Determination of Fracture Energy from Size Effect and Brittleness Number

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Title: Determination of Fracture Energy from Size Effect and Brittleness Number

Author(s): Zdenek P. Bazant and Phillip A. Pfeiffer

Publication: Materials Journal

Volume: 84

Issue: 6

Appears on pages(s): 463-480

Keywords: concretes; cracking (fracturing); crack propagation; energy; dimensional analysis; finite element method; measurement; specimens; tests; Materials Research

Date: 11/1/1987

Abstract:
A series of tests on the size effect due to blunt fracture is reported and analyzed. It is proposed to define the fracture energy as the specific energy required for crack growth in an infinitely large specimen. Theoretically, this definition eliminates the effects of specimen size, shape, and the type of loading on the fracture energy values. The problem is to identify the correct size-effect law to be used for extrapolation to infinite size. It is shown that Bazant's recently proposed simple size-effect law is applicable for this purpose as an approximation. Indeed, very different types of specimens, including three-point bent, edge-notched tension, and eccentric compression specimens, are found to yield approximately the same fracture energy values. Furthermore, the R-curves calculated from the size effect measured for various types of specimens are found to have approximately the same final asymptotic values for very long crack lengths, although they differ very much for short crack lengths. The fracture energy values found from the size effect approximately agree with the values of fracture energy for the crack band model when the test results are fitted by finite elements. Applicability of Bazant's brittleness number, which indicates how close the behavior of specimen or structure of any geometry is to linear elastic fracture mechanics and to plastic limit analysis, is validated by test results. Comparisons with Mode II shear fracture tests are also reported.