Delamination and fracture

Any material that transmits mechanical load from one place to another is susceptible to fracture. This susceptibility is enhanced if the geometry of the object includes reentrant corners, internal defects or other geometrical variations which serve as sites of stress concentration. At these sites, the local stress can be much larger than the nominal stress, which is loosely defined as the average stress transmitted at a cross-sectional area. As a consequence of stress concentration, the local stress can exceed the strength of the material and fracture ensues, even though the nominal stress is well below the fracture strength. 

Mechanical interactions between a thin film and a substrate to which it is bonded were the focus of discussion in the preceding chapters. These interactions, when occurring in the absence of any failure or delamination processes, are manifested in a number of ways the constraint of the substrate prevents the film from relaxing its internal stress, and the film-substrate system accommodates the internal stress by in-plane stretch or contraction, substrate curvature, and/or plastic yielding of the film. However, when edge effects are neglected, the traction exerted by the film and substrate material on each other across the film-substrate interface is zero everywhere./ If this is the case, how do the film and substrate interact  

The paradox of interaction without traction on the shared interface is resolved by recalling that the thickness of the film-substrate system is much smaller than its in-plane dimensions. If the mechanical state of the material is examined at various points on the film-substrate interface more distant from the film edge than several times the film thickess h, these 

In this chapter, the goal is to discuss the stress concentration at the edge of a film bonded to a substrate in terms of material and geometrical parameters. Since stress concentration can lead to film fracture and interfacial delamination, attention is also directed to quantitative descriptions of the growth of a crack or delamination. The study of stress concentration is based on continuum constitutive behavior and equilibrium stress analysis, and its extension to the study of interface delamination and crack growth requires introduction of a fracture criterion as an additional physical postulate of material behavior. Such fracture criteria are inevitably linked to the mechanisms of material separation which, in turn, can be influenced by microstructure and environment. 

The discussion of stress concentration near a film edge in the next section is followed by a brief review of linear elastic fracture mechanics concepts, a prelude to a discussion of delamination and cracking due to film residual stress. A survey of these topics set in the context of fracture mechanics has been presented by Hutchinson and Suo (1992). The chapter also includes descriptions of various experimental techniques for evaluating the fracture resistance of interfaces between films and substrates. In addition, representative experimental results on the interface fracture resistance, as a function of interface chemistry and environment, are presented for a variety of thin film and multilayer systems of scientific and technological interest. 

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The production of mica for polymer applications has been reviewed by Hawley [89]. The aim of the processing is to purify the deposit and to produce particles of relatively small diameter with an aspect ratio of 50-200. The natural minerals are generally of much larger size than required and so the milling has both to delaminate and fracture the particles. The milling is the key process and a variety of methods, both wet and dry, are used, accompanied by various classification methods. Surface modification is important in many mica applications and a variety of treatments are used, especially organo-silanes. The methods of treatment are generally not disclosed. 

In comparison with die compaction, isostatic pressing can provide compacts with much less defects or flaws. However, delamination and fracture caused by springback could be present if the pressure is released too fast. In addition, isostatic pressing has been rarely used to directly compact ceramic powders, due to its difficulty in handling powder samples. In most cases, it is used to further increase the density of green bodies either before or after the calcination step. Usually, the increase in density after isostatic compaction is less than 10 %, but that is sufficient to promote the densification of green bodies of most transparent ceramics. 

In many particular cases, there is a direct correspondence between the Irwin and Griffith criteria, as was noted above an connection with the result in (4.27). However, the latter criterion has the distinct advantage that the energy release rate can often be determined, or at least estimated, without the need for a complete solution of the boundary value problem for the stress field in the body. For this reason, it is selected as the basis for the present discussion. Many of its special features and numerous extensions of the basic concept will become evident in the sections that follow, in the course of discussing various issues concerned with delamination and fracture in thin film configurations. 

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