PSI - Issue 28

G. Clerc et al. / Procedia Structural Integrity 28 (2020) 1761–1767 Gaspard Clerc / Structural Integrity Procedia 00 (2019) 000–000

1763

3

sample, the crack was placed in the middle of the sample, the sample was loaded under 3-points flexure. The approach to solve the crack equation was based on the Euler-Bernoulli Beam equation as applied for example by Williams, 1987 for central crack sample. The main difference is that a notch was present on the tension side of the sample. To the author’s knowledge it is the first time, that the 3-CCF geometry is proposed. 1.1. Application of fracture mechanics to 3-ENF sample The first equation of fracture mechanics is the Griffith equation (1): � � � 2 ∙ (1) where P is the load, b is the width, C the compliance and a the crack length. The compliance should be expressed according to the crack length. This is generally done using the Euler-Bernoulli equation: � � � �� � (2) EI is the flexural rigidity, w the deflection and q(x) is the load depending of the length of the sample. This equation should be solved for the 3-ENF sample geometry:

⎩⎪ ⎨ ⎪ ⎧ � 8 � � � � 1 4 ������ � � � � � � � � 1 2 ���������������� � � � � � � � � � 1 2 � �������� � � 2 � (3)

Figure 1: Left. 3-ENF sample geometry, Right. System of equation to solve for the 3-ENF sample. according to Yoshihara et al. (2000)

The system of equations can be solved to obtain the deflection v of the beam at the middle point: � �2 � � � � � 12 � From equation 5, the compliance is obtained according to:

(4)

� � 2 � � � � 12 �

(5)

This expression can then be inserted in the equation 1: