PSI - Issue 42

Michal Vyhlídal et al. / Procedia Structural Integrity 42 (2022) 1000–1007 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 The crack propagates when the mean value of tangential stress σ̅ θθ ( 0 ) exceeds its critical value ̅ ,c . ̅ ( 0 ) ≥ ̅ , In the case of bi-material combinations, the crack propagates into direction θ 0 and material m corresponding to the lowest value of critical applied force F crit, m . The critical applied force F crit, m depends on fracture toughness of particular material K Ic, m and on the ratio of the critical value ̅ , and the average tangential stress corresponding to the applied force F appl . crit, = appl ̅ ,c ( Ic, ) ̅ ( 0, ) (5) 1003 4 (4)

3. Numerical study 3.1. Numerical model

A simplified 2D model of the specimen was created in Ansys Inc. software (2021). The dimensions of the specimen are in Fig. 1. The specimen contains a steel inclusion with dimensions 8×8×40 mm placed in the middle of the span. The specimens include an initial notch with a depth of 12 mm.

Fig. 1. Designed specimen geometry (dimensions in mm).

Materials were modelled as linear, elastic, and isotropic and they were represented by the elastic constants, i.e. Young’s modulus E , and Poisson’s ratio ν . Fracture properties were defined by the fracture toughness K Ic (Table 1).

Table 1. Overview of the material’s parameters used in the numerical model. Material E [GPa] ν [ – ]

K Ic [MPa∙m 1/2 ]

Matrix (MTX) – fine-grained cement-based composite

39.3 14.7 210

0.20 0.20 0.30

0.58

ITZ

0.7  K Ic, MTX

Inclusion – steel S235

irrelevant

Young’s modulus of elasticity of the ITZ E ITZ was estimated according to approaches in Zacharda et al. (2018). Fracture toughness of the ITZ was chosen as 0.7  K Ic, MTX . The crack was modelled as ideally sharp. Because of high stress gradients surrounding crack tips and edges, highly refined meshes were required near the crack tip, bottom, left and upper corner of steel inclusion, see Fig. 2. In the following study of crack propagation, the resulting critical forces will be compared to a reference specimen. The reference specimen has the same geometry but is made of homogeneous material with the properties of matrix. In the graphs of results, the critical forces corresponding to the specimens with steel inclusion are labeled as STE, while F crit for the reference specimens are labeled as REF.