PSI - Issue 18

Mikhail Eremin / Procedia Structural Integrity 18 (2019) 135–141

139

Mikhail Eremin / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 2. Fracture patterns combined with pores distribution for loading conditions: a - confined sliding, b - free sliding, thin black lines indicate the cells, where parameter D = 1. c - loading diagrams for two types of loading.

shows that several pores in the upper part of a specimen are located exactly in this zone of stagnated deformation, thus the conditions for cracking are poorly provided. The majority of small-scale cracks are concentrated in the lower part of the specimen and coalescence into macroscopic crack oriented at an angle of about 30 ◦ to the direction of the load. It indicates that shear failure mechanism prevails over the tensile mechanism for confined sliding which is prone for more high peak stress, see Fig. 2c. In the case of free sliding, several mostly tensile small-scale cracks coalescence into macroscopic crack subvertical oriented. In comparison with the confined sliding case, macroscopic crack occupies the entire length of computational domain and dissipate an accumulated energy more e ff ectively. It results in lower peak stress. Length, orientation and sub-structure of the macro-crack indicate that the main failure mechanism is tensile for free sliding. Possible macroscopic crack paths are schematically shown by ellipses in the Fig. 2a,b. Let’s trace the stages of crack development and try to match them with loading diagram. We will focus on free sliding case since it appears to be more representative of crack formation to our mind. Fig. 3b,c,d illustrate the stages of deformation of porous sandstone matched with corresponding points of loading diagram. It is obtained that microcrack closure (stage (a) in the loading diagram, see Fig. 3a) occurs at axial stress σ ≈ 23% of peak stress, which is quite high in comparison with the values reported, e.g. by Hoek and Martin (2014). However, for weak, porous sandstone specimens such an estimation of initial nonlinearity is satisfactory. Magnified window in the Fig. 3a illustrates that the stage of initial nonlinearity results in gradual increase of Young’s modulus until the micro-cracks closure is completed. When axial stress σ ≈ 60% of peak stress (stage (b)), crack nucleation and propagation starts (see Fig. 3b). Esti mation of crack nucleation onset by the model under development is in good agreement with data reported by Hoek and Martin (2014). They argued that crack nucleation onset occurs when axial stress is in the range of 40-60% of peak stress. Prior to the initiation of softening stage (stage (c)), loading diagram illustrates the deformation range related to small fluctuations near the peak stress. This range stands for the further development of cracks. The softening stage, after the point (c), finally results in coalescence of small-scale cracks into the macroscopic crack and turn to residual strength at point (d) of the loading diagram. It indicates that exactly the post-peak deformation behavior of specimen is responsible for the final fracture pattern. Formation of macroscopic crack breaks the specimen into two parts. According to the results of numerical simulation, we obtained the following characteristics of porous sandstone: Young’s modulus E = 16.528 GPa, uniaxial compressive strength (UCS) σ c = 9.72 MPa.