doi:10.1016/j.engfracmech.2005.04.002 
Copyright © 2005 Elsevier Ltd All rights reserved.
Initiation and arrest of an interfacial crack in a four-point bend test
Zhenyu Huanga, Z. Suoa, 
, 
, Guanghai Xub, Jun Heb, J.H. Prévostc and N. Sukumard
aDivision of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
bIntel Corporation, 2501 NW 229th Avenue, Hillsboro, OR 97124, USA
cCivil and Environmental Engineering Department, Princeton University, Princeton, NJ 08544, USA
dCivil and Environmental Engineering Department, University of California, Davis, CA 95616, USA
Received 24 February 2005;
revised 13 April 2005;
accepted 23 April 2005.
Available online 29 June 2005.
References and further reading may be available for this article. To view references and further reading you must
purchase this article.
Abstract
This paper describes a framework to study the initiation and arrest of an interfacial crack, using a combination of experiment and computation. We consider a test configuration widely used in the microelectronic industry: a sample of two substrates bonded by a stack of thin films, with a pre-crack in one of the substrates, perpendicularly impinging upon the films. When the sample is loaded to a critical level, the pre-crack initiates a new crack on one of the interfaces in the sample. The new crack often runs rapidly on the interface for a considerable length, and then arrests. We introduce a quantity, the initiation energy, to characterize the condition under which the pre-crack initiates the interfacial crack. The initiation energy is independent of the test configuration on the scale of the substrates, but changes greatly with the materials and stacking sequence of the films. We measure the initiation energy experimentally, interpret the data using mechanistic models, and use the initiation energy to predict the arrest crack length.
Keywords: Thin film; Interfacial fracture; Crack initiation; Crack arrest; Four-point bend
Fig. 1. A schematic of the four-point bend test system. Place the sample between the four load pins. Program the actuator to ramp up the displacement Δ. The load cell reads the force P.
Fig. 2. A schematic of a sample. Representative dimensions: width of the substrates B = 7.8 mm, thickness of the substrates H1 = H2 = 0.75 mm, distance between the inner and outer pins L = 4 mm, and distance between the inner pins, 2D = 27 mm. The thickness of the film stack is on the order of microns.
Fig. 3. A schematic of the force–displacement diagram. The actuator is programmed to ramp up the displacement. Initially, the force increases linearly with the displacement. At a certain force, marked by a square in the diagram, a pre-crack emanates from the notch root and stops at the interface. The displacement ramps up further. At a critical force Pc, the pre-crack initiates an interfacial crack. The new crack runs rapidly on an interface in the film stack, and then arrests. During the process, the displacement remains at Δc, and the force drops. As the displacement ramps up further, the interfacial crack extends stably, and the force attains a plateau Pplateau.
Fig. 4. A film stack used in experiments, and an experimental record of the force–displacement diagram.
Fig. 5. A second film stack used in experiments. The pre-crack ruptures the epoxy layer first, and then initiates a crack on the CDO/SiN interface. After initiation, the interfacial crack runs rapidly to the inner load pin. No plateau is recorded.
Fig. 6. The film stack is much thinner than the substrates. The inner radius of the annulus is some multiple of the film thickness, and the outer radius some fraction of the substrate thickness. The stress field in the annulus is the universal square-root singularity that prevails around a crack in a homogeneous elastic solid. At a length comparable to the film thickness, the stress field depends on details of the film stack (i.e., on inelastic deformation and flaws). At a length comparable to the substrate thickness, the stress field depends on details of the test configuration (i.e., on the sample geometry and the load distribution).
Fig. 7. Schematic of the energy release rate G as a function of the crack length a at several constant level of the displacement Δ. The crack extension energy Γ is taken to be a constant, and the crack extends if G > Γ. At the critical displacement Δc, the crack initiates at the flaw size aflaw, runs unstably, and arrests at the length aarrest. As the displacement ramps up further, the crack extends stably.
Fig. 8. The ratio gpre/gplateau as a function of the substrate thickness ratio.
Fig. 9. The arrest crack length as a function of the substrate thickness ratio, at several values of the initiation-to-extension energy ratio Λ/Γ. The substrate of thickness H1 is notched. The machine compliance is taken to be negligible compared to the sample. (3D + L)/(H1 + H2) = 29.66.
Fig. 10. The energy release rate of the interfacial crack as a function of the crack length, while the actuation displacement is held constant. The two substrates have the same thickness, H, and (3D + L)/H = 59.32.
Fig. 11. The arrest crack length as a function of the initiation-to-extension energy ratio Λ/Γ and the machine compliance. The two substrates have the same thickness, H, and (3D + L)/H = 59.32.
Fig. 12. Initiation-to-extension energy ratio as a function of the flaw size. The film is more compliant than the substrates. The crack propagates on the lower interface.
Fig. 13. The pre-crack first ruptures a ductile layer before initiates an interfacial crack.
Fig. 14. Schematic of force–displacement curve for quasi-equilibrium crack propagation, where G = Γ is maintained at all crack lengths. After the interfacial crack initiates, both the force and displacement decrease. The compliance is nearly constant when the crack length is smaller than the substrate thickness. When the crack length is comparable to the substrate thickness, the force attains a plateau.
Fig. A.1. A comparison of the computed energy release rate with the fitting formula. This plot assumes that H/h = 750.
Table 1.
Experimental values of the crack extension energy Γ and the crack initiation energy Λ
The film stack is shown in Fig. 4.
Table 2.
Experimental values of the crack initiation energy for the film stack shown in Fig. 5
Abstract
Purchase PDF (470 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (3)
Purchase PDF (796 K)
