Determination Of New K_R Extension Resistance In Concrete Using Practical Analytical Approach

In new KR extension resistance model,KR-resistance curve is computed with crack cohesive stress which is distributed on fictitious fracture zone, and KR extension resistance is compared with stress intensity factor KI, at the tip of propagating crack caused by external load. Through the comparison, the state of crack propagation in concrete structures can be described. New KR extension resistance model introduced two fracture parameters:initiation toughness KICim and unstable fracture toughness KICun, it make up the defect that most fracture models before only paid attention to critical unstable state. However, in the solution procedure of new KR-curve based on crack cohesive force, the equation of stress intensity factor at the tip of propagating crack is unintegrable because of a complicated Tada Green function. A great deal of iterative computation and numerical integration is needed, this makes computation procedure difficult. Based on this, this article is trying to use a simple method to get new KR-resistance curve in three-point bending concrete beams.1. This article first introduces double-K fracture model and new KR extension resistance model proposed by Shilang Xu and Reinhardt. Double-K fracture model describes two instantaneous states in concrete:crack begins to propagation and crack becomes unstable. New KR extension resistance model illuminates material's ability to resist crack propagating varies in the whole propagating process. Inspired by Shilang Xu, Zhimin Wu et al. determinate double-K fracture parameters using practical analytical approach, for concrete specimen with cohesive stress distribution on fictitious fracture zone linear or bilinear, new KR extension resistance can be determined by practical analytical approach. Practical analytical approach is a method that transforms the integral expression of stress intensity factor at the crack tip caused by cohesive force into a simple algebraic expression, through using a simple function instead of Tada Green's function. In this article, simple expression and Tada Green's function are put together to contrast and errors are calculated. Analyze nationality and applicable areas that high accuracy can be gained.2. Test results of concrete three-point bending beams are adopted. Four types of specimens with different sizes are tested, during the test, initiation load and load-crack mouth opening displacement curve (P-CMOD curve) need to be measured. With experiment data, numerical integration method and practical analytical approach are separately used in computing new KR-resistance curve. Compare curves from two methods and calculate the accuracy of practical analytical approach in determining new KR-resistance curve.3. Expression of cohesive stress distribution on fictitious fracture zone are decided by softening curve, values of c1,c2 and w0 directly reflect the shape of softening curve. So, change values of c1,c2 and w0, when they are different, new KR-resistance curves gained from practical analytical approach are contrasted with curves achieved from numerical integration method. Analyze the impact of three parameters'variations on the accuracy of adopting practical analytical approach to compute new KR-resistance curve.4. Xiufang Zhang found that at the different stage, length of fracture process zone is variational. Computations of the paper demonstrate that when CTOD