Mechanisms model Common joints

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

Viscoelastic characteristics of polymers may be measured by either static or dynamic mechanical tests. The most common static methods are by measurement of creep, the time-dependent deformation of a polymer sample under constant load, or stress relaxation, the time-dependent load required to maintain a polymer sample at a constant extent of deformation. The results of such tests are expressed as the time-dependent parameters, creep compliance J t) (instantaneous strain/stress) and stress relaxation modulus Git) (instantaneous stress/strain) respectively. The more important of these, from the point of view of adhesive joints, is creep compliance (see also Pressure-sensitive adhesives - adhesion properties). Typical curves of creep and creep recovery for an uncross-Unked rubber (approximated by a three-parameter model) and a cross-linked rubber (approximated by a Voigt element) are shown in Fig. 2. 

Mechanical. Mechanical vibration and shock can cause solder joint failures, particularly for large, rigid components or components with large, heavy heat sinks. Mechanical shock tests are nsnally modeled after drops that may occnr during transportation or use. The test drops are generally quite severe, but few in nnmber, since the system is not expected to be subjected to repeated drops in service. One common test uses a maximum acceleration of about 600 g, a maximum velocity of about 300 in/s, and a shock puke of about 2.5 ms duration. The test setnp k shown schematically in Fig. 57.26. 

Typical applications of the boundary element method in the context of adhesion technology are commonly found for the modeling of cracks (fi-acture mechanics) and other types of stress singularities, cf the bibliography of (Mackerle 1995a). The article by (Vable and Maddi 2010) addresses the specific problems (i.e., numerical modeling considerations which limited the application of BEM in the past) related to bonded joints and boundary element simulation. In addition, numerical results of lap joints, cf. O Fig. 26.18, with several spew angles were presented which demonstrate the potential of the boundary element method in analysis of bonded joints. 

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