M.Y. He

Crack deflection at an interface between dissimilar elastic-materials

Abstract A crack impinging an interface joining two dissimilar materials may arrest or may advance by either penetrating the interface or deflecting into the interface. The competition between deflection and penetration is examined in this paper when the materials on either side of the interface are elastic and isotropic. The energy release rate for the deflected crack is compared with the maximum energy release rate for a penetrating crack. The results can be used to determine the range of interface toughness relative to bulk material toughness which ensures that cracks will be deflected into the interface.

Kinking of a Crack Out of an Interface

Kinking of a plane strain crack out of the interface between two dissimilar isotropic elastic solids is analyzed. The focus is on the initiation of kinking and thus the segment of the crack leaving the interface is imagined to be short compared to the segment in the interface. Accordingly, the analysis provides the stress intensity factors and energy release rate of the kinked crack in terms of the corresponding quantities for the interface crack prior to kinking. Roughly speaking, the energy release rate is enhanced if the crack heads into the more compliant material and is diminished if it kinks into the stiff material. The results suggest a tendency for a crack to be trapped in the interface irrespective of the loading when the compliant material is tough and the stiff material is at least as tough as the interface.

Mechanics-based scaling laws for the durability of thermal barrier coatings

The durability of thermal barrier systems is governed by a sequence of crack nucleation, propagation and coalescence events that accumulate prior to final failure by large scale buckling and spalling. This sequence is governed by the σzz stresses that develop normal to the substrate, around imperfections, as the thermally grown oxide (TGO) thickens. Their effect is manifest in the stress intensity factor, K, caused by the σzz stresses acting on cracks emanating from them. In turn, these events are governed by scaling laws, ascribed to non-dimensional groups governing σzz and K. In this article the basic scaling relations are identified and used to gain some understanding of the relative importance of the various mechanisms that arise for application scenarios with minimal thermal cycling. These mechanisms are based on stresses that develop because of TGO growth strains in combination with thermal expansion misfit. The results are used to identify a critical TGO thickness at failure and express it in terms of the governing material variables. The changes in behavior that arise upon extensive thermal cycling, in the presence of TGO ratcheting, are elaborated elsewhere.

The ratcheting of compressed thermally grown thin films on ductile substrates

An analysis of the displacements experienced by undulating thermally grown thin films upon thermal cycling has been presented. The film has been assigned a thermal expansion coefficient that causes it to be compressed upon cooling. It has also been allowed to thicken at high temperature by oxidation of the substrate. It is shown that, in some circumstances, ratcheting occurs, wherein the undulation amplitude, a, increases with each thermal cycle. When such a response happens, undesirable cyclic failure modes are induced. The analysis reveals that there is a critical undulation amplitude, ac, below which ratcheting does not occur. This critical size is related to the expansion misfit, the substrate yield strength and the growth strain in the film per cycle. Connections between these variables and ac are derived.

Edge effects in thin film delamination

Thin films bonded to a substrate often sustain large in-plane residual stresses that are transferred to the film via shear stresses on the interface near their edges. These edge zones play a significant role in film delamination. A new method is introduced to analyze both the residual stress distribution in a film near its edge and the energy release rate and mode mix for an interface delamination crack emerging from, or converging upon, an edge. Two two-dimensional configurations are considered: (a) a film whose edge lies in the interior of the substrate and (b) a film whose edge is aligned with the edge of the substrate (i.e. the film/substrate geometry is a quarter-plane). There are significant differences between the two cases. For the former, (a), the energy release rate approaches the steady-state, limiting rate for a long interface crack when the crack has extended less than one film thickness. By contrast, the energy release rate in case (b) remains far below the steady-state rate until the crack extends to ten or more film thicknesses from the edge. In case (b), the edge effect provides a significant protection against edge delamination, whereas in case (a) it does not. Elastic mismatch between the film and the substrate is significant in case (b), but not in case (a). A second set of behaviors is investigated wherein the interface crack approaches the edge of the film from the interior. For both types of edges, the energy release rate drops well below the steady-state rate at remaining ligament lengths that are very large compared to the film thickness, approaching zero as the delamination converges on the edge. Analytic features which account for the various behaviors will be highlighted, and practical implications for thin film delamination will be discussed.

The Penny-Shaped Crack and the Plane Strain Crack in an Infinite Body of Power-Law Material

A study is carried out of the problem of a penny-shaped crack in an infinite body of power-law material subject to general remote axisymmetric stressing conditions. The plane strain version of the problem is also examined. The material is incompressible and is characterized by small strain deformation theory with a pure power relation between stress and strain. The solutions presented also apply to power-law creeping materials and to a class of strain-rate sensitive hardening materials. Both numerical and analytical procedures are employed to obtain the main results. A perturbation solution obtained by expanding about the trivial state in which the stress is everywhere parallel to the crack leads to simple formulas which are highly accurate even when the remote stress is perpendicular to the crack.

On crack path selection and the interface fracture energy in bimaterial systems

The intent of this article is to apply recent solutions for the mechanics of cracks at and near bimaterial interfaces to rationalize crack trajectories observed by experiment and to provide a basis for interpreting measurements of the interface fracture energy, Γi. It is demonstrated that the choice of test specimen governs the tendency of cracks to either remain at interfaces or deviate away, based on considerations of the phase angle of loading, ψ. It is further revealed that the measured interface fracture energy may be strongly influenced by the crack trajectory, as governed by ψ, through crack shielding and plasticity effects. Consequently, interfaces do not typically have unique fracture energies, but instead Γi depends on ψ which, in turn, is influenced by the test method.

The influence of imperfections on the nucleation and propagation of buckling driven delaminations

The influence of prototypical imperfections on the nucleation and propagation stages of delamination of compressed thin films has been analyzed. Energy release rates for separations that develop from imperfections have been calculated. These demonstrate two characteristic quantities: a peak that governs nucleation and a minimum that controls propagation and failure. These quantities lead to two separate criteria that both need to be satisfied to cause failure. They involve a critical film thickness for nucleation and a critical imperfection wavelength for buckling. Implications for the avoidance of failure are discussed.

Effect of interface undulations on the thermal fatigue of thin films and scales on metal substrates

Oxide scales that form on superalloys eventually spall, especially upon thermal cycling. This phenomenon is motivated by the large residual compression in the oxide. Buckling and interface crack propagation are known aspects of this behavior, but the origin of the interface separation that precedes and activates buckling is not understood. One mechanism is described and analyzed in this article. It relies on the observation that the interfaces are typically non-planar. Such non-planarity can result in cyclic straining of the substrate, near the interface, leading to crack initiation by fatigue. The conditions that lead of cyclic plasticity are analyzed for a typical range of parameters.

Analysis of the double cleavage drilled compression specimen for interface fracture energy measurements over a range of mode mixities

The double cleavage drilled compression (DCDC) configuration has been analyzed using the finite element method. Mode I and mixed-mode configuration have been described and results presented for the energy release rate, the mixity angle and the crack opening displacement. The results have been expressed as simple analytical formulae having good accuracy. The application of the configuration to interface fracture measurements has been described.