Strength of laminates

When a composite is made up of many plies, it is unlikely that all plies will fail simultaneously. Therefore we should expect that failure will occur in one ply before it occurs in the others. To determine which ply will fail first it is simply a question of applying the above method to each ply in turn. Thus it is necessary to determine the stresses or strains in the local (1-2) directions for each ply and then check for the possibility of failure using any or all of the above criteria. This is illustrated in the following Example. 

Example 3.21 A carbon-epoxy composite has the properties listed below. If the stacking sequence is [0/-30/30]s and stresses of r = 400 MN/m, Oy = 

160 MN/m and Xxy = —100 MN/m are applied, determine whether or not failure would be expected to occur according to (a) the Maximum Stress (b) the Maximum Strain and (c) the Tsai-Hill criteria. The thickness of each ply is 0.2 mm. 

Solution It is necessary to work out the global strains for the laminate (these will be the same for each ply) and then get the local strains and stresses. Thus, for the 30 ply 

If this is repeated for each ply, then the data in Fig. 3.31 is obtained. It may be seen that failure can be expected to occur in the +30° plies in the 2-direction because the stress exceeds the boundary shown by the dotted line. 

Because of the various characteristics of composite laminates, it is difficult to determine a strength criterion in which all failure modes and their interactions are properly accounted for. Moreover, the verification of a proposed strength criterion is greatly complicated by scatter in measured strengths caused by inconsistent processing techniques (that 

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 

Finally, both the state of the material and the state of stress affect the laminate strength evaluation. That is, the actual temperature and moisture conditions influence the laminae strengths. Taken together with the laminae stresses, the laminae strengths and the laminate loads lead to an evaluation of the laminate capabilities. 

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. 

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. 

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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 ... 

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). 

A surface is that part of an object which is in direct contact with its environment and hence, is most affected by it. The surface properties of solid organic polymers have a strong impact on many, if not most, of their apphcations. The properties and structure of these surfaces are, therefore, of utmost importance. The chemical stmcture and thermodynamic state of polymer surfaces are important factors that determine many of their practical characteristics. Examples of properties affected by polymer surface stmcture include adhesion, wettability, friction, coatability, permeability, dyeabil-ity, gloss, corrosion, surface electrostatic charging, cellular recognition, and biocompatibility. Interfacial characteristics of polymer systems control the domain size and the stability of polymer-polymer dispersions, adhesive strength of laminates and composites, cohesive strength of polymer blends, mechanical properties of adhesive joints, etc. 

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... 

Figure 11.16. Tensile strength of laminates with fibers oriented parallel to the surface. [Adapted, by permission, from Selzer R, Friedrich K, Composites, Part A, 28A, 1997, 595-604.]...

The mechanism of photolamination has been proposed by the authors [ 133,136,137] as illustrated in Scheme 13.22. It is based on an initial primary grafting reaction followed by a secondary growth period, filling the spaces with branched chains. In most cases, addition of a small amount of cross-linking agents increases the strength of laminates by forming a network between the substrate films. 

The measurement of "toughness" properties is one area where the particular nature of composites (i.e., poor interlaminar strength of laminated composites) affects both the use of existing tests and the creation of new test methods. 

Buckling and compressive strength of laminates with optimized fibre-steering and layer-stacking for aerospace applications... 

The second method shown in Figure 20.9b laminates a dry SU-8 or Kapton film on top of the open microchannels. Although this process is relatively simple, the alignment and the bonding strength of lamination could be a challenging problem. 

The use of fillers tends, with few exceptions, to reduce the damage tolerance, tensile and flexural strength of laminates. The effect on the interlaminar shear strength of glass fabric/epoxy laminates depends on the filler and is shown in Fig. 1.10. Note that glass beads and quartz had no adverse effect whereas the extremely thin-walled hollow glass microspheres were damaging [23]. Thicker walled spheres would have improved the performance. 

Griffis, C.A., Nemes, J.A., Stonesfiser, F.R., and Chang, C.I. (1986) Degradation in strength of laminated composites subjected to intense heating and mechanical loading. /. Compos. Mater., 20(3), 216-235. 

Fig. 22. Adhesion rating based on flexural strengths of laminates of poly(styrene) with glass treated with various silane coupling agents vs. solubility parameter of the organo-fiinctional group of the coupling agent. From ref. [117], by permission.

Gross cross-sectional area tensile strength of laminate... 

Characteristic tensile, compressive strength of laminate or panel... 

The Hart Smith criterion proposes that the strength of laminates be characterised by generalizing the maximum-shear-stress criterion for ductile isotropic metals. 

Electrical. The dielectric strength of laminates will decrease with increasing thickness and is highly dependent upon the direction of the electric field stress. This property will show higher when tested across the sample s thickness whereas end-to-end testing will show lower values. Laminates with higher resin content will show better electrical properties but poorer physical properties than laminates with lower resin content. 

Table L.l Strength of Laminates made with Style 181 Glass Fabric (Ref Harper, C.A., Laminates and Reinforced Plastic Materials and Processes " Handbook of Plastics, Elastomers, and Composites, 3 ed., C.A. Harper, ed., McGraw-Hill, New York, 1996)...

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