Fracture mechanics concepts

The preceding section dealt with the issue of load transfer between a film and its substrate, particularly with the stress concentration in the vicinity of a free edge in a film-substrate system. An important outcome of the study 

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The discussion of fracture mechanics will be divided in two parts. First, basic principles of fracture mechanics will be described. Second, the application of fracture mechanics concepts to composite materials will be discussed. In both parts, the basic approach is that of Wu [6-12],... 

We can consider the spreading of a sessile drop on a soft, lossy substrate rather like the advance of a negative crack and thus use fracture mechanics concepts, as was the case in the derivation of Eq. (15) for the separation of an elastomer from a rigid solid. The term negative is used since the spreading of a drop leads to the creation of solid/liquid interface rather than separation. 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

A final consequence of this reconciliation between the kinetic theory and fracture mechanics concepts, is that the effective surface energy S should vary somewhat as Regime I gives way to Regime II. In the former, the stress field is required to provide energy (in the absence of losses) of the order of AG upwards, since the balance of the activation energy G is provided by thermal fluctuations. In Regime II virtually the whole of G must be provided by the stress field so that we have. 

Examples. To illustrate the use of fracture mechanics concepts, we will present several examples. Because these examples are intended to demonstrate the methods involved, they have been necessarily oversimplified the reader is cautioned against using them as exact patterns for actual fracture design and is referred to the references cited at the end of this chapter for additional details on practical problems. 

Then, with a further increase in thickness, it becomes impossible to obtain the necessary impact strength either to prevent fracture initiation or to provide for fracture arrest. The only means of protection in the latter thickness range is to limit the maximum size of defects to subcritical dimensions in accordance with fracture mechanics concepts. 

Nevertheless, if materials arc to be evaluated in more than a simple comparative manner, then tests are needed as a function of at least the amplitude of deformation. Perhaps because they are newer materials, it is more common to find this being allowed for in procedures for plastics and composites. Amplitude effects can also be studied in the more recently introduced tension fatigue test for rubbers. This allows the application of fracture mechanics concepts to the results, as will be discussed in a later section. 

Fracture of heterogeneous fibres is a more complex problem and the few available models are based on linear elastic fracture mechanics concepts and thus restricted to this area. An outstanding aspect of heterogeneous fibre failures is the role of interfaces neither strong or very weak interfaces give optimum results. 

Stress cycling tests in imnotched samples do not readily distinguish between crack initiation and crack propagation. Further progress requires a similar approach to that adopted in fracture studies, namely the introduction of very sharp initial cracks in order to examine crack propagation utilizing fracture mechanics concepts. 

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. 

Fracture mechanics concepts terms of the stress state as... 

We employ the finite element method and interface fracture mechanics concepts to parametrieally examine interfacial crack path selection in a unit brick-and-mortar structure. The analysis methodology, to be described below briefly, is based on the analyses of cracks kinking into and out of a bi-material interface as discussed by He and Hutchinson [5], He et al [6,7], and Suo and Hutchinson [8]. 

Within this volume, the reader will find several approaches within this general framework. Chapter 2 introduces the concept of fracture mechanics, which is treated in more detail in Chapters 7 and 8. Chapter 3 provides an elegant overview of the energy approach to adhesion. Stresses and driving energies for contact problems relevant to adhesion are given in Chapter II, and Chapter 15 uses fracture mechanics concepts to help interpret the failure modes occurring in bonded joints. 

The main emphasis of this chapter will be on the basic fracture mechanics concepts for cohesive and adhesive fracture with some extension to crack branching and crack nucleation from bimaterial comers. Most of the current fracture mechanics practice in testing adhesives and designing of adhesively bonded joints is limited to linear elastic fracture mechanics concepts. The development of the background material presented here will therefore be similarly constrained, except for the last section. Historically, fracture mechanics developed from energy balance concepts and examinations of stresses around crack tips. The adhesive fracture community has tended to favor the former, but both have useful features and will be carried forward in the discussions that follow. 

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