PSI - Issue 2_B
Shimada Y. et al. / Procedia Structural Integrity 2 (2016) 1593–1600 Yusuke Shimada / Structural Integrity Procedia 00 (2016) 000–000
1597
5
on yield strength can be expressed by Eq. (6). ( ) A e R T ln ・ =
(5)
exp(a R) a (6) where T is the temperature, e is the strain rate (/s), σ Y is the yield strength, and A , a 1 , and a 2 are the respective material constants. Furthermore, it has been reported by Minami et al. (2001) that the parameter R can also express the dependence of the tensile strength on both strain rate and temperature. The dependence of yield strength and tensile strength on both the strain rate and temperature was therefore evaluated using the parameter R for virgin and pre-strained steels. The relationship between the yield strength σ Y or tensile strength σ T and parameter R for virgin and pre-strained SM490A steels are shown in Fig. 8. The values of 10 8 /s and 10 9 /s gave the best correlation and were used as the constant A for σ Y and σ T , respectively. The dependence of yield strength and tensile strength on both the strain rate and temperature can be expressed in terms of the parameter R even for pre-strained steel. σ 1 1 Y =
Tensile strength
Yield strength
900
900
0 / ) 1743 exp( 484 0.0 R ・
σ ε
=
pre
0 / ) 1981 exp( 495 0.1 R ・
=
σ ε
=
800
800
pre
Y
0 / ) 2182 exp( 408 0.05 R ・
=
σ ε
=
pre
T
700
700
=
Y
600
600
0 / ) 1917 exp( 479 0.05 R ・
=
σ ε
σ T (MPa)
σ Y (MPa)
pre
/ ) 3989 exp( 201 0 R ・
=
σ ε
500
500
/ ) 1687 exp( 475 0 R ・ T =
=
σ ε
pre
pre
=
=
Y
400
T
400
3000 4000 5000 6000 7000 8000 9000 300 Strain rate - temperature parameter, R (K) ln(10 / ) 8 e R T ・ =
3000 4000 5000 6000 7000 8000 9000 300 Strain rate - temperature parameter, R (K) ln(10 / ) 9 e R T ・ =
Fig. 8 Relationship between strength and strain rate-temperature parameter (SM490A)
The relationships between strength and both strain rate and temperature have been investigated separately. Furthermore, it has been reported by Inoue et al. (1987) that the dependence of strength on both the strain rate and temperature can be expressed using a single formula. In this study, a strength estimation formula was proposed using both the Arrhenius type temperature dependence of strength and the strain rate-temperature parameter R. The Arrhenius-type temperature dependence of both yield strength and tensile strength was estimated by Eq. (7). where σ and σ 0 are the strengths at temperatures T and T 0 and B is the function of σ 0 with consideration for the temperature dependence. The relationship between strength and both temperature and strain rate can be expressed by Eq. (8) by substituting R shown in Eq. (5) for the temperature in Eq. (7). ( ) ( ) − = + T A e T A e B ln 1 ln 1 ln ln 0 ・ ・ σ σ (8) ( σ 0 /E) γ according to Inoue et al.(1987), and B for virgin and pre-strained steel of 400 - 590 MPa classes was calculated for the case of T 0 (=293K) and e 0 (=10 -4 /s), where E is Young’s modulus (= 206 GPa), and A=10 8 /s (for yield strength) and A=10 9 /s (for tensile strength). The relationships between B and T 0 ～ (σ 0 /E) γ are shown in Fig. 9. The values of α=8×10 -4 and γ= -1.5 can be obtained for both yield strength and tensile strength. In WES2808, the variation in strength of 400 - 590 MPa class steel due to dynamic loading and temperature was estimated by Eq. (9) and (10). However, Kubo et al. (2007) reported that strength estimated by Eq. (9) and (10) is lower than the experimental results for 780 MPa class steel. In addition, they proposed Eq. (11) and (12) for 780 MPa class steel. Therefore, Eq. (9) - (12) can be used to estimate the strength. The results of the estimation are shown in Fig. 10, and these formulas were recognized for have good accuracy. ( ) ( ) ( ) ( ) ( ) − × = − − 0 8 0 8 1.5 0 0 0 4 0 0 ln 10 1 ln 10 1 exp 8 10 , e e T T E T T T e T Y Y Y ・ ・ σ σ σ ・ (9) − = + ln 0 0 1 1 T T ln B σ σ (7) 0 Here, α and γ were decided as the values which gave the best correlation with T 0 ～ (σ 0 /E) γ by defining B=α ～ T 0 ～
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