A physically-based abrasive wear model for composite materials Page: 6 of 22
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an interfacial crack (Fig. 4). The maximum tensile load is applied at the matrix/reinforcement
interface when the abrasive medium plows the reinforcement, i.e.,
(F,) =(F,)R (6)
At this point, the size, 1, of the interfacial crack will be a function of the net tensile stress and the
relative toughness of the interface and the matrix:
= g 1 , (')n} (7)
where Gf is the interface fracture toughness. By combining Eqs. (5) and (7), the length of the
interfacial crack can be expressed as:
Z=g , F,) R~d,(F'P)n (8)
C. Particle removal
In a given tribo-system, the size of the interfacial crack / under the maximum tensile load is
assumed to be constant. The continuous plowing of the abrasive particles reduces the level of the
surface until the tip of the interfacial crack finally reaches the bottom of the reinforcement (Fig.
Continued plowing of the abrasive medium causes further propagation of the interfacial
crack, its trajectory depending on the relative toughness of the interface. When the ratio of the
fracture toughness of the interface and the matrix is less than approximately 0.25 for this
geometry (this ratio does vary with the orientation of the crack), the interfacial crack will deflect
along the interface , i.e., when:
f< - (9)
where Gfand Gm are, respectively, the fracture toughness of the interface and matrix material.
Further motion of the abrasive medium can cause the complete removal of the remaining
portion of the reinforcement leaving a void of the same size on the surface. As a portion of
reinforcement is now removed as a large mass (due to the interfacial failure), it cannot contribute
to the wear resistance. The fraction of this "non-contributing portion" is:
(x +1) (10)
where x is the depth of penetration of the abrasive medium, / is the size of the interfacial crack,
and DR is the size of the reinforcement (Fig. 5(b)).
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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/m1/6/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.