Fracture in Joints
Cracks in joints differ from cracks in bulk material in three respects. (1) Cracks in concrete usually (albeit probably not always) propagate in the direction normal to the maximum principal stress ns in. Mode I, but a crack in a joint is subjected to normal as well as shear loading and is of a mixed-mode. (2) The roughness of a crack in a smooth joint can be much smaller than the roughness of a crack in the bulk of concrete. Thus, aggregate interlock plays a lesser role and friction dominates as a means of transferring
0 0.5 1 1.5 2
joint length (m)
Figure 10.5.8 Fracture of joints: (a) sketch of tests by Reinhardt (1982); (b~c) tests by Buyitkozturk and Lee (1992b); (d) average shear stress-slip curves for Reinhardt’s tests; (e) size effect in Reinhardt’s tests.
shear stresses across a joint. (3) Л crack in concrete exhibits considerable dilalancy associated with shear slip, but in a smooth joint, the dilatancy may be quite small.
The behavior of joints of dissimilar materials was investigated experimentally by Reinhardt (1982) and by Buyukozturk and Lee (1992b). Reinhardt tested joints of strong concrete and mortar of variable strength subjected to various compressive normal stresses (Fig. 10.5.8a). Buyuko/.turk and Lee tested sandwich specimens of granite and mortar with an interfacial crack (Fig. 10.5.8a) as a means of characterizing the aggregate-mortar interface, although their results could be useful for macroscopic structures as well.
Fig. 10.5.8d shows shear stress-slip curves for the same joint length, two different mortar strengths and, in each case, three different compressive normal stresses across the joint. It is seen that the stress first rises abruptly with very little slip up to a certain maximum and then, for the joints made in high strength mortar, a steep drop of stress follows, while for the joints made in low strength mortar only a mild drop is seen. After the development of a full crack, a frictional plateau gets established with the residual shear capacity determined by the compressive stress across the joint. This capacity does not depend on the slip magnitude, nor on the mortar strength. (It might be noted, though, that the response shown could have been influenced by the stiffness of the loading frame as well as the response frequency of the servo-controller.)
A plot of the normalized shear strength of the three different joints vs. the length of the joint is shown in Fig. 10.5.8e. The joint made with low strength mortar was found to exhibit rio dependence of the shear strength on the joint length, i. e., no size effect. On the other hand, the joint made with a mortar of high strength exhibited a strong size effect close to LEFM (in this case, the joint strength decreased as L-1/2, with l = joint length). The joint made with a mortar of medium strength was found to exhibit an intermediate size effect.
The interfacial crack propagation was interpreted by Reinhardt (1982) on the basis of the LEFM
solutions of Sih (1973), Rice and Sih (1965), and Erdogan (1963) for particular geometries of cracks at the interface of two dissimilar ltalfspaces. Buyukozturk and Lee (1992b) also interpreted their tests in terms of LEFM, based on solutions by Suo and Hutchinson (1989). The LEFM treatment of interfacial crack theory is outside the scope of this book; it is a conceptually involved topic, because the power series expansion that is relatively simple to handle for the single material problem (Section 4.3) has complex exponents for the bimaterial case. The dominant solution of the displacement field still decays as r1/2 near the tip, but displays an oscillating behavior near the origin. For example, it can be shown that the dominant term for the crack opening at a distance r from the crack tip takes the form
w(r) oc – Jr cos(ф + ш In r)
where ф and ui depend on the loading, geometry, and elastic properties of the two materials; ui = 0 if the two bodies have identical clastic constants. Note that when r approaches zero (the crack tip), the factor cos(ф + tulnr) oscillates between -1 and 1 with frequency tending to infinity (because limr-,o(lnr) = — oo). This means that the solution always includes negative crack openings, which are not physically admissible (there would be interpenetration of the opposite faces of the crack). This is but one of the difficulties involved in the interfacial crack problem. The interested reader is referred to the original papers and to recent papers by Rice (1988), Hutchinson (1990), and He and Hutchinson (1989).