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Fatigue properties of transformation-induced plasticity and dual-phase steels for auto-body lightweight: Experiment, modeling and application
Materials and Design 31 (2010) 2884–2890
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Fatigue properties of transformation-induced plasticity and dual-phase steels for auto-body lightweight: Experiment, modeling and application Z.G. Hu, P. Zhu *, J. Meng State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
a r t i c l e
i n f o
Article history: Received 25 September 2009 Accepted 18 December 2009 Available online 24 December 2009 Keywords: A. Ferrous metals and alloys E. Fatigue H. Failure analysis
a b s t r a c t The substitution of conventional high strength steels (HSS) with advanced high strength steels (AHSS), e.g., low-alloy multiphase transformation-induced plasticity steel (TRIP steel) or dual-phase steel (DP steel), for body lightweight brings about increased stress of notched components. Thus the fatigue properties of TRIP and DP steels and the fatigue life of notched lightweight design are important considerations for reasonable material selection during the design stage of auto-body. For the mentioned issue, cyclic strain-controlled fatigue properties of TRIP and DP steels with equivalent grade and lightweight result were investigated experimentally. Different cyclic behaviors of TRIP and DP steels were observed due to different interior microstructures. The cyclic stress behavior of TRIP steel is characterized by cyclic hardening followed by stable at lower strain amplitudes, and softening at higher strain amplitudes; however cyclic softening followed by stable occurs consistently for DP steel throughout entire strain amplitude range of test. TRIP steel possesses enhanced fatigue life and cyclic stress at the same strain amplitude than DP steel. Furthermore, local strain-life models of two steels were developed by linear regression of experimental data, to predict and compare the fatigue life of notched body structures made of them by finite element method. The simulation result illustrates that TRIP steel can provide more beneficial potential than DP steel for the lightweight design of notched body structures from the viewpoint of fatigue resistance. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction AHSS can realize the lightweight of auto-body, reduce fuel consumption and exhaust emissions on one hand; improve service performances, e.g., stiffness, strength, crashworthiness [1], and fatigue durability [2] on the other hand. DP steel and low-alloy multiphase TRIP steel are two typical kinds of AHSS, of which TRIP steel has attracted more and more attention in the ground vehicle industry. TRIP steels with 5–15% initial volume fraction of retained austenite possess improved formability due to TRIP effect of retained austenite [3]. The applications of TRIP steel include structural components, reinforcement components and suspension components, e.g., pillars, rails, cross members, door reinforcement beam, bumper inner reinforcement, suspension arm. AHSS can provide superior static tensile strength, but this merit of materials cannot imply superior fatigue characterizations of body structures with notch geometry. The substitution of conventional HSS with AHSS for body lightweight brings about decreased thickness but increased stress of components. Cyclic micro-plasticity in the stress concentration regions of body components will re* Corresponding author. Tel./fax: +86 21 34206787. E-mail address: [email protected] (P. Zhu). 0261-3069/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2009.12.034
sult in the initiation of fatigue cracks [4]. Fatigue cracks degrade the continuity of material state; hence influence other performances of auto-body during its service life, e.g., stiffness, strength, NVH, and crashworthiness. Consequently, the fatigue resistance, especially the low-cycle fatigue resistance, is an important consideration for structure design and material selection of auto-body [5]. The results of stress-controlled fatigue tests on smooth specimens [3,6] demonstrate that the fatigue strength of TRIP steel is superior to HSS and DP steel with equivalent strength. It can be concluded from Yokoi and Takahashi [6] that the fatigue strength of TRIP steel is also higher than DP steel and high-strength low-alloy steel (HSLA steel) under the stress concentration conditions. In the case of smooth specimens, the fatigue limit and fatigue strength of steel materials increase with static tensile strength. But for specimens with stress concentration, the fatigue limit and fatigue strength of HSS do not always increase with static tensile strength, while those of the DP and TRIP steels still increase with static tensile strength. The results of strain-controlled fatigue tests indicate that different microstructures and their mechanical properties, and different environment can influence the cyclic stress response of TRIP steels. Yasuki et al. [7] mentioned that the cyclic stress response of TRIP steel was characterized by severe initial
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Z.G. Hu et al. / Materials and Design 31 (2010) 2884–2890 Table 1 Chemical composition (wt.%) of TRIP590 and DP590 sheet steels. Material
C
Mn
Si
Cr
Mo
V
Ni
Cu
Ti
Al
P
S
TRIP590 DP590
0.11 0.11
1.55 1.43
1.05 0.4
0.1 0.21
0.03 –
0.008 0.01
0.08 0.03
0.1 0.01
– 0.02
– 0.02
– 0.01
– 0.01
hardening followed by slight hardening or softening. The amount of initial cyclic hardening increases with initial retained austenite content and total strain amplitude. Sugimoto et al. [8] pointed out that large cyclic hardening occurred at room temperature, while with increasing deformation temperature or retained austenite stability, the amount of cyclic hardening decreased with a significant decrease in plastic strain amplitude. The effect of microstructures on improved crack initiation life and fatigue crack growth resistance of TRIP steel versus DP steel were described in [5] and [9] respectively. As the finite element method is widely employed in ground vehicle industry, appraising the fatigue characterizations of components with notch geometry in the design stage is a prerequisite for realizing the potential of TRIP steel in auto-body [10,11]. Compared with other performances, the prediction accuracy of fatigue life has not been satisfactory. The main influence factors include the selection of prediction method and the relevant description
of cyclic behavior of materials. It is local strain-life method that is suitable, effective and predominant for this case to date, because the fatigue life of structures with stress concentration is dependent on the local stress–strain state of hot point [12,13]. Unfortunately, few local strain-life models of TRIP steels have been developed in literature until now. In the present work, static tension and strain-controlled fatigue experiments on smooth specimens of TRIP and DP steels with the same grade were performed at ambient temperature. Experimental procedures are detailed. Experimental result comparisons of static mechanical characterization, cyclic stress response, fatigue life and cyclic stabilized stress–strain behavior between TRIP and DP steels were drawn. At the same time, local strain-life models of two kinds of steels were developed by linear regression of experimental data. Furthermore, the fatigue durability comparison between notched TRIP and DP component for the body lightweight was carried out by finite element analysis based on the developed models.
2. Materials preparation and experimental procedures
(a)
2.1. Microstructure of materials
20μm
(b)
TRIP steel considered in the present study is a 590 MPa grade commercial steel sheet with a thickness of 0.7 mm, the steel sheet for comparison is a commercial DP590 and 2.25 mm in thickness. The chemical composition is listed in Table 1. A two-stage etching procedure, 4% picral etching followed by 1% aqueous solution of Na2S2O5 tinting, was employed to reveal the multiphase microstructure of TRIP steel. The picral solution was mixed with a few drops of HCl to sharpen the grain boundaries. DP steel was etched with a 5% Nital solution. The volume fraction of retained austenite was quantified from the integrated intensity of (2 1 1)a, (2 0 0)a, (2 2 0)c and (2 0 0)c diffraction peaks according to ASTM E975-03. X-ray diffraction data were collected by a Proto iXRD Combo diffractometer (25 kV, 4 mA) equipped with a Vanadium filter and Cr Ka radiation. Volume fraction analysis was carried out by Proto software. The microstructures of TRIP and DP steels are shown in Fig. 1. The microstructure of TRIP590 consists of ferrite (large off-white), bainite (brown)1 and retained austenite (bluish background). The initial volume fraction of retained austenite is 5.7% measured by XRD diffractometry. The microstructure of DP590 is comprised of ferrite (bright) and martensite (dark). The measured volume fraction of retained austenite in TRIP590 is 5.1% in the vicinity of crack tip of fatigued specimens at the total strain amplitude of 0.6%.
2.2. Experimental procedures Static tensile tests were performed on a Zwick Roell tensile testing machine with 20 kN load capacity in accordance with ASTM E8M-04. Standard tensile specimens electric discharge machined along the rolling direction have a gauge length of 50 mm and a width of 12.5 mm. The crosshead velocity was maintained at 0.5 mm/min.
Fig. 1. Optical micrograph of (a) TRIP590 and (b) DP590.
1 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.
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Strain-controlled fatigue tests were conducted for smooth specimens on a closed-loop servo-hydraulic fatigue testing machine of Shimadzu with 50 kN load capacity according to ASTM E606-04. Standard fatigue specimens electric discharge machined along the rolling direction have a parallel length of 7.9 mm and a width of 5 mm. The edges of fatigue specimens were well polished before testing. A fully reversed (R = 1) triangular total strain–time waveform was applied at a constant strain rate of 0.005 s1, controlled by an Epsilon extensometer with 5 mm gage length. Fatigue failure was determined as a tensile load drop of 20% from that of the stabilized hysteresis loops. Results of failure between or at knife edges of extensometer were adopted, while results of failure outside knife edges were discarded. Three geometrically similar specimens glued together by a modified acrylate adhesive were employed to prevent buckling of TRIP590 (ASTM E606-04). 3. Results and discussions 3.1. Static mechanical characterization The engineering stress–strain curves of TRIP590 and DP590 are illustrated in Fig. 2a, and true stress–strain curves up to uniform elongation are given in Fig. 2b. The main static mechanical properties are summarized in Table 2. The uniform elongation, total elongation and the ratio of uniform elongation to total elongation of TRIP590 are all superior to those of DP590, representing TRIP steel offers improved ductility than DP steel. TRIP590 shows characteristic yield point elongation phenomenon during yielding due to the
(a)
700
Engineering Stress (MPa)
600
Material
YS (MPa)
UTS (MPa)
UE (%)
TE (%)
UE/TE (%)
TRIP590 DP590
421 400
635.6 601
28.18 17.01
39.49 30.95
71.36 54.96
YS: yield strength or 0.2% offset yield strength, UTS: ultimate tensile strength, UE: uniform elongation, TE: total elongation.
transformation of austenite to martensite, whereas DP590 is characterized by a continuous yielding behavior. DP590 possesses higher strain hardening level than TRIP590 during the initial stage of deformation up to true strain of 0.12; however TRIP590 sustains superior uniform hardening capacity to DP590 in the higher strain regime. The calculated instantaneous strain hardening exponent (n-value) of TRIP590 and DP590 is shown in Fig. 3 as square and triangle symbols. TRIP590 has less initial n-value than DP590, but the n-value of TRIP590 increases and sustains a high level within a broad strain scope, whereas the increase in n-value of DP590 is restricted to the initial deformation stage. The n-value of DP590 is less than that of TRIP590 almost throughout the entire deformation process. The maximum n-value of TRIP590 is 0.2576 at strain of 0.1864, and the maximum n-value of DP590 is 0.1664 at strain of 0.0370. The terminal n-value of TRIP and DP steels is 0.2460 and 0.1529 respectively. The enhanced ductility and strength of TRIP steel are due to the gradually strain-induced transformation of retained austenite to martensite. The product martensite phase has a higher strength than the parent austenite phase. The phase transformation is accompanied by a volume expansion, resulting in plastic deformation and work hardening of the surrounding ferrite and bainite phases. Both effects improve the strain hardening and suppress the onset of macroscopic necking of TRIP steels.
500
3.2. Cyclic stress response 400
DP590
TRIP590
300 200 100 0 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Engineering Strain (mm/mm)
(b)
Table 2 Static mechanical properties of TRIP590 and DP590 sheet steels.
The cyclic stress amplitude of TRIP590 and DP590 versus number of cycles are illustrated in Fig. 4. Cyclic stress behavior of TRIP590 is characterized by cyclic hardening or softening at different strain amplitudes. Cyclic hardening followed by cyclic stable occurred at strain amplitudes of 0.3% and below; however cyclic stable or slight cyclic softening and successive cyclic softening occurred at strain amplitudes above 0.3%. Cyclic stress behavior of DP590 is characterized by consistent cyclic softening and successive stable throughout entire strain amplitude scope of test. Thanks
900 0.300
700
0.275
TRIP590 DP590
600 500 400 300 200 100
0.250
Instantaneous n-value
True Stress (MPa)
800
TRIP590
0.225 0.200 0.175 0.150 0.125
DP590
0.100 0.075 0.050 0.025
0 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275
True Strain (mm/mm)
0.000 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250
True Strain (mm/mm) Fig. 2. (a) Engineering stress–strain curves and (b) true stress–strain curves up to uniform elongation of TRIP590 and DP590.
Fig. 3. Instantaneous n-value of TRIP590 and DP590.
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500
0.7% 0.6% 0.4% 0.3% 0.25% 0.2%
480 460 440 420 400 380 360 340 320
True Total Strain Amplitude (mm/mm)
(a)
Engineering Cyclic Stress Amplitude (MPa)
Z.G. Hu et al. / Materials and Design 31 (2010) 2884–2890
300 10
100
1000
10000
0.01 0.009 0.008 0.007 0.006
ε=εae+εap=814.1417/206000*(2Nf)-0.06788 +0.7845*(2Nf)-0.6204
0.005 0.004 0.003
εap=0.7845*(2Nf)-0.6204 RMSE=0.04391 R2=0.9879
0.002
εae=814.1417/206000*(2Nf)-0.06788 RMSE=0.04796 R2=0.9873 1E-3 1000
10000
100000
(a)
450
0.6% 0.5% 0.4% 0.3% 0.2%
425 400 375 350 325 300 275 250 225
True Total Strain Amplitude (mm/mm)
Engineering Cyclic Stress Amplitude (MPa)
N (cycle)
(b)
200 10
100
1000
1000000
2Nf (reversal)
100000
10000
0.01 0.009 0.008 0.007 0.006
εa=εae+εap=896.8091/206000*(2Nf)-0.09869 +0.3355*(2Nf)-0.5290
0.005 0.004 0.003
εap=0.3355*(2Nf)-0.5290 RMSE=0.03020 R2=0.9917
0.002
εae=896.8091/206000*(2Nf)-0.09869 RMSE=0.05125 R2=0.9893
1E-3 1000
10000
100000
100000
1000000
2Nf (reversal)
N (Cycle)
(b)
Fig. 4. Cyclic stress amplitude versus cycle number of (a) TRIP590 and (b) DP590.
Fig. 5. Experimental result of fatigue life and strain-life regression model of (a) TRIP590 and (b) DP590.
to the strain hardening behavior of parent retained austenite and product martensite, the cyclic softening resistance of TRIP steel is superior to that of DP steel. Cyclic loadings change the interior microstructures of multiphase steel; hence influence the distribution of interior microdeformation within different phases, which determines the macro mechanical behavior of multiphase steel. Generally, materials will cyclically harden in the initial cycles due to high dislocation density and reduced dislocation mobility. Cyclic softening is primarily due to the generation of additional mobile dislocations, reconfiguration of the existing dislocation structures, and formation of a dislocation cell structure of lowered internal stress [5,13]. Another factor for the cyclic softening of TRIP590 at higher strain amplitudes is the relaxation of local internal stress due to the transformation of retained austenite to martensite. 3.3. Local strain-life analysis The experimental results of strain-controlled fatigue life and relevant cyclic stabilized stress–strain behavior of smooth specimens of TRIP590 and DP590 are presented in Figs. 5 and 6 as the square and triangle symbols. The superimposed regression curves are derived for the life prediction of the notched body component with finite element method in the next section. The experimental curve of monotonic tension is also superimposed in Fig. 6 to compare the difference between monotonic and cyclic mechanical behavior of materials.
3.3.1. Regression analysis of strain-life relationship The Basquin equation for stress amplitude versus fatigue life takes the following form:
ra ¼ r0f ð2Nf Þb
ð1Þ
hence, the elastic strain amplitude versus fatigue life equation can be expressed as:
eea ¼
r0f E
ð2N f Þb
ð2Þ
The Coffin–Manson equation for plastic strain amplitude versus fatigue life is:
epa ¼ e0f ð2N f Þc
ð3Þ
Combining Eqs. (2) and (3) gives the relationship between the total strain amplitude and fatigue life:
ea ¼ eea þ epa ¼
r0f E
ð2N f Þb þ e0f ð2Nf Þc
ð4Þ
where ea, eea , epa , r0f , b, e0f , c and 2Nf are total strain amplitude, elastic strain amplitude, plastic strain amplitude, fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient, fatigue ductility exponent and fatigue life in reversals to failure, respectively. The total strain amplitude-life equation is the summation of two separate curves for elastic strain amplitude-life (eea 2N f ) and plastic strain amplitude-life (epa 2N f ), both of which are repre-
(a)
Z.G. Hu et al. / Materials and Design 31 (2010) 2884–2890
550 500
monotonic stress-strain curve
450
True Stress (MPa)
400 350 300
cyclic stress-strain curve
250
ε=σ/206000+(σ/784)1/0.0982
RMSE=0.006324
200
R2=0.99999996
150 100 50
0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
True Strain (mm/mm)
(b)
0.01 0.009 0.008 0.007 0.006 0.005
TRIP590
0.004 0.003
DP590 0.002
1E-3 1000
10000
100000
1000000
2Nf (reversal) 550
Fig. 7. Comparison of strain-life curves between TRIP590 and DP590.
500 450
True Stress (MPa)
True Total Strain Amplitude (mm/mm)
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monotonic stress-strain curve
400
3.3.2. Regression analysis of cyclic stabilized stress–strain relationship Steady-state cyclic stress–strain relationship can be described by Ramberg–Osgood model
350 300 250 200 150 100
ea ¼ eea þ epa ¼
cyclic stress-strain curve ε=σ/206000+(σ/1466)1/0.2323
RMSE=0.003166 R2=0.9976
50 0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
True Strain (mm/mm)
sented with straight lines on log–log scale. The nonlinear leastsquares method might be employed to determine the total strainlife model (Eq. (4)), but the approach preferred is to fit elastic strain amplitude-life (Eq. (2)) and plastic strain amplitude-life (Eq. (3)) on log–log scale separately with a linear least-squares method, because it gives less weight to misleading low-cycle and high-cycle data and provides better results [4,14]. Taking the logarithm on both sides of Eqs. (1) and (3), the following linear regression expressions can be derived:
1 ðlog ra log r0f Þ b 1 logð2N f Þ ¼ ðlog epa log e0f Þ c
E
þ
ra
1=n0
K0
ð5Þ ð6Þ
Firstly, the elastic and plastic strain amplitudes are calculated to estimate the transition fatigue life roughly; then r0f , b and e0f , c can be determined from the experimental data of elastic strain dominant high-cycle fatigue region and plastic strain dominant low-cycle fatigue region by linear least-squares regression analysis of Eqs. (5) and (6), respectively. The logarithms of true stress amplitude in the vicinity of 0.5 Nf and true plastic strain amplitude are treated as statistically independent variables, and the logarithm of the failure life in reversals as dependent variable. A threshold of plastic strain amplitude of 0.0005 is selected for Eq. (6) to avoid measurement errors [14]. The regression parameters, root mean square error (RMSE) and coefficient of determination (R2) regression statistic of strain-life relationship of TRIP590 and DP590 are given in Fig. 5.
ð7Þ
where K0 and n0 are cyclic strength coefficient and cyclic strain hardening exponent. 0 Taking the logarithm on both sides of equation epa ¼ ra =K 0 1=n gives the following linear regression equation for K0 and n0 :
log ra ¼ n0 log epa þ log K 0
Fig. 6. Comparison between monotonic and regressive cyclic stabilized stress– strain curves of (a) TRIP590 and (b) DP590.
logð2N f Þ ¼
ra
ð8Þ
The logarithm of true plastic strain amplitude is treated as statistically independent variable, and the logarithm of the stress amplitude as dependent variable in the linear regression procedure. Plastic strain amplitudes less than 0.0005 are discarded [14]. The regression parameters and effectiveness of cyclic stabilized stress–strain relationship of TRIP590 and DP590 are given in Fig. 6. 3.3.3. Discussion on local strain-life properties Fig. 6 illustrates that, compared with the monotonic tension behavior, the yield point elongation phenomenon of TRIP590 during monotonic tension is replaced with continuous yielding in the cyclic case, and TRIP590 and DP590 exhibit cyclic mixed and cyclic softening behavior within the test scope, respectively. The cyclic stabilized stress–strain data and curve of two steels do not have evident yield point, and the 0.2% offset cyclic yield strength of TRIP590 and DP590 are 426 and 346 MPa respectively. Figs. 7 and 8 give the comparisons of strain-life and cyclic stabilized stress–strain behavior between TRIP590 and DP590. It can be concluded that the fatigue life and cyclic stabilized stress of TRIP590 are superior to those of DP590 throughout entire strain amplitude range of test. The contribution factors to enhanced fatigue life of TRIP steel versus DP steel mainly include [5,9]: higher ductility, higher cyclic yield strength and cyclic stress, and the transformation of retained austenite. The uniform elongation of TRIP590 is 28.18% versus 17.01% of DP590 (Table 2), higher ductility improves the tolerance to accumulated plastic strain. The higher cyclic yield strength and cyclic stress (Fig. 8) imply higher elastic strain component at specific total strain amplitude, and consequently lower plastic strain component. Since the mechanism of fatigue damage is the accumulation of cyclic plastic strain, lower plastic strain component will result in less accumulated fatigue damage in every reversal.
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True Stress Amplitude (MPa)
600
500
TRIP590
400
300
DP590 200
100
0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
(a)
True Strain Amplitude (mm/mm) Fig. 8. Comparison of cyclic stabilized stress–strain curves between TRIP590 and DP590.
The volume fraction reduction of retained austenite from initially 5.7% to 5.1% in the fatigued specimen under total strain amplitude of 0.6% demonstrates that the austenite in the vicinity of crack tip has partly transformed into martensite. Phase transformation can absorb deformation energy, relax local stress concentration and bring about compressive internal stress in the matrix, all of which will suppress the initiation and retard the propagation of micro cracks. 4. Application in the lightweight design of body component The potential of TRIP590 versus DP590 in offering enhanced fatigue durability for the lightweight case of body structures with stress concentration was explored on a front shock-absorber tower of a sports utility vehicle. The shock-absorber tower is the main load-carrying component whose fatigue life needs to be ensured. Material of DC04 is used in the baseline design, TRIP590 and DP590 are selected in the lightweight design. According to the thickness of AHSS for body lightweight proposed in [15], 35% weight saving can be achieved by this material substitution. The geometry of the shock-absorber tower is shown in Fig. 9a. Stress analysis and life prediction were performed on whole auto-body with finite element software MSC.Nastran and MSC.Fatigue respectively. One block of typical road spectrum was imposed on the tires to simulate the service environment. The local strain-life models of TRIP590 and DP590 developed in the preceding section were implemented in the finite element analysis. The predicted fatigue life contour of the shock-absorber tower with TRIP590 and DP590 material is shown in Fig. 9b and c, respectively. It is revealed that the minimum life of TRIP and DP component is 90,700 repeats and 7570 repeats respectively, and the minimum life of TRIP steel component is nearly 12 times as high as that of DP steel. This application case illustrates that TRIP steel can provide superior fatigue life for the same notched geometry, exterior loading and lightweight result. According to Neuber’s hypothesis on the local true notch stress and local true notch strain after local yielding, the fatigue strength reduction factor Kf is the geometric mean of true stress amplitude concentration factor and true strain amplitude concentration factor under a plane stress cyclic condition, hence the following equation can be derived:
where DS and De are the nominal elastic stress and strain ranges, Dr and De are the local true notch stress and strain ranges. In the case of nominally elastic behavior, De = DS/E, so the following expression can be obtained:
DrDe ¼ K 2f DSDe
EDrDe ¼ K 2f DS2
ð9Þ
(b)
(c) Fig. 9. (a) Geometry of the considered shock-absorber tower, and the predicted fatigue life made of (b) TRIP590 and (c) DP590.
ð10Þ
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Z.G. Hu et al. / Materials and Design 31 (2010) 2884–2890 900 TRIP590 DP590
Neuber Factor (MPa)
800 700
600
500
400 300
200 1000
10000
100000
ever cyclic softening followed by stable occurs consistently for DP steel throughout entire strain amplitude range of test. Moreover the cyclic stress response shows that the cyclic softening resistance of TRIP steel is superior to that of DP steel. Thirdly, the experimental results on fatigue life and cyclic stabilized stress, and the developed local strain-life models of two steels indicate that TRIP steel has enhanced life and cyclic stress than DP steel at the same strain amplitude. Fourthly, the finite element application case illustrates that the TRIP component can provide improved fatigue durability than DP one for the same notched geometry, exterior loading and lightweight result. Finally, all above indicate that TRIP steel is more ideal for auto-body lightweight, especially for heavy loading components, due to its improved ductility and fatigue resistance resulted from the unique strengthening mechanism.
1000000
2Nf (reversal) Fig. 10. Comparison of experimental Neuber factor-life between TRIP590 and DP590.
qffiffiffiffiffiffiffiffiffiffiffiffiffi The Neuber factor is defined as E D2r D2e or K f D2S. Kf equals unity if the stress results for local strain-life method are determined from linear-elastic finite element analysis, hence, Neuber factor is the elastic stress at the stress concentration location. Linear-elastic stress analysis is dependent on geometry, exterior loading and elastic properties of material, while independent of the fatigue properties of material. Therefore, Neuber factor, considering all six local strain-life parameters (r0f , b, e0f , c, K0 and n0 ), can clarify different fatigue resistance of notched component made of different materials [16,17]. The comparison of Neuber factor-life between TRIP590 and DP590 illustrated in Fig. 10 manifests that TRIP590 has superior fatigue life to DP590 throughout entire range of test. This accounts for the fatigue life prolongation of the shock-absorber tower with TRIP590 material. The fatigue resistance of TRIP steel component is enhanced due to the simultaneously improved life and cyclic stress amplitude at the same strain amplitude. Hence, TRIP steel is an excellent substitute for DP steel to achieve equivalent strength and lightweight results, because TRIP steel is more suitable to manufacture notched body components from the viewpoint of design against fatigue failures. 5. Conclusions To evaluate the fatigue performance of notched body components made of low-alloy TRIP or DP steel, and select reasonable material from a fatigue durability viewpoint during the auto-body design stage, monotonic and cyclic strain-controlled fatigue experiments on smooth specimens of TRIP and DP steels with 590 MPa grade were conducted. Local strain-life models of two steels were developed by linear regression of the fatigue experiment data, which were employed to predict and compare the fatigue life of notched body structures made of them by finite element method. Different monotonic and cyclic mechanical behaviors were observed due to different interior microstructures, despite equivalent strength. Firstly, the static tension result demonstrates that TRIP steel can preserve superior ductility to DP steel without compromising strength. Secondly, the cyclic stress behavior of TRIP steel is characterized by cyclic hardening followed by stable at lower strain amplitudes, and softening at higher strain amplitudes; how-
Acknowledgements The research was supported by the National Natural Science Foundation of China (Grant No. 50875164). A great appreciation should be given to Prof. Songlin Zheng from University of Shanghai for Science and Technology, China for his invaluable and fruitful technical discussion. References [1] Van Slycken J, Verleysen P, Degrieck J, Samek L, De Cooman BC. High-strainrate behavior of low-alloy multiphase aluminum- and silicon-based transformation-induced plasticity steels. Metall Mater Trans A Phys Metall Mater Sci 2006;37A(5):1527–39. [2] Laxman S, Mohan Iyengar R, Roche C, Amaya M. Application of advanced high strength steels for enhanced durability of a shock tower assembly. In: 2005 SAE world congress, SAE technical paper series no. 2005-01-0501. Detroit (MI): Society of Automotive Engineers; 2005. [3] Senuma T. Physical metallurgy of modern high strength steel sheets. ISIJ Int 2001;41(6):520–32. [4] Lee Y, Pan J, Hathaway R, Barkey M. Fatigue testing and analysis. Burlington (MA): Elsevier Butterworth-Heinemann; 2005. [5] 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 Phys Metall Mater Sci 2009;40A(2):342–53. [6] Yokoi T, Takahashi M. Effect of microstructure on fatigue properties of hotrolled sheet steels. In: 2003 SAE world congress, SAE technical paper series no. 2003-01-2880. Detroit (MI): Society of Automotive Engineers; 2003. [7] Yasuki S, Sugimoto K, Kobayashi M, Hashimoto S. Low cycle fatigue-hardening of TRIP-aided dual-phase steels. Nippon Kinzoku Gakkaishi 1990;54(12):1350–7 (in Japanese). [8] Sugimoto K, Kobayashi M, Yasuki S. Cyclic deformation behavior of a transformation-induced plasticity-aided dual-phase steel. Metall Mater Trans A Phys Metall Mater Sci 1997;28A(12):2637–44. [9] Cheng X, Petrov R, Zhao L, Janssen M. Fatigue crack growth in TRIP steel under positive R-ratios. Eng Fract Mech 2008;75(3–4):739–49. [10] Medekshas H, Balina V. Assessment of low cycle fatigue strength of notched components. Mater Des 2006;27(2):132–40. [11] Fourlaris G, Ellwood R, Jones TB. The reliability of test results from simple test samples in predicting the fatigue performance of automotive components. Mater Des 2007;28(4):1198–210. [12] American Iron and Steel Institute. Automotive steel design manual. 6.1 ed. Southfield (MI): American Iron and Steel Institute; 2002. [13] Stephens RI, Fatemi A, Stephens RR, Fuchs HO. Metal fatigue in engineering. 2nd ed. New York (NY): John Wiley & Sons; 2001. [14] Williams CR, Lee YL, Rilly JT. A practical method for statistical analysis of strain-life fatigue data. Int J Fatigue 2003;25(5):427–36. [15] Li YX, Lin ZQ, Jiang AQ, Chen GL. Use of high strength steel sheet for lightweight and crashworthy car body. Mater Des 2003;24(3):177–82. [16] Yan B, Belanger P, Citrin K. Effect of forming strain on fatigue performance of a mild automotive steel. In: 2001 SAE world congress, SAE technical paper series no. 2001-01-0083. Detroit (MI): Society of Automotive Engineers; 2001. [17] Khosrovaneh A, Pattu R, Schnaidt W. Discussion of fatigue analysis techniques in automotive applications. In: 2004 SAE world congress, SAE technical paper series no. 2004-01-0626. Detroit (MI): Society of Automotive Engineers; 2004.
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Materials and Design journal homepage: www.elsevier.com/locate/matdes
Fatigue properties of transformation-induced plasticity and dual-phase steels for auto-body lightweight: Experiment, modeling and application Z.G. Hu, P. Zhu *, J. Meng State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
a r t i c l e
i n f o
Article history: Received 25 September 2009 Accepted 18 December 2009 Available online 24 December 2009 Keywords: A. Ferrous metals and alloys E. Fatigue H. Failure analysis
a b s t r a c t The substitution of conventional high strength steels (HSS) with advanced high strength steels (AHSS), e.g., low-alloy multiphase transformation-induced plasticity steel (TRIP steel) or dual-phase steel (DP steel), for body lightweight brings about increased stress of notched components. Thus the fatigue properties of TRIP and DP steels and the fatigue life of notched lightweight design are important considerations for reasonable material selection during the design stage of auto-body. For the mentioned issue, cyclic strain-controlled fatigue properties of TRIP and DP steels with equivalent grade and lightweight result were investigated experimentally. Different cyclic behaviors of TRIP and DP steels were observed due to different interior microstructures. The cyclic stress behavior of TRIP steel is characterized by cyclic hardening followed by stable at lower strain amplitudes, and softening at higher strain amplitudes; however cyclic softening followed by stable occurs consistently for DP steel throughout entire strain amplitude range of test. TRIP steel possesses enhanced fatigue life and cyclic stress at the same strain amplitude than DP steel. Furthermore, local strain-life models of two steels were developed by linear regression of experimental data, to predict and compare the fatigue life of notched body structures made of them by finite element method. The simulation result illustrates that TRIP steel can provide more beneficial potential than DP steel for the lightweight design of notched body structures from the viewpoint of fatigue resistance. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction AHSS can realize the lightweight of auto-body, reduce fuel consumption and exhaust emissions on one hand; improve service performances, e.g., stiffness, strength, crashworthiness [1], and fatigue durability [2] on the other hand. DP steel and low-alloy multiphase TRIP steel are two typical kinds of AHSS, of which TRIP steel has attracted more and more attention in the ground vehicle industry. TRIP steels with 5–15% initial volume fraction of retained austenite possess improved formability due to TRIP effect of retained austenite [3]. The applications of TRIP steel include structural components, reinforcement components and suspension components, e.g., pillars, rails, cross members, door reinforcement beam, bumper inner reinforcement, suspension arm. AHSS can provide superior static tensile strength, but this merit of materials cannot imply superior fatigue characterizations of body structures with notch geometry. The substitution of conventional HSS with AHSS for body lightweight brings about decreased thickness but increased stress of components. Cyclic micro-plasticity in the stress concentration regions of body components will re* Corresponding author. Tel./fax: +86 21 34206787. E-mail address: [email protected] (P. Zhu). 0261-3069/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2009.12.034
sult in the initiation of fatigue cracks [4]. Fatigue cracks degrade the continuity of material state; hence influence other performances of auto-body during its service life, e.g., stiffness, strength, NVH, and crashworthiness. Consequently, the fatigue resistance, especially the low-cycle fatigue resistance, is an important consideration for structure design and material selection of auto-body [5]. The results of stress-controlled fatigue tests on smooth specimens [3,6] demonstrate that the fatigue strength of TRIP steel is superior to HSS and DP steel with equivalent strength. It can be concluded from Yokoi and Takahashi [6] that the fatigue strength of TRIP steel is also higher than DP steel and high-strength low-alloy steel (HSLA steel) under the stress concentration conditions. In the case of smooth specimens, the fatigue limit and fatigue strength of steel materials increase with static tensile strength. But for specimens with stress concentration, the fatigue limit and fatigue strength of HSS do not always increase with static tensile strength, while those of the DP and TRIP steels still increase with static tensile strength. The results of strain-controlled fatigue tests indicate that different microstructures and their mechanical properties, and different environment can influence the cyclic stress response of TRIP steels. Yasuki et al. [7] mentioned that the cyclic stress response of TRIP steel was characterized by severe initial
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Z.G. Hu et al. / Materials and Design 31 (2010) 2884–2890 Table 1 Chemical composition (wt.%) of TRIP590 and DP590 sheet steels. Material
C
Mn
Si
Cr
Mo
V
Ni
Cu
Ti
Al
P
S
TRIP590 DP590
0.11 0.11
1.55 1.43
1.05 0.4
0.1 0.21
0.03 –
0.008 0.01
0.08 0.03
0.1 0.01
– 0.02
– 0.02
– 0.01
– 0.01
hardening followed by slight hardening or softening. The amount of initial cyclic hardening increases with initial retained austenite content and total strain amplitude. Sugimoto et al. [8] pointed out that large cyclic hardening occurred at room temperature, while with increasing deformation temperature or retained austenite stability, the amount of cyclic hardening decreased with a significant decrease in plastic strain amplitude. The effect of microstructures on improved crack initiation life and fatigue crack growth resistance of TRIP steel versus DP steel were described in [5] and [9] respectively. As the finite element method is widely employed in ground vehicle industry, appraising the fatigue characterizations of components with notch geometry in the design stage is a prerequisite for realizing the potential of TRIP steel in auto-body [10,11]. Compared with other performances, the prediction accuracy of fatigue life has not been satisfactory. The main influence factors include the selection of prediction method and the relevant description
of cyclic behavior of materials. It is local strain-life method that is suitable, effective and predominant for this case to date, because the fatigue life of structures with stress concentration is dependent on the local stress–strain state of hot point [12,13]. Unfortunately, few local strain-life models of TRIP steels have been developed in literature until now. In the present work, static tension and strain-controlled fatigue experiments on smooth specimens of TRIP and DP steels with the same grade were performed at ambient temperature. Experimental procedures are detailed. Experimental result comparisons of static mechanical characterization, cyclic stress response, fatigue life and cyclic stabilized stress–strain behavior between TRIP and DP steels were drawn. At the same time, local strain-life models of two kinds of steels were developed by linear regression of experimental data. Furthermore, the fatigue durability comparison between notched TRIP and DP component for the body lightweight was carried out by finite element analysis based on the developed models.
2. Materials preparation and experimental procedures
(a)
2.1. Microstructure of materials
20μm
(b)
TRIP steel considered in the present study is a 590 MPa grade commercial steel sheet with a thickness of 0.7 mm, the steel sheet for comparison is a commercial DP590 and 2.25 mm in thickness. The chemical composition is listed in Table 1. A two-stage etching procedure, 4% picral etching followed by 1% aqueous solution of Na2S2O5 tinting, was employed to reveal the multiphase microstructure of TRIP steel. The picral solution was mixed with a few drops of HCl to sharpen the grain boundaries. DP steel was etched with a 5% Nital solution. The volume fraction of retained austenite was quantified from the integrated intensity of (2 1 1)a, (2 0 0)a, (2 2 0)c and (2 0 0)c diffraction peaks according to ASTM E975-03. X-ray diffraction data were collected by a Proto iXRD Combo diffractometer (25 kV, 4 mA) equipped with a Vanadium filter and Cr Ka radiation. Volume fraction analysis was carried out by Proto software. The microstructures of TRIP and DP steels are shown in Fig. 1. The microstructure of TRIP590 consists of ferrite (large off-white), bainite (brown)1 and retained austenite (bluish background). The initial volume fraction of retained austenite is 5.7% measured by XRD diffractometry. The microstructure of DP590 is comprised of ferrite (bright) and martensite (dark). The measured volume fraction of retained austenite in TRIP590 is 5.1% in the vicinity of crack tip of fatigued specimens at the total strain amplitude of 0.6%.
2.2. Experimental procedures Static tensile tests were performed on a Zwick Roell tensile testing machine with 20 kN load capacity in accordance with ASTM E8M-04. Standard tensile specimens electric discharge machined along the rolling direction have a gauge length of 50 mm and a width of 12.5 mm. The crosshead velocity was maintained at 0.5 mm/min.
Fig. 1. Optical micrograph of (a) TRIP590 and (b) DP590.
1 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.
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Strain-controlled fatigue tests were conducted for smooth specimens on a closed-loop servo-hydraulic fatigue testing machine of Shimadzu with 50 kN load capacity according to ASTM E606-04. Standard fatigue specimens electric discharge machined along the rolling direction have a parallel length of 7.9 mm and a width of 5 mm. The edges of fatigue specimens were well polished before testing. A fully reversed (R = 1) triangular total strain–time waveform was applied at a constant strain rate of 0.005 s1, controlled by an Epsilon extensometer with 5 mm gage length. Fatigue failure was determined as a tensile load drop of 20% from that of the stabilized hysteresis loops. Results of failure between or at knife edges of extensometer were adopted, while results of failure outside knife edges were discarded. Three geometrically similar specimens glued together by a modified acrylate adhesive were employed to prevent buckling of TRIP590 (ASTM E606-04). 3. Results and discussions 3.1. Static mechanical characterization The engineering stress–strain curves of TRIP590 and DP590 are illustrated in Fig. 2a, and true stress–strain curves up to uniform elongation are given in Fig. 2b. The main static mechanical properties are summarized in Table 2. The uniform elongation, total elongation and the ratio of uniform elongation to total elongation of TRIP590 are all superior to those of DP590, representing TRIP steel offers improved ductility than DP steel. TRIP590 shows characteristic yield point elongation phenomenon during yielding due to the
(a)
700
Engineering Stress (MPa)
600
Material
YS (MPa)
UTS (MPa)
UE (%)
TE (%)
UE/TE (%)
TRIP590 DP590
421 400
635.6 601
28.18 17.01
39.49 30.95
71.36 54.96
YS: yield strength or 0.2% offset yield strength, UTS: ultimate tensile strength, UE: uniform elongation, TE: total elongation.
transformation of austenite to martensite, whereas DP590 is characterized by a continuous yielding behavior. DP590 possesses higher strain hardening level than TRIP590 during the initial stage of deformation up to true strain of 0.12; however TRIP590 sustains superior uniform hardening capacity to DP590 in the higher strain regime. The calculated instantaneous strain hardening exponent (n-value) of TRIP590 and DP590 is shown in Fig. 3 as square and triangle symbols. TRIP590 has less initial n-value than DP590, but the n-value of TRIP590 increases and sustains a high level within a broad strain scope, whereas the increase in n-value of DP590 is restricted to the initial deformation stage. The n-value of DP590 is less than that of TRIP590 almost throughout the entire deformation process. The maximum n-value of TRIP590 is 0.2576 at strain of 0.1864, and the maximum n-value of DP590 is 0.1664 at strain of 0.0370. The terminal n-value of TRIP and DP steels is 0.2460 and 0.1529 respectively. The enhanced ductility and strength of TRIP steel are due to the gradually strain-induced transformation of retained austenite to martensite. The product martensite phase has a higher strength than the parent austenite phase. The phase transformation is accompanied by a volume expansion, resulting in plastic deformation and work hardening of the surrounding ferrite and bainite phases. Both effects improve the strain hardening and suppress the onset of macroscopic necking of TRIP steels.
500
3.2. Cyclic stress response 400
DP590
TRIP590
300 200 100 0 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Engineering Strain (mm/mm)
(b)
Table 2 Static mechanical properties of TRIP590 and DP590 sheet steels.
The cyclic stress amplitude of TRIP590 and DP590 versus number of cycles are illustrated in Fig. 4. Cyclic stress behavior of TRIP590 is characterized by cyclic hardening or softening at different strain amplitudes. Cyclic hardening followed by cyclic stable occurred at strain amplitudes of 0.3% and below; however cyclic stable or slight cyclic softening and successive cyclic softening occurred at strain amplitudes above 0.3%. Cyclic stress behavior of DP590 is characterized by consistent cyclic softening and successive stable throughout entire strain amplitude scope of test. Thanks
900 0.300
700
0.275
TRIP590 DP590
600 500 400 300 200 100
0.250
Instantaneous n-value
True Stress (MPa)
800
TRIP590
0.225 0.200 0.175 0.150 0.125
DP590
0.100 0.075 0.050 0.025
0 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275
True Strain (mm/mm)
0.000 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250
True Strain (mm/mm) Fig. 2. (a) Engineering stress–strain curves and (b) true stress–strain curves up to uniform elongation of TRIP590 and DP590.
Fig. 3. Instantaneous n-value of TRIP590 and DP590.
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500
0.7% 0.6% 0.4% 0.3% 0.25% 0.2%
480 460 440 420 400 380 360 340 320
True Total Strain Amplitude (mm/mm)
(a)
Engineering Cyclic Stress Amplitude (MPa)
Z.G. Hu et al. / Materials and Design 31 (2010) 2884–2890
300 10
100
1000
10000
0.01 0.009 0.008 0.007 0.006
ε=εae+εap=814.1417/206000*(2Nf)-0.06788 +0.7845*(2Nf)-0.6204
0.005 0.004 0.003
εap=0.7845*(2Nf)-0.6204 RMSE=0.04391 R2=0.9879
0.002
εae=814.1417/206000*(2Nf)-0.06788 RMSE=0.04796 R2=0.9873 1E-3 1000
10000
100000
(a)
450
0.6% 0.5% 0.4% 0.3% 0.2%
425 400 375 350 325 300 275 250 225
True Total Strain Amplitude (mm/mm)
Engineering Cyclic Stress Amplitude (MPa)
N (cycle)
(b)
200 10
100
1000
1000000
2Nf (reversal)
100000
10000
0.01 0.009 0.008 0.007 0.006
εa=εae+εap=896.8091/206000*(2Nf)-0.09869 +0.3355*(2Nf)-0.5290
0.005 0.004 0.003
εap=0.3355*(2Nf)-0.5290 RMSE=0.03020 R2=0.9917
0.002
εae=896.8091/206000*(2Nf)-0.09869 RMSE=0.05125 R2=0.9893
1E-3 1000
10000
100000
100000
1000000
2Nf (reversal)
N (Cycle)
(b)
Fig. 4. Cyclic stress amplitude versus cycle number of (a) TRIP590 and (b) DP590.
Fig. 5. Experimental result of fatigue life and strain-life regression model of (a) TRIP590 and (b) DP590.
to the strain hardening behavior of parent retained austenite and product martensite, the cyclic softening resistance of TRIP steel is superior to that of DP steel. Cyclic loadings change the interior microstructures of multiphase steel; hence influence the distribution of interior microdeformation within different phases, which determines the macro mechanical behavior of multiphase steel. Generally, materials will cyclically harden in the initial cycles due to high dislocation density and reduced dislocation mobility. Cyclic softening is primarily due to the generation of additional mobile dislocations, reconfiguration of the existing dislocation structures, and formation of a dislocation cell structure of lowered internal stress [5,13]. Another factor for the cyclic softening of TRIP590 at higher strain amplitudes is the relaxation of local internal stress due to the transformation of retained austenite to martensite. 3.3. Local strain-life analysis The experimental results of strain-controlled fatigue life and relevant cyclic stabilized stress–strain behavior of smooth specimens of TRIP590 and DP590 are presented in Figs. 5 and 6 as the square and triangle symbols. The superimposed regression curves are derived for the life prediction of the notched body component with finite element method in the next section. The experimental curve of monotonic tension is also superimposed in Fig. 6 to compare the difference between monotonic and cyclic mechanical behavior of materials.
3.3.1. Regression analysis of strain-life relationship The Basquin equation for stress amplitude versus fatigue life takes the following form:
ra ¼ r0f ð2Nf Þb
ð1Þ
hence, the elastic strain amplitude versus fatigue life equation can be expressed as:
eea ¼
r0f E
ð2N f Þb
ð2Þ
The Coffin–Manson equation for plastic strain amplitude versus fatigue life is:
epa ¼ e0f ð2N f Þc
ð3Þ
Combining Eqs. (2) and (3) gives the relationship between the total strain amplitude and fatigue life:
ea ¼ eea þ epa ¼
r0f E
ð2N f Þb þ e0f ð2Nf Þc
ð4Þ
where ea, eea , epa , r0f , b, e0f , c and 2Nf are total strain amplitude, elastic strain amplitude, plastic strain amplitude, fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient, fatigue ductility exponent and fatigue life in reversals to failure, respectively. The total strain amplitude-life equation is the summation of two separate curves for elastic strain amplitude-life (eea 2N f ) and plastic strain amplitude-life (epa 2N f ), both of which are repre-
(a)
Z.G. Hu et al. / Materials and Design 31 (2010) 2884–2890
550 500
monotonic stress-strain curve
450
True Stress (MPa)
400 350 300
cyclic stress-strain curve
250
ε=σ/206000+(σ/784)1/0.0982
RMSE=0.006324
200
R2=0.99999996
150 100 50
0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
True Strain (mm/mm)
(b)
0.01 0.009 0.008 0.007 0.006 0.005
TRIP590
0.004 0.003
DP590 0.002
1E-3 1000
10000
100000
1000000
2Nf (reversal) 550
Fig. 7. Comparison of strain-life curves between TRIP590 and DP590.
500 450
True Stress (MPa)
True Total Strain Amplitude (mm/mm)
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monotonic stress-strain curve
400
3.3.2. Regression analysis of cyclic stabilized stress–strain relationship Steady-state cyclic stress–strain relationship can be described by Ramberg–Osgood model
350 300 250 200 150 100
ea ¼ eea þ epa ¼
cyclic stress-strain curve ε=σ/206000+(σ/1466)1/0.2323
RMSE=0.003166 R2=0.9976
50 0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
True Strain (mm/mm)
sented with straight lines on log–log scale. The nonlinear leastsquares method might be employed to determine the total strainlife model (Eq. (4)), but the approach preferred is to fit elastic strain amplitude-life (Eq. (2)) and plastic strain amplitude-life (Eq. (3)) on log–log scale separately with a linear least-squares method, because it gives less weight to misleading low-cycle and high-cycle data and provides better results [4,14]. Taking the logarithm on both sides of Eqs. (1) and (3), the following linear regression expressions can be derived:
1 ðlog ra log r0f Þ b 1 logð2N f Þ ¼ ðlog epa log e0f Þ c
E
þ
ra
1=n0
K0
ð5Þ ð6Þ
Firstly, the elastic and plastic strain amplitudes are calculated to estimate the transition fatigue life roughly; then r0f , b and e0f , c can be determined from the experimental data of elastic strain dominant high-cycle fatigue region and plastic strain dominant low-cycle fatigue region by linear least-squares regression analysis of Eqs. (5) and (6), respectively. The logarithms of true stress amplitude in the vicinity of 0.5 Nf and true plastic strain amplitude are treated as statistically independent variables, and the logarithm of the failure life in reversals as dependent variable. A threshold of plastic strain amplitude of 0.0005 is selected for Eq. (6) to avoid measurement errors [14]. The regression parameters, root mean square error (RMSE) and coefficient of determination (R2) regression statistic of strain-life relationship of TRIP590 and DP590 are given in Fig. 5.
ð7Þ
where K0 and n0 are cyclic strength coefficient and cyclic strain hardening exponent. 0 Taking the logarithm on both sides of equation epa ¼ ra =K 0 1=n gives the following linear regression equation for K0 and n0 :
log ra ¼ n0 log epa þ log K 0
Fig. 6. Comparison between monotonic and regressive cyclic stabilized stress– strain curves of (a) TRIP590 and (b) DP590.
logð2N f Þ ¼
ra
ð8Þ
The logarithm of true plastic strain amplitude is treated as statistically independent variable, and the logarithm of the stress amplitude as dependent variable in the linear regression procedure. Plastic strain amplitudes less than 0.0005 are discarded [14]. The regression parameters and effectiveness of cyclic stabilized stress–strain relationship of TRIP590 and DP590 are given in Fig. 6. 3.3.3. Discussion on local strain-life properties Fig. 6 illustrates that, compared with the monotonic tension behavior, the yield point elongation phenomenon of TRIP590 during monotonic tension is replaced with continuous yielding in the cyclic case, and TRIP590 and DP590 exhibit cyclic mixed and cyclic softening behavior within the test scope, respectively. The cyclic stabilized stress–strain data and curve of two steels do not have evident yield point, and the 0.2% offset cyclic yield strength of TRIP590 and DP590 are 426 and 346 MPa respectively. Figs. 7 and 8 give the comparisons of strain-life and cyclic stabilized stress–strain behavior between TRIP590 and DP590. It can be concluded that the fatigue life and cyclic stabilized stress of TRIP590 are superior to those of DP590 throughout entire strain amplitude range of test. The contribution factors to enhanced fatigue life of TRIP steel versus DP steel mainly include [5,9]: higher ductility, higher cyclic yield strength and cyclic stress, and the transformation of retained austenite. The uniform elongation of TRIP590 is 28.18% versus 17.01% of DP590 (Table 2), higher ductility improves the tolerance to accumulated plastic strain. The higher cyclic yield strength and cyclic stress (Fig. 8) imply higher elastic strain component at specific total strain amplitude, and consequently lower plastic strain component. Since the mechanism of fatigue damage is the accumulation of cyclic plastic strain, lower plastic strain component will result in less accumulated fatigue damage in every reversal.
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True Stress Amplitude (MPa)
600
500
TRIP590
400
300
DP590 200
100
0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
(a)
True Strain Amplitude (mm/mm) Fig. 8. Comparison of cyclic stabilized stress–strain curves between TRIP590 and DP590.
The volume fraction reduction of retained austenite from initially 5.7% to 5.1% in the fatigued specimen under total strain amplitude of 0.6% demonstrates that the austenite in the vicinity of crack tip has partly transformed into martensite. Phase transformation can absorb deformation energy, relax local stress concentration and bring about compressive internal stress in the matrix, all of which will suppress the initiation and retard the propagation of micro cracks. 4. Application in the lightweight design of body component The potential of TRIP590 versus DP590 in offering enhanced fatigue durability for the lightweight case of body structures with stress concentration was explored on a front shock-absorber tower of a sports utility vehicle. The shock-absorber tower is the main load-carrying component whose fatigue life needs to be ensured. Material of DC04 is used in the baseline design, TRIP590 and DP590 are selected in the lightweight design. According to the thickness of AHSS for body lightweight proposed in [15], 35% weight saving can be achieved by this material substitution. The geometry of the shock-absorber tower is shown in Fig. 9a. Stress analysis and life prediction were performed on whole auto-body with finite element software MSC.Nastran and MSC.Fatigue respectively. One block of typical road spectrum was imposed on the tires to simulate the service environment. The local strain-life models of TRIP590 and DP590 developed in the preceding section were implemented in the finite element analysis. The predicted fatigue life contour of the shock-absorber tower with TRIP590 and DP590 material is shown in Fig. 9b and c, respectively. It is revealed that the minimum life of TRIP and DP component is 90,700 repeats and 7570 repeats respectively, and the minimum life of TRIP steel component is nearly 12 times as high as that of DP steel. This application case illustrates that TRIP steel can provide superior fatigue life for the same notched geometry, exterior loading and lightweight result. According to Neuber’s hypothesis on the local true notch stress and local true notch strain after local yielding, the fatigue strength reduction factor Kf is the geometric mean of true stress amplitude concentration factor and true strain amplitude concentration factor under a plane stress cyclic condition, hence the following equation can be derived:
where DS and De are the nominal elastic stress and strain ranges, Dr and De are the local true notch stress and strain ranges. In the case of nominally elastic behavior, De = DS/E, so the following expression can be obtained:
DrDe ¼ K 2f DSDe
EDrDe ¼ K 2f DS2
ð9Þ
(b)
(c) Fig. 9. (a) Geometry of the considered shock-absorber tower, and the predicted fatigue life made of (b) TRIP590 and (c) DP590.
ð10Þ
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Z.G. Hu et al. / Materials and Design 31 (2010) 2884–2890 900 TRIP590 DP590
Neuber Factor (MPa)
800 700
600
500
400 300
200 1000
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ever cyclic softening followed by stable occurs consistently for DP steel throughout entire strain amplitude range of test. Moreover the cyclic stress response shows that the cyclic softening resistance of TRIP steel is superior to that of DP steel. Thirdly, the experimental results on fatigue life and cyclic stabilized stress, and the developed local strain-life models of two steels indicate that TRIP steel has enhanced life and cyclic stress than DP steel at the same strain amplitude. Fourthly, the finite element application case illustrates that the TRIP component can provide improved fatigue durability than DP one for the same notched geometry, exterior loading and lightweight result. Finally, all above indicate that TRIP steel is more ideal for auto-body lightweight, especially for heavy loading components, due to its improved ductility and fatigue resistance resulted from the unique strengthening mechanism.
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2Nf (reversal) Fig. 10. Comparison of experimental Neuber factor-life between TRIP590 and DP590.
qffiffiffiffiffiffiffiffiffiffiffiffiffi The Neuber factor is defined as E D2r D2e or K f D2S. Kf equals unity if the stress results for local strain-life method are determined from linear-elastic finite element analysis, hence, Neuber factor is the elastic stress at the stress concentration location. Linear-elastic stress analysis is dependent on geometry, exterior loading and elastic properties of material, while independent of the fatigue properties of material. Therefore, Neuber factor, considering all six local strain-life parameters (r0f , b, e0f , c, K0 and n0 ), can clarify different fatigue resistance of notched component made of different materials [16,17]. The comparison of Neuber factor-life between TRIP590 and DP590 illustrated in Fig. 10 manifests that TRIP590 has superior fatigue life to DP590 throughout entire range of test. This accounts for the fatigue life prolongation of the shock-absorber tower with TRIP590 material. The fatigue resistance of TRIP steel component is enhanced due to the simultaneously improved life and cyclic stress amplitude at the same strain amplitude. Hence, TRIP steel is an excellent substitute for DP steel to achieve equivalent strength and lightweight results, because TRIP steel is more suitable to manufacture notched body components from the viewpoint of design against fatigue failures. 5. Conclusions To evaluate the fatigue performance of notched body components made of low-alloy TRIP or DP steel, and select reasonable material from a fatigue durability viewpoint during the auto-body design stage, monotonic and cyclic strain-controlled fatigue experiments on smooth specimens of TRIP and DP steels with 590 MPa grade were conducted. Local strain-life models of two steels were developed by linear regression of the fatigue experiment data, which were employed to predict and compare the fatigue life of notched body structures made of them by finite element method. Different monotonic and cyclic mechanical behaviors were observed due to different interior microstructures, despite equivalent strength. Firstly, the static tension result demonstrates that TRIP steel can preserve superior ductility to DP steel without compromising strength. Secondly, the cyclic stress behavior of TRIP steel is characterized by cyclic hardening followed by stable at lower strain amplitudes, and softening at higher strain amplitudes; how-
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