Science China Technological Sciences

, Volume 61, Issue 12, pp 1872–1881 | Cite as

Experimental investigation on the cracking behavior of 3D printed kinked fissure

  • GuoWei MaEmail author
  • QianQian Dong
  • Li Wang


Uniaxial compression tests were carried out for 3D printed samples having various types of kinked fissures by using the rock mechanics servo-controlled testing system. Photo-elastic technique is adopted to characterize and visualize the stress distribution and evolution of 3D printed models subjected to vertical compression. The stress field in the loading process can clearly be captured via a high-speed camera. The results showed that fringes around the kinked fissure tips formed a central symmetrical interference fringe pattern, and failure firstly occurred at interference fringe of highest order. Two failure types i.e. tip-cracking and non-tip-cracking are categorized on the basis of crack propagation pattern of 3D printed samples. Tensile crack propagation of wing cracks is the main form of failure of the antisymmetric kinked fissures, but the inclination of the branch fissures also played a key role on the location of initial fracture. The finite element method was applied to numerically simulate the process of crack propagation. The isochromatic fringe patterns are in good agreement with the experimental investigation. The current work gives an insight for implication of advanced technique to quantify and visualize the distribution of stress field, and provides further understanding of kinked fissure behavior at failure.


kinked fissure 3D printing cracking behavior stress field non-tip-cracking photo-elasticity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chen Y Z. Stress intensity factors for curved and kinked cracks in plane extension. Theor Appl Fract Mech, 1999, 31: 223–232CrossRefGoogle Scholar
  2. 2.
    Carpinteri A, Spagnoli A, Vantadori S, et al. Influence of the crack morphology on the fatigue crack growth rate: A continuously-kinked crack model based on fractals. Eng Fract Mech, 2008, 75: 579–589CrossRefGoogle Scholar
  3. 3.
    Chen B, Dillard D A, Dillard J G, et al. Crack path selection in adhesively bonded joints: The roles of external loads and specimen geometry. Int J Fract, 2002, 114: 167–190CrossRefGoogle Scholar
  4. 4.
    Brace W F, Bombolakis E G. A note on brittle crack growth in compression. J Geophys Res, 1963, 68: 3709–3713CrossRefGoogle Scholar
  5. 5.
    Isida M, Noguchi H. Stress intensity factors at tips of branched cracks under various loadings. Int J Fract, 1992, 54: 293–316CrossRefGoogle Scholar
  6. 6.
    Meggiolaro M A, Miranda A C O, Castro J T P, et al. Stress intensity factor equations for branched crack growth. Eng Fract Mech, 2005, 72: 2647–2671CrossRefGoogle Scholar
  7. 7.
    Nairn J A. The strain energy release rate of composite microcracking: A variational approach. J Compos Mater, 1989, 23: 1106–1129CrossRefGoogle Scholar
  8. 8.
    Wu C H. Elasticity problems of a slender Z-crack. J Elasticity, 1978, 8: 183–205MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Nuismer R J. An energy release rate criterion for mixed mode fracture. Int J Fract, 1975, 11: 245–250CrossRefGoogle Scholar
  10. 10.
    Gao H, Cheng-Hsin C. Slightly curved or kinked cracks in anisotropic elastic solids. Int J Solids Struct, 1992, 29: 947–972CrossRefzbMATHGoogle Scholar
  11. 11.
    Nemat-Nasser S, Horii H. Compression-induced nonplanar crack extension with application to splitting, exfoliation, and rockburst. J Geophys Res, 1982, 87: 6805–6821CrossRefGoogle Scholar
  12. 12.
    Yang S Q, Jiang Y Z, Xu W Y, et al. Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression. Int J Solids Struct, 2008, 45: 4796–4819CrossRefzbMATHGoogle Scholar
  13. 13.
    Yang S Q, Jing H W. Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. Int J Fract, 2011, 168: 227–250CrossRefGoogle Scholar
  14. 14.
    Wong L N Y, Einstein H H. Crack coalescence in molded gypsum and carrara marble: Part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng, 2009, 42: 475–511CrossRefGoogle Scholar
  15. 15.
    Huang D, Jin H H, Huang R Q. Mechanism of fracture mechanics and physical model test of rocks crack expanding under tension-shear stress (in Chinese). Rock Soil Mech, 2011, 32: 997–1002Google Scholar
  16. 16.
    Yang S Q, Huang Y H, Tian W L, et al. An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression. Eng Geol, 2017, 217: 35–48CrossRefGoogle Scholar
  17. 17.
    Fan L F, Wu Z J, Wan Z, et al. Experimental investigation of thermal effects on dynamic behavior of granite. Appl Thermal Eng, 2017, 125: 94–103CrossRefGoogle Scholar
  18. 18.
    Jiang C, Zhao G F. A preliminary study of 3D printing on rock mechanics. Rock Mech Rock Eng, 2015, 48: 1041–1050CrossRefGoogle Scholar
  19. 19.
    Buckberry C, Towers D. New approaches to the full-field analysis of photoelastic stress patterns. Opt Lasers Eng, 1996, 24: 415–428CrossRefGoogle Scholar
  20. 20.
    Pinit P, Umezaki E. Digitally whole-field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique. Opt Lasers Eng, 2007, 45: 795–807CrossRefGoogle Scholar
  21. 21.
    Baldi A, Bertolino F, Ginesu F. A temporal phase unwrapping algorithm for photoelastic stress analysis. Opt Lasers Eng, 2007, 45: 612–617CrossRefGoogle Scholar
  22. 22.
    Lee H, Jeon S. An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int J Solids Struct, 2011, 48: 979–999CrossRefzbMATHGoogle Scholar
  23. 23.
    Ju Y, Xie H, Zheng Z, et al. Visualization of the complex structure and stress field inside rock by means of 3D printing technology. Chin Sci Bull, 2014, 59: 5354–5365CrossRefGoogle Scholar
  24. 24.
    Shi Y, Wang Y, Cai M, et al. An aviation oxygen supply system based on a mechanical ventilation model. Chin J Aeron, 2017Google Scholar
  25. 25.
    Niu J, Shi Y, Cai M, et al. Detection of sputum by interpreting the time-frequency distribution of respiratory sound signal using image processing techniques. Bioinformatics, 2017, 38Google Scholar
  26. 26.
    Ma G W, Wang H D, Fan L F, et al. Simulation of two-phase flow in horizontal fracture networks with numerical manifold method. Adv Water Resour, 2017, 108: 293–309CrossRefGoogle Scholar
  27. 27.
    Niu J L, Shi Y, Cao Z X, et al. Study on air flow dynamic char-acteristic of mechanical ventilation of a lung simulator. Sci China Tech Sci, 2017, 60: 243–250CrossRefGoogle Scholar
  28. 28.
    Tang C A, Liu H, Lee P K K, et al. Numerical studies of the influence of microstructure on rock failure in uniaxial compression—Part I: Effect of heterogeneity. Int J Rock Mech Min Sci, 2000, 37: 555–569CrossRefGoogle Scholar
  29. 29.
    Vásárhelyi B, Bobet A. Modeling of crack initiation, propagation and coalescence in uniaxial compression. Rock Mech Rock Eng, 2000, 33: 119–139CrossRefGoogle Scholar
  30. 30.
    Wu Z, Fan L, Liu Q, et al. Micro-mechanical modeling of the macromechanical response and fracture behavior of rock using the numerical manifold method. Eng Geol, 2017, 225: 49–60CrossRefGoogle Scholar
  31. 31.
    Zhou X, Fan L, Wu Z. Effects of microfracture on wave propagation through rock mass. Int J Geomech, 2017, 17Google Scholar
  32. 32.
    Fan L F, Yi X W, Ma G W. Numerical manifold method (NMM) simulation of stress wave propagation through fractured rock mass. Int J Appl Mech, 2013, 05: 1350022CrossRefGoogle Scholar
  33. 33.
    Garg S, Pant M. Numerical simulation of thermal fracture in functionally graded materials using element-free Galerkin method. Sādhanā-Acad Proc Eng Sci, 2017, 42: 417–431MathSciNetzbMATHGoogle Scholar
  34. 34.
    Garg S, Pant M. Numerical simulation of adiabatic and isothermal cracks in functionally graded materials using optimized element-free Galerkin method. J Thermal Stresses, 2017, 40: 846–865CrossRefGoogle Scholar
  35. 35.
    Pant M, Singh I V, Mishra B K. Evaluation of mixed mode stress intensity factors for interface cracks using EFGM. Appl Math Model, 2011, 35: 3443–3459MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Pant M, Singh I V, Mishra B K. A novel enrichment criterion for modeling kinked cracks using element free Galerkin method. Int J Mech Sci, 2013, 68: 140–149CrossRefGoogle Scholar
  37. 37.
    Pant M, Bhattacharya S. Fatigue crack growth analysis of functionally graded materials by EFGM and XFEM. Int J Comput Methods, 2016, 14: 1750004MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Zi G, Song J H, Budyn E, et al. A method for growing multiple cracks without remeshing and its application to fatigue crack growth. Model Simul Mater Sci Eng, 2004, 12: 901–915CrossRefGoogle Scholar
  39. 39.
    Ramesh K, Tamrakar D K. Improved determination of retardation in digital photoelasticity by load stepping. Opt Lasers Eng, 2000, 33: 387–400CrossRefGoogle Scholar
  40. 40.
    Prasad V S, Madhu K R, Ramesh K. Towards effective phase unwrapping in digital photoelasticity. Opt Lasers Eng, 2004, 42: 421–436CrossRefGoogle Scholar
  41. 41.
    Ajovalasit A, Zuccarello B. Limitation of Fourier transform photoelasticity: Influence of isoclinics. Exp Mech, 2000, 40: 384–392CrossRefGoogle Scholar
  42. 42.
    Bobet A, Einstein H H. Numerical modeling of fracture coalescence in a model rock material. Int J Fract, 1998, 92: 221–252CrossRefGoogle Scholar
  43. 43.
    Lajtai E Z. Brittle fracture in compression. Int J Fract, 1974, 10: 525–536CrossRefGoogle Scholar
  44. 44.
    Poston T, Stewart I, Plaut R H. Catastrophe theory and its applications. Pitman, 1978, 21: 572–573zbMATHGoogle Scholar
  45. 45.
    Sanford R J. Application of the least-squares method to photoelastic analysis. Exp Mech, 1980, 20: 192–197CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Architecture and Civil EngineeringBeijing University of TechnologyBeijingChina
  2. 2.School of Civil and Transportation EngineeringHebei University of TechnologyTianjinChina

Personalised recommendations