PSI - Issue 2_B

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

1596

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

4

effect of pre-straining on both yield strength and tensile strength were estimated by experimental equations. As can be seen in Fig. 2, the yield strength logarithmically increases and tensile strength lineally increases when the pre strain increases. In addition, Minami et al. reported that the pre-straining effect on yield strength is small in the high strength range. Thus, the strength variation due to pre-strain was estimated by Eq. (3) and (4), and the results are shown in Fig. 5. For the entire strength range of this study, a good accuracy can be recognized. ( ) ( ) pre 1/ 4 Y0 0 Y0 0 0 Pre Y0 34 ε ln 1 (T ) σ 34 E ＋ (T ) σ T σ  +    = (3)  

( ) 0 T σ = Pre T0

(4)

T0 0 750 ＋ ε (T ) σ

pre

pre ( T

0 ) and σ T0

pre ( T 0 ) are the static yield strength and tensile strength(MPa), respectively, at room

where σ Y0

temperature T 0 (=293K) with a pre-strain ε pre , and E is Young’s modulus (=206GPa).

Yield strength

Tensile strength

1,000

1,000

800

800

200 Estimated yield stress σ Y (MPa) 400 600

200 Estimated yield stress σ T (MPa) 400 600

200 400 600 800 1000 Measured yield stress σ Y (MPa)

200 400 600 800 1000 Measured yield stress σ T (MPa)

Fig. 5 Relationship between measured strength and estimated strength

4. Effect of dynamic loading on yield strength and tensile strength Fig. 6 shows the strength difference between static loading and dynamic loading at 20 °C. Yield strength and tensile strength increase as the strain rate increases. However, differences in the strain rate have no effect on the strength increase between yield strength and tensile strength.

Yield strength

150

Tensile strength

150

100

100

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

50 Δσ Y (MPa)

Δσ T (MPa)

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

50

0

0

1.0E-4 1.0E-2 1.0E+0 1.0E+2

1.0E-4 1.0E-2 1.0E+0 1.0E+2

Strain rate e (1/s)

Strain rate e (1/s)

Fig. 6. Effect of dynamic loading on both yield strength and tensile strength

800

The nominal yield strength, nominal tensile strength and nominal strain increase with increases in the strain rate for virgin steel, as shown in Fig. 7. This finding has been reported by Minami et al. (2001). At the same time, it is well known that the yield strength of steel depends on the strain rate and also shows Arrhenius-type temperature dependence. The strain rate-temperature parameter R has been proposed as a parameter for evaluating the effect of both strain rate and temperature on yield strength equivalently, and is can be expressed by Eq. (5), as reported by Bennett (1961). The dependence of both the strain rate and temperature

s 10 / 0

s 10 / 1

s 10 / 2

600

400

s / 10 4 −

s / 10 2 −

200

Nominal stress (MPa)

0 0

10

20

30

40

Nominal strain (%)

Fig. 7 Nominal stress - nominal strain curve of static loading and dynamic loading for virgin steel (SM490A)