**3. Data reduction to obtain interlaminar fracture toughness and energy release rate**

There are many analysis methods available for analyzing DCB data. The compliance is defined as the opening displacement measured at the load application points divided by the applied load. Many of the compliance methods are based upon the expression (assuming a linear load-deflection relation): the interlaminar fracture can be calculated by compliance or compliance calibration method, which assumes linear elastic behavior such as [25].

$$\mathbf{G}\_{\rm IC} = \frac{P\_{\varepsilon}^2}{2B} \frac{dc\left(a\right)}{da} \tag{1}$$

where; *Pc* is the critical load, *a* is crack length, *B* is the specimen width, and c / = δ *P* shows the compliance and *δ* is the CMOD. The compliance values were used to fit versus curve, leading to the critical energy release rate *G*IC, which is determined by three methods: MBT (Modified Beam Theory), CCM, MCCM (modified compliance calibration method) differed by not more than 3.1%, none of the them were superior to the others [26]. Therefore, *G*IC for linear elastic material behavior CCM as;

$$\mathbf{G}\_{\rm IC} = \frac{nP\_c \delta}{\mathbf{2}Ba} \tag{2}$$

where; *Pc* is the critical load, a is crack length, *B* is the specimen width, *δ* is load point displacement in mm. *n* is the ratio between the slope of the log *δ <sup>i</sup>* /*P <sup>i</sup>* , which is the compliance of the system and the index *i* represents the total number of samples and changes from 1 to 5, and *P* and *δ* represent simultaneously measured values of load *DOI: http://dx.doi.org/10.5772/intechopen.99268 Failure Modes in Fiber Reinforced Composites and Fracture Toughness Testing of FRP*

and displacement, respectively during the test, and log *a* where *a* represents the crack length. Using a least squares approximation, the slope of log *c* versus log *a* yields the value of *n* for different types of specimen. The mean compliance calibration graphs for different test groups are obtained and given in **Figures 11**–**14**. According to Castiglione's principle using the relation between the displacement and strain energy (*U*) as follows:

$$
\varepsilon = \frac{1}{P} \frac{dU}{dP} \tag{3}
$$

The CCM was applied to measure the crack growth in each test. Mode I interlaminar fracture toughness values were calculated by means of the following fracture toughness equation:

$$K\_{IC} = \sqrt{EG\_{IC}} \tag{4}$$

**Figure 11.** *Curve for slope of log c vs. log a, 'n' for sample 4 woven [0°/90°]16 with 25 mm width.*

**Figure 12.** *Curve for slope of log c vs. log a, 'n' for sample 4 woven [0°/90°]16 with 40 mm width.*

**Figure 13.** *Curve for slope of log c vs. log a, 'n' for sample 3 woven [±45°]16 with 25 mm width.*

**Figure 14.** *Curve for slope of log c vs. log a, 'n' for sample 5 woven [±45°]16 with 40 mm width.*

The fracture toughness can be obtained as the function of crack length. In the case of a plane strain condition, the relationship between *G*IC and *K*IC is given as follows:

$$G\_{IC} = \frac{K\_{IC}^2}{E} \left(1 - \nu^2\right) \tag{5}$$

where *E* is the modulus of elasticity, ν is the Poisson's ratio.

The average *G*IC values are compared and drawn with error bars for 4 types of samples with different width and are given in **Figure 15a** and **b**. As it is seen from the figure, the influence of width on average *G*IC for [0°/90°] fiber orientation specimens, and [±45°] fiber orientation specimens for different width is small or in other words, as the increasing width of specimen there is a little decrease in average SERR value.

For materials with high interlaminar fracture toughness, it may be necessary to increase the number of plies, that is, increase the laminate thickness or decrease the *DOI: http://dx.doi.org/10.5772/intechopen.99268 Failure Modes in Fiber Reinforced Composites and Fracture Toughness Testing of FRP*

#### **Figure 15.**

*Influence of width on average GIC for a) [0°/90°] fiber orientation specimens, b) [±45°] fiber orientation specimens. Error bars are ± 1 standard deviations.*

delamination length. Thus, for most studies the results indicate a trend of increasing propagation *G*IC values with increasing DCB thickness [27].
