A strength and damage model for rock under dynamic loading Page: 4 of 7
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APS Topical Conference on Shock Compression of Condensed Matter in Snowbird, Utah,
June27-July2, 1999More details about the numerical algorithm can
be found in [3].
STRENGTH OF MATERIAL
The physical phenomena that influence the
yield strength Y are accounted for by assuming a
simple multiplicative form with Y being given by
[1]Pressure, GPa
FIGURE 1. Yield and failure surface.
The divergent flow of spherical shock loading
leads to a wide variety of stress states in contrast
to plane waves, where the locus of all states is
represented by a straight line in yield-pressure
space.
POROUS COMPACTION AND BULKING
The equations used to describe the evolution of
porosity are given in [1]. Here we only provide a
brief description.
To describe the increase of porosity due to
distortional deformation (bulking), the following
equation is used:
= (I _ 0) nd (, P)Q , max < 0 ,min < a(D (5)
where Q is the rate of dissipation given byThe functions F in (3) represent hardening
effects due to plastic strain (F) and pressure
sensitivity (F2), as well as softening due to
distortional deformation damage (F,) and
melting (F). F is a function of the Lode angle.
In our study of spherical wave propagation in
granite we have found that the response of the
material is most sensitive to the first three
functions in Eq. (3). The analytical forms of the
functions F are described in [1]. The damage
parameter, n, used in the function (I) is
evaluated using the relation
(Tmax - Tth)dt . ,
d dam=O if c, e (4)
ZdamY0
where Tmax is the most compressive principal
stress, Tth is the threshold stress for damage
growth, and Zdam is a characteristic time for
damage. The onset of damage is controlled by a
critical plastic strain parameter, E*, which can
be chosen to describe the failure surface
measured in static experiments [4] (see Fig.1).=Z L () G(B'-B'),P
0
0(3)
(6)
B' is the deviator of B and 0max, Omin are the
maximum and the minimum porosities for all
times. The maximum bulking porosity is
specified by 0*. The rate of bulking mad is
choosen to be a linear function of porosity and
pressure asmd - md0 + ai + a2P, 0 < md <1
(7)
Figure 2 shows how well it is possible to fit this
model to laboratory bulking data.Y = YoF1(cp)F2(p)F3(n)F4(#)F5(0)
failure surface damage
Y=YoF-( )
-uniaxial strain path
bulking -
s35m - ' " yield surface
' Y=YoF2
' path in spherical loading
500 m
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Antoun, T H; Glenn, L A; Lomov, I N & Vorobiev, O. A strength and damage model for rock under dynamic loading, article, June 14, 1999; California. (https://digital.library.unt.edu/ark:/67531/metadc794876/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.