A physically-based abrasive wear model for composite materials Page: 7 of 22
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In terms of these three primary wear mechanisms, the wear behavior of a two-phase
composite is akin to that of a three-phase composite composed of a matrix, reinforcement and
pores. The volume fraction of the porous section is equal to the volume fraction of the non-
contribution portion of the reinforcement, which is the product of volume fraction of
reinforcement VR and the fraction of the non-contributing portion (Eq. (11)).
Vpore -VR VR 0.5 (11)
Thus, the net volume fraction of the reinforcement, which contributes to the wear resistance can
be written as:
Vnet =VR - I(+) VR < 0.5 (12)
The wear rate of the three-phase composite can again be obtained based on the "equal wear rate
S V V V
-=-'c+C).R R VR O0.5 (13)
Wc W WR Wpore
where W, Win, WR and Wpore are the wear rates of composite, matrix, reinforcement and pores, Vm
and VR are the volume fractions of the matrix and the reinforcement, and C is a new parameter,
which we term the contribution coefficient of reinforcement. This parameter describes the
relative contribution of each of the primary wear mechanisms and is defined by the size of the
reinforcement, the plowing depth and the interfacial crack size as:
C = 1-, (14)
Since the third term on the right side of Eq. (13) will vanish because the wear resistance of pores
is equal to zero, 1/Wp0r = 0, we can obtain a final expression for the abrasive wear rate of a
composite from this physically-based mechanistic model as:
1 - - +C R VR 0.5 (15)
Wc Wm WR
The contribution coefficient parameter represents the effects of critical factors, including the
interfacial toughness and the relative size of the reinforcement; its magnitude varies from zero to
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Lee, Gun Y.; Dharan, C.K.H. & Ritchie, Robert O. A physically-based abrasive wear model for composite materials, article, May 1, 2001; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc780737/m1/7/: accessed May 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.