PSI - Issue 33

Irina A. Bannikova et al. / Procedia Structural Integrity 33 (2021) 1146–1151 Author name / Structural Integrity Procedia 00 (2019) 000–000

1149

4

The relaxation properties of a continuous medium under shock wave loading were determined by analyzing the velocity profiles of the free surface using the methods and formulas given in (Bogach and Utkin (2000), Bannikova et al. (2014), Uvarov et al. (2015), Bannikova et al. (2018). The figure below shows the dependences of the strain rate at the compression wave front on the compression pulse amplitude ε˙*(P 0 ) (see Fig. 3, a), the dependence of the values of the spall strength of liquids on the strain rate P S (ε˙) (see Fig. 3, b). The ε˙*(P 0 ) values for all liquids are located on the diagram in approximately the same area. Previously in work Bannikova et al. (2014) for water a power law dependence ε˙*(P 0 ) with a power value of 3.2 was obtained at strain rates ε˙*~10 5 ÷10 7 1/s. At this work the strain rate value is less than ~ 10 5 1/s. With an increase in the strain rate at the rarefaction wave front, the spall strength of distilled water increased from 1 MPa to 22 MPa; for Guar and Surfogel, the spall strength P S changed insignificantly, from 5.6 to 7.6 MPa, and from 1.1 to 10.7 MPa, respectively. The temperature of the liquids during the experiment corresponded to the temperature of the laboratory room, 20 °C.

25

10

Guar Surfogel Water

b

a

for all data ε˙* = 0.53∙P 0 R² = 0.48

0.53

20

P S = 11.95ε̇ R² = 0.57

0.84

15

1

ε̇*, 10 4 1/s

P S = 6.14ε̇

0.28

10

P S , MPa

R² = 1

ε̇ * = 1.6∙P 0 R² = 1 ε̇ * = 0.18∙P 0 R² = 0.89

0.25

5

Guar Surfogel Water

P S = 4.99 ε̇ R² = 0.28

0.40

1.06

0

0

0 0,4 0,8 1,2 1,6 2 2,4

1

10

100

P 0 , MPa

ε̇, 10 4 1/s

Fig. 3. a - dependences of the strain rate at the compression wave front versus the compression pulse amplitude ε˙*(P 0 ), logarithmic axes; b - dependences of the values of the spall strength of liquids versus the strain rate P S (ε˙).

Under conditions of plane high-rate deformation, momentum transfer occurs due to the plasticity of the medium. Shear viscosity according to Bazaron et al. (1990), Derjaguin et al. (1992) was found as the product of the relaxation time and the shear modulus of elasticity. In this work, the shear viscosity was estimated from the experimentally obtained profiles of the free surface velocity and the curves of the shock adiabats of liquids (data for water was used) using the following formula by Uvarov et al. (2015):

2

0 * ( )

2 0 0 S P c   

3 4

~

*



(1)

.

Fig. 4 shows the dependence of the estimated values of shear viscosity on the strain rate at the front of the compression wave. In the case of Guar (circles), the shear viscosity increased by a factor of 10. The shear viscosity of Surfogel changed insignificantly in this range of deformation rates from 1.1 to 9.5 Pa×s. Distilled water (triangles) exhibits a pseudoplastic character: shear viscosity first decreased, then increased and again decreased with increasing strain rate (see Fig. 4, triangles, shown by arrows).