PSI - Issue 13

Ondřej Krepl et al. / Procedia Structural Integrity 13 (2018) 1279 – 1284 Ond ř ej Krepl & Jan Klusák / Structural Integrity Procedia 00 (2018) 000–000

1281

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2. Stability criteria of sharp material inclusion A sharp material inclusion exhibit singular stress distribution similarly as a crack in homogeneous material. Thus we suppose that the mechanism of crack initiation in a sharp material inclusion is the same as the mechanism of crack propagation in single material. This is the basic assumption for generalization of the approaches of classical fracture mechanics. The criteria of the direction of crack initiation at a SMI tip and the criteria of its stability are derived in analogy to the approaches of a crack in homogeneous material. Note that the definition of the stability of SMI means determination of conditions under which a crack initiates from the SMI tip. Because the dimension of generalized stress intensity factors depends on λ k and is [ H k ] = MPa  m 1− λ k , the stability criterion must be expressed by means of GSIF and its critical value instead of the values K I and K Icrit : (2) The stability condition can be understood in the following way. A crack is not initiated at the SMI tip if the value H 1 is lower than its critical value H 1,crit . The value H 1 (σ appl ,…) follows from a numerical solution and depends mainly on the level of external loading, on materials used and on the global geometry. Its critical value H 1,crit depends on the critical material characteristic K Ic or K Ith and has to be deduced with the help of the controlling variable L , see Knésl et al. (2007). The controlling variable L needs to have a clear and identical physical meaning in the case of assessing both a crack in homogeneous material and a sharp material inclusion. With respect to particularities of the SMI the average value of the strain energy density factor Σ has been chosen as the controlling variable L in the paper. Krepl and Klusák (2017b) used modified maximum tangential stress criterion to identify conditions of crack onset at the SMI tip. Similarly Klusák et al. (2016) studied behaviour of a crack in a corner or at a tip of a polygon-like particle. 3. The average strain energy density factor criterion The strain energy density factor (SEDF) criterion, developed by Sih, found many applications in assessment of crack problems. The problem of a sharp material inclusion, modelled as a bi-material junction can be assessed by this criterion as well, Sih (1973), Sih (1991). In the case of general singular stress concentrators the direction of the extreme (minimum) of the SEDF depends on radial distance. Therefore, an average value of the SEDF over a distance d , which is a distance related to fracture mechanism or material microstructure, is used. Klusák and Krepl (2018) applied the average value of the SEDF with consideration of not only singular but also higher non-singular terms to assess the stability of sharp and bi-material notches. Here we use the criterion to estimate critical conditions of crack initiation in SMI tip. The theoretical multi-parameter approach is identical to the case of sharp and bi-material notches, as stated in Klusák and Krepl (2018). The minimum of the SEDF is again found as a potential crack initiation direction. This direction  0 is found as solution of the equation: 1 1 1 1 ( ) 0 n n k l klm k l k l k l k U d                   (3) Here the  k 1,  l 1 are the ratios between GSIFs defined: appl I,cri 1 1,cr t it ( , ) ( , )  K H H   

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