Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Mixed mode cracking in layered materials

Calculations are reported for the mixed mode toughness of an interface joining an elastic-plastic solid to a solid which does not yield plastically. A potential function of the components of the crack face displacements is used to generate the tractions along the interface where the fracture processes causing separation occur. The two main parameters characterizing this potential are the work of separation per unit area and a peak normal stress. This description of the interface separation process is embedded within the continuum description as a boundary condition on the interface linking the adjoining solids. Small-scale yielding in plane strain is considered with the remote field specified by the magnitude and phase of the mixed mode stress intensity factors. Crack growth resistance curves are computed for a range of the most important nondimensional material parameters and for various combinations of remote mixed mode loading. Particular emphasis is placed on the ratio of the steady-state interface toughness to the “intrinsic” work of separation as it depends on plastic yielding and on the combination of modes 1 and 2. Plasticity enhances the interface toughness for all modes of loading, but substantially more so in the presence of a significant mode 2 component of loading than in near-mode 1 conditions.

The influence of plasticity on mixed mode interface toughness

http://www.eng.usf.edu/~volinsky/VolinskyActaMatReview2002.pdf

Interfacial toughness measurements for thin films on substrates

Thin films and multilayers comprised of different classes of material are often used for various functional requirements. As these become relatively large in section and geometrically more complex, thermomechanical integrity is a major concern. It influences performance, yield and reliability. A methodology for thermomechanical design is needed that complements procedures used for circuit design. This article elaborates the principles of fail-safe thermomechanical design, based on the damage mechanisms known to occur in these systems. Among the important mechanisms are delamination and crazing of brittle layers. thermomechanical fatigue of metallic constituents and interface decohesion. The damage mechanisms are generally activated by residual stress, both thermal and ‘intrinsic’. The origins of these stresses are discussed, as well as stress redistribution effects that arise because of bending, discontinuities, etc. Emphasis is given to measurement methods which provide those data needed for implementation of the fail-safe design methodology.

The thermomechanical integrity of thin films and multilayers

The toughness of a glass/'epoxy interface was measured over a wide range of mode mixes. A toughening effect was associated with increasing positive and negative in-plane shear components. Optical interference measurements of normal crack opening displacements near the crack front and complementary finite element analyses were used to examine near-front behavior during crack initiation. Estimates of the tough­ening based on plastic dissipation, bulk viscoelastic dissipation, and interface asperity shielding did not fully account for the measured values. The results suggest that the inelastic behavior of the epoxy, frictional, and, perhaps, three-dimensional effects should be considered. 1 Introduction Interfacial crack growth occurs in a number of applications of technological importance. Because of the fact that the frac­ture path is constrained irrespective of the orientation of the globally applied loads and also because of the mismatch of material properties across the interface, crack growth is in­herently mixed mode. Critical and subcritical crack growth must then be governed by some combination of mode I, II, and III fracture parameters. The simplest approach, using one parameter, seeks to determine an effective parameter that can account for all mode mixes in a unifying manner. This is particularly useful for subcritical crack growth where corre­lations of crack growth rates fall on one curve for all mode mixes when the proper parameter is found. An alternative is to consider a two-parameter approach where one parameter represents the mode mix or direction and the other a magni­tude. For critical crack growth, the magnitude will generally be a function of mode mix. The form the function is usually determined experimentally but may, as mechanisms are better understood, even be predicted. The most common approach for examining interfacial crack initiation has been to consider the interfacial fracture tough­ness, G

Asymmetric Shielding in Interfacial Fracture Under In-Plane Shear

The paper establishes the range of in-plane fracture mode mixtures and contact zone sizes that can be obtained from an edge-cracked bimaterial strip under biaxial applied displacements. The development of a suitable loading device for and the application of crack opening interferometry to interfacial crack initiation experiments is described. The crack initiation process under bond-normal loading is examined in detail for a glass/epoxy interface in order to establish a hybrid optical interference/finite element analysis technique for extracting mixed-mode fracture parameters.

Biaxial Loading Experiments for Determining Interfacial Fracture Toughness

Abstract Fretting in the partial-slip and gross-slip regimes under a constant normal load is considered. The tangential force—displacement relations for the forward and backward motions are described based the generalized Cattaneo—Mindlin theory of tangential contact and Masing’s hypothesis on modelling the force—displacement hysteretic loop. Besides the critical force and displacement parameters (characterizing the triggering of sliding), the model includes one dimensionless fitting parameter that tunes the tangential contact stiffness of the friction—contact interface. Explicit expressions are derived for the main tribological parameters of the fretting loop, including the slip index and the signal index. The presented phenomenological modelling approach has been applied to the analysis of two sets of experimental data taken from the literature. It has been shown that the experimentally observed simple relation of a rational type between the slip index and the slip ratio corresponds to the gross-slip asymptotics of the corresponding model-based predicted relation. The known quantitative criteria for the transition from the partial slip regime to the gross slip regime are expressed in terms of the stiffness parameter, and a novel geometric transition criterion is formulated. 

/pdf/a-theoretical-justification-of-the-slip-index-concept-in-2rzf3i28.pdf

Y. S. Chai

Papers

Asymmetric Shielding in Interfacial Fracture Under In-Plane Shear

Biaxial Loading Experiments for Determining Interfacial Fracture Toughness

A theoretical justification of the slip index concept in fretting analysis