Laminate behavior

This section is devoted to those special cases of laminates for which the stiffnesses take on certain simplified values as opposed to the general form in Equation (4.24). The general force-moment-strain-curvature relations in Equations (4.22) and (4,23) are far too comprehensive to easily understand. Thus, we build up our understanding of laminate behavior from the simplest cases to more complicated cases. Some of the cases are almost trivial, others are more specialized, some do not occur often in practice, but the point is that all are contributions to the understanding of the concept of laminate stiffnesses. Many of the cases result from the common practice of constructing laminates from laminae that have the same material properties and thickness, but have different orientations of the principal material directions relative to one another and relative to the laminate axes. Other more general cases are examined as well. 

The laminate behavior of these special angle-ply laminates can be described with the number of layers, N, the laminae orientation, a, and the laminae stiffnesses, Q , in addition to the total laminate thickness, t. The laminate stiffnesses,... 

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... 

Some basic lamina and laminate behavioral characteristics were deliberately overlooked in the preceding discussion. Among them are plastic or nonlinear deformations, viscoelastic behavior, and wave propagation. 

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]. 

On the other hand, for aircraft and spacecraft structures, real laminate behavior is pretty typically linear. Laminate behavior is reasonably linear even with some 45° layers which you would expect to contribute their nonlinear shear deformation characteristic to the overall laminate and degrade its relative performance. If you go beyond the behavior of a laminate and look at a large structure, typically the load-response characteristics are linear. Even around a cutout, linear behavior exists. Beyond that apparent linear performance of many laminates, you might not like to operate in some kind of a nonlinear response regime. Certainly not when in a fatigue environment and probably not in a creep environment either would you like to operate in a nonlinear behavior range. 

O Brien, T.K. (1985). Analysis of local deaminations and their influence on composite laminate behavior. In Delamination and Debonding of Materials, ASTM STP 876 (W.S. Johnson, ed.) ASTM, Philadelphia, PA. p 282. 

To appear in the pellet fraction after centrifugation, lamin must be assembled into relatively large aggregates (Lin and Fisher, 1990). Hence, the apparently abrupt transition in lamin behavior seen by microcentrifugation when mitotic/ meiotic lamin is mixed with interphase lamin at a ratio of 1 8 versus 1 4 (Fig. 3) does not, in our estimation, reflect an abrupt change in lamin polymerization. Rather, it reflects an operational peculiarity of the centrifugation assay. Centrifugation is nevertheless useful in that it is easily and rapidly performed. 

R.T. Bhatt and ILE. Phillips, Laminate Behavior for SiC Fiber-Reinforced Reaction-Bonded Silicon Nitride Matrix Composites, J. Comp. Techn. Res. 12, p. 13, 1990. 

As the laminate industry grew, this anisotropic behavior was accepted and fabrication techniques adapted to it. For example, expansion and contraction space was left between wall panels, very strong adhesives were developed for bonding the product to substrates, special substrates were qualified, and where it was necessary to cut holes into the laminates the corners were radiused to prevent cracking from stress concentration. 

During the press operation, which is actually a form of compression mol ding, the resin-treated laminate pHes are heated under pressure and the resins cured. The initial heating phases cause the resin to melt and flow into voids in the reinforcing ply and bond the individual pHes together. The appHed heat simultaneously causes the resin to polymerize and eventually to cross-link or gel. Therefore, resin viscosity reaches a minimum during the press cycle. This is the point at which the curing process becomes dominant over the melt flow process. Dynamic mechanical and dielectric analyses (11) are excellent tools for study of this behavior. 

In the case of the fibrous laminate not much work has been done, but it has been observed that a significant loss of stiffness in boron—aluminum laminate occurs when cycled in tension—tension (43,44). Also, in a manner similar to that in the laminated PMCs, the ply stacking sequence affects the fatigue behavior. For example, 90° surface pHes in a 90°/0° sequence develop damage more rapidly than 0° pHes. In the case of laminates made out of metallic sheets, eg, stainless steel and aluminum, further enhanced resistance against fatigue crack propagation than either one of the components in isolation has been observed (45). 

For the remainder of this book, fiber-reinforced composite laminates will be emphasized. The fibers are long and continuous as opposed to whiskers. The concepts developed herein are applicable mainly to fiber-reinforced composite laminates, but are also valid for other laminates and whisker composites with some fairly obvious modifications. That is, fiber-reinforced composite laminates are used as a uniform example throughout this book, but concepts used to analyze their behavior are often applicable to other forms of composite materials. In many Instances, the applicability will be made clear as an example complementary to the principal example of fiber-reinforced composite laminates. 

First, the stress-strain behavior of an individual lamina is reviewed in Section 4.2.1, and expressed in equation form for the k " lamina of a laminate. Then, the variations of stress and strain through the thicyiess of the laminate are determined in Section 4.2.2. Finally, the relation of the laminate forces and moments to the strains and curvatures is found in Section 4.2.3 where the laminate stiffnesses are the link from the... 

Although the word balanced is ambiguous and not definitive, the common meaning for a balanced laminate is a laminate in which all equal-thickness laminae at angles 0 other than 0° and 90° to the reference axis occur only in 0 pairs. The individual -n O and - 0 layers are not necessarily adjacent to each other. Note also that balanced laminates are required to be symmetric about the laminate middle surface, so there must be two + Q laminae and two - 0 laminae for each 0 pair. The behavioral characteristics of a balanced laminate are that shear-... 

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