EFFECTS OF HIGH STRAIN RATE ON LOW-CYCLE FATIGUE BEHAVIOR OF STRUCTURAL STEEL IN LARGE PLASTIC STRAIN REGION

Transcription

1 Journal o JSCE, Vol. 4, , 2016 EFFECTS OF HIGH STRAIN RATE ON LOW-CYCLE FATIGUE BEHAVIOR OF STRUCTURAL STEEL IN LARGE PLASTIC STRAIN REGION Natdanai SINSAMUTPADUNG 1, Eiichi SASAKI 2 and Hiroshi TAMURA 3 1 Member o JSCE, Graduate student, Department o Civil Engineering, Tokyo Institute o Technology ( M1-23 Ookayama, Meguro-ku, Tokyo , Japan) sinsamutpadung.n.aa@m.titech.ac.jp 2 Member o JSCE, Associate proessor, Department o Civil Engineering, Tokyo Institute o Technology ( M1-23 Ookayama, Meguro-ku, Tokyo , Japan) sasaki.e.ab@m.titech.ac.jp 3 Member o JSCE, Assistant proessor, Department o Civil Engineering, Tokyo Institute o Technology ( M1-23 Ookayama, Meguro-ku, Tokyo , Japan) tamura.h.ad@m.titech.ac.jp This study aims to investigate the eects o very high strain rate on low-cycle atigue behavior o structural steel under large plastic strain with strain rate order o 1.0 s -1 as expected during earthquakes. Low-cycle atigue tests were conducted using compact-tension specimens at various strain rate levels. Fatigue lie based on crack size indicated that the higher strain rate caused lower atigue lie in large plastic strain region. The energy approach was employed to clariy the low-cycle atigue mechanism in this region. Finally, a prediction method or atigue lie regarding high strain rate eect in large plastic strain region is proposed in this study. Key Words : low-cycle atigue, high strain rate, large plastic strain, compact tension specimens, atigue lie, crack initiation, crack propagation 1. INTRODUCTION In the past decades, earthquakes caused various types o damage to steel structures 1). Low-cycle atigue is considered one o the most dominant damage types o steel structures during earthquakes. Low-cycle atigue damage occurred in the orm o cracks. Low-cycle atigue is characterized by plastic strain and general ailure in a small number o cycles. During earthquakes, steel structures suer rom cyclic loading with large plastic strain at the local area o steel member 2), 3), which could cause low-cycle atigue crack damage. Furthermore, low-cycle atigue damage could induce brittle racture. For example, during the 1995 Kobe earthquake, brittle racture occurred in steel bridge piers. Investigations o these ailures ound that brittle racture was triggered by cracks caused by plastic strain including low-cycle atigue cracks 2)-8). Consequently, there had been extensive studies ocusing on low-cycle atigue behavior o steel structures during earthquakes 1)-12). However, the eects o high strain rate in large plastic strain region expected during earthquakes have not been clariied yet. According to recent investigations 13)-15), strain rate could be an important actor in the low-cycle atigue behavior o steel components, but the eects o very high strain rate in large plastic strain region expected in steel structures during earthquakes have not been investigated so ar. Recently, there had been investigations on the eects o strain rate on low-cycle atigue behavior and the results indicated that atigue lie in low-cycle atigue region o the steel signiicantly depends on strain rate 13)-15). For instance, Luo et al. 13) ound that the eect o strain rate on atigue lie has transition in trend. Structural steel under lower strain rate will have a lower atigue lie until the strain rate exceeds the transition point (around 0.01 s -1 ) and then the higher strain rate will have a lower atigue lie instead. However, these investigations conducted ex- 118

2 periments in the strain rate range below the order o 0.10 s -1. According to the previous studies, there is a possibility that the strain rate expected during earthquakes might exceed the order o 1.0 s -1 2), 3), which is considered higher than those in earlier studies 13)-15) and expected behavior above the aorementioned transition point. The atigue lie o steel members during earthquakes could be aected by higher strain rate reerred to as very high strain rate in this study. In this study, the eects o very high strain rate on low-cycle atigue behavior o structural steel in large plastic region expected during earthquakes were investigated via experiment. In this study, low-cycle atigue tests were conducted on compact-tension specimens in various cyclic loading rates to clariy the eects o very high strain rate on low-cycle atigue behaviors including load-range drop, crack initiation, and propagation behavior. Especially, behaviors at early stage o the cracking process were ound to inluence the occurrence o brittle racture 2)-8). The energy approach was then used to clariy the low-cycle atigue mechanism o structural steel subjected to high strain rate in large plastic strain. Finally, the prediction method or atigue lie regarding the strain rate eect on the large plastic strain region is proposed in this study. stress-strain relationship and the undamental material properties were obtained by tensile tests with static rate and 1.0 s -1 nominal strain rate. The material s stress-strain relationship is shown in Fig.2 while the material properties and chemical compositions are shown in Table 1. (2) FEM analysis to design specimens According to earthquakes characteristics, large plastic strain level could occur at the local area and strain rate could occur in the order o s -1 2), 3). Thus, the experiment coniguration is required to satisy these earthquakes characteristics. In order to determine the experiment conigurations, numerical analysis using cyclic loading were conducted on FEM models o CT-specimens using eective notch according to the recommendations or atigue design by Hobbacher 17). The FEM models o CT-specimens are shown in Fig DESIGN OF SPECIMENS (1) Dimension o material specimens In this study, we investigated the structural steel behaviors concerning the eect o high strain rate in large plastic region expected during earthquakes, using round notch-type compact tension specimens (CT-specimens). These CT-specimens were designed by reerencing the guidelines rom the standard test method or measurement o racture toughness by ASTM 16) or the shape o CT-specimens by using eective notch shape 17) or round notch. The dimensions o CT-specimen are shown in Fig.1. The specimens were made rom mild steel plate (JIS-SM400), which is a widely used structural steel in Japan. In this study, the strain rate level was taken into consideration. Thus, the Fig.1 Dimensions o material specimen. Fig.2 Stress-strain relationship o specimens. Table 1 Material properties. Mechanical properties Chemical composition (%wt) Material SM400A Yield strength, σ (MPa) y Tensile strength, σ (MPa) u Fracture stress, σ (MPa) Strain rate C Si Mn P S STATIC s

3 Fig.3 FEM models o CT-specimens. a) Material models or strain rate level In order to conduct FEM analysis on strain rate level, material properties o the strain rate level are necessary. In this study, the material properties were obtained by conducting tensile test on round bar specimens as shown in Fig.4 with various loading rates corresponding to static rate and strain rate equal to 1.0 s -1 (Fig.2). In the static rate case, a diameter gauge was used during the tests. Thus, the true stress-strain curves were calculated rom the diameter value. In the 1 s -1 strain rate case, nominal strain was obtained by attaching the strain gauge at the middle o the round bar. The true stress-strain was then calculated rom nominal stress-strain via logarithm ormula beore necking occurred. In addition, true stress-strain was obtained rom the reduction o the area at racture point. FEM models o round bar with 2 mm mesh size were conducted to veriy material properties with load-displacement curve as shown in Fig.5. Then, material properties o the intermediate strain rate level could be calculated using the material model. According to the ABAQUS manual 19), material properties corresponding to the intermediate strain rate level were interpolated between material properties corresponding to the static rate and strain rate equal to 1.0 s -1. Finally, experiment coniguration could be determined by FEM models o CT-specimens (Fig.3). b) Calculation o eective notch strain range Since FEM models used the eective notch shape, the equivalent total strain range could be calculated by using the eective notch concept 10). The eective notch concept was employed in the elements along the notch. The eective notch strain range, which combines the elastic and plastic components is expressed in Fig.6 and Equation (1). The elastic com- Fig.4 Round bar specimen or tensile tests. Fig.5 Load-displacement o tensile test. Fig.6 Expression o eective notch concept. 120

4 ponent and plastic component are expressed in Equations (2) and (3) respectively. σ εe = εt = + ε p E (1) ( σ σ ) + ( σ σ ) 1 2 σ = + ( σ σ ) z x x y y z ( τ τ τ xy yz zx ) (2) 2.40 mm 0.10 Hz 2.40 mm 1.00 Hz 2.40 mm 2.50 Hz 2.40 mm 5.00 Hz 3.60 mm 0.10 Hz 3.60 mm 1.00 Hz 3.60 mm 3.00 Hz 3.60 mm 5.00 Hz Fig.7 Plastic strain at local area o specimens subjected to various test conigurations. 121

5 1 ε p = ( ε ε ) px, py, ( ε ε ) + py, pz, ( ε ε ) + pz, px, ( γ γ γ p, xy p, yz p, zx ) 2 2 (3) where σ : the normal stress range τ : the shear stress range ε p : the normal plastic strain range γ p : the shear plastic strain range x, y, z : x, y, z directions, respectively ε e : the eective notch strain range ε t : the equivalent total strain range σ : the equivalent stress range : the equivalent plastic strain range ε p 2.40 mm 0.10 Hz 2.40 mm 1.00 Hz 2.40 mm 2.50 Hz 2.40 mm 5.00 Hz 3.60 mm 0.10 Hz 3.60 mm 1.00 Hz 3.60 mm 3.00 Hz 3.60 mm 5.00 Hz Fig.8 Stress at local area o specimens subjected to various test conigurations. 122

6 In this study, the maximum and average eective notch strain ranges were calculated rom eight elements along the notch as indicated in Fig.3. The stress and strain components at the integration point o each element were used in the calculation process by Equations (1)-(3). In addition, strain rate levels ε e (s-1 ) could be calculated by using loading rate (Hz) as shown in Equation (4). This equation was used in previous studies 13)-15). However, these previous studies conducted experiments on round bar specimens, which had strain only in the axial direction. Thus, it would be more realistic to calculate strain rate levels rom equivalent plastic strain history ε p (t), which were obtained rom FEM analysis as shown in Equation (5). c) Local behaviors o the strain rate level Local area behavior o the strain rate could be observed rom the FEM results. Plastic strain level and stress level at maximum opening o various loading rates are shown in Fig.7 and Fig.8 respectively. It can be seen that high strain rate at the local area could cause slightly smaller plastic strain. However, high strain rate could cause relatively larger stress value. This means that the local area o specimens subjected with higher loading rate could have a larger plastic strain energy density. According to a previous study 13), larger plastic strain energy density could lead to lower atigue lie. However, investigation on large plastic strain and high strain rate in the order o 1.0 s -1 expected during earthquakes has not been done yet. Thereore, this study could clariy the eect o strain rate on atigue lie o structural steel in this region. d) Eective notch strain range and strain rate According to the eective notch strain range as shown in Fig.9, loading amplitudes equal 1.20 mm, 2.40 mm, and 3.60 mm corresponded to approximately 5%, 12%, and 18% strain range, respectively. Thereore, these loading amplitudes were chosen or the purpose o this study. Moreover, the loading rate chosen in this study also corresponded to s -1 strain rate range as shown in Fig.10. Hence, earthquakes characteristics could be satisied by the experiment conigurations in this study. In addition, a loading waveorm was generated using two types o waveorms in this study, namely, the triangle waveorm and the sine waveorm as shown in Fig.11. The triangle waveorm is characterized by a constant velocity, which suddenly changes direction at the transition point o the waveorm. The sine waveorm is characterized by variable velocity, which smoothly changes direction at the transition point o the waveorm. Under large plastic strain and high loading rate, the actual strain rate level could be aected by the loading waveorm type, which might have an inluence on the behavior o structural steel. Thus, the purpose o the two types o waveorm is to observe the eects o the loading waveorm characteristics. e ε = 2 ε (4) e dε p () t ε p = (5) dt Fig.9 Eective notch strain value o loading rate. Fig.10 Strain rate level o loading rate. Fig.11 Waveorm o input motion. 123

7 Table 2 Coniguration o specimens in the experiment. Specimen Amplitude Loading rate Waveorm Average strain Maximum strain Strain rate Strain rate type range range Eq.(4) Eq.(5) 18-5-S 3.60 mm 5.00 Hz Sine s s S 3.60 mm 3.00 Hz Sine s s _1-S 3.60 mm 0.10 Hz Sine s s S 2.40 mm 5.00 Hz Sine s s S 2.40 mm 3.00 Hz Sine s s _1-S 2.40 mm 0.10 Hz Sine s s T 3.60 mm 5.00 Hz Triangle s s T 3.60 mm 3.00 Hz Triangle s s T 3.60 mm 1.00 Hz Triangle s s _1-T 3.60 mm 0.10 Hz Triangle s s T 2.40 mm 5.00 Hz Triangle s s _5-T 2.40 mm 2.50 Hz Triangle s s T 2.40 mm 1.00 Hz Triangle s s _1-T 2.40 mm 0.10 Hz Triangle s s T 1.20 mm 5.00 Hz Triangle s s T 1.20 mm 3.00 Hz Triangle s s T 1.20 mm 1.00 Hz Triangle s s -1 For reerence to each experiment coniguration, specimens were named according to strain range, loading rate, and loading waveorm type. Details o the experiment coniguration in this study including name, amplitude, loading rate, loading waveorm type, equivalent total strain range, and strain rate levels are shown in Table EXPERIMENTAL PROCEDURE (1) Experiment system As shown in Fig.12, this experiment used a material testing machine to generate the cyclic displacement control loading, and the eedback to control the displacement was obtained rom a displacement transducer at the opening o CT-specimens. In this study, a non-linear adjustment eedback control algorithm, i.e., PID control, was implemented on the material testing machine to control the exact displacement at the openings o CT-specimens. Finally, the experiment system or cyclic displacement eedback control that was capable o high loading rate in large plastic region was developed. (2) Observation o crack behavior According to the previous study, Murakami 20) proposed that low-cycle atigue behavior was dominated by growth behavior o small cracks. Thereore, observing all o the moments o crack initiation and propagation behavior o low-cycle during earthquakes is considered critical and signiicant. In this study, the high-speed microscope has a capacity o 200 rames recording speed per second with 640x480 resolution. In addition, to observe the crack length in every cycle o the experiment, a recorded Fig.12 Control algorithm or experiment. Fig.13 Microscope and motion analysis sotware. video rom a microscope was processed by motion analysis sotware with 0.01 mm precision. The microscope and one sample picture o CT-specimen captured by the motion analysis sotware are shown in Fig EXPERIMENTAL RESULTS (1) Relationships between load and displacement (P-δ curves) The relationships between load (P) and displacement (δ) are shown in Fig.14. The results show that load range decreases every cycle due to plastic 124

8 Fig.14 P-δ curves o specimens subjected to displacement control cyclic loading. Fig.15 P-δ curves o specimens with dierent loading rate. Fig.16 Cumulative cyclic energy o specimens. deormation and crack propagation in the CT-specimens. As shown in Fig.15, CT-specimens subjected to higher loading rate (higher strain rate) will have steeper slope o load-displacement curve due to the rate-dependent eect. Consequently, specimens subjected to higher strain rate will have a larger area o the load-displacement curve, which can represent 125

9 Fig.17 Load drop o specimens subjected to sine loading waveorm with various loading rates. Fig.18 Load drop o specimens subjected to triangle loading waveorm with various loading rates. the cyclic energy per cycle. Similarly, cumulative cyclic energy can be calculated rom the cumulative area o the P-δ curve. To clariy the amount o cyclic energy, Fig.16 shows the relationship between cumulative cyclic energy and number o cycles. The results conirmed that specimens suered larger amount o energy with higher strain rate. (2) Load-drop range due to the strain rate eect Figure 17 and Fig.18 show the load range in every cycle or each specimen. The load ranges have been normalized by the maximum value o each specimen so that the eect o strain rate can be compared. The results show that specimens subjected to a higher strain rate tend to have an earlier load drop, leading to a lower load range than those subjected to a lower strain rate. This load drop could be an evidence that indicates lower atigue lie with high strain rate. However, specimens subjected to higher strain rate tend to have signiicant larger load range at irst cycle due to the higher loading rate. This considered biased criteria or indicated atigue lie o structural Fig.19 Load drop curves o specimens subjected to loading amplitude = 1.20 mm with various loading speeds. steel or the present study. Thereore, there should be urther investigation on atigue lie based on crack length. 126

10 Fig.20 Load drop curves o specimens various loading rates due to the waveorm type. Fig.21 First observed crack o specimens subjected to displacement control by triangle loading waveorm with various loading speeds. (3) Signiicance o strain rate eect due to the plastic strain level The experiment using 1.20 mm displacement amplitude (corresponding to 5% strain range) represents the intermediate region between low-cycle atigue and high-cycle atigue due to the smaller amount o plastic strain level. Figure 19 shows that specimens subjected to a higher strain rate have a lower atigue lie, but the eect o strain rate is not as signiicant as or those subjected to 2.40 mm and 3.60 mm (corresponding to 12% and 18% strain range, respectively). This result is similar to those o the previous studies 21)-23), as loading requency has no eect on high cycle atigue regions, shown by the act that much smaller scale o plastic strain occurred in high cycle atigue compared to low-cycle atigue. During earthquakes, plastic strain could exceed 15% 2)-3). Thereore, the eect o strain rate could become more signiicant during earthquakes due to the large plastic strain. (4) Load-drop due to the loading waveorm-type eect In this study, two series o loading waveorm shown in Fig.11 were used. Figure 20 shows the dierence in atigue lie o specimen due to the eect o the loading waveorm type. Specimens subjected to the sine waveorm tend to have an earlier load drop than the triangle waveorm with the same loading rate. One o the reasons could be explained in terms o maximum strain range as shown in Table 2, where it indicates that the sine waveorm could cause larger strain range and strain rate level at the local area o specimens. (5) Crack initiation behaviors The surace crack initiation was investigated using high-speed microscope camera. The number o cycles at the irst observed crack in each specimen is deined as crack initiation lie (N c ) and the results are shown in Table 3. It is ound that specimens sub- 127

11 Table 3 Specimens irst observed crack. Specimen 1st observed surace crack (N c ) Number o cycles 18-5-T 1.8x T 2.6 x T 2.4 x _1-T 2.4 x T 6.0 x _5-T 6.2 x T 6.2 x _1-T 5.8 x10 1 Fig.22 Operative deinition or compliance method. Fig.23 Compliance slope o specimens on number o cycles. Fig.24 Compliance slope o specimens on cumulative energy. jected to lower strain rate tend to have earlier surace crack initiation with smaller crack size. Figure 21 shows that the size o the irst observed crack that could be observed in lower strain rate is considered smaller compared with high strain rate case. This behavior is in agreement with the previous studies 13)-15), which indicated that in the low strain rate crack initiation will occur earlier in the orm o secondary crack (i.e., crack that propagates rom micro-cracks) and crack initiation in the high strain rate will have originated rom nucleation o void instead. Moreover, the previous studies 13)-15) also indicated that longer loading time due to low strain rate case allows more time to develop creep damage. This might be one o the explanations or crack initiation earlier in low strain rate. However, there are possibilities that high strain rate could cause the earlier crack initiation point ound in this study (specimen: 18-5-T, 12-5-T). To clariy the crack initiation mechanism, compliance method was implemented with the unloading line o load-displacement curve at each cycle (see Fig.22) deined as compliance slope. The compliance slope could be an indicator o stiness related to crack size and geometry o specimens. Thus, the change in compliance slope could be used to detect the crack initiation point. In addition, the compliance slope was normalized with a maximum slope value o each specimen in order to observe the eect o strain rate. The results o the compliance method are shown in Fig.23. The igure shows that the knee point o the compliance slope has correlation with the irst observed crack, and the compliance slope o 128

12 specimens with high strain rate (18-5-T, 12-5-T) tends to decrease earlier. In addition, this tendency could be clearly observed with specimens subjected to large plastic strain as shown in Fig.23 (b). Then, the compliance slope was plotted against aorementioned cumulative energy (see Fig.16) as shown in Fig.24. The result indicated that the change in compliance slope is related to the amount o energy absorbed by specimens without signiicant dierences between strain rate levels. Thus, crack initiation behaviors will be mainly dominated by the amount o energy, which results in earlier crack initiation on the higher strain rate due to larger amount o energy. To observe the signiicance o strain rate, crack initiation lie (N c ) was plotted against strain range as shown in Fig.25. High strain rate (18-5-T) was ound to have inluence on crack initiation lie. However, the eect o strain rate on crack initiation lie was ound to be less signiicant than the strain range. In addition, the Manson our-point correlation method 24)-27) as expressed in Equation (6) was implemented or comparison with previous studies. S α ε = ε ( N ) + ( N ) E α 1 2 c c (6) where ε : total strain range ε : atigue ductility S : atigue strength coeicients α 1 : atigue ductility exponents α 2 : atigue strength exponents E : modulus o elasticity : crack initiation lie. N c Fig.25 Crack initiation lie o specimens. Fig.26 Operative deinition or obtaining atigue constants. Fig.27 Crack initiation lie on equivalent plastic strain range. Table 4 Fatigue constants obtained rom Manson our-point correlation method. Fatigue constants Present study STATIC 1.0 s -1 Average R.L. Jones (1989) Fatigue ductility coeicient, ε Fatigue ductility exponent, α Fatigue strength coeicient, S Fatigue strength exponent, α

13 In order to obtain atigue constants, two straight lines corresponding to the elastic line and plastic line were generated. According to previous study 24), elastic line could be generated rom two points based on tensile test as shown in Fig.26. The irst point is located at ¼ cycle with an ordinate (2.5σ )/E, where σ is the true racture stress. The second point is located at 10 5 cycles with an ordinate (0.9σ u )/E, where σ u is the ultimate tensile strength. Then, power-itted equation was used to determine S and α 2. To generate the plastic line, the plastic part o eective notch strain as expressed in Eq. (3) was plotted against crack initiation lie as shown in Fig.27. Then, the curve was itted by power law equation to determine ε and α 1. Since tensile tests were conducted in dierent strain rates in this study, thereore, atigue constants could be determined in two sets with various strain rates and average value as shown in Table 4. Furthermore, as the large plastic strain region is the main ocus in this study, rom the comparison between Fig.25 and Fig.27, it could be seen that the plastic line is the dominant component in the relationship between the eective notch strain range and the crack initiation lie. (6) Crack propagation behaviors Figure 28 shows the values o crack length in each cycle. The results show that specimens subjected to a higher strain rate tend to have a higher crack propagation rate than those subjected to a lower strain rate. The signiicance o strain rate due to large plastic strain also can be observed in crack propagation behaviors. However, there is a possibility that lower strain rate could have larger crack length due to earlier crack initiation as ound in comparison between specimens 12-0_1-T and 12-1-T. Moreover, larger energy caused by higher strain rate could overcome the earlier crack initiation by low strain rate ater a certain number o cycles as ound in specimen 18-0_1-T in which the crack length got overtaken by specimen 18-1-T ater crack length around 2.7 mm. In this study, appropriate atigue lie criteria based on crack length had to be deined or creating nonbiased situation to evaluate the strain rate eect. One o the reasons is that CT-specimens have long span o crack propagation state and the order o crack length could be overtaken by high strain rate ater a certain number o cycles. Thus, choosing large crack length to deine atigue lie might not be appropriate or low strain rate. As seen rom the results, the crack length was overtaken when the crack length reached around 2.7 mm. Thus, the appropriate atigue lie based on crack length should be smaller than 2.7 mm. Fig.28 Crack length o specimens on number o cycles. Table 5 Fatigue lie o specimens. Specimen Fatigue lie (Number o cycles) N c /N 18-5-T 2.1 x T 3.0 x T 3.2 x _1-T 2.9 x T 6.9 x _5-T 7.7 x T 7.9 x _1-T 7.7 x To be precise, the crack length reaching 2 mm could be the proper atigue lie criteria in this study. As shown in Fig.24, specimens compliance slope already reaches over knee point and tends to drop drastically. Thereore, or this study, atigue lie (N ) was deined as the number o cycles that the crack length reached 2 mm. (7) Fatigue lie due to the strain rate eect Fatigue lie based on crack length is shown in Table 5. Results indicated that high strain rate caused lower atigue lie in the order o 1.0 s -1. To explain the eect o strain rate on atigue lie, higher strain rate caused larger cyclic energy and atigue lie o structural steel in high strain rate and large plastic strain region expected during earthquakes was dominated by the amount o cyclic energy. Thereore, higher strain rate will cause lower atigue lie due to larger amount o energy. In addition, Table 5 also shows the ratio between crack initiation lie and atigue lie (N c /N ) to be larger than 0.75, which implies that atigue lie was dominated by the crack initiation process in this study. One o the reasons could be notch shape. Previous studies 24)-26) indicated that stress concen- 130

14 tration actor could be aected by notch shape, which resulted in dierent ractions o crack initiation lie. These studies indicated that the smooth notch shape will result in higher raction o crack initiation lie due to the blunt notch at the start o crack initiation process. To clariy the signiicance o strain rate, the atigue lie based on crack length was plotted against the strain range as shown in Fig.29. Fatigue lie was ound to be dominated by total strain range rather than strain rate eect. In addition, a previous study 10) proposed atigue lie based on strain as shown in Equation (7). However, the previous study conducted experiments on load-carrying cruciorm joint, which was considered a sharp notch shape. Thus, the atigue lie in the previous study was mainly dominant on crack propagation lie. Hence, the proposed atigue lie based on strain level rom the previous study should be modiied in order to compare results with those o the present study. strain range) and 3.60 mm (18% strain range) could be considered an extremely low-cycle atigue region where the number o cycles to ailure was less than 100 cycles. Thus, strain rate could cause signiicantly lower atigue lie in the large plastic region. To illustrate, atigue lie in each plastic strain level has been normalized by atigue lie o low strain rate in order to compare the eects o strain rate. Figure 30 shows that high strain rate in the order o 1.0 s -1 could result in approximately 10%-30% decrease in atigue lie in the large plastic strain region. This situation is expected on structural steel during earthquakes. Thereore, the eects o strain rate on a large plastic region should be considered to improve saety and accuracy o atigue strength assessment in this region. Thus, this present study proposed predicted atigue lie o strain rate eects using strain rate level and atigue lie conducted on low strain rate level, which can be expressed in Equation (10). ε = ( p ) N (7) It is well known that atigue lie N could be separated into crack initiation lie N c and crack propagation lie N p as shown in Equation (8). Since crack initiation lie in this study was determined by Equation (6) and coeicient rom the average line in Table 4 was ound to be in good correlation with the results (Fig.25), thereore, reerence or atigue lie based on strain level or comparison with this study could be determined by combining Equation (6) with coeicient rom average line and Equation (7) as shown in equation (9). N = Nc + N p (8) ( N ) c ε 5 ( ) e = + N c ( N p ) (9) Fig.29 Fatigue lie o specimens. This relationship can also be shown by the ollowing equation using only atigue lie N by power-itted equation as shown in Fig.29. ε = 1.01( ) e N (10) It is clear that atigue lie was dominated by total strain range rather than strain rate eect. However, atigue lie in large plastic strain region (10%-18%) as represented by loading amplitude 2.40 mm (12% Fig.30 Normalized atigue lie-strain rate relationship. 131

15 where ε N : predicted atigue lie ε : strain rate N,low : atigue lie based on static rate Figure 31 shows the plot o predicted atigue lie and experimental atigue lie in the present study. Time-dependent mechanism 13)-15) was also ound in this study. The results can be expressed in the relationship between time to ailure t (s) and strain rate ε (s -1 ) in the order o 1.0 s -1 as shown in Fig.32 and results could be expressed by the ollowing power law equation: Fig.31 Comparison experimental atigue lie and predicted atigue lie based on strain rate. t = ε (12) Table 6 shows the time-dependent relationship proposed by the previous studies 13)-15). The results o the present study extended the investigated range o strain rate order o 0.1 s s -1. In addition, the tendency o power law expression itted by the present study is in agreement with the previous studies 13)-15). However, time to ailure was ound to signiicantly decrease at high strain rate (1.0 s -1 ) in this study. Moreover, the power law equation also gives a time-dependent mechanism that becomes less signiicant on a higher strain rate. Thereore, atigue lie on a high strain rate region expected during earthquakes will mainly be dominated by energy while time-dependent mechanism inluence will decrease. Fig.32 Relationship between time to ailure o specimens and strain rate. Table 6 Time-dependent relationship proposed by the previous studies. Name Kanchanomai et al. (2002) Luo et al. (2013) Present study Power law expression t t t t Investigated strain rate order 0.93 = ε 10-3 s s = ε 10-6 s s = ε 10-5 s s = ε 0.1 s s Note that this correction actor has applicable range in strain range o 10% to 18% and strain rate order o s -1. ε 2.46 N = ( ε ) N (11), low 5. CONCLUSIONS In this study, the eects o high strain rate on low-cycle atigue behaviors o structural steel in large plastic strain region, which are expected during earthquakes were investigated via experiment. CT-specimens with eective round notch type were used to clariy atigue lie based on crack initiation and propagation behaviors. The results showed that low-cycle atigue behaviors in the strain rate order o 1.0 s -1 in large plastic strain region including load drop, crack initiation, crack propagation were dominated by the amount o cyclic energy. Higher strain rate and larger plastic strain expected during earthquakes could cause the release o larger amount o energy, which could result in lower atigue lie. However, total strain range was ound to be more signiicant on atigue lie than on strain rate. Despite the act that atigue lie dominated on total strain range, strain rate could not be neglected in the 132

16 extremely low-cycle atigue region where large plastic strain (more than 10%) occurred. In this region, strain rate order o 1.0 s -1 could cause 10%-30% decrease in atigue lie. The prediction method or atigue lie regarding strain rate eect in this region is proposed in this study. REFERENCES 1) Miki, C. and Sasaki, E.: Fracture in steel bridge piers due to earthquakes, Int. J. Steel. Struct., Vol. 5, pp , ) Tamura, H., Sasaki, E., Yamada, Y. and Katsuchi, H.: Study on cause o brittle racture during earthquakes in steel bridge bents ocusing on dynamic loading eect, JSCE, Series A1, Vol. 68, No. 2, pp , (in Japanese) 3) Okashita, K., Ohminami, R., Michiba, K., Yamamoto, A., Tomimatsu, M., Tanji, Y. and Miki, C.: Investigation o the brittle racture at the corner o P75 rigid-rame pier in Kobe harbor highway during the Hyogoken-nanbu earthquake, Journal o Structural Mechanics and Earthquake Engineering, JSCE, No. 59/I-43, pp , (in Japanese) 4) Miki, C., Aizawa, T. and Anami, K.: Brittle racture at beam-to-column connection during earthquake, Journal o Structural Mechanics and Earthquake Engineering, JSCE, No. 591/I-43, pp , (in Japanese) 5) Ge, H., Gao, S. and Usami, T.: Stiened steel box columns, Part 1: Cyclic behavior, Earthq. Eng. Struct. Dyn., No. 29, pp , ) Ge, H., Ohashi, M. and Tajima, R.: Experimental study on ductile crack initiation and its propagation in steel bridge piers o thick-walled box sections, Journal o Structural Engineering, JSCE, Vol. 53A, pp , (in Japanese) 7) Ge, H.: Extremely low-cycle atigue tests o thick-walled steel bridge piers, J. Bridge. Eng., Vol. 18, No. 9, pp , ) Sasaki, E., Arakawa, T., Miki, C. and Ichikawa, A.: Required racture toughness o steel to prevent brittle racture during earthquakes in steel bridge piers, JSCE, No. 731/I-63, pp , (in Japanese) 9) Saiprasertkit, K., Sasaki, E. and Miki, C.: Experimental study on low-cycle atigue strength o beam-to-column connections in steel bridge bents with dierent plate assembling and material mismatching, Int. J. Steel. Struct., Vol. 12, No. 3, pp , ) Saiprasertkit, K., Hanji, T. and Miki, C.: Fatigue strength assessment o load-carrying cruciorm joints with material mismatching in low- and high-cycle atigue regions based on the eective notch concept, Int. J. Fatigue, Vol. 40, pp , ) Hanji, T., Saiprasertkit, K. and Miki, C.: Low-and high-cycle atigue behavior o load-carrying cruciorm joints with incomplete penetration and strength under-match, Int. J. Steel. Struct., Vol. 11, No. 3, pp , ) Hanji, T., Miki, C. and Saiprasertkit, K.: Low- and high-cycle atigue behavior o load-carrying cruciorm joints containing incomplete penetration and strength mismatch, Welding in the World XIII , Published in issue 5/ o Welding in the World, ) Luo, Y., Huang, C., Tian, R. and Wang, Q.: Eects o strain rate on low-cycle atigue behaviors o high-strength structural steel, Journal o Iron and Steel Research, International, Vol. 20, No. 7, pp , ) Kanchanomai, C., Miyashita, Y. and Mutoh, Y.: Strain-rate eects on low-cycle atigue mechanism o eutectic Sn-Pb solder, Int. J. Fatigue, Vol. 24, pp , ) Begun, S., Chen, D. L., Xu, S. and Luo, A. A.: Eect o strain ratio and strain rate on low-cycle atigue behavior o AZ31 wrought magnesium alloy, Material Science and Engineering A, Vol. 517, pp , ) ASTM E : Standard test method or measurement o racture toughness, American Society or Testing and Materials (ASTM) International, ) Hobbacher, A.: Recommendations or atigue design o welded joints and components, IIW Documentation XIII /XV , ) Ziegler, H.: A modiication o Prager s hardening rule, Quarterly o Appl. Mathematics, Vol. 17, pp , ) ABAQUS Inc.: ABAQUS Analysis User s Manual, Version 6.11, ) Murakami, Y.: Role o small cracks or discussion o atigue damage in low-cycle atigue o metals, Procedia Materials Science, Vol. 3, pp , ) Stanzl-Tschegg, S. E. and Mayer, H.: Fatigue and atigue crack growth o aluminium alloys at very high numbers o cycles, Int. J. Fatigue, Vol. 23, pp. S231-S237, ) Papakyriacou, M., Mayer, H., Pypen, C., Plenk Jr., H. and Stanzl-Tschegg, S.: Inluence o loading requency on high-cycle atigue properties o b.c.c. and h.c.p. metals, Materials Science and Engineering A, Vol. 308, pp , ) Mayer, H., Papakyriacou, M., Pippan, R. and Stanzl-Tschegg, S.: Inluence o loading requency on the high-cycle atigue properties o AlZnMgCu1.5 aluminium alloy, Materials Science and Engineering A, Vol. 314, pp , ) Jones, R. L., Phoplonker, M. A. and Byrne, J.: Local strain approach to atigue crack ormation lie at notches, Int. J. Fatigue, Vol. 11, No. 4, pp , ) Maiya, P. S.: Eects o notches on crack initiation in low-cycle atigue, Materials Science and Engineering, Vol. 38, pp , ) Verreman, Y. and Limodin, N.: Fatigue notch and short crack propagation, Engineering Fracture Mechanics, Vol. 75, pp , ) Manson, S. S.: Fatigue: A complex subject some simple approximations, Experimental Mechanics, Vol. 5, No. 7, pp , ) Hertzberg, R.: Deormation and Fracture Mechanics o Engineering Materials, Wiley, GB, US, ) Anderson, T. L.: Fracture Mechanics Third Fundamentals and Applications, Taylor and Francis Group, US, (Received October 2, 2015) 133