The damage mechanism of tension-tension fatigue interaction with creep damage of the compacted graphite cast iron alloy at high temperatures

The tension-tension fatigue test of the compacted graphite cast iron (CGI) alloy was carried out by RDL100 universal testing at 500 °C and 550 °C, respectively. A tension-tension trapezoidal load is applied to the CGI specimen. Because of the time-dependent deformation at elevated temperatures, the stress–strain curve presents hysteresis loops, and the area of the hysteresis loop increases gradually with continuous cyclic loading and sustained loading times. Intergranular and transgranular cracks in the microstructure accelerate the CGI alloy fracture failure. The fatigue life is sensitive to the short loading time and decreases with the sustained loading time exponentially under the tension-tension fatigue condition. The short holding time has a great influence on the fatigue life of CGI. The fatigue behavior of CGI alloys and the influence of holding time on the fatigue life can be characterized by y = aexp(bx) (a and b are constants, can be fitted through the test data). In addition, the fatigue life of CGI alloy can be predicted by the ductility depletion method. But the equivalent stress amplitude needs to be modified to eliminate the effects of oxidation damage.


Introduction
The high power density (HPD) diesel engine is one of the advanced engines in the future.Compared with the traditional diesel engine, the volume and weight of HPD are reduced by more than 50%, but the rotation speed of the crankshaft and explosion pressure increase by 100% and 200%, respectively [1][2][3].As an essential hightemperature component, the cylinder head made of compacted graphite cast iron (CGI) alloys is usually experiencing 400 °C-500 °C and 20-30 MPa explosion pressure [4][5][6].When the engine is running, the service life of CGI alloy is greatly affected by irregular mechanical load changes and high temperature, often referred to as the start-operate-stop cycle.In the case of the cylinder head, when the engine is heated, the thermal expansion creates compression loads and leads to plastic deformation, creep and stress relaxation.Oppositely, tensile stress usually develops as the engine cools due to the accumulation of compressive inelastic strain at high temperatures.Therefore, the reliability at elevated temperatures of CGI has become a crucial point [7,8], and there are an increasing number of research papers about the properties of CGI alloys at high temperatures in the last two decades.
It is generally believed that the static strength of CGI alloy is closely related to the stability and service life at high temperatures, and has been used as an evaluation of the performance at elevated temperatures for a long time.Chao, Shao, and Selin have successively studied the tensile strength variation of CGI at high temperatures at first [9][10][11], they found the strength degradation of CGI alloy can be delayed by the dynamic strain aging at 200 °C-400 °C.However, when the temperature exceeds 400 °C, the interatomic diffuses faster and the dynamic strain aging disappears, which causes the strength decreasing rapidly.Then, Qiu analyzed the tensile damage mechanism of CGI at elevated temperatures [12].Both dynamic strain aging, precipitation strengthening, and strain strengthening can slow down the strength degradation of CGI below 400 °C.When the temperature exceeds 400 °C, the grain boundary slip becomes more active, and the intergranular damage becomes serious.In addition, high temperature leads to atomic diffusion faster, and the carbon atoms in the matrix will diffuse to the adjacent graphite, resulting in the graphite gradually growing.Pearlite in the matrix will gradually change from lamellar to granular [3].
However, with the wide application at high temperatures, the service condition of CGI alloy is becoming rigorous and complex damages happened in the microstructure due to the time-dependent plastic deformation.The intergranular cracks will present in the microstructure with increment of the temperature.Besides, with the increment of service temperature, the CGI alloys began to present time-dependent deformation during the fatigue test, which generates unique damage modes and produces the typical creep-fatigue interaction damage [13,14].It is not appropriate to evaluate the stability of high temperature service only by the strength of alloy [15].Therefore, more attention has been paid to the fatigue property of CGI at high temperatures.
As conducted by Qiu, the fatigue life of CGI mainly depends on the ratio of graphite to ferrite [16].The initial cracks formed in the ferrite cluster and increased gradually at first, and then rapidly expanded.In addition, the morphology of graphite and temperature has great effect on the fatigue damage evolution.As conducted by Hosdez [17], the fatigue crack can spread easily and propagate through the vermicular graphite breaking rather than spheroidal graphite.The crack growth rate of CGI is higher than that of spheroidal graphite cast iron (SGI).The effect of graphite shape on fatigue crack growth rate is obvious.In addition, the orientation of graphite can affect the direction of maximum stress, which has a great influence on the crack propagation mechanism adjacent the graphite particles.Besides, the fatigue behavior of CGI is also relative to the matrix.Graphite fracture seems to be the main mode of fatigue crack propagation and rack propagates over length equal to the vermicule size after the matrix/graphite interfaces debonding.Then, Kihlberg [15] has analyzed the thermalmechanical fatigue (TMF) properties of CGI and found the graphite morphology have a strong influence on the TMF performance.There are a function correlations between microstructural parameters and TMF properties.The area-weighted average graphite length, a, has a linear correlation with the TMF coefficient, C. Interestingly, he found no evident connection between matrix and TMF properties of CGI.
It is generally believed that materials mainly present time-dependent deformation when T/T m exceeds 0.3 or 0.5 (T, service temperature, T m , melting point).The vacancy diffusion is accelerated and dislocations can cross the obstructions easily.In our previous research results [18], the CGI alloys can present obvious creep deformation when the temperature exceeds 450 °C.The creep rate increases exponentially with temperature and stress.There are mainly three damage modes in the microstructure, such as intergranular voids, micro-cracks, and debonding cracking at the interface between graphite and matrix.Because of the three-dimensional connectivity of vermicular graphite, oxygen atoms can easily diffuse into the cracks, causing intergranular oxidation damage.These complex damages can cause complex evolution in the microstructure and accelerate the damage propagation of materials.Wu has analyzed the thermo-mechanical fatigue behavior of ductile iron exhaust pipes at high temperatures [19].It is found that there are mainly four damage modes during the fatigue test (fatigue, intergranular fracture, creep, and oxidation).In addition, creep damage can interact with fatigue crack, which affects the fatigue fracture mechanism under cyclic loading at high temperatures.Although there is a difference in the service temperature between the two alloys, the effect of creep on damage propagation is important.
Although initially used in non-high-temperature environments, CGI alloys are increasingly serviced at high-temperature conditions due to their excellent mechanical and physical properties, such as the heatresisting parts of advanced engines.Regardless of the application speed of the cycle load, CGI always has a certain degree of creep deformation when the temperature is great than 450 °C.Hence, the time-dependent deformation should be taken into account to evaluate the reliability of CGI at high temperatures during the fatigue test.The purpose of this paper is to investigate the influence of loading time on fatigue life by applying different loading time and evaluate the creep-fatigue interaction damage of the CGI alloys at elevated temperatures.

Experimental procedures
Becaues the thermal conductivity of the matrix decreases with the silicon contents [20,21].Hence, the silicon content of CGI alloys is controlled below 2% to get good thermal conductivity.The chemical compositon of CGI alloy is shown in table 1. Pig iron and 45 steel were melted in GGW-0.01 medium-frequency induction furnace and poured into casting ladle at temperature 1470 °C.The CGI melt was poured into sand mould and solidified to the wedge block after deterioration treatment by 75FeSi and RE-Mg-Ca respectively.The microstructure of the CGI alloy is shown in figure 1.As can be shown, the microtructure of CGI are mainly constist of graphite (black), pearilite (brown) and ferrite (white).The graphite is mainly present vermicular and is surrounded by a few ferrite.The matrix of CGI alloys mainly consists of pearlite.The tensile test was carried out on The CMT5105A electronic universal testing machine and the tensile test was processed according to GB/T 228-2002.The tensile specimen is shown in figure 2 and the tensile strength of experimental CGI at different temperatures are listed in table 2. When the temperature increases to 550 °C, the tensile strength decreases by 34%.The fracture of tensile sample is shown in figure 3, it can be seen that there is a river-like pattern in the fracture.
The creep-fatigue test was conducted in the RDL100 multi-functional testing device, as shown in figure 4(a).The trapezoidal loading was applied in the whole test, as shown in figure 4(b).The creep-fatigue test sample is shown in figure 5.The creep damage will happen at the prolongation of the maximum load holding stage (2-3 loading stage), and the holding time is set to 30 s, 60 s, and 90 s during the fatigue test, respectively.The fatigue damage occurs at the cyclic loading stage (1-2, 3-4).Two groups of creep-fatigue tests were carried out and stress amplitude is set to 15-150 MPa and 15-200 MPa respectively.The experimental parameters are shown in the table 3.Because the creep damage is prominent when the temperature exceeds 450 °C, the test temperature is set   to 500 °C and 550 °C.The extensometer was installed during the whole test to measure the strain values.The fatigue test was processed according to GB/T 2039-2012 and the relevant procedure of the experiment is referred to the previous article [7,18].After the creep-fatigue test, the fracture morphologies of the sample will be observed by SEM, the specimen after test is shown in figure 6.After the creep fatigue test, the sample was cut axially by electric sparker, grinded with SiC sandpaper, and etched with 4% nitric acid solution to obtain the metallographic sample.The samples were then observed by scanning electron microscopy.

Hysteresis loops of creep-fatigue test 3.1.1. The stress-strain curves of CGI during the fatigue test
With the increase of temperature, the time-dependent deformation of materials is gradually significant, resulting in the 'hysteresis' phenomenon.As shown in figure 7, the stress-strain curves of CGI during the fatigue test under 15-150 MPa without holding time at 500 °C and 550 °C are presented.The stress-strain curves present 'hysteresis loops', which is mainly caused by the time-dependent deformation under cyclic loading at high temperatures.Because of affected by the tension-tension cyclic loading, the hysteresis loop is not completely closed and moving to the right of the X-axis.It can be seen that the area of hysteresis loops increases with cyclic loading and temperature gradually.
When the maximum cyclic loading is prolonged, the obvious time-dependent deformation presents, and the creep damage will happen in the microstructure.The stress-strain curves of CGI with different holding times at 550 °C are shown in figure 8.The hysteresis loops with holding times present an obvious platform at the maximum load holding stage.The gap in the hysteresis loops increases gradually with continuous cyclic loading and the prolongation of maximum cyclic loading.

Strain energy density of CGI during the fatigue test
The strain energy density is defined as the area of hysteresis loops, which can reflect the damage accumulation in the sample.The strain energy density under 15-150 MPa with holding 90 s at 500 °C and 550 °C is shown in figure 9(a).It can be seen that the strain energy density increases with temperature and continuous cycling.
When the holding time increases, the strain energy density mainly presents three stages in the curves, as shown in figure 9(b).In the first stage, the strain energy density increases with cycling gradually, but the rising rate is slowing down gradually, which may relate to the strain hardening during the cycling test.In the second stage, the effect of cyclic loading gradually stabilizes and the strain energy density is mainly present constant with cycling.
It can be regarded as the process of damage accumulation during the fatigue test.At the last stage, the strain  energy density increases with cycling again and the rising rate is increasing rapidly, which indicates rapid damage accumulation in the microstructure.
In addition, when the temperature rises to 550 °C, the strain energy density generated by stress range (15-150 MPa) is greater than that of 500 °C generated by stress range (15-200 MPa), as shown in figure 9(c).Compared with stress, temperature has more influence on the plastic deformation of GCI alloy.It can also be seen from table 4 that the CGI fatigue life is shorter under the condition of high temperature and low stress range.This indicates that the CGI alloy will present larger plastic deformation under the condition of low stress at high temperatures.

The effect of different holding times on the creep-fatigue life
The fatigue life of CGI under 15-150 MPa with the different holding times at 550 °C is shown in figure 10.With the increment of holding time, the fatigue life decreases exponentially and the relationship follows the below function:  It can be seen that when the holding time increases to a certain value, the declining trend of fatigue life presents gentle.This shows that the short holding time has a great influence on the fatigue life of CGI at elevated temperatures.It should be emphasized that the aim of the fitting procedure is not to make predictions, but rather to characterize the fatigue behavior of CGI alloys and the influence of holding time on the fatigue life.If the holding time is extended indefinitely, the CGI cyclic fatigue test is equivalent to the creep test.However, according to our previous research results [18], the creep life of the same CGI sample is significantly longer than the fatigue life affected by different holding times, which is obviously not consistent with the equation (2).Therefore, the equation (2) only describes the fatigue behavior and influence of holding times on fatigue life under cyclic load.

The microstructure damage of CGI during the creep-fatigue test 3.3.1. Cracks during the fatigue test
Affected by the trapezoidal cyclic loading, both creep and fatigue damage happen in the microstructure.The intergranular crack, the stress amplitude is 15-150 MPa with holding 30 s, in the ferrite boundary is shown in figure 11(a), which is the typical creep damage at high temperatures.Because of the stress concentration at the tip of graphite, the transgranular crack happened in the ferrite, the stress amplitude is 15-150 MPa with holding 60 s, as shown in figure 11(b), which usually occurs under fatigue or high stress creep conditions.It can be concluded that graphite is the crack initiation.The cracks grow up gradually and coalesce with adjacent graphite, the stress amplitude is 15-150 MPa with holding 90 s, as shown in figure 11(c).Due to low strength, the crack propagates along the ferrite preferentially.When the crack size increases to the critical value, it directly penetrates the pearlite, the stress amplitude is 15-200 MPa with holding 90 s, as shown in figure 11(d).It can be seen that with the increase of stress amplitude and the extension of loading time, the crack transforms from intergranular to transgranular mechanism.

The fracture morphology of CGI after the creep-fatigue test
The morphologies of creep-fatigue fracture are shown in figure 12.The fatigue fractography consists of several different zones, including fatigue crack initiation, slow, fast propagation and final fracture.However, the fracture of CGI mainly present crack initiation and final fracture according to figure 12(a).The morphology of the crack initiation is relatively flat, and there are secondary cracks, as shown in figure 12(b).The microstructure morphology of the final fracture zone is fluctuant and rough.The matrix near the graphite is mainly consisting of ferrite and the morphology presents some torn edges and typical ductile fracture partly, as shown in figure 9(c).In addition, some oxide particles present in the fracture, as shown in figure 12(d).In additon, there are oxidized particles in the fracture, as shown in figure 12(e).Firstly, the test temperature is directly related to the damage model.In our previous research, when the temperature is greater than 450 °C, that is, T/T m exceeds 0.5 (T is the test temperature, T m is the melting point of CGI alloys), the deformation mechanism of CGI has changed to the grain boundary sliding stage from the slip band stage.The CGI alloys can present obvious time-dependent deformation and the creep damages are inevitable in the microstructure.Creep micro-cracks are usually connected with graphite and the propagation of the cracks is usually accelerated by the stress concentration at the tip of the graphite.Meanwhile, the oxygen atoms can diffuse to the inner matrix through the vermicular graphite, which can cause oxidation cracks and accelerate the propagation of cracks.
In addition, the fatigue damage mechanism is changing with the increment of temperature.According to Qiu's research results [22], the fatigue cracks initiate at the graphite debonding at first, and then the cracks mainly propagate through the ferrite at room temperature.Fatigue crack propagation is through the coalescence of adjacent micro-crack induced by graphite debonding.When the temperature increases gradually, the plastic deformation mode of ferrite evolves from slip band passing the grain to grain boundary sliding, which causes a different crack propagation model.It can be seen that the ferrite is a weak point in the crack initiation stage.There are mainly two reasons explaining the phenomenon.
Firstly, because the cementite in the pearlite can hamper the dislocation movement effectively, pearlite has greater mechanical strength than ferrite.Based on the minimum energy criterion of crack propagation, the cracks usually propagate along the ferrite.Secondly, the graphite is surrounded by a few ferrite and the stress concentration of ferrite in the adjacent graphite is serious, which promotes the plastic deformation accumulated and damage initiation in the ferrite.We can assume that the shape of vermicular graphite is an ideal ellipse.According to the study of Qiu [23], the stress concentration coefficient at the tip of graphite can be expressed by: ( ) α is the stress concentration coefficient, A and B are the long and short axis of the ellipse respectively, and A/B is the aspect ratio of graphite.According to previous studies by Qiu, the aspect ratio of vermicular graphite will increase with the temperature and the duration time at the elevated temperature, which means the stress concentration at the tip of graphite is becoming serious.Hence, the damage is more likely to occur in ferrite.

Creep-fatigue damage mechanism
There are mainly three stages of the creep-fatigue damage evolution, as shown in figure 13.At first, the interface between graphite and matrix is fractured easily under continuous cyclic loading at high temperatures.Graphite debonding caused by mechanical and thermal stress is the initial source of crack propagation in both creep and fatigue conditions.It can be seen from our previous research results that the interfacial debonding is more sensitive to the temperature.The interface between graphite and matrix is prone to crack at high temperatures, even under low stress.Because of continuous cyclic loading, there is serious plastic deformation in the matrix.Then, crack propagation is through the coalescence of adjacent micro-cracks induced by graphite debonding and the intergranular creep damage in the eutectic cells.The micro-cracks coalesced one by one to form a large crack and the stress concentration coefficient at the crack tip increased gradually.Finally, the cracks penetrate through the eutectic cells and propagate through the intergranular creep damages or the transgranular cracks in the pearlite caused by continuous cyclic loading.

The creep-fatigue life prediction
According to the ductile depletion theory, the microstructure damages are caused by viscous flow at elevated temperatures.Fatigue and creep damage are caused by the intracrystalline and intergranular ductility depletion, respectively, which is mainly resulted from the plastic strains.The superposition of the two damages leads to the material fracture eventually, the judgment is as follows: v d is the dynamic viscosity and equals the tensile stress multiplied by cycling time.T n is the material toughness and equal to the ductility multiplied by cycling strength.Because trapezoidal loading is used in the test, it can be considered that creep deformation only occurs in the latter half and upper retaining stage of loading.According to Fan's results [24], the plastic deformation presents when the stress reaches to ( ) s s s -. max max a s max is the cyclic maximum stress and s a is the cyclic stress amplitude.v d can be expressed as follows: s v is the loading rate, t h is the holding time and ∆s eqv is the equivalent stress amplitude.Assuming there is a power function relationship between cycle time and cycle life.
∆e in is the inelastic strain range of half-life, e v m is the mean strain rate of half-life and N f is the fracture life of the material.The life prediction equation can be obtained by combining equation (7) and equation (8) Table 5 shows the test parameters of creep-fatigue interaction, and parameters A, m, C in equation ( 9) can be obtained.The fitting results are shown in figure 14.It can be seen that the fitting accuracy is higher at 550 °C, while the data are scattered and the fitting accuracy is low at 500 °C.The effect of oxidation on plastic deformation is not considered in this prediction model and the low fitting accuracy may be related to the oxidation damage at high temperatures.Because of higher temperature, the creep-fatigue life of CGI alloy decreases dramatically at 550 °C under the same stress amplitude, which leads to a shorter residence time and a lower percentage of oxidative damage at high temperature.Besides, the variation of elastic modulus of CGI alloy at high temperature is different from that of 1.25Cr0.5Mosteel used in the prediction model, which leads to the difference in equivalent stress amplitude and the decrease in data fitting accuracy.As for the effect of oxidation on the damage evolution of CGI alloy and the mechanism of oxidative damage, it needs analysis systematically for further study.
(1) Inelastic strain range of half-life ∆e in is the strain difference of half-life between point 4 and point 1 in the loading waveform, as shown in figure 2 ( ).After taking its derivative the e v m is obtained 500

Conclusions
The creep-fatigue behavior of CGI was analyzed and observed through the tension-tension fatigue test.The fatigue damages were present in the pull alternating load stages and the creep damage occurs in the holding stages.The two kinds of damage will occur and interact in the microstructure at the same time.The main conclusions of the paper are as follows: (1) Owing to the time-dependent deformation, the stress-strain curve will present hysteresis loops, and the area of the hysteresis loop increases in three stages gradually with continuous cyclic loading and sustained load time at high temperatures.That is I decelerating stage, II constant stage, and III acceleration stage, respectively.The fatigue life decreases with the sustained load time exponentially, which indicates that the fatigue life is sensitive to the short sustained load time.
(2) The creep-fatigue fracture can be divided into the source and transient fracture approximately.The fatigue source is flat, but the transient fracture is relatively rough.There are both creep damage and fatigue crack in the microstructure.Intergranular and transgranular cracks can be found in ferrite and pearlite.The creep damages and fatigue cracks interact with each other, forming cracks through the material and causing fracture failure.
(3) The short holding time has a great influence on the fatigue life of CGI.The fatigue behavior of CGI alloys and the influence of holding time on the fatigue life can be characterized by y = aexp(bx).The creep-fatigue life of CGI alloy can be predicted by the ductility depletion method.However, because of the effect of oxidation on the damage evolution of CGI alloy, the prediction accuracy at 500 °C is relatively low.The prediction model needs to be fixed and the equivalent stress amplitude of CGI needs to be modified accurately.

Figure 1 .
Figure 1.Microstructure of the experimental CGI alloy.

Figure 2 .
Figure 2. Schematic diagram of tensile test sample.

Figure 4 .
Figure 4.The test device (a) and loading waveform of the test (b).

Figure 5 .
Figure 5. Diagram of test sample for CGI.

Table 4 .y
Fatigue cycle to failure affected by different stress amplitudes and holding times at 500 °C and 550 °C.presents the fatigue life, x presents holding time, a and b are constant.Through data fitting, the equation (1) is expressed below:

Figure 10 .
Figure 10.The fatigue life under 15-150 MPa with different holding times at 550 °C.

4 .
Analyses and discussions 4.1.The effect of temperature on the propagation of creep-fatigue cracks Affected by cyclic loading at high temperatures, both creep and fatigue cracks happened in the microstructure of CGI.These two different crack modes can cause the specific damage mechanism of the CGI alloys during the creep-fatigue test.

1 Figure 14 .
Figure 14.Data fitting by ductile depletion method: (a) fitting of parameters, (b) contrast of calculate data and test data.

Table 2 .
Strength of experimental CGI.

Table 3 .
The experimental parameters of creep-fatigue test.
2) Mean strain e m can be calculated by hysteresis loops of each cycle (