Laminate strength analysis

LAMINATE STRENGTH EVALUATION Figure 4-35 Laminate Strength-Analysis Elements... 

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. 

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 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... 

The laminate stress-analysis elements are affected by the state of the material and, in turn, determine the state of stress. For example, the laminate stiffnesses are usually a function of temperature and can be a function of moisture, too. The laminae hygrothermomechanical properties, thicknesses, and orientations are important in determining the directional characteristics of laminate strength. The stacking sequence... 

A laminate can be subjected to thermal, moisture, and mechanical loads with the objective of surviving those loads. A method of strength analysis is required to determine either (1) the maximum loads a given laminate can withstand or (2) the laminate characteristics necessary to withstand a given load. The maximum loads problem is, of course, an analysis situation, and the laminate characteristics problem is a design situation that will be discussed in Chapter 7. 

Figure 4-36 Analysis of Laminate Strength and Load-Deformation Behavior...

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 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 apparent inierlantinar shear lest uses a short beam flexure loading mode to measure the shear strength along the plane of lamination. The analysis of the test is... 

Ramkumar RL, Saether ES, Appa K. Strength analysis of laminated and metallic plates holted together hy many fasteners. Air Force Wright Aeronautical Lahoratories Technical Report. AFWAL-TR-86—3034 1986. 

Fibers are often regarded as the dominant constituents in a fiber-reinforced composite material. However, simple micromechanics analysis described in Section 7.3.5, Importance of Constituents, leads to the conclusion that fibers dominate only the fiber-direction modulus of a unidirectionally reinforced lamina. Of course, lamina properties in that direction have the potential to contribute the most to the strength and stiffness of a laminate. Thus, the fibers do play the dominant role in a properly designed laminate. Such a laminate must have fibers oriented in the various directions necessary to resist all possible loads. 

In particular, the techniques based on the termination of certain plies within the laminate has also shown promise. Static tensile tests of [30°/-30°/30°/90°]s carbon-epoxy laminates containing terminals of [90°] layers at the mid-plane show that premature delamination is completely suppressed with a remarkable 20% improvement in tensile strength, compared to those without a ply terminal. Cyclic fatigue on the same laminates confirms similar results in that the laminate without a ply terminal has delamination equivalent to about 40% of the laminate width after 2x10 cycles, whereas the laminates with a ply terminal exhibit no evidence of delamination even after 9x10 cycles. All these observations are in agreement with the substantially lower interlaminar normal and shear stresses for the latter laminates, as calculated from finite element analysis. A combination of the adhesive interleaf and the tapered layer end has also been explored by Llanos and Vizzini, (1992). 

S.4.3.2 Strength of Laminate Composites. The strength of angle-ply laminates can be calculated using the same type of elastic analysis as for modulus in the previous section. The strains produced in the laminate by a given set of applied stresses are first calculated, using the computed laminate moduli. Stresses corresponding to these strains are then calculated for each layer of the laminate. These stresses are then expressed in terms of stresses parallel and normal to the fibers, and the combination of stresses... 

Classical stress analysis proves that hoop stress (stress trying to push out the ends of the tank) is twice that of longitudinal stress. To build a tank of conventional materials (steel, aluminum, etc.) requires the design to use sufficient materials to resist the hoop stresses that result in unused strength in the longitudinal direction. In RP, however, the designer specifies a laminate that has twice as many fibers in the hoop direction as in the longitudinal direction.1... 

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. 

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