Stiffness laminate properties

Because of the analytical complications involving the stiffnesses Ai6, A26, D g, and D26, a laminate is sometimes desired that does not have these stiffnesses. Laminates can be made with orthotropic layers that have principal material directions aligned with the laminate axes. If the thicknesses, locations, and material properties of the laminae are symmetric about the middle surface of the laminate, there is no coupling between bending and extension. A general example is shown in Table 4-2. Note that the material property symmetry requires equal [Q j], of the two layers that are placed at the same distance above and below the middle surface. Thus, both the orthotropic material properties, [Qjjlk. of the layers and the angle of the principal material directions to the laminate axes (i.e., the orientation of each layer) must be identical. 

Engineering Sciences Data Unit (ESDU), Estimation of the stiffnesses and properties of laminated flat plates, Item No. 83035, VI, 1989. 

In order to confirm theoretical estimates of stiffness necessary for a finite element analysis, experimental determination of laminate properties are required. Measurement of laminate thickness and fibre and resin content as well as mechanical properties are also required. 

Tests for laminate properties indicate that the moduli and stiffness of laminates made with each type of glass are identical. Tensile, flexural, and shear strengths are generally equal or slightly higher with E-CR. Long-term behaviour (tension -creep in air) is identical. 

Energy absorption, stiffness and a low weight (reduction by 57%) [83], and also technical looks and good hot laminating properties i.e., thermoplastic color film) each play an important role for trimming components. The applied color film shown in the example is not optimal, because a complicated adhesion promotion must be carried out on the PP-surface prior to hot laminating the surface coating. 

Many grades of interlayer are produced to meet specific length, width, adhesion, stiffness, surface roughness, color (93,94), and other requirements of the laminator and end use. Sheet can be suppHed with vinyl alcohol content from 15 to about 23 wt %, depending on the suppHer and appHcation. A common interlayer thickness for automobile windshields is 0.76 mm, but interlayer used for architectural or aircraft glaring appHcations, for example, may be much thinner or thicker. There are also special grades to bond rear-view mirrors to windshields (95,96) and to adhere the components of solar cells (97,98). Multilayer coextmded sheet, each component of which provides a separate property not possible in monolithic sheet, can also be made (99—101). 

Quasi-isotropic laminates have the same ia-plane stiffness properties ia all directions (1), which are defined ia terms of the [A] matrix of the laminate. For the laminate to be quasi-isotropic. 

Composites need not be made of fibres. Plywood is a lamellar composite, giving a material with uniform properties in the plane of the sheet (unlike the wood from which it is made). Sheets of GFRP or of CFRP are laminated together, for the same reason. And sandwich panels - composites made of stiff skins with a low-density core - achieve special properties by combining, in a sheet, the best features of two very different components. 

Laminated composite materials consist of layers of at least two different materials that are bonded together. Lamination is used to combine the best aspects of the constituent layers and bonding material in order to achieve a more useful material. The properties that can be emphasized by lamination are strength, stiffness, low weight, corrosion resistance, wear resistance, beauty or attractiveness, thermal insulation, acoustical insulation, etc. Such claims are best represented by the examples in the following paragraphs in which bimetals, clad metals, laminated glass, plastic-based laminates, and laminated fibrous composite materials are described. 

Some engineers have tried to characterize laminates with effective laminate stiffnesses, E, Ey, v y, and G y, and indeed such properties can be determined for a laminate by the usual measurements. However, it is crucial to recognize that with an effective laminate stiffness approach... 

Derive the summation expressions for extensional, bending-extension coupling, and bending stiffnesses for laminates with constant properties in each orthotropic lamina that is, derive Equation (4.24) from Equations (4.20) and (4.21). 

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. 

For a single isotropic layer with material properties, E and v, and thickness, t, the laminate stiffnesses of Equation (4.24) reduce to... 

For laminates that are symmetric in both geometry and material properties about the middle surface, the general stiffness equations. Equation (4.24), simplify considerably. That symmetry has the form such that for each pair of equal-thickness laminae (1) both laminae are of the same material properties and principal material direction orientations, i.e., both laminae have the same (Qjjlk and (2) if one lamina is a certain distance above the middle surface, then the other lamina is the same distance below the middle surface. A single layer that straddles the middle surface can be considered a pair of half-thickness laminae that satisfies the symmetry requirement (note that such a lamina is inherently symmetric about the middle surface). ... 

The stiffnesses of an antisymmetric laminate of anisotropic laminae do not simplify from those presented in Equations (4.22) and (4.23). However, as a consequence of antisymmetry of material properties of generally orthotropic laminae, but symmetry of their thicknesses, the shear-extension coupling stiffness A.,6,... 

The term quasi-isotropic iaminate is used to describe laminates that have isotropic extensionai stiffnesses (the same in all directions in the plane of the laminate). As background to the definition, recall that the term isotropy is a material property whereas laminate stiffnesses are a function of both material properties and geometry. Note also that the prefix quasi means in a sense or manner. Thus, a quasi-isotropic laminate must mean a laminate that, in some sense, appears isotropic, but is not actually isotropic in all senses. In this case, a quasi-isotropic... 

Prove that the bending-extenslon coupling stiffnesses. By, are zero for laminates that are symmetric in both material properties and geometry about the middle surface. 

Quasi-isotroplc laminates do not behave like Isotropic homogeneous materials. Discuss why not, and describe how they do behave. Why is a two-ply laminate with a [0°/90°] sacking sequerx and equat-thickness layers not a quasi-isotropic laminate Determine whether the extensional stiffnesses are the same irrespective of the laminate axes for the two-ply and three-ply cases. Hint use the invariant properties In Equation (2.93). 

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... 

If no laminae have failed, the load must be determined at which the first lamina fails (so-called first-ply failure), that is, violates the lamina failure criterion. In the process of this determination, the laminae stresses must be found as a function of the unknown magnitude of loads first in the laminate coordinates and then in the principal material directions. The proportions of load (i.e., the ratios of to Ny, to My,/ etc.) are, of course, specified at the beginning of the analysik The loaa parameter is increased until some individual lamina fails. The properties, of the failed lamina are then degraded in one of two ways (1) totally to zero if the fibers in the lamina fail or (2) to fiber-direction properties if the failure is by cracking parallel to the fibers (matrix failure). Actually, because of the matrix manipulations involved in the analysis, the failed lamina properties must not be zero, but rather effectively zero values in order to avoid a singular matrix that could not be inverted in the structural analysis problem. The laminate strains are calculated from the known load and the stiffnesses prior to failure of a lamina. The laminate deformations just after failure of a lamina are discussed later. 

The degraded laminate then has stiffnesses based on the original properties of the outer layer and the following properties of the inner layer... 

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