Mixed-mode cracking

We can clearly observe on Fig. 11 the crack deviation from the middle of the adhesive layer to the upper interface. Moreover, the distance between crack lips increases with loading to reach a mixed mode crack propagation, as observed in the experimental part. As a consequence, if it remains a poor cohesion area close to the interface, the crack will naturally fork to this area for a brittle failure. 

Sato, A., Hirakawa, Y. and Sugawara, K. 2(X)1. Mixed mode crack propagation of homogenized cracks by the two-dimensional DDM analysis. Construction and Building Materials, 15(5-6), pp.247-261. 

With increase of the roadway depth, the left side and the right side of the roadway are subjected to tensile, shear, or combined stress state. Thus, tension crack, shear crack or mixed mode crack are existed in these locations. 

The above approach does not consider the crack propagation direction. Observations have shown a mixed mode crack will not continue to propagate in the same plane. Indeed, a mixed mode crack is found to propagate at an angle to... 

One result which was analyzed in a hydro-fracturing test is shown in Fig. 8.10. Eight AE events are analyzed and plotted in the elevation view. AE events are plotted at their locations from the location analysis. Then, cracks are classified based on the shear ratio. Tensile crack are indicated by arrow s3Tnbols, of which directions are determined from the direction el. Shear cracks are represented by cross symbols, of which two directions correspond to the two vectors 1 and n. Only the event No. 14 was classified into the mixed-mode cracking, and both orientations of the tensile and the shear are indicated. Results are so successful that AE events are located along the dip plane presumed from the dip angle. Remarkably, the directions of crack opening of the tensile cracks are vertical to, and the orientations of the shear cracks seem parallel to the dip plane. 

Kinematics of these 46 events are plotted in Fig. 8.16. Here, shear and mixed-mode cracks are indicated with the cross symbol, and tensile cracks are denoted by the arrow symbol. In the all cracks, directions of crack normal and crack motion are illustrated. It is found that AE sources of tensile types are mostly concentrated inside the pipe, where the water pressure was applied. The opening directions of tensile cracks are almost vertical to the slit surface, suggesting that water flows due to leakage open the slit. 

Experiments were conducted by using the same reinforcement concrete beams as shown in Fig. 8.11. As shown in Fig. 8.18 (a), at the first stage, a few tensile cracks (Fig. 8.17 (a)) and mixed-mode cracks (Fig. 8.17 (c)) are mostly observed near reinforcement at the central region. Then, delamination between concrete and reinforcement occurred. Activity of cracking increased as the increase in mixed-mode cracks. Bending cracks were... 

Fig. 8.17. 3-D display models for tensile, shear, and mixed-mode cracks.

G.C. Sih (1974), "Strain-energy-density Factor Applied to Mixed Mode Crack Problems, Inter. J. Fract., 10,3,305-21. 

Hutchinson, J.W., Suo, Z., 1991. Mixed-mode cracking in layered structures. Adv. Appl. Mech. 29, 64. 

Arrea, M., Ingraffea, A. R. (1982) Mixed-Mode Crack Propagation in Mortar and Concrete. Ithaca, NY Department of Structural Engineering, Cornell University, Rep pp. 81-13. 

Carpinteri, A. (1987) Interaction between tensile strength failure and mixed mode crack propagation in concrete, Rep. Subcomm. C., RILEM TC89-PMT, Italy Dept.of Struct. Eng., Politecnico di Torino. 

Shah, S. P. (1989) On the fundamental issues of mixed mode crack propagation in concrete, in Fracture Mechanics of Concrete Structures From Theory to Application. Report ofTC90 ofRILEM, L. Elfgren, ed., London Chapman and Hall pp. 27-38. 

Hutchinson, J. W. and Suo, Z. (1992), Mixed mode cracking in layered materials, Advances in Applied Mechanics 29, 63-191. 

Two-Dimensional Mixed Mode Crack Simulation Using the Material Point Method. 

Much of what is summarized here is presented in more detail in the excellent article on mixed-mode cracking in layered materials by Hutchinson and Suo [55]. In that reference, the authors consider not only interfacial fracture, but also cracking within coatings and cracking in substrates below coatings. Only interfacial cracking (delamination) will be considered in detail here. Before proceeding however, we will first discuss some basic concepts of fracture mechanics. 

An example of such a fracture envelope, in this case developed for the case of mixed-mode cracking of an adhesive joint system consisting of 7075-T6 aluminium adherends bonded with a 0.4 mm thick structural epoxy appears in... 

Hutchinson JW, Suo Z (1992) Mixed mode cracking in layered materials. Adv Appl Mech 29 63-191 Humi M, Miller W (1988) Second course in ordinary differential equations for scientists and engineers. Springer, New York... 

At present the shadow optical method represents a powerful tool in experimental fracture mechanics for the determination of stress intensity factors at the tips of quasistatically extending and fast running cracks, respectively. Further, the method of caustics can also be applied for mixed-mode crack problems as well as for the investigation of plastic zones around crack tips propagating in elasto-plastic materials. Moreover, due to the possibility of applying the method auf caustics in transmission as well as in reflection the treatment of cracked opaque model materials can also be performed. A comprehensive review about the shadow optical method of caustics has been given In reference [16]. 

Hasselman, D.P.H. and Singh, J.P., Role of mixed-mode crack propagation in thermally shocked brittle materials, Theoret. Appl. Fracture Mech., 1984, 2, 59-65. 

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