PSI - Issue 6

A. Martemyanov et al. / Procedia Structural Integrity 6 (2017) 336–343 A. Martemyanov et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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3

3. Experimental results interpretation

Proposing a linear increase of deformation on time before the achievement of maximum value the local stresses is written by the Hooke’s law .

( ) t

E t H t  

t H t

(2)

( )

( ).



 





Here, E is the Young’s modulus,   is a strain rate, H(t) is Heaviside step function and   is a loading stress rate. The local stress in the fracture moment * t is identified as a limiting stress ( ) * t dyn    . Defining the dependence of the fracture time on strain rate Eq. (2) to Eq. (1) in the rupture moment, we express the ultimate stress in terms of strain rate:

   

    t ; ,

2



c

*

(3)

( )

   

2 1

dyn

t

, 

. 









st

*

Observe that the obtained fracture stress is relatively separated by two cases. The lower expression in the right-hand part of Eq. (2) describes slow processes, in which the fracture time is comparable or higher than the incubation time  . The upper expression corresponds to the opposite case the fast dynamic loading when the rupture time is shorter that  . Thus, the fracture stress under the quasi-static and dynamic loading is predicted based on three macroscopic parameters: the Young’s modulus, the critical value of strength under quasi -static loading (static strength) and the incubation time. The behaviour of the average ultimate stress in wide a range of strain rate can be predicted by Eq. (2). Note that the Eq. (2) can be written as a function fracture stress on loading stress rate ( )    dyn substituting     E  by the Eq. (1). The incubation time is defined by the least square method using experimental data ( )    dyn . It is important noted, that the introduced constant of temporal parameter of criterion (1) is sensitivity to changes of the inner structures of brittle material and invariant to any one impact history. Analysis of rock test data was related with luck of information about lithological, mineralogical and filtration capacitive material properties which makes comparisons difficult. Sample shapes, sizes and experimental techniques varies with respect to article and that makes its contribution too. It should be noted that most of the time we perceive σ st as known and reliable, but if happens that set of dynamic measurements is accompanied by the only static test or no information about elastic properties we resort to minimization procedure by both corresponding parameters. Laurentian granite seems like interesting case for our goals. It is well known that rock materials strongly depends on its mineral composition, pore space structure and sedimentation conditions. Because of this reasons mechanical properties of granites taken from different fields may change significantly. Laurentian granite has been studied by different techniques, its dynamic tensile strength behavior studied by Brazilian Disc (BD) method in Dai et al. (2010a), by flexural (3-points) notched test (FT) in Dai et al. (2010b) and spall test (ST) based method in Huang et al. (2010) work. All experimental methods were modified by Split Hopkinson Bar technique. 3.1. Laurentian granite dynamic tests results