Park, D. Nelson, Evaluation of an energy-based approach and a critical plane approach for predicting constant amplitude multi-axial fatigue life, Int. J. Fatigue 22 (2000) 23–39. [27] R. Liu, Z.J. Zhang, P. Zhang, et al., Extremely-low-cycle fatigue behaviors of Cu and Cu–Al alloys: damage mechanisms and life prediction, Acta Mater. 83 (2015) 341–356. [28] S. Suresh, Fatigue of Materials, Cambridge University Press, Cambridge, 1998. [29] Z.F. Zhang, H.C. Gu, Plastic work model for fatigue damage and life prediction, Struct. Env. Eng. 3 (1998) 55–59.
[17] F. Bagnoli, F. Dolce, M. Bernabei, Thermal fatigue cracks of fire fighting vehicles gray iron brake discs, Eng. Fail. Anal. 16 (2009) 152–163. [18] X. Wu, G. Quan, R. MacNeil, et al., Thermomechanical fatigue of ductile cast iron and its life prediction, Metall. Mater. Trans. A 6 (2015) 2530–2543. [19] H. Zhang, Y.C. Wang, F. Liu, et al., Thermal-mechanical fatigue behavior and life analysis of cast Ni-base superalloy K417, J. Mater. Sci. Technol. 18 (2009) 176–180. [20] V.L. Diaconu, T. Sj€ ogren, P. Skoglund, et al., Influence of molybdenum alloying on thermomechanical fatigue life of compacted graphite irons, Int. J. Cast Metals Res. 25 (2012) 277–286. [21] C.L. Zou, J.C. Pang, M.X. Zhang, et al., The high cycle fatigue, deformation and fracture of compacted graphite iron: influence of temperature, Mater. Sci. Eng. A 724 (2018) 606–615. [22] Y. Qiu, J.C. Pang, C.L. Zou, et al., Fatigue strength model based on microstructures and damage mechanism of compacted graphite iron, Mater. Sci. Eng. A 724 (2018) 324–329.
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