PSI - Issue 13

Sze Ki Ng et al. / Procedia Structural Integrity 13 (2018) 304–310 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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2.3. Optical Analysis An optical microscope was used to observe the notch- tip radius, ρ of each pre -crack after broaching. This was to ensure a ‘sharp’ pre -crack and to avoid any crack- tip with ρ greater than the material crack opening displacement, COD, in the specimens used for testing. A Hitachi S-3400N scanning electron microscopy (SEM) was used to observe the fracture surface for any crazing mechanisms and used to distinguish between the relaxation-controlled, flow controlled and ‘in - air’ regions within the crack growth. Each specimen was finely sputter-coated with gold for conductivity. An accelerating voltage of 10kV, working distance of 10 mm, tilt angle of 15 o and a magnification of x50 were used on all specimens. 2.4. Data Analysis A linear elastic fracture mechanics (LEFM) approach was employed to investigate the crack initiation and propagation during ESC. The compliance model from (Kamaludin et al. 2017) was used: ( ) = ( ) = ( 1 6 ) [ 9 8 + 9 2 ∫ 2 ( ) ∙ 0 ] = ( 1 6 ) ( ) (2) where is the compliance of the sharp-notched specimen at the applied load, P and displacement, , is the Young’s modulus, is the specimen thickness and is the normalised crack length against specimen width. The bending and shear contribution is expressed by the first term in square brackets, while the second term accounts for the presence of the crack tip and growth. The geometry factor, Y of an SENB specimen under three-point bending condition can be expressed as: ( ) = 1.93 − 3.07 + 14.53 2 − 25.11 3 + 25.8 4 (3) The compliance of a blunt-notched specimen can be found using the same compliance model. Thus the point of crack initiation can be defined when the compliance ratio between a sharp and blunt notched specimen differs by 2%. Hence, the crack length, can be found using a straight line fit given > 0.25 : = (1 − ) 2 + (4) where and are the fitting constants used relating to as shown in table 1. Table 1. Fitting constants for > 0.25 (Kamaludin et al. 2017). 0.25 1.56 1.86 0.01 0.30 1.76 2.11 0.01 0.35 2.02 2.42 0.02 0.40 2.36 2.83 0.02 0.45 2.81 3.37 0.02 0.50 3.42 4.09 0.03 0.55 4.25 5.09 0.03 0.60 5.44 6.51 0.04 Rearranging the compliance equation, an instantaneous modulus, can be found. Thus, substituting into the equation below, the instantaneous fracture toughness throughout the test can be determined: = 2 (1 − 2 ) = 2 2 (1 − 2 ) (5) where is the fracture energy, is the fracture toughness and is the Poisson ’s ratio.