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Study of the interaction of matrix crack with inclusions of different shapes using the method of caustic

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Abstract

In this study, the interactions of matrix crack with inclusions of different shapes were investigated using the method of caustic. First, the specimens with inclusions of different shapes were prepared, where glass was used as inclusion and epoxy was used as matrix. Then, caustic experiments were conducted, and the typical caustic spots at the crack tip with varied distances from three different shapes of inclusions were obtained. Ultimately, the stress intensity factors of the cracks shielded by different shapes of inclusions were extracted from the caustic spots, and finite element simulations were conducted to verify the experimental results using the ABAQUS software. The results show that the stress intensity factors measured by the caustic method are in good agreement with the finite element simulation results.

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References

  1. Hao, W., Ge, D., Ma, Y., Yao, X., Shi, Y.: Experimental investigation on deformation and strength of carbon/epoxy laminated curved beams. Polym. Test. 31, 520–526 (2012)

    Article  Google Scholar 

  2. Khludnev, A.M., Novotny, A.A., Sokołowski, J., Żochowski, A.: Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions. J. Mech. Phys. Solids 57, 1718–1732 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hao, W., Tang, C., Yuan, Y., Yao, X., Ma, Y.: Experimental study on the fiber pull-out of composites using digital gradient sensing technique. Polym. Test. 41, 239–244 (2015)

    Article  Google Scholar 

  4. Lei, H., Zhu, X., Chen, H., Fan, H., Chen, M., Fang, D.: Macroscopic response of carbon-fiber pyramidal truss core panel taking account of local defect. Compos. Part B Eng. 79, 311–321 (2015)

    Article  Google Scholar 

  5. Zhang, D.D., Zhao, Q.L., Huang, Y.X., Li, F., Chen, H.S., Miao, D.S.: Flexural properties of a lightweight hybrid FRP-aluminum modular space truss bridge system. Compos. Struct. 108, 600–615 (2014)

    Article  Google Scholar 

  6. Li, F., Zhao, Q.L., Chen, H.S., Wang, J.Q., Duan, J.H.: Prediction of tensile capacity based on cohesive zone model of bond anchorage for fiber-reinforced polymer tendon. Compos. Struct. 92, 2400–2405 (2010)

    Article  Google Scholar 

  7. Yang, J., Li, H., Li, Z.: Approximate analytical solution for plane stress mode II crack interacting with an inclusion of any shape. Eur. J. Mech. A Solid. 49, 293–298 (2015)

    Article  Google Scholar 

  8. Tang, C.: Experimental investigation of the fiber bundle shielding effect on the dynamic matrix crack using optical caustic method. Polym. Test. 40, 46–53 (2014)

    Article  Google Scholar 

  9. Zhou, C., Li, Z.: The effect of T-stress on crack–inclusion interaction under mode I loading. Mech. Res. Commun. 34, 283–288 (2007)

    Article  MATH  Google Scholar 

  10. Yang, L., Chen, Q., Li, Z.: Crack-inclusion interaction for mode II crack analyzed by Eshelby equivalent inclusion method. Eng. Fract. Mech. 71, 1421–1433 (2004)

    Article  Google Scholar 

  11. Li, Z., Chen, Q.: Crack–inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method. Int. J. Fract. 118, 29–40 (2002)

    Article  Google Scholar 

  12. Yang, L., Li, Z.: The interaction of mode I crack with multi-inclusions in a three-phase model. Int. J. Fract. 127, 193–200 (2004)

    Article  MATH  Google Scholar 

  13. Li, Z., Sheng, Q., Sun, J.: A generally applicable approximate solution for mixed mode crack–inclusion interaction. Acta Mech. 187, 1–9 (2006)

    Article  MATH  Google Scholar 

  14. Li, H., Yang, J., Li, Z.: An approximate solution for the plane stress mode I crack interacting with an inclusion of arbitrary shape. Eng. Fract. Mech. 116, 190–196 (2014)

    Article  Google Scholar 

  15. Peng, B., Li, Z., Feng, M.: The mode I crack–inclusion interaction in orthotropic medium. Eng. Fract. Mech. 136, 185–194 (2015)

    Article  Google Scholar 

  16. Peng, B., Feng, M., Fan, J.: Study on the crack–inclusion interaction with coupled mechanical and thermal strains. Theor. Appl. Fract. Mech. 75, 39–43 (2015)

    Article  Google Scholar 

  17. Peng, B., Feng, M.: Study on the plane stress mode II crack–inclusion interaction with coupled mechanical and thermal strains. Arch. Appl. Mech. 85, 725–733 (2015)

    Article  Google Scholar 

  18. Zhou, K., Wei, R.: Modeling cracks and inclusions near surfaces under contact loading. Int. J. Mech. Sci. 83, 163–171 (2014)

    Article  Google Scholar 

  19. Wei, R., Zhou, K., Keer, L.M., Fan, Q.: Modeling surface pressure, interfacial stresses and stress intensity factors for layered materials containing multiple cracks and inhomogeneous inclusions under contact loading. Mech. Mater. 92, 8–17 (2016)

    Article  Google Scholar 

  20. Jajam, K.C., Tippur, H.V.: An experimental investigation of dynamic crack growth past a stiff inclusion. Eng. Fract. Mech. 78, 1289–1305 (2011)

    Article  Google Scholar 

  21. Jajam, K.C., Tippur, H.V.: Role of inclusion stiffness and interfacial strength on dynamic matrix crack growth: an experimental study. Int. J. Solids Struct. 49, 1127–1146 (2012)

    Article  Google Scholar 

  22. Savalia, P.C., Tippur, H.V.: A study of crack–inclusion interactions and matrix-inclusion debonding using moiré interferometry and finite element method. Exp. Mech. 47, 533–547 (2007)

    Article  Google Scholar 

  23. Savalia, P.C., Tippur, H.V., Kirugulige, M.S.: A numerical study of inclusion-matrix debonding in the presence of a nearby crack. Eng. Fract. Mech. 75, 926–942 (2008)

    Article  Google Scholar 

  24. Kitey, R., Tippur, H.V.: Dynamic crack growth past a stiff inclusion: optical investigation of inclusion eccentricity and inclusion-matrix adhesion strength. Exp. Mech. 48, 37–53 (2008)

    Article  Google Scholar 

  25. O’Toole, B.J., Santare, M.H.: Photoelastic investigation of crack–inclusion interaction. Exp. Mech. 30, 253–257 (1990)

    Article  Google Scholar 

  26. Hao, W., Tang, C., Yuan, Y., Ma, Y.: Photoelastic investigation of interaction between matrix crack and different shapes of inclusions. J. Test. Eval. 44, 1–9 (2016)

    Article  Google Scholar 

  27. Hao, W., Tang, C., Ma, Y.: Study on crack–inclusion interaction using digital gradient sensing method. Mech. Adv. Mater. Struct. 23, 845–852 (2016)

    Article  Google Scholar 

  28. Hao, W., Tang, C., Yuan, Y., Ma, Y.: Study on the effect of inclusion shape on crack–inclusion interaction using digital gradient sensing method. J. Adhes. Sci. Technol. 29, 2021–2034 (2015)

    Article  Google Scholar 

  29. Hao, W., Yao, X., Ma, Y., Yuan, Y.: Experimental study on interaction between matrix crack and fiber bundles using optical caustic method. Eng. Fract. Mech. 134, 354–367 (2015)

    Article  Google Scholar 

  30. Tang, C.: A study of crack-fiber interaction in fiber-reinforced composites using optical caustic method. Polym. Eng. Sci. 55, 852–857 (2015)

    Article  Google Scholar 

  31. Yao, X.F., Xu, W., Yeh, H.Y.: Investigation of crack tip evolution in functionally graded materials using optical caustics. Polym. Test. 26, 122–131 (2007)

    Article  Google Scholar 

  32. Xu, W., Yao, X.F., Xu, M.Q., Jin, G.C., Yeh, H.Y.: Fracture characterizations of V-notch tip in PMMA polymer material. Polym. Test. 23, 509–515 (2004)

    Article  Google Scholar 

  33. Yao, X.F., Xu, W., Xu, M.Q., Arakawa, K., Mada, T., Takahashi, K.: Experimental study of dynamic fracture behavior of PMMA with overlapping offset-parallel cracks. Polym. Test. 22, 663–670 (2003)

    Article  Google Scholar 

  34. Yao, X.F., Jin, G.C., Arakawa, K., Takahashi, K.: Experimental studies on dynamic fracture behavior of thin plates with parallel single edge cracks. Polym. Test. 21, 933–940 (2002)

    Article  Google Scholar 

  35. Papadopoulos, G.A.: New formula of experimental stress intensity factor evaluation by caustics. Int. J. Fract. 171, 79–84 (2011)

    Article  MATH  Google Scholar 

  36. Yao, X., Chen, J., Jin, G., Arakawa, K., Takahashi, K.: Caustic analysis of stress singularities in orthotropic composite materials with mode-I crack. Compos. Sci. Technol. 64, 917–924 (2004)

    Article  Google Scholar 

  37. Yao, X.F., Xu, W., Arakawa, K., Takahashi, K., Mada, T.: Dynamic optical visualization on the interaction between propagating crack and stationary crack. Opt. Laser Eng. 43, 195–207 (2005)

    Article  Google Scholar 

  38. Yao, X.F., Xu, W., Bai, S.L., Yeh, H.Y.: Caustics analysis of the crack initiation and propagation of graded materials. Compos. Sci. Technol. 68, 953–962 (2008)

    Article  Google Scholar 

  39. Yao, X.F., Xu, W.: Recent application of caustics on experimental dynamic fracture studies. Fatigue Fract. Eng. M. 34, 448–459 (2011)

    Article  Google Scholar 

  40. Yao, X.F., Xu, W., Xu, M.Q., Jin, G.C., Yeh, H.Y.: Caustic study on stress singularities in laminated composites under concentrated loads. Int. J. Solids Struct. 41, 3383–3393 (2004)

    Article  MATH  Google Scholar 

  41. Periasamy, C., Tippur, H.V.: Measurement of crack-tip and punch-tip transient deformations and stress intensity factors using Digital Gradient Sensing technique. Eng. Fract. Mech. 98, 185–199 (2013)

    Article  Google Scholar 

  42. Chen, H.S., Xia, Y., Zhou, G.Y., Fang, D.N.: Dynamic fracture toughness of piezoelectric ceramics. J. Am. Ceram. Soc. 96, 2036–2038 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the financial support provided by the National Natural Science Foundation of China (Grant Nos. 11502260, 11672279), Project funded by China Postdoctoral Science Foundation(Grant No. 2017M610300) and the Foundation for Advanced Talent of Jiangsu University (Grant No. 16JDG027).

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Authors and Affiliations

  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Guoqi Zhao, Wenfeng Hao, Xixuan Sheng & Yin Luo

  2. Beijing Key Laboratory of Aeronautical Materials Testing and Evaluation, Beijing Institute of Aeronautical Materials, Beijing, 100095, China

    Wenfeng Hao & Guangping Guo

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  1. Guoqi Zhao
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  2. Wenfeng Hao
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  3. Xixuan Sheng
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  5. Guangping Guo
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Correspondence to Wenfeng Hao or Yin Luo.

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Zhao, G., Hao, W., Sheng, X. et al. Study of the interaction of matrix crack with inclusions of different shapes using the method of caustic. Arch Appl Mech 87, 1427–1438 (2017). https://doi.org/10.1007/s00419-017-1261-x

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  • DOI: https://doi.org/10.1007/s00419-017-1261-x

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