Deformation behavior

Figure 4-34 Analogy between Buckled Plate and Laminate Load-Deformation Behavior...

The overall procedure of laminate-strength analysis, which simultaneously results in the laminate load-deformation behavior, is shown schematically in Figure 4-36. There, load is taken to mean both forces and moments similarly, deformations are meant to include both strains and curvatures. The analysis is composed of two different approaches that depend on whether any laminae have failed. 

Note that the lamina failure criterion was not mentioned explicitly in the discussion of Figure 4-36. The entire procedure for strength analysis is independent of the actual lamina failure criterion, but the results of the procedure, the maximum loads and deformations, do depend on the specific lamina failure criterion. Also, the load-deformation behavior is piecewise linear because of the restriction to linear elastic behavior of each lamina. The laminate behavior would be piecewise nonlinear if the laminae behaved in a nonlinear elastic manner. At any rate, the overall behavior of the laminate is nonlinear if one or more laminae fail prior to gross failure of the laminate. In Section 2.9, the Tsai-Hill lamina failure criterion was determined to be the best practical representation of failure... 

For angle-ply laminates, no such knee or change in slope occurs in the load-deformation behavior. Simultaneous failure (fracture) of all layers occurs. 

Figure 5-20 Load-Deformation Behavior for an In-Plane Loaded Plate...

Shear-stress-shear-strain curves typical of fiber-reinforced epoxy resins are quite nonlinear, but all other stress-strain curves are essentially linear. Hahn and Tsai [6-48] analyzed lamina behavior with this nonlinear deformation behavior. Hahn [6-49] extended the analysis to laminate behavior. Inelastic effects in micromechanics analyses were examined by Adams [6-50]. Jones and Morgan [6-51] developed an approach to treat nonlinearities in all stress-strain curves for a lamina of a metal-matrix or carbon-carbon composite material. Morgan and Jones extended the lamina analysis to laminate deformation analysis [6-52] and then to buckling of laminated plates [6-53]. 

The evaluation of the load-carrying capacity of a specific laminate (including the load-deformation behavior) is a straightforward deterministic process and is described in Section 4.5. For example, a 20-layered laminate has a certain load-carrying capacity tor one type of loading (and a different capacity tor a different type of loading). 

The mechanism of droplet deformation can be briefly summarized as follows. The factors affecting the droplet deformation are the viscosity ratio, shear stress, interfacial tension, and droplet particle size. Although elasticity takes an important role for general thermoplastics droplet deformation behavior, it is not known yet how it affects the deformation of TLCP droplet and its relationship with the processing condition. Some of... 

The purpose of our calculation was to quantitatively evaluate the deformational behavior of the TLCP droplets and their fibrillation under the processing conditions, and finally, to establish a relationship among the calculated Weber number, the viscosity ratio, and the measured aspect ratio of the fibers. Figure 13 illustrates this procedure. All calculated results were plotted as... 

According to the criteria, the dispersed phase embedded in the matrix of sample 1 must have been deformed to a maximum aspect ratio and just began or have begun to break up. By observing the relative position of the experimental data to the critical curve, the deformational behavior of the other samples can be easily evaluated. Concerning the fibrillation behavior of the PC-TLCP composite studied, the Taylor-Cox criteria seems to be valid. 

Pharr, G. M., Harding, D. S., and Oiiver, W. C., Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, M. Nastasi, D. M. Parkin, and H. Gieiter, Eds., Kluwer Academic Pubiishers, Netherlands, 1993. 

J Hasa, J Janacek. Effect of diluent content during polymerization on equilibrium deformational behavior and structural parameters of polymer network. J Polym Sci Part C 16 317-328, 1967. 

If the ordered, crystalline regions are cross sections of bundles of chains and the chains go from one bundle to the next (although not necessarily in the same plane), this is the older fringe-micelle model. If the emerging chains repeatedly fold buck and reenter the same bundle in this or a different plane, this is the folded-chain model. In either case the mechanical deformation behavior of such complex structures is varied and difficult to unravel unambiguously on a molecular or microscopic scale. In many respects the behavior of crystalline polymers is like that of two-ph ise systems as predicted by the fringed-micelle- model illustrated in Figure 7, in which there is a distinct crystalline phase embedded in an amorphous phase (134). 

M. Bram et al., Deformation Behavior and Leakage Tests of Alternate Sealing Materials for SOFC Stacks, Journal of Power Sources, 138, pp. 111-119 (2004). 

Bicakci, E., Zhou, X. and Cakmak, M., Phase and uniaxial deformation behavior of ternary blends of poly(ethylene naphthalate), poly(ether imide) and poly(ether ether ketone), in Proceedings of the 55th SPE ANTEC 97 Conference, May 5-8, 1997, Toronto, ON, Canada, Society of Plastics Engineers, Brookfield, CT, 1997, Vol. 2, pp. 1593-1599. 

The fiber industry has long been aware of PTT s good tensile elastic recovery [3], Ward et al. [4] studied the deformation behavior of PET, PTT and PBT fibers and found the tensile elastic recoveries were ranked in the unexpected descending order of PTT > PBT > PET. Chuah [47] found that the PTT elastic recovery and permanent set nearly tracked that of nylon 66 up to 30% strain (Figure 11.12). 

As the laser beam can be focused to a small diameter, the Raman technique can be used to analyze materials as small as one micron in diameter. This technique has been often used with high performance fibers for composite applications in recent years. This technique is proven to be a powerful tool to probe the deformation behavior of high molecular polymer fibers (e.g. aramid and polyphenylene benzobisthiazole (PBT) fibers) at the molecular level (Robinson et al., 1986 Day et al., 1987). This work stems from the principle established earlier by Tuinstra and Koenig (1970) that the peak frequencies of the Raman-active bands of certain fibers are sensitive to the level of applied stress or strain. The rate of frequency shift is found to be proportional to the fiber modulus, which is a direct reflection of the high degree of stress experienced by the longitudinally oriented polymer chains in the stiff fibers. 

Mahajan, Deformation Behavior of Compound Semiconductors J. P. Hirth, Injection of Dislocations into Strained Multilayer Structures D. Kendall, C. B. Fleddermann, and K. J. Malloy, Critical Technologies for the Micromachining of Silicon... 

Figure 5.46 Effect of temperature and strain rate on deformation behavior in single-crystal AI2O3. From W. D. Kingery, H. K. Bowen, and D. R. Uhhnann, Introduction to Ceramics. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

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