PSI - Issue 13

Mina Iskander et al. / Procedia Structural Integrity 13 (2018) 976–981 Iskander and Shrive/ Structural Integrity Procedia 00 (2018) 000 – 000

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difference between crack propagation in compression compared to that in tension. The change in the reaction force is also minimal due to the 6 mm crack propagation, 0.08 kN for C10 and 0.26 kN for C20. These numbers fit with what is seen experimentally where small load drops may be seen as cracks appear in compressively loaded specimens. The drops in load are 0.006% and 0.20% of the peak values (before cracking) and the highest changes occur around the same values for crack length as mentioned earlier for strain energy.

5. Conclusions and future studies

In this study five models for crack propagation in compression were investigated using two software packages ABAQUS and FRANC2D. Three parameters were studied to determine the relationship between K I and crack length in compression due to the presence of a void: size, height and width. Only void size was included to study the changes in total strain energy and reaction. It can be concluded that the mode I (opening) stress intensity factor (K I ) rises during initial crack propagation but reaches a peak value after which it declines consistently. The peak value occurs at crack lengths which depend on the size and geometry of the void studied. This conclusion is in stark contrast to what happens when a tension load is applied to similar models: in that case, K I increases with the square root of crack length as the crack grows, as per Eq 1. It can also be concluded that a bigger void size results in a higher K I and a longer crack as shown in Fig.4 and Table 2. When comparing voids of the same width but different height, it appears that the flatter void is more critical (i.e. a horizontal ellipse appears more critical than a circle or a vertical ellipse). The same conclusion may be drawn when comparing two voids of the same height but different widths - the wider appears more critical. This result is counterintuitive as one would expect a wide, flat crack simply to close under compressive loading. Thus, the effect of void shape requires more study. Finally, the reduction of strain energy due to the presence of circular voids is directly proportional to the volume of the void and the change in strain energy due to crack propagation is minimal with the largest changes occurring at crack lengths where the highest K I values were recorded. Clearly, to gain better comprehension of the effects of the various parameters studied, more voids sizes, shapes and volumes need to be examined. The study also needs to be extended to 3D as voids will be 3 dimensional in real materials.

Acknowledgements

The authors gratefully acknowledge the financial support of NSERC (The Natural Sciences and Engineering Research Council of Canada), and also thank the Cornell Fracture Group for providing FRANC2D online for free.

References

Griffith, A. A., 1921. The Phenomena of Rupture and Flow in Solids, Philos. Trans. R. Soc. London. Ser. A, Contain. Pap. a Math. or Phys. Character, vol. 221, no. 582–593, p. 163 LP-198. http://cfg.cornell.edu/software/ Iskander, M., Shrive, N., 2018. Fracture of Brittle and Quasi-Brittle Materials in Compression: a Review of the Current State of Knowledge and a Different Approach, Submitted and under revision at Theoretical and Applied Fracture Mechanics, Submission ID: TAFMEC_2018_185_R1. Van Vlack, L. H., 1989. Elements of Materials Science and Engineering, Sixth Edition, Addison-Wesley Publishing Co., ISBN 0-201-09314-6. Westergaard, H.M., 1939. Bearing pressures and cracks, Journal of Applied Mechanics, 61, pp. A49–A53. doi: /publication/216756690.