PSI - Issue 13

Jan Klusák et al. / Procedia Structural Integrity 13 (2018) 1261–1266 Author name / Structural Integrity Procedia 00 (2018) 000–000

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two singular and two non-singular terms gives almost identical angle of 186.2°. Nevertheless there is a difference in the values of resulting fracture toughness, see the right side of the Table 1. This is in accordance to the apparent differences in m  as shown in Fig. 3 which is calculated by either singular (yellow makers) or singular and non singular terms (cyan markers). For both the local minimum and interface the  0,2 =  0,interface = 225° and resulting values of H 1C, m listed in the Table 1. Please note that the eigenfunction f rrkm (  ) which is an input for the augmented function U klm (  ) is discontinuous at the interface. To calculate H 1c , interface the radial function of epoxy material region is used. The lowest critical value of generalized fracture toughness is found in the epoxy, therefore it is expected the crack initiation in this direction.

Fig. 2. Three point bending specimen model with the bi-material notch.

Fig. 3. Resulting distribution of averaged strain energy density.

Table 1. Bi-material notch material properties.

H 1c, m singular terms [MPa∙mm p 1 ]

H 1c, m non-singular terms [MPa∙mm p 1 ]

Material

Young modulus [MPa]

Poisson ratio

Fracture toughness [MPa∙mm 1/2 ]

Epoxy

2.98×10 3 70×10 3

0.38 0.33

62.93 758.95 140.36

2.01 20.47 2.72

2.17 21.50 3.34

Aluminum Interface

It is evident that the multi-parameter criterion provides a feasible toll for the stability assessment of singular stress concentrations. It enables more accurate estimation of crack initiation conditions. Acknowledgements Financial support from the Czech Science Foundation (project No. 16-18702S) is gratefully acknowledged.