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Thin bonded films have many applications ( i.e. in information storage and processing systems, and etc.). In many cases, thin bonded films are in a state of residual tension, which can lead to film cracking and crack extension in one layer often accompanies failure in whole systems. In this paper, we analyze a channel crack advanced throughout thickness of an elastic thin film bonded to a dissimilar semi-infinite substrate material via finite element method (FEM). In order to simplify modeling, the problem is idealized as plane strain and a two-dimensional model of a film bonded to an elastic substrate is proposed for simulating channel crack in thin elastic film. Film is modeled by common 4-node and substrate by infinite 4-node meshes. The stress intensity factor (SIF) for cracked thin film has been obtained as a function of elastic mismatch between the substrate and the film. The results indicate that in elastic mismatch state, SIF is more than match state. On the other hand, mismatch state is more sensitive to crack than match state. And SIF has also increased by increasing Young’s modulus and Poisson ratio of film.

Many modern materials and material systems are layered. The potential applications of fracture mechanics of layered materials range over a broad spectrum of problem areas; included are: protective coating, multilayer capacitors, thin film/substrate systems for electronic packages, layered structural composites of many varieties, reaction product layers, and adhesive joints [

Many cracking patterns in film-substrate systems have been observed and analyzed [

Irwin [

The objective of this study is investigating sensitivity of two bonded elastic layers to a single crack perpendicular to the interface between film and substrate. This paper also has considered different elastic ratio of film and substrate. Because there are similar works in the literature (The problem of a crack perpendicular to the interfaces may be found in [

In this section, we first give an overview of the fracture mechanics modes and then previous analytical works of SIF on both homogeneous and layered systems.

Three linearly independent cracking modes are used in fracture mechanics. These load types are categorized as Mode I, II, or III as shown in the

The SIF equation for a single edge notch and homogeneous properties in an infinite specimen is [

where,

where,

Range of applicability of this equation: The defect depth, a, should be less than the specimen width, w, [

For the fully cracked film problem, with its crack tip at the interface (_{I} is as the following form [

where

For plane strain problems α and β are given by [

where

combinations, values of a typically lie between β = 0 and β = α/4. The stress singularity exponent, s in Equation 7, is a function of α and β, too, and satisfies the following equation derived by Zak and Williams [

Values of s as a function of α for β = 0 and β = a/4 are plotted in

Consider a composite consisting of an infinite layer of width h and a half space (

_{f}/E_{s} and ν_{f}/ν_{s} in order to obtain the asymptotic solution for an isolated single crack with a semi-infinite substrate.

The finite element meshes are generated as follows. First divide the whole domain into two regions, as indicated in

For the two-dimensional analysis, the two type of SIF (K_{I} and K_{II}) are related to the energy release rate, G, as follow [

In the previous studies of cracking in thin films (e.g., [

where

For the channeling crack in the present study, the first type of SIF (K_{I}) of a two bonded elastic layers was calculated using finite element method. Different Poisson’s ratios, ν_{f}/ν_{s}, of 0.5, 0.9, 1, 2, 3, 4, 5 and the elastic modulus ratios, E_{f}/E_{s}, of 0.1, 0.2, 0.3, ・・・, 8, 9, 10 were choosing for calculation, because all different materials can be located in this range.

The variation of the SIF for different elastic ratios is presented in _{I} value for different modulus ratios decreases by decreasing Poisson’s rations. In the case of no elastic mismatch (α = β = 0), the stress singularity reduces to the square root singularity of a crack tip in a homogeneous elastic material, i.e. s = 0.5 (Equation (7)), and K_{I} has the minimum values (_{I} values are lower. When the substrate is more compliant than the film (α > 0), the singularity is stronger, i.e. s > 0.5, and K_{I} values are higher. For an extremely compliant substrate (α → 1), the singularity exponent approaches 1(s → 1) and K_{I} has the maximum value.

The results can be tabulated in

The infinite elements, for an elastic fracture mechanic problem, have been used to characterize the cracking of thin films bonded to thick substrate materials. The SIF has been extracted from the simulations. The SIF of the plane-strain problem depends on the elastic mismatch between the film and the substrate. The result demonstrates that the infinite elements can be applied to model problems with different elastic properties of films and

Property | Dundurs’ parameters | S | SIF | Non-dimensional energy release rate [ | ||
---|---|---|---|---|---|---|

E_{s}_{ }↑ | E_{f}- | α↓ | β- | s↓ | K_{I}_{ }↓ | ω_{I}↓ |

ν_{s}_{ }↑ | ν_{f}- | α↓ | β- | s↓ | K_{I}_{ }↓ | ω_{I}↓ |

E_{f}_{ }↑ | E_{s}- | α↑ | β- | s↑ | K_{I}_{ }↑ | ω_{I}↑ |

ν_{f}_{ }↑ | ν_{s}- | α↑ | β- | s↑ | K_{I}_{ }↑ | ω_{I}↑ |

substrates. SIF for channeling crack has obtained as a function of elastic mismatch ratio between the substrate and the film. Results show that K_{I} has the minimum value in E_{f}/E_{s} = 0.1 and ν_{f}/ν_{s} = 0.5 condition and it has the maximum value in E_{f}/E_{s} = 10 and ν_{f}/ν_{s} = 5. In general view K_{I} has the minimum value when ν_{f} = ν_{s}. Because there is no result in this form, qualitative comparisons with the available previous studies (i.e. Non-dimensional energy release rate [