PSI - Issue 2_B

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

1598

Yusuke Shimada / Structural Integrity Procedia 00 (2016) 000–000

6

( )

   

)       

1.5

−

  

( ln 10 1

( ln 10 1

  

  

(10)

σ

( ) , e T 

( ) T

4

−

0 0 E T T T 0

× exp 8 10

−

=

σ σ ・

)

T

T

0 0

9

9

T

e T 

e 

・

0 ・

0

( )

       

)        )       

1.1

−

     

( ln 10 1 ln 10 1 (

( ln 10 1 ln 10 1 (

     

     

(11)

σ

( ) , e T 

( ) T

2 ・

−

0 0 E T T Y 0

× exp 1 10

−

=

σ σ ・

・

)

Y

Y

0 0

8

8

T

e T 

e 

・

0 ・

0

( )

1.1

−

(12)

σ

( ) , e T 

( ) T

4 ・

−

0 0 E T T T 0

× exp 1 10

−

=

σ σ ・

・

)

T

T

0 0

9

9

T

e T 

e 

・

0 ・

0

where e, ・

EA is the static strain rate (=10

-4 /sec).

Yield strength

Tensile strength

3000 2500 2000 1500 1000 500

6000 5000 4000 3000 2000 1000

B

B

(

)

(

)

γ

γ

B T

E

B T

E

/

= − = × = α

σ

/

= − = × = α

σ

・ ・

・ ・

T

0

0

Y

0

0

4

−

4

−

1.5 8 10

γ α

1.5 8 10

γ α

0 0.5 1 1.5 2 2.5 3 0

0 1 2 3 4 5 6 0

(

) γ

(

) γ

σ T E Y / 0 0 ・

σ T E T / 0 0 ・

( × 10

6 )

( × 10

6 )

Fig. 9 Relationship between coefficient B and strength of steel

5. Superposition effect of pre-straining and dynamic loading on yield strength and tensile strength Figure 10 shows the changes in yield strength Δ σ Y and tensile strength Δσ T due to pre-straining. Each increases with an increase in pre-strain.

Fig. 10 Increment in strength due to pre-straining (SM490A, at room temperature, at 10 -4 /s) Δσ Y , Δσ T (MPa) 350 300 250 200 150 100 50 0 0 0.02 0.04 0.06 0.08 0.10 0.12 Pre-strain, ε pre Tensile strength Yield strength ( 0 0.1) 800 = − ∆ = pre pre T ε ε σ ( 0 0.05) 4400 = − ∆ = pre pre Y ε ε σ ( ) ( 0.05 0.1) 5 220 14 100 = − − + ∆ = pre pre Y ε ε σ

The relationship between the strain rate and Δ σ Y and that between the strain rate and Δ σ T are shown in Fig. 11. Δ σ Y and Δ σ T also increase with increases in the strain rate, but the change decreases as higher pre-strain levels. The cause of this tendency can be regarded as the amount of strength variation due to pre straining. This tendency also agrees with the results of Minami et al. (2001), which found that the strain rate dependence of strength becomes smaller as the strength of the steels increase.

Δσ Y (MPa) 160 140 120 100 80 60 40

(  Tensile strength ) [ ] 0 4 = − pre ε

Yield strength ( ) [ ] ( ) [ 0 4 4 = = − − pre pre e e ε ε  

Δσ Y (MPa) 160 140 120 100 80 60 40

( /10 9.5log /10 16.6 log /10 25.0 log − e 

∆ = ∆ = ∆ = Y Y σ σ σ

( /10 14.6 log /10 24.2 log e e 

∆ = ∆ = T σ σ

]

) [

] 0.05,0.1

0.05

4

−

ε

=

Y

pre

) [

] 0.1

4

=

ε

Y

pre

0 20 10 -4 10 -3 10 -2

0 20 10 -4 10 -3 10 -2

10 -1 10 0

10 1

10 2

10 -1 10 0

10 1

10 2

Strain rate, e (1/s) ・

Strain rate, e (1/s) ・

Fig. 11 Amount of strength variation due to dynamic loading (SM490A, at room temperature)

Next, the change in the strength of steel subjected to both pre-straining and dynamic loading was examined. Figure 12 compares the estimated dynamic strengths and experimental results for pre-strained steels. The horizontal axes show the strengths obtained by experiment, while the vertical axes show the strengths calculated by adding the changes in strengths due to pre-straining and dynamic loading, Δ σ Y and Δ σ T , shown in Figs. 10 and 11 to the static