Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part III: Compact tension specimens and wedge splitting specimens

This paper shows how the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un can be determined for concrete using CT-specimens and wedge splitting specimens. The experimental results collected from the fracture tests the very large size CT-specimens and small size wedge splitting specimens carried out by many researchers are utilized to investigate the characters of the obtained double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un . It was found that the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un determined from fracture tests on the large size CT-specimens are size-independent. And the values of K _Ic ⁱⁿⁱ and K _Ic ^un determined from small size wedge splitting specimens with same dimensions are independent of the relative preformed notch length a₀/D. However, when the dimensions of small size wedge splitting specimens change from 150×150×150 mm³ to 450×450×450 mm³, the values of K _Ic ⁱⁿⁱ and K _Ic ^un slightly depend on the heights of the specimens and do not depend on the thickness of the specimens.     

混凝土Ⅰ型裂缝扩展准则比较研究

采用小跨高比三点弯曲梁研究了混凝土的断裂性能。基于对跨高比为2.5和4的三点弯曲梁断裂参数计算公式的线性插值,给出了计算小跨高比三点弯曲梁断裂参数的公式。通过开展3种小跨高比三点弯曲梁试验及文献中的试验数据对该文公式进行了验证,结果表明：随试件高度从100 mm增大至200 mm,基于小跨高比三点弯曲梁所得的起裂断裂韧度基本保持不变,而失稳断裂韧度则逐渐增大,但增幅较小。该文所给公式计算所得的双K断裂参数与文献中已有方法所得结果基本相同。解析法得到的起裂断裂韧度与试验法所得结果吻合较好。通过对文献中的试验数据的分析,进一步验证了该文所给的方法可以用于研究小跨高比三点弯曲梁的断裂性能。     

Determination of double-Determination of double-K criterion for crack propagation in quasi-brittle fracture Part I: experimental investigation of crack propagation

The results of experimental investigations using laser speckle interferometry on small size three-point bending notched beams and using photoelastic coating and the strain gauges on very large size compact tension specimens of concrete are presented in detail. The investigations showed that there exists a stage of stable crack propagation before unstable fracture occurs. The results are in agreement with other researchers' investigations using moire interferometry, holographic interferometry, dye-impregnation method and microscope. Further detailed study shows that the three different states, i.e., crack initiation, stable crack propagation and unstable fracture can be distinguished in the fracture process in concrete structures. In order to predict the crack propagation during the fracture process in quasi-brittle materials a double-K criterion is proposed. The double-K criterion consists of two size-independent parameters. Both of them are expressed in terms of the stress intensity factors. One of them reflects the initial cracking toughness, denoted with Kⁱⁿⁱ, which can be directly evaluated by the initial cracking load, P_ini, and the precast crack length, a₀, using a formula of LEFM. The other one refers to the unstable fracture toughness, denoted with K^un, which can be obtained inserting the maximum load, P_max, and the effective crack length, a, into the same formula of LEFM. The values of the two parameters, K _Ic ⁱⁿⁱ and K _Ic ^un , obtained from the small size three-point bending notched beams and the large size compact tension specimens show that K _Ic ⁱⁿⁱ and K _Ic ^un are size-independent. Evaluating with the K-resistance curves obtained from the same test data, it is found that the proposed double-K criterion is equivalent to it in basic principle, but, the double-K criterion can be applied more easily than the K-resistance curve. Finally, as a practical example, the application of the double-K criterion to the prediction of the crack propagation in a concrete dam is discussed.     

A simplified method for determining double-K fracture parameters for three-point bending tests

A simplified method for determining the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un for three-point bending tests is proposed. Two empirical formulae are used to describe the crack mouth opening displacement CMOD and the stress intensity factor K _I ^c caused by the cohesive force (x) on the fictitious crack zone for three-point bending beams. It has been found that the two empirical formulae are accurate for a large practical region of a/D. Experiments carried out by many researchers showed that the new formula of CMOD for three-point bending beams can be directly used to predict the initial crack length for precracked beams, the notch depth and the critical effective crack length, as well as the crack length in the post-critical situation with a satisfactory accuracy. Further verification is demonstrated to determine the double-K parameters K _Ic ⁱⁿⁱ and K _Ic ^un. They are very close to those determined by the method proposed in our previous work. Using the simplified procedure, the experiments can be performed even without a closed-loop testing facility and the calculation can be carried out on a pocket calculator.