Laminate analysis procedure

The procedure of laminate strength analysis outlined in Section 4.5.2, with the Tsai-Hill lamina failure criterion will be illustrated for cross-ply laminates that have been cured at a temperature above their service or operating temperature in the manner of Tsai [4-10]. Thus, the thermal effects discussed in Section 4.5.3 must be considered as well. For cross-ply laminates, the transformations of lamina properties are trivial, so the laminate strength-analysis procedure is readily interpreted. 

The predicted strengths in Figure 4-44 are generally somewhat above the measured values. The predicted and observed stiffnesses, both initial (below the knee) and final, are in very good agreement. Thus, the stiffness aspects of classical lamination theory, as well as the present strength-analysis procedure, are verified. 

The example considered to illustrate the strength-analysis procedure is a three-layered laminate with a [4-15°/-15°/+15°] stacking sequence [4-10]. The laminae are the same E-glass-epoxy as in the cross-ply laminate example with thickness. 005 in (.1270 mm), so that the total laminate thickness is. 015 in (.381 mm). In laminate coordinates, the transformed reduced stiffnesses are... 

The manner in which the laminate design is approached can be expressed in flow-chart form as in Figure 7-59. There, some initial laminate is arbitrarily selected to start the procedure. Then, the laminate load-deflection behavior is evaluated by use of the laminate strength analysis procedure described in Section 4.5. That evaluation is theoretical in nature. The next step is to evaluate the laminate fatigue life, and that evaluation can only be done experimentally, although progress is... 

Fixed arm peel and T-peel test procedures are used to measure peel strength for flexible laminates. Analysis of the contributions from elastic and plastic deformations of the peel arms during these tests enables the energy contribution from plastic effects to be subtracted from the energy required to peel the laminate. In this way, the adhesive fracture toughness is determined. 

As at this stage, accurate modeling of failure after hrst damage is very complicated and not very accurate. For general laminates, failure theories used in practice conservatively equate hnal failure with failure of the first ply in the laminate. The procedure requires determination of the stresses or strains in each ply in the ply axes and uses one of the many failure criteria. The steps followed in a typical failure analysis are as follows ... 

The same or different materials are combined in the form of sandwich structures (Fig. 4.10). They can be used in products with an irregular distribution of the different materials, and in the form of large structures or sub-structures. A sandwich material composed of two skins and a different core material is similar to RP laminates. Overall load-carrying capabilities depend on average local sandwich properties, but materials failure criteria depend on local detailed stress and strain distributions. Design analysis procedures for sandwich materials composed of linear elastic constituents are well developed. In principle, sandwich materials can be analyzed as composite structures, but incorporation of viscoelastic properties will be subject to the limitations discussed throughout this book. 

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... 

The intimate contact data shown in Figure 7.16 were obtained from three-ply, APC-2, [0°/90o/0o]7- cross-ply laminates that were compression molded in a 76.2 mm (3 in.) square steel mold. The degree of intimate contact of the ply interfaces was measured using scanning acoustic microscopy and image analysis software (Section 7.4). The surface characterization parameters for APC-2 Batch II prepreg in Table 7.2 and the zero-shear-rate viscosity for PEEK resin were input into the intimate contact model for the cross-ply interface. Additional details of the experimental procedures and the viscosity data for PEEK resin are given in Reference 22. 

Analysis of the data follows a similar route to that for the fixed arm procedure. However, for the T-peel there are adhesive fracture toughness values to determine for each peel arm, (Ga) and (Ga). The adhesive fracture toughness for the laminate (Ga) is then the sum of these two values. 

Knight Jr NF, Rankin CC, Brogan FA. STAGS computational procedure for progressive failure analysis of laminated composite structures. Int J Non-Linear Mech 2002 37(4) 833—49. 

Another application of microspectroscopy is characterization of laminated polymer films. Multilayer polymer films of different fimctionality are common in the packaging industry and identification of the different layers is of commercial importance. The layers vary from about 1 /xm in thickness (adhesive) to 10-50 /zm and there are often several layers. If there are only two layers, attenuated total reflectance (ATR) methods can be used for identification. For films with more than two layers, the normal procedure is to microtome a 10-20 fj,m cross section for edgewise analysis using microspectroscopy. A comparison of infrared and Raman microspectroscopies for some multilayer films has been pubhshed (Fig. 25) (193). 

The test procedure is specified in IPC-TM-650, method 2.4.24.2. The test specimen should consist of a strip of laminate material compatible to the measuring equipment. For all samples with woven reinforcement, it is necessary to make siue that the specimens are cnt parallel or perpendicular to the woven structure. The analysis is based on an assumption of constant specimen geometry therefore, the test specimens must be stiff enough not to deform plastically during the experiment. AH copper needs to be etched off... 

The problem of calculation of the stress-strain state in multilayer and reinforced structural elements is becoming ever more actual The complexity of this problem is explicable by the principal necessity of the structural specifics of such structures to be taken into account Namely, the mechanical inhomogeneity of reinforced materials and the presence of layers having different mechanical characteristics in laminates These specific features require that special approaches to the numerical analysis should be elaborated Thus, for example, when solving the problem by the theory of elasticity in terms of displacements using the finite-element or finite-difference methods, certain additional procedures for... 

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