PSI - Issue 42

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Liviu Marsavina et al. / Procedia Structural Integrity 42 (2022) 1259–1265 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3. The size effect evaluation The size effect was defined as the dependence of the nominal strength,  N as function of the characteristic specimen size, considering the radius R for SCB specimens (here taken as the specimen radius). Thus, the nominal strength is a parameter of the maximum load, having the dimension of stress, Bazant (2002). The size effect is best highlighted in a plot of Log (  N ) versus log ( R ), shown in Fig. 4. If the failure of the component obeyed linear elastic fracture mechanics (LEFM), the logarithmic size effect plot would have to be a straight line with the slope -1/2, Bazant (2002), shown dotted and point in Fig. 4. A ductile behavior with no size effect according with the strength of material would be a horizontal line  N =  f , with  f failure or yield stress. The asymptotic behavior to these two approaches could be expressed in the form: σ = σ 0 √1+ 0 (1) where R 0 represents the transitional size. The transitional size R 0 could be obtained as the intersection point of LEFM asymptote and the strength of materials horizontal line.

Fig. 4 The asymptotic size effect, after Bazant (2002) Fig. 5 Linear regression according with size effect In order to determine the material fracture characteristics eq. (1) could be rearranged in a linear regression plot for 1/(  N ) 2 versus R , Fig. 5. According with Bazant (2002) the regression coefficients can be used to determine: - the energy release rate = 1 (2) with E the Young modulus, - the effective size of fracture process zone = (3) Having determined these fracture characteristics the fitting parameters from eq. (1) could be obtained also as: = √ (4)