Prediction of Fatigue Strength in Plain and Reinforced Concrete Beams

ACI Structural Journal, Sep/Oct 2007 by Sain, Trisha, Kishen, J M Chandra

RESEARCH SIGNIFICANCE

The purpose of this work is to develop a method for assessing the residual fatigue strength of damaged plain and reinforced concrete beams. This is done by proposing an improved fatigue crack propagation law that takes into account the loading history, frequency of the applied load, and the size effect parameters. The residual strength of plain and reinforced concrete beams are assessed in terms of the number of load cycles that are needed for a structure to fail by unstable crack propagation.

IMPROVED FATIGUE CRACK PROPAGATION MODEL FOR CONCRETE

Based on linear elastic fracture mechanics concepts, the fatigue crack propagation law proposed by Slowik et al. (1996) includes parameters such as fracture toughness, loading history, and specimen size, except the frequency of externally applied load, and is described by

... (1)

where KIsup is the maximum stress intensity factor ever reached by the structure in its past loading history; KIC is the fracture toughness; KImax is the maximum stress intensity factor in a cycle; N is the number of load cycles; a is the crack length; ΔKI is the stress intensity factor range; and m, n, and p are constants. These constant coefficients are determined by Slowik et al. (1996) through an optimization process using experimental data and they obtained 2.0, 1.1, and 0.7, respectively. Parameter C represents the crack growth rate per fatigue load cycle, and function F(a, Δσ) describes the effect of sudden overload onto the crack propagation. In the subsequent sections, the procedures for estimating C and F(a, Δσ) are explained.

Discussion on parameter C

Parameter C in empirical Eq. (1) basically gives a measure of crack growth per load cycle. In concrete members, this parameter indicates the crack growth rate for a particular grade of concrete and is also size dependent. Slowik et al. (1996) have determined the value of C to be equal to 9.5 × 10-3 and 3.2 × 10-2 mm/cycle for small and large size specimens, respectively. It should be noted herein that the stress intensity factor be expressed in MNm-3/2. These values were determined for a particular loading frequency of 3 Hz. Because parameter C gives an estimation of crack propagation rate in fatigue analysis, it should also depend upon the frequency of loading. Further, the fatigue crack propagation takes place primarily within the fracture process zone; hence, C should be related to the relative size of the fracture process zone, which itself is related to characteristic length. Therefore, C should depend on the characteristic length lch and ligament length L, where lch = EGf /ft'2, and E is the elastic modulus of concrete, ft' is the tensile strength of the concrete, and Gf is the specific fracture energy. Slowik et al. (1996) proposed a linear relationship between parameter C and the ratio of ligament length L to characteristic length lch given by

... (2)

This equation does not account for the frequency of fatigue loading. Hence, in this study, a modified equation to include the effect of loading frequency has been proposed. This is established through a regression analysis using the experimental results of Slowik et al. (1996) and Bazant and Kangming (1991). While Slowik et al. (1996) have used compact tension specimens of two different sizes with loading frequency 3 Hz and interrupted by spikes, Bazant and Kangming (1991) have tested a series of geometrically similar three-point beams under fatigue with a loading frequency of 0.033 Hz. In a compact tension specimen, tensile force is applied in a direction perpendicular to the notch, thereby causing the propagation of the notch through the opening mode. The geometrical properties of these compact tension and beam specimens are shown in Table 1.