Determination of the kink point in the bilinear softening model for concrete

Kyoungsoo Park, Glaucio H. Paulino, Jeffery R. Roesler

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83 Citations (Scopus)


The characterization of the softening curve from experimental results is essential for predicting the fracture behavior of quasi-brittle materials like concrete. Among various shapes (e.g. linear, exponential) to describe the softening behavior of concrete, the bilinear softening relationship has been extensively used and is the model of choice in this work. Currently, there is no consensus about the location of the kink point in the bilinear softening curve. In this study, the location of the kink point is proposed to be the stress at the critical crack tip opening displacement. Experimentally, the fracture parameters required to describe the bilinear softening curve can be determined with the "two-parameter fracture model" and the total work of fracture method based on a single concrete fracture test. The proposed location of the kink point compares well with the range of kink point locations reported in the literature, and is verified by plotting stress profiles along the expected fracture line obtained from numerical simulations with the cohesive zone model. Finally, prediction of experimental load versus crack mouth opening displacement curves validate the proposed location of the kink point for different concrete mixtures and also for geometrically similar specimens with the same concrete mixture. The experiments were performed on three-point bending specimens with concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 50-50 blend of RCA and virgin coarse aggregate. The verification and validation studies support the hypothesis of the kink point occurring at the critical crack tip opening displacement.

Original languageEnglish
Pages (from-to)3806-3818
Number of pages13
JournalEngineering Fracture Mechanics
Issue number13
Publication statusPublished - 2008 Sep

Bibliographical note

Funding Information:
This paper was prepared from a study conducted in the “Center of Excellence for Airport Technology (CEAT),” funded by the Federal Aviation Administration (FAA) under Research Grant No. 95-C-001 and the University of Illinois. The contents of this paper reflect the views of the authors, who are responsible for the facts and accuracy of the data presented within. The contents do not necessarily reflect the official views and policies of the sponsors. This paper does not constitute a standard, specification, or regulation.

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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