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Fatigue behavior and retained austenite transformation of Al-containing TRIP steels
International Journal of Fatigue 91 (2016) 220–231
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Fatigue behavior and retained austenite transformation of Al-containing TRIP steels P.I. Christodoulou a, A.T. Kermanidis a,⇑, D. Krizan b a b
Laboratory of Mechanics and Strength of Materials, Department of Mechanical Engineering, University of Thessaly, Volos, Greece Research and Development Department, Business Unit Coil, voestalpine Steel Division GmbH, Linz, Austria
a r t i c l e
i n f o
Article history: Received 27 January 2016 Received in revised form 31 May 2016 Accepted 2 June 2016 Available online 3 June 2016 Keywords: Transformation induced plasticity (TRIP) steel Low cycle fatigue High cycle fatigue Fatigue crack initiation Retained austenite transformation
a b s t r a c t In material selection for the design of advanced lightweight automotive steel components, fatigue performance is of particular significance. High strength TRIP steels offer very good cyclic behavior, especially under cyclic plastic strains, which is assisted by the Transformation Induced Plasticity effect (TRIP). In the present study the TRIP effect has been quantified under both elastic (HCF regime) and plastic (LCF regime) cyclic strains for two Al-containing TRIP steels with similar chemical composition and different initial retained austenite (RA) content. The results illustrate that transformation behavior differs for the two materials under elastic and plastic cyclic straining and fatigue behavior is in both cases linked to the amount of RA transformation. The latter is discussed in the paper considering relevant RA microstructural aspects like content and particle size. In the investigation the fatigue crack initiation resistance of the materials has been experimentally evaluated, resulting in different damage tolerance ability for the two steels. A numerical simulation is developed to determine the local strains at the notch tip under monotonic loading conditions and is used with the LCF material characteristics to discuss the differences obtained in crack initiation resistance. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction The excellent formability and strength properties of TRIP steels [1,2] have made them competitive materials with regard to new aluminum alloys for use in automotive industry to meet the criteria for reduced structural weight. The unique properties of TRIP steels are attributed to the deformation induced transformation of metastable retained austenite [3–6]. The amount of transformation mainly depends on deformation conditions and on the size [7], dispersion, and stability of retained austenite [8]. Under cyclic plastic deformation, TRIP steels offer excellent performance [9–12] and the cyclic material response is considerably influenced by the plastic strain amplitude and TRIP material microstructure [13,14]. In [13], cyclic hardening at low strain amplitudes followed by cyclic softening at higher strain amplitudes was reported for a TRIP750 steel. In [14] a reversed behavior was observed for a TRIP780 steel with cyclic softening diminishing with increasing strain amplitude. In [15] cyclic hardening was found to be dependent on the martensite formation rate, related to the plastic strain amplitude in cast austenitic TRIP steel. ⇑ Corresponding author. E-mail addresses: [email protected] (P.I. Christodoulou), akermanidis@mie. uth.gr (A.T. Kermanidis), [email protected] (D. Krizan). http://dx.doi.org/10.1016/j.ijfatigue.2016.06.004 0142-1123/Ó 2016 Elsevier Ltd. All rights reserved.
Austenite transformation was found not to influence significantly the cyclic hardening effect of TRIP steels but contribute to a low softening ratio. The High Cycle Fatigue (HCF) performance of TRIP steels has also been linked with deformation induced transformation resulting in an improvement of fatigue strength [16,17]. Under elastic alternating stresses the transformation effect still exists [17] and fatigue limit values close to the material’s yield strength have been reported [18,19]. In [20] the high fatigue limit value of quenched and partitioned steel was attributed to a delay in crack propagation caused by phase transformation. Fatigue strength was found to be dependent on the initial retained austenite (RA) volume fraction, while similar observation was reported in [21]. In [17] it was demonstrated that the stability of retained austenite is a significant parameter affecting the fatigue performance of TRIP steels. It was concluded that the TRIP steel with more stable retained austenite (lower Mr s value) exhibits more gradual transformation with increasing elastic alternating stresses, improving the fatigue behavior. Despite the importance of RA transformation on cyclic behavior of TRIP steels, experimental evidence with quantification of the transformation effect under both elastic and plastic cyclic strains on a specific TRIP material is missing. In this experimental study the Low and High cycle fatigue behavior (including notch effect
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Nomenclature A25 b c E FL FLN H H0 Kf Kt n n0 Nf Ninitiation q
elongation at fracture fatigue strength exponent fatigue ductility exponent Young’s modulus fatigue limit fatigue limit notched strength coefficient cyclic strength coefficient fatigue notch factor elastic stress concentration factor strain hardening exponent cyclic strain hardening exponent fatigue life number of cycles required for detection of a 250 lm crack notch sensitivity factor
analysis) is investigated for two Al-containing TRIP steels. The deformation induced martensitic transformation in the LCF and HCF regimes is quantified by performing RA measurements using the saturation magnetization technique. The fatigue results are discussed with regard to the RA microstructural characteristics of the materials. Another significant fatigue problem associated with the design of structural components is the material’s crack initiation resistance. At locations with stress concentrations (e.g. notches), local plasticity at the root of the geometrical discontinuity favors RA transformation and the local material behavior at the notch tip controls the crack initiation problem. Limited attention has been paid in the literature on this issue and most investigations have focused on the notch effect on fatigue limit. In [19] it has been reported that the formation of hard martensite due to strain induced transformation, suppresses the crack initiation in notched TRIP aided-annealed martensitic steel. In [18] the notched fatigue limit of TRIP-aided bainitic ferrite steels with 10–13.7% initial RA volume fraction linearly increased with increasing hardness, while the notch sensitivity decreased. In [22,23], among several high strength steels used in automotive industry, TRIP steels presented the highest smooth and notched fatigue limit values. Retained austenite to martensite transformation has been also found to be beneficial on the rate of the growing crack. In [11,24] the transformation ahead of the crack tip was found to reduce the energy absorption leading to high fatigue crack growth resistance in a low alloy TRIP steel. Crack initiation from the notch tip is assessed in the present study for both Al-containing TRIP steels experimentally. The differences obtained in crack initiation behavior of the steels are discussed considering local LCF conditions at the notch root taking into account the LCF material behavior. A numerical simulation is performed to determine the local monotonic material response at the notch root resulting to the development of local strains at the notch tip.
2. Experimental procedure
R
stress/strain ratio crack length Da/DN|avg average crack growth rate Dr stress amplitude ee elastic strain amplitude ef 0 fatigue ductility coefficient ep plastic strain amplitude etotal total strain amplitude eyy normal strain in the loading direction m Poisson’s ratio ra stress amplitude rf0 fatigue strength coefficient rmax maximum stress in the loading direction rUTS ultimate tensile strength ryy normal stress in the loading direction ry0.2 yield strength (offset 0.2%)
a
Section 2.4.1. The RA values were 11.8 vol.-% and 15.8 vol.-% for TRIP700 steels (A) and (B) respectively. Both materials are Alcontaining steels with small differences in chemical composition, as shown in Table 1. 2.2. Metallography The microstructural characteristics in as-received condition were assessed using optical microscopy. A stepped color tintetching procedure was employed using the De-etching method [25] in order to reveal the steels’ microstructures. The samples were first dipped into a 3% Nital solution for 5 s and then placed into a solution of 10% Na2S2O5 for 60 s. The average grain sizes of ferrite and retained austenite of the steels were measured using image analysis software, with data taken from several micrographs to avoid estimation errors due to the large dispersion of the phases. The retained austenite volume fraction after the mechanical tests was measured using the saturation magnetization technique. 2.3. Mechanical testing Static tensile tests were carried using an INSTRON 8801 servohydraulic machine with 100 kN load capacity. Mechanical properties were determined in accordance with ASTM E8M at a constant crosshead velocity of 0.5 mm/min. The specimens were tested in the longitudinal (L) direction using a 25-mm gage length clip-on extensometer. Fully reversed (R = 1) cyclic tests were performed in accordance with SEP 1240 [26] specification. The geometry of the LCF specimen is shown in Fig. 1. Strain amplitudes in the range of 0.002–0.02 were applied using a 10-mm gage length clip-on extensometer at a frequency range of 0.1–3 s1. To prevent buckling under compressive strains, an anti-buckling external fixture was used. The stabilized hysteresis loop was determined from the half number of cycles required for onset of crack initiation. Crack initiation is determined as the number of cycles that corresponds to a 10% change of the maximum cyclic load [26]. For determining the
2.1. Materials The materials used in the investigation were a hot-rolled TRIP700(A) steel with thickness of 1.8 mm and a cold-rolled, 1.5 mm thick, TRIP700(B) steel in sheet form. The percentage (%) retained austenite (RA) values were measured with the saturation magnetization technique, which is described in more detail in
Table 1 Chemical composition of TRIP700 steels (wt.-%). Steel
C
Mn
Al
Si
P
Fe
(A) (B)
0.18 0.202
1.61 1.99
1.45 1.07
0.7 0.35
– 0.009
Balance Balance
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Fig. 1. Geometry of LCF test specimen (dimensions in mm).
Fig. 3. Schematic representation of the SM method.
" J Fe S
# X ðan An Þ J m n
Vg ¼
J Fe S
X ðan An Þ
100%
ð1Þ
n
where an and An (in vol.%) are related to the effect of the alloying element n on the saturation magnetization in the specimen. JSFe represents the saturation magnetization of the pure ferrite and Jm is the saturation magnetization of the specimen calculated based on the following formula:
R Jm ¼
Fig. 2. Geometry of (a) smooth and (b) notched HCF test specimen (dimensions in mm).
total fatigue life Nf, as failure criterion the fracture of the specimen was considered. Constant amplitude HCF tests were carried out at a stress ratio R = 0.1 and a frequency of 25 Hz. Smooth fatigue specimens were prepared according to ASTM E466 with a geometry shown in Fig. 2a. To investigate the notched fatigue behavior, specimens with a single, 60° V-shape notch were used (Fig. 2b) with an elastic stress concentration factor of Kt = 3.5, calculated from the Noda et al. approach [27]. 2.4. Retained austenite measurements 2.4.1. Saturation magnetization method The SM measuring equipment is depicted schematically in Fig. 3. It consists of a magnetic yoke, which produces a high and homogeneous magnetic field between its poles. A magnetic flux sensing coil mounted in the centre of this magnetic field is used as the measurement coil. The specimen used for measurement is positioned through the measurement coil with its axis aligned to the direction of magnetic field. The amount of retained austenite is calculated from the measured integral of the voltage pulse induced in the coil [28]. Ferrite and austenite differ in their magnetic behavior, with ferrite being ferromagnetic and austenite paramagnetic. For this reason, only the amount of ferrite of the sample contributes to the induced voltage pulse in the measurement coil. The saturation magnetization decreases with arising amount of austenite, which cannot be magnetized in the case of a two phase mixture of ferrite and austenite. The addition of alloying elements also causes a change of the saturation magnetization. The volume fraction of retained austenite was calculated as follows:
U ind dt N V L
ð2Þ
where Uind is a voltage-pulse in the coil, V is the volume of the specimen, N, the number of windings of the pick up coil, and L, the length of the measured coil. This method presents significant advantages compared to other methods due to the fact that the entire volume of the sample is measured. The method shows higher precision compared to other methods [29] for determination of RA volume fraction and exhibits good repeatability in the performed measurements [28]. Small uncertainties may exist due to the presence of alloying elements, which can cause a small change of the saturation magnetization. 2.4.2. Sampling of specimens Retained austenite transformation under cyclic loading has been investigated by performing RA measurements on small samples extracted from the specimens. The location adjacent to the fractured surface where the samples have been extracted from after mechanical testing is shown in Fig. 4. Samples were extracted approximately 2 mm away from the fractured surface inside the gauge section of the specimen, to avoid additional transformation effects caused by localized plastic deformation at the fracture area. Specifically for the HCF specimens due to the continuous radius of curvature in the gauge section, certain non uniform distribution of stresses is present in the longitudinal axis of the sample. This was taken into account by calculating average stress values along the axis of the extracted sample. 2.5. Crack initiation monitoring Fatigue crack initiation at the notch root area was monitored using the replica technique. The fatigue tests were interrupted at regular cycle intervals and a small tensile load was applied to reveal open crack surfaces. Foils of 0.1 mm thickness wetted with acetone, were used to take replicas from both sides of the notch root and were examined in an optical microscope. Then, cyclic stressing was continued and the procedure was repeated until a
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Fig. 4. Location of extracted sample for RA measurements in, (a) HCF (b) LCF, (c) tensile test specimen (dimensions in mm).
short crack was observed. The procedure was continued by making the interruption intervals more frequent. The length of the fatigue crack was measured using image analysis software.
Table 2 Grain size measurements of TRIP steels. Average grain size (lm)
Steel Ferrite
Retained austenite Mean value (Standard deviation)
3. Experimental results 3.1. Microstructure and mechanical properties The TRIP steel basic microstructural characteristics are shown in Fig. 5. Based on the etching solution used [25], the tinting effect resulted in ferrite-straw brown, bainite-dark and retained austenite-white color. The ferrite and retained austenite grain sizes were determined using an image analysis software. To increase the accuracy of measurements a method, which calculates the average grain diameter measured at 2° intervals passing through the particle’s centroid was used. The latter is recommended in cases where high grain shape irregularity exists in the structure [30]. The grain size measurements of ferrite and retained austenite are presented in Table 2. The average size of retained austenite particles is 1.03 lm in (A) and 0.70 lm in (B) steel. The average ferrite grain size of (A) and (B) steels was found 3.62 lm and 9.47 lm, respectively. For both steels the RA grain size distribution in as-received condition is shown in Fig. 6. The distribution of average RA particle diameter is broader for steel (A) compared to steel (B). This is indicated also by the higher standard deviation value of 0.73 vs. 0.34 in steel (A). It denotes a more uniform particle size distribution for steel (B) with regard to steel (A).
(A) (B)
3.62 (0.92) 9.47 (2.48)
1.03 (0.73) 0.70 (0.34)
The engineering stress–strain curves of the materials are illustrated in Fig. 7 and the resulting mechanical properties are given in Table 3. Steel (A) has a higher yield strength but lower elongation at fracture compared to (B). The yield strength values are 606 MPa vs. 515 MPa and the elongation 23.2% vs. 28.6% for steels (A) and (B) respectively. The strain hardening exponent n was calculated between the true strain values e = 2% and e = n (onset of necking) for both materials. Significant is the difference in the strain hardening behavior of the two steels with (B) exhibiting a higher strain hardening exponent n = 0.196 compared to n = 0.102 for (A) accompanied by a higher uniform elongation of 24.9% compared to 16.2%. Hot rolling in steel (A) is not beneficial for the yield strength compared to cold rolling in steel (B), but the finer ferrite grain size of steel (A) is expected to contribute in the strain hardening behavior, however the amount of strain hardening is higher in steel (B). This is a result of the lower yield strength which promotes higher initial work hardening and the TRIP effect, which is controlled by the RA content and its stability [31]. SM measurements taken from
Fig. 5. Microstructure of (a) TRIP700(A) and (b) TRIP700(B) steel.
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3.2. Cyclic stress–strain behavior The strain-life curves of the materials are presented in Figs. 8a, b and are compared in Fig. 8c. The total strain amplitude is given as the sum of elastic and plastic parts, in the form:
etotal ¼ ee þ ep ¼ The cyclic
r0f E
ðNf Þb þ e0f ðNf Þc
material
parameters
ð3Þ
r0f ; b; e0f ; c are given in
Figs. 8a and 7b for the two steels. Differences in fatigue behavior exist at fatigue regions where either the plastic or elastic component is dominant in the total strain amplitude. The transition fatigue life from LCF to HCF behavior, is estimated approximately at 2 103 cycles. Below the transition life, where plastic strains are dominant, steel (A) shows a better fatigue performance, while above the transition life, steel (B) has a higher fatigue limit. In both cases the differences are small. The fatigue limit for both materials is evaluated in Section 3.4, while the transition observed in the fatigue behavior is discussed taken into account the transformation effect as determined in Sections 3.3 and 3.4. In Figs. 9a and b the cyclic stress–strain curves resulting from the stabilized hysteresis loops for both materials are presented and are compared with the monotonic behavior in Fig. 9c. The cyclic strain hardening exponent n0 and cyclic strength coefficient H0 were assessed with the Ramberg–Osgood equation (Eq. (4)) [33]. The cyclic properties are given in Table 4 with regard to the monotonic properties of the steels.
Fig. 6. Histogram of RA grain size distribution.
etotal ¼
ra E
þ
ra H
10 n
0
ð4Þ
Both steels show an initial cyclic softening followed by an extended cyclic hardening with increasing plastic strain values. The cyclic yield strength of steel (A) is higher compared to (B) (554 MPa vs. 456 MPa), but cyclic strain hardening is more pronounced in (B), yielding in a higher cyclic strain hardening exponent, as shown in Table 4. The strain hardening behavior is consistent with the monotonic behavior analyzed in Section 3.1. 3.3. Cyclic behavior and RA transformation
Fig. 7. Engineering stress–strain curves of TRIP700 steels (A) and (B).
Table 3 Mechanical properties of TRIP steels. Steel
ry0.2 (MPa)
rUTS (MPa)
A25 (%)
n
(A) (B)
606 515
707 749
23.2 28.2
0.102 0.196
fractured specimens revealed that the RA transformed during the tensile test was 51.3% and 77.2%, for steels (A) and (B) respectively. The amount of transformation depends on the RA content and its stability. The content of RA is higher in steel (B). Stability of the phase against transformation is controlled by the carbon content [29], RA particle size and strength of the surrounding phases. RA particles are smaller in steel (B) and have been associated with enhanced ductility against transformation [4,32]. On the other hand the higher content of alloying elements Al and Si in steel (A) makes the precipitation of carbides more difficult and enriches the carbon content in austenite, contributing to a more stable RA phase.
The cyclic tensile stress peaks with the number of cycles are illustrated in Fig. 10. For both steels a gradual transition from cyclic softening to cyclic hardening with increasing strain amplitude is observed. The gradual shift to cyclic hardening is observed when the plastic strain amplitude increases. In particular at strain levels above 1% a clear hardening effect is observed, which becomes more pronounced when strain amplitudes reach the value of 2%. The change from cyclic softening to cyclic hardening is associated with the increase of RA transformation with increasing strain amplitude [34–36]. The RA measurements after the cyclic tests reveal an increase in percent RA transformation with increasing applied strain amplitude as shown in Fig. 11. Under strain amplitudes with very small plastic component (0.25–0.4% total strain amplitude) cyclic softening occurs in both materials and is more pronounced in steel (B). The smaller amount of cyclic softening of steel (A) may be explained by its more stable transformation behavior under elastic cyclic strains, which will be discussed in the following section. With increasing strain amplitude the plastic strain component becomes more significant in the cyclic behavior. Cyclic softening still exists but steel (B) presents reduced softening compared to (A). For strain levels above 1% strain hardening controls the materials’ behavior with the amount of hardening being higher for steel (B). Beneficial to this behavior is the higher %RA transformation in (B) compared to (A), as shown from the RA measurements of Fig. 11.
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Fig. 8. Strain-life curves of (a) TRIP700(A) and (b) TRIP700(B) steel. (c) Strain-life curves compared for both TRIP steels.
3.4. High cycle fatigue behavior and RA transformation The smooth and notched fatigue behavior of the TRIP700 materials is shown in Fig. 12. The fixed fatigue limits (N = 107 cycles), were approximated with the 4-parameter Weibull function of equation Eq. (3), with fitting parameters C1, C2, C3 and C4 given in Table 5. For the calculation of fixed fitting parameter C2, the rUTS value of the materials under investigation was used. It is assumed that the presence of notch due to the ductile behavior of the two materials, does not affect the rUTS value. For the fixed fitting parameter C1, the lower bound of the maximum stress at 107 cycles was used. Fitting parameters C3 and C4 are independent variables.
rmax ¼ C 1 ðC 1 C 2 Þeððlog NÞ=C3 Þ 4 C
ð3Þ
TRIP700(B) exhibits excellent unnotched fatigue performance with the fatigue limit (535 MPa) lying close to the material’s yield strength (515 MPa). Steel (A) exhibits a slightly lower fatigue limit
(502 MPa) and a tendency for improved fatigue resistance at higher fatigue stresses, behavior which is in line with the LCF behavior presented in Section 3.2. The presence of the notch results in a drastic decrease in fatigue limit in both steels, which was found 165 MPa for (B) and 155 MPa for steel (A). The reduction in fatigue strength is 69% with regard to the unnotched specimens. At higher stresses the curves tend to deviate with steel (B) showing better fatigue performance. It is an indication of steel (B) exhibiting better crack initiation resistance. The fatigue notch factor Kt and the notch sensitivity parameter q assessed from the experimental curves of Fig. 12, are presented in Table 6. The high values of Kf and q indicate a detrimental effect of the notch on fatigue crack initiation in both steels. The crack initiation behavior of both steels is evaluated in Section 3.5. Transformation of retained austenite was assessed by measuring the RA volume fraction after fatigue testing and the results are given in Fig. 13. The amount of RA transformation increases with increasing maximum stress and becomes significant when
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Fig. 9. Cyclic stress–strain curves of (a) TRIP700(A) and (b) TRIP700(B) steel. (c) Comparison of monotonic and cyclic stress–strain curves.
Table 4 Monotonic and cyclic properties of TRIP700 steels. Steel
ry0.2 (MPa)
n
H (MPa)
r0 y (MPa)
n0
H0 (MPa)
(A) (B)
606 515
0.102 0.196
982.7 1312
554 456
0.119 0.197
1160 1550
rmax exceeds the materials’ yield point. This is evident in Fig. 13 by observing the transformed RA for both steels at stresses above their yield point. The fatigue limit in TRIP steels is assisted by the deformation induced transformation of RA [16,17,20]. Examination of Fig. 13 reveals that for the stress range examined in the S–N curve, steel (A) exhibits more transformation under elastic stresses compared to steel (B). This behavior may be associated with a less stable RA microstructure of steel (A) under elastic stresses. Similar results have been reported in [17], where in TRIP materials with the same chemical composition the superior fatigue limit belonged to the steel with higher austenite stability, hence ability for gradual RA transformation with increasing stress.
The HCF and LCF performances of the materials are different and are associated in each case with the amount of transformed RA [17,37]. Steel (B) shows a higher transformation potential under plastic strains (Fig. 11), while steel (A) transforms more in the elastic region. The transition in the behavior, may be explained by closer examination of RA microstructural features of the two materials. In [38,39] it has been shown that in a tensile test under small plastic strains the larger RA particles have the tendency to transform first, while the smaller particles transform at higher strains. In [38] the transformation behavior of steel (B), investigated in the present study, revealed that the smaller the RA particle size the higher is the amount of plastic deformation required to enable transformation. The role of RA particle size on transformation has also been discussed in [7,40]. In [7] it was found that retained austenite with a grain size smaller than 0.01 lm will not transform to martensite, while RA particles with grain size larger than 1 lm (which is the case for steel (A) in the present study), will immediately transform to martensite upon application of small stress. Then, it is reasonable to assume that under elastic strains (HCF) the larger RA particles of steel (A) are favorable for
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Fig. 10. Cyclic stress peaks in tension of (a) TRIP700(A) and (b) TRIP700(B).
Table 5 Weibull equation fitting parameters. Steel
Fitting parameters C1
C2
C3
C4
(A)
Smooth Notched
502 155
707 707
12.0923 8.7557
14.00281 3.61503
(B)
Smooth Notched
535 165
749 749
11.03327 9.33309
6.53394 4.22789
Table 6 Fatigue notch factors. Steel
FL (MPa)
FLN (MPa)
Kt
Kf
q
(A) (B)
502 535
155 165
3.5 3.5
3.238 3.24
0.895 0.896
Fig. 11. Percent RA transformed with regard to the applied strain amplitude.
Fig. 13. Percent RA transformed with regard to the applied maximum stress.
Fig. 12. S–N curves of TRIP700(A) and (B) steels (arrows indicate run out tests).
transformation, while steel (B) with smaller RA particles has limited transformation potential (see Fig. 11). As the plastic strains become large (LCF) they provide the necessary driving force for the smaller particles of steel (B) to transform. Hence, the% amount
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of transformation of steel (B) increases and exceeds the transformation levels of steel (A). The RA measurements from the tensile tests confirm this trend, where at fracture after the materials have undergone severe plastic deformation, steel (B) exhibits higher RA transformation. Contributing to the higher RA transformation is the higher initial RA content, which is higher in steel (B). The transformation dependency on particle size under cyclic plastic staining has been reported in [20]. 3.5. Crack initiation and growth from notch tip Notched fatigue experiments were performed to extract information regarding the materials’ resistance to crack initiation. Crack initiation was assumed when the length of the short crack at the notch root reached 250 lm. In Fig. 14, images of the initiation and advance of the crack from the notch tip are displayed for both materials for the case of maximum stress rmax = 200 MPa. The fatigue crack growth curves vs. number of cycles are shown in Fig. 15. Steel (B) exhibits higher fatigue crack growth resistance compared to (A).The average number of cycles for detection of the 250 lm crack, was 80,300 cycles and 114,600 cycles for steels (A) and (B) respectively, indicating a better crack initiation resistance of steel (B). The delay in crack initiation in steel (B) compared to (A) is examined in more detail in Section 3.6. The average crack growth rate Da/DN|avg, measured for a crack advancement from 0.250 mm to 1.5 mm, is 5.42 lm/cycle and 11.48 lm/cycle for steels (B) and (A) respectively, as shown in Table 7. The average fatigue life was 174,000 cycles for steel (B) and 107,700 cycles for steel (A). The influence of transformation effect on crack growth rate has been reported in literature (e.g. [11]) and may have an impact on the obtained fatigue life values. Detailed investigation of the specific influence exceeds the purpose of the present study, which focuses on the crack initiation problem. A discussion is included here about specific aspects that may influence crack initiation behavior. In order to evaluate the possible influence on crack initiation of localized RA transformation at the notch root during machining, the plastic deformation field ahead of the notch tip induced by the machining process has to be assessed. The magnitude of deformation depends on various parameters such as material, processing and conditions of machining (lubrication, wear state of machining tool etc.). From the
Fig. 15. Fatigue crack growth curves of TRIP700(A) and TRIP700(B) steels for maximum stress rmax = 200 MPa.
Table 7 Fatigue crack initiation (rmax = 200 MPa). Steel
Nf (cycles)
Ninitiation (cycles)
Da/DN|avg (lm/cycle)
(A)
122,419 143,377 57,510
87,700 111,500 41,700
8.68 13.84 11.93
(B)
188,800 202,948 130,279
124,000 154,000 66,000
4.36 8.82 3.09
limited information available the large amount of subsurface plasticity occurs in the material at an average scale length of 10 lm [41–43] from the machining surface. At larger depths, plastic strains are reduced rapidly within a length scale of 50–100 lm. This length scale is significantly smaller compared to, (a) the length scale examined from the notch root for crack initiation, (b) the magnitude of plastic strains at the notch root induced by the external loading of 200 MPa. This is expected to reduce the influence of the machining deformation effect since it is embedded inside a locally, more extended plasticity caused by the external loading
Fig. 14. Replica images showing crack evolution from notch tip in (a) TRIP700(A) and (b) TRIP700(B) steel. Loading axis is in the horizontal direction.
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during the first cycle. The zone of plastic deformation at the notch root has been calculated using a finite element analysis presented in the next section.
3.6. Local stress/strain behavior at the notch tip A numerical simulation of the elasto-plastic stress–strain behavior of a material element at the tip of the notch was performed using the Abaqus finite element software. In the simulation, a monotonic loading case is considered corresponding to a quarter of a cycle in the fatigue test where the specimen is subjected to a far from the notch tip maximum tensile stress of 200 MPa. A 3D finite element model was constructed and a step loading analysis was performed. The values of the elastic material properties used in the analysis are m = 0.3 and E = 205.9 GPa. The modulus of elasticity (E) was obtained from the tensile tests in Section 3.1. For localized stresses exceeding the material’s yield strength, an isotropic hardening behavior was implemented to describe the material element response. During loading a fixed constraint in the upper bolt hole was applied (Fig 16). The monotonic tensile load is 4395.6 N and 3538 N for TRIP700(A) and TRIP700(B) respectively, due to the different material thickness. Linear hexahedral solid 3D elements were used in the numerical analysis, while the characteristic element width in the vicinity of the notch tip was set to 250 lm, size which is equal to the crack length assumed for crack initiation. To reduce the computational time and for optimizing the mesh in the model, an increasing element size with increasing distance from the notch was chosen. The fine mesh consisted of a total number of 25,650 and 30,130 elements for steel (A) and (B), respectively. Mesh sensitivity validation has also been performed. A step load increment was applied until the tensile stress of 200 MPa was reached. In Fig. 17 the calculated stress–strain behavior of the element at the notch tip is presented and in Fig. 18 the detail of the model with the distribution of normal stress and normal strain in the loading direction for the two materials, is shown. The maximum stress and strain of the selected element is
Fig. 17. Stress–strain behavior of the material element at notch tip.
ryy = 675 MPa and eyy = 0.0034 for material (A) and ryy = 606.9 MPa, eyy = 0.0046 for material (B). The local behavior presented in Fig. 17 is used to describe the loading event, which corresponds to a quarter of the first cycle, of an element at the notch tip during the HCF test. Since the stresses exceed the materials’ yield strength, the material element depicted in Fig. 17 can be assumed to be subjected to LCF conditions with an initial stress–strain response calculated in the model. Considering now the stabilized cyclic behavior after the initial local maximum stresses 675 MPa and 606.9 MPa have been applied (since the fatigue test of the notched specimen is stress controlled), the experimental cyclic stress–strain curve of Fig. 9c results in the stabilized strain values of ey = 0.0195 and ey = 0.0117 for materials (A) and (B) respectively. These strain values are higher than the strains calculated numerically from the monotonic loading event at the notch tip (eyy = 0.0034 and eyy = 0.0046). Assuming that the cyclic response of Fig. 9 applies for the material element of Fig. 17, at strain amplitudes lower than 0.8%, both materials exhibit cyclic softening at the notch root. This justifies the increase in strain amplitude from the initial calculated value to the stabilized value taken from the cyclic stress–strain curve of Fig. 9c. Using the above approach, the strain values of the material element at the stabilized cyclic response may explain the differences in the crack initiation resistance of the two steels. In particular, the reduced fatigue life for detection of a 250 lm crack in steel (A) compared to (B), is due to the higher imposed strains at the notch tip region after the cyclic softening effect is exhausted. Using the results of the FE analysis, which takes into account the cyclic material behavior observed experimentally, the reduced fatigue life for crack initiation in steel (A) (80,300 cycles and 114,600 cycles, respectively) is due to the higher strains at the notch tip with regard to steel (B). It should be noted that the above approach serves only purposes for estimating the differences in crack initiation behavior of the materials, taking into account the numerically calculated stresses and strains at the notch tip and combining it with the cyclic stress–strain material response in Fig. 9. 4. Conclusions
Fig. 16. Finite element model to simulate the notch stress–strain behavior. (a) Boundary conditions used in the simulation. (b) Meshing at the vicinity of the notch.
The Low and High cycle fatigue performance as well as crack initiation resistance of Al-containing TRIP700 steels was investigated and the role of retained austenite transformation during cyclic loading was examined. The main findings of the investigation are the following:
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Fig. 18. Normal stress and strain distribution at the vicinity of the notch for (a) TRIP700(A) and (b) TRIP700(B) material.
1. The cyclic behavior of the materials is characterized by cyclic softening at small strain amplitudes, which gradually shifts to cyclic strain hardening with increasing strain amplitude. 2. Both TRIP materials exhibit very good fatigue performance with the fatigue limit in steel (B) exceeding slightly the yield strength of the material. The presence of the notch reduces drastically the fatigue limit and yields in high notch sensitivity parameter values for both materials. 3. Steel (B) with higher initial (%) RA content and smaller RA particle size, shows a higher cyclic hardening capacity and a higher potential for retained austenite transformation under plastic cyclic strains. Steel (A) with larger austenite particle size shows a higher potency for transformation under elastic cyclic strains. The smaller % amount of transformation is favorable for fatigue performance of steel (B) under elastic strains and for steel (A) under plastic strains. 4. Steel (B) presents higher resistance to crack initiation and increased fatigue crack growth resistance from the notch tip compared to steel (A). Based on the experimental cyclic behavior and a numerical analysis to calculate the local stress–strain
response during first cycle loading at the notch root for both materials, the local cyclic strains at the notch tip for steel (A) were found higher compared to (B) accelerating crack initiation.
Acknowledgements This work was partially funded by the project ‘‘Smart Pole for Specialization and Development of Thessaly: Research, Innovation, Strategies”, implemented in the framework of the ‘‘KRIPIS” Programme of the General Secretariat for Research and Technology (GSRT), National Strategic Reference Framework (NSRF) 2007– 2013. The authors are grateful to Mr. M. Khalife for his contribution on fatigue crack initiation experiments. References [1] Vasilakos AN, Ohlert J, Giasla K, Haidemenopoulos GN, Bleck W. Low-alloy TRIP steels: a correlation between mechanical properties and the retained austenite stability. Steel Res 2002;73:249–52.
P.I. Christodoulou et al. / International Journal of Fatigue 91 (2016) 220–231 [2] Mamalis AG, Haidemenopoulos GN. Aspects of ductility, toughness and formability of steel sheet in relation to transformation plasticity. J Mater Process Technol 1992;30:211–30. [3] Dan WJ, Zhang WG, Li SH, Lin ZQ. A model for strain-induced martensitic transformation of TRIP steel with strain rate. Comput Mater Sci 2007;40: 101–7. [4] Timokhina IB, Hodgson PD, Pereloma EV. Effect of microstructure on the stability of retained austenite in transformation-induced-plasticity steels. Metall Mater Trans A 2004;35A:2331–41. [5] Lee CG, Kim SJ, Lee TH, Lee SH. Effects of volume fraction and stability of retained austenite on formability in a 0.1C–1.5Si–1.5Mn–0.5Cu TRIP-aided cold-rolled steel sheet. Mat Sci Eng A – Struct 2004;371:16–23. [6] Tamura I. Deformation-induced martensitic transformation and transformation-induced plasticity in steels. Metal Sci 1982;16:245–53. [7] Wang JJ, van der Zwaag S. Stabilization mechanisms of retained austenite in transformation-induced plasticity steel. Metall Mater Trans A 2001;32: 1527–39. [8] Jacques PJ. Transformation-induced plasticity for high strength formable steels. Curr Opin Solid State Mater Sci 2004;8:259–65. [9] Hilditch T, Beladi H, Hodgson P, Stanford N. Role of microstructure in the low cycle fatigue of multi-phase steels. Mat Sci Eng A – Struct 2012;534:288–96. [10] Smaga M, Walther F, Eifler D. Deformation-induced martensitic transformation in metastable austenitic steels. Mater Sci Eng, A 2008;483– 484:394–7. [11] Cheng X, Petrov R, Zhao L, Janssen M. Fatigue crack growth in TRIP steel under positive R-ratios. Eng Fract Mech 2008;75:739–49. [12] Baudry G, Pineau A. Influence of strain-induced martensitic transformation on the low-cycle fatigue behavior of a stainless steel. Mater Sci Eng, A 1977;28:229–42. [13] Hu ZG, Zhu P, Meng J. Fatigue properties of transformation-induced plasticity and dual-phase steels for auto-body lightweight: experiment, modeling and application. Mater Des 2010;31:2884–90. [14] Hilditch TB, Timokhina IB, Robertson LT, Pereloma EV, Hodgson PD. Cyclic deformation of advanced high-strength steels: mechanical behavior and microstructural analysis. Metall Mater Trans A 2009;40:342–53. [15] Ackermann S, Kulawinski D, Henkel S, Biermann H. Biaxial in-phase and outof-phase cyclic deformation and fatigue behavior of an austenitic TRIP steel. Int J Fatigue 2014;67:123–33. [16] Olson GB, Chait R, Azrin M, Gagne R. Fatigue strength of TRIP steels. Metall Trans A 1980;11:1069–71. [17] Haidemenopoulos GN, Kermanidis AT, Malliaros C, Dickert HH, Kucharzyk P, Bleck W. On the effect of austenite stability on high cycle fatigue of TRIP 700 steel. Mater Sci Eng, A 2013;573:7–11. [18] Yoshikawa N, Kobayashi J, Sugimoto K. Notch-fatigue properties of advanced TRIP-aided bainitic ferrite steels. Metall Mater Trans A 2012;43A: 4129–36. [19] Sugimoto KI, Fiji D, Yoshikawa N. Fatigue strength of newly developed highstrength low alloy TRIP-aided steels with good hardenability. Procedia Eng 2010;2:359–62. [20] Diego-Calderón ID, Rodriguez-Calvillo P, Lara A, Molina-Aldareguia JM, Petrov RH, De Knijf D, et al. Effect of microstructure on fatigue behavior of advanced high strength steels produced by quenching and partitioning and the role of retained austenite. Mater Sci Eng, A 2015;641:215–24. [21] Abareshi M, Emadoddin E. Effect of retained austenite characteristics on fatigue behavior and tensile properties of transformation induced plasticity steel. Mater Des 2011;32:5099–105. [22] Ma M, Yi H. Lightweight car body and application of high strength steels. Adv Steels 2011:187–98.
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Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue behavior and retained austenite transformation of Al-containing TRIP steels P.I. Christodoulou a, A.T. Kermanidis a,⇑, D. Krizan b a b
Laboratory of Mechanics and Strength of Materials, Department of Mechanical Engineering, University of Thessaly, Volos, Greece Research and Development Department, Business Unit Coil, voestalpine Steel Division GmbH, Linz, Austria
a r t i c l e
i n f o
Article history: Received 27 January 2016 Received in revised form 31 May 2016 Accepted 2 June 2016 Available online 3 June 2016 Keywords: Transformation induced plasticity (TRIP) steel Low cycle fatigue High cycle fatigue Fatigue crack initiation Retained austenite transformation
a b s t r a c t In material selection for the design of advanced lightweight automotive steel components, fatigue performance is of particular significance. High strength TRIP steels offer very good cyclic behavior, especially under cyclic plastic strains, which is assisted by the Transformation Induced Plasticity effect (TRIP). In the present study the TRIP effect has been quantified under both elastic (HCF regime) and plastic (LCF regime) cyclic strains for two Al-containing TRIP steels with similar chemical composition and different initial retained austenite (RA) content. The results illustrate that transformation behavior differs for the two materials under elastic and plastic cyclic straining and fatigue behavior is in both cases linked to the amount of RA transformation. The latter is discussed in the paper considering relevant RA microstructural aspects like content and particle size. In the investigation the fatigue crack initiation resistance of the materials has been experimentally evaluated, resulting in different damage tolerance ability for the two steels. A numerical simulation is developed to determine the local strains at the notch tip under monotonic loading conditions and is used with the LCF material characteristics to discuss the differences obtained in crack initiation resistance. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction The excellent formability and strength properties of TRIP steels [1,2] have made them competitive materials with regard to new aluminum alloys for use in automotive industry to meet the criteria for reduced structural weight. The unique properties of TRIP steels are attributed to the deformation induced transformation of metastable retained austenite [3–6]. The amount of transformation mainly depends on deformation conditions and on the size [7], dispersion, and stability of retained austenite [8]. Under cyclic plastic deformation, TRIP steels offer excellent performance [9–12] and the cyclic material response is considerably influenced by the plastic strain amplitude and TRIP material microstructure [13,14]. In [13], cyclic hardening at low strain amplitudes followed by cyclic softening at higher strain amplitudes was reported for a TRIP750 steel. In [14] a reversed behavior was observed for a TRIP780 steel with cyclic softening diminishing with increasing strain amplitude. In [15] cyclic hardening was found to be dependent on the martensite formation rate, related to the plastic strain amplitude in cast austenitic TRIP steel. ⇑ Corresponding author. E-mail addresses: [email protected] (P.I. Christodoulou), akermanidis@mie. uth.gr (A.T. Kermanidis), [email protected] (D. Krizan). http://dx.doi.org/10.1016/j.ijfatigue.2016.06.004 0142-1123/Ó 2016 Elsevier Ltd. All rights reserved.
Austenite transformation was found not to influence significantly the cyclic hardening effect of TRIP steels but contribute to a low softening ratio. The High Cycle Fatigue (HCF) performance of TRIP steels has also been linked with deformation induced transformation resulting in an improvement of fatigue strength [16,17]. Under elastic alternating stresses the transformation effect still exists [17] and fatigue limit values close to the material’s yield strength have been reported [18,19]. In [20] the high fatigue limit value of quenched and partitioned steel was attributed to a delay in crack propagation caused by phase transformation. Fatigue strength was found to be dependent on the initial retained austenite (RA) volume fraction, while similar observation was reported in [21]. In [17] it was demonstrated that the stability of retained austenite is a significant parameter affecting the fatigue performance of TRIP steels. It was concluded that the TRIP steel with more stable retained austenite (lower Mr s value) exhibits more gradual transformation with increasing elastic alternating stresses, improving the fatigue behavior. Despite the importance of RA transformation on cyclic behavior of TRIP steels, experimental evidence with quantification of the transformation effect under both elastic and plastic cyclic strains on a specific TRIP material is missing. In this experimental study the Low and High cycle fatigue behavior (including notch effect
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Nomenclature A25 b c E FL FLN H H0 Kf Kt n n0 Nf Ninitiation q
elongation at fracture fatigue strength exponent fatigue ductility exponent Young’s modulus fatigue limit fatigue limit notched strength coefficient cyclic strength coefficient fatigue notch factor elastic stress concentration factor strain hardening exponent cyclic strain hardening exponent fatigue life number of cycles required for detection of a 250 lm crack notch sensitivity factor
analysis) is investigated for two Al-containing TRIP steels. The deformation induced martensitic transformation in the LCF and HCF regimes is quantified by performing RA measurements using the saturation magnetization technique. The fatigue results are discussed with regard to the RA microstructural characteristics of the materials. Another significant fatigue problem associated with the design of structural components is the material’s crack initiation resistance. At locations with stress concentrations (e.g. notches), local plasticity at the root of the geometrical discontinuity favors RA transformation and the local material behavior at the notch tip controls the crack initiation problem. Limited attention has been paid in the literature on this issue and most investigations have focused on the notch effect on fatigue limit. In [19] it has been reported that the formation of hard martensite due to strain induced transformation, suppresses the crack initiation in notched TRIP aided-annealed martensitic steel. In [18] the notched fatigue limit of TRIP-aided bainitic ferrite steels with 10–13.7% initial RA volume fraction linearly increased with increasing hardness, while the notch sensitivity decreased. In [22,23], among several high strength steels used in automotive industry, TRIP steels presented the highest smooth and notched fatigue limit values. Retained austenite to martensite transformation has been also found to be beneficial on the rate of the growing crack. In [11,24] the transformation ahead of the crack tip was found to reduce the energy absorption leading to high fatigue crack growth resistance in a low alloy TRIP steel. Crack initiation from the notch tip is assessed in the present study for both Al-containing TRIP steels experimentally. The differences obtained in crack initiation behavior of the steels are discussed considering local LCF conditions at the notch root taking into account the LCF material behavior. A numerical simulation is performed to determine the local monotonic material response at the notch root resulting to the development of local strains at the notch tip.
2. Experimental procedure
R
stress/strain ratio crack length Da/DN|avg average crack growth rate Dr stress amplitude ee elastic strain amplitude ef 0 fatigue ductility coefficient ep plastic strain amplitude etotal total strain amplitude eyy normal strain in the loading direction m Poisson’s ratio ra stress amplitude rf0 fatigue strength coefficient rmax maximum stress in the loading direction rUTS ultimate tensile strength ryy normal stress in the loading direction ry0.2 yield strength (offset 0.2%)
a
Section 2.4.1. The RA values were 11.8 vol.-% and 15.8 vol.-% for TRIP700 steels (A) and (B) respectively. Both materials are Alcontaining steels with small differences in chemical composition, as shown in Table 1. 2.2. Metallography The microstructural characteristics in as-received condition were assessed using optical microscopy. A stepped color tintetching procedure was employed using the De-etching method [25] in order to reveal the steels’ microstructures. The samples were first dipped into a 3% Nital solution for 5 s and then placed into a solution of 10% Na2S2O5 for 60 s. The average grain sizes of ferrite and retained austenite of the steels were measured using image analysis software, with data taken from several micrographs to avoid estimation errors due to the large dispersion of the phases. The retained austenite volume fraction after the mechanical tests was measured using the saturation magnetization technique. 2.3. Mechanical testing Static tensile tests were carried using an INSTRON 8801 servohydraulic machine with 100 kN load capacity. Mechanical properties were determined in accordance with ASTM E8M at a constant crosshead velocity of 0.5 mm/min. The specimens were tested in the longitudinal (L) direction using a 25-mm gage length clip-on extensometer. Fully reversed (R = 1) cyclic tests were performed in accordance with SEP 1240 [26] specification. The geometry of the LCF specimen is shown in Fig. 1. Strain amplitudes in the range of 0.002–0.02 were applied using a 10-mm gage length clip-on extensometer at a frequency range of 0.1–3 s1. To prevent buckling under compressive strains, an anti-buckling external fixture was used. The stabilized hysteresis loop was determined from the half number of cycles required for onset of crack initiation. Crack initiation is determined as the number of cycles that corresponds to a 10% change of the maximum cyclic load [26]. For determining the
2.1. Materials The materials used in the investigation were a hot-rolled TRIP700(A) steel with thickness of 1.8 mm and a cold-rolled, 1.5 mm thick, TRIP700(B) steel in sheet form. The percentage (%) retained austenite (RA) values were measured with the saturation magnetization technique, which is described in more detail in
Table 1 Chemical composition of TRIP700 steels (wt.-%). Steel
C
Mn
Al
Si
P
Fe
(A) (B)
0.18 0.202
1.61 1.99
1.45 1.07
0.7 0.35
– 0.009
Balance Balance
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Fig. 1. Geometry of LCF test specimen (dimensions in mm).
Fig. 3. Schematic representation of the SM method.
" J Fe S
# X ðan An Þ J m n
Vg ¼
J Fe S
X ðan An Þ
100%
ð1Þ
n
where an and An (in vol.%) are related to the effect of the alloying element n on the saturation magnetization in the specimen. JSFe represents the saturation magnetization of the pure ferrite and Jm is the saturation magnetization of the specimen calculated based on the following formula:
R Jm ¼
Fig. 2. Geometry of (a) smooth and (b) notched HCF test specimen (dimensions in mm).
total fatigue life Nf, as failure criterion the fracture of the specimen was considered. Constant amplitude HCF tests were carried out at a stress ratio R = 0.1 and a frequency of 25 Hz. Smooth fatigue specimens were prepared according to ASTM E466 with a geometry shown in Fig. 2a. To investigate the notched fatigue behavior, specimens with a single, 60° V-shape notch were used (Fig. 2b) with an elastic stress concentration factor of Kt = 3.5, calculated from the Noda et al. approach [27]. 2.4. Retained austenite measurements 2.4.1. Saturation magnetization method The SM measuring equipment is depicted schematically in Fig. 3. It consists of a magnetic yoke, which produces a high and homogeneous magnetic field between its poles. A magnetic flux sensing coil mounted in the centre of this magnetic field is used as the measurement coil. The specimen used for measurement is positioned through the measurement coil with its axis aligned to the direction of magnetic field. The amount of retained austenite is calculated from the measured integral of the voltage pulse induced in the coil [28]. Ferrite and austenite differ in their magnetic behavior, with ferrite being ferromagnetic and austenite paramagnetic. For this reason, only the amount of ferrite of the sample contributes to the induced voltage pulse in the measurement coil. The saturation magnetization decreases with arising amount of austenite, which cannot be magnetized in the case of a two phase mixture of ferrite and austenite. The addition of alloying elements also causes a change of the saturation magnetization. The volume fraction of retained austenite was calculated as follows:
U ind dt N V L
ð2Þ
where Uind is a voltage-pulse in the coil, V is the volume of the specimen, N, the number of windings of the pick up coil, and L, the length of the measured coil. This method presents significant advantages compared to other methods due to the fact that the entire volume of the sample is measured. The method shows higher precision compared to other methods [29] for determination of RA volume fraction and exhibits good repeatability in the performed measurements [28]. Small uncertainties may exist due to the presence of alloying elements, which can cause a small change of the saturation magnetization. 2.4.2. Sampling of specimens Retained austenite transformation under cyclic loading has been investigated by performing RA measurements on small samples extracted from the specimens. The location adjacent to the fractured surface where the samples have been extracted from after mechanical testing is shown in Fig. 4. Samples were extracted approximately 2 mm away from the fractured surface inside the gauge section of the specimen, to avoid additional transformation effects caused by localized plastic deformation at the fracture area. Specifically for the HCF specimens due to the continuous radius of curvature in the gauge section, certain non uniform distribution of stresses is present in the longitudinal axis of the sample. This was taken into account by calculating average stress values along the axis of the extracted sample. 2.5. Crack initiation monitoring Fatigue crack initiation at the notch root area was monitored using the replica technique. The fatigue tests were interrupted at regular cycle intervals and a small tensile load was applied to reveal open crack surfaces. Foils of 0.1 mm thickness wetted with acetone, were used to take replicas from both sides of the notch root and were examined in an optical microscope. Then, cyclic stressing was continued and the procedure was repeated until a
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Fig. 4. Location of extracted sample for RA measurements in, (a) HCF (b) LCF, (c) tensile test specimen (dimensions in mm).
short crack was observed. The procedure was continued by making the interruption intervals more frequent. The length of the fatigue crack was measured using image analysis software.
Table 2 Grain size measurements of TRIP steels. Average grain size (lm)
Steel Ferrite
Retained austenite Mean value (Standard deviation)
3. Experimental results 3.1. Microstructure and mechanical properties The TRIP steel basic microstructural characteristics are shown in Fig. 5. Based on the etching solution used [25], the tinting effect resulted in ferrite-straw brown, bainite-dark and retained austenite-white color. The ferrite and retained austenite grain sizes were determined using an image analysis software. To increase the accuracy of measurements a method, which calculates the average grain diameter measured at 2° intervals passing through the particle’s centroid was used. The latter is recommended in cases where high grain shape irregularity exists in the structure [30]. The grain size measurements of ferrite and retained austenite are presented in Table 2. The average size of retained austenite particles is 1.03 lm in (A) and 0.70 lm in (B) steel. The average ferrite grain size of (A) and (B) steels was found 3.62 lm and 9.47 lm, respectively. For both steels the RA grain size distribution in as-received condition is shown in Fig. 6. The distribution of average RA particle diameter is broader for steel (A) compared to steel (B). This is indicated also by the higher standard deviation value of 0.73 vs. 0.34 in steel (A). It denotes a more uniform particle size distribution for steel (B) with regard to steel (A).
(A) (B)
3.62 (0.92) 9.47 (2.48)
1.03 (0.73) 0.70 (0.34)
The engineering stress–strain curves of the materials are illustrated in Fig. 7 and the resulting mechanical properties are given in Table 3. Steel (A) has a higher yield strength but lower elongation at fracture compared to (B). The yield strength values are 606 MPa vs. 515 MPa and the elongation 23.2% vs. 28.6% for steels (A) and (B) respectively. The strain hardening exponent n was calculated between the true strain values e = 2% and e = n (onset of necking) for both materials. Significant is the difference in the strain hardening behavior of the two steels with (B) exhibiting a higher strain hardening exponent n = 0.196 compared to n = 0.102 for (A) accompanied by a higher uniform elongation of 24.9% compared to 16.2%. Hot rolling in steel (A) is not beneficial for the yield strength compared to cold rolling in steel (B), but the finer ferrite grain size of steel (A) is expected to contribute in the strain hardening behavior, however the amount of strain hardening is higher in steel (B). This is a result of the lower yield strength which promotes higher initial work hardening and the TRIP effect, which is controlled by the RA content and its stability [31]. SM measurements taken from
Fig. 5. Microstructure of (a) TRIP700(A) and (b) TRIP700(B) steel.
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3.2. Cyclic stress–strain behavior The strain-life curves of the materials are presented in Figs. 8a, b and are compared in Fig. 8c. The total strain amplitude is given as the sum of elastic and plastic parts, in the form:
etotal ¼ ee þ ep ¼ The cyclic
r0f E
ðNf Þb þ e0f ðNf Þc
material
parameters
ð3Þ
r0f ; b; e0f ; c are given in
Figs. 8a and 7b for the two steels. Differences in fatigue behavior exist at fatigue regions where either the plastic or elastic component is dominant in the total strain amplitude. The transition fatigue life from LCF to HCF behavior, is estimated approximately at 2 103 cycles. Below the transition life, where plastic strains are dominant, steel (A) shows a better fatigue performance, while above the transition life, steel (B) has a higher fatigue limit. In both cases the differences are small. The fatigue limit for both materials is evaluated in Section 3.4, while the transition observed in the fatigue behavior is discussed taken into account the transformation effect as determined in Sections 3.3 and 3.4. In Figs. 9a and b the cyclic stress–strain curves resulting from the stabilized hysteresis loops for both materials are presented and are compared with the monotonic behavior in Fig. 9c. The cyclic strain hardening exponent n0 and cyclic strength coefficient H0 were assessed with the Ramberg–Osgood equation (Eq. (4)) [33]. The cyclic properties are given in Table 4 with regard to the monotonic properties of the steels.
Fig. 6. Histogram of RA grain size distribution.
etotal ¼
ra E
þ
ra H
10 n
0
ð4Þ
Both steels show an initial cyclic softening followed by an extended cyclic hardening with increasing plastic strain values. The cyclic yield strength of steel (A) is higher compared to (B) (554 MPa vs. 456 MPa), but cyclic strain hardening is more pronounced in (B), yielding in a higher cyclic strain hardening exponent, as shown in Table 4. The strain hardening behavior is consistent with the monotonic behavior analyzed in Section 3.1. 3.3. Cyclic behavior and RA transformation
Fig. 7. Engineering stress–strain curves of TRIP700 steels (A) and (B).
Table 3 Mechanical properties of TRIP steels. Steel
ry0.2 (MPa)
rUTS (MPa)
A25 (%)
n
(A) (B)
606 515
707 749
23.2 28.2
0.102 0.196
fractured specimens revealed that the RA transformed during the tensile test was 51.3% and 77.2%, for steels (A) and (B) respectively. The amount of transformation depends on the RA content and its stability. The content of RA is higher in steel (B). Stability of the phase against transformation is controlled by the carbon content [29], RA particle size and strength of the surrounding phases. RA particles are smaller in steel (B) and have been associated with enhanced ductility against transformation [4,32]. On the other hand the higher content of alloying elements Al and Si in steel (A) makes the precipitation of carbides more difficult and enriches the carbon content in austenite, contributing to a more stable RA phase.
The cyclic tensile stress peaks with the number of cycles are illustrated in Fig. 10. For both steels a gradual transition from cyclic softening to cyclic hardening with increasing strain amplitude is observed. The gradual shift to cyclic hardening is observed when the plastic strain amplitude increases. In particular at strain levels above 1% a clear hardening effect is observed, which becomes more pronounced when strain amplitudes reach the value of 2%. The change from cyclic softening to cyclic hardening is associated with the increase of RA transformation with increasing strain amplitude [34–36]. The RA measurements after the cyclic tests reveal an increase in percent RA transformation with increasing applied strain amplitude as shown in Fig. 11. Under strain amplitudes with very small plastic component (0.25–0.4% total strain amplitude) cyclic softening occurs in both materials and is more pronounced in steel (B). The smaller amount of cyclic softening of steel (A) may be explained by its more stable transformation behavior under elastic cyclic strains, which will be discussed in the following section. With increasing strain amplitude the plastic strain component becomes more significant in the cyclic behavior. Cyclic softening still exists but steel (B) presents reduced softening compared to (A). For strain levels above 1% strain hardening controls the materials’ behavior with the amount of hardening being higher for steel (B). Beneficial to this behavior is the higher %RA transformation in (B) compared to (A), as shown from the RA measurements of Fig. 11.
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Fig. 8. Strain-life curves of (a) TRIP700(A) and (b) TRIP700(B) steel. (c) Strain-life curves compared for both TRIP steels.
3.4. High cycle fatigue behavior and RA transformation The smooth and notched fatigue behavior of the TRIP700 materials is shown in Fig. 12. The fixed fatigue limits (N = 107 cycles), were approximated with the 4-parameter Weibull function of equation Eq. (3), with fitting parameters C1, C2, C3 and C4 given in Table 5. For the calculation of fixed fitting parameter C2, the rUTS value of the materials under investigation was used. It is assumed that the presence of notch due to the ductile behavior of the two materials, does not affect the rUTS value. For the fixed fitting parameter C1, the lower bound of the maximum stress at 107 cycles was used. Fitting parameters C3 and C4 are independent variables.
rmax ¼ C 1 ðC 1 C 2 Þeððlog NÞ=C3 Þ 4 C
ð3Þ
TRIP700(B) exhibits excellent unnotched fatigue performance with the fatigue limit (535 MPa) lying close to the material’s yield strength (515 MPa). Steel (A) exhibits a slightly lower fatigue limit
(502 MPa) and a tendency for improved fatigue resistance at higher fatigue stresses, behavior which is in line with the LCF behavior presented in Section 3.2. The presence of the notch results in a drastic decrease in fatigue limit in both steels, which was found 165 MPa for (B) and 155 MPa for steel (A). The reduction in fatigue strength is 69% with regard to the unnotched specimens. At higher stresses the curves tend to deviate with steel (B) showing better fatigue performance. It is an indication of steel (B) exhibiting better crack initiation resistance. The fatigue notch factor Kt and the notch sensitivity parameter q assessed from the experimental curves of Fig. 12, are presented in Table 6. The high values of Kf and q indicate a detrimental effect of the notch on fatigue crack initiation in both steels. The crack initiation behavior of both steels is evaluated in Section 3.5. Transformation of retained austenite was assessed by measuring the RA volume fraction after fatigue testing and the results are given in Fig. 13. The amount of RA transformation increases with increasing maximum stress and becomes significant when
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Fig. 9. Cyclic stress–strain curves of (a) TRIP700(A) and (b) TRIP700(B) steel. (c) Comparison of monotonic and cyclic stress–strain curves.
Table 4 Monotonic and cyclic properties of TRIP700 steels. Steel
ry0.2 (MPa)
n
H (MPa)
r0 y (MPa)
n0
H0 (MPa)
(A) (B)
606 515
0.102 0.196
982.7 1312
554 456
0.119 0.197
1160 1550
rmax exceeds the materials’ yield point. This is evident in Fig. 13 by observing the transformed RA for both steels at stresses above their yield point. The fatigue limit in TRIP steels is assisted by the deformation induced transformation of RA [16,17,20]. Examination of Fig. 13 reveals that for the stress range examined in the S–N curve, steel (A) exhibits more transformation under elastic stresses compared to steel (B). This behavior may be associated with a less stable RA microstructure of steel (A) under elastic stresses. Similar results have been reported in [17], where in TRIP materials with the same chemical composition the superior fatigue limit belonged to the steel with higher austenite stability, hence ability for gradual RA transformation with increasing stress.
The HCF and LCF performances of the materials are different and are associated in each case with the amount of transformed RA [17,37]. Steel (B) shows a higher transformation potential under plastic strains (Fig. 11), while steel (A) transforms more in the elastic region. The transition in the behavior, may be explained by closer examination of RA microstructural features of the two materials. In [38,39] it has been shown that in a tensile test under small plastic strains the larger RA particles have the tendency to transform first, while the smaller particles transform at higher strains. In [38] the transformation behavior of steel (B), investigated in the present study, revealed that the smaller the RA particle size the higher is the amount of plastic deformation required to enable transformation. The role of RA particle size on transformation has also been discussed in [7,40]. In [7] it was found that retained austenite with a grain size smaller than 0.01 lm will not transform to martensite, while RA particles with grain size larger than 1 lm (which is the case for steel (A) in the present study), will immediately transform to martensite upon application of small stress. Then, it is reasonable to assume that under elastic strains (HCF) the larger RA particles of steel (A) are favorable for
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Fig. 10. Cyclic stress peaks in tension of (a) TRIP700(A) and (b) TRIP700(B).
Table 5 Weibull equation fitting parameters. Steel
Fitting parameters C1
C2
C3
C4
(A)
Smooth Notched
502 155
707 707
12.0923 8.7557
14.00281 3.61503
(B)
Smooth Notched
535 165
749 749
11.03327 9.33309
6.53394 4.22789
Table 6 Fatigue notch factors. Steel
FL (MPa)
FLN (MPa)
Kt
Kf
q
(A) (B)
502 535
155 165
3.5 3.5
3.238 3.24
0.895 0.896
Fig. 11. Percent RA transformed with regard to the applied strain amplitude.
Fig. 13. Percent RA transformed with regard to the applied maximum stress.
Fig. 12. S–N curves of TRIP700(A) and (B) steels (arrows indicate run out tests).
transformation, while steel (B) with smaller RA particles has limited transformation potential (see Fig. 11). As the plastic strains become large (LCF) they provide the necessary driving force for the smaller particles of steel (B) to transform. Hence, the% amount
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of transformation of steel (B) increases and exceeds the transformation levels of steel (A). The RA measurements from the tensile tests confirm this trend, where at fracture after the materials have undergone severe plastic deformation, steel (B) exhibits higher RA transformation. Contributing to the higher RA transformation is the higher initial RA content, which is higher in steel (B). The transformation dependency on particle size under cyclic plastic staining has been reported in [20]. 3.5. Crack initiation and growth from notch tip Notched fatigue experiments were performed to extract information regarding the materials’ resistance to crack initiation. Crack initiation was assumed when the length of the short crack at the notch root reached 250 lm. In Fig. 14, images of the initiation and advance of the crack from the notch tip are displayed for both materials for the case of maximum stress rmax = 200 MPa. The fatigue crack growth curves vs. number of cycles are shown in Fig. 15. Steel (B) exhibits higher fatigue crack growth resistance compared to (A).The average number of cycles for detection of the 250 lm crack, was 80,300 cycles and 114,600 cycles for steels (A) and (B) respectively, indicating a better crack initiation resistance of steel (B). The delay in crack initiation in steel (B) compared to (A) is examined in more detail in Section 3.6. The average crack growth rate Da/DN|avg, measured for a crack advancement from 0.250 mm to 1.5 mm, is 5.42 lm/cycle and 11.48 lm/cycle for steels (B) and (A) respectively, as shown in Table 7. The average fatigue life was 174,000 cycles for steel (B) and 107,700 cycles for steel (A). The influence of transformation effect on crack growth rate has been reported in literature (e.g. [11]) and may have an impact on the obtained fatigue life values. Detailed investigation of the specific influence exceeds the purpose of the present study, which focuses on the crack initiation problem. A discussion is included here about specific aspects that may influence crack initiation behavior. In order to evaluate the possible influence on crack initiation of localized RA transformation at the notch root during machining, the plastic deformation field ahead of the notch tip induced by the machining process has to be assessed. The magnitude of deformation depends on various parameters such as material, processing and conditions of machining (lubrication, wear state of machining tool etc.). From the
Fig. 15. Fatigue crack growth curves of TRIP700(A) and TRIP700(B) steels for maximum stress rmax = 200 MPa.
Table 7 Fatigue crack initiation (rmax = 200 MPa). Steel
Nf (cycles)
Ninitiation (cycles)
Da/DN|avg (lm/cycle)
(A)
122,419 143,377 57,510
87,700 111,500 41,700
8.68 13.84 11.93
(B)
188,800 202,948 130,279
124,000 154,000 66,000
4.36 8.82 3.09
limited information available the large amount of subsurface plasticity occurs in the material at an average scale length of 10 lm [41–43] from the machining surface. At larger depths, plastic strains are reduced rapidly within a length scale of 50–100 lm. This length scale is significantly smaller compared to, (a) the length scale examined from the notch root for crack initiation, (b) the magnitude of plastic strains at the notch root induced by the external loading of 200 MPa. This is expected to reduce the influence of the machining deformation effect since it is embedded inside a locally, more extended plasticity caused by the external loading
Fig. 14. Replica images showing crack evolution from notch tip in (a) TRIP700(A) and (b) TRIP700(B) steel. Loading axis is in the horizontal direction.
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during the first cycle. The zone of plastic deformation at the notch root has been calculated using a finite element analysis presented in the next section.
3.6. Local stress/strain behavior at the notch tip A numerical simulation of the elasto-plastic stress–strain behavior of a material element at the tip of the notch was performed using the Abaqus finite element software. In the simulation, a monotonic loading case is considered corresponding to a quarter of a cycle in the fatigue test where the specimen is subjected to a far from the notch tip maximum tensile stress of 200 MPa. A 3D finite element model was constructed and a step loading analysis was performed. The values of the elastic material properties used in the analysis are m = 0.3 and E = 205.9 GPa. The modulus of elasticity (E) was obtained from the tensile tests in Section 3.1. For localized stresses exceeding the material’s yield strength, an isotropic hardening behavior was implemented to describe the material element response. During loading a fixed constraint in the upper bolt hole was applied (Fig 16). The monotonic tensile load is 4395.6 N and 3538 N for TRIP700(A) and TRIP700(B) respectively, due to the different material thickness. Linear hexahedral solid 3D elements were used in the numerical analysis, while the characteristic element width in the vicinity of the notch tip was set to 250 lm, size which is equal to the crack length assumed for crack initiation. To reduce the computational time and for optimizing the mesh in the model, an increasing element size with increasing distance from the notch was chosen. The fine mesh consisted of a total number of 25,650 and 30,130 elements for steel (A) and (B), respectively. Mesh sensitivity validation has also been performed. A step load increment was applied until the tensile stress of 200 MPa was reached. In Fig. 17 the calculated stress–strain behavior of the element at the notch tip is presented and in Fig. 18 the detail of the model with the distribution of normal stress and normal strain in the loading direction for the two materials, is shown. The maximum stress and strain of the selected element is
Fig. 17. Stress–strain behavior of the material element at notch tip.
ryy = 675 MPa and eyy = 0.0034 for material (A) and ryy = 606.9 MPa, eyy = 0.0046 for material (B). The local behavior presented in Fig. 17 is used to describe the loading event, which corresponds to a quarter of the first cycle, of an element at the notch tip during the HCF test. Since the stresses exceed the materials’ yield strength, the material element depicted in Fig. 17 can be assumed to be subjected to LCF conditions with an initial stress–strain response calculated in the model. Considering now the stabilized cyclic behavior after the initial local maximum stresses 675 MPa and 606.9 MPa have been applied (since the fatigue test of the notched specimen is stress controlled), the experimental cyclic stress–strain curve of Fig. 9c results in the stabilized strain values of ey = 0.0195 and ey = 0.0117 for materials (A) and (B) respectively. These strain values are higher than the strains calculated numerically from the monotonic loading event at the notch tip (eyy = 0.0034 and eyy = 0.0046). Assuming that the cyclic response of Fig. 9 applies for the material element of Fig. 17, at strain amplitudes lower than 0.8%, both materials exhibit cyclic softening at the notch root. This justifies the increase in strain amplitude from the initial calculated value to the stabilized value taken from the cyclic stress–strain curve of Fig. 9c. Using the above approach, the strain values of the material element at the stabilized cyclic response may explain the differences in the crack initiation resistance of the two steels. In particular, the reduced fatigue life for detection of a 250 lm crack in steel (A) compared to (B), is due to the higher imposed strains at the notch tip region after the cyclic softening effect is exhausted. Using the results of the FE analysis, which takes into account the cyclic material behavior observed experimentally, the reduced fatigue life for crack initiation in steel (A) (80,300 cycles and 114,600 cycles, respectively) is due to the higher strains at the notch tip with regard to steel (B). It should be noted that the above approach serves only purposes for estimating the differences in crack initiation behavior of the materials, taking into account the numerically calculated stresses and strains at the notch tip and combining it with the cyclic stress–strain material response in Fig. 9. 4. Conclusions
Fig. 16. Finite element model to simulate the notch stress–strain behavior. (a) Boundary conditions used in the simulation. (b) Meshing at the vicinity of the notch.
The Low and High cycle fatigue performance as well as crack initiation resistance of Al-containing TRIP700 steels was investigated and the role of retained austenite transformation during cyclic loading was examined. The main findings of the investigation are the following:
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Fig. 18. Normal stress and strain distribution at the vicinity of the notch for (a) TRIP700(A) and (b) TRIP700(B) material.
1. The cyclic behavior of the materials is characterized by cyclic softening at small strain amplitudes, which gradually shifts to cyclic strain hardening with increasing strain amplitude. 2. Both TRIP materials exhibit very good fatigue performance with the fatigue limit in steel (B) exceeding slightly the yield strength of the material. The presence of the notch reduces drastically the fatigue limit and yields in high notch sensitivity parameter values for both materials. 3. Steel (B) with higher initial (%) RA content and smaller RA particle size, shows a higher cyclic hardening capacity and a higher potential for retained austenite transformation under plastic cyclic strains. Steel (A) with larger austenite particle size shows a higher potency for transformation under elastic cyclic strains. The smaller % amount of transformation is favorable for fatigue performance of steel (B) under elastic strains and for steel (A) under plastic strains. 4. Steel (B) presents higher resistance to crack initiation and increased fatigue crack growth resistance from the notch tip compared to steel (A). Based on the experimental cyclic behavior and a numerical analysis to calculate the local stress–strain
response during first cycle loading at the notch root for both materials, the local cyclic strains at the notch tip for steel (A) were found higher compared to (B) accelerating crack initiation.
Acknowledgements This work was partially funded by the project ‘‘Smart Pole for Specialization and Development of Thessaly: Research, Innovation, Strategies”, implemented in the framework of the ‘‘KRIPIS” Programme of the General Secretariat for Research and Technology (GSRT), National Strategic Reference Framework (NSRF) 2007– 2013. The authors are grateful to Mr. M. Khalife for his contribution on fatigue crack initiation experiments. References [1] Vasilakos AN, Ohlert J, Giasla K, Haidemenopoulos GN, Bleck W. Low-alloy TRIP steels: a correlation between mechanical properties and the retained austenite stability. Steel Res 2002;73:249–52.
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