Issue 42

M. Davydova et alii, Frattura ed Integrità Strutturale, 42 (2017) 170-180; DOI: 10.3221/IGF-ESIS.42.18

where m is the fragment mass, and

T M is total fragment mass.

4.0

Quartz Syminal ZiO2 SiC Granite Zr

3.0

2.0

Power law exponent, D

1.0

0.0

1

10

100

1000

10000

Number of fragments per unit mass , N m

Figure 11: Power law exponent of fragment size distribution for five tested materials.

The analysis of Fig.10 and Fig.11 shows that we can get the similar distribution for granite, quartz and ceramics, but at different value m N . In this case the relation for fragmentation intensity, m N , is:

(5)





N

N

ZrO N

granite

quarz

ceramic

m

m

m

2

ZrO ceramics (even with

Inequality (5) describes the real resistance to fracture of these materials. For fragmentation of 2 high porosity about 30%), we need to expend more energy than for fragmentation of quartz and granite.

y = -2.0951x - 0.4222 R² = 0.9803 y = -2.0336x - 0.6172 R² = 0.9817 y = -1.952x - 0.6266 R² = 0.9905

Quartz ZrO2 Granite Zr 2

12

10

8

6

ln(N)

4

2

0

-6

-5

-4

-3

-2

-1

0

ln(r)

 1.95 D ; for quartz

 2.09 D ; for

Figure 12: Fragment size distribution for 3 materials with power law exponents: for granite

2 ZrO .  2.03 D

178