Maximum stress criterion

If the fibres are aligned at 15° to the jc-direction, calculate what tensile value of Ox will cause failure according to (i) the Maximum Stress Criterion (ii) the Maximum Strain Criterion and (iii) the Tsai-Hill Criterion. The thickness of the composite is 1 mm. 

A single ply glass/epoxy composite has the properties Usted below. If the fibres are aligned at 30° to the x-direction, determine the value of in-plane stresses, a, which would cause failure according to (a) the Maximum Stress criterion (b) the Maximum Strain criterion and (c) the Tsai-Hill criterion. 

Hence the Maximum Stress Criterion also predicts = 606 MN/m as the limiting condition. 

In applications of the maximum stress criterion, the stresses in the body under consideration must be transformed to stresses in the principal material coordinates. For example, Tsai [2-21] considered a unidirec-tionally reinforced composite lamina subjected to uniaxial load at angle 6 to the fibers as shown in Figure 2-35. The biaxial stresses in the principal material coordinates are obtained by transformation of the uniaxial stress, a, as... 

For a unidirectionally reinforced composite material subject to uniaxial load at angle 0 to the fibers (the example problem in Section 2.9.1 on the maximum stress criterion), the allowable stresses can be found from the allowable strains X, Y , etc., in the following manner. 

The Tsai-Hill failure criterion appears to be much more applicable to failure prediction for this E-glass-epoxy composite material than either the maximum stress criterion or the maximum strain failure criterion. Other less obvious advantages of the Tsai-Hill failure criterion are ... 

A criterion has been developed based on the tensile normal stress and the anisotropic tensile strength on arbitrary planes about the crack tip. It is assumed that the crack grows along the plane on which the stress ratio is maximum (Buezek and Herakovich, 1985). A maximum stress criterion is also proposed (Gupta et al., 1993) for a crack which deflects along the interface... 

The results of the experiments were analysed according to continuum mechanics as v/ell as fracture mechanics principles. The evaluation of the stress at failure as well as the energy released are used to evaluate the validity of, respectively, a maximum stress criterion energy approach as a failure criterion. 

The total stress at the occurrence of the first transverse crack is the principal stress, and it is therefore possible to use a Maximum Stress Criterion as a failure criterion. It is simply performed by comparing the stress at the occurrence of the first transverse crack to the strength of the layer. In other words, failure occurs when ... 

A maximum stress criterion (using the strength of a unidirectional beam as a reference) applies for the structure considered when taking into account the residual stress relaxation. 

Maximum strain This is completely analogous to the maximum stress criterion, but instead of stresses, strain values are used ... 

The denominators in the first two of Eqn (6.34) are the tensile or compressive ultimate strains in the corresponding direction depending on whethCT or ey are tensile or compressive, respectively. It should be noted that for a material that is linear to failure, the predictions from the maximum strain criterion would differ from those from the maximum stress criterion only by a factor depending on the Poisson s ratios and Vyx- As with the maximum stress criterion, the maximum strain criterion provides some feedback on the type of failure mode occurring. 

This stress distribution is the basis for the determination of the adhesion strength at the interface. In such a case, the maximum stress criterion can be applied to determine the debonding strength ... 

Note that in the assessment of the effective process volume it has been considered only a surface layer 0.5 mm thick because it is only that surface layer that takes place in the high cycle fatigue process. The beam under consideration has a much larger process volume. The bending stress reaches its maximum at the fix end on the farthest fibers from the neutral axis. The 90 % of the maximum stress criterion is adopted (see Sect. 7.5) to evaluate the process volimie. Stresses maintain equal or larger than 90 % of the maximum value within a distance d from the surface equal to... 

Maximum-stress-and-strain-based failure criteria were used by Harris and Adams (1984) to predict the failure of single lap joints. A nonlinear finite element analysis with an elasto-plastic material model for the adhesive and adherends was carried out. The selection of stressor strain-based failure criterion was based on the results of uniaxial tensile test results. For an un-toughened adhesive, a brittle failure was observed and a maximum stress criterion was used, while for a toughened adhesive, failure was ductile and a maximum-strain-based criteria was used. However, these criteria are difficult to implement when highly localized stress concentrations or stress singularities exist in an adhesive joint. 

Assuming the elements are elastic and the problem strictly one dimensional and time independent, the failure criterion for an element can be expressed either as a maximum strain or maximum stress criterion. Assuming a chain fails when an extension e or equivalently stress exceeded, the following equation is obtained... 

Failure Analysis Using Maximum Stress Criterion... 

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