Critical Effective Crack Length Research Articles

The Series <i>K</i> Criterion of Unstable Fracture of Concrete and its Application

The knowledge from extensive investigations showed that the non-linearity of the load and loading point displacement curve is mainly associated with crack propagation. Based on the linear asymptotic superposition assumption, the critical effective crack length is evaluated by analyzing the nonlinear characteristics of the load and loading point displacement curves of a series of the fracture tests. Furthermore, the unstable fracture toughness is determined by inserting the peak load and the critical effective crack length into a formula developed from LEFM. Based on the calculated results, the series K criterion of unstable fracture of concrete fracture is established. At last, an engineering example of cracking analysis of the upstream lock-head foundation of the ship-lift of the Three Gorges Project is given.

An analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams

An analytical model to predict the effective fracture toughness K IC s of concrete was proposed based on the fictitious crack model. Firstly, the equilibrium equations of forces in the section were formed in combination with the plane section assumption. Then a Lagrange function was presented through the equilibrium equations and the relationship formula between the effective crack length and crack tip opening displacement. Taking into account Lagrange Multiplier Method, the maximum load P max was obtained, as well as the critical effective crack length a c. Furthermore, K IC s was gained in an analytical manner. Subsequently, some material and structural parameters from other literatures were adopted into the proposed model for the calculation. Compared with the experimental results, most of the calculated values show a good agreement for P max and a c. In order to study the influence of the softening curve in the fictitious crack on the calculated fracture parameters, three series of constants determining the shape of the softening curve were chosen in the calculation. The results show that the calculated fracture parameters are not sensitive to the shape of the softening curve. Therefore, only if the elastic modulus E c and flexural tensile strength f r were measured, P max, a c and K IC s can be predicted accurately using the proposed model. Finally, the variations of the calculated fracture parameters with the specimen size and a 0/ h (i.e., the ratio of the initial crack length to the depth of the specimen) were studied. It was found that both K IC s and the pre-critical crack propagation length Δ a c increase with the specimen size. However, the two parameters increase to the maximums and then decrease gradually with a 0/ h. Moreover, the theories of free surface effect were utilized to explain the observed size effects.

The fracture and fatigue performance in flexure of carbon fiber reinforced concrete

The fracture parameters and fatigue performances of carbon fiber reinforced concrete is investigated by three point bending tests. In comparison with the results of quasi-static tests where no pre-cyclic loading is applied, the influence of pre-cyclic loading history on fracture parameters was researched by using compliance calibration. The test results show that the fracture parameters of carbon fiber reinforced concrete and plain concrete will be reduced if the pre-cyclic loading stress levels are higher than a certain threshold, and this threshold value for carbon fiber reinforced concrete is higher than that of plain concrete. The critical effective crack length for carbon fiber reinforced concrete is significantly larger than that of plain concrete and independent of the pre-cyclic loading history and fatigue life. Carbon fiber reinforced concrete has a considerable beneficial effect on the behaviour of concrete subjected to flexure fatigue loading.

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 σ(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.

Determination of double- K criterion for crack propagation in quasi-brittle fracture, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams

In this paper, an attempt is made to determine the double-K fracture parameters K Ic ini and K Ic un using three-point bending notched beams. First, based on the knowledge from extensive investigations which showed that the nonlinearity of P-CMOD curve is mainly associated with crack propagation, a linear asymptotic superposition assumption is proposed. Then, the critical effective crack length a is analytically evaluated by inserting the secant compliance c into the formula of LEFM. Furthermore, an analytical result of a fictitious crack with cohesive force in an infinite strip model was obtained. The double-K fracture parameters K Ic ini and K Ic un as well the critical crack tip opening displacement CTODc were analytically determined. The experimental evidence showed that the double-K fracture parameters K Ic ini and K Ic un are size-independent and can be considered as the fracture parameters to describe cracking initiation and unstable fracture in concrete structures. The testing method required to determine K Ic ini and K Ic un is quite simple, without unloading and reloading procedures. So, for performing this test, a closed-loop testing system is not necessary.