Failure criteria strength

Figure 7 gives the results of an experiment in which freestanding films were exposed to constant elevated temperatures in air-circulating ovens for periods of weeks to months the failure criterion was a 50% loss in tensile strength. Because the test is destmctive, each data point (failure time at a given... 

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 ... 

Most comparisons of a failure criterion with failure data will be for the glass-epoxy data shown in Figure 2-36 as a function of off-axis angle 0 for both tension and compression loading [2-21]. The tension data are denoted by solid circles, and the compression data by solid squares. The tension data were obtained by use of dog-bone-shaped specimens, whereas the compression data were obtained by use of specimens with uniform rectangular cross sections. The shear strength for this glass-epoxy is 8 ksi (55 MPa) instead of the 6 ksi (41 MPa) in Table 2-3. 

In the maximum stress failure criterion, each and every one of the stresses in principal material coordinates must be less than the respective strengths otherwise, fracture is said to have occurred. That is, for tensile stresses,... 

A single failure criterion is used in all quadrants of o,-02 space instead of the segments in separate quadrants for the Tsai-Hill failure criterion because of different strengths in tension and compression. 

The terms that are linear in the stresses are useful in representing different strengths in tension and compression. The terms that are quadratic in the stresses are the more or less usual terms to represent an ellipsoid in stress space. However, the independent parameter F,2 is new and quite unlike the dependent coefficient 2H = 1/X in the Tsai-Hill failure criterion on the term involving interaction between normal stresses in the 1- and 2-directions. 

At this point, recali that all interaction between normal stresses o, and 02 iri the Tsai-Hill failure criterion is related to the strength in the 1-direction ... 

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). 

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... 

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. 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

Equation 116 was also derived in Sect. 2. It shows that the fibre strength according to the shear failure criterion increases with improved alignment of the chains, and that it is proportional to the shear modulus g. 

The presented derivations of the load rate and the lifetime relationships applying the shear failure criterion are based on a single orientation angle for the characterisation of the orientation distribution. Therefore these relations give only an approximation of the lifetime of polymer fibres. Yet, they demonstrate quite accurately the effect of the intrinsic structural parameters on the time and the temperature dependence of the fibre strength. 

Life prediction methodology embraces all aspects of the numerous processes that could affect the function of the element—in this case the bulk adhesive. The first step is to define the function of the adhesive clearly enough for a failure criterion to be derived. This failure criterion may be an unacceptable reduction in tensile strength, time to creep failure under a given stress, reduction in modulus due to moisture ingression, increase in modulus due to oxidation, unacceptable crack depth, or a variety of other possible criteria. It is also important that the criteria be related to practical adhesive joint performance. This is where it is difficult, and one must presume, at least for this limited analysis, that the adhesive will fail via a bulk (cohesive) property. 

---