PSI - Issue 6

Ivan Smirnov et al. / Procedia Structural Integrity 6 (2017) 34–39 Ivan Smirnov et al. / Structural Integrity Procedia 00 (2017) 000 – 000

37

4

Note, that the values of limit stresses in the case of overloaded pulses for both durations fall on the same curve. This curve can be obtained by using the incubation time criterion of failure (1). The curves on Figure 2 are obtained according to the criterion for the following set of parameters: σ c = 189 MPa and τ = 13 µs for the compression tests; σ c = 27.4 MPa and τ = 17 µs for the splitting tests. The values of quasi-static strength σ c were obtained in quasi-static tests. The stress rate d σ /dt was determined by the slope of an elastic portion in the timing diagram of the stress. The incubation time of failure was determined semi-empirically using the nonlinear approximation. Parameter τ was selected in such a way that theoretical curve (1) fits the experimental points with a minimal deviation.

4.2. Substitution effect of limiting stresses

Figures 3 and 4 show the results on rate dependence of ultimate stresses for the compression and splitting of the rocks and concrete. The figures are supplemented with data for the tests of fiber-reinforced concrete (CARDIFRC) presented in the paper of Bragov et al. (2013).

400

500

b

a

Granit CARDIFRC Limestone Concrete Marble

Concrete Concrete_s Concrete_f Limestone Limestone_s Limestone_z

400

300

300

200

200

 * (MPa)

 * (MPa)

100

100

0

10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 0

10 -2

10 -1

10 0

10 1

10 2

10 3

de/dt (1/s)

de/dt (1/s)

Fig. 3. Strain rate dependencies of ultimate stresses in rocks and concrete under compression. a) different rocks; b) dry, saturated (s) and frozen (f) materials.

b

20

50

a

Concrete Concrete_s Concrete_f Limestone Limestone_s Limestone_z

Granit CARDIFRC Limestone Marble Concrete

16

40

12

30

8

20

 * (MPa)

 * (MPa)

4

10

10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 0

10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 0

d  /dt (GPa/s*10 3 )

d  /dt (GPa/s*10 3 )

Fig. 4. Stress rate dependencies of ultimate stresses in rocks and concrete under splitting. a) different rocks; b) dry, saturated (s) and frozen (f) materials.