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Laminates discussion

In addition to the possible causes of capping and lamination discussed previously, one should also consider the possibility that shape of the tooling and tooling defects are sources of capping. In such cases the problem can simply be alleviated by repairing or altering press tooling. [Pg.1158]

Calculate Young s moduli in the principal directions for the unidirectional and cross-plied laminates discussed in the foregoing example. [Pg.398]

Firstly, Moore and Williams [55J have reported results from T-peel tests using the five-layer structure laminate discussed above. The values of Gc were obtained from T-peel tests via the above analytical method, allowing for plastic bending of the peel arms. (Thus, measurement of the angles 9 and 62, see Fig. 3, was also undertaken since they are required for the plastic-bending analysis.) The results from the T-peel and the fixed-arm peel test, where the peel angle was varied as discussed above, were not significantly different. [Pg.293]

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... [Pg.14]

To reduce the no-load iron losses caused by such harmonics the machine core may be formed of thinner low-loss laminates (see also Section 1.6,2(A-iv)). When the machine has already been manufactured and there is a need to suppress these harmonics, filter circuits may be employed along the lines discussed in Section 23.9. [Pg.275]

In addition to the polymers, copolymers and alloys already discussed, styrene and its derivatives have been used for the polymerisation of a wide range of polymers and copolymers. Two of the more important applications of styrene, in SBR and in polyester laminating resins, are dealt with in Chapters 11 and 25 respectively. [Pg.452]

Reaction of polyhydroxy compounds with polybasic acids gives rise to condensation polymers containing ester (—COO—) groups. Because of the presence of these groups such polycondensates are known as polyesters and find use in such diverse applications as fibres, surface coatings, plasticisers, rubbers and laminating resins. These materials are discussed in detail in Chapter 25. [Pg.556]

Because of their favourable price, polyesters are preferred to epoxide and furane resins for general purpose laminates and account for at least 95% of the low-pressure laminates produced. The epoxide resins find specialised uses for chemical, electrical and heat-resistant applications and for optimum mechanical properties. The furane resins have a limited use in chemical plant. The use of high-pressure laminates from phenolic, aminoplastic and silicone resins is discussed elsewhere in this book. [Pg.707]

Numerous multiphase composite materials exhibit more than one characteristic of the various classes, fibrous, laminated, or particulate composite materials, just discussed. For example, reinforced concrete is both particulate (because the concrete is composed of gravel in a cement-paste binder) and fibrous (because of the steel reinforcement). [Pg.10]

The basic terminology of fiber-reinforced composite laminates will be introduced in the following paragraphs. For a lamina, the configurations and functions of the constituent materials, fibers and matrix, will be described. The characteristics of the fibers and matrix are then discussed. Finally, a laminate is defined to round out this introduction to the characteristics of fiber-reinforced composite laminates. [Pg.15]

Unlike most conventional materials, there is a very close relation between the manufacture of a composite material and its end use. The manufacture of the material is often actually part of the fabrication process for the structural element or even the complete structure. Thus, a complete description of the manufacturing process is not possible nor is it even desirable. The discussion of manufacturing of laminated fiber-reinforced composite materials is restricted in this section to how the fibers and matrix materials are assembled to make a lamina and how, subsequently, laminae are assembled and cured to make a laminate. [Pg.18]

Discussion of invariance concepts for laminates will be deferred until Chapter 7 after the development of lamination concepts in Chapter 4. [Pg.87]

Stiffnesses for single-layered configurations are treated first to provide a baseline for subsequent discussion. Such stiffnesses should be recognizable in terms of concepts previously encountered by the reader in his study of plates and shells. Next, laminates that are symmetric about their middle surface are discussed and classified. Then, laminates with laminae that are antisymmetrically arranged about their middle surface are described. Finally, laminates with complete lack of middle-surface symmetry, i.e., unsymmetric laminates, are discussed. For all laminates, the question of laminae thicknesses arises. Regular laminates have equal-thickness laminae, and irregular laminates have non-equal-thickness laminae. [Pg.203]

The purpose of the remainder of this section is to discuss two important classes of antisymmetric laminates, the antisymmetric cross-ply laminate and the antisymmetric angle-ply laminate. Neither laminate is used much in practice, but both add to our understanding of laminates. [Pg.215]

Discuss wfhether this relation is valid for anisotropic materials. That is, denwistrate whether a a angle-ply laminate of the same anisotropic laminae that are symmetric geometrically is antisymmetric or not. The transformation equations for anisotropic materials are given in Section 2.7. [Pg.222]

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). [Pg.222]

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. [Pg.240]

The analysis of stresses in the laminae of a laminate is a straight-fonvard, but sometimes tedious, task. The reader is presumed to be familiar with the basic lamination principles that were discussed earlier in this chapter. There, the stresses were seen to be a linear function of the applied loads if the laminae exhibit linear elastic behavior. Thus, a single stress analysis suffices to determine the stress field that causes failure of an individual lamina. That is, if all laminae stresses are known, then the stresses in each lamina can be compared with the lamina failure criterion and uniformly scaled upward to determine the load at which failure occurs. [Pg.240]

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. [Pg.240]

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... [Pg.241]

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. [Pg.246]

Note that if Bn is zero, then T13 and T23 are also zero, so Equation (5.81) reduces to the specially orthotropic plate solution. Equation (5.65), if D11 =D22- Because Tn, T12, and T22 are functions of both m and n, no simple conclusion can be drawn about the value of n at buckling as could be done for specially orthotropic laminated plates where n was determined to be one. Instead, Equation (5.81) is a complicated function of both m and n. At this point, recall the discussion in Section 3.5.3 about the difference between finding a minimum of a function of discrete variables versus a function of continuous variables. We have already seen that plates buckle with a small number of buckles. Consequently, the lowest buckling load must be found in Equation (5.81) by a searching procedure due to Jones involving integer values of m and n [5-20] and not by equating to zero the first partial derivatives of N with respect to m and n. [Pg.308]

The real point of this example is that the deflection effects just discussed are very significant for numbers of layers that, in our studies of antisymmetric laminates earlier in this chapter, we concluded that bending-extension coupling had disappeared Here, the exact solution exceeds the orthotropic solution by 165% at 6 layers, 165% at 10 layers, 90% at 20 layers, and 30% at 50 layers. Even at 100 layers, the discrepancy is still 11%. These differences are well within the consideration... [Pg.324]

The basic nature of composite materials was introduced in Chapter 1. An overall classification scheme was presented, and the mechanical behavior aspects of composite materials that differ from those of conventional materials were described in a qualitative fashion. The book was then restricted to laminated fiber-reinforced composite mafeffals. The basic definitions and how such materials are made were then treated. Finally, the current and potential advantages of composite materials were discussed along with some case histories that clearly reveal how composite materials are used in structures. [Pg.332]

The macromechanical behavior of a lamina was quantitatively described in Chapter 2. The basic three-dimensional stress-strain relations for elastic anisotropic and orthotropic materials were examined. Subsequently, those relations were specialized for the plane-stress state normally found in a lamina. The plane-stress relations were then transformed in the plane of the lamina to enable treatment of composite laminates with different laminae at various angles. The various fundamental strengths of a lamina were identified, discussed, and subsequently used in biaxial strength criteria to predict the off-axis strength of a lamina. [Pg.332]

A collection of the basic building block, a lamina, was bonded together to form a laminate in Chapter 4. The behavior restrictions were covered in the section on classical lamination theory. Special cases of laminates were discussed to learn about laminate characteristics and behavior. Predicted and measured laminate stiffnesses were favorably compared to give credence to classical lamination theory. Then, the strength of laminates was discussed and found to be reasonably predictable. Finally, interlaminar stresses were analyzed because of their apparent strong influence on laminate strength (and life). [Pg.332]

Obviously, the foregoing description of problems in the mechanics of composite materials is incomplete. Some topics do not fit well within the logical framework just described. Other topics are too advanced for an introductory book, even at the graduate level. Thus, the rest of this chapter is devoted to a brief discussion of some basic lamina and laminate analysis and behavior characteristics that are not included in preceding chapters. [Pg.332]

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. [Pg.345]

Study of transverse shearing stress effects is divided in two parts. First, some exact elasticity solutions for composite laminates in cylindrical bending are examined. These solutions are limited in their applicability to practical problems but are extremely useful as checl oints for more broadly applicable approximate theories. Second, various approximations for treatment of transverse shearing stresses in plate theory are discussed. [Pg.346]


See other pages where Laminates discussion is mentioned: [Pg.275]    [Pg.320]    [Pg.275]    [Pg.320]    [Pg.88]    [Pg.741]    [Pg.886]    [Pg.298]    [Pg.215]    [Pg.18]    [Pg.119]    [Pg.210]    [Pg.222]    [Pg.226]    [Pg.245]    [Pg.259]    [Pg.260]    [Pg.272]    [Pg.278]    [Pg.290]    [Pg.292]    [Pg.315]    [Pg.323]   
See also in sourсe #XX -- [ Pg.30 ]




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