Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech An analytical solution for double cantilever beam based on elastic–plastic bilinear cohesive law: Analysis for mode I fracture of fibrous composites Dongsheng Huang a,b, ⁎ , Baolu Sheng b,c , Yurong Shen b , Ying-Hei Chui d a National Engineering Research Center of Biomaterials, Nanjing Forestry University, Nanjing 210037, China b School of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China c Jiangsu Co-Innovative Center for Efficient Application of Forestry Resources, Nanjing 210037, China d Department of Civil & Environmental Engineering, University of Alberta, Edmonton T6G1H9, Canada ARTICLE INFO Keywords: Cohesive law Cohesive zone model R-curve Fracture process zone Fibrous composites ABSTRACT The most difficult problem in mode I fracture test for fibrous composites using double cantilever beam (DCB) specimen is to identify crack tip without ambiguity. Consequently to evaluate fracture toughness through compliance method is a tricky matter. This study was conducted to solve this problem by developing an analytical solution for DCB fibrous composite specimen tested for mode I fracture. Cohesive law was employed to model separation constitution of cracking. Based on this analytical solution, the length of fracture process zone (FPZ) can be evaluated. Compliance equations of DCB specimen which take FPZ length into consideration were provided. Therefore, R-curve can be directly obtained by differentiating the compliance with respect to crack length. The model was validated by DCB tests of parallel strand bamboo (PSB), a bamboo-based fibrous composite. Good agreement between the predicted and test load–displacement were achieved. It was found that the R-curve behavior of PSB is similar to that of many other fibrous composites, which undergoes a nonlinear increase stage during FPZ for- mation and then reaches a constant after FPZ fully developed. Finally, general solutions for common used linear-type cohesive laws are provided. 1. Introduction Double cantilever beam (DCB) is probably the most common configuration for testing the fracture properties of composites. It was standardized by ASTM [1] and ISO [2] for testing fracture of unidirectional composites. The test uses a rectangular specimen, with constant thickness, width, and length. The specimen contains a pre-implanted, non-adhesive insert which serves as an initial dela- mination or crack at one end. The opening load is applied at the pre-crack end to induce mode I cracking, as schematically illustrated in Fig. 1. According to the theories of linear elastic fracture mechanics (LEFM) [3], the relationship between compliance and crack length of DCB specimen can be obtained by Euler beam theory, and the energy release rate, G Ic , can be obtained by differentiating compliance with respect to crack length, i.e., = ∂ ∂ G P B C a 2 c Ic 2 (1) https://doi.org/10.1016/j.engfracmech.2018.02.019 Received 30 November 2017; Received in revised form 15 February 2018; Accepted 18 February 2018 ⁎ Corresponding author at: National Engineering Research Center of Biomaterials, Nanjing Forestry University, Nanjing 210037; School of Civil Engineering, Nanjing Forestry University, Nanjing, 210037. E-mail addresses: [email protected], [email protected] (D. Huang). Engineering Fracture Mechanics 193 (2018) 66–76 Available online 20 February 2018 0013-7944/ © 2018 Elsevier Ltd. All rights reserved. T
An analytical solution for double cantilever beam based on elastic–plastic bilinear cohesive law: Analysis for mode I fracture of fibrous composites
May 30, 2023
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