Issue 42

Frattura ed Integrità Strutturale, 42 (2017); International Journal of the Italian Group of Fracture

Table of Contents

I. Milošević, G. Winter, F. Grün, Martin Kober Influence of the stress gradient on the fatigue life calculation of a martensitic high strength steel …............. 1 M. C. Vasco, P. Polydoropoulou, A. N. Chamos, S. G. Pantelakis. Effect of corrosion and sandblasting on the high cycle fatigue behavior of reinforcing B500C steel bars … 9 D. Rozumek, S. Faszynka Fatigue crack growth in 2017A-T4 alloy subjected to proportional bending with torsion …………… 23 R.Pawliczek, C.T Lachowicz Modeling of the stress-strain relationship for specimens made of S355J0 steel subjected to bending block loading with mean load ........................................................................................................................ 30 D. Rozumek, Z. Marciniak Crack growth of explosive welding zirconium-steel bimetal subjected to cyclic bending …….....……… 40 M. Olzak, J. Piechna, P. Pyrzanowski Numerical analysis of the influence of liquid on propagation of a rolling contact fatigue crack ………….. 46 S. Seitl, J. D. Ríos, H. Cifuentes Comparison of fracture toughness values of normal and high strength concrete determined by three point bend and modified disk-shaped compact tension specimens ………………………………………. 56 O. Krepl, J. Klusák Crack onset assessment near the sharp material inclusion tip by means of modified maximum tangential stress criterion …………………………………………………………………………...... 66 P.J. Huffman, J. Ferreira, J.A.F.O. Correia, A.M.P. De Jesus, G. Lesiuk, F. Berto, A. Fernández-Canteli, G. Glinka Fatigue crack propagation prediction of a pressure vessel mild steel based on a strain energy density model 74 M. Kowalski Identification of fatigue and mechanical characteristics of explosively welded steel - titanium composite.…….................................................................................................................................... 85 H. Carvalho, R. Hallal Fakury, P. Moura Leite Vilela Structural integrity assessment and rehabilitating of Hercilio Luz bridge …………………………... 93 P. Raposo, J.A.F.O. Correia, A.M.P. De Jesus, R.A.B. Calçada, G. Lesiuk, M. Hebdon, A. Fernández-Canteli Probabilistic fatigue S-N curves derivation for notched components ………………………................ 105

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Fracture and Structural Integrity, 42 (2017); ISSN 1971-9883

Stanislav Seitl, Petr Miarka Evaluation of mixed mode I/II fracture toughness of C 50/60 from Brazilian disc test ……………... 119 V. R ů ži č ka, L. Malíková, S. Seitl Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms ………………………………………………………………………...… 128 J.A.F.O. Correia, A.M.P. De Jesus, R. Calçada, B. Pedrosa, C. Rebelo, Luis Simões da Silva, G. Lesiuk Statistical analysis of fatigue crack propagation data of materials from ancient portuguese metallic bridges 136 W. De Corte, P. Helincks, V. Boel, J. Klusák, S. Seitl, G. De Schutter Generalised fracture mechanics approach to the interfacial failure analysis of a bonded steel-concrete joint 147 J. Klon, S. Seitl, H. Šimonová, Z. Keršner, I. Kumpová, D. Vav ř ík Pilot evaluation of a fracture process zone in a modified compact tension specimen by X-ray tomography 161 M. Davydova, I. Panteleev, O. Naimark Fragmentation of Mansurov granite under quasi-static compression …………………………...….. 170 A. De Santis, D. Iacoviello, V. Di Cocco, F. Iacoviello Classification of ductile cast iron specimens: a machine learning approach ………………………..… 231 A. Khitab, S. Ahmad, R. A. Khushnood, S. A. Rizwan, G. A. Ferro, L. Restuccia, M. Ali, I. Mehmood Fracture toughness and failure mechanism of high performance concrete incorporating carbon nanotubes .. 239 A. Jadidi, E. Zeighami, M. Amiri Experimental evaluation of steel fiber effect on mechanical properties of steel fiber-reinforced cement matrix 249 J.-f. He, Q.-l. Yin, K. Yin Study on the abrasion property of the anvil inside a hydraulic DTH hammer fitted with horizontal oriented sliders ………………………………………………………………………..…... 263 A. Brotzu, F. Felli, D.Pilone Investigation on some factors affecting crack formation in high resistance aluminum alloys …………….. 272 J.-M. Nianga, D. Marhabi Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks ……… 280 D. V. Orlova, A. G. Lunev, L. V. Danilova, L. B. Zuev Macroscopic criteria for the deformation and fracture of iron based alloys …………...……………… 293 T. V. Tretyakova, V. E. Wildemann Influence the loading conditions and the stress concentrators on the spatial-time inhomogeneity due to the yield delay and the jerky flow: study by using the digital image correlation and the infrared analysis …….. 303 G. Testa, N. Bonora, D. Gentile, A. Ruggiero, G. Iannitti, A. Carlucci, Y. Madi Strain capacity assessment of API X65 steel using damage mechanics …………………………….. 315 G. Bolzon, M. Shahmardani, R. Liu, E. Zappa Failure analysis of thin metal foils …………………………………..……………………….. 328

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Frattura ed Integrità Strutturale, 42 (2017); International Journal of the Italian Group of Fracture

M. Tocci, A. Pola, L. Montesano, G. M. La Vecchia, M. Merlin, G. L. Garagnani Investigation of mechanical properties of AlSi3Cr alloy ……………………………………..…... 337 A. Strafella, A. Coglitore, P. Fabbri, E. Salernitano 15-15Ti(Si) austenitic steel: creep behaviour in hostile environment ………………………………. 352

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Fracture and Structural Integrity, 42 (2017); ISSN 1971-9883

Editor-in-Chief Francesco Iacoviello

(Università di Cassino e del Lazio Meridionale, Italy)

Associate Editors Alfredo Navarro

(Escuela Superior de Ingenieros, Universidad de Sevilla, Spain)

Thierry Palin-Luc

(Arts et Metiers ParisTech, France ) (University of Sheffield, UK) (University of Manchester, UK)

Luca Susmel John Yates

Guest Editors ( “ Mechanical Fatigue of Metals”) J.A.F.O. Correia

(University of Porto, Portugal) (University of Porto, Portugal ) (University of Oviedo, Spain) (University of Oviedo, Spain)

A.M.P. De Jesus

M. Calvente

A. Fernández-Canteli

Advisory Editorial Board Harm Askes

(University of Sheffield, Italy) (Tel Aviv University, Israel) (Politecnico di Torino, Italy) (Università di Parma, Italy) (Politecnico di Torino, Italy)

Leslie Banks-Sills Alberto Carpinteri Andrea Carpinteri Emmanuel Gdoutos Youshi Hong M. Neil James Gary Marquis Ashok Saxena Darrell F. Socie Shouwen Yu Ramesh Talreja David Taylor Robert O. Ritchie Cetin Morris Sonsino Donato Firrao

(Democritus University of Thrace, Greece) (Chinese Academy of Sciences, China)

(University of Plymouth, UK)

(Helsinki University of Technology, Finland)

(University of California, USA)

(Galgotias University, Greater Noida, UP, India; University of Arkansas, USA)

(University of Illinois at Urbana-Champaign, USA)

(Tsinghua University, China) (Fraunhofer LBF, Germany) (Texas A&M University, USA) (University of Dublin, Ireland)

Editorial Board Stefano Beretta

(Politecnico di Milano, Italy)

Filippo Berto Nicola Bonora

(Norwegian University of Science and Technology, Norway) (Università di Cassino e del Lazio Meridionale, Italy)

Elisabeth Bowman

(University of Sheffield) (Università di Parma, Italy) (Politecnico di Torino, Italy) (University of Porto, Portugal) (EADS, Munich, Germany)

Luca Collini

Mauro Corrado

José António Correia Claudio Dalle Donne Manuel de Freitas

(EDAM MIT, Portugal)

Abílio de Jesus

(University of Porto, Portugal)

Vittorio Di Cocco

(Università di Cassino e del Lazio Meridionale, Italy)

Daniele Dini

(Imperial College, UK)

Giuseppe Ferro Tommaso Ghidini

(Politecnico di Torino, Italy)

(European Space Agency - ESA-ESRIN) (Universitat Politecnica de Valencia, Spain) (National Technical University of Athens, Greece)

Eugenio Giner

Stavros Kourkoulis

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Frattura ed Integrità Strutturale, 42 (2017); International Journal of the Italian Group of Fracture

Paolo Lonetti Carmine Maletta Liviu Marsavina

(Università della Calabria, Italy) (Università della Calabria, Italy) (University of Timisoara, Romania) (University of Porto, Portugal)

Lucas Filipe Martins da Silva

Hisao Matsunaga Mahmoud Mostafavi

(Kyushu University, Japan) (University of Sheffield, UK)

Marco Paggi Oleg Plekhov

(IMT Institute for Advanced Studies Lucca, Italy)

(Russian Academy of Sciences, Ural Section, Moscow Russian Federation)

Alessandro Pirondi

(Università di Parma, Italy)

Luis Reis

(Instituto Superior Técnico, Portugal)

Luciana Restuccia Giacomo Risitano Roberto Roberti Aleksandar Sedmak Andrea Spagnoli Sabrina Vantadori Natalya D. Vaysfel'd Charles V. White Marco Savoia

(Politecnico di Torino, Italy) (Università di Messina, Italy) (Università di Brescia, Italy) (Università di Bologna, Italy) (University of Belgrade, Serbia) (Università di Parma, Italy) (Università di Parma, Italy)

(Odessa National Mechnikov University, Ukraine)

(Kettering University, Michigan,USA)

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Fracture and Structural Integrity, 42 (2017); ISSN 1971-9883

Journal description and aims Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is the official Journal of the Italian Group of Fracture. It is an open-access Journal published on-line every three months (July, October, January, April). Frattura ed Integrità Strutturale encompasses the broad topic of structural integrity, which is based on the mechanics of fatigue and fracture, and is concerned with the reliability and effectiveness of structural components. The aim of the Journal is to promote works and researches on fracture phenomena, as well as the development of new materials and new standards for structural integrity assessment. The Journal is interdisciplinary and accepts contributions from engineers, metallurgists, materials scientists, physicists, chemists, and mathematicians. Contributions Frattura ed Integrità Strutturale is a medium for rapid dissemination of original analytical, numerical and experimental contributions on fracture mechanics and structural integrity. Research works which provide improved understanding of the fracture behaviour of conventional and innovative engineering material systems are welcome. Technical notes, letters and review papers may also be accepted depending on their quality. Special issues containing full-length papers presented during selected conferences or symposia are also solicited by the Editorial Board. Manuscript submission Manuscripts have to be written using a standard word file without any specific format and submitted via e-mail to gruppofrattura@gmail.com. Papers should be written in English. A confirmation of reception will be sent within 48 hours. The review and the on-line publication process will be concluded within three months from the date of submission. Peer review process Frattura ed Integrità Strutturale adopts a single blind reviewing procedure. The Editor in Chief receives the manuscript and, considering the paper’s main topics, the paper is remitted to a panel of referees involved in those research areas. They can be either external or members of the Editorial Board. Each paper is reviewed by two referees. After evaluation, the referees produce reports about the paper, by which the paper can be: a) accepted without modifications; the Editor in Chief forwards to the corresponding author the result of the reviewing process and the paper is directly submitted to the publishing procedure; b) accepted with minor modifications or corrections (a second review process of the modified paper is not mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. c) accepted with major modifications or corrections (a second review process of the modified paper is mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. d) rejected. The final decision concerning the papers publication belongs to the Editor in Chief and to the Associate Editors. The reviewing process is usually completed within three months. The paper is published in the first issue that is available after the end of the reviewing process.

Publisher Gruppo Italiano Frattura (IGF) http://www.gruppofrattura.it ISSN 1971-8993 Reg. Trib. di Cassino n. 729/07, 30/07/2007

Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0)

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Frattura ed Integrità Strutturale, 42 (2017); International Journal of the Italian Group of Fracture

International colloquium on fatigue of metals

J.A.F.O. Correia, A.M.P. De Jesus INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal M. Calvente, A. Fernández-Canteli Department of Construction and Manufacturing Engineering, Univ. of Oviedo, 33203 Gijón, Spain he first International Colloquium on Mechanical Fatigue of Metals (ICMFM) was organized in Brno, Czech Republic in 1968. Afterwards, regular Colloquia on Mechanical Fatigue of Metals started in 1972 also in Brno and were originally limited to participants from the countries of the former “Eastern Block”. They continued until the 12th Colloquium in 1994 (Miskolc, Hungary) every two years. After a twelve years long break, the Colloquia restarted in 2006 (Ternopil, Ukraine), followed by the ones in 2008 (Varna, Bulgaria), 2010 (Opole, Poland), 2012 (Brno, Czech Republic), until the last one, which was organized in 2014 in Verbania, Italy, with the aim of opening the Colloquia to participants from all countries interested in the subject of fatigue of metallic materials. The XVIII International Colloquium on Mechanical Fatigue of Metals (ICMFM XVIII) was organized in Gijón, in September 2016, which is a city located at seaside in the delightful northern coast of Spain. This conference is aimed at facilitating and encouraging the exchange of knowledge and experiences among the different communities involved in both basic and applied research in this field, the fatigue of metals, looking at the problem of fatigue from microscopic, analytical, simulative and applicative points of view. Conference chairs express their gratitude to the members of the ICM Executive Committee and the International Advisory Committee for their strong support. This special issue is related with the selected papers of the contributions presented in ICMFM XVIII conference. The selected papers cover a significant range of the following topics: - Cyclic plasticity and internal structure; - Low and high cycle fatigue; - Mechanisms of fatigue damage; - Fracture Mechanics; - Life prediction; - Fatigue modelling; - Multiaxial fatigue; - Fatigue-corrosion. As guest editors, we would also like to express our gratitude to all authors for their contributions and to all reviewers for their generous work. Finally, the guest editors would like to dedicate special thanks to Prof. Francesco Iacoviello, editor-in-chief of Frattura ed Integrità Strutturale/Fracture and Structural Integrity by the availability and support during the preparation of this volume. T

VII

I. Milošević et alii, Frattura ed Integrità Strutturale, 42 (2017) 1-8; DOI: 10.3221/IGF-ESIS.42.01

Focused on Mechanical Fatigue of Metals

Influence of the stress gradient on the fatigue life calculation of a martensitic high strength steel

Igor Milošević, Gerhard Winter, Florian Grün Montanuniversität Leoben, Franz-Josef-Strasse 18, 8700 Leoben, Austria igor.milosevic@unileoben.ac.at, gerhard.winter@unileoben.ac.at, Florian.gruen@unileoben.ac.at Martin Kober LEC GmbH, Inffeldgasse 19/11, 8010 Graz, Austria Martin.kober@lec.tugraz.at A BSTRACT . Nowadays lifetime calculation in the high cycle fatigue region is commonly based on S/N curves which are modified by different influences to ensure accurate results. Especially the application of these models is important when small components with complex stress distributions are used. The influence of the stress distribution was considered by the stress gradient approach which is implemented in the lifetime tool FEMFAT. Specimens with diameters of D4mm and D7.5mm were used to examine the effect of the calculation modified by the stress gradient. On the one hand regarding different types of this approach it can be shown that the results fit very well compared to the testing results but on the other hand a big difference was observed when the gradient increases by smaller specimen sizes. K EYWORDS . High cycle fatigue; stress gradient approach; lifetime calculation; stress based approaches; martensitic high strength steel.

Citation: Milošević, I., Winter, G., Gruen, F., Kober, M., Influence of the stress gradient on the fatigue life calculation of a martensitic high strength steel, 42 (2017) 1-8.

Received: 31.05.2017 Accepted: 07.06.2017 Published: 01.10.2017

Copyright: © 2017 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

I NTRODUCTION

resent technical applications regarding weight reduction and higher loads lead to increasingly complex component geometries. These complex shapes require high demands on the lifetime and therefore the lifetime calculation based on different models. Since the finite element analysis (FEA) is capable of determining different load situations and the resulting stress and strain distributions the influence of the stress distribution is implemented into commonly used simulation tools like FEMFAT known as the stress gradient approach. In the actual case, the focus is mainly set on the lifetime calculation under the stress gradient influence. Material testing is always affected by other additional influences as size effect, temperatures, residual stresses and the stress distribution itself through different types of loads, which could cause an impact on the material properties. This has to be considered within the lifetime calculation of complex components. P

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I. Milošević et alii, Frattura ed Integrità Strutturale, 42 (2017) 1-8; DOI: 10.3221/IGF-ESIS.42.01

The lifetime is being calculated by consideration of appearing stresses (bending loading). This was implemented into the post processing process and is going to be parameterized. In this paper it will be shown how the different size of tested specimens affect the lifetime compared to testing results.

S TRESS CALCULATION

T

he fact that local stress concentrations decrease the expected components lifetime has been known for a long time investigated first through the work of Neuber [1]. The geometrical properties of mechanical components are designed to fulfil essential functions like transfer of forces and motion for example. Therefore, a practical way has to be found how to observe these geometrical influences and to implement the effect into lifetime calculations. Before the effect of stress concentrations is discussed regarding the FEA results a closer look at the difference between notched and unnotched shapes will be presented. In the unavoidable event of geometrical discontinuities, the difference of the stress distribution is shown by two examples in Fig. 1. [2]

Figure 1 : Difference between the nominal stress σn and the maximal stress at the notch σ max [2].

On the left a smooth machined specimen is described where the nominal stress (σ n ) can be calculated through easy analytical approaches. In case of simple shapes the FEA results fits the analytical results very well. The stress will be evenly distributed (as long as no major defects within the microstructure are present) throughout the cross section. A highly uneven distributed stress curve is caused by a notched geometry, on the right, which is described by the maximum stress (σ max ) occurring in the notch root. As there can be observed a clear deviation from nominal stresses another sufficient description has to be applied to notched components. [1–3]. To describe the effect of notches depending on unnotched areas and their nominal stress behaviour an elastic stress intensity factor (K t ) was invented (1). The maximum stress is connected with the nominal stress through K t . The stress intensity factor is only dependant on the geometry of the notch. K t is determined by the local geometrical properties [2].





n 

K

(1)

*

max

t

Not only the intensity factor has an influence on the notch effect, the course of the stress at the notch root is being a matter of importance. The amount of stress increase is given by the differential quotient dσ/dx. To define a stress gradient at the notch root just under the surface the quotient is divided by the maximum stress in order to provide an evaluation criterion. The mathematical and graphical description of the relative stress gradient   , is given by (2) and Fig. 2 [2–6].

d      dx  

1 





(2)



max

2

I. Milošević et alii, Frattura ed Integrità Strutturale, 42 (2017) 1-8; DOI: 10.3221/IGF-ESIS.42.01

Figure 2 : Description oft the relative stress gradient χ’ [2].

The relative gradient is dependent on the application of different types of stress to a certain geometry (bending loading in Fig. 3). This natural stress gradient, shown in Fig. 3, is pointing out that for example smaller specimen sizes lead to different stress gradients. In this case the gradient is represented by the function of the specimen thickness 2 / b    . [2]

Figure 3 : Influence of the loading type to the stress gradient occurrence [2].

Different approaches have been invented regarding the assessment of a stress gradient, which are used to determine local component strengths. The approach of interest was introduced by Eichlseder [6] being applied as an exponential function to describe the nonlinear behavior of the fatigue limit increase caused by the stress gradient. The fatigue limits of compression/ tension loaded specimens f ,t σ ( 0    ) and bending loaded specimens f ,b σ ( 2 / b    ), both unnotched behave according to this approach. Taking f ,t σ as the initial condition the local fatigue limit f ,l σ according to the local   is calculated by the multiplication with the notch sensitivity factor χ n which are pointed out below in (3) and (4). Since this nonlinear behavior is material specific the material parameter D K has to be determined. [3–6]







n

*

( 3 )



, f l

, f t

     

     

K

   

  

D

  

 

 



, f b

1    

n

1 * 

(4)



2    

  

, f t

    

b

For a sufficient lifetime calculation the adjustment of the local strength is not enough as common high cycle fatigue damage models are defined by S/N curves which are given by the fatigue limit, the slope k and the cycles at the fatigue limit D N [2].

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I. Milošević et alii, Frattura ed Integrità Strutturale, 42 (2017) 1-8; DOI: 10.3221/IGF-ESIS.42.01

max K k k 

min  

k k

min

( 5 )

n

k



( K log N log N  ) ( D max

)

  D log N log N  





D min

(6)

D min

n

n



Eqs. (5) and (6) explain the mathematical background behind the adjustment of the local S/N curve modification. S/N parameters are modified by another set of key ratios k K and n K which are dependent on the group of materials used in the calculation. The min and max values of k and D N are given by the limits of fatigue testing. All these influences were implemented into the calculation tool establishing a contribution to the calculation process of complex components. [2]

E XPERIMENTAL

T

he material used in the actual investigations was a high strength martensitic steel commonly known as 1.4542, X5CrNiCuNb16-4 according to EN standards and A480 (630) according to ASTM standards. An extract of the chemical composition is given in the Tab. 1 below. Depending on the type of application different heat treatments can be carried out to achieve the final condition.

C

Si

Cr

Ni

Cu

0.04

0.25

15.30

4.50

3.25

Table 1 : Chemical composition in percent by weight (wt%, EN 10088-3).

Figure 4 : Test setup for rotating bending tests, a constant bending moment is applied over the cross section

Bending loading fatigue tests were carried out on a testing rig which was developed by the Chair of Mechanical Engineering at the Montanuniversität in Leoben. The setup provides a constant bending moment over the whole cross section of the specimen geometry. Two different specimen sizes (testing diameter 4mm and 7.5mm) were used to examine the influence of the stress gradient. A fillet radius of 50mm was used at both specimens as displayed in the technical drawing in Fig. 5.

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I. Milošević et alii, Frattura ed Integrità Strutturale, 42 (2017) 1-8; DOI: 10.3221/IGF-ESIS.42.01

Figure 5 : Shape of the tested specimens, D=4mm.

L IFETIME VALUATION

T

he FEA calculations were carried out through Abaqus/CAE. According to the sketch above the specimen geometry was built up and the boundary conditions were modified. Bending loading was applied on the modelled geometry. For a sufficient stress gradient calculation different parameters had to be adjusted to guarantee accurate results. Best results at the stress assessment process were achieved through the usage of quadratic elements without reduced integration (C3D8). High distortion of the elements should be prevented otherwise poor results occured. The most critical parameter was the number of elements used in this simulation. Altogether 3200 elements should be used to reach a stabilized (more elements - no significant improvement) stress level [7].

D4

D7.5

χ’ 0.279 Table 2 : Calculated stress gradients at the surface of different specimen sizes. 0.511

In Tab. 2 the calculated stress gradients can be see depending on the specimen diameter. The stress gradient decreased with increasing specimen size nearly being halfed. Both specimens were applied with a nominal stress (direction in the axis of the specimen) of 1.0 MPa which also showed no real value of K t . The fatigue calculations were carried out with FEMFAT 5.2a. Modifications were done according the FEA results and the appropriate material parameters from testing results. Especially the material parameters had to be adjusted to the actual material properties in order to evaluate the fatigue calculations. A good estimation can be done by using the proposed parameters from the FKM guideline (section 4.2.1, [8]). A rough guide is suggested by literature data where ultimate tensile strength (UTS) values are given in a range from 1300 up to 1450 MPa. The standard values were optimized after testing to improve results. The modifications, which can be applied with respect to the actual stress gradient, are chosen within the FEMFAT influence parameters. Mainly three different approaches are implemented where one possibility approach was to neglect the stress gradient influence which represents a conservative assessment of the lifetime calculation. The fatigue limit was adjusted by picking option 2 and the fatigue limit and the slope were adjusted by picking option 3.

R ESULTS AND DISCUSSION

D N . I

n the following, the results are presented with respect to testing and simulation results. The S/N data concerning the base material is described as “Material” which can be seen in Fig. 6. This is used as reference for further calculations where every S/N curve being clearly defined by the fatigue limit f σ , the slope k and the cycles to the fatigue limit

As described in Eq. (3) – (6) the local fatigue limit is calculated where different parameters of the S/N curve were adjusted. As expected the calculations showed increasing values of certain parameters. In Fig. 6 two different S/N curves representing

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I. Milošević et alii, Frattura ed Integrità Strutturale, 42 (2017) 1-8; DOI: 10.3221/IGF-ESIS.42.01

different specimen sizes were marked as D4 (red) and D7.5 (blue) lines. The curve marked as broken-dotted line represents the option 2 adjustment. Just the fatigue limit was adjusted according to the present stress gradient. The option 3 adjustment of the parameters is done by modification of the fatigue limit, the slope and the cycles to the fatigue limit. It can be seen that with increasing stress gradient the local fatigue limit t,2/3 σ increases and N D decreases.

Figure 6 : Comparison of different local S/N curves modified by the stress gradient approach.

Attention should be attracted to the region near D N in Fig. 7 where smaller specimens having apparently lower lifetimes. Through the modification of S/N parameters, such an aggressive behaviour was observed. Tested specimens (D4 and D7.5) showed the same result in this particular load area. Although it’s commonly known that smaller specimen sizes tend to have higher lifetimes it could be observed that in the region of the fatigue limit bigger specimens showed higher lifetimes. In this case, the gradient approach could be applied very well. A material model, which is implemented into FEMFAT, was parameterised and simulations were made to observe the validity of the stress gradient approach from a standardized specimen (D7.5) to a smaller specimen size (D4). In Fig. 8 and Fig. 9 the testing life and the simulation life were compared depending on option 2 and option 3 stress gradient approach. In both figures, there are three groups of data included. The circular shaped data points represent calculations without applying the stress gradient approach (conservative) to the lifetime estimation process. The quadratic shaped data points represent option 2 calculations and the triangular shaped data points represent option 3 calculations where all mentioned parameters were modified.

Figure 7 : Location of the area where the stress gradient concept showed identical results as the rotating bending tests.

The data points within the broken-dotted and dotted lines are located within a scatter band of two respectively five. The presented lifetime data is located in a range from 1E5 up to 1E6. The equal values of simulation and testing results were given through a red continuous line (angle of 45°) as seen in the figures. A conservative calculation was defined by lower simulation results than testing results. In the actual case data points, being located on left of the red continuous line were desirable for applying the approaches. In case of D4 data points, it can be seen that applying option 2 calculations were more suitable than the option 3 calculations. Most of the data points are within a scatter of 2. Drifting into non-conservative calculations was observed at option 3

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I. Milošević et alii, Frattura ed Integrità Strutturale, 42 (2017) 1-8; DOI: 10.3221/IGF-ESIS.42.01

calculations (all parameters) where all data points were still within a scatter of five but located in the non-conservative area. The application at higher stress gradients could lead to an overestimation of the lifetime due to the modification of the gradient approach.

Figure 8 : Lifetime evaluation of D4 specimens depending on the type of stress gradient approach.

Figure 9 : Lifetime evaluation of D7.5 specimens depending on the type of stress gradient approach.

C ONCLUSION AND OUTLOOK

T

he actual work represents the involvement of the stress distribution, more precisely the local stress gradient, and the impact of application when different specimen respectively component sizes are involved. Higher stress gradients '  lead to a significant impact on the lifetime calculation, which depends mainly on the local modification of S/N parameters. Further investigations will focus on the applicability of actual models and the usage when even smaller component sizes are considered. Especially when the full stress gradient approach should be applied and how the over-estimation could be handled, will be analysed through further research.

A CKNOWLEDGEMENTS

T

he authors would like to acknowledge the financial support of the "COMET - Competence Centres for Excellent Technologies Programme" of the Austrian Federal Ministry for Transport, Innovation and Technology (BMVIT), the Austrian Federal Ministry of Science, Research and Economy (BMWFW) and the Provinces of Styria, Tyrol and Vienna for the K1-Centre LEC EvoLET. The COMET Programme is managed by the Austrian Research Promotion Agency (FFG).

R EFERENCES

[1] Neuber, H., Kerbspannungslehre: Theorie der Spannungskonzentration Genaue Berechnung der Festigkeit, 4th ed., Springer Berlin Heidelberg; Imprint: Springer, Berlin, Heidelberg, (2001). [2] Eichlseder, W., Fatigue analysis by local stress concept based on finite element results, Computers & Structures 80 (27-30) (2002) 2109–2113. [3] Eichlseder, W., Leitner, H., Influences of notches on components of Al-alloys, (2002).

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I. Milošević et alii, Frattura ed Integrità Strutturale, 42 (2017) 1-8; DOI: 10.3221/IGF-ESIS.42.01

[4] Dannbauer, H., Eichlseder, W., Steinwender, G., Unger, B., Rechnerische Kerbmodelle – Anwendung auf nicht geschweisste metallische Bauteile, DVM-Bericht Nr. 127 (2000) 121–133. [5] Eichlseder, W., Lebensdauervorhersage auf Basis von Finite Elemente Ergebnissen, Mat.-wiss. u. Werkstofftech. 34 (9) (2003) 843–849. [6] Eichlseder, W., Rechnerische Lebensdaueranalyse von Nutzfahrzeugkomponenten mit der Finite Elemente Methode. Dissertation, (1989). [7] Milošević, I., Winter, G., Grün, F., Kober, M., Influence of Size Effect and Stress Gradient on the High-cycle Fatigue Strength of a 1.4542 Steel, Procedia Engineering, 160 (2016) 61–68. [8] Rodenburg, A., Rechnerischer Festigkeitsnachweis für Maschinenbauteile: FKM-Richtlinie 6.Auflage, 6th ed., VDMA Verl., Frankfurt am Main, (2012).

N OMENCLATURE

FEA UTS

Finite element analysis Ultimate tensile strength Specimen thickness

b

Nominal stress

σ n

Maximum notch stress

σ max

Elastic stress concentration factor Material group parameter - k Material group parameter - N

K t K k K n n χ σ f,b σ f,t σ f,l χ’

Notch sensitivity Relative stress gradient Bending fatigue limit

Tension/ compression fatigue limit

Local fatigue limit Slope S/N curve

k

Tested extreme values of k Number of cycles at the fatigue limit Tested extreme values of N D

k max,min

N D

N Dmax,min

Material exponent

K D

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M. Vasco et alii, Frattura ed Integrità Strutturale, 42 (2017) 9-22; DOI: 10.3221/IGF-ESIS.42.02

Focused on Mechanical Fatigue of Metals

Effect of corrosion and sandblasting on the high cycle fatigue behavior of reinforcing B500C steel bars

Marina C. Vasco, Panagiota Polydoropoulou, Apostolos N. Chamos, Spiros G. Pantelakis. Department of Mechanical Engineering & Aeronautics, University of Patras, Greece marina.mcv@gmail.com, ppolydor@mech.upatras.gr, hamosa@mech.upatras.gr, pantelak@mech.upatras.gr

A BSTRACT . In a series of applications, steel reinforced concrete structures are subjected to fatigue loads during their service life, what in most cases happens in corrosive environments. Surface treatments have been proved to represent proper processes in order to improve both fatigue and corrosion resistances. In this work, the effect of corrosion and sandblasting on the high cycle fatigue behavior reinforcing steel bars is investigated. The investigated material is the reinforcing steel bar of technical class B500C, of nominal diameter of 12 mm. Steel bars specimens were first exposed to corrosion in alternate salt spray environment for 30 and 60 days and subjected to both tensile and fatigue tests. Then, a series of specimens were subjected to common sandblasting, corroded and mechanically tested. Metallographic investigation and corrosion damage evaluation regarding mass loss and martensitic area reduction were performed. Tensile tests were conducted after each corrosion exposure period prior to the fatigue tests. Fatigue tests were performed at a stress ratio, R, of 0.1 and loading frequency of 20 Hz. All fatigue tests series as well as tensile test were also performed for as received steel bars to obtain the reference behavior. The results have shown that sandblasting hardly affects the tensile behavior of the uncorroded material. The effect of sandblasting on the tensile behavior of pre-corroded specimens seems to be also limited. On the other hand, fatigue results indicate an improved fatigue behavior for the sandblasted material after 60 days of corrosion exposure. Martensitic area reductions, mass loss and depth of the pits were significantly smaller for the case of sandblasted materials, which confirms an increased corrosion resistance. K EYWORDS . Steel B500C; Corrosion; High Cycle Fatigue; Sandblasting.

Citation: Vasco, M., Polydoropoulou, P., Chamos, A., Pantelakis, S., Effect of Corrosion and Sandblasting on the High Cycle Fatigue Behavior of Reinforcing B500C Steel bars, Frattura ed Integrità Strutturale, 42 (2017) 9-22.

Received: 31.05.2017 Accepted: 07.06.2017 Published: 01.10.2017

Copyright: © 2017 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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M. Vasco et alii, Frattura ed Integrità Strutturale, 42 (2017) 9-22; DOI: 10.3221/IGF-ESIS.42.02

I NTRODUCTION

R

einforced concrete structures are widely used in civil engineering constructions. Rebars represent the basic strengthening element of reinforced structures, being responsible for carrying loads and controlling displacements. In many cases, these structures are subjected to cyclic loading due to their operational lifespans, thus making it necessary to investigate their high cycle fatigue behavior [1]. In a wide range of applications the operational environment of the steel bars is corrosive. Corrosion of reinforced concrete is one of the major durability problems concerning civil construction [2–4], mainly when the rebar in the concrete is exposed to chlorides, either provided by concrete components or penetrated from the surrounding chloride bearing environment. Corrosion mechanism in reinforcement steel bars can be presented in the form of an electrochemical cell, as illustrated in Fig. 1 [4], with anodic and cathodic reactions varying depending on the pH of the surroundings.

Figure 1 : Schematic representation of the corrosion of reinforcement steel in concrete – as an electrochemical process.

It is worth mentioning that in coastal locations, the climatic conditions constitute one of the most aggressive environments for concrete structures due to the severe ambient salinity, high temperature and humidity, and also the ingress of chlorine through wind-borne salt spray [5]. It is obvious that corrosion damage degrades the mechanical behavior of steel bars. A wide range of experimental investigations have shown a decrease of tensile strength and ductility of the corroded steel bars, as well as a reduction of the bonding strength between the concrete and the steel bar [5–10]. In a number of studies [5, 6, 9–12] the local decrease of cross section and the consequential mass loss of the rebar were measured. Apostolopoulos and colleagues [7, 9, 10, 13, 14] have studied extensively the influence of corrosion on the mechanical properties of reinforcement steel bars, observing that it implies significant reductions in bar’s strength and ductility, with progressive loss of mass with exposure time. Furthermore, the ability of the corroded steel bars to carry seismic loads has been reduced [5, 6]. On the other hand, there is still not enough information regarding life expectancy of pre corroded reinforcing materials employed after the changes performed in European regulations [7]. The design demands for strength and ductility, based on new requirements and principles, obliged the European Union to introduce to service dual-phase high performance steel such as S500s and B500c. The dual-phase steels of RC show an outer high strength core (martensitic phase) and a softer core (ferrite-perlite phase) with a bainitic transition zone. The mechanical performance of B500c steel results from the combination of the mechanical properties in each of the individual phases. The increased strength properties are credited to the presence of the outer martensitic zone and the increased ductility to the presence of the ferrite-pearlite core [7]. However, corrosion damage seems to be more severe on the new steel bars, questioning its improvements [15]. Several works [5, 6, 13] have been made aiming to better understand the effect of corrosion on the mechanical behavior of this specific steel, with both static and fatigue loads. It was observed that the corrosion resistance of BSt420 grade steel is higher than that of B500C in low cycle fatigue analysis [7], while a similar steel grade, BSt500s, presented considerable reduction in its post-corrosion fatigue limit due to a reduction of the exterior hard layer of Martensite [5]. The studies referring to the fatigue behavior of corroded rebar are by far less [5, 6, 16–18] as compared to the the studies referring to the quasistatic behavior of the material. It evidentiates the fact that the problem of fatigue of reinforced concrete structures has been for years underestimated. Zhang et al. [19] have shown that the mechanical behavior of pre corroded rebars is less affected in tensile tests than in fatigue tests, while the work of Ma et al. [16], coupling together the

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M. Vasco et alii, Frattura ed Integrità Strutturale, 42 (2017) 9-22; DOI: 10.3221/IGF-ESIS.42.02

corrosion growth kinetics and fatigue crack growth kinetics, shows that the stress intensity factor under corrosive environment presents an initial increase and later decrease with the increase of corrosion-induced mass loss. To overcome the shortcomings mentioned above, alternative concrete reinforcement concepts have been considered. To these belong the employment of materials such as CFRPs and GFRPs [2, 20, 21]. Yet, their high costs make their widespread use prohibitive and limited to specific applications. Therefore, several efforts are in progress to improve both the corrosion and fatigue behavior of rebars by involving appropriate surface treatments. Sandblasting is a process of using compressed air to propel abrasive grits at a very high speed at an object in order to remove oxide layers or any other debris from its surface [22]. The impact of the grits against the object’s surface inserts compressive stresses in the material, contributing to the increase of fatigue live and diminishing corrosion damage in reinforcement steel bars [3, 6, 23]. Al-Dulaijan et al. [24] have studied the effect of two rebar cleaning procedures and repair materials on reinforcement corrosion and flexural strength of repaired concrete beams, observing that specimens subjected to sandblasting cleaning had higher corrosion resistance than uncleaned bars and the ones cleaned by wire brush. Akinlabi et al. [25] observed that sandblasting has an improving effect on mechanical properties of formed mild steel samples when compared to non-sandblasted ones, due to increase in the degree of grain elongation, as well as an improvement in the hardness of the material by strain hardening. This behavior was studied by several authors separately, but the amount of material available in the literature that combines studies regarding the effect of sandblasting, fatigue behavior and corrosion in rebars is quite scarce. In the present work, the effect of corrosion and sandblasting on the high cycle fatigue behavior of reinforcing steel bars is investigated. Specimens of reinforcing steel bar of technical class B500C, of nominal diameter of 12 mm were first exposed to corrosion in alternate salt spray environment for 30 and 60 days and subjected to both tensile and fatigue tests. Then, a series of specimens were subjected to common sandblasting, corroded and mechanically tested. Tensile tests were conducted after each corrosion exposure period prior to the fatigue tests. Fatigue tests were performed at a stress ratio, R, of 0.1 and loading frequency of 20 Hz.

E XPERIMENTAL PROCEDURE

Material and specimens he selected material was hot-rolled concrete reinforcing steel B500C, which is widely used since 2006 in civil constructions (buildings, bridges etc.), according to the Hellenic standard ELOT 1421-3 [26].The material has been produced by Sidenor Group (SD) according to DIN488 [27]. SD B500C has two longitudinal ribs and additional transverse ribs on two sides. Moreover, SD Steel bears the clear “SD” mark, for identification. A schematic drawing of the ribs pattern is given in Fig. 2. T

Figure 2 : Ribs pattern.

Both as-received and pre-corroded bars were subjected to tensile and fatigue testing. The material was delivered in the form of ribbed bars of 1 m length and nominal diameter of 12 mm, with nominal cross-section of 113 mm 2 and weight of 0.888±0.04 kg/m. The chemical composition of the final product according to the manufacturer is given in Tab. 1.

HEAT CHEMICAL ANALYSIS (%) max C S P N C eq

Grade

B500C

0.24

0.055

0.055

0.014

0.52

Table 1 : Chemical Composition.

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M. Vasco et alii, Frattura ed Integrità Strutturale, 42 (2017) 9-22; DOI: 10.3221/IGF-ESIS.42.02

For the tensile tests, specimens of 460mm total length were cut according to standard ISO/FDIS15630-1 [28]. For the fatigue tests, specimens of a total length of 270 mm were cut. A free length (r) of 170mm was selected in accordance with standard ISO/FDIS 15630-1 [28]. The free length in axial tests should be of at least 140mm or 14 times the specimen diameter, whichever value is greater. Fig. 3 shows a schematic drawing of a fatigue specimen, with gripping sections (a) of 50mm and free length (r) of 170mm.

Figure 3 : Fatigue specimen

The sandblasting method For the surface treatment an ordinary sandblasting facility was employed to retain the costs as low as possible and avoid the use of expensive equipment. Yet, it is acknowledged that the applied sandblasting method is associated to increased scatter of mechanical properties. The sandblasting method was performed by propelling a stream of abrasive material against the steel bar surface under high pressure in a blast cabinet, as shown in Fig. 4a. A blast cabinet is a closed loop system that allows the operator to blast the part and recycle the abrasive. It usually consists of four components; the cabinet (Fig. 4a), the abrasive blasting system (Fig. 4b), the abrasive recycling system (Fig. 4c) and the dust collection. In this work, the process of sandblasting was performed manually; the operator blasts the parts for about one minute from the outside of the cabinet by placing his arms in gloves attached to glove holes on the cabinet, viewing the part through a view window. The material used as a sintershot was a common aluminum oxide of compound with spherical shape of 1.2 mm mean diameter, hardness value of 2035 HV and density of 2100 Kg/m 3 . For flat surfaces the selected sintershot is suitable for achieving a uniform and clean surface as well as uniform compressive layers in the surface of the blasted material. Yet, the ribs of the investigated bars do not allow achieving a uniform blasting and compressive layer.

Figure 4 : Sandblasting cabinet (a) , process (b) and material (c) .

Corrosion exposure and evaluation Following to the surface treatment, specimens have been exposed in a salt spray environment. The salt spray water solution consisted of 5% NaCl and the exposure periods were set to 30 and 60 days. A cyclic exposure was employed, consisting of a 3 hours cycle with 1.5 hours exposure in salt fog and 1.5 hours in dry mode. After corrosion exposure, mass loss of both sandblasted (SB) and as-received (NB) specimens have been evaluated and compared. Mass loss evaluation was made in accordance with ASTM G1-03 [29] in order to determine the degree or level of corrosion. The weight of each specimen was measured before exposure initiation (M i ) and the final weight (M f ) was considered to be

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M. Vasco et alii, Frattura ed Integrità Strutturale, 42 (2017) 9-22; DOI: 10.3221/IGF-ESIS.42.02

stable when the difference between weight measurements after consecutive cleaning procedures became smaller than 0.04g. The percentage mass loss was calculated as shown in Eq. 1:

M 

M M

i

f

(1)





M

100

1

i

For the metallographic analysis, namely, martensitic area reduction and mean corrosion depth measurements, five cross sections of specimens subjected to each exposure period were employed. The cross sections were embedded in metallographic resin, grinded and polished. Chemical etching was made utilizing Nital 5% to evidentiate the martensitic region. Tensile tests All specimens were subjected to tensile tests performed according to the DIN 488 specification [27]. For the tests a servo hydraulic MTS 250 KN machine was used. The employed deformation rate was of 2 mm/min and upper yield stress (R p ), ultimate stress (R m ) and elongation to fracture (A 100 ) were evaluated. Five specimens of as-received material and five specimens of sandblasted material were employed for each period of corrosion exposure. Fatigue tests Τhe effect of corrosion and sandblasting on the high cycle fatigue behavior of reinforcing steel bars of technical class B500C was investigated first according to ELOT 10080. The specification defines the as minimum requirements that specimens shall withstand a number of cycles equal to 2x10 6 . The stress should vary sinusoidally, over the specified range of stress 2σ a from the specified σ max . The parameters used for the fatigue testing were: maximum stress σ max =300 MPa and frequency f= 20 Hz. Furthermore, a number of fatigue tests was conducted to obtain the S-N curves for both materials at a stress ratio R=0.1 and frequency of 20 Hz. Tension-tension fatigue tests were performed using an MTS servo-hydraulic test machine with load capacity of 250 KN. The specimens were subjected to fatigue up to final failure. To consider an experiment as valid, the fracture of the specimen should occur at at least 25mm from the clamped part of the bar. The number of cycles to failure was set to 5x10 6 cycles. The S-N curves were obtained by using the Weibull distribution of 4 parameters. In order to estimate the effect of sandblasting on fatigue resistance of the material, the largest period of corrosion was considered for comparison. In Tab. 2 the total number of valid fatigue tests for all corrosion exposure periods for both materials, as-received and sandblasted is displayed.

NB

SB

0 days 30 days 60 days

17 11

- -

9 7 Table 2 : Number of valid specimens of fatigue tests.

R ESULTS

Metallography he surface of the steel bars has been observed by involving an optical microscope, as it is illustrated in Fig. 5. Fig. 5a shows the surface of an untreated specimen, while Fig. 5b shows the surface of a sandblasted specimen. As it can be seen, a more uniform surface has been achieved by implementing the sandblasting treatment. Furthermore, no initial microcracks after the surface treatment could be observed. Corrosion evaluation Tab. 3 displays the results obtained by the mass loss evaluation for both corrosion exposure periods, 30 and 60 days. These values are in accordance with other values found in the literature. Koulouris et al. [3] observed that mass loss of as received materials after 30 days of corrosion in a salt spray chamber with 5% NaCl was of 3.77%, while after 60 days the material lost 7.23% of its mass, while in [4] a mass reduction of 2.92% after 30 days and 5.43% after 60 days of exposure has been observed. It is noticeable that the mass reduction of specimens subjected to sandblasting is significantly smaller than the one presented by the as-received material. The same behavior was noticed in the work in [20] where the T

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