13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A CMOD-Based Hybrid Approach to Determine Fracture Resistance Curve Wuchao Yang1, Xudong Qian1,* 1 Department of Civil and Environmental Engineering, National University of Singapore, Singapore 117576, Singapore * Corresponding author: qianxudong@nus.edu.sg Abstract This study proposes a hybrid approach that relies both on the numerically computed and on the experimentally measured load (P) versus the crack-mouth opening displacement (CMOD) relationships to derive the fracture resistance curve (J-R curve) for the mixed-mode I and II fracture specimen. The CMOD-based hybrid approach utilizes a single experimental specimen with a growing crack and multiple finite element (FE) models, each with a different crack depth. The experimental procedure measures the P-CMOD curve from a standard fracture specimen with a growing crack. The intersections between the experimental P-CMOD curve and the numerical P-CMOD curves from multiple FE models dictate the CMOD levels to compute the strain energy (U). This approach simplifies the J-R curve test for the single-edge-notched bend, SE(B), specimen by eliminating the multiple unloading and reloading procedures in determining the variation of the compliance during the test. This method also provides an alternative simple measurement of the J-R curves for mixed-mode I and II specimens. The validation procedure shows accurate predictions of the J-R curves for both SE(B) specimens and mixed-mode I and II specimens. Keywords mixed-mode fracture, fracture resistance, J-R curve, hybrid approach. 1. Introduction The traditional load-line displacement (LLD) based incremental method has become widely implemented as a convenient experimental method to determine the fracture resistance curve, namely the J-R curve, for the SE(B) specimen, as recommended by the testing standards [1, 2]. The measurement of the specimen compliance at the each unloading and reloading procedure leads to a direct evaluation of the crack extension (Δa). The area under the load versus the LLD curve corresponding to different crack lengths allows the calculation of the energy release rate, J-value [3]. However, the measurement of the LLD for the SE(B) specimen requires extreme effort to prevent the potential errors introduced by the indentation at the loading point and the deformation of the testing frame [4]. In addition, the fracture toughness tests for the mixed-mode I and II specimens face critical challenges such as the calculation of the J-value and the determination of Δa [5]. The evaluation of the bending strain energy, which contributes to the J-value, depends on the current crack size (ai) which cannot be determined via the traditional compliance approach for mixed-mode I and II specimens due to the unknown crack path prior to the test. Therefore, the experimental determination of the fracture resistance curve for both pure mode I SE(B) specimen and the mixed-mode I and II specimen requires a simplified and accurate approach based on the readily measurable quantities from the tests. This study proposes a hybrid, numerical and experimental approach to determine the fracture resistance curve based on the readily measureable load versus CMOD (or Δ) relationship for SE(B) specimen (CMOD-hybrid approach). This research also extends the same approach to determine the fracture resistance for the mixed-mode I and II specimens. The J-value is derived from the variation in the total strain energy (including the bending and shear strain energy) with respect to the change in the crack depth, using the P-Δ curve measured from a single experimental specimen and P-Δ curves computed from multiple FE models with different crack sizes. The comparison of the fracture resistance curve obtained using the CMOD-hybrid approach with those obtained from the experimental results for both the SE(B) specimens and mixed-mode I and II specimens confirms the accuracy of the proposed CMOD-hybrid approach.
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