On the Reference Length and Mode Mixity for a Bimaterial Interface

We investigate properties that govern interfacial fracture within the framework of linear elastic fracture mechanics, including interfacial fracture toughness, mode mixity, and the associated reference length. The reference length describes the arbitrary location where the mode mixity is evaluated, ahead of the crack tip, in a bimaterial system. A method for establishing a reference length that is fixed for a given bimaterial system is proposed. This is referred to as the “characteristic reference length,” with the associated “characteristic mode mixity.” The proposed method is illustrated with an experimental investigation, utilizing a four-point bend test of a bimaterial system.

PHYSICAL PROPERTIES OBTAINED FROM MEASURED THERMAL PROFILES IN THE FILM/SUBSTRATE BIMATERIAL SYSTEM

The microelectronic devices are formed by a substrate that supports the functional thin film material. The thermal, electrical, and mechanical properties of the system depend strongly on the interfacial properties between a film and a substrate. The interfacial nature in a film/substrate system originates the thermal contact resistance (R tc ). We discuss the thermal and the electrical behavior in a film/substrate system (bimaterial system) making emphasis on the R tc of the interface. Au /glass samples with different thicknesses were prepared by thermal evaporation for experimentation. The bimaterial system was heated by a DC electrical current to obtain thermal profiles. Film and substrate thermal profiles acquired with high resolution combined with a developed bimaterial model are used as an alternative method to estimate the R tc value at atmospheric pressure, the electrical resistivity ρ, and the thermal resistive coefficient α r in the bimaterial system. The calculated R tc values ranged from 7.7 × 10-4 to 1.2 × 10-3 m2 K/W for the Au /glass system, in good agreement with previously reported values. The ρ values obtained from the thermal profile data present a more reliable value due to the global character than the local values measured by the four-probe technique. Dependence on film thickness was also found in the α r coefficient determination.

STUDY OF A BIMATERIAL SYSTEM BY AN IMPROVED DYNAMICAL THERMAL MODEL

We present an improved dynamical thermal model and the corresponding experimental efforts to determine thermal profiles of thin metallic films deposited on thick substrates (bimaterial system) as are usually used in microelectronics. A dynamical thermal model to characterize the Joule heating of a metallic film/substrate system, as a function of the applied energy and the thickness is discussed. Good agreement between theoretical and measured thermal profiles on different bimaterial systems support the theoretical model obtained by solving a harmonic oscillator equation. By combining the thermal model and the experimental results it is possible to determine the convective coefficient of the room conditions, the diffusive time constant, and to quantify the different mechanisms of heat loss as a function of the physical properties and the geometrical parameters. The improved thermal model can be useful to rapidly predict a thermal behavior of film/substrate systems that are used for microelectronics.

Crack Kinking Criterion for Bimaterial System

This paper is aimed to find out a suitable criterion for predicting the interfacial crack in the bimaterial system. An investigation was undertaken into the interfacial crack kinking phenomena in a bimaterial specimen of epoxy and aluminum alloy using a combination of experimental method and numerical simulation. It was found that all kinked fractures occurred at loading angles equal to or larger than 120°, so the kinking direction heavily dependeds on the loading mode mixity. Three categories of fracture pattern were identified (A, B and C). In the case of type A fracture, the (J10)kink integrals were generally higher than the homogeneous epoxy Jic at loading angles of 120° and above. In contrast, for types B and C fracture, the J10 integrals were consistently lower than the homogeneous epoxy Jic. Predictions of crack kinking behavior made using the Maximum Energy Release Rate Criterion (MG-criterion) were found to agree well with the observed experimental results. The kinked deformation of crack tip observed by moire´ interferometry, is well agreed with the result of numerical simulation.