Advances in Materials Science and Engineering

Volume 2015, Article ID 413737, 7 pages

http://dx.doi.org/10.1155/2015/413737

## Numerical Investigation on Stress Concentration of Tension Steel Bars with One or Two Corrosion Pits

^{1}Department of Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, China^{2}School of Civil Engineering, Central South University, 22 Shaoshan South Road, Changsha 410075, China

Received 1 April 2015; Accepted 10 August 2015

Academic Editor: Ana S. Guimarães

Copyright © 2015 Jian Hou and Li Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Pitting corrosion has been observed in steel bars of existing reinforced concrete (RC) structures in different erosion environments and has been identified as a potential origin for fatigue crack nucleation. In the present study, under uniaxial tension loading, stress distribution in the steel bars with one or two semiellipsoidal corrosion pits has systematically been investigated by conducting a series of three-dimensional semiellipsoidal pitted models. Based on the finite element analyses, it is shown that stress concentration factor (SCF) increases linearly with increasing pit aspect ratio (*a/b*) and increases nonlinearly with increasing pit relative depth (*a/R*) for single corrosion pit problem. For double corrosion pits problem, the SCF decreases nonlinearly with increasing angle of two transverse pits (*θ*). The interaction of two longitudinal pits can be ignored in the calculation of SCF even if the distance of two pits (*d*) is very small.

#### 1. Introduction

Steel reinforcement in RC structures is generally protected by a passive film formed in the alkaline environment due to the hydration products of cement [1, 2]. However, the protective film can be destroyed by attack of aggressive ions such as chloride and carbon dioxide [3]. Due to varying external environments, nonhomogeneous properties of both concrete cover and passive film, and metallurgical and compositional nonuniformity of steel, corrosion in applications is often observed to be nonuniformly distributed along the length of a steel bar. Pitting corrosion is a localized form of corrosion by which cavities or holes are produced in the material. Corrosion pits, acting as geometric discontinuities, lead to stress concentration and facilitate fatigue crack initiation and propagation [4–6]. A small, narrow pit with minimal overall steel loss can lead to the failure of an entire RC structure. Consequently, pitting is considered to be more dangerous than uniform corrosion damage.

Understanding and predicting the effect of corrosion pits on mechanical properties of corroded steel bars is very important for the integrity and safety of existing RC structure in erosion environments. Some tensile tests have been conducted to characterize the reduction of the mechanical properties of corroded steel bars [7, 8]. However, these studies used the average corrosion loss without considering the nonuniform distribution of corrosion pits. Tang et al. [9] detected the nonuniform distribution of corrosion pits using the 3D laser scanner and experimentally investigated the effect of corrosion nonuniformity on the mechanical property degradation of deformed steel bars. But these studies only investigated the macromechanical properties such as yield strength, ultimate strength, and elongation, without considering the nonuniform distribution of stress around corrosion pits before steel bars fracture, which is important for fatigue failure of steel bars. Cerit [10] numerically investigated the stress concentration factor (SCF) at the corrosion pit of tension circular cross section shaft, in which the shape of corrosion pit was simplified as semiellipsoid. Although there are some experimental and numerical works on the effect of corrosion pits on mechanical properties of corroded steel bars, few or no three-dimensional (3D) and systematic studies, which cover different aspect ratios and two interacting corrosion pits on estimation of SCF, have been cited in the literature.

In the present study, the stress concentration effect of single semiellipsoidal corrosion pits with various aspect ratios and pit depths has systematically been investigated for uniaxial tension loading by conducting a series of 3D stress analyses. Also, the contribution of two interacting corrosion pits to value of SCF has been examined for various angles in transverse direction and distances in longitudinal direction.

#### 2. Finite Element Model

In the computations, the shape of corrosion pits is ideally simplified as semiellipsoid, which is also adopted in the literatures [10, 11]. The length () and radius () of steel bars are, respectively, 100 mm and 10 mm. A linear elastic model was used, and modulus of elasticity and Poisson’s ratio are taken as 200 GPa and 0.3, respectively. SCF is calculated by using the ratio of maximum tension stress to nominal tension stress. Since the cross-sectional area of pit is very small compared with that of the steel bar, it is neglected in the calculation of the nominal tension stress. A uniform stress of 100 MPa is applied on the end of steel bar. For single corrosion pit problem (see Figure 1(b)), the longitudinal radius of pit () is varied from 10 mm to 0.2 mm while the transverse radius and pit depth () are set to be 2 mm, corresponding to the value of pit aspect ratio () from 0.2 to 10. Also, the pit depth is varied from 0.5 mm to 5 mm while the value of is set to be 0.5, corresponding to the value of pit relative depth () from 0.05 to 0.5. For two transverse pits’ problem (see Figure 2(a)), the angle of two pits () is varied from 25° to 60° while the values of and are set to be 2 mm and 4 mm, respectively. For two longitudinal pits’ problem (see Figure 3(a)), the distance of two pits () is varied while the values of and are set to be 2 mm and 4 mm, respectively.