Article

The Corrosion Characteristics and Tensile Behavior of Reinforcement under Coupled Carbonation and Static Loading Yidong Xu Received: 16 September 2015; Accepted: 3 December 2015; Published: 9 December 2015 Academic Editors: Raman Singh and Peter J. Uggowitzer School of Civil Engineering & Architecture, Ningbo Institute of Technology of Zhejiang University, Ningbo 315100, China; [email protected]; Tel.: +86-138-5748-8759; Fax: +86-574-8822-9132

Abstract: This paper describes the non-uniform corrosion characteristics and mechanical properties of reinforcement under coupled action of carbonation and static loading. The two parameters, namely area-box (AB) value and arithmetical mean deviation (Ra ), are adopted to characterize the corrosion morphology and pitting distribution from experimental observations. The results show that the static loading affects the corrosion characteristics of reinforcement. Local stress concentration in corroded reinforcement caused by tensile stress drives the corrosion pit pattern to be more irregular. The orthogonal test results from finite element simulations show that pit shape and pit depth are the two significant factors affecting the tensile behavior of reinforcement. Under the condition of similar corrosion mass loss ratio, the maximum plastic strain of corroded reinforcement increases with the increase of Ra and load time-history significantly. Keywords: reinforcement; carbonation; static loading; coupled effect; non-uniform corrosion; corrosion morphology; finite element analysis

1. Introduction The corrosion of reinforcement is one of the major deterioration mechanisms for reinforced concrete (RC) structures. Once reinforcement corrodes, its mechanical properties are affected and as a consequence the durability and serviceability of RC structures. In order to promote the effective application of reinforced concrete and to ensure that an RC structure has good performance during its service life, it becomes necessary to understand the mechanisms of how reinforcement corrodes in a given environment and how its deterioration affects the performance of the structure. Considerable research work has been carried out on the description of morphology and distribution of corroded metal. Rivas [1] applied extreme value analysis to pitting corrosion experiments in low-carbon steel. Caleyo and Valor [2–4] described the evolution of pitting depth by using Weibull, Fréchet, and Gumbel distribution functions. A Monte Carlo simulation was proposed by Caleyo [2] to estimate the probability distributions of the maximum pit depth and pit growth rate. Codaro [5] and Demis [6] developed a digital image processing and analysis method to evaluate the shape and size of corrosion pits. Horner [7] and Huang [8] adopted X-ray microtomography and confocal imaging profiler to observe the three-dimensional corrosion pit morphology of 3NiCrMoV disc steel and 7075-T6 aluminum alloy. Cerit [9] investigated the stress concentration factor (SCF) at the semielliptical corrosion pit by using finite element analysis. Pidaparti [10] analyzed the morphological features of corroded aluminum 5059 alloy samples by using a statistical method, and finite element analysis was adopted to predict surface stresses distribution. Many researchers have investigated the bond behavior [11–13] and concrete cover cracking due to corrosion expansion [14–18]. The work of Apostolopoulos is quite extensive in this field [19–24]. By Materials 2015, 8, 8561–8577; doi:10.3390/ma8125479

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Materials 2015, 8, 8561–8577

using accelerated electrochemical corrosion tests, Almusallam [25] found that reinforcing bars with 12.6% or more reinforcement corrosion have brittle behavior. Du [26] discussed the influence of type, diameter and corrosion time of reinforcing bars on their residual capacity. Moreno [27] established the mathematical models to predict the mechanical behavior of reinforcements depending on the corrosion degree and diameter of the rebars. Cobo [28] conducted the experiment on the mechanical properties of corroded B500SD high ductility reinforcement. Results show that the elongation of the bars diminishes and the ratio between the maximum tensile stress and the elastic limit increases as the corrosion degree advances. Zhang [29] conducted an experimental study on the static tensile and fatigue behavior of corroded reinforcement. Compared with the tensile behavior, the fatigue behavior of corroded reinforcement was more affected by corrosion. Souza [30] established a damage evolution model of corroded reinforcement by using damage mechanicals. The above-mentioned studies, however, are mainly focused on the effects of chemical corrosion, such as chloride and carbonation, yet the coupled chemo-mechanical process has not been considered. Furthermore, the influence of pitting geometry and distribution on the tensile behavior of corroded reinforcement was not thoroughly discussed apart from a few exemptions [6]. The aim of this paper is to investigate the relationship between the macro- and meso-material characteristics, in which the former is related to the mechanical weakening of the material and the latter is associated with a large number of randomly distributed corrosion pits of irregular shapes, sizes, and orientations. In particular, it studies whether there is any difference for the corrosion characteristics of the reinforcement under carbonation attack and under the coupled effect of carbonation and static loading, and what sort of impact the different corrosion characteristics have on the tensile behavior of the reinforcement. Based on stereological method and surface roughness characterization technology, in this work the pitting geometry and distribution of reinforcement under coupled effects of carbonation and static loading have been characterized. The effect of different pitting geometry and distribution on the tensile behavior of reinforcement has been analyzed using finite element analysis. 2. Corrosion Characteristics of Reinforcement under Different Corrosion Conditions 2.1. Materials The designed concrete compressive strength (measured on cubes) is 30 MPa, and the actual measurement is 36.2 MPa, according to Chinese Standards GB/T 50081 [31]. The mix proportion of concrete is shown in Table 1. The cement used was Type 42.5 Portland cement according to Chinese Standards GB175 [32]. The fine aggregate used was river sand. The coarse aggregate used was natural dolomite gravel with a maximum diameter of 31.5 mm. Hot rolled plain steel bar of type HPB235 (with nominal diameter of 12 mm) was used as reinforcement. When the corrosion test was completed, the reinforcements were taken out from the concrete and washed using a rust removing solution to remove corrosion products. The rust removing solution was prepared by mixing 3 parts by mass of hexamethylene tetramine into 97 parts diluted hydrochloric acid. Table 1. Mix proportion of concrete specimen (kg/m3 ). Portland Cement

Water

Fine Aggregate

Coarse Aggregate

365

192

730

1095

2.2. Accelerated Corrosion Test Procedures Specimens under carbonation attack (denoted as RT) and under the coupled action of carbonation and static loading (denoted as RTL) were prepared. Figure 1 shows the details of the reinforced concrete specimens tested. After curing in a fog room (20 ˘ 2 ˝ C, 95% relative humidity) for 28 days, the specimens were demolded and then used for the accelerated corrosion test.

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  (a)    (a) 

  (b)    Figure 1. Details of the tested reinforced concrete specimens: (a) RT (the specimen under carbonation attack);  Figure 1. Details of the tested reinforced concrete(b)  specimens: (a) RT (the specimen under carbonation (b) RTL (the specimen under the coupled action of carbonation and static loading).  attack); (b) RTL (the specimen under the coupled action of carbonation and static loading).

Figure 1. Details of the tested reinforced concrete specimens: (a) RT (the specimen under carbonation attack);  The RTL specimen was loaded by using a self‐equilibrium loading frame, shown in Figure 2.   (b) RTL (the specimen under the coupled action of carbonation and static loading). 

In the loading system, the tested concrete specimen was connected to a steel plate (base plate) using  The RTL specimen was loaded by using a self-equilibrium loading frame, shown in Figure 2. In two spring‐controlled loading bolts, and was thus subjected to a four‐point bending. The magnitude  The RTL specimen was loaded by using a self‐equilibrium loading frame, shown in Figure 2.   the loading system, the tested concrete specimen was connected to a steel plate (base plate) using two of  the  load  applied  was  1.6  kN  (90%  of  the  cracking  load),  which  was  calculated  following  the  In the loading system, the tested concrete specimen was connected to a steel plate (base plate) using  spring-controlled loading bolts, and was thus subjected to a four-point bending. The magnitude of method  described  in  ref.  [33],  in  order  to  prevent  cracking  in  concrete.  The  applied  load  was  two spring‐controlled loading bolts, and was thus subjected to a four‐point bending. The magnitude  the load applied was 1.6 kN (90% of the cracking load), which was calculated following the method measured  the  deformation  of (90%  a  spring.  In cracking  order  to  load),  prevent  the  stress  relaxation following  of  the  spring,   of  the  load by  applied  was  1.6  kN  of  the  which  was  calculated  the  described in ref. [33], in order to prevent cracking in concrete. The applied load was measured by the load correction was conducted every week in the first month, and then the correction procedure was  method  described  in  ref.  [33],  in  order  to  prevent  cracking  in  concrete.  The  applied  load  was  deformation of a spring. In order to prevent the stress relaxation of the spring, load correction was conducted every month until all the specimens were tested.  measured  by  the  deformation  of  a  spring.  In  order  to  prevent  the  stress  relaxation  of  the  spring,   conducted every week in the first month, and then the correction procedure was conducted every load correction was conducted every week in the first month, and then the correction procedure was  month until all the specimens were tested. conducted every month until all the specimens were tested. 

  Figure 2. Schematic illustrations of the loading frame. 

 

Four RT specimens and another four RTL specimens were prepared for this experiment. All of  Figure 2. Schematic illustrations of the loading frame.  Figure 2. Schematic illustrationstank  of thewith  loading the  tested  specimens  were  placed  into  a  carbonation  20% frame. ±  3%  CO2  concentration  and   70% Four RT specimens and another four RTL specimens were prepared for this experiment. All of  ±  5%  RH  to  cause  the  corrosion  of  reinforcement  in  concrete.  According  to  the  experimental  plan,  each  pair  of  RT and and another RTL  specimens  was  broken  every  three  months.  After  the  carbonation  Four RT specimens foura RTL specimens were prepared this experiment. All of the  tested  specimens  were  placed  into  carbonation  tank  with  20%  ±  3% for CO 2  concentration  and   tests, the reinforcing bars were removed from the concrete and washed by using the rust removing  70%  ± specimens 5%  RH  to  cause  corrosion  reinforcement tank in  concrete.  According  to  the  experimental  and the tested werethe  placed into of  a carbonation with 20% ˘ 3% CO 2 concentration solution to remove corrosion products, from which the corrosion mass loss ratio of the reinforcement  plan,  of  RT the and  RTL  specimens  was  broken  every  three  months.  After to the  carbonation  70% ˘ 5%each  RH pair  to cause corrosion of reinforcement in concrete. According the experimental (denoted as S) was calculated. The detailed corrosion mass loss ratios are shown in Table 2.  tests, the reinforcing bars were removed from the concrete and washed by using the rust removing 

plan, each pair of RT and RTL specimens was broken every three months. After the carbonation tests, solution to remove corrosion products, from which the corrosion mass loss ratio of the reinforcement  3 and washed by using the rust removing solution the reinforcing bars were removed from the concrete (denoted as S) was calculated. The detailed corrosion mass loss ratios are shown in Table 2.  to remove corrosion products, from which the corrosion mass loss ratio of the reinforcement (denoted as S) was calculated. The detailed corrosion mass 3loss ratios are shown in Table 2. 8563

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Table 2. Corrosion mass loss ratio (S) of corroded reinforcement. S/%

Code

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S/%

Code

RT-P1 1.10 RTL-P1 0.69 RT-P2 1.99 RTL-P2 1.55 Table 2. Corrosion mass loss ratio (S) of corroded reinforcement.  RT-P3 2.10 RTL-P3 2.51 S/% Code S/% 3.73 RT-P4Code  3.65 RTL-P4 RT‐P1  1.10  RTL‐P1  0.69  RT‐P2  1.99  RTL‐P2  1.55  2.3. Image Acquisition and Characterization of Corrosion Morphology RT‐P3  2.10  RTL‐P3  2.51  RT‐P4  images 3.65  RTL‐P4  3.73  taken by using a ME-61 The corrosion morphology of the reinforcement were

stereomicroscope (Micro-shot Technology Co., Guangzhou, China) with magnification of 7ˆ, which 2.3. Image Acquisition and Characterization of Corrosion Morphology  covered the central region of 100 mm long in the corroded part [34]. The  corrosion  morphology  images geometry, of  the  reinforcement  were  descriptor taken  by  using  a  ME‐61  To simplify the description of pitting a classical shape parameter, namely, stereomicroscope  (Micro‐shot  Technology  Co.,  Guangzhou,  China)  with  magnification  of between 7×,   the area-box (AB) parameter was used [34,35]. The AB parameter is defined as the ratio which covered the central region of 100 mm long in the corroded part [34].   the pit area and the area of minor surrounding rectangle that encloses the pit, which facilitates the To simplify the description of pitting geometry, a classical shape descriptor parameter, namely,  characterization of pitting morphology, as is shown in Table 3. The typical pit patterns are shown in the area‐box (AB) parameter was used [34,35]. The AB parameter is defined as the ratio between the  Figure 3. For calculating the AB parameter, the Image Pro Plus 6.0 (Media Cybernetics Inc., Rockville, pit  area  and  the  area  of  minor  surrounding  rectangle  that  encloses  the  pit,  which  facilitates  the  MD, USA) was used. characterization of pitting morphology, as is shown in Table 3. The typical pit patterns are shown in  Figure 3. For calculating the AB parameter, the Image Pro Plus 6.0 (Media Cybernetics Inc., Rockville,  Table 3. The corresponding area-box (AB) parameter for pit pattern with different MD, USA) was used.  geometrical characteristics. Table 3. The corresponding area‐box (AB) parameter for pit pattern with different geometrical characteristics. 

AB Parameter AB Parameter  Interval Interval  corrosion pit corrosion pit  pattern pattern  geometrical geometrical  characteristic characteristic 

0–0.5 0–0.5 

0.5–0.54 0.5–0.54 

irregular irregular 

triangles triangles  conical conical  pits pits 

-

‐ 

0.54–0.72 0.54–0.72  transition transition  zone A zone A  ‐ 

(a) 

0.72–0.86 0.72–0.86  circles circles  spherical spherical  pits pits 

0.86–0.98 0.86–0.98  transition transition  zone B zone B  ‐ 

0.98–1.0 0.98–1.0  rectangles rectangles  cylindrical cylindrical  pits pits 

(b) 

Figure 3. Typical pit patterns for different AB parameter: (a) Circular pits, AB parameter for the two pits is 

Figure 3. Typical pit patterns for different AB parameter: (a) Circular pits, AB parameter for the 0.73; (b) Transition zone A pits, AB parameters are 0.63, 0.65 and 0.59 for the three pits, respectively.  two pits is 0.73; (b) Transition zone A pits, AB parameters are 0.63, 0.65 and 0.59 for the three pits, respectively. 2.4. Pitting Depth Acquisition and Characterization of Corroded Surface Profiles 

Along the 100 mm length of the corroded reinforcement, pitting depths were measured using a  surface profilometer (with accuracy of 0.01 mm, Sanhe Measuring Implement Co., Wenzhou, China)  at intervals of 2.5 mm in the longitudinal direction and 45° in the radial direction. Eight curves along  Along the 100 mm length of the corroded reinforcement, pitting depths were measured using a the axial direction, equally distributed on the reinforcement surface, were established.  surface profilometer (with accuracy of 0.01 mm, Sanhe Measuring Implement Co., Wenzhou, China) Researchers  proposed  many direction statistical and roughness  parameters  relating  Eight to  the curves vertical  at intervals of 2.5 mmhave  in the longitudinal 45˝ in the radial direction. along features  of  a  surface  roughness  profile,  with  the  most  widely  used  being  the  arithmetical  mean  the axial direction, equally distributed on the reinforcement surface, were established. deviation  (denoted  as  Ra)  [36].  It  is  defined  as  the  average  absolute  deviation  of  the  roughness  Researchers have proposed many statistical roughness parameters relating to the vertical irregularities  from  mean  line  over  one  sampling  length  as  shown  in  Figure  4.  The  mathematical  features of a surface roughness profile, with a are shown in Equation (1) [37].  the most widely used being the arithmetical mean definition and the digital implementation of R

2.4. Pitting Depth Acquisition and Characterization of Corroded Surface Profiles

deviation (denoted as Ra ) [36]. It is defined as the average absolute deviation of the roughness 4

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irregularities from mean line over one sampling length as shown in Figure 4. The mathematical definition and the digital implementation of Ra are shown in Equation (1) [37]. Materials 2015, 8, page–page 

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Figure 4. Schematic diagram of the arithmetical mean deviation (Ra). 

Figure 4. Schematic diagram of the arithmetical mean deviation (Ra ).

1 l 1 n nm   Ra  1 żzl m dx   1z ÿ n i“ 1 |z ´ m| Ra “l 0 |z ´ m|dx l 0 n

(1) 

(1)

i “1 m  is the height of mean line, l is the sampling length, and n is  where z is the height of profile peak,  Figure 4. Schematic diagram of the arithmetical mean deviation (R a). 

where zthe number of measuring points.  is the height of profile peak, m is the height of mean line, l is the sampling length, and n is n the number of measuring points. l 2.5. Results and Discussion  R  1 z  m dx  1 zm   (1)   a  0 l n i 1 2.5. Results and The Discussion proportions  of  AB  parameters  for  specimens  under  different  corrosion  conditions  were  analyzed by using frequency statistics; the changing tendency of corrosion characteristics of RT and  m  is the height of mean line, l is the sampling length, and n is  where z is the height of profile peak,  TheRTL is similar. The typical pit patterns for RT and RTL specimens are shown in Figure 5. Here the  proportions of AB parameters for specimens under different corrosion conditions were the number of measuring points.  analyzed by using frequency statistics; the changing tendency of corrosion characteristics of RT experimental results of two specimens, RT‐P4 and RTL‐P4, are discussed because the two specimens  2.5. Results and Discussion  and RTL is almost  similar.the The pitmass  patterns for As  RTis and RTL specimens shown in for  Figure 5. have  same typical corrosion  loss  ratio.  shown  in  Figure  6,  the are AB  parameters  different  specimens  are  mainly  located  in  the  following  two  intervals,  [0.54,  0.72]  and  [0.72,  0.86].  Here the experimental results ofparameters  two specimens, RT-P4 under  and RTL-P4, discussed because The  proportions  of  AB  for  specimens  different are corrosion  conditions  were the two Under carbonation attack, the proportion of circular shape pits in the reinforcement is the highest  specimens have almost the same corrosion mass loss ratio. As is shown in Figure 6, the AB parameters analyzed by using frequency statistics; the changing tendency of corrosion characteristics of RT and  and  the  proportion  of  transition‐zone‐A  shape  pits  is  lower.  Irregular,  transition‐zone‐B,  and  RTL is similar. The typical pit patterns for RT and RTL specimens are shown in Figure 5. Here the  for different specimens are mainly located in the following two intervals, [0.54, 0.72] and [0.72, triangle‐shape pits take only very small proportions. While under the coupled action of carbonation  experimental results of two specimens, RT‐P4 and RTL‐P4, are discussed because the two specimens  0.86]. Under carbonation attack, the proportion of circular shape pits in the reinforcement is the and static loading, the proportion of transition‐zone‐A shape pits is slightly higher than that of the  have  almost  the  same  corrosion  mass  loss  ratio.  As  is  shown  in  Figure  6,  the  AB  parameters  for  highest circle  and shape  the proportion of transition-zone-A shape is stress  lower. transition-zone-B, pits.  The  statistical  results  indicate  that  the pits tensile  can Irregular, make  the  corrosion  pit  different  specimens  are  mainly  located  in  the  following  two  intervals,  [0.54,  0.72]  and  [0.72,  0.86].  pattern  more  pits complicated.  The very coupled  action  of  carbonation  and  static  loading  affects  the  and triangle-shape take only small proportions. While under the coupled action of Under carbonation attack, the proportion of circular shape pits in the reinforcement is the highest  distribution  of  corrosion  pit  pattern.  Indeed,  previous  works  have  also  shown  that  pitting  carbonation andproportion  static loading, the proportion ofpits  transition-zone-A shape pits is slightly and  the  of  transition‐zone‐A  shape  is  lower.  Irregular,  transition‐zone‐B,  and  higher susceptibility and pitting potential in stainless steel is dependent on the type of load and the level of  than that of the circle shape pits. The statistical results indicate that the tensile stress can make triangle‐shape pits take only very small proportions. While under the coupled action of carbonation  applied stress [38,39]. To evaluate if concrete carbonation can promote brittle fracture of pre‐stressed  and static loading, the proportion of transition‐zone‐A shape pits is slightly higher than that of the  the corrosion pit pattern more complicated. The coupled action of carbonation and static loading reinforcement, constant load tests in bicarbonate aqueous solutions under anodic polarization were  circle  shape  pits.  The  statistical  pit results  indicate  that  the  tensile  stress  can have make also the  corrosion  pit  pitting affects the distribution of corrosion pattern. Indeed, previous works shown that carried out by Proverbio [40], and deep internal voids close to the surface were observed. Owing to  pattern  more  complicated.  The  coupled  action  of  carbonation  and  static  loading  affects  the  susceptibility and pitting potential in stainless steel is dependent on the type of load and the level of the local stress concentration in corroded reinforcement caused by tensile stress, the corrosion pits  distribution  of  corrosion  pit  pattern.  Indeed,  previous  works  have  also  shown  that  pitting  grow along the preferred orientation, which makes the corrosion pit pattern more irregular.  appliedsusceptibility and pitting potential in stainless steel is dependent on the type of load and the level of  stress [38,39]. To evaluate if concrete carbonation can promote brittle fracture of pre-stressed reinforcement, constant load tests in bicarbonate aqueous solutions under anodic polarization were applied stress [38,39]. To evaluate if concrete carbonation can promote brittle fracture of pre‐stressed  reinforcement, constant load tests in bicarbonate aqueous solutions under anodic polarization were  carried out by Proverbio [40], and deep internal voids close to the surface were observed. Owing to the localcarried out by Proverbio [40], and deep internal voids close to the surface were observed. Owing to  stress concentration in corroded reinforcement caused by tensile stress, the corrosion pits the local stress concentration in corroded reinforcement caused by tensile stress, the corrosion pits  grow along the preferred orientation, which makes the corrosion pit pattern more irregular. grow along the preferred orientation, which makes the corrosion pit pattern more irregular. 

  (a) 

(b) 

Figure 5. Typical pit patterns for reinforcement under different corrosion conditions: (a) RT specimen,  AB  parameters  are  0.74,  0.68,  0.80  and  0.76  for  the  four  pits,  respectively;  (b)  RTL  specimen,   AB parameters are 0.44 and 0.74 for the two pits, respectively. 

  (a) 

(b) 

Figure 5. Typical pit patterns for reinforcement under different corrosion conditions: (a) RT specimen, 

Figure 5. Typical pit patterns for reinforcement under different corrosion conditions: (a) RT specimen, AB  parameters  are  0.74,  0.68,  0.80  and  0.76  for  5 the  four  pits,  respectively;  (b)  RTL  specimen,   AB parameters are 0.74, 0.68, 0.80 and 0.76 for the four pits, respectively; (b) RTL specimen, AB AB parameters are 0.44 and 0.74 for the two pits, respectively.  parameters are 0.44 and 0.74 for the two pits, respectively.

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  (a) 

(b) 

Figure 6. The proportion of AB parameters for different corroded reinforcement: (a) RT‐P4; (b) RTL‐P4. 

Figure 6. The proportion of AB parameters for different corroded reinforcement: (a) RT-P4; (b) RTL-P4. The  maximum  and  average  values  of  arithmetical  mean  deviation  (Ra)  of  surface  profiles  at  lines  as  described  above values were  calculated  and  are  shown  Table  4.  Under  condition profiles of  Theeight  maximum and average of arithmetical meanin  deviation (Ra ) the  of surface at similar corrosion mass loss ratio (S), the surface roughness of the RT specimen is found to be lower  eight lines as described above were calculated and are shown in Table 4. Under the condition of than that of the RTL specimen, which indicates that the coupled chemo‐mechanical process affects  similar corrosion mass loss ratio (S), the surface roughness of the RT specimen is found to be lower the distribution of pitting depth [41].  than that of the RTL specimen, which indicates that the coupled chemo-mechanical process affects Table 4. Surface roughness of corroded reinforcement.  Ra: Arithmetical mean deviation.  the distribution of pitting depth [41]. Code 

S/%

(Ra)ave/μm

(Ra)max/μm

3.73 

64.5 

114.7 

Table 4. Surface roughness Ra : Arithmetical mean deviation. RT‐P4 of corroded 3.65  reinforcement. 55.21  92.00  RTL‐P4 

Code

S/%

(Ra )ave /µm

(Ra )max /µm

3. Influence of Pitting Geometry on the Tensile Behavior of Reinforcement  RT-P4 3.65 55.21 92.00

RTL-P4 3.73 64.5 114.7 For  reinforced  concrete  structures  exposed  to  the atmospheric  environment, corrosion  relates  mainly to the carbonation of concrete cover. Once CO2 penetrates in the concrete cover and reaches  to the surface of reinforcement, the protective film around the reinforcement is broken and the active  3. Influence of Pitting Geometry on the Tensile Behavior of Reinforcement corrosion of steel occurs [42]. As is shown in Section 2.5, there exist a lot of pits in the reinforcement,  Forand the pit pattern has different geometrical characteristics. The influence of pitting geometry on the  reinforced concrete structures exposed to the atmospheric environment, corrosion relates mainly tensile behavior of reinforcement has become a new focus. In this section, orthogonal array method  to the carbonation of concrete cover. Once CO2 penetrates in the concrete cover and reaches and finite element analysis (FEA) are used to investigate this problem.   to the surface of reinforcement, the protective film around the reinforcement is broken and the active

corrosion of steel occurs [42]. As is shown in Section 2.5, there exist a lot of pits in the reinforcement, 3.1. Orthogonal Array of Pitting Geometry  and the pit pattern has different geometrical characteristics. The influence of pitting geometry on the Using  orthogonal  array  testing,  we  can  maximize  the  test  coverage  while  minimizing  the  tensile behavior of reinforcement has become a new focus. In this section, orthogonal array method number of test cases to consider [43,44]. The experimental arrangement can be optimized by adopting  and finite element analysis (FEA) are used to investigate this problem. appropriate arrays for different variables and levels. By using range analysis and variance analysis,  the influence of every variable on experimental results can be described quantitatively. In this study, 

3.1. Orthogonal Array ofarray  PittingL9Geometry the  orthogonal  (34)  was  used  for  experimental  arrangement  and  data  analysis.   The  experimental  runs  with  four  parameters  are  operated  using  Orthogonality  Experiment 

Using orthogonal array testing, we can maximize the test coverage while minimizing the number Assistant,  a  statistical  software  which  incorporates  a  L9(34)  orthogonal  array  table.  The  software  of test cases to consider [43,44]. The experimental arrangement can be optimized by adopting determines nine significant experimental runs instead of 81 runs in the case of 4 variables, with 3 levels  appropriate arrays for different variables and levels. By using range analysis and variance analysis, 4 = 81) [45]. The selected physical variables are the pit shape, corrosion mass loss ratio, and pit  each (3 the influence oforder  every onʺaccidental  experimental can be experiment,  described the  quantitatively. depth.  In  to  variable estimate  the  errorʺ  results occurring  in  the  variable  of  last  In this column is usually adopted as blank, denoted as ʺerrorʺ. The experimental levels are shown in Table 5.  study, the orthogonal array L9 (34 ) was used for experimental arrangement and data analysis. The The ductile fracture process of corroded reinforcement is as follows. Local plastic deformation  experimental runs with four parameters are operated using Orthogonality Experiment Assistant, a develops along the pit, which causes a stress redistribution. The re‐distributed stresses will affect the  statistical software which incorporates a L9 (34 ) orthogonal array table. The software determines overall  stress  in  the  specimen,  which  can  generate  plastic  deformation  in  other  places.  This  could  nine significant experimental runs instead of 81 runs in the case of 4 variables, with 3 levels each cause a necking and/or fracture with dimple cleavage in the weak place of the specimen. Obviously,  (34 = 81) [45]. Theof  selected physical variables are the shape, plastic  corrosion mass loss ratio, and pit the  fracture  corroded  reinforcement  originates  the pit excessive  deformation  in  pitting.  depth. In order to estimate the "accidental error" occurring in the experiment, the variable of last 6 column is usually adopted as blank, denoted as "error". The experimental levels are shown in Table 5. The ductile fracture process of corroded reinforcement is as follows. Local plastic deformation develops along the pit, which causes a stress redistribution. The re-distributed stresses will affect the overall stress in the specimen, which can generate plastic deformation in other places. This could cause a necking and/or fracture with dimple cleavage in the weak place of the specimen. 8566

Materials 2015, 8, 8561–8577

Obviously, the fracture of corroded reinforcement originates the excessive plastic deformation in pitting. Therefore, the maximum equivalent plastic strain (denoted as PEEQ in ABAQUS) is adopted as theMaterials 2015, 8, page–page  index for this numerical simulation. Therefore, the maximum equivalent plastic strain (denoted as PEEQ in ABAQUS) is adopted as the  Table 5. Variables and levels for orthogonal test. index for this numerical simulation.  Level

(A) Pit Shape

(a) Level  Spherical (A) Pit Shape  (b) Ellipsoidal (c) (a) Triangular pyramid Spherical 

(b) 

Variables (B) Corrosion Mass Loss Ratio(S)/%

Table 5. Variables and levels for orthogonal test. 

Ellipsoidal 

3.2. Finite Model (c)  Element Triangular pyramid 

1.0 Variables  (B) Corrosion Mass Loss Ratio (S)/% 1.5 2.01.0 

1.5  2.0 

(C) Pit Depth/mm

(D) Error

1.0 (C) Pit Depth/mm  (D) Error 1.5 2.0 1.0  ‐  1.5  ‐  2.0  ‐ 

Finite element analysis (FEA) was carried out using ABAQUS/Standard implicit solver and the 3.2. Finite Element Model  models used are shown in Figure 7. The overall length of the specimen is 50 mm. The pit was assumed Finite element analysis (FEA) was carried out using ABAQUS/Standard implicit solver and the  as spherical pit, ellipsoidal pit, and triangular pyramid pit, the size of which was determined based models  used  are  shown  in  Figure  7.  The  overall  length  of  the  specimen  is  50  mm.  The  pit  was  on three parameters: the size of the surface, the depth of the pit, and the volume of the pit. Owing assumed  as  spherical  pit,  ellipsoidal  pit,  and  triangular  pyramid  pit,  the  size  of  which  was  to thedetermined based on three parameters: the size of the surface, the depth of the pit, and the volume of  existence of pits, the model was partitioned into three parts in order to generate different mesh grid. the pit. Owing to the existence of pits, the model was partitioned into three parts in order to generate  The two end regions of the model were meshed by using an eight-node brick element with reduced integration (C3D8R). The middle part of the model with pits was meshed by using a 10-node different mesh grid. The two end regions of the model were meshed by using an eight‐node brick  quadratic tetrahedral element (C3D10). A fine mesh was used in the middle part of the model in element with reduced integration (C3D8R). The middle part of the model with pits was meshed by  orderusing a 10‐node quadratic tetrahedral element (C3D10). A fine mesh was used in the middle part of  to achieve accurate results. The boundary conditions employed are as follows: one end of the the model in order to achieve accurate results. The boundary conditions employed are as follows:  cylinder was assumed to be fully fixed and the other end was subjected to a tensile force. The applied one end of the cylinder was assumed to be fully fixed and the other end was subjected to a tensile  displacement was 8.5 mm. The material used is classical metal plasticity and the related stress-strain force. The applied displacement was 8.5 mm. The material used is classical metal plasticity and the  data used are shown in Figure 8. The number of element used in each model was 9831, 13201, 12831, related stress‐strain data used are shown in Figure 8. The number of element used in each model was  18361, 22437, 16500, 29765 and 27830, respectively. These were based on the trials to achieve good 9831, 13201, 12831, 18361, 22437, 16500, 29765 and 27830, respectively. These were based on the trials  accuracy but without increasing extra computational efforts. to achieve good accuracy but without increasing extra computational efforts. 

(a) 

(b) 

(c)  Figure 7. Finite element models: (a) FEA model of corroded reinforcement with circular pits; (b) FEA 

Figure 7. Finite element models: (a) FEA model of corroded reinforcement with circular pits; (b) FEA model of corroded reinforcement with ellipsoidal pits; (c) FEA model of corroded reinforcement with  model of corroded reinforcement with ellipsoidal pits; (c) FEA model of corroded reinforcement with triangular pyramid pits.  triangular pyramid pits.

7

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  FigureFigure 8. Stress‐strain curves of uncorroded reinforcing bar.  8. Stress-strain curves of uncorroded reinforcing bar. When  using  ABAQUS  for  elastic‐plastic  analysis,  the  modeling  of  materials  nonlinearity  the  definition  a  true  stress‐strain  relationship  for  isotropic  [46].  Therefore,  the  requires Whenrequires  using ABAQUS forof elastic-plastic analysis, the modeling ofmetals  materials nonlinearity nominal stress‐strain relation should be converted to the true stress‐strain relation. The transformation  the definition of a true stress-strain relationship for isotropic metals [46]. Therefore, the nominal formula is shown in Equation (2):   stress-strain relation should be converted to the true stress-strain relation. The transformation (2)  formula is shown in Equation (2): ε true =ln 1+εnom  , σtrue =σnom 1+εnom    where εtrue is the true strain, σtrue is the true stress, εnom is the nominal strain, and σnom is the nominal stress.  q , σtrue “ reinforcement  εtrue “ ln p1`ε σnom p1`εnom nomuncorroded  Tensile  testing  was  conducted  for  the  by qusing  a  servo‐hydraulic  testing machine. The detailed testing procedure is reported in a previous study [47]. The nominal  curves  of  the  uncorroded  reinforcement  shown  in  Figure  8,  from  which  where εtrueand  is true  thestress‐strain  true strain, σtrue is the true stress, εnom isare  the nominal strain, and σnom Young’s modulus and Poisson’s ratio were found to be Es = 200 GPa and μ = 0.3.  nominal stress.

(2) is the

Tensile testing was conducted for the uncorroded reinforcement by using a servo-hydraulic 3.3. Results and Discussion  testing machine. The detailed testing procedure is reported in a previous study [47]. The nominal The detailed conditions for FEA are shown in Table 6. As is shown in Figure 9, the existence of  and true stress-strain curves of the uncorroded reinforcement are shown in Figure 8, from which pits leads to stress concentration in the reinforcement, which causes to the deterioration of the plastic  Young’s modulus and Poisson’s ratio were found to be Es = 200 GPa and µ = 0.3. deformation of the reinforcement. The stress concentration around corrosion pits is obvious. As is  expected, all of the maximum equivalent plastic strains (PEEQ) occur around the corrosion pits.  6  and  7  show  the  range  analysis  and  variance  analysis  of  the  maximum  equivalent  3.3. Results andTables  Discussion plastic strain (PEEQ). In the range analysis of orthogonal test, Ki is the average PEEQ for a certain 

The detailed conditions FEA are shown inoptimal  Table level  6. Asof isvariables  showncan  in Figure 9, theThe  existence of variable  at  level  i,  and for by  comparing  to  Ki,  the  be  confirmed.  definition of parameter Y is  max{ K , K , K }  max{ K , K , K } , and Y scales the effect of variables  pits leads to stress concentration in the reinforcement, I II III I which II III causes to the deterioration of the plastic on the result. A high Y value of a certain variable means that this variable has a relatively strong effect  deformation of the reinforcement. The stress concentration around corrosion pits is obvious. As is on the result [48,49]. Obviously, the Y value of column D (error) should be the minimum among the  expected, all of the maximum equivalent plastic strains (PEEQ) occur around the corrosion pits. four columns, which means the experimental results are reliable. In the variance analysis, the F‐test is  Tablessensitive  6 and 7to show the range and variance analysis of in  thethe  maximum equivalent plastic non‐normality  and analysis the  related  F  value  is  a  key  parameter  F‐test  statistic.  If  the  obtained F value is equal to or larger than the critical F value, then the result is significant at that level of  strain (PEEQ). In the range analysis of orthogonal test, Ki is the average PEEQ for a certain variable probability. In this case, F 0.05 = 6.94. Since FPit shape and FPit depth are all greater than 6.94, the results are  at level i, and by comparing to Ki , the optimal level of variables can be confirmed. The definition significant at the 5% significance level. It is observed from the tables that the orders of influence of  u ´shape  max> tK andratio  Y scales the effect of variables on the of parameter Y is max tK I , Kdepth  I I , K I> I Ipit  I , KI I , K I I I u,loss  each  variable  are  pit  corrosion  mass  >  error.  The  two  variables,  pit  result. A high Y value of a certain variable means that this variable has a relatively strong depth  and  pit  shape,  are  significant  factors  affecting  the  tensile  behavior  of  reinforcement.  The  effect on maximum  equivalent  plastic  strain  (PEEQ)  increases  remarkably  with  the  increase  of  pit  depth,  the result [48,49]. Obviously, the Y value of column D (error) should be the minimum among the which leads to the failure of corroded reinforcement under low loads. Since the F value of corrosion  four columns, which means the experimental results are reliable. In the variance analysis, the F-test mass  loss  ratio  is  less  than  the  critical  value  (F0.05),  corrosion  mass  loss  ratio  is  not  a  significant  is sensitivevariable regarding the mechanical properties of reinforcement. Given the same amount of mass loss in  to non-normality and the related F value is a key parameter in the F-test statistic. If the obtained Freinforcement,  value is equal to or corrosion  larger than the to  critical value, then the resulttype  is significant at that level localized  appears  be  the Fmore  dangerous  damage  than  uniform  corrosion, owing to the localized and concentrated material deterioration, which causes local stress  of probability. In this case, F0.05 = 6.94. Since FPit shape and FPit depth are all greater than 6.94, the results concentration and could lead to catastrophic failure of the material in that area.  are significant at the 5% significance level. It is observed from the tables that the orders of influence of each variable are pit depth > pit shape > corrosion mass loss ratio > error. The two variables, pit depth and pit shape, are significant factors affecting the 8tensile behavior of reinforcement. The maximum equivalent plastic strain (PEEQ) increases remarkably with the increase of pit depth, which leads to the failure of corroded reinforcement under low loads. Since the F value of corrosion mass loss ratio is less than the critical value (F0.05 ), corrosion mass loss ratio is not a significant variable regarding the mechanical properties of reinforcement. Given the same amount of mass loss in reinforcement, localized corrosion appears to be the more dangerous damage type than uniform corrosion, owing to the localized and concentrated material deterioration, which causes local stress concentration and could lead to catastrophic failure of the material in that area.

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Materials 2015, 8, page–page 

(a) 

(b) 

(c) 

(d) 

(e) 

(f) 

(g) 

(h) 

(i)  Figure 9. Results of equivalent plastic strains (PEEQ) obtained from FEA based on Table 6: (a) 1#; (b) 2#;  Figure 9. Results of equivalent plastic strains (PEEQ) obtained from FEA based on Table 6: (a) 1#; (c) 3#; (d) 4#; (e) 5#; (f) 6#; (g) 7#; (h) 8#; (i) 9#.  (b) 2#; (c) 3#; (d) 4#; (e) 5#; (f) 6#; (g) 7#; (h) 8#; (i) 9#.

 

 

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Table 6. Experimental arrangement and range analysis. PEEQ: Equivalent plastic strain. (A) Pit Shape

Experiment No.

(B) S/%

(C) Pit Depth/mm

(D) Error

Index PEEQ

1# Spherical (a) 1.0 (a) 1.0 (a) (a) 2# Spherical (a) 1.5 (b) 1.5 (b) (b) Materials 2015, 8, page–page  3# Spherical (a) 2.0 (c) 2.0 (c) (c) 4# Ellipsoidal (b) 1.0 (a) 1.5 (b) (c) Table 6. Experimental arrangement and range analysis. PEEQ: Equivalent plastic strain.  5# Ellipsoidal (b) 1.5 (b) 2.0 (c) (a) (A)  (B) (C) 1.0 (a) (D)  6# 2.0 (c) (b) Index Experiment No.  Ellipsoidal (b) S/% Error  7# TriangularPit Shape  pyramid (c) 1.0 (a) Pit Depth/mm 2.0 (c) (b) PEEQ 1#  Spherical (a)  1.0 (a)  1.0 (a)  1.0 (a) (a)  8# Triangular pyramid (c) 1.5 (b) (c) 0.4053  2#  Spherical (a)  1.5 (b)  1.5 (b)  (b)  9# Triangular pyramid (c) 2.0 (c) 1.5 (b) (a) 0.5948  3#  Spherical (a)  2.0 (c)  2.0 (c)  (c)  Range Analysis PEEQ PEEQ PEEQ PEEQ0.8123  4#  Ellipsoidal (b)  1.0 (a)  1.5 (b)  0.376 (c)  KI 0.609 0.624 0.5700.4859  5#  Ellipsoidal (b)  1.5 (b)  2.0 (c)  0.559 (a)  KII 0.492 0.568 0.6200.6951  6#  Ellipsoidal (b)  2.0 (c)  1.0 (a)  (b)  KIII 0.659 0.568 0.825 0.5710.2964  7#  Triangular pyramid (c)  1.0 (a)  2.0 (c)  (b)  Y 0.167 0.056 0.449 0.05 0.9687  8#  Triangular pyramid (c)  1.5 (b)  1.0 (a)  9#  Triangular pyramid (c)  2.0 (c)  1.5 (b)  Table 7. Analysis Range Analysis  PEEQ  PEEQ of variance. PEEQ KI  0.609  0.624  0.376  KII  0.492  Sum of Squares 0.568  of 0.559  Degree of SourceKIII  Index 0.659  0.568  0.825  Deviations Freedom Y  0.167  0.056  0.449 

pit shape corrosion mass loss ratio (S) pit depth

PEEQ PEEQ PEEQ

0.044

2 2 2

0.006 Table 7. Analysis of variance.  0.306

Sum of Squares  Degree of  Index  ** means of Deviations  significantly affected. Freedom 

Source 

pit shape  PEEQ  0.044  corrosion mass loss ratio (S)  PEEQ  0.006  on the Different pit shape also has an obvious influence pit depth  corrosion PEEQ 0.306  reinforcement. A growing pit  will essentially be

0.4053 0.5948 0.8123 0.4859 0.6951 0.2964 0.9687 0.4133 0.5952

-

(c)  0.4133  (a)  0.5952  PEEQ  0.570  ‐  0.620  Critical F Value 0.571  Value 0.05  **

8.00 1.091 55.636 **

F Value 

F0.05 = 6.94

Critical  Value 

2  8.00 **  F0.05 = 6.94  2  1.091  mechanical properties of the corroded **  2  55.636  inducing a corresponding increase in

** means significantly affected. stress and strain [7]. Huang summarizes the stress concentration factor for different corrosion pit Different pit shape also has an obvious influence on the mechanical properties of the corroded  shape ratios. The stress concentration factor increases with the depth of the pit, and the stress tends reinforcement.  A  growing  corrosion  pit  will  essentially  be  inducing  a  corresponding  increase  in  to increasestress  when pit[7].  is Huang  more elongated direction normal tofor  thedifferent  applied load [8]. and the strain  summarizes in the the stress  concentration  factor  corrosion  pit  Figure 10 shows an shape ratios. The stress concentration factor increases with the depth of the pit, and the stress tends  ellipsoidal pit in a 2-dimensional infinite solid under far-field tensile forces [50]. According to increase when the pit is more elongated in the direction normal to the applied load [8]. Figure 10  to the results of Inglis on the stress concentration around an elliptical hole [51], the stress distribution shows an ellipsoidal pit in a 2‐dimensional infinite solid under far‐field tensile forces [50]. According  is described in Equation (3) and Equation (4). Based on three-dimensional reconstruction techniques, to the results of Inglis on the stress concentration around an elliptical hole [51], the stress distribution  Azevedo is described in Equation (3) and Equation (4). Based on three‐dimensional reconstruction techniques,  [52] calculated the stress concentration factor of corroded SAE 2205 duplex stainless steel samples with 3D pits. The results showed that 3D factor  reconstruction of pits is valid for steel  the calculation Azevedo  [52]  calculated  the  stress  concentration  of  corroded  data SAE  2205  duplex  stainless  samples with 3D pits. The results showed that 3D reconstruction data of pits is valid for the calculation  of stress concentration factors using the Inglis equation. In this sense, the use of the data of 3D pits of stress concentration factors using the Inglis equation. In this sense, the use of the data of 3D pits  along with FEA might lead to interesting calculations of stress concentration factor in irregular pits.

along with FEA might lead to interesting calculations of stress concentration factor in irregular pits. 

  (a) 

(b) 

Figure 10. Elliptical hole defect of infinite‐plate model: (a) Elliptical hole in infinite plate; (b) Crack propagation. 

Figure 10. Elliptical hole defect of infinite-plate model: (a) Elliptical hole in infinite plate; (b) Crack propagation.   10

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when λ ≠ 1,  when λ ­“ 1,

σ 1  2λ λρ λ 2σ   σ b  b ( (1  ρ)2  ρ 2 (1  λ)2  λρ)( )  2 2 λ (1  ρ)2  ρλρ (1  λ 2 ) (1  λ )λ2 σ σ 1 λ 1 1´2λ 2 2 2

σb “ p p1 ` ρq ´ ρ p1 ´ λq ´ λρqp 1´λ 1´λ when λ = 1, 

`b

p1 ` ρq2 ´ ρ2 p1 ´ λ2 q

q`

p1 ´ λ2 q

σ (4ρ3  5ρ2  2ρ) σ b  σ (2  p4ρ3 ` 5ρ2 `3 2ρq ) (1  ρ)3 q σb “ 2p2 `

when λ = 1,

(3)  (3)

(4)  (4)

2 p1 ` ρq where σb is the largest stress concentration, σ is the macroscopic stress, λ = b1/a1, and ρ = a1/l, a and b  where σb is the largest stress concentration, σ is the macroscopic stress, λ = b1 /a1 , and ρ = a1 /l, a and are the major and minor axes, respectively.  b are the major and minor axes, respectively. Figure  11  shows  the  relationship  between  defect  size  and  failure  strength  [50].  When  λ  =  1,   Figure 11 shows the relationship between defect size and failure strength [50]. When λ = 1, an an ellipsoidal hole reduces to a spherical hole and the strength of materials reaches its maximum.  ellipsoidal hole reduces to a spherical hole and the strength of materials reaches its maximum. With With the decrease of λ, an ellipsoidal hole gradually transits to a slender hole and the strength of  the decrease of λ, an ellipsoidal hole gradually transits to a slender hole and the strength of materials materials decreases rapidly. It explains that a corrosion pit with a circle pattern has a blunt feature,  decreases rapidly. It explains that a corrosion pit with a circle pattern has a blunt feature, which leads which leads to less stress concentration. Obviously, a triangular pyramid‐shaped pit is more irregular,  to less stress concentration. Obviously, a triangular pyramid-shaped pit is more irregular, which which  causes  localized  and  concentrated  material  deterioration  and  leads  to  larger  equivalent   causes localized and concentrated material deterioration and leads to larger equivalent plastic strain. plastic strain. 

Figure 11. Influence of defect on failure stress.  Figure 11. Influence of defect on failure stress.

To  further  discuss  the  effect  of  non‐uniform  corrosion  on  the  mechanical  properties  of  To furtheranother  discussFEA  the analysis  effect ofwas  non-uniform the mechanical of reinforcement,  conducted. corrosion It  is  hard  on to  establish  different properties FEA  models  reinforcement, another FEA analysis was conducted. It is hard to establish different FEA models with identical corrosion mass loss ratios but with different pit distributions. Here, three models with  with identical corrosion mass loss ratios but with different pit distributions. Here, three models with different arithmetical mean deviations but with similar corrosion mass losses were constructed. The  different arithmetical mean deviations but with similar corrosion mass losses were constructed. The maximum difference of corrosion mass loss ratio is only 0.38%, as is shown in Table 8.  maximum difference of corrosion mass loss ratio is only 0.38%, as is shown in Table 8. Table 8. Constructor parameters of corroded reinforcement.  Table 8. Constructor parameters of corroded reinforcement. Code 

Pit Shape 

S/% 

Pit

S/% RaCode ‐1  Spherical  1.72  Shape Ra‐2  Spherical  1.82  Spherical 2.10  1.72 RaR ‐3 a -1 Spherical  Ra -2 Ra -3

Spherical 1.82 Spherical 2.10

Ra of Quadrant   Ra of Quadrant  Ra of Quadrant  Ra of Quadrant  (Ra)ave/μm  (Ra)max/μm  Surface‐1/μm  Surface‐2/μm  Surface‐3/μm  Surface‐4/μm  Ra of Quadrant Ra of Quadrant Ra of Quadrant Ra of Quadrant (Ra )ave / (Ra )max / 417  202  179  251  262  417  Surface-1/µm Surface-2/µm Surface-3/µm Surface-4/µm µm µm 287  491  223  456  364  491  417 417 467  610 202 440  179 340  251 464  262 610 

287 467

491 610

223 440

456 340

364 464

491 610

Figure  12  shows  the  finite  element  model  with  different  pit  distribution.  The  element  type,  mesh,  boundary  condition  and  constitution  model  are  the  same  as  those  described  in  Section  3.2.   Figure 12 shows the finite element model with different pit distribution. The element type, mesh, The overall length of the model is 100 mm. The spherical pits are distributed on the surface profiles  boundary condition and constitution model are the same as those described in Section 3.2. The overall at four lines along the axial direction, equally distributed on the reinforcement surface. Each surface  length of the model is 100 mm. The spherical pits are distributed on the surface profiles at four lines has eight pits with different depth. By using Equation (1), the related arithmetical mean deviation  along the axial direction, equally distributed on the reinforcement surface. Each surface has eight (Ra) was calculated, as is shown in Table 8. Figure 13 plots the related surface profile curves of the  pits with Byseen from  using Equation (1), the related arithmetical mean deviation ratios  (Ra ) was three  FEA different models. depth. It  can be  the  figure  that,  although  the  corrosion mass loss  (S)  11 8571

Materials 2015, 8, 8561–8577

calculated, as is shown in Table 8. Figure 13 plots the related surface profile curves of the three Materials 2015, 8, page–page  FEA models. It can be seen from the figure that, although the corrosion mass loss ratios (S) have Materials 2015, 8, page–page  no significant differences between the three the tortuosity of each curve is curve  found is  tofound  increase have  no  significant  differences  between  the models, three  models,  the  tortuosity  of  each  to  with increased arithmetical mean deviation (R ). This indicates that the non-uniform distribution of have  no  significant  differences  between  the  three  models,  the  tortuosity  of  each  curve  is  found  to  a increase  with  increased  arithmetical  mean  deviation  (Ra).  This  indicates  that  the  non‐uniform  pit depth with  increases with surface roughness of reinforcement. increase  increased  arithmetical  mean  deviation  (Ra).  This  indicates  that  the  non‐uniform  distribution of pit depth increases with surface roughness of reinforcement.  distribution of pit depth increases with surface roughness of reinforcement. 

(a)  (a) 

   

(b)  (b) 

(c)  (c) 

Figure 12. FEA models with different pit distributions based on Table 8: (a) Ra‐1; (b) Ra‐2; (c) Ra‐3.  Figure 12. FEA models with different pit distributions based on Table 8: (a) Raa-1; (b) Raa-2; (c) Raa‐3.  -3. Figure 12. FEA models with different pit distributions based on Table 8: (a) R ‐1; (b) R ‐2; (c) R

(a)  (a) 

(b)  (b) 

   

(c)  (c) 

Figure 13. Surface profile curves of finite element models based on Table 8: (a) Ra‐1; (b) Ra‐2; (c) Ra‐3.  Figure 13. Surface profile curves of finite element models based on Table 8: (a) Ra‐1; (b) Ra‐2; (c) Ra‐3.  Figure 13. Surface profile curves of finite element models based on Table 8: (a) Ra -1; (b) Ra -2; (c) Ra -3.

As is shown in Figures 14 and 15, the non‐uniform distribution of pits has a significant influence on  As is shown in Figures 14 and 15, the non‐uniform distribution of pits has a significant influence on  the mechanical properties of the corroded reinforcement. In general, under the condition of similar  As is shown in Figures 14 and 15 the non-uniform distribution of pits has a significant influence the mechanical properties of the corroded reinforcement. In general, under the condition of similar  corrosion mass loss ratios, the maximum equivalent plastic strain (PEEQ) of corroded reinforcement  on the mechanical properties of the corroded reinforcement. In general, under the condition of similar corrosion mass loss ratios, the maximum equivalent plastic strain (PEEQ) of corroded reinforcement  increases with the increase of Ra. The maximum equivalent plastic strain (PEEQ) on Ra‐1 is 0.7059,  increases with the increase of R a. The maximum equivalent plastic strain (PEEQ) on Ra‐1 is 0.7059,  hence  0.7059  increases  up  to  0.737  on  Ra‐2.  The  increment  is  4.4%.  However,  on  Ra‐3  the  PEEQ  is  8572 hence  0.7059  increases  up ato  0.737  on  Ra‐2.  The  increment  is  4.4%.  However,  on  Ra‐3  the  PEEQ  is  1.176; hence, compared to R ‐1 is an increase of 66.5%, which is very substantial. As shown in Table 8, the  1.176; hence, compared to R a‐1 is an increase of 66.5%, which is very substantial. As shown in Table 8, the  maximum arithmetical mean deviation (Ra)max on Ra‐1 is 417 μm, hence 417 μm increases up to 491 μm  maximum arithmetical mean deviation (Ra)max on Ra‐1 is 417 μm, hence 417 μm increases up to 491 μm  12

Materials 2015, 8, 8561–8577

corrosion mass loss ratios, the maximum equivalent plastic strain (PEEQ) of corroded reinforcement increases with the increase of Ra . The maximum equivalent plastic strain (PEEQ) on Ra -1 is 0.7059, hence 0.7059 increases up to 0.737 on Ra -2. The increment is 4.4%. However, on Ra -3 the PEEQ is 1.176; hence, compared to Ra -1 is an increase of 66.5%, which is very substantial. As shown in Table 8, the maximum arithmetical mean deviation (Ra )max on Ra -1 is 417 µm, hence 417 µm increases up to Materials 2015, 8, page–page  491 µm on Ra -2. The increment is 74 µm. However, on Ra -3 the (Ra )max is 610; hence, compared to Raa-2, an increase of 119 µm. Therefore, the influence of maximum arithmetical mean deviation on R ‐2. The increment is 74 μm. However, on R a‐3 the (Ra)max is 610; hence, compared to Ra‐2, an  (R location a )max may be the main reason for the rapid increment of PEEQ. The most disadvantageous increase of 119 μm. Therefore, the influence of maximum arithmetical mean deviation (R a)max may be  coincides with the pit with the maximum depth. The maximum equivalent plastic strain (PEEQ) the main reason for the rapid increment of PEEQ. The most disadvantageous location coincides with the  increases generally with the increase of load time-history, which leads to the failure of corroded pit with the maximum depth. The maximum equivalent plastic strain (PEEQ) increases generally with  reinforcement under low loads. the increase of load time‐history, which leads to the failure of corroded reinforcement under low loads. 

  (a) 

  (b) 

  (c)  Figure 14. Results of finite element analysis based on Table 8: (a) Ra‐1; (b) Ra‐2; (c) Ra‐3.  Figure 14. Results of finite element analysis based on Table 8: (a) Ra -1; (b) Ra -2; (c) Ra -3.

8573 Figure 15. Load time‐history of maximum equivalent plastic strain. 

  Materials 2015, 8, 8561–8577

(c) 

Figure 14. Results of finite element analysis based on Table 8: (a) Ra‐1; (b) Ra‐2; (c) Ra‐3. 

Figure 15. Load time‐history of maximum equivalent plastic strain.  Figure 15. Load time-history of maximum equivalent plastic strain.

In  order  to  verify  the  results  of  FEA,  tensile  tests  of  the  two  specimens,  RT  and  RTL,   In order to Figure  verify 16  theshows  resultsthe  of stress‐strain  FEA, tensilecurves  tests of RT and was was  conducted.  of the the two two  specimens, reinforcements.  It  is RTL, observed  conducted. Figure 16 shows the stress-strain curves of the two reinforcements. It is observed from from the figure that there exists an obvious difference in the strength. Owing to the more complicated  Materials 2015, 8, page–page  the figure that there exists an obvious difference in the strength. Owing to the more complicated 13 corrosion pitting morphology of reinforcement under the combined effects of carbonation and static corrosion pitting morphology of reinforcement under the combined effects of carbonation and static  loading, the mechanical properties of RTL are remarkably lower than those of the RT specimen. Since loading, the mechanical properties of RTL are remarkably lower than those of the RT specimen. Since the  the two specimens have similar corrosion mass loss ratios, the results indicate that the yield strength two specimens have similar corrosion mass loss ratios, the results indicate that the yield strength and  and ultimate strength of RTL reached 340 and 470 MPa, at values of 92% and 94% of RT, respectively. ultimate strength of RTL reached 340 and 470 MPa, at values of 92% and 94% of RT, respectively. 

  Figure 16. Stress‐strain curves of RT and RTL specimens.  Figure 16. Stress-strain curves of RT and RTL specimens.

4. Conclusions  4. Conclusions This paper has presented an investigation of the corrosion characteristics and tensile behavior  This paper has presented an investigation of the corrosion characteristics and tensile behavior of of  reinforcement  under  the  coupled  action  of  carbonation  and  static  loading.  The  experimental  reinforcement under the coupled action of carbonation and static loading. The experimental results results  showed  that  the  existence  of  a  static  load  affects  the  corrosion  characteristics  of  the  showed that the existence of a static load affects the corrosion characteristics of the reinforcement reinforcement  significantly.  Owing  to  the  coupled  action  of  carbonation  and  static  loading,  the  significantly. Owing to the coupled action of carbonation and static loading, the corrosion pits corrosion  pits  grow  along  the  preferred  orientation,  which  makes  the  corrosion  pit  pattern  more  grow along the preferred orientation, which makes the corrosion pit pattern more angular, and the angular, and the non‐uniform distribution of pit depth in the reinforcement increases significantly.  non-uniform distribution of pit depth in the reinforcement increases significantly. A finite element analysis performed showed that the existence of corrosion pits leads to stress  A finite element analysis performed showed that the existence of corrosion pits leads to stress concentration  in  the  corroded  reinforcement.  The  order  of  the  influence  of  each  variable  are  pit  concentration in the corroded reinforcement. The order of the influence of each variable are pit depth > pit shape > corrosion mass loss ratio > error. The two variables, pit depth and pit shape, are  depth > pit shape > corrosion mass loss ratio > error. The two variables, pit depth and pit shape, the  significant  factors  affecting  the  maximum  equivalent  plastic  strain.  Under  the  condition  of  are the significant factors affecting the maximum equivalent plastic strain. Under the condition of similar corrosion mass loss ratios, the maximum equivalent plastic strain of corroded reinforcement  similar corrosion mass loss ratios, the maximum equivalent plastic strain of corroded reinforcement increases with the increase of Ra and load time‐history. The tensile test has demonstrated that the  increases with the increase of Ra and load time-history. The tensile test has demonstrated that the yield strength and ultimate strength of RTL‐P4 reached 340 and 470 MPa, at values of 92% and 94% of  yield strength and ultimate strength of RTL-P4 reached 340 and 470 MPa, at values of 92% and 94% RT‐P4, respectively.  of RT-P4, respectively. Acknowledgments: The authors wish to acknowledge the financial support of ʺZhejiang Provincial Natural Science  Foundation (Grant No. LY15E080025)ʺ, ʺNational Natural Science Foundation of Chinaʺ (Grant No. 51008276),  ʺNingbo  Science  and  Technology  Service  Demonstration  Projectʺ  (Grant  No.  2014F10016)  and  China  Scholarship  8574 Council  (Grant  No.  201308330417).  The  technical  assistance  of  Professor  Chungxiang  Qian  and  Longyuan  Li  is  greatly appreciated. 

Materials 2015, 8, 8561–8577

Acknowledgments: The authors wish to acknowledge the financial support of "Zhejiang Provincial Natural Science Foundation (Grant No. LY15E080025)", "National Natural Science Foundation of China" (Grant No. 51008276), "Ningbo Science and Technology Service Demonstration Project" (Grant No. 2014F10016) and China Scholarship Council (Grant No. 201308330417). The technical assistance of Professor Chungxiang Qian and Longyuan Li is greatly appreciated. Conflicts of Interest: The authors declare no conflict of interest.

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