The Influence Of Weight Function And T-stress On Fracture Toughness Of Concrete

A weight function is nowadays an effective device to determine the stress intensity factor in a cracked body. In this case, weight function, by its nature, is dependent only on the specimen geometry and has nothing to do with the applied loads. The paper presents a new method for determining the weight function by using the crack-tip profile in three-point bending notched beams, where the stress intensity factor and corresponding crack opening displacement are well formulated. As two examples for application, weight function derived here is applied to deduce stress intensity factors for direct tension and pure bending on the same geometry as the three-point bending beams. The favorably agreement with the existing numerical calculations validates the proposed weight function. Therefore, the weight function can be extended to determine the stress intensity factor for any geometry same as three-point bending beam under any symmetrical loading system, which is one of the main advantages of the weight function method.When determining the double-K fracture toughness of concrete, the accuracy of the initiation fracture toughness is directly influenced by the calculated cohesive fracture toughness. A comparative study is conducted on the three typical weight functions for a stress intensity factor problem in a single edge-cracked geometry:weight function from chapter two, Tada green function and Shah green function. What’s more, expressions for calculating cohesive fracture toughness is developed by using weight function from chapter two and Tada green function. In the paper, three-point bending beams under mode-I fracture are used to compute the double-K fracture toughness parameters using the developed expression, and then they are compared with the values calculated using the Shah green function integral approach. The results show that:weight functions have no influence on unstable fracture toughness; these three weight functions share almost the same value only for a very shallow crack. When crack-depth ratio is larger than0.1, the result of cohesive fracture toughness and initiation fracture toughness using weight function and Tada green function agree well and the maximum error between them is less than3%. However a significant error as large as15%exists for Shah green function case.For linear-elastic materials, the presence of T-stress, which acts parallel to a crack, will strongly affect fracture onset and fracture toughness. For concrete-like quasi-brittle materials, however, little attention has been focused on the T-stress influence on fracture toughness, including initiation fracture toughness and unstable fracture toughness. In the paper, three-point-bending beams and wedge-splitting specimens under mode-I fracture are used to compute T-stress, and then its influence on the crack path and fracture toughness are analyzed based on modified maximum tangential stress criterion and minimum strain energy density criterion. It is shown that T-stress for these commonly used specimens is so small compared to its corresponding stress intensity factor K, dominant factor around the crack tip. The pre-fabricated crack propagates along the line of the initial crack, i.e., the crack will stay under mode-I fracture. In addition, T-stress has no influence on concrete fracture toughness, which indicates the commonly used specimens for determining concrete fracture toughness are reliable and reasonable.