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Low Cycle Fatigue Performance Evaluation of TMT rebar
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 4 (2017) 2554–2563
www.materialstoday.com/proceedings
5th International Conference of Materials Processing and Characterization (ICMPC 2016)
Low Cycle Fatigue Performance Evaluation of TMT rebar Bimal Dasa,*, Md Abu Bakkarb, Niloy Khutiaa, Debdulal Dasb a
Department of Aerospace Engineering and Appiled Mechanics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India b Department of Metallurgy and Materials Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India
Abstract In this study, the strain controlled low cycle fatigue performance of thermo-mechanically treated (TMT) rebar is experimentally evaluated and compared with results of finite element simulation considering Chaboche and Ohno-Wang phenomenological cyclic plasticity models. The experimental results reveal that TMT rebar undergoes cyclic softening in all strain ranges and the fatigue crack is observed at the transverse rib region. The finite element simulation results demonstrate that localized plastic deformation and positive strain accumulation occurs at the transverse rib root from which fatigue damage initiates. Evaluation of ductile damage criteria and stress triaxiality shows that fatigue crack initiate and propagate along the transverse rib. ©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords:Type your keywords here, separated by semicolons ;
1. Introduction Reinforcing bars or simply rebars represent the basic strengthening elements of steel reinforced concrete structures. These are responsible for carrying, distributing and controlling loads and displacement of concrete structure. Therefore, rebar finds widespread application in bridges, flyovers, dams, high rise buildings, industrial structures, concrete roads, underground structures etc. In reinforced concrete structure, rebar is used as a basic tensioning element that carries tensile part of loading, whereas, concrete can only withstand compressive load.
* Corresponding author. Tel.: +91-890-059-8039; fax:+91-33-26682916. E-mail address: [email protected] 2214-7853©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).
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In seismic prone areas, reinforced concrete structures are subjected to dynamic loading due to ground motion during their life time. In the event of earthquake, the severe ground motion causes rapid cracking of brittle concrete, and then, rebars are subjected to dynamic loading with large tension and compressive strain reversals. The failure of rebars leads to catastrophic collapse of the whole structure resulting in many causalities and enormous losses. Therefore, performance of rebars under dynamic loading is considered the primary factor for anti-seismic design of civil structure [1]. The failures of rebars under very high strain cycles are due to many factors such as cracking, excessive buckling, corrosion etc. Therefore, it is imperative to design steel reinforced structure in such a way that it can absorb and simultaneously dissipate the load in the form of strain energy, and must undergo high deformation before fracture [2]. Sheng and Gong [3] have investigated the seismic ruin of Tangshan, China occurred in 1976 and it has been concluded that the failure of building is due to low cycle fatigue (LCF) failure of steel rebars. Therefore, it is important to understand LCF performance of steel rebars [4]. Commonly used rebars in the civil engineering structures is thermo-mechanically treated (TMT) rebars. A few investigators [4-9] have examined the LCF behaviour of various grade of rebars [4,5], rebars with different types of rib profiles [6] and rebars after different degree of corrosion [7-9]. Abdalla et al. [10] have analyzed different energy-based models for predicting LCF life of BS460B and BS B500B steel rebars. These investigators have concluded that the hysteresis plastic strain energy dissipated during fatigue loading measured on the basis of average cycles is an accurate parameter for predicting the fatigue life of steel reinforcing bars. Paul et al. [1] have carried out experimental study related to low and high cycle fatigue behaviour of TMT and micro-alloyed rebars. It has been concluded that micro-alloyed rebar yield better fatigue performance over TMT rebar. Earlier, MacGregor et al. [11] and Helgason et al. [12] have demonstrated that the profiled reinforcing bars show better mechanical properties in concrete structure than the smooth bars of same grade of steel. However, Paul et al. [13] recently shown that fatigue performance of rebars deteriorates due to presence of transverse ribs irrespective of stress or strain controlled loading conditions. Apostolopoulos [5] has assessed seismic performance of rebars of S500s grade tempcore in coastal area using laboratory salt spray method and LCF test conditions. It has been shown that the corroded steel bars exhibit a gradual reduction in both the load bearing ability and the number of cycles to failure [5,14]. Jha et al. [2] have demonstrated that corrosion resistant reinforcing bars rather than ordinary steel bars should be used for construction in the seismic prone region. Recently, Lv et al. [15] have studied the high strain LCF behaviour of 400 MPa grades of steel rebars produced by two different methods; namely, micro-alloying and quenched and self tempered methods. These researchers have reported that although the static mechanical properties of two types of rebars is similar, the micro-alloyed rebars exhibit higher cyclic toughness, fatigue life indicating better seismic performance [15] The present investigation focuses on the evaluation of LCF performance of TMT rebar by experimentation and simulation. Elasto-plastic simulation by Finite element analysis using Chaboche and Ohno-Wang models has been performed in addition to the evaluation of ductile damage criteria for the fatigue failure of the rebar. Nomenclature
σ σ
p 0
a i a d
p (i )
f (a ) i i
C
:
,
,r
(i )
stress tensor plastic strain tensor size of current yield surface deviatoric total backstress tensor components of total deviatoric backstress tensor increment in plastic strain tensor magnitude of decomposed back stress tensor kinematic hardening coefficients inner product between tensors
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2. Experimental procedures 2.1. Material and microstructure Commercially available steel rebars of 12 mm diameter of grade Fe 500D as per IS:1786-2008 have been selected for the present investigation. The selected rebars were produced by thermo-mechnical treatment (TMT) that generally carried out in three stages [2]. The first stage constitutes of quenching of hot rolled bars by pressurized water jets that results in formation of martensite on the outer surface, commonly refers to as rim. In the next stage, tempering of the outer surface occurs and the martensitic layer becomes self-tempered. In the last stage, product is left in air to cool down by normal cooling up to ambient temperature that results in the transformation of austenite core into ferrite and pearlite. In order to examine microstructure, specimens of rebars were mechanically polished and etched using nital solution. Typical macro and microstructure of the chosen rebars is shown in Fig. 1. Macrostructure in Fig. 1(a) reveals three distinct zone in the rebars; namely, rim, transition and core regions. As expected for TMT rebars, rim region exhibits tempered martensite structure Fig. 1(b). The thickness of the rim region is measured to be approximately 1 mm. The core region shows ferrite and pearlite structure Fig. 1(d), whereas, the transition zone Fig. 1(c) is expected to be consists of mixture of polygonal ferrite, acicular ferrite, lower/upper bainite and fine pearlite [16].
a
b
Rim
c
Transition
d
Core
Fig. 1. Macro and microstructures of the selected rebar. (a) Overall view showing different regions, whereas (b), (c) and (d) microstructures of rim, transition and core regions, respectively. Specimen is etched using Nital solution.
2.2. Tensile properties Specimens of gauge length 170 mm (total length is 270 mm) were cut from the rebar to evaluate tensile properties. Tensile tests were conducted using closed-loop servo-hydraulic controlled universal testing machine
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(INSTRON 8801) at room temperature in ambient air under constant strain rate of 10-3 s-1. Tensile properties are tabulated in Table 1. Results in Table 1 establish the desired level of tensile properties of the selected grade of rebars. Table 1. Tensile properties of the selected rebar. Yield strength (MPa)
Ultimate tensile strength (MPa)
Uniform elongation (%)
Total elongation (%)
406
630
14.8
20.1
2.3. Low cycle fatigue tests ASTM E606-12 standard recommends use of machined test specimen for low cycle fatigue evaluation. Usually, the specimens are machined to obtain a smooth reduced section having a parallel profile over the gauge length. Generally external geometry of the rebar has various profiles of ribs in order to obtain better bonding with concrete. Moreover, microstructures of TMT rebar in the core and rib are different as earlier (Fig. 1). If the outer surface is removed by machining, the obtain results may not accurately reflect the actual behavior of the rebar [4,5,13]. Therefore, the original cross section of the TMT rebars left unaltered, i.e., as-received un-machine rebars were used as test specimens. The selected gauge length of TMT rebar sample is 20 mm. The strain controlled low cycle fatigue tests were carried out using closed-loop electromechanical actuator controlled (Instron 8862) model attached with 100 kN load cell (Fig. 2). The tests were conducted at five different total axial strain amplitudes of ±0.5%, ±1%, ±1.5%, ±2%, ±2.5% at room temperature in ambient air. Frequency is suitably adjusted so that strain rate is maintained at 10-3 s-1 for all tests. The strain was measured by an external extensometer with gauge length of 12.5 mm (Fig. 2). Sine wave was applied with strain ratio of -1, i.e., fully reversed symmetric cycling. Stress and strain data are stored in a personal computer by an automatic online data acquisition system.
Rebar
Extensometer
Fig. 2. Low cycle fatigue testing arrangement.
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3. Cyclic plasticity models Kinematic hardening models are widely used in finite element simulation to study the cyclic plastic deformation characteristics. In the current work Chaboche and Ohno-Wang kinematic hardening model is selected and the capability to simulate the low cycle fatigue hysteresis loop of TMT rebar is investigated. Many engineering materials loaded in elasto-plastic region during cyclic loading shows hardening/ softening behavior can be modelled and analyzed by incorporating isotropic hardening component to evaluate the yield surface [17]. 3.1. Chaboche model Chaboche kinematic hardening model, a superposition of three Armstrong and Frederick hardening models is used to simulate low cycle fatigue behavior of the material. The expression of backstress increment in the kinematic hardening model proposed by Lemaitre and Chaboche [18] has been expressed as follows:
da
i C i d p 1 σ a i a i d p 1 a i C 0 i
(1)
C
M
Total back stress is computed from the relation, a a
i
(2)
i 1
Expression of yield surface is determined as: σ
0
p b 0 Q 1 e
(3)
Where, 0 is the yield surface size at zero plastic strain, Q and b are material constants that must be calibrated from the test data. Material constants for Chaboche kinematic hardening model are listed in Table 2.
Table 2. Material constants of rebar for Chaboche model (Calibrated from stabilized LCF cycle of ±1.0% strain amplitude) E(GPa)
σ0 (MPa)
C1(GPa)
C2(GPa)
C3(GPa)
γ1
γ2
γ3
Qα(MPa)
b
200
340
125
10
3.3
600
250
0
100
4
3.2 Ohno-Wang model The Ohno-Wang model [19] have incorporated critical state of dynamic recovery on each back stress component based on the plastic strain increment. This rule is composed of several kinematic hardening rules having M number of back stress components, which are expressed as: M
da da
(i )
(4)
i 1
da
(i )
(i ) f (a (i ) ) 2 (i ) p a p (i ) (i ) C d ε γ a d ε : (i ) (i ) 3 f (a ) r
m(i)
(5)
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da
(i ) i r (i ) C γ (i )
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(6)
3 (i ) (i ) (i ) f (a ) a : a 2
(7)
Table 3. Material constants of rebar for Ohno-Wang model Category
Constants (Calibrated from stabilized LCF cycle of ±1.0% strain amplitude)
TMT rebar
C1-C12== 213592.24, 122218.44, 83180.40, 64756.23, 39533.42, 23778.274, 11732.85, 3896.35, 1230.08, 801.47, 418.12, 3545.24 γ1-γ12 =10.34,14.39, 17.23,27.83, 33.30, 39.10, 40.29, 24.47, 10.11, 8.15, 5.07,49.94
4. Experimental results The recorded hysteresis loops of the selected TMT rebar under different applied strain amplitudes are presented in Fig. 3(a). Cyclic softening curve i.e., stress amplitude versus number of cycles plot for different strain amplitude controlled LCF tests of TMT rebar is shown in Fig. 3(b). The results in Fig. 3(b) reveal that irrespective of applied strain amplitudes, stress amplitude gradually decreases with number of cycles which is clear indication of cyclic softening of the material. This is except at very high strain amplitudes (2.0% and 2.5%) where the TMT rebar exhibits a few cycles of initial hardening, i.e., increase of stress amplitudes with number of cycles [13]. The degree of softening is found to be higher in low strain amplitudes when compared to the same obtained in the higher strain amplitudes. For example, the extent of softening is measured as 195 MPa and 82 MPa at strain amplitudes of 0.5% and 2.5%, respectively. Moreover, the number of cycles to failure reduces significantly with increasing strain amplitude Fig. 3(b). However, the rate of softening appears to independent on the magnitude of strain. Typical photographs of fatigue fractured specimens are shown in Fig. 4. It can be seen from Fig. 4(a) that the fatigue crack is initiated from the transverse rib root and propagated along the transverse rib root. Two distinct regions in the facture surface can be observed even in naked eye, one is shiny fatigue fractured region and other one is dull which correspond to the fast fracture region Fig. 4(b). These observations can easily be explained using finite element simulation results which is discussed in the subsequent sections. 5. Finite element simulation results Finite element simulation has been executed using ABAQUS-6.10 commercial software package. The model has been meshed with four noded reduced integration axi-symmetric element (CAX4R). Material constants for OhnoWang and Chaboche were calibrated using the stabilized hysteresis cycle for 1.0% strain amplitude. The material parameter for Chaboche and Ohno-Wang models are listed in Tables 2 and 3, respectively. The finite element simulation of TMT rebar is conducted using these calibrated material constants for all strain amplitudes. The Fig. 5(a), (c)and (e) show the comparison of first cycle hysteresis loop between experiment and simulation results using Chaboche and Ohno-Wang models for 0.5%, 1.0% and 1.5% strain amplitude in low cycle fatigue test. The hysteresis loop obtained from simulation using Chaboche model suitably matches with the experimental for 0.5% and 1.0% strain amplitude. Chaboche model gives better results in comparison with Ohno-Wang model for 0.5% and 1.0% strain amplitudes except 1.5% strain amplitude. The deviation of the simulated results from the experimental at higher strain amplitudes may be due to the calibration of material constants for 1.0 % strain amplitude.
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Fig. 3 (a) Hysteresis loops showing cyclic softening (b) Cyclic softening curve of rebar for different strain amplitude propagation of fatigue crack.
Fast fracture
Fatigue fracture
Fatigue crack origin
Fatigue crack
a
b
Fig. 4. Low cycle fatigue tested rebars at strain amplitude of 1.0%. (a) Showing the fatigue cracking along the transverse rib, and (b) Fracture surface illustrating origin and propagation of fatigue crack.
In the present analysis, axi-symmetric model of TMT rebar has been used in this analysis [6]. The meshing and the distribution of total stress (S22) as shown in Fig.6 (a) explains that the presence of rib on the outer surface leads to stress concentration at the root of the transverse rib. Fig. 6 (b) substantiates the observation of crack initiation from the root of transverse rib where the plastic deformation (PE22) is maximum. The criteria for the damage initiation is well explained by the ductile damage initiation criteria (DUCTRT) shown in Fig. 6(d) which depends on Stress triaxiality (Table 4), fracture strain and strain rate. The positive accumulation of strain and localized plastic deformation in loading direction degrades material stiffness which initiates fatigue crack during cyclic loading. The distribution of stress triaxiality, the ratio of hydrostatic stress and equivalent stress in Fig. 6(c) shows that stress triaxiality is higher, implies a two dimensional plain strain assumption in transverse ribs root region causing propagation of the crack through the region of the transverse rib root. Multiple defects such as porosities, inclusions and presence of flaws heavily influences the fatigue damage [20,21].
Das B/ Materials Today: Proceedings 4 (2017) 2554–2563
Fig. 5 Comparison between experimental and simulation results of first cycle of hysteresis loop tested at strain amplitude of (a) 0.5%, (b) 1.0 %, (c) 1.5%. Stress amplitude versus number of cycles showing cyclic softening at strain amplitude of (d) 0.5%, (e) 1.0 %, (f) 1.5%.
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a
b
c
d
Fig. 6. Distribution of (a) stress in the loading direction (S22), (b) plastic strain in loading direction (PE22), (c) stress triaxiality, and (d) ductile damage initiation criteria during first cycle’s tensile peak for imposed strain amplitude of 1%. Table 4. Damage parameters from analysis Stress Strain Ductile Damage Triaxiality Amplitude(%) (First cycle) (First Cycle) 0.5 1.0 1.5 2.0 2.5
6.52e-01 5.67e-01 6.71e-01 6.72e-01 6.73e-01
2.21e-02 4.00e-02 5.67e-02 6.47e-02 8.02e-02
Number of cycles to failure 689 247 144 84 49
6. Conclusions Low cycle fatigue behaviour of TMT rebar is evaluated with the help of experiment and finite element simulation. The simulation model of the specimen is prepared in 2D framework of ABAQUS Finite Element simulation environment and the phenomenological cyclic plasticity models of Lemaitre and Chaboche as well as Ohno Wang have been used to simulate the low cycle fatigue characteristics. The following conclusions can be drawn from the present work:
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Experiment and simulation results reveal that TMT rebar undergoes cyclic softening under strain controlled loading cycles. At lower strain amplitudes, the softening is intense compared to the amount of softening in higher strain amplitudes. The hysteresis loops for first cycle simulated by the kinematic hardening models of Chaboche and Ohno-Wang matches suitably well with the experimental results except at higher strain amplitudes. It is also demonstrated that the simulation with Chaboche model predicts the hysteresis loop and cyclic softening behaviour of the material better than the Ohno-Wang model. Elasto-plastic finite element analysis results reveal that during cyclic loading, plastic strain gets accumulated near the vicinity of the transverse rib root leading to crack initiation. The simulation has also demonstrated higher triaxiality in the transverse rib root causing propagation of crack along the transverse rib root region irrespective of strain amplitudes. Acknowledgements The support and cooperation received from the Centre of Excellence on Microstructurally Designed Advanced Materials Development, TEQIP-II to carry out a part of this work is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
Paul SK, Rana PK, Das D, Chandra S,Kundu S. High and low cycle fatigue performance comparison between micro-alloyed and TMT rebar. Construction and Building Material 2014;54: 170–179. Jha G, Singh AK, Bandyopadhyay N,Mohanty ON. Seismic Resistant ReinforcingBars. Research and Development Division, Tata Steel, Jamshedpur 2001; 5:53-56. Sheng GM, Gong SH. Investigation of low cycle fatigue behavior of building structural steels under earthquake loading. Acta Metallurgica Sinica 1997;10 (1):51–5. Mander JB, Panthaki FD. Low-cycle fatigue behavior of reinforcing steel. ASCE J Material Civil Engineering 1994;6(4):453–68. Apostolopoulos CA. Mechanical behavior of corroded reinforcing steel bars S500s tempcore under low cycle fatigue. Construction and Building Materials 2007;21(7):1447–56. Zheng H, Abel A. Stress concentration and fatigue of profiled reinforcing steels. International Journal of Fatigue 1998; 20(10):767–73. Apostolopulos C, Passialis V. Use of quality indices in comparison of corroded technical steel bars B500c and S500s on their mechanical performance basis. Construction and Building Materials 2008;22(12):2325–34. Panigrahi BK, Srikanth S, Sahoo G.Effect of Alloying Elements on Tensile Properties, Microstructure, and Corrosion Resistance of Reinforcing Bar Steel. Journal of Materials Engineering and Performance 2009,18:1102–1108. Ray A, Mukerjee D, Sen SK, Bhattacharya A, Dhua SK, Prasad MS,B anerjee N, Popli AM, andSahu AK. Microstructure and Properties of Thermo mechanically Strengthened Reinforcement Bars: A Comparative Assessment of Plain-Carbon and Low-Alloy Steel Grades. Journal of Materials Engineering and Performance 1997;6(3):335-343. Abdalla JA, Hawileh RA, Oudah F, Abdelrahman K. Energy-based prediction of low-cycle fatigue life of BS 460B and BS B500B steel bars. Materials and Design 2009;30:4405–13. MacGregor, J. G., Jhamb, I. C, Nuttall, N. American concrete Institute Journal, 1971March.169. Helgason, T., Hanson, J. M, Somes, N. F., Corley,W. G. and Hognestad, E. Fatigue strength of high-yeld reinforcing bars. National Cooperative highway research program report164, Transportation research board national research council,1976, Washington, D.C. Paul SK,Majumdar S,Kundu S.Low cycle fatigue behavior of thermo-mechanically treated rebar. Materials and Design 2014;58:402–411. Papadopoulos MP, Apostolopoulos CA, Alexopoulos ND, Pantelakis SG. Effect of salt spray corrosion exposure on the mechanical performance of different technical class reinforcing steel bars. Materials and Design 2007;28(8):2318–28. Lv Y., Sheng G , Huang Z. High strain and low cycle fatigue behaviors of rebars produced by QSTand V-N microalloying technology. Construction and Building Materials 2013;48: 67–73 Panigrahi BK , Jain SK. Impact toughness of high strength low alloy TMT reinforcement ribbed bar. Building Material science. 2002;25(4):319–324. Bari S., T. Hassan. An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation. International Journal of Plasticity 2002;Vol.18:873-894. Lemaitre J.,Chaboche J.L.,Mechanics of solid materials, Cambridge University Press,1990. Ohno N, Wang JD. Kinematic hardening rule with critical state of dynamic recovery. International Journal of Plasticity 1993;Vol.9:375403. Singh IV., Mishra B. K, Kumar S., Shedbale A. S. Shedbale. Nonlinear Fatigue Crack Growth Analysis of a Center Crack Plate by XFEM. Advanced Materials Manufacturing & Characterization 2014;4(1). Ramesha C.S, Keshavamurthy R, Madhusudhan J. Fatigue behavior of Ni-P coated Si3N4 reinforced Al6061 composites. Procedia Materials Science 2014;6:1444 – 1454.
ScienceDirect Materials Today: Proceedings 4 (2017) 2554–2563
www.materialstoday.com/proceedings
5th International Conference of Materials Processing and Characterization (ICMPC 2016)
Low Cycle Fatigue Performance Evaluation of TMT rebar Bimal Dasa,*, Md Abu Bakkarb, Niloy Khutiaa, Debdulal Dasb a
Department of Aerospace Engineering and Appiled Mechanics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India b Department of Metallurgy and Materials Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India
Abstract In this study, the strain controlled low cycle fatigue performance of thermo-mechanically treated (TMT) rebar is experimentally evaluated and compared with results of finite element simulation considering Chaboche and Ohno-Wang phenomenological cyclic plasticity models. The experimental results reveal that TMT rebar undergoes cyclic softening in all strain ranges and the fatigue crack is observed at the transverse rib region. The finite element simulation results demonstrate that localized plastic deformation and positive strain accumulation occurs at the transverse rib root from which fatigue damage initiates. Evaluation of ductile damage criteria and stress triaxiality shows that fatigue crack initiate and propagate along the transverse rib. ©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords:Type your keywords here, separated by semicolons ;
1. Introduction Reinforcing bars or simply rebars represent the basic strengthening elements of steel reinforced concrete structures. These are responsible for carrying, distributing and controlling loads and displacement of concrete structure. Therefore, rebar finds widespread application in bridges, flyovers, dams, high rise buildings, industrial structures, concrete roads, underground structures etc. In reinforced concrete structure, rebar is used as a basic tensioning element that carries tensile part of loading, whereas, concrete can only withstand compressive load.
* Corresponding author. Tel.: +91-890-059-8039; fax:+91-33-26682916. E-mail address: [email protected] 2214-7853©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).
Das B/ Materials Today: Proceedings 4 (2017) 2554–2563
2555
In seismic prone areas, reinforced concrete structures are subjected to dynamic loading due to ground motion during their life time. In the event of earthquake, the severe ground motion causes rapid cracking of brittle concrete, and then, rebars are subjected to dynamic loading with large tension and compressive strain reversals. The failure of rebars leads to catastrophic collapse of the whole structure resulting in many causalities and enormous losses. Therefore, performance of rebars under dynamic loading is considered the primary factor for anti-seismic design of civil structure [1]. The failures of rebars under very high strain cycles are due to many factors such as cracking, excessive buckling, corrosion etc. Therefore, it is imperative to design steel reinforced structure in such a way that it can absorb and simultaneously dissipate the load in the form of strain energy, and must undergo high deformation before fracture [2]. Sheng and Gong [3] have investigated the seismic ruin of Tangshan, China occurred in 1976 and it has been concluded that the failure of building is due to low cycle fatigue (LCF) failure of steel rebars. Therefore, it is important to understand LCF performance of steel rebars [4]. Commonly used rebars in the civil engineering structures is thermo-mechanically treated (TMT) rebars. A few investigators [4-9] have examined the LCF behaviour of various grade of rebars [4,5], rebars with different types of rib profiles [6] and rebars after different degree of corrosion [7-9]. Abdalla et al. [10] have analyzed different energy-based models for predicting LCF life of BS460B and BS B500B steel rebars. These investigators have concluded that the hysteresis plastic strain energy dissipated during fatigue loading measured on the basis of average cycles is an accurate parameter for predicting the fatigue life of steel reinforcing bars. Paul et al. [1] have carried out experimental study related to low and high cycle fatigue behaviour of TMT and micro-alloyed rebars. It has been concluded that micro-alloyed rebar yield better fatigue performance over TMT rebar. Earlier, MacGregor et al. [11] and Helgason et al. [12] have demonstrated that the profiled reinforcing bars show better mechanical properties in concrete structure than the smooth bars of same grade of steel. However, Paul et al. [13] recently shown that fatigue performance of rebars deteriorates due to presence of transverse ribs irrespective of stress or strain controlled loading conditions. Apostolopoulos [5] has assessed seismic performance of rebars of S500s grade tempcore in coastal area using laboratory salt spray method and LCF test conditions. It has been shown that the corroded steel bars exhibit a gradual reduction in both the load bearing ability and the number of cycles to failure [5,14]. Jha et al. [2] have demonstrated that corrosion resistant reinforcing bars rather than ordinary steel bars should be used for construction in the seismic prone region. Recently, Lv et al. [15] have studied the high strain LCF behaviour of 400 MPa grades of steel rebars produced by two different methods; namely, micro-alloying and quenched and self tempered methods. These researchers have reported that although the static mechanical properties of two types of rebars is similar, the micro-alloyed rebars exhibit higher cyclic toughness, fatigue life indicating better seismic performance [15] The present investigation focuses on the evaluation of LCF performance of TMT rebar by experimentation and simulation. Elasto-plastic simulation by Finite element analysis using Chaboche and Ohno-Wang models has been performed in addition to the evaluation of ductile damage criteria for the fatigue failure of the rebar. Nomenclature
σ σ
p 0
a i a d
p (i )
f (a ) i i
C
:
,
,r
(i )
stress tensor plastic strain tensor size of current yield surface deviatoric total backstress tensor components of total deviatoric backstress tensor increment in plastic strain tensor magnitude of decomposed back stress tensor kinematic hardening coefficients inner product between tensors
2556
Das B/ Materials Today: Proceedings 4 (2017) 2554–2563
2. Experimental procedures 2.1. Material and microstructure Commercially available steel rebars of 12 mm diameter of grade Fe 500D as per IS:1786-2008 have been selected for the present investigation. The selected rebars were produced by thermo-mechnical treatment (TMT) that generally carried out in three stages [2]. The first stage constitutes of quenching of hot rolled bars by pressurized water jets that results in formation of martensite on the outer surface, commonly refers to as rim. In the next stage, tempering of the outer surface occurs and the martensitic layer becomes self-tempered. In the last stage, product is left in air to cool down by normal cooling up to ambient temperature that results in the transformation of austenite core into ferrite and pearlite. In order to examine microstructure, specimens of rebars were mechanically polished and etched using nital solution. Typical macro and microstructure of the chosen rebars is shown in Fig. 1. Macrostructure in Fig. 1(a) reveals three distinct zone in the rebars; namely, rim, transition and core regions. As expected for TMT rebars, rim region exhibits tempered martensite structure Fig. 1(b). The thickness of the rim region is measured to be approximately 1 mm. The core region shows ferrite and pearlite structure Fig. 1(d), whereas, the transition zone Fig. 1(c) is expected to be consists of mixture of polygonal ferrite, acicular ferrite, lower/upper bainite and fine pearlite [16].
a
b
Rim
c
Transition
d
Core
Fig. 1. Macro and microstructures of the selected rebar. (a) Overall view showing different regions, whereas (b), (c) and (d) microstructures of rim, transition and core regions, respectively. Specimen is etched using Nital solution.
2.2. Tensile properties Specimens of gauge length 170 mm (total length is 270 mm) were cut from the rebar to evaluate tensile properties. Tensile tests were conducted using closed-loop servo-hydraulic controlled universal testing machine
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(INSTRON 8801) at room temperature in ambient air under constant strain rate of 10-3 s-1. Tensile properties are tabulated in Table 1. Results in Table 1 establish the desired level of tensile properties of the selected grade of rebars. Table 1. Tensile properties of the selected rebar. Yield strength (MPa)
Ultimate tensile strength (MPa)
Uniform elongation (%)
Total elongation (%)
406
630
14.8
20.1
2.3. Low cycle fatigue tests ASTM E606-12 standard recommends use of machined test specimen for low cycle fatigue evaluation. Usually, the specimens are machined to obtain a smooth reduced section having a parallel profile over the gauge length. Generally external geometry of the rebar has various profiles of ribs in order to obtain better bonding with concrete. Moreover, microstructures of TMT rebar in the core and rib are different as earlier (Fig. 1). If the outer surface is removed by machining, the obtain results may not accurately reflect the actual behavior of the rebar [4,5,13]. Therefore, the original cross section of the TMT rebars left unaltered, i.e., as-received un-machine rebars were used as test specimens. The selected gauge length of TMT rebar sample is 20 mm. The strain controlled low cycle fatigue tests were carried out using closed-loop electromechanical actuator controlled (Instron 8862) model attached with 100 kN load cell (Fig. 2). The tests were conducted at five different total axial strain amplitudes of ±0.5%, ±1%, ±1.5%, ±2%, ±2.5% at room temperature in ambient air. Frequency is suitably adjusted so that strain rate is maintained at 10-3 s-1 for all tests. The strain was measured by an external extensometer with gauge length of 12.5 mm (Fig. 2). Sine wave was applied with strain ratio of -1, i.e., fully reversed symmetric cycling. Stress and strain data are stored in a personal computer by an automatic online data acquisition system.
Rebar
Extensometer
Fig. 2. Low cycle fatigue testing arrangement.
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3. Cyclic plasticity models Kinematic hardening models are widely used in finite element simulation to study the cyclic plastic deformation characteristics. In the current work Chaboche and Ohno-Wang kinematic hardening model is selected and the capability to simulate the low cycle fatigue hysteresis loop of TMT rebar is investigated. Many engineering materials loaded in elasto-plastic region during cyclic loading shows hardening/ softening behavior can be modelled and analyzed by incorporating isotropic hardening component to evaluate the yield surface [17]. 3.1. Chaboche model Chaboche kinematic hardening model, a superposition of three Armstrong and Frederick hardening models is used to simulate low cycle fatigue behavior of the material. The expression of backstress increment in the kinematic hardening model proposed by Lemaitre and Chaboche [18] has been expressed as follows:
da
i C i d p 1 σ a i a i d p 1 a i C 0 i
(1)
C
M
Total back stress is computed from the relation, a a
i
(2)
i 1
Expression of yield surface is determined as: σ
0
p b 0 Q 1 e
(3)
Where, 0 is the yield surface size at zero plastic strain, Q and b are material constants that must be calibrated from the test data. Material constants for Chaboche kinematic hardening model are listed in Table 2.
Table 2. Material constants of rebar for Chaboche model (Calibrated from stabilized LCF cycle of ±1.0% strain amplitude) E(GPa)
σ0 (MPa)
C1(GPa)
C2(GPa)
C3(GPa)
γ1
γ2
γ3
Qα(MPa)
b
200
340
125
10
3.3
600
250
0
100
4
3.2 Ohno-Wang model The Ohno-Wang model [19] have incorporated critical state of dynamic recovery on each back stress component based on the plastic strain increment. This rule is composed of several kinematic hardening rules having M number of back stress components, which are expressed as: M
da da
(i )
(4)
i 1
da
(i )
(i ) f (a (i ) ) 2 (i ) p a p (i ) (i ) C d ε γ a d ε : (i ) (i ) 3 f (a ) r
m(i)
(5)
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da
(i ) i r (i ) C γ (i )
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(6)
3 (i ) (i ) (i ) f (a ) a : a 2
(7)
Table 3. Material constants of rebar for Ohno-Wang model Category
Constants (Calibrated from stabilized LCF cycle of ±1.0% strain amplitude)
TMT rebar
C1-C12== 213592.24, 122218.44, 83180.40, 64756.23, 39533.42, 23778.274, 11732.85, 3896.35, 1230.08, 801.47, 418.12, 3545.24 γ1-γ12 =10.34,14.39, 17.23,27.83, 33.30, 39.10, 40.29, 24.47, 10.11, 8.15, 5.07,49.94
4. Experimental results The recorded hysteresis loops of the selected TMT rebar under different applied strain amplitudes are presented in Fig. 3(a). Cyclic softening curve i.e., stress amplitude versus number of cycles plot for different strain amplitude controlled LCF tests of TMT rebar is shown in Fig. 3(b). The results in Fig. 3(b) reveal that irrespective of applied strain amplitudes, stress amplitude gradually decreases with number of cycles which is clear indication of cyclic softening of the material. This is except at very high strain amplitudes (2.0% and 2.5%) where the TMT rebar exhibits a few cycles of initial hardening, i.e., increase of stress amplitudes with number of cycles [13]. The degree of softening is found to be higher in low strain amplitudes when compared to the same obtained in the higher strain amplitudes. For example, the extent of softening is measured as 195 MPa and 82 MPa at strain amplitudes of 0.5% and 2.5%, respectively. Moreover, the number of cycles to failure reduces significantly with increasing strain amplitude Fig. 3(b). However, the rate of softening appears to independent on the magnitude of strain. Typical photographs of fatigue fractured specimens are shown in Fig. 4. It can be seen from Fig. 4(a) that the fatigue crack is initiated from the transverse rib root and propagated along the transverse rib root. Two distinct regions in the facture surface can be observed even in naked eye, one is shiny fatigue fractured region and other one is dull which correspond to the fast fracture region Fig. 4(b). These observations can easily be explained using finite element simulation results which is discussed in the subsequent sections. 5. Finite element simulation results Finite element simulation has been executed using ABAQUS-6.10 commercial software package. The model has been meshed with four noded reduced integration axi-symmetric element (CAX4R). Material constants for OhnoWang and Chaboche were calibrated using the stabilized hysteresis cycle for 1.0% strain amplitude. The material parameter for Chaboche and Ohno-Wang models are listed in Tables 2 and 3, respectively. The finite element simulation of TMT rebar is conducted using these calibrated material constants for all strain amplitudes. The Fig. 5(a), (c)and (e) show the comparison of first cycle hysteresis loop between experiment and simulation results using Chaboche and Ohno-Wang models for 0.5%, 1.0% and 1.5% strain amplitude in low cycle fatigue test. The hysteresis loop obtained from simulation using Chaboche model suitably matches with the experimental for 0.5% and 1.0% strain amplitude. Chaboche model gives better results in comparison with Ohno-Wang model for 0.5% and 1.0% strain amplitudes except 1.5% strain amplitude. The deviation of the simulated results from the experimental at higher strain amplitudes may be due to the calibration of material constants for 1.0 % strain amplitude.
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Fig. 3 (a) Hysteresis loops showing cyclic softening (b) Cyclic softening curve of rebar for different strain amplitude propagation of fatigue crack.
Fast fracture
Fatigue fracture
Fatigue crack origin
Fatigue crack
a
b
Fig. 4. Low cycle fatigue tested rebars at strain amplitude of 1.0%. (a) Showing the fatigue cracking along the transverse rib, and (b) Fracture surface illustrating origin and propagation of fatigue crack.
In the present analysis, axi-symmetric model of TMT rebar has been used in this analysis [6]. The meshing and the distribution of total stress (S22) as shown in Fig.6 (a) explains that the presence of rib on the outer surface leads to stress concentration at the root of the transverse rib. Fig. 6 (b) substantiates the observation of crack initiation from the root of transverse rib where the plastic deformation (PE22) is maximum. The criteria for the damage initiation is well explained by the ductile damage initiation criteria (DUCTRT) shown in Fig. 6(d) which depends on Stress triaxiality (Table 4), fracture strain and strain rate. The positive accumulation of strain and localized plastic deformation in loading direction degrades material stiffness which initiates fatigue crack during cyclic loading. The distribution of stress triaxiality, the ratio of hydrostatic stress and equivalent stress in Fig. 6(c) shows that stress triaxiality is higher, implies a two dimensional plain strain assumption in transverse ribs root region causing propagation of the crack through the region of the transverse rib root. Multiple defects such as porosities, inclusions and presence of flaws heavily influences the fatigue damage [20,21].
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Fig. 5 Comparison between experimental and simulation results of first cycle of hysteresis loop tested at strain amplitude of (a) 0.5%, (b) 1.0 %, (c) 1.5%. Stress amplitude versus number of cycles showing cyclic softening at strain amplitude of (d) 0.5%, (e) 1.0 %, (f) 1.5%.
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a
b
c
d
Fig. 6. Distribution of (a) stress in the loading direction (S22), (b) plastic strain in loading direction (PE22), (c) stress triaxiality, and (d) ductile damage initiation criteria during first cycle’s tensile peak for imposed strain amplitude of 1%. Table 4. Damage parameters from analysis Stress Strain Ductile Damage Triaxiality Amplitude(%) (First cycle) (First Cycle) 0.5 1.0 1.5 2.0 2.5
6.52e-01 5.67e-01 6.71e-01 6.72e-01 6.73e-01
2.21e-02 4.00e-02 5.67e-02 6.47e-02 8.02e-02
Number of cycles to failure 689 247 144 84 49
6. Conclusions Low cycle fatigue behaviour of TMT rebar is evaluated with the help of experiment and finite element simulation. The simulation model of the specimen is prepared in 2D framework of ABAQUS Finite Element simulation environment and the phenomenological cyclic plasticity models of Lemaitre and Chaboche as well as Ohno Wang have been used to simulate the low cycle fatigue characteristics. The following conclusions can be drawn from the present work:
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Experiment and simulation results reveal that TMT rebar undergoes cyclic softening under strain controlled loading cycles. At lower strain amplitudes, the softening is intense compared to the amount of softening in higher strain amplitudes. The hysteresis loops for first cycle simulated by the kinematic hardening models of Chaboche and Ohno-Wang matches suitably well with the experimental results except at higher strain amplitudes. It is also demonstrated that the simulation with Chaboche model predicts the hysteresis loop and cyclic softening behaviour of the material better than the Ohno-Wang model. Elasto-plastic finite element analysis results reveal that during cyclic loading, plastic strain gets accumulated near the vicinity of the transverse rib root leading to crack initiation. The simulation has also demonstrated higher triaxiality in the transverse rib root causing propagation of crack along the transverse rib root region irrespective of strain amplitudes. Acknowledgements The support and cooperation received from the Centre of Excellence on Microstructurally Designed Advanced Materials Development, TEQIP-II to carry out a part of this work is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
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