PSI - Issue 2_B

Shimada Y. et al. / Procedia Structural Integrity 2 (2016) 1593–1600 Yusuke Shimada / Structural Integrity Procedia 00 (2016) 000–000

1599

7

strengths of the virgin steel, σ Y and σ T . In this study, two cases were investigated. The value of virgin steel and that of pre-strained steel were used as the change in strength by dynamic loading, Δ σ Y and Δ σ T . The estimated value agreed with the experimental result when the strain rate dependence of pre-strained steel was used, while the estimated value was larger than the experimental result when the strain rate dependence of virgin steel was used. In other words, the change in the strength of the steel when both pre-straining and dynamic loading were applied can be estimated as the sum of the amount of strength variation due to pre-straining and the amount of strength variation due to dynamic loading of the pre-strained steel.

Yield strength

Tensile strength

800

750

Estimated σ Y = σ Y ( ε pre =0, e=10 -4 /s) + Δσ Y due to pre-straining + Δσ Y due to dynamic loading

Estimated σ Y = σ Y ( ε pre =0, e=10 -4 /s) + Δσ Y due to pre-straining + Δσ Y due to dynamic loading

750

700

Estimated σ T (MPa) 700 650 600

Estimated σ Y (MPa) 650 600

550 500 500 550 600 650 700 750 Experiment σ Y (MPa)

550

800

550 600 650 700 750 Experiment σ T (MPa)

Fig. 12 Comparison between estimated strength and experimental one of pre-strained steel (SM490A, at room temperature)

In this study, the changes in strength due to pre-straining and dynamic loading can be calculated by Eq. (13) and (15) for yield strength and by Eq. (14) and (16) for tensile strength. The results of the estimation are shown in Fig. 13. For the entire strength range in this study, is was recognized that these formulas have good accuracy ( ) ( ) ( ) ( ) ( )  − × = − − 8 8 1.5 0 0 0 4 0 0 pre ln 10 1 ln 10 1 exp 8 10 , , ε e e T T E T T T e T pre Y pre Y Y    ・ ・ σ ・ σ σ (13)

   

  

   

   

  

  

0

0

)       

   

1.5

   −

( ) 0 T

  

pre

  

( ln 10 1

( ln 10 1

(

)

(14)

σ

( ) 0 T ・

pre

= pre , , ε  σ σ e T T T

4

−

T

× exp 8 10

−

T

0

)

0

0

9

9

E

T

e T 

e 

・

0 ・

0

)        )       

       

1.1

   −    −

( ) 0 T

     

pre

     

( ln 10 1 ln 10 1 (

( ln 10 1 ln 10 1 (

(

)

(15)

σ

( ) 0 T ・

pre

= pre , , ε  σ σ e T Y Y

2 ・

−

T

× exp 1 10

−

Y

0

・

)

0

0

8

8

E

T

e T 

e 

・

0 ・

0

1.1

( ) 0 T

pre

(

)

(16)

σ

( ) 0 T ・

pre

= pre , , ε  σ σ e T T T

4 ・

−

T

× exp 1 10

−

T

0

・

)

0

0

9

9

E

T

e T 

e 

・

0 ・

0

Tensile strength

Yield strength

1,000

1,000

200 Estimated yield stress σ Y (MPa) 400 600 800

800

200 Estimated yield stress σ Y (MPa) 400 600

○ Steel plate (490 MPa class) □ Steel plates (590 MPa class) ◇ Steel plates (780 MPa class) △ H-section steel (400MPa class) ▲ H-section steel (490MPa class)

○ Steel plate (490 MPa class) □ Steel plates (590 MPa class) ◇ Steel plates (780 MPa class) △ H-section steel (400MPa class) ▲ H-section steel (490MPa class)

200

400

600

800

1000

200

400

600

800 1000

Measured yield stress σ Y (MPa)

Measured yield stress σ Y (MPa)

Fig. 13 Estimation of variation on strength due to dynamic loading and temperature