Strain contour mapping

In this chapter we discuss double-crystal topography, in which we obtain a map of the diffracting power of a crystal compared to that of a reference. We first treat the principles and geometries, the mechanisms of image contrast and resolution and the ttse of laboratory and synchrotron radiation. We then discuss applicatiorrs wafer inspection, strain contour mapping, topography of curved crystals. 

Fig. 12 Contour maps of strain mapped over the graphene monolayer in a model composite. Maps are shown for the original flake before coating with the top polymer layer and then after coating with the top polymer layer at different levels of matrix strain indicated. (After ref 132.)... 

Recently [40], a novel numerical approach, the object-oriented finite element (OOF) [41,42] analysis has been utilized by mapping the real micro/nano morphological images of PP/clay nanocomposites with varied clay contents between 1 and 10 wt%. Such morphological images are captured by two different microscopic techniques, the scanning electron microscopic (SEM) and transmission electron microscopic (TEM) analyses. The tensile moduli of nanocomposites are nmnerically predicted and subsequently compared with the tensile test data. Fuithermore, the available composites models aie used to validate the numerical approach developed in the same [40] study. Finally, the effect of particle distribution on the deformation behavior is also evaluated through the tensile stress and elastic strain contours of such nanocomposites [40]. 

Recent advances in the development of TMF predictive models have included the incorporation of solder microstructure as a state variable in the constitutive equation [92,93]. A contour map (Fig. 30) shows the Pb-rich phase coarsening predicted in a leadless chip solder joint subjected to six thermal cycles having temperature limits of —50° and 80°C, ramp rates of 6°C/ sec, and dwell times of 10 min at both limits. The microstructure-based, viscoplastic constitutive equation for Pb-Sn solder improves the accuracy of solder fatigue strain predictions throughout the interconnection geometry. It provides a real-time adjustment of the local solder mechanical properties resulting from local changes in the solder microstructure (i.e., the Pb-rich phase). 

The main outputs of flow modeling are flow visualizations, to illustrate the process mechanism and to compare with experimental marker techniques (section 10.3.7, Experimental Row Validation ). These include streamlines, particle tracks, velocity maps, and strain-rate contour plots. Elow models can also be validated... 

Creep data of this nature are represented pictorially for some well-studied systems in the form of stress-temperature diagrams, which are termed deformation mechanism maps. These maps indicate stress-temperature regimes (or areas) over which various mechanisms operate. Constant-strain-rate contours are often also included. Thus, for some creep situation, given the appropriate deformation mechanism map and any two of the three parameters—temperature, stress level, and creep strain rate—the third parameter may be determined. 

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