Lamina strength

What is the Tsai-Hili failure criterion when the fibers of a unidirectional lamina in the 1-2 plane are aligned in the 2-direction Denote the lamina strength in the fiber direction by X as usual thus, the strength in the 1 -direction is Y. Compare this criterion with Equation (2.132). 

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. 

The subscripts T and m in the above formulae relate to the fibres and matrix respectively i.e. on is the strength of the fibres in tension. The characteristic lamina strengths, namely ou, Oic, 02t, 02c and 012, which have been calculated from raw material data, can then be used with Equation (4.56) to check for possible failure of the lamina. 

Calculate lamina strength in accordance with 4.10.4.1(b). This will demonstrate whether any lamina has failed within the laminate, first ply failure. 

Note that these calculations are conservative and are included to allow the designer to use the Tsai-Wu failure criterion in the absence of measured data. However, for an economic design it is recommended that the lamina strengths be determined experimentally and that the HartSmith failure criterion be employed. 

Laminate strength has been covered in 4.10 Lamina strength. 

Failure of the lamina will occur if any stress component in principal material directions exceeds the corresponding lamina strength value. That is to avoid failure. 

Determine the allowable stress for uniaxial off-axis loading of the unidirectional fiber-reinforced composite lamina, shown in Figure 8.17. Assume that the lamina strength properties Xl, Xf Xp, Xt, and S are known. Use the maximum stress theory of failure. 

The maximum allowable uniaxial stress. Ox will be the smallest absolute value obtained using Equations 9.11a and 9.11b for a specified loading angle 0 and lamina strength properties Xy, X[, Xj, X, and S. 

The tensile strength of a unidirectional lamina loaded ia the fiber direction can be estimated from the properties of the fiber and matrix for a special set of circumstances. If all of the fibers have the same tensile strength and the composite is linear elastic until failure of the fibers, then the strength of the composite is given by... 

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 ... 

These values are determined by experiment. It is, however, by no means a trivial task to measure the lamina compressive and shear strengths (52,53). Also the failure of the first ply of a laminate does not necessarily coincide with the maximum load that the laminate can sustain. In many practical composite laminates first-ply failure may be accompanied by a very small reduction in the laminate stiffness. Local ply-level failures can reduce the stress-raising effects of notches and enhance fatigue performance (54). 

Boron fibers exhibit the highest stiffness and strength efficiencies in Figure 1-24. When placed in a lamina as unidirectional fibers, the... 

What has been accomplished in preceding sections on stiffness relationships serves as the basis for determination of the actual stress field what remains is the definition of the allowable stress field. The first step in such a definition is the establishment of allowable stresses or strengths in the principal material directions. Such information is basic to the study of strength of an orthotropic lamina. 

For a lamina stressed in its own plane, there are three fundamental strengths if the lamina has equal strengths in tension and compression ... 

Figure 2-16 Fundamental Strengths for a Unidirectionally Reinforced Lamina...

That the principal stresses are not of interest in determining the strength of an orthotropic lamina is illustrated with the following example. Consider the lamina with unidirectionai fibers shown in Figure 2-16. Say that the hypotheticai strengths of the lamina in the 1-2 piane are... 

Then, obviously the maximum principal stress is lower than the largest strength. However, 02 is greater than Y, so the lamina must fail under the imposed stresses (perhaps by cracking parallel to the fibers, but not necessarily). The key observation is that strength is a function of orientation of stresses relative to the principal material coordinates of an orthotropic lamina. In contrast, for an isotropic material, strength is independent of material orientation relative to the imposed stresses (the isotropic material has no orientation). 

A key element in the experimental determination of the stiffness and strength characteristics of a lamina is the imposition of a uniform stress state in the specimen. Such loading is relatively easy for isotropic materials. However, for composite materials, the orthotropy introduces coupling between normal stresses and shear strains and between shear stresses and normal and shear strains when loaded in non-principal material coordinates for which the stress-strain relations are given in Equation (2.88). Thus, special care must be taken to ensure obtaining... 

Another test used to determine the shear modulus and shear strength of a composite material is the sandwich cross-beam test due to Shockey and described by Waddoups [2-17]. The composite lamina... 

Now that the basic stiffnesses and strengths have been defined for the principal material coordinates, we can proceed to determine how an orthotropic lamina behaves under biaxial stress states in Section 2.9. There, we must combine the information in principal material coordinates in order to define the stiffness and strength of a lamina at arbitrary orientations under arbitrary biaxial stress states. 

The failure strength parameters F, G, H, L, M, and N were related to the usual failure strengths X, Y, and S for a lamina by Tsai [2-21]. If only x- 2 acts on the body, then, because its maximum value is S,... 

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