Strength of Angle-Ply Laminates

Angle-ply laminates have more complicated stiffness matrices than cross-ply laminates because nontrivial coordinate transformations are involved. However, the behavior of simple angle-ply laminates (only one angle, i.e., a) will be shown to be simpler than that of cross-ply laminates because no knee results in the load-deformation diagram under uniaxial loading. Other than the preceding two differences, analysis of angle-ply laminates is conceptually the same as that of cross-ply laminates. 

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 

Note that the stresses Cy are very small in comparison to the shearing stresses. Thus, the Tsai-Hill lamina failure criterion can be simplified for this lamina to 

in the outer layer, the largest average laminate stress is - = 11.14AT psi/ F + 37,400 psi (.1383AT MPa/ C + 257.9 MPa) 

---

Figure 4-45 Strength of Angle-Ply Laminates (After Tsai [4-10])...

Herakovich, C.T. (1982). Influence of layer thickness on the strength of angle ply laminates. J. Composite Mater. 16, 217-227. 

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... 

Strength chart for a [0, 0 ] cartxin-epoxy laminate containing 60 vol.% fibres, showing the maximum allowable stress in 0° direction as a function of 0 and A, the fraction of angled plies (after R. Tetlow). 

Angle-ply laminate n. A laminate in which equal numbers of plies are oriented at equal plus and minus angles from the plies in the length direction, making the laminate orthotropic. The most commonly chosen angles are+60°, giving nearly equal strengths in all directions in the plane of the laminate. 

A failure theory which combines classical lamination theory with ffee-edge interlaminar stress was employed to predict the strength of laminates with free edges. Laminates studied were [ 0]2s angle-ply laminates, [ 0/9O]s laminates, and fiber-dominated 7t/4 laminates. The present theory was capable of predicting failure loads for [ 0]2s and [ 0/9O]s laminates as well as delamination on-set loads for 7t/4 laminates. 

Therefore, moisture absorption has a larger effect on the transverse properties of a typical composite system. Despite this, the strength of a 0° composite is also affected by moisture ingress since the reloading of a broken fibre occurs through shear stress transfer Ifom the interphasal matrix. To achieve isotropy, unidirectional plies are stacked at a set of angles such as 0°, 45° and 90° to form a laminate. In this situation, moisture ingress will modify the residual stress state in the individual laminae. 

The anisotropy, or directional nature, of unidirectional fibre composites is mentioned in Chapter 1. To improve the modulus and strength for intermediate angles (i.e. between 0° and 90°) woven fabrics or multiple constructions are used. The latter is made up of a series of unidirectional plies laid up so that there is an angle, say, 10°, 20°, 30° or 45°, etc., between successive plies. To avoid the laminate distorting it is necessary to balance the construction about the centre plane — i.e. to have as many —0 plies as +0 ones. A typical balanced laminate is [0 45 0]s-Because there are now some plies in intermediate directions the modulus and strength of the laminate in these directions is increased. The exact values for thermoelastic properties can be calculated from classical laminate theory, see Jones (1975). It is more difficult to calculate the effect on strength because of interaction between failure modes and individual plies, etc. 

In-plane properties (e.g., modulus of elasticity and strength) of unidirectional laminates are highly anisotropic. Cross-, angle-, and multidirectional laminates are designed to increase the degree of in-plane isotropy multidirectional can be fabricated to be most isotropic degree of isotropy decreases with angle- and cross-ply materials. 

In-plane laminate properties depend on layer-to-layer high-strength-direction sequencing—in this regard, there are fonr laminate types nnidirectional, cross-ply, angle-ply, and multidirectional. Mnltidirectional laminates are the most isotropic, whereas unidirectional laminates have the highest degree of anisotropy. 

Angle-ply [ 0]2s laminates of T300/5208 graphite/epoxy composite were analyzed using the proposed failure criterion. In ensence, Tsai-Hill, interfacial failure, and surface-ply failure loads were obtained first and the laminate strength was taken to be the lowest failure load among the three. 

---