An improved over-deterministic method for determining Young's modulus and Poisson's ratio of materials using specimens with cracks

Young's modulus and Poisson's ratio are the two most basic mechanical properties of materials that determine the linear elastic deformation behaviours of materials. In this paper, a new method was proposed for determining the Young's modulus and Poisson's ratio of materials using specimens with pure mode I, pure mode II or mixed mode I/II cracks, on the basis of the concept of the over-deterministic method (ODM). Using this method, the strains of the nodes around the crack tip obtained from numerical simulation or experiments were brought into the Williams’ strain series. Then, a set of over-deterministic matrix equations could be obtained and solved using the least square method. Several numerical and experimental examples of cracked bodies were conducted to verify the effectiveness and accuracy of the improved ODM. Finally, the effects of the number of terms in Williams’ series expansion, the number and location of the nodes selected around the crack tip and the specimen geometry on the results were discussed in detail. Results indicate that the improved ODM can be used to effectively and accurately determine the Young's modulus and Poisson's ratio of materials from specimens with pure mode I, pure mode II or mixed mode I/II cracks. Accurate Young's modulus and Poisson's ratio can be obtained if the strains of the nodes around the crack tip are sufficient and accurate.