Classical failure criteria

Craze Initiation. Although the effect of multiaxial states of stress on the brittle and ductile failure of isotropic polymers is sufficiently well represented by the above classical failure criteria, this is not the case for crazing or the failure of anisotropic polymers, ie, oriented sheets, fibers, single crystals, etc. For craze initiation we will cite the stress-bias criterion as proposed by Stemstein (54) ... 

In predicting limit (threshold) conditions, such as the elastic Kmit, yield, and failure conditions, classical failure criteria, such as the maximum normal stress criterion, maximum shear stress criterion and the distortion energy (von Mises) criterion can be employed. 

Many reports have shown that for a tc/4 quasi-isotropic laminate, when the interlaminar normal stress is tensile and is the dominant component among the free edge stresses, then open mode delamination may occur. Examples of such laminates include [ 45/90/0]s, [ 45/0/90]s, and [0/ 45/90]s laminates. In these laminates, the open-mode delamination crack may propagate into the laminate before final failure of the laminate. For these laminates, classical failure criteria are not suitable for laminate strength prediction. 

In this chapter an overview of conceptually different fracture theories is presented which have in common that they do not make explicite reference to the characteristic properties of the molecular chains, their configurational and super-molecular order and their thermal and mechanical interaction. This will be seen to apply to the classical failure criteria and general continuum mechanical models. Rate process fracture theories take into consideration the viscoelastic behavior of polymeric materials but do not derive their fracture criteria from detailed morphological analysis. These basic theories are invaluable, however, to elucidate statistical, non-morphological, or continuum mechanical aspects of the fracture process. 

In conclusion, classical lamination theory enables us to calculate forces and moments if we know the strains and curvatures of the middle surface (or vice versa). Then, we can calculate the laminae stresses in laminate coordinates. Next, we can transform the laminae stresses from laminate coordinates to lamina principal material directions. Finally, we would expect to apply a failure criterion to each lamina in its own principal material directions. This process seems straightfonward in principle, but the force-strain-curvature and moment-strain-curvature relations in Equations (4.22) and (4.23) are difficult to completely understand. Thus, we attempt some simplifications in the next section in order to enhance our understanding of classical lamination theory. 

It is worthwhile to consider whether the classical theories (or criteria) of failure can still be applied if the stress (or strain) concentration effects of geometric discontinuities (eg., notches and cracks) are properly taken into account. In other words, one might define a (theoretical) stress concentration factor, for example, to account for the elevation of local stress by the geometric discontinuity in a material and still make use of the maximum principal stress criterion to predict its strength, or load-carrying capability. 

Comparisons with experimental data show that the stress required to produce fracture actually approached a constant (Fig. 2.3). Thus, the maximum principal stress criterion for failure, as well as the other classical criteria, is inadequate and inappropriate. 

This has led many researchers to posmlate a simple shear stress criterion for failure. This idea persists to this day despite some early analysis, such as that of Goland and Reissner who used classical mechanics of material concepts to demonstrate that the joint includes shear, bending, and cleavage stresses [5], This is more recently substantiated by several numerical analyses, some of which are cited in [1]. 

The model of the thermoplastie matrix reinforeed with short fibres, in its different forms, was widely exploited, in the elaboration of the theory eoneerning the eomposite materials fracture. A first approach belongs to the material resistanee field, which uses the classical criterion of fracture of the ideal material, without faults the fracture mechanic studies the initiation and propagation of a fault, preexistent or artificially created, and, finally, the failure mechanic investigates the material behaviour until to the apparition of a microscopic fault, which corresponds to the catastrophic fracture initiation. 

For in-plane failure in a lamina, the Tsai-Hill criterion was used with classical lamination theory to predict failure load. The Tsai-Hill criterion is given by... 

For the fiber-dominated laminate (0 = 0°) and highly matrix- dominated laminates (0 > 30°), failure initiates from the interior of the laminate and the classical Tsai-Hill criterion is accurate. 

The failure loads predicted using classical Tsai-Hill criterion are 93.4 ksi for [ 30/90]g laminate and 48 ksi for [ 45/90]s laminate. These predicted failure loads are much higher than the test data. Thus, failure in these laminates must have initiated from the free edges. 

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