The Shape Change Energy Criterion of Iso-σθεθ Line for Mixed Mode Crack and the Application in Concrete

Abstract:

In order to study the concrete compound crack and fracture extension problem such as brittle material, based on the analysis of the fracture criterion theory ,on the analysis of some measured data, and the near crack tip portion of the shape change energy, the strain energy criterion of Iso- line for Ⅰ-Ⅱ mixed mode crack was proposed, a crack initiation angle formula and the fracture criterion were established, and the variation law among ， with Poisson ratio was discussed . Using the criterion, the concrete compound crack was analyzed. Results show that the theoretical values are consistent with the measured values. So the criterion can be applied to analyze the mixed mode crack fracture of brittle material such as concrete.

• Periodical: Applied Mechanics and Materials (Volumes 253-255)
• Pages: 512-517
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.253-255.512
• Online since: December 2012
• Authors: Si Li Chen, Huang Jie, Jian Jun Shi, Yu Tao
• Keywords: Brittle Fracture, Concrete, Fracture Criterion, Mixed Mode Crack, Shape Change Energy

References

[7] Measured Reference

[8] Reference

[9] Reference

[10] θ0/(°) -70.5 -65.03 -78.46 -68.06 -67.51 -57.9 -62.6 -64.3 KIIC/KIC 0.87 0.644 1.074 0.736 0.787 0.68 0.65 0.95 Tab.2 The analysis of different v 0 0.1 0.167 0.2 0.24 0.3 0.35 0.4 θ0/(°) -70.52 -69.23 -68.44 -68.06 -67.62 -66.98 -66.48 -65.99 KIIC/KIC 0.782 0.761 0.745 0.736 0.725 0.705 0.687 0.665 As shown in Table 1 and 2, the crack angle and fracture toughness ratio of pure ModeII are located in among several other theories, and close to the measured values. The and KIIC/KIC reduce with an increase of. The theory values of critical fracture curve compared with the measured values Relationship of mixed mode fracture andcan be obtained by equation (15): (18) Now the values of mixed mode fracture and derived from formula (18) are plotted in Figure 1, in order to facilitate comparative analysis, and has been on the concreteI-II mixed mode fracture criterion and a large number of experimental studies testing the values drawing in Figure 1 together. It can be seen from the figure that this theory are very close to the tensile strain theory and experimental data. Fig.1 The curve of fracture criterion Conclusions Based on the analysis of the fracture criterion theory and some experiment data, the area fracture criterion of Iso- line for mixed mode crack was proposed, the formulas were easy to be derived and convenient to apply. The results showed that the crack angle and fracture toughness ratio of pure Mode II are located in among several other theories. The and KIIC/KIC reduce with an increase of . The predictive value and the experimental value are basically consistent. So the criterion can be applied to analyze the mixed mode crack fracture of brittle material such as concrete. Acknowledgement This work was financially supported by the Department 0f education Liaoning Province Foundation (L2010393) References

[1] F. Erdogan ,G. C. Sih. On crack extension in plates under plane loading and transverse shear [J]. Trans. ASME., Journal of Basic Engng, vol.85 (1963) p.519~527

DOI: 10.1115/1.3656898

[2] G. C. Sih. Energy-density concept in fracture mechanics [J].Engng. Fracture Mech., vol.5 (1973) p.1037~1040.

DOI: 10.1016/0013-7944(73)90072-6

[3] Sili Chen. The strain energy criterion of Iso-W line for mixed mode crack. Journal of Shenyang University of Technology, vol. 3 (1992) pp.65-68.(in Chinese)

[4] Dongxia Li, Pengcheng Feng. a Analysis of the shape change energy criterion forI-II mixed mode crack, Journal of Zhongyuan University of Technology,vol.6 (2008) p.52~54(in Chinese)

[5] Yuchuan Jiang, Shuangwu Xu, Hui Chen. Mixed mode crack in brittle material fracture criterion, Engineering Mechanics, vol.4 (2008) pp.50-54(in Chinese)

[6] Jin Cheng, Shushan Zhao. Fracture Mechanics. Science Press (2006) (in Chinese)

[7] Sili Chen, Kun Qu, Jianjun Shi, et al. The strain-energy criterion of Iso-σqeq line for mixed mode crack in concrete, Vol. 250-253(2011) pp.50-57

DOI: 10.4028/www.scientific.net/amr.250-253.50

[8] Daoyuan Xu, Xiaoling Fu. Testing research the fracture criterion of concrete I-II mixed mode crack determined by four-point shear test. Journal of Hydraulic Engineering,vol.9 (1984)p.63~69.

[9] Daoyuan Xu, Zhengping Liang, Dejun Wang, et al. Testing research the critical fracture curves of concrete K_(Ic), K_(IIc) and I-II mixed mode crack. Concrete and aerated Concrete, vol.6 (1983) p.33~36. (in Chinese)

[10] Daoyuan Xu, Zhengping Liang, Dejun Wang, et al. Discussion of Concrete I-II mixed mode fracture criterion. Journal of Hydraulic Engineering, vol.6 (1982) p.57~61. (in Chinese)