Biaxial strength criteria

The macromechanical behavior of a lamina was quantitatively described in Chapter 2. The basic three-dimensional stress-strain relations for elastic anisotropic and orthotropic materials were examined. Subsequently, those relations were specialized for the plane-stress state normally found in a lamina. The plane-stress relations were then transformed in the plane of the lamina to enable treatment of composite laminates with different laminae at various angles. The various fundamental strengths of a lamina were identified, discussed, and subsequently used in biaxial strength criteria to predict the off-axis strength of a lamina. 

Figure 12.9 Strength test results of a silicon nitride ceramic. Shown are data from uniaxial and biaxial strength tests. To determine the equivalent stress, the PIA criterion was used. Plotted in log-log scale is the characteristic strength of sets of specimens versus their effective volume. The solid line indicates the...

The preceding biaxial failure criteria suffer from various inadequacies in their representation of experimental data. One obvious way to improve the correlation between a criterion and experiment is to increase the number of terms in the prediction equation. This increase in curvefitting ability plus the added feature of representing the various strengths in tensor form was used by Tsai and Wu [2-26]. In the process, a new strength definition is required to represent the interaction between stresses in two directions. 

Here F, denotes the tensile strength of the material, Fc is the compressive strength, and Ybc represents equal biaxial compression strength of the material. The reader is directed to Palko25 where the specific forms of B and A are presented. This model is termed a three-parameter model, referring to the three material strength parameters (F FC, and Ybc) used to characterize the model. Failure is defined when / = 0, and the multiaxial criterion is completely defined in the six-dimensional stress space. 

Despite the improvement in differentiating between tension and compression strength values, the Tsai—Wu failure criterion remains a curve fit and does not capture well the mechanism of failure, nor the failure load itself, especially in cases of combined loading with biaxial compression being one of the major problem areas [7]. However, it has been shown to work well in many cases especially when substantiated, and, if necessary, modihed, by experimental results. 

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