PSI - Issue 28

1764 G. Clerc et al. / Procedia Structural Integrity 28 (2020) 1761–1767 Gaspard Clerc/ Structural Integrity Procedia 00 (2020) 000–000 � 9 � � 24 (6) This final equation describes the energy of the sample depending on its flexural rigidity, crack length and load. This value should then be lower than a critical G so that � ���� to avoid the further propagation of the crack and ultimately the failure of the sample. This method was then applied to a new designed sample geometry. For this sample, the crack is present at the middle of the sample, both ends are adhesively bonded as shown in Fig. 2. 4

Figure 2: Geometry of the 3 point central crack flexure (3-CCF) sample

1.2. Application of fracture mechanics to 3-CCF sample

For 3-CCF sample geometry a new system of equation should be written as : ⎨⎩ ⎧ � � � � � � 2 � � � 2 � � � 8 � � � � � 2 � � 2 � � � � 2 �

(7)

Solving this system of equations gives the following expression for the beam deflection at the middle point: � � 48 ��6 � � � � 84 � � 42 � � (8)

This expression can then be inserted in equations 5 and 6 to obtain equation (9) for the energy release rate of the 3 CCF: �� � 7 � 16 � � 2 � � (9)