How to cite this paper
Fayed, A. (2018). Numerical evaluation of mode I/II SIF of quasi-brittle materials using cracked semi-circular bend specimen.Engineering Solid Mechanics, 6(2), 175-186.
Refrences
Abd-Elhady, A. (2013). Mixed mode I/II stress intensity factors through the thickness of disc type specimens. Engineering Solid Mechanics, 1(4), 119-128.
Akbardoost, J., & Ayatollahi, M. R. (2014). Experimental analysis of mixed mode crack propagation in brittle rocks: The effect of non-singular terms. Engineering Fracture Mechanics, 129, 77–89.
Akbardoost, J., Ayatollahi, M. R., Aliha, M. R. M., Pavier, M. J., & Smith, D. J. (2014). Size-dependent fracture behavior of Guiting limestone under mixed mode loading. International Journal of Rock Mechanics and Mining Sciences, 71, 369-380.
Alfano, M., Furgiuele, F., Leonardi, A., Maletta, C., & Paulino, G. H. (2009). Mode I fracture of adhesive joints using tailored cohesive zone models. International Journal of Fracture, 157(1–2), 193–204.
Aliha, M. R. M., Ayatollah, M. R., Smith, D. J., & Pavier, M. J. (2010). Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Engineering Fracture Mechanics, 77(11), 2200–2212.
Aliha, M. M., Behbahani, H., Fazaeli, H., & Rezaifar, M. H. (2014). Study of characteristic specification on mixed mode fracture toughness of asphalt mixtures. Construction and Building Materials, 54, 623-635.
Aliha, M. R. M., Bahmani, A., & Akhondi, S. (2016). Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens. European Journal of Mechanics, A/Solids, 58, 148–162.
Aliha, M. R. M., Heidari-Rarani, M., Shokrieh, M. M., & Ayatollahi, M. R. (2012). Experimental determination of tensile strength and K (IC) of polymer concretes using semi-circular bend(SCB) specimens. Structural Engineering and Mechanics, 43(6), 823-833.
Aliha, M. R. M., & Ayatollahi, M. R. (2013). Two-parameter fracture analysis of SCB rock specimen under mixed mode loading. Engineering Fracture Mechanics, 103, 115-123.
Aliha, M. R. M., & Saghafi, H. (2013). The effects of thickness and Poisson’s ratio on 3D mixed-mode fracture. Engineering Fracture Mechanics, 98, 15-28.
Aliha, M. R. M., & Fattahi Amirdehi, H. R. (2017). Fracture toughness prediction using Weibull statistical method for asphalt mixtures containing different air void contents. Fatigue & Fracture of Engineering Materials & Structures, 40(1), 55-68.
Aliha, M. R. M., Berto, F., Bahmani, A., & Gallo, P. (2017). Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion. Physical Mesomechanics, 20(2), 149-156.
Ameri, M., Mansourian, A., Pirmohammad, S., Aliha, M. R. M., & Ayatollahi, M. R. (2012). Mixed mode fracture resistance of asphalt concrete mixtures. Engineering Fracture Mechanics, 93, 153-167.
Ameri, M., Nowbakht, S., Molayem, M., & Aliha, M. R. M. (2016). Investigation of fatigue and fracture properties of asphalt mixtures modified with carbon nanotubes. Fatigue & fracture of engineering materials & structures, 39(7), 896-906.
Artamendi, I., & Khalid, H. A. (2006). A comparison between beam and semi-circular bending fracture tests for asphalt. Road Materials and Pavement Design, 7(sup1), 163-180.
Ayatollahi, M. R., & Aliha, M. R. M. (2007a). Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Computational materials science, 38(4), 660-670.
Ayatollahi, M. R., & Aliha, M. R. M. (2007b). Fracture toughness study for a brittle rock subjected to mixed mode I/II loading. International Journal of Rock Mechanics and Mining Sciences, 44(4), 617-624.
Ayatollahi, M. R., & Akbardoost, J. (2013). Size effects in mode II brittle fracture of rocks. Engineering Fracture Mechanics, 112–113, 165–180.
Ayatollahi, M. R., Aliha, M. R. M., & Hassani, M. M. (2006). Mixed mode brittle fracture in PMMA—an experimental study using SCB specimens. Materials Science and Engineering: A, 417(1), 348-356.
Ayatollahi, M. R., & Aliha, M. R. M. (2004). Fracture parameters for a cracked semi-circular specimen. International Journal of Rock Mechanics and Mining Sciences, 41(SUPPL. 1), 1–6.
Ayatollahi, M. R., & Aliha, M. R. M. (2006). On determination of mode II fracture toughness using semi-circular bend specimen. International Journal of Solids and Structures, 43(17), 5217–5227.
Ayatollahi, M. R., Aliha, M. R. M., & Saghafi, H. (2011). An improved semi-circular bend specimen for investigating mixed mode brittle fracture. Engineering Fracture Mechanics, 78(1), 110–123.
Chong, K. P., & Kuruppu, M. D. (1984). New specimen for fracture toughness determination for rock and other materials. International Journal of Fracture, 26(2).
Elghazel, A., Taktak, R., & Bouaziz, J. (2016). Combined numerical and experimental mechanical characterization of a calcium phosphate ceramic using modified Brazilian disc and SCB specimen. Materials Science and Engineering A, 670, 240–251.
Erdogan, F., & Sih, G. C. (1963). On the crack extension in plane loading and transverese shear. Journal Basic Engr., 85(4), 519–527.
Fakhri, M., Amoosoltani, E., & Aliha, M. R. M. (2017). Crack behavior analysis of roller compacted concrete mixtures containing reclaimed asphalt pavement and crumb rubber. Engineering Fracture Mechanics, 180, 43–59.
Fakhri, M., Kharrazi, E. H., Aliha, M. R. M., &Berto, F. (2018). The effect of loading rate on fracture energy of asphalt mixture at intermediate temperatures and under different loading modes. Frattura ed Integrità Strutturale, 12(43), 113-132.
Funatsu, T., Kuruppu, M., & Matsui, K. (2014). Effects of temperature and confining pressure on mixed-mode (I–II) and mode II fracture toughness of Kimachi sandstone. International Journal of Rock Mechanics and Mining Sciences, 67, 1-8.
Fathipour Azar, H., Choupani, N., Afshin, H., & Hamidzadeh Moghadam, R. (2015). Effect of mineral admixtures on the mixed-mode (I/II) fracture characterization of cement mortar: CTS, CSTBD and SCB specimens. Engineering Fracture Mechanics, 134, 20–34.
Fayed, A. S. (2002). Mixed mode crack tip deformation due to multi-axial cyclic loading. Ph.D. Thesis; Department of Mechanical Eng; Al-Azhar University; Cairo; Egypt;
Fayed, A. S. (2008). Size Effect of Asymmetric Four Point Bend Specimen on Crack Propagation in Ceramics. Ain Shams University , Faculty of Engineering Journal, 1(1), 227–237.
Fayed, A. S. (2017). Numerical analysis of mixed mode I/II stress intensity factors of edge slant cracked plates. Engineering Solid Mechanics, 5(1), 61–70.
Fayed, A. S., Sherbini, H. S., & Sallam, H. E. M. (2008). Crack Path in Steel Fiber Reinforced Concrete Composite under Mixed Mode. Ain Shams University , Faculty of Engineering Journal, 1(1), 17–26.
Fowell, R. J., Hudson, J. A., C., X., J., F. C., & X., Z. (1995). Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc (CCNBD) specimens. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 32(7), 322A.
Hammouda, M.M.I. & Fayed A.S. (2017). Modes I/II SIF of a diametrically compressed Brazilian disc having a central inclined crack with frictional surfaces. Fatigue Fract Eng Mater Struct; 1–13.
Hammouda, M. M. I., Fayed, A. S., & Sallam, H. E. M. (2002). Mode II stress intensity factors for central slant cracks with frictional surfaces in uniaxially compressed plates. International Journal of Fatigue, 24(12), 1213–1222.
Hammouda, M. M. I., Fayed, A. S., & Sallam, H. E. M. (2003a). Stress intensity factors of a shortly kinked slant central crack with frictional surfaces in uniaxially loaded plates. International Journal of Fatigue, 25(4), 283–298.
Hammouda, M. M. I., Fayed, A. S., & Sallam, H. E. M. (2003b). Simulation of mixed mode I/II cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces. International Journal of Fatigue, 25(8), 743–753.
Hammouda, M. M. I., Fayed, A. S., & Sallam, H. E. M. (2004). Stress intensity factors of a central slant crack with frictional surfaces in plates with biaxial loading. International Journal of Fracture, 129(2), 141–148.
Hammouda, M. M. I., Pasha, R. A., & Fayed, A. S. (2007). Modelling of cracking sites/development in axial dovetail joints of aero-engine compressor discs. International Journal of Fatigue, 29(1), 30-48.
Kataoka, M., Mahdavi, E., Funatsu, T., Takehara, T., Obara, Y., Fukui, K., & Hashiba, K. (2017). Estimation of Mode I Fracture Toughness of Rock by Semi-Circular Bend Test under Confining Pressure Condition. Procedia Engineering, 191, 886–893.
Kato, T., & Nishioka, T. (2005). Analysis of micro-macro material properties and mechanical effects of damaged material containing periodically distributed elliptical microcracks. International Journal of Fracture, 131(3), 247–266.
Ke, C. C., Chen, C. S., & Tu, C. H. (2008). Determination of fracture toughness of anisotropic rocks by boundary element method. Rock Mechanics and Rock Engineering, 41(4), 509–538.
Kuruppu, M. D., & Chong, K. P. (2012). Fracture toughness testing of brittle materials using semi-circular bend (SCB) specimen. Engineering Fracture Mechanics, 91, 133–150.
Lim, I. L., Johnston, I. W., & Choi, S. K. (1993). Stress intensity factors for semi-circular specimens under three-point bending. Engineering Fracture Mechanics, 44(3), 363–382.
Lim, I. L., Johnston, I. W., Choi, S. K., & Boland, J. N. (1994). Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 1-mode I. International Journal of Rock Mechanics and Mining Sciences and, 31(3), 185–197.
Mirsayar, M., Shi, X., & Zollinger, D. (2017). Evaluation of interfacial bond strength between Portland cement concrete and asphalt concrete layers using bi-material SCB test specimen. Engineering Solid Mechanics, 5(4), 293-306.
Rashidi Moghaddam, M., Ayatollahi, M. R., & Berto, F. (2017). Mixed mode fracture analysis using generalized averaged strain energy density criterion for linear elastic materials. International Journal of Solids and Structures, 120, 1339–1351.
Roy, D. G., Singh, T. N., Kodikara, J., & Das, R. (2017a). Effect of water saturation on the fracture and mechanical properties of sedimentary rocks. Rock Mechanics and Rock Engineering, 50(10), 2585-2600.
Roy, D. G., Singh, T. N., & Kodikara, J. (2017b). Influence of joint anisotropy on the fracturing behavior of a sedimentary rock. Engineering Geology, 228, 224-237.
Razmi, A., & Mirsayar, M. M. (2017). On the mixed mode I/II fracture properties of jute fiber-reinforced concrete. Construction and Building Materials, 148, 512–520.
Saghafi, H., Zucchelli, A., & Minak, G. (2013). Evaluating fracture behavior of brittle polymeric materials using an IASCB specimen. Polymer Testing, 32(1), 133–140.
Wei, M. D., Dai, F., Xu, N. W., Liu, J. F., & Xu, Y. (2016). Experimental and Numerical Study on the Cracked Chevron Notched Semi-Circular Bend Method for Characterizing the Mode I Fracture Toughness of Rocks. Rock Mechanics and Rock Engineering, 49(5), 1595–1609.
Wei, M. D., Dai, F., Xu, N. W., Liu, Y., & Zhao, T. (2017a). Fracture prediction of rocks under mode I and mode II loading using the generalized maximum tangential strain criterion. Engineering Fracture Mechanics, 186, 21-38.
Wei, M. D., Dai, F., Xu, N. W., Zhao, T., & Liu, Y. (2017b). An experimental and theoretical assessment of semi-circular bend specimens with chevron and straight-through notches for mode I fracture toughness testing of rocks. International Journal of Rock Mechanics and Mining Sciences, 99, 28-38.
Whittaker, B. N., Singh, R. N., & Sun, G. (1992). Rock fracture mechanics : principles, design, and applications. Elsevier.
Yoshihara, H., & Kawamura, T. (2006). Mode I fracture toughness estimation of wood by DCB test. Composites Part A: Applied Science and Manufacturing, 37(11), 2105–2113.
Zhang, Z. X. (2002). An empirical relation between mode I fracture toughness and the tensile strength of rock. International Journal of Rock Mechanics and Mining Sciences, 39(3), 401–406.
Zhou, Y. X., Xia, K., Li, X. B., Li, H. B., Ma, G. W., Zhao, J., … Dai, F. (2012). Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials. International Journal of Rock Mechanics and Mining Sciences, 49, 105–112.
Akbardoost, J., & Ayatollahi, M. R. (2014). Experimental analysis of mixed mode crack propagation in brittle rocks: The effect of non-singular terms. Engineering Fracture Mechanics, 129, 77–89.
Akbardoost, J., Ayatollahi, M. R., Aliha, M. R. M., Pavier, M. J., & Smith, D. J. (2014). Size-dependent fracture behavior of Guiting limestone under mixed mode loading. International Journal of Rock Mechanics and Mining Sciences, 71, 369-380.
Alfano, M., Furgiuele, F., Leonardi, A., Maletta, C., & Paulino, G. H. (2009). Mode I fracture of adhesive joints using tailored cohesive zone models. International Journal of Fracture, 157(1–2), 193–204.
Aliha, M. R. M., Ayatollah, M. R., Smith, D. J., & Pavier, M. J. (2010). Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Engineering Fracture Mechanics, 77(11), 2200–2212.
Aliha, M. M., Behbahani, H., Fazaeli, H., & Rezaifar, M. H. (2014). Study of characteristic specification on mixed mode fracture toughness of asphalt mixtures. Construction and Building Materials, 54, 623-635.
Aliha, M. R. M., Bahmani, A., & Akhondi, S. (2016). Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens. European Journal of Mechanics, A/Solids, 58, 148–162.
Aliha, M. R. M., Heidari-Rarani, M., Shokrieh, M. M., & Ayatollahi, M. R. (2012). Experimental determination of tensile strength and K (IC) of polymer concretes using semi-circular bend(SCB) specimens. Structural Engineering and Mechanics, 43(6), 823-833.
Aliha, M. R. M., & Ayatollahi, M. R. (2013). Two-parameter fracture analysis of SCB rock specimen under mixed mode loading. Engineering Fracture Mechanics, 103, 115-123.
Aliha, M. R. M., & Saghafi, H. (2013). The effects of thickness and Poisson’s ratio on 3D mixed-mode fracture. Engineering Fracture Mechanics, 98, 15-28.
Aliha, M. R. M., & Fattahi Amirdehi, H. R. (2017). Fracture toughness prediction using Weibull statistical method for asphalt mixtures containing different air void contents. Fatigue & Fracture of Engineering Materials & Structures, 40(1), 55-68.
Aliha, M. R. M., Berto, F., Bahmani, A., & Gallo, P. (2017). Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion. Physical Mesomechanics, 20(2), 149-156.
Ameri, M., Mansourian, A., Pirmohammad, S., Aliha, M. R. M., & Ayatollahi, M. R. (2012). Mixed mode fracture resistance of asphalt concrete mixtures. Engineering Fracture Mechanics, 93, 153-167.
Ameri, M., Nowbakht, S., Molayem, M., & Aliha, M. R. M. (2016). Investigation of fatigue and fracture properties of asphalt mixtures modified with carbon nanotubes. Fatigue & fracture of engineering materials & structures, 39(7), 896-906.
Artamendi, I., & Khalid, H. A. (2006). A comparison between beam and semi-circular bending fracture tests for asphalt. Road Materials and Pavement Design, 7(sup1), 163-180.
Ayatollahi, M. R., & Aliha, M. R. M. (2007a). Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Computational materials science, 38(4), 660-670.
Ayatollahi, M. R., & Aliha, M. R. M. (2007b). Fracture toughness study for a brittle rock subjected to mixed mode I/II loading. International Journal of Rock Mechanics and Mining Sciences, 44(4), 617-624.
Ayatollahi, M. R., & Akbardoost, J. (2013). Size effects in mode II brittle fracture of rocks. Engineering Fracture Mechanics, 112–113, 165–180.
Ayatollahi, M. R., Aliha, M. R. M., & Hassani, M. M. (2006). Mixed mode brittle fracture in PMMA—an experimental study using SCB specimens. Materials Science and Engineering: A, 417(1), 348-356.
Ayatollahi, M. R., & Aliha, M. R. M. (2004). Fracture parameters for a cracked semi-circular specimen. International Journal of Rock Mechanics and Mining Sciences, 41(SUPPL. 1), 1–6.
Ayatollahi, M. R., & Aliha, M. R. M. (2006). On determination of mode II fracture toughness using semi-circular bend specimen. International Journal of Solids and Structures, 43(17), 5217–5227.
Ayatollahi, M. R., Aliha, M. R. M., & Saghafi, H. (2011). An improved semi-circular bend specimen for investigating mixed mode brittle fracture. Engineering Fracture Mechanics, 78(1), 110–123.
Chong, K. P., & Kuruppu, M. D. (1984). New specimen for fracture toughness determination for rock and other materials. International Journal of Fracture, 26(2).
Elghazel, A., Taktak, R., & Bouaziz, J. (2016). Combined numerical and experimental mechanical characterization of a calcium phosphate ceramic using modified Brazilian disc and SCB specimen. Materials Science and Engineering A, 670, 240–251.
Erdogan, F., & Sih, G. C. (1963). On the crack extension in plane loading and transverese shear. Journal Basic Engr., 85(4), 519–527.
Fakhri, M., Amoosoltani, E., & Aliha, M. R. M. (2017). Crack behavior analysis of roller compacted concrete mixtures containing reclaimed asphalt pavement and crumb rubber. Engineering Fracture Mechanics, 180, 43–59.
Fakhri, M., Kharrazi, E. H., Aliha, M. R. M., &Berto, F. (2018). The effect of loading rate on fracture energy of asphalt mixture at intermediate temperatures and under different loading modes. Frattura ed Integrità Strutturale, 12(43), 113-132.
Funatsu, T., Kuruppu, M., & Matsui, K. (2014). Effects of temperature and confining pressure on mixed-mode (I–II) and mode II fracture toughness of Kimachi sandstone. International Journal of Rock Mechanics and Mining Sciences, 67, 1-8.
Fathipour Azar, H., Choupani, N., Afshin, H., & Hamidzadeh Moghadam, R. (2015). Effect of mineral admixtures on the mixed-mode (I/II) fracture characterization of cement mortar: CTS, CSTBD and SCB specimens. Engineering Fracture Mechanics, 134, 20–34.
Fayed, A. S. (2002). Mixed mode crack tip deformation due to multi-axial cyclic loading. Ph.D. Thesis; Department of Mechanical Eng; Al-Azhar University; Cairo; Egypt;
Fayed, A. S. (2008). Size Effect of Asymmetric Four Point Bend Specimen on Crack Propagation in Ceramics. Ain Shams University , Faculty of Engineering Journal, 1(1), 227–237.
Fayed, A. S. (2017). Numerical analysis of mixed mode I/II stress intensity factors of edge slant cracked plates. Engineering Solid Mechanics, 5(1), 61–70.
Fayed, A. S., Sherbini, H. S., & Sallam, H. E. M. (2008). Crack Path in Steel Fiber Reinforced Concrete Composite under Mixed Mode. Ain Shams University , Faculty of Engineering Journal, 1(1), 17–26.
Fowell, R. J., Hudson, J. A., C., X., J., F. C., & X., Z. (1995). Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc (CCNBD) specimens. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 32(7), 322A.
Hammouda, M.M.I. & Fayed A.S. (2017). Modes I/II SIF of a diametrically compressed Brazilian disc having a central inclined crack with frictional surfaces. Fatigue Fract Eng Mater Struct; 1–13.
Hammouda, M. M. I., Fayed, A. S., & Sallam, H. E. M. (2002). Mode II stress intensity factors for central slant cracks with frictional surfaces in uniaxially compressed plates. International Journal of Fatigue, 24(12), 1213–1222.
Hammouda, M. M. I., Fayed, A. S., & Sallam, H. E. M. (2003a). Stress intensity factors of a shortly kinked slant central crack with frictional surfaces in uniaxially loaded plates. International Journal of Fatigue, 25(4), 283–298.
Hammouda, M. M. I., Fayed, A. S., & Sallam, H. E. M. (2003b). Simulation of mixed mode I/II cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces. International Journal of Fatigue, 25(8), 743–753.
Hammouda, M. M. I., Fayed, A. S., & Sallam, H. E. M. (2004). Stress intensity factors of a central slant crack with frictional surfaces in plates with biaxial loading. International Journal of Fracture, 129(2), 141–148.
Hammouda, M. M. I., Pasha, R. A., & Fayed, A. S. (2007). Modelling of cracking sites/development in axial dovetail joints of aero-engine compressor discs. International Journal of Fatigue, 29(1), 30-48.
Kataoka, M., Mahdavi, E., Funatsu, T., Takehara, T., Obara, Y., Fukui, K., & Hashiba, K. (2017). Estimation of Mode I Fracture Toughness of Rock by Semi-Circular Bend Test under Confining Pressure Condition. Procedia Engineering, 191, 886–893.
Kato, T., & Nishioka, T. (2005). Analysis of micro-macro material properties and mechanical effects of damaged material containing periodically distributed elliptical microcracks. International Journal of Fracture, 131(3), 247–266.
Ke, C. C., Chen, C. S., & Tu, C. H. (2008). Determination of fracture toughness of anisotropic rocks by boundary element method. Rock Mechanics and Rock Engineering, 41(4), 509–538.
Kuruppu, M. D., & Chong, K. P. (2012). Fracture toughness testing of brittle materials using semi-circular bend (SCB) specimen. Engineering Fracture Mechanics, 91, 133–150.
Lim, I. L., Johnston, I. W., & Choi, S. K. (1993). Stress intensity factors for semi-circular specimens under three-point bending. Engineering Fracture Mechanics, 44(3), 363–382.
Lim, I. L., Johnston, I. W., Choi, S. K., & Boland, J. N. (1994). Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 1-mode I. International Journal of Rock Mechanics and Mining Sciences and, 31(3), 185–197.
Mirsayar, M., Shi, X., & Zollinger, D. (2017). Evaluation of interfacial bond strength between Portland cement concrete and asphalt concrete layers using bi-material SCB test specimen. Engineering Solid Mechanics, 5(4), 293-306.
Rashidi Moghaddam, M., Ayatollahi, M. R., & Berto, F. (2017). Mixed mode fracture analysis using generalized averaged strain energy density criterion for linear elastic materials. International Journal of Solids and Structures, 120, 1339–1351.
Roy, D. G., Singh, T. N., Kodikara, J., & Das, R. (2017a). Effect of water saturation on the fracture and mechanical properties of sedimentary rocks. Rock Mechanics and Rock Engineering, 50(10), 2585-2600.
Roy, D. G., Singh, T. N., & Kodikara, J. (2017b). Influence of joint anisotropy on the fracturing behavior of a sedimentary rock. Engineering Geology, 228, 224-237.
Razmi, A., & Mirsayar, M. M. (2017). On the mixed mode I/II fracture properties of jute fiber-reinforced concrete. Construction and Building Materials, 148, 512–520.
Saghafi, H., Zucchelli, A., & Minak, G. (2013). Evaluating fracture behavior of brittle polymeric materials using an IASCB specimen. Polymer Testing, 32(1), 133–140.
Wei, M. D., Dai, F., Xu, N. W., Liu, J. F., & Xu, Y. (2016). Experimental and Numerical Study on the Cracked Chevron Notched Semi-Circular Bend Method for Characterizing the Mode I Fracture Toughness of Rocks. Rock Mechanics and Rock Engineering, 49(5), 1595–1609.
Wei, M. D., Dai, F., Xu, N. W., Liu, Y., & Zhao, T. (2017a). Fracture prediction of rocks under mode I and mode II loading using the generalized maximum tangential strain criterion. Engineering Fracture Mechanics, 186, 21-38.
Wei, M. D., Dai, F., Xu, N. W., Zhao, T., & Liu, Y. (2017b). An experimental and theoretical assessment of semi-circular bend specimens with chevron and straight-through notches for mode I fracture toughness testing of rocks. International Journal of Rock Mechanics and Mining Sciences, 99, 28-38.
Whittaker, B. N., Singh, R. N., & Sun, G. (1992). Rock fracture mechanics : principles, design, and applications. Elsevier.
Yoshihara, H., & Kawamura, T. (2006). Mode I fracture toughness estimation of wood by DCB test. Composites Part A: Applied Science and Manufacturing, 37(11), 2105–2113.
Zhang, Z. X. (2002). An empirical relation between mode I fracture toughness and the tensile strength of rock. International Journal of Rock Mechanics and Mining Sciences, 39(3), 401–406.
Zhou, Y. X., Xia, K., Li, X. B., Li, H. B., Ma, G. W., Zhao, J., … Dai, F. (2012). Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials. International Journal of Rock Mechanics and Mining Sciences, 49, 105–112.