PSI - Issue 28

Ezio Cadoni et al. / Procedia Structural Integrity 28 (2020) 964–970 Author name / Structural Integrity Procedia 00 (2020) 000–000

967

4

Then, by applying the one-dimensional elastic plane stress wave propagation theory the stress (1), the strain (2) and the strain-rate (3) versus time within the specimen can be evaluated: σ ( t ) = E 0 · A 0 A · T ( t ) (1)

L

t

2 C 0

( t ) = −

R ( t )

(2)

0

2 C 0

R ( t )

(3)

˙ ( t ) = −

L ·

Three target strain-rates were set at 850 s − 1 , 1400 s − 1 and 2200 s − 1 obtained imposing a preload of 26kN, 35kN and 50kN, respectively. During the tests the signals from strain-gauges were acquired by a HBM-Gen2 data acquisition system while the specimens were filmed at high speed by a fast camera IDT- MotionPro Y4-S3 at 43kfps.

4.1. High strain-rate results

The stress versus strain curves under tension at high strain-rate are depicted in Fig. 3. In Table 2 are reported the high strain-rate results. The results highlight the brittle behaviour of this material. In fact, the photos (one every 23 µ s) in Fig. 4 reveal for di ff erent rates how the specimen fails. Moreover, the uniform strain, even if it growths with increasing strain-rate, is limited to a maximum of 1.3% while the fracture strain does not exceed 6.7%. Both proof and ultimate tensile strengths increase with increasing strain-rate, but their ratio f u / f p , 0 . 2 passes from 1.12 for quasi-static tests to 1.01 for higher strain-rate. This ratio is usually adopted as measure of the ductility (Cadoni and Forni (2019); Forni et al. (2016); Cadoni et al. (2013)), this means that with increasing of the rate the material becomes more brittle.

Table 2. High strain-rate results. Target strain-rate f p , 0 . 2 ( MPa )

3 )

f u ( MPa )

u ( % )

f f ( MPa )

f ( % )

˙ e f f

W u ( MJ / m

Z ( % )

850

2216 (86) 2336 (56) 2748 (157)

2233 (64) 2444 (77) 2770 (156)

1.08 (0.08) 1.28 (0.14) 1.32 (0.15)

2009 (83) 2015 (37) 1437 (484)

5.75 (0.55) 5.49 (0.91) 6.70 (0.79)

843 (27) 1405 (40) 2200 (13)

113.56 (10.07) 110.52 (19.37) 133.46 (18.12)

9.27 (3.15) 9.37 (3.20) 7.90 (1.74)

1400 2200

5. Discussion and final remarks

The representative stress versus strain curves under tension and strain-rate, ranging from 10 − 3 s − 1 to 2200 s − 1 , are depicted in Fig. 5. At the quasi-static regime and at 850 s − 1 the material works as an elasto-plastic material while for higher rate the material softens with strain after yielding. In order to investigate the strain-rate sensitivity of a specific mechanical property, the dynamic increase factor (DIF) such as the ratio between the dynamic to the quasi-static values was used. This parameter was evaluated for the proof ( f p 0 . 2% ) and the ultimate ( f u ) tensile strengths. Figure 6 shows the evolution of these values with increasing of strain-rate. From Table 2 it is possible to note the 78% of increment for uniform strain, the 64% of increment for modulus of toughness and the 40% of decrement for reduction area. With the aim to use these data in numerical codes, the rate-dependency of this tungsten alloy was finally analysed by calibrating the well-known Cowper-Symonds (Cowper and Symonds (1957)) model. It describes the evolution of the ratio between quasi-static ( f p 0 . 2 , s ) and dynamic ( f p 0 . 2 , s ) proof strength in function of the strain-rate as follow:

˙ D

= 1 +

1 / q

f p 0 . 2 , d f p 0 . 2 , s

(4)