Models for the Mechanics of Joining Dissimilar Materials - Structural Interfaces and Attachments in Biology - page 48

Fig. 3.5 Dependence of peel strength on peeling angle ' in a fictional tendon-to-bone attachment
in which the critical energy release rate does not depend upon the peeling angle

that causes pealing. Unlike the case of a rigid tendon, a crack between tendon and
bone can advance in this system even if the peel angle is 0 . The crack will advance
and the tendon will peel away if the elastic energy released when the crack
advances a certain distance exceeds that needed to drive the crack this distance.
The elastic term is clearly important for a tendon such as the Achilles tendon, whose
functioning is at times like an elastic spring.
The expression ( 3.11 ) provides a lower bound on the value of

G c needed to
ensure that a crudely attached tendon would rupture before becoming detached. We
consider the case of an idealized Achilles tendon with ' 0 . Following Wren

et al. [ 12 ], we assume a tendon failure strain value of e u ¼ f c / E T wt 0.1, and a
failure stress of s u ¼ f c / wt 80 MPa. Assuming a thickness t of between 2 mm
and 2 cm yields a required

G c ¼ (1/2) s u e u t on the order of 8-80 kJ/m 2 . This is a
fracture toughness range associated with tough engineering materials such as
aluminum alloys, high strength steels, and fiberglass [ 13 ]. This back-of-the-
envelope calculation points to a need for a careful interface design and highlights
the difficulty one could expect to encounter in trying to surgically reattach tendon
directly to bone: a direct attachment of tendon to bone would not likely ever
succeed in gaining the toughness needed to withstand the forces associated with
tendon rupture at midsubstance.
Another way that this solution provides insight is through the relative magnitudes
of the two terms in ( 3.11 ). Even for a highly elastic tendon, the elastic term can
be small compared to the crack-opening term (1-cos

'

) unless the opening angle
is close to 0 . For a tendon, we plotted the two terms in Fig. 3.5 ; note that Fig. 3.5
is drawn for a fictional attachment in which

. The line shown
is for the above numbers for tendon, with E T ¼ 450 MPa [ 14 ] so that the normalized

G c does not vary with '