Effect of multiphase microstructure on fatigue crack propagation behavior in TRIP-assisted steels

Journal Pre-proofs Effect of multiphase microstructure on fatigue crack propagation behavior in TRIP-assisted steels Chenghao Song, Haoliang Wang, Zhenzhong Sun, Zhengying Wei, Hao Yu, Haibin Chen, Yanlin Wang, Jun Lu PII: DOI: Reference:

S0142-1123(19)30529-8 https://doi.org/10.1016/j.ijfatigue.2019.105425 JIJF 105425

To appear in:

International Journal of Fatigue

Received Date: Revised Date: Accepted Date:

16 June 2019 9 October 2019 16 December 2019

Please cite this article as: Song, C., Wang, H., Sun, Z., Wei, Z., Yu, H., Chen, H., Wang, Y., Lu, J., Effect of multiphase microstructure on fatigue crack propagation behavior in TRIP-assisted steels, International Journal of Fatigue (2019), doi: https://doi.org/10.1016/j.ijfatigue.2019.105425

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Effect of multiphase microstructure on fatigue crack propagation behavior in TRIP-assisted steels Chenghao Songa,b, *, Haoliang Wanga, Zhenzhong Suna, Zhengying Weib, Hao Yuc, Haibin Chena, Yanlin Wanga, Jun Luc a School

of Mechanical Engineering, Dongguan University of Technology, No.1 Daxue Road, Songshan Lake, Dongguan 523808, Guangdong Province, P.R. China

bSchool

of Mechanical Engineering, Xi'an Jiao Tong University, No.28 Xianning West Road, Xi'an

cSchool

of Materials Science and Engineering, University of Science & Technology Beijing, No.30

710049, Shaanxi Province, P.R. China Xueyuan Road, Haidian District, Beijing 100083, P.R. China *Corresponding

author. Tel.: +86 0769-22862106

E-mail address: [email protected] Abstract The effect of various multiphase microstructures on the fatigue properties of intercritical annealing,

quenching

and

partitioning

(I&Q&P)

steel,

transformation-induced

plasticity

(TRIP)-assisted annealed martensite (TAM) steel and TRIP steel was investigated by S-N curve, fatigue crack growth (FCG) rate and in-situ scanning electron microscopy tests. The fatigue limits of I&Q&P, TAM and TRIP steels, determined by a derivation of the Stromeyer relationship, are 670 MPa, 770 MPa and 795 MPa, respectively. The region II of FCG curve was fitted by Paris and exponential models, and the result indicates that I&Q&P steel has the highest FCG rate, followed by TAM steel and TRIP steel. In I&Q&P steel, fatigue crack mainly propagates along the interfaces between ferrite and martensite or ferrite and martensite and austenite islands, resulting in the presence of many secondary cracks; in TAM steel, the fatigue crack propagation (FCP) can be retarded when the crack passes through the mixed microstructure containing annealed martensitic laths and film-like retained austenite at an angle (not parallel); in TRIP steel, the crack branching and interlocking can hinder the FCP effectively, benefitting from bainite densely distributing in ferrite matrix as strengthening phase and the two phases having almost identical grain size. Therefore, the multiphase microstructure of TRIP steel has the best effect on retarding FCP among the three steels. The findings are essential for the optimization of multiphase microstructure in designing a steel with excellent fatigue properties. Keywords: Multiphase microstructure; Steel; Fatigue limit; Martensite; Fatigue crack propagation

1

Nomenclature Abbreviation

Full name

AHSS

advanced high-strength steel

Abbreviation f

RA

Full name volume fraction of RA

UTS

ultimate tensile strength

wc

carbon content of RA

TRIP

transformation-induced plasticity

HV

Vickers hardness

RA

retained austenite

σa

stress amplitude

TEL

total elongation

Nf

fatigue life

YS

yield strength

σf´

fatigue strength coefficient

I&Q&P

intercritical annealing, quenching and partitioning

n

fatigue strength exponent

TAM

TRIP-assisted annealed martensite

σfl

extrapolated fatigue limit

PSE

product of strength and elongation

μ

fitting coefficient

FCP

fatigue crack propagation

λ

fitting exponent

FCG

fatigue crack growth

ΔK

stress intensity factor

SEM

scanning electron microscopy

EBSD

electron backscatter diffraction

TEM

transmission electron microscope

XRD

X-ray diffraction

HCF

high cycle fatigue

1. Introduction Since the development of the third generation advanced high-strength steel (AHSS) so far, scientists have paid great attention to elucidating the origin of their combination of high strength and good ductility [1–8]. It is well established that martensite and bainite are responsible for increasing ultimate tensile strength (UTS) up to the level of above 1 GPa due to their high dislocation density [9– 13]. The occurrence of transformation-induced plasticity (TRIP) effect in retained austenite (RA) can increase work-hardening rate and delay the onset of necking, thus contributing transformation strain to total elongation (TEL) [14–19]. In addition to strengthening phases (martensite and bainite) and RA, a certain amount of soft ferrite phase can coordinate the contradiction between strength and ductility. Tan et al. [20] and Xu et al. [21] reported that an introducing of about 40 vol. % ferrite can effectively enhance the TEL of quenching and partitioning steel without significant reduction of UTS and yield strength (YS), because the ferrite can facilitate the strain accommodation among different phases [14]. Therefore, a multiphase microstructure containing strengthening phase, soft phase and RA can offer a good combination of strength and ductility. The following will focus on the microstructure and mechanical properties of three typical 3rd generation AHSSs, including intercritical annealing, quenching and partitioning (I&Q&P) steel, TRIP-assisted annealed martensite (TAM) steel and TRIP steel. The salient feature shared by the three AHSSs is the diversity in microstructure. I&Q&P steel is one of the most promising and innovative 3rd generation AHSSs due to over 30 GPa·% product of strength and elongation (PSE) and low-cost alloying elements, and its microstructure comprises martensite, intercritical ferrite and RA [2]. TAM steel shows an outstanding mechanical property with PSE higher than 40 GPa·% [22], benefitting from its constituent phases consisting of bainite, annealed martensite and RA, which are obtained through a series heat treatments composed of fully austenization, intercritical annealing and isothermal holding in bainitic transformation region [22]. 2

TRIP steel, whose strength and ductility can be improved by forming ultra-fine grain [23], also consists of several phases containing bainite, intercritical ferrite and RA. The integrated effect of multiphase microstructure can significantly improve the mechanical properties of AHSSs. The potential application of 3rd generation AHSS mainly lies within automotive sector, especially in load-bearing structures, which are commonly subjected to cyclic load, non-static strength, and thus fatigue failure is one of the key reasons for traffic accidents. To further exploit the potential of 3rd generation AHSS in automotive applications, the fatigue properties of 3rd generation AHSSs, e.g., I&Q&P steel, TAM steel and TRIP steel mentioned above, require in-depth investigation. However, little work has been done so far, especially on the effect of multiphase microstructure on fatigue crack propagation (FCP) behavior, which is of significance in the development and application of 3rd generation AHSS. The above three typical 3rd generation AHSSs all contain a certain amount of RA, which plays an important role in retarding FCP. When fatigue crack extends to the vicinity of RA, the stress field near crack tip can induce martensitic transformation, thus blunting the crack tip, absorbing much energy used for FCP and relieving stress concentration [24]. However, the occurrence of TRIP effect has a negative effect due to volume expansion and shear strain from martensitic transformation, which reduces the deformation coordination between martensite and adjacent phases [25], and consequently results in crack propagating along phase interfaces [26]. Therefore, the role of RA on FCP behavior deserves further investigation. Up to now, the effect of microstructure on the FCP behavior of ferrite-pearlite (FP) and ferrite-bainite/martensite (dual phase, DP) steels has been widely investigated. It is found that the second strengthening phase, e.g., martensite or bainite, dispersed in soft ferrite matrix, can more effectively decrease fatigue crack growth (FCG) rate compared with that of FP steel [27–31]. Nevertheless, there are few studies about the effect of multiphase microstructure on FCP behavior. In present study, the different multiphase microstructures of three typical 3rd generation AHSSs were compared using scanning electron microscopy (SEM), electron backscatter diffraction (EBSD) and transmission electron microscope (TEM). The fatigue properties of the three steels were investigated using S-N curve and FCG rate tests. In addition, the effect of various multiphase microstructures on FCP behavior was analyzed in detail using in-situ SEM observation. The current work provides a comprehensive understanding of the relationship among multiphase microstructure morphology, FCP path and fatigue fractography, and guidelines for designing a steel with excellent fatigue properties. 2. Experimental procedure

2.1 Materials and heat treatments The chemical compositions of the three investigated steels are given in Table 1, and the thicknesses of the as-received cold-rolled sheets are all 2 mm. The microalloying element vanadium was added in TAM and TRIP steels to make the three steels obtain almost identical UTS. The phase transformation

temperatures

of

the

three

steels,

measured

by

dilatometry

(DIL805A,

BAHR-Thermoanalyse GmbH, Hullhorst, Germany), are also shown in Table 1. It can be seen that Ac3 and Ms are both directly proportional to vanadium content, which may be related to prior austenite grain size [32]. Different heat treatment processes on the three cold-rolled steels were performed in a 3

continuous annealing simulation equipment (CCT-AY-II, Ulvac-Riko INC., Tokyo, Japan), as shown in Fig. 1. The selection of heat treatment process parameters for each steel was described in our previous works [2, 8, 23], and it is not shown here for brevity. Table 1 Chemical composition and transformation temperatures of the three investigated steels Steel

Chemical composition (wt. %)

Transformation temperature (°C)

C

Si

Mn

V

N

Ac1

Ac3

Ms

I&Q&P

0.2

1.4

2.0

0

0.002

744

865

237

TAM

0.2

1.5

2.1

0.05

0.003

740

870

278

TRIP

0.2

1.5

2.1

0.20

0.005

750

910

330

Fig. 1 Schematic diagrams of heat treatment processes corresponding to the three investigated steels, (a) I&Q&P steel, (b) TAM steel and (c) TRIP steel. 2.2 Microstructural and mechanical characterization X-ray diffraction (XRD) tests were performed in a Bragg-Brentano diffractometer (SmartLab, Rigaku Corporation, Tokyo, Japan) with Cu-Kα tube using a step size of 0.02° and a scan speed of 2°/min, operating at 40 kV, 150 mA. The volume fraction of RA (f RA) was calculated by a comparison method of the integrated intensities, including the (200)γ, (220)γ and (311)γ peaks, and the (200)α and (211)α peaks [33]. The carbon content of RA (wC) was calculated based on the (220)γ and (311)γ peaks [1]. The volume fractions of the other phases were determined by color etching with LePera reagent [34]. The microstructures were analyzed using field emission SEM (Zeiss ULTRA 55, Zeiss Ltd., Braunschweig, Germany), operating at 20 kV, after the specimens were ground, polished and etched in 4

a 4 vol. % nital solution. EBSD tests were performed in the FE-SEM under the following conditions: tilt angle of 70° and step size of 0.03 μm, and then the data were post-processed using Channel 5 software. The specimens for XRD and EBSD tests were first mechanically polished, and then electro-polished in 5 vol. % perchlorate alcohol solution at 30 V for 15 s. TEM experiments were performed in a JEM-2100 (HR) (JEOL Ltd., Tokyo, Japan) microscope, operating at 200 kV. The TEM specimens were first ground to a thickness of 70 μm, and then punched to the discs with 3 mm diameter. Finally, they were thinned to 40 μm, subsequently electro-polished in a twin jet electro-polisher (MTP-1A, Shanghai Jiaoda Electromechanical Technology Development Co., Ltd., Shanghai, China) using a solution of 5 vol. % perchlorate alcohol at 50 V and a temperature of −35 °C for 2 min. The grain sizes of the various phases of the three steels were statistically measured by different methods, in which the grain size of RA was measured by EBSD, the thickness of annealed martensitic lath of TAM steel was determined by TEM, and the ones of the other phases were measured using color etched micrographs. The tensile tests were carried out at room temperature, with the axis parallel to the rolling direction and a crosshead speed of 3 mm/min, using a universal testing machine (WDW-2000D, Shanghai Xieqiang Instrument Technology Co., Ltd., Shanghai, China), and the tensile properties were the averages of three samples for each steel. Hardness tests were performed in a Vickers tester with a load of 300 gf, and the Vickers hardness (HV) was the average of 10 measurements for each specimen. 2.3 Fatigue testing The stress-controlled high cycle fatigue (HCF) tests with a frequency of 100 Hz were performed in a high frequency fatigue test machine (Amsler 100 HFP 5000, Amsler Company, German) at room temperature. The stress amplitudes were different for the three investigated steels, as shown in Fig. 6, and at least three specimens were evaluated at each stress level. Fig. 2 (a) shows the plate specimen geometry for HCF test, and the thickness is 2 mm. FCG rate tests with a frequency of 10 Hz were performed in an electro-hydraulic servo testing machine (MTS 810, MTS Systems Corporation, Eden Prairie, USA) at ambient temperature. Compact tension specimens were machined to the dimension (see Fig. 2 (b)), and the FCG direction was perpendicular to the rolling direction. Constant stress-controlled fatigue tests with a frequency of 10 Hz were performed in an SEM chamber equipped with an electro-hydraulic servo testing machine (SS550, Shimadzu Corporation, Kyoto, Japan). Fig. 2 (c) shows the specimen geometry for in-situ SEM test with the length parallel to the rolling direction, in which a notch with 0.3 mm in width and 0.45 mm in length was introduced by electro discharge machining, so that the crack growth direction was transverse to the rolling direction. Before in-situ SEM testing, the sample surface near the notch was ground, polished and etched by a 4 vol. % nital. The above three fatigue tests all used a constant amplitude sinusoidal waveform loading with a stress ratio of R=0.1.

5

Fig. 2 Specimen geometries for (a) HCF, (b) FCG rate and (c) in-situ SEM tests (in mm) 3. Results 3.1 Mechanical properties and microstructures The tensile properties of the three steels are summarized in Table 2. It can be seen that the PSE of the three steels are all above 30 GPa·%, which indicates that they satisfy the requirement of 3rd generation AHSSs. The UTS and TEL of the three steels are almost identical, but YS determined by the 0.2 % offset plastic strain shows large difference. I&Q&P steel shows the largest YS and yield ratio among the three steels, followed by TAM and TRIP steels having almost identical tensile properties. The elastic limits and HVs of the three steels are also listed in Table 2, and it can be seen that I&Q&P steel has the largest elastic limit, and TAM and TRIP steels have higher HVs than the one of I&Q&P steel, which may be caused by precipitation strengthening. Fig. 3 (a) shows the representative engineering stress-strain curves of the three steels. I&Q&P and TAM steels exhibit continuous yielding phenomenon, while TRIP steel shows a discontinuous one, as marked by red rectangle in the inset of Fig. 3 (a), possibly due to the existence of more ferrite fraction 6

(see Table 3) and carbide precipitation [35]. The f RA and wC of the three steels are shown in Table 3, and the XRD patterns are shown in Fig. 3 (b). It can be seen that f RA and wC of the three steels are almost identical. Fig. 4 (left) shows the optical micrographs by color etching, where in I&Q&P steel, ferrite appears in yellow color, and martensite and RA in white; in TAM steel, annealed martensite in yellow and bainite in reddish brown, as indicated by yellow and red arrows, respectively, and RA in white; in TRIP steel, ferrite in yellow, bainite in blue and RA in white. The various multiphase microstructures of the three steels were further confirmed by SEM, as shown in Fig. 4 (right). In addition to RA, the volume fractions of the other microstructural components were statistically analyzed based on 10 randomly photographed images, and the results are listed in Table 3. The grain sizes of various multiphase microstructures of the three steels were statistically measured, and the results are shown in Table 4. From Fig. 4 and Table 4, it can be seen that in I&Q&P steel, the small martensite is dispersed in the large ferrite matrix; in TAM steel, the bainite is dispersed in the annealed martensitic lath; in TRIP steel, the bainite densely distributes in the ferrite matrix and their grain sizes are almost identical. Table 2 Mechanical properties of the three investigated steels Elastic limit (MPa)

TEL

Yield ratio

HV

31.9±1.5

0.74

363±3

28.6±0.8

30.3±1.5

0.63

378±4

27.7±0.8

30.2±1.5

0.61

384±4

Steel

UTS (MPa)

YS (MPa)

I&Q&P

1080±20

800±16

530±10

29.5±0.8

TAM

1060±20

665±13

337±7

TRIP

1090±20

660±13

343±7

(%)

PSE (GPa·%)

Fig. 3 (a) and (b) showing representative engineering stress-strain curves and XRD patterns of the three investigated steels, respectively. Table 3 Volume fractions of various multiphase microstructures and wc of the three investigated steels Bainite

Annealed

Ferrite

Martensite

I&Q&P

0.400±0.025

0.467±0.030

––

––

0.133±0.005

1.13±0.02

TAM

––

––

0.350±0.018

0.516±0.032

0.134±0.005

1.16±0.02

TRIP

0.460±0.030

––

0.396±0.025

––

0.144±0.005

1.16±0.02

7

martensite

RA

wc (wt. %)

Steel

Fig. 4 Optical (left) and SEM (right) micrographs of (a) I&Q&P steel, (b) TAM steel and (c) TRIP steel. Table 4 Grain sizes of various multiphase microstructures of the three investigated steels (μm) Steel

Ferrite

Martensite

Bainite

Annealed martensitic lath thickness

RA

I&Q&P

4.0±0.4

2.0±0.2

––

––

0.21±0.02

TAM

––

––

2.2±0.2

0.20±0.02

0.22±0.02

TRIP

2.8±0.3

––

2.4±0.2

––

0.33±0.04

To further analyze the characteristics of various multiphase microstructures of the three steels, TEM and EBSD tests were performed. Fig. 5 (left) displays the EBSD micrographs with combined BCC band contrast and FCC phase maps, in which ferrite and annealed martensite appear in bright gray color, martensite and bainite in dark gray and RA in blue. In TAM steel, annealed martensite originates from the tempering of lath martensite during partial austenization, and thus it is essentially soft intercritical ferrite phase. In the three steels, the BCC matrix contains soft phases (ferrite and annealed 8

martensite) and strengthening phases (martensite and bainite), and they can be distinguished from each other according to their different image quality (IQ) values from EBSD maps. The strengthening phase has a low IQ value due to its high dislocation density, and thus it shows dark gray. Fig. 5 (a) shows the microstructure of I&Q&P steel, in which lath martensite is dispersed in the ferrite matrix, and RA exists within ferrite, among martensitic laths and at grain boundaries, which is consistent with the results of our previous work [2]. In TAM steel, annealed martensitic laths are separated by film-like RA, and bainite is mainly located at prior austenite grain boundaries, as shown in Fig. 5 (b). Fig. 5 (c) shows the microstructure of TRIP steel, in which bainite distributes in the ferrite matrix, and a lot of nano-precipitates can be observed within ferrite, as indicated by red triangles, which may result in the discontinuous yielding and higher HV.

Fig. 5 TEM (left) and EBSD (right) micrographs of (a) I&Q&P steel, (b) TAM steel, and (c) TRIP steel. EBSD micrographs show combined BCC band contrast and FCC phase maps, in which soft phase appears in bright gray color, strengthening phase in dark gray and RA in blue. 3.2 S-N curves of the three investigated steels S-N curves of I&Q&P, TAM and TRIP steels are shown in Fig. 6 (a), (b) and (c), respectively, in which circles stand for the fatigue data of broken samples, and red arrows indicate the data of the unbroken samples surviving 107 cycles. It is well-known that the Basquin equation [36] can well 9

describe the relationship between stress amplitude (σa) and fatigue life (Nf) in the stress-controlled fatigue tests, which is given as below: σ a  σ f ' (2N f )n

(1)

where σf´ represents the fatigue strength coefficient (positive number) and n represents the fatigue strength exponent (negative number). From the equation (1), when Nf approaches infinity, σa trends to zero. However, Stromeyer [37] suggested that fatigue limit exists in an infinite number of stress cycles; therefore, the equation (1) cannot reveal the true fatigue limit. In general, the stress amplitude at which the samples endured 107 cycles was defined as fatigue limit [30, 31, 38]; however, fatigue strength can decrease steadily beyond the knee point of S-N curve in the range of high cycles (>107) [39], and thus the definition of fatigue limit may be inappropriate. The Stromeyer model [37] can exhibit the true fatigue limit and the relationship between σa and Nf. In the present work, the experimental results show practically straight lines in the coordinates of (106/Nf)0.25 and σa, and thus here a derivation of the Stromeyer model was adopted as follows: σ a  σ fl +μ(N f ) λ

(2)

where σfl represents the extrapolated fatigue limit, μ represents a coefficient affecting the endurance under severer stresses and λ represents the fitting exponent (λ=−0.25 in the original Stromeyer model). In order to better analyze the relationship between σa and Nf, the equation (2) can be transformed to the following form: lg N f  a  b lg( σ a  σ fl )

(3)

where a= −lgμ/λ and b= −1/λ. According to the equation (3), S-N curves and fitting formulas were obtained, as shown in Fig. 6 (a–c), and the fitting parameters are given in Table 5. It can be seen that the derivation of the Stromeyer model can offer a good agreement with the experimental results. The fatigue limits of I&Q&P, TAM and TRIP steels are 670, 770 and 795 MPa, respectively, which are higher than the ones of the steels having almost identical level of strength and ductility [38, 40, 41]. From Fig. 6 (d), it can be seen that fatigue limit is inversely proportional to YS and yield ratio. Fleck et al. [42] reported that fatigue limit should be directly proportional to YS, and the abnormal phenomenon may be caused by cyclic hardening. Moreover, the fatigue limits of TAM and TRIP steels are higher than their YS, which may be also due to the cyclic hardening as well as the existence of precipitates [43, 44]. In TRIP steel, stress concentration should be prone to occur at the interfaces between ferrite and bainite during cycle fatigue testing, resulting in FCP along the interfaces; however, in the present work, more vanadium content was added in TRIP steel to enhance the strength of ferrite matrix (see Fig. 5 (e)) and improve the plastic accommodation between soft and strengthening phases, which is the one of the main reasons for TRIP steel having the highest fatigue limit. Due to the fatigue limit located in infinite cycle fatigue zone, the representative fatigue strengths at 107 cycles (σ1) and 2×106 cycles (σ2) are given in Table 5, and it can be seen that they are still higher than the ones of other steels [38, 40, 41], and TRIP and TAM steels have the higher σ1 and σ2 compared with the ones of I&Q&P steel. In high-cycle regime, a decrease of fatigue strength can occur with increasing cycles, e.g., after the knee point of S-N curve, a decrease per decade is below 5 % for steels [39]. Therefore, in order to better make fatigue design, this fact must be considered, even though the three investigated steels have high fatigue strength at 107 cycles.

10

Fig. 6 S-N curves of (a) I&Q&P steel, (b) TAM steel and (c) TRIP steel. The red arrows represent that specimen does not fail up to 107 cycles. (d) YS and yield ratio plot against fatigue limit. Table 5 Fitting parameters of the derived Stromeyer model and fatigue strength at different cycles of the three investigated steels. σ1 and σ2 represent the fatigue strength at 107 and 2×106 cycles, respectively. Steel

Fitting parameters

Fatigue strength (MPa)

a

b

μ

λ

σfl

σ1

σ2

I&Q&P

8.0379

1.4270

429265.5127

-0.7008

670

690

705

TAM

9.1529

1.9569

47560.3040

-0.5110

770

810

860

TRIP

10.1638

2.5129

11082.8029

-0.3979

795

833

875

3.3 Investigation of FCG behavior Generally, FCG curve can be divided into three regions: (I) low rate region, (II) mediate rate region and (III) high rate region. In region I, FCG rate goes asymptotically to zero as ΔK (stress intensity factor, MPa·m1/2) approaches ΔKth (threshold stress intensity factor, MPa·m1/2), i.e., no crack growth occurs and fatigue limit appears [45]. In region III, FCG rate is very high, and thus its contribution to the whole fatigue life should be ignored. In region II, fatigue crack can experience a stable propagation process. In this section, the region II of FCG curve was investigated to comparatively analyze the FCG behavior of the three steels. The experimental FCG results of the three steels are shown in Fig. 7 (a). It can be seen that the relationship between ΔK and da/dN is approximately linear in double logarithmic coordinates; however, in TRIP steel, the characteristic of region I appears when FCG rate is below 2×10−5 11

mm/cycle. Under the condition of the same ΔK, the FCG rate of I&Q&P steel is the largest, followed by TAM steel and TRIP steel. The ranges of ΔK in region II for I&Q&P steel, TAM steel and TRIP steel are 18.1–51.6 MPa·m1/2, 18.6–50.6 MP·m1/2 and 23.7–49.0 MP·m1/2, respectively, which indicates that the FCG behavior of TRIP steel reaches steady state earlier than those of I&Q&P and TAM steels. Then the Paris model [46] and the exponential model [47] were adopted to fit the FCG curves in region II, as follows: da/dN=C(ΔK)m

(4)

da/dN=eαeβ/ΔK

(5)

where C, m, α and β are the material-dependent constants. Fig. 7 (b–d) show the FCG curves fitted by the two models as well as the experimental results of the three investigated steels. The fitted constants C, m, α, β and the correlation coefficient R2 are shown in Table 6. It can be seen that the Paris model has a better agreement with the experimental data than that of the exponential model. In Paris model, m represents the slope of the straight line in double logarithmic coordinates and is inversely proportional to FCG rate. From Table 6, I&Q&P steel has the lowest m, and thus its FCG rate is the highest, followed by TAM steel and TRIP steel. In I&Q&P steel, although the martensite is tempered during partitioning, it is still the main strengthening phase; in addition, the strength of intercritical ferrite can be lowered through carbon partitioning from intercritical ferrite to austenite during intercritical annealing. Therefore, the strength difference between martensite and intercritical ferrite is high, resulting in the highest FCG rate. In TRIP steel, the precipitates containing vanadium can strengthen the ferrite matrix and reduce the strength difference between ferrite and bainite; furthermore, the distribution of bainite and ferrite is more uniform than that of I&Q&P steel (see Section 3.1). Consequently, TRIP steel has the optimum fatigue property.

Fig. 7 (a) Experimental FCG results of the three investigated steels, and fitting curves by the Paris and exponential models of (b) I&Q&P steel, (c) TAM steel and (d) TRIP steel. 12

Table 6 Fitting parameters of Paris and exponential models for the three investigated steels Steel

Paris model

Exponential model

C

m

R2

α

β

R2

I&Q&P

7.285×10−9

2.793

0.9938

−5.886

−99.941

0.9838

TAM

1.395×10−9

3.195

0.9949

−5.561

−119.501

0.9802

TRIP

7.824×10−11

3.927

0.9930

−4.910

−153.106

0.9816

4. Discussion 4.1 Effect of various multiphase microstructures on retarding FCP The above mainly analyzed comparatively fatigue limits, fatigue strength at different cycles and FCG rates of the three steels. The following will focus on the effect of multiphase microstructure on FCP behavior. Fig. 8 shows the characteristics of FCP paths after different cycles for the three steels. It can be seen that the fatigue crack of I&Q&P steel is more straight and wider than the ones of TAM and TRIP steels. Moreover, the required cycles for I&Q&P steel are the least (1.3×105 cycles) and the ones for TRIP steel are the largest (4.0×105 cycles) under the condition that the two steels have almost identical crack length, which indicates that the multiphase microstructure of I&Q&P steel has less effect on retarding the FCP than that of TRIP steel. TAM and TRIP steels have more tortuous crack paths than the one of I&Q&P steel, and they show crack branching phenomenon (see the red arrows in Fig. 8 (b) and (c)). Furthermore, TRIP steel has finer fatigue crack and more crack branching and interlocking compared with that of TAM steel, suggesting that the multiphase microstructure of TRIP steel plays a more important role in hindering the FCP. To further elucidate the effect of multiphase microstructure on FCP behavior, the micrographs at certain cycles were extracted, as shown in Fig. 9 (a–f), in which the red lines in (a), (c) and (e) were drawn according to the real propagation paths as shown in (b), (d) and (f), respectively. In I&Q&P steel, when crack encounters martensite or M/A islands, it prefers to propagate along the interfaces between martensite and ferrite or M/A islands and ferrite, as indicated by red and yellow arrows, respectively (see Fig. 9 (a)). This is because the strength difference between soft and strengthening phases causes strain incompatibility and interfacial adhesion loss [28]. Conversely, FCP along the interfaces can increase total propagation path due to crack deflection and bypassing the strengthening phase; furthermore, 46.7 vol. % martensite dispersed in the ferrite matrix (see Fig. 4 (a)) can increase the opportunity of crack propagating along the interfaces. Therefore, the fatigue limit of I&Q&P steel is higher than the ones having almost identical level of strength and ductility [38, 40, 41]. When the crack encounters ferrite, it can pass through ferrite quickly due to the ineffectiveness of soft phase on retarding the FCP. Moreover, plastic deformation can easily occur in ferrite near the crack tip, as marked by red circle in Fig. 9 (b). Consequently, I&Q&P steel has the worst fatigue property among the three steels mainly due to the strain incompatibility between soft and strengthening phases. In TAM steel, when crack encounters bainite or M/A islands, it also prefers to propagate along the interfaces between blocky bainite or M/A islands and adjacent phases, as indicated by red arrows in Fig. 9 (c). Due to the less blocky microstructure than the one of I&Q&P steel, there is relatively low possibility for crack encountering them (blocky bainite and M/A islands marked by green circles in Fig. 9 (c)). When crack encounters the mixed microstructure containing annealed martensitic laths and 13

film-like RA, the crack preferentially propagates parallel to the longitudinal direction of the laths due to the minimum resistance for FCP, as indicated by yellow arrows. However, when the crack passes through the mixed microstructure at a certain angle (not parallel), as marked by blue circle, FCG rate decreases quickly. Consequently, TAM steel has better fatigue property than the one of I&Q&P steel mainly due to the existence of annealed martensitic laths and film-like RA. In TRIP steel, the FCP resistance is mainly from crack branching and interlocking, as indicated by red arrows and red triangles in Fig. 9 (f), respectively. For crack branching, the length of one branched crack is usually less than one ferrite grain and the crack stops as soon as it encounters strengthening phase, becoming an arrested crack, and the other branched crack can propagate as a main crack. Moreover, in Fig. 9 (e), multi-cracks branching occurs, as marked by blue lines, which can further reduce the FCG rate due to more energy absorbed. The crack branching can reduce the crack driving force and play a significant role in crack retardation [48, 49]. In Fig. 9 (f), the red triangles show the presence of crack interlocking near the strengthening phase. In TRIP steel, the interfaces between ferrite and bainite are not the main sites for nucleation and propagation of crack due to the existence of a large number of precipitates in ferrite [23], reducing the strength difference between soft and strengthening phases and making them more compatible. Consequently, the multiphase microstructure of TRIP steel plays the best role in retarding FCP. Fig. 10 schematically summaries the effect of various multiphase microstructures on FCP of

the three investigated steels. In TRIP steel, bainite and ferrite have almost identical grain size, and the bainite densely distributes in ferrite matrix as second strengthening phase. By contrast, in I&Q&P steel, the grain size of ferrite is twice as large as the one of martensite, and the strengthening phase sparsely distributes in the ferrite matrix. Korda et al. [48] suggested that the extent of deformation can be strongly inhibited in the steel containing the hard phase with shorter spacing and uniform distribution, and this also plays an important role in crack closure. Consequently, the multiphase microstructure of TRIP steel can effectively hinder the FCP, resulting in the optimum fatigue property.

14

Fig. 8 (a–c) showing FCP paths after 1.3×105 cycles for I&Q&P steel, 1.7×105 cycles for TAM steel and 4.0×105 cycles for TRIP steel, respectively.

15

Fig. 9 Detailed description of the effect of multiphase microstructure on FCP behavior after different fatigue cycles, (a) 1.5×105 cycles and (b) 1.6×105 cycles for I&Q&P steel, (c) 1.8×105 cycles and (d) 1.9×105 cycles for TAM steel, and (e) 3.5 ×105 cycles and (f) 3.8 ×105 cycles for TRIP steel.

16

Fig. 10 Schematic diagrams showing the effect of various multiphase microstructures on FCP of (a) I&Q&P steel, (b) TAM steel and (c) TRIP steel. 4.2 Effect of the mechanical stability of RA on FCP In order to analyze the effect of the mechanical stability of RA on FCP, interrupted tensile tests combined with the XRD measurements of f RA were performed, and the results are shown in Fig. 11. It is found that in TRIP steel, almost 80 vol. % RA can transform into martensite when pre-strain is 5 %, while in I&Q&P steel, only 10 vol. % RA transforms. Furthermore, from Fig. 11, the stability of RA in TRIP steel is the lowest among the three steels, although it has the optimum fatigue property. Therefore, the mechanical stability of RA is not directly proportional to fatigue property. In TRIP steel, the fatigue limit is higher than its YS, and at this stress amplitude, TRIP effect can occur after a certain accumulation of cyclic plasticity, resulting in the improvement of work hardening [50–52] and favorable for fatigue performance of the steel [53]. In I&Q&P steel, TRIP effect hardly occurs due to higher stability of RA. Consequently, designing the RA with suitable stability is crucial to improving the fatigue property of steel, and this deserves further investigation in the future.

Fig. 11 Volume fraction of RA as a function of different pre-strains of the three investigated steels 17

4.3 Comparatively analysis of fatigue fractography in the three investigated steels In order to further investigate the effect of various multiphase microstructures on FCP micromechanisms, SEM analysis of fracture surface was performed. Fig. 12 shows the representative fracture surface morphologies in region II (ΔK=30 MPa·m1/2) after FCG tests. It is found that the three fracture surfaces all show fatigue striations, as indicated by red triangles. In TRIP steel, the fatigue striations spread throughout the fracture surface (see Fig. 12 (c)), which indicates that the FCP mainly relies on the cyclic effects [27]. Fatigue striations are essentially a series of parallel and slightly curved wavy stripes, which are perpendicular to the local FCP direction [28]. Laird et al. [54] suggested that fatigue striation is formed through continuous crack blunting and sharpening modes. Guan et al. [27] also reported that fatigue striation has an important influence on retarding crack propagation, because it can cause a considerably longer fracture path and side faces, which are unfavorable for crack propagation and can slow down FCG rate. Moreover, the occurrence of fatigue striation also suggests that FCP can be retarded by the misorientation of grain boundaries [27]. In I&Q&P steel, much more secondary cracks appear in fatigue fracture surface compared with the ones of TAM and TRIP steels, as indicated by red arrows in Fig. 12 (a). This is because fatigue crack mainly propagates along the interfaces between soft and strengthening phases, resulting in the occurrence of many secondary cracks, acceleration of FCG rate and premature failure of the steel.

Fig. 12 SEM micrographs showing fatigue fracture surfaces in region II (ΔK=30 MPa·m1/2) after FCG tests of (a) I&Q&P steel, (b) TAM steel and (c) TRIP steel 5. Conclusions In the present work, the fatigue properties of the three steels were investigated using S-N curve and FCG rate tests. Moreover, the effect of various multiphase microstructures on FCP behavior was analyzed by in-situ SEM tests. The findings are essential for the optimization of multiphase microstructure in designing a steel with excellent fatigue properties. The following concluding remarks 18

are made here: (1) The three investigated steels all consist of multiphase microstructure. I&Q&P steel comprises ferrite, martensite and RA, TAM steel comprises annealed martensite, bainite and RA, and TRIP steel comprises ferrite, bainite and RA. (2) The fatigue limits of I&Q&P, TAM and TRIP steels, determined by a derivation of the Stromeyer relationship, are 670 MPa, 770 MPa and 795 MPa, respectively. The TRIP steel has the highest fatigue limit, followed by TAM steel and I&Q&P steel. (3) The region II of FCG curve was fitted by Paris and exponential models, and the result indicates that Paris model can offer a better agreement with the experimental results than that of exponential model. In Paris model, I&Q&P steel has the lowest m, suggesting that it has the highest FCG rate, followed by TAM steel and TRIP steel. (4) In I&Q&P steel, fatigue crack mainly propagates along the interfaces between ferrite and martensite or ferrite and M/A islands, resulting in the occurrence of many secondary cracks. In TAM steel, FCP can be hindered when crack passes through the mixed microstructure containing annealed martensitic laths and film-like RA at an angle (not parallel). In TRIP steel, crack branching and interlocking can retard FCP effectively, benefiting from bainite densely distributing in ferrite matrix and the two phases having almost identical grain size. Acknowledgments This research project is financially supported by China Postdoctoral Science Foundation (2019TQ0250) and Scientific Research Foundation of Advanced Talents (Innovation Team), DGUT (No. KCYCXPT2016004). References [1] Jing Sun, Hao Yu. Microstructure development and mechanical properties of quenching and partitioning (Q&P) steel and an incorporation of hot-dipping galvanization during Q&P process. Materials Science & Engineering A, 2013, 586: 100–107. [2] Chenghao Song, Hao Yu, Lili Li, Tao Zhou, Jun Lu, Xihui Liu. The stability of retained austenite at different locations during straining of I&Q&P steel. Materials Science & Engineering A, 2016, 670: 326–334. [3] B.B. He, B.M. Huang, S.H. He, Y. Qi, H.W. Yen, M.X. Huang. Increasing yield strength of

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

Fatigue limit of transformation-induced plasticity steel is the highest.

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Crack branching and interlocking can retard fatigue crack propagation effectively.

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Fatigue crack propagates along phase boundary leading to secondary cracks.

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

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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