Page 296 - Mechanics Analysis Composite Materials

Chapter 6. Failure criteria and strength of laminates 28 1

6.1.2. Approximation strength criteria

In contrast to structural strength criteria, approximation criteria do not indicate
the mode of failure and are constructed by approximation of available experimental
results with some proper function depending on stresses 01, 02 and 212. The simplest
and the most widely used criterion is a second-order polynomial approximation
typical forms of which are presented in Fig. 6.14. In the stress space shown in Fig.
6.2, the polynomial criterion corresponding to Fig. 6.14(a) can be written as

To determine coefficients R and S, we need to perform three tests providing material
strength under uniaxial loading in 1 and 2 directions and in shear. Then, applying
the following conditions:

F(o1 = 01, 02 = 0, 212 = 0) = 1,
F(01 = 0, 02 = 52, 212 = 0) = 1, (6.10)
F(0l = 0, 02 = 0, 212 = 212) = 1 ,

we can find R and S and write Eq. (6.9) in its final form

V

V

Fig. 6.14. Typical shapes of the curves corresponding to the second-order polynomials.