PSI - Issue 23

Stanislav Žák et al. / Procedia Structural Integrity 23 (2019) 239 – 244

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Stanislav Žák et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction

Nowadays, in electronic industry the composite materials are mostly used for creation of circuit boards and other electronical or electro-mechanical devices. Such a composite, which is commonly used, consists of the combination of Si substrate and thin Cu films. Despite the low probability of ordinary electronical components to undergo severe mechanical stresses, a significant fatigue loading can occur e.g. due to thermal loading. Hence, the crack driving force investigation for cases of such composite materials plays significant role in the design of electronical components. It has been proved that the material properties mismatch at such interfaces influences the crack propagation. Related research on cracks in bodies consisting of two linear elastic materials (e.g. interfacial cracks (Rice, 1988; Williams, 1959), cracks perpendicular to the interface (Cook and Erdogan, 1972; Pan and Amadei, 1999; Romeo and Ballarini, 1997; Zak and Williams, 1963) or crack in elastic bi-materials with special composition (Bleeck et al., 1998; Erdogan, 1995; Rousseau and Tippur, 2000)) showed in general that the local stress intensity factors (SIFs) or crack driving force G or J -integral at the crack tip approaching the interface from stiffer to softer material (from area with higher to area with lower Young’s modulus E ) increases and for the opposite case (crack propagation from lower to higher E ) the local SIFs, G or J -integral values should decrease. When elastic-plastic material properties are taken into account, the size and evolution of the crack tip plastic zone strongly influences the G . Early works aimed at small scale yielding (Delfin et al., 1995; Romeo and Ballarini, 1997; Shih, 1991) and numerical solutions (Kim et al., 1997; Sugimura et al., 1995) of elastic-plastic interface crack problems showed the differences between the applied far-field crack driving force and the local tip J -integral. This deviation was closely related with the plastic zone reaching the interface. More recent works (Kolednik et al., 2010; Pippan et al., 2000; Pippan and Riemelmoser, 1998; Simha et al., 2003) showed the development of the crack plastic zone throughout the bi-material interface from computational and experimental point of view. The decrease of both crack driving force and crack tip opening displacement (CTOD) was observed for soft to hard material transitions and vice versa for the hard to soft material transition. In comparison to simple elastic solution, these results suggest some sort of transition between G values for both materials for cracks approaching the interface and the same applies for CTOD. However, the mentioned works took into account only small-scale yielding conditions or a relatively small crack tip plastic zones in comparison to the crack length or the thickness of the respective material layer. Contrary to them, this research is aimed at the evaluation of crack driving force (in terms of the J -integral) in a relatively thin film layer in elastic-plastic Cu material on top of the purely elastic Si substrate. The material combination simulates real electronical devices (such as printed circuit boards) subjected to external loading. Used numerical procedures enables to evaluate even extreme cases when the Cu layer is completely plastically deformed with the Si substrate still under elastic conditions.

2. Model and methods

Fig. 1. Used FE model: (a) geometry model with highlighted main parameters (orange color represents the thin Cu film on top of the grey Si substrate); (b) detail of FE mesh around the crack tip (area denoted by blue rectangle on the left, tip element dimensions ~ 5e -4 · t )