Issue 36

Frattura ed Integrità Strutturale, 36 (2016); International Journal of the Italian Group of Fracture

Table of Contents

I. Camagic, N. Vasic, B. Cirkovic, Z. Burzic, A. Sedmak, A. Radovic Influence of temperature and exploitation period on fatigue crack growth parameters in different regions of welded joints …………………………………………..………………………………. 1 V. Petrova, S. Schmauder, A. Shashkin Modeling of edge cracks interaction ………………………………………………………… 8 M. Arsic, Z. Savic, A. Sedmak, S. Bosnjak, S. Sedmak Experimental examination of fatigue life of welded joint with stress concentration …………................ 27 Sz. Szávai, Z. Bezi, C. Ohms Numerical simulation of dissimilar metal welding and its verification for determination of residual stresses …………………............................................................................................................... 36 L. L. Vulićević, A. Rajić, A. Grbović, A. Sedmak, Ž. Šarkočević Fatigue life prediction of casing welded pipes by using the extended finite element method …………….. 46 J. Kováčik, J. Jerz, N. Mináriková, L. Marsavina, E. Linul Scaling of compression strength in disordered solids: metallic foams ………………………...……... 55 A. Sedmak, S. Bosnjak, M. Arsic, S.A. Sedmak, Z. Savic Integrity and life estimation of turbine runner cover in a hydro power plant …………........................... 63 F.A. Stuparu, D.A. Apostol, D.M. Constantinescu, M. Sandu, S. Sorohan Failure analysis of dissimilar single-lap joints ……………………………………………...… 69 T. Fekete Methodological developments in the field of structural integrity analyses of large scale reactor pressure vessels in Hungary ……………………………………………...……………………...… 78 T. Fekete Review of pressurized thermal shock studies of large scale reactor pressure vessels in Hungary ………... 99 M. Ouarabi, R. P. Mora, C. Bathias, T. Palin-Luc Very high cycle fatigue strength and crack growth of thin steel sheets …….......................................... 112 R. Tovo, L. Susmel, M.N. James, D.G. Hattingh, E. Maggiolini Crack initiation and propagation paths in small diameter FSW 6082-T6 aluminium tubes under fatigue loading ………………………………............................................................................. 119

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Fracture and Structural Integrity, 36 (2016); ISSN 1971-9883

P. Jinchang, L. Ronggui Improvement of performance of ultra-high performance concrete based composite material added with nano materials …………………………………………………………………………... 130 F. Liu, Y. Zhao Effects of hydrogen induced delay fracture on high-strength steel plate of automobile and the improvement 139 R. H. Talemi Numerical simulation of dynamic brittle fracture of pipeline steel subjected to DWTT using XFEM- based cohesive segment technique ……………………………………………...…………...... 151 R. Citarella Multiple crack propagation by DBEM in a riveted butt-joint: a simplified bidimensional approach ..... 160 A. Namdar, E. Darvishi, X. Feng, I. Zakaria, F. M. Yahaya Effect of flexural crack on plain concrete beam failure mechanism - A numerical simulation………….. 168 S.R. Wang, C.Y. Li, Z.S. Zou,X.L. Liu Acoustic emission characteristics of instability process of a rock plate under concentrated loading ……… 182 H. Zhu Crack formation of steel reinforced concrete structure under stress in construction period …...………… 191 L. C. H. Ricardo, C. A. J. Miranda Influence of the crack propagation rate in the obtaining opening and closing stress intensity factor by finite element method …………...………………………………………………………..…….. 201

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Frattura ed Integrità Strutturale, 36 (2016); International Journal of the Italian Group of Fracture

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) (Ecole Nationale Supérieure d'Arts et Métiers, Paris, France)

Thierry Palin-Luc

Luca Susmel John Yates

(University of Sheffield, UK) (University of Manchester, UK)

Guest Editors L. Marsavina

(University of Timisoara, Romania) (University of Belgrade, Serbia)

A. Sedmak

Advisory Editorial Board Harm Askes

(University of Sheffield, Italy) (Politecnico di Torino, Italy) (Università di Parma, Italy) (Politecnico di Torino, Italy) (University of Plymouth, UK)

Alberto Carpinteri Andrea Carpinteri Donato Firrao M. Neil James Gary Marquis Ashok Saxena Darrell F. Socie Shouwen Yu Ramesh Talreja David Taylor Robert O. Ritchie Cetin Morris Sonsino Elisabeth Bowman Roberto Citarella Claudio Dalle Donne Manuel de Freitas Vittorio Di Cocco Giuseppe Ferro Eugenio Giner Tommaso Ghidini Daniele Dini Editorial Board Stefano Beretta Nicola Bonora

(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)

(Politecnico di Milano, Italy)

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Sheffield) (Università di Salerno, Italy) (EADS, Munich, Germany) (EDAM MIT, Portugal)

(Università di Cassino e del Lazio Meridionale, Italy)

(Imperial College, UK)

(Politecnico di Torino, Italy)

(Universitat Politecnica de Valencia, Spain) (European Space Agency - ESA-ESRIN)

Paolo Leonetti 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

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

Mahmoud Mostafavi

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)

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Fracture and Structural Integrity, 36 (2016); ISSN 1971-9883

Giacomo Risitano Roberto Roberti Marco Savoia Andrea Spagnoli Charles V. White

(Università di Messina, Italy) (Università di Brescia, Italy) (Università di Bologna, Italy) (Università di Parma, Italy)

(Kettering University, Michigan,USA)

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Frattura ed Integrità Strutturale, 36 (2016); International Journal of the Italian Group of Fracture

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 iacoviello@unicas.it. 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 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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Fracture and Structural Integrity, 36 (2016); ISSN 1971-9883

Fracture Mechanics in Central and East Europe

This issue of Frattura ed Integrità Strutturale contains ten research papers focused on Fracture Mechanics in Central and East Europe. Four papers from Serbia deal with fatigue crack growth, presenting experimental and numerical results, obtained in the Military Institute, Institute for material testing and Faculty of Mechanical Engineering, all from Belgrade. Paper Integrity and life estimation of turbine runner cover in a hydro power plant by A.Sedmak, M. Arsić, S. Bošnjak, S. Sedmak and Z. Savić, presents integrity and life estimation of turbine runner cover in a vertical pipe turbine. Fatigue and corrosion-fatigue interaction have been taken into account using experimentally obtained material properties, as well as analytical and numerical calculations of stress state, to estimate appropriate safety factors. Fatigue crack growth rate was also calculated, indicating that internal defects of circular or elliptical shape, detected by ultrasonic testing, do not affect integrity of runner cover. Paper Experimental examination of fatigue life of welded joint with stress concentration by M. Arsic , A. Sedmak, S. Bosnjak, S. Sedmak and Z. Savic, presents results of experimental examinations of stress concentration influence on fatigue life of butt welded joints with K-groove, produced from the structural steel S355J2+N. Specimens with short cracks (with limited length of initial crack), defined on the basis of the experiences from fracture mechanics by the three points bending examinations, have been examined according to standard for the determination of S-N curve, and used to determine permanent fatigue strengths for different lengths of initial crack. In the paper Fatigue life prediction of casing welded pipes by applying the extended finite element method , Lj. Lazić Vulićević, A. Grbović, A. Sedmak, Ž. Šarkočević and A. Rajić use the extended finite element (XFEM) method to simulate fatigue crack growth in casing pipe, made of API J55 steel by high-frequency welding, in order estimate its structural integrity and life. Based on the critical value of stress intensity factor K Ic , measured in different regions of welded joint, the crack was located in the base metal as the region with the lowest resistance to crack initiation and propagation. The XFEM was first applied to the three point bending specimens to verify numerical results with the experimental ones, and afterwards to simulate fatigue crack growth and estimate its remaining life. In the paper Influence of exploitation duration and temperature on the fatigue growth parameters in different regions of a welded joints by I. Camagic, Z. Burzic, A. Sedmak, N. Vasic, B. Cirkovic and A. Radovic, the influence of exploitation duration and temperature on the fatigue crack growth parameters in different regions of a welded joint is analysed for new and exploited low-alloyed Cr-Mo steel A-387 Gr . B . Fatigue crack growth parameters, threshold value  K th , coefficient C and exponent m, have been determined, both at room and exploitation temperature. Based on testing results, fatigue crack growth resistance in different regions of welded joint is compared. The authors of the other six papers are from Germany, Hungary, Romania, Russia, Slovakia. Paper Numerical Simulation of Dissimilar Metal Welding and its Verification for Determination of Residual Stresses with authors Sz. Szávai, Z. Bezi and C. Ohms presents the through-thickness residual stress distributions on dissimilar metal weld (DMW) mock-up. DMWs, were considered as joints between ferritic steels

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Frattura ed Integrità Strutturale, 36 (2016); International Journal of the Italian Group of Fracture

and either austenitic stainless steels or nickel-based alloys. The numerical simulations were performed using commercial finite element code MSC.Marc, and residual stress measurements were performed on welded joints to validate the simulation results. The validated residual stress distributions can be used for the life time assessment and failure mode predictions of the welded joints. In the paper Scaling Of Compression Strength in Disordered Solids: Metallic Foams, authors J. Kováčik, J. Jerz, N. Mináriková, L. Marsavina, E. Linul, the scaling of compression strength with porosity for aluminium foams was investigated. Three different compositions Al 99.96, AlMg1Si0.6 and AlSi11Mg0.6 foams of various porosity, sample size with and without surface skin were tested in compression. It was observed that the compression strength of aluminium foams scales near the percolation threshold with T f ≈ 1.9 - 2.0 almost independently on the matrix alloy, sample size and presence of surface skin. V. Petrova, S. Schmauder, A. Shashkin in Modeling of edge cracks interaction investigated the effects of the interaction of edge cracks on further crack formation. The solution of singular integral equations is obtained by a numerical method which is based on Gauss-Chebyshev quadrature. The main fracture characteristics, such as, stress intensity factors, fracture angles and critical loads are provided in this study. A series of illustrative examples are presented for different geometries of arbitrarily inclined edge cracks . Paper titled Failure analysis of dissimilar single-lap joints having authors F.A. Stuparu, D.A. Apostol. D.M. Constantinescu, M. Sandu, S. Sorohan investigates the single-lap joints made of aluminium and carbon fibre adherends of different thickness. The experimental tests and the use of 2D Digital Image Correlation were employed in order to understand better the behaviour of such dissimilar joints. The obtained results are suggesting that a complete monitoring of the failure processes in the overlap region can be fully understood only if local deformation measurements are possible. The Special Issue is closed by two papers of T. Fekete Review of Pressurized Thermal Shock Studies of Large Scale Reactor Pressure Vessels in Hungary and Methodological Developments in the Field of Structural Integrity Analyses of Large Scale Reactor Pressure Vessels in Hungary. In the first one presents a comparative review of the methodologies used to investigate pressurized thermal shock which appear in the four nuclear power units from Hungary. The concept of structural integrity was the basis of research and development. The second paper presents in the first part of the paper, a short historic overview with the origins of the Structural Integrity concept are presented, and the beginnings of Structural Integrity in Hungary are summarized. In the second part, a new conceptual model of Structural Integrity is introduced. In the third part, a brief description of the VVER-440 V213 type RPV and its surrounding primary system is presented. In the fourth part, a conceptual model developed for PTS Structural Integrity Analyses is explained.

Aleksandar SEDMAK , University of Belgrade, Serbia Liviu MARSAVINA , University Politehnica Timisoara, Roamnia

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I. Camagic et alii, Frattura ed Integrità Strutturale, 36 (2016) 1-7; DOI: 10.3221/IGF-ESIS.36.01

Focused on Fracture Mechanics in Central and East Europe

Influence of temperature and exploitation period on fatigue crack growth parameters in different regions of welded joints

Ivica Camagic, Nemanja Vasic, Bogdan Cirkovic Faculty of Technical Sciences, Kosovska Mitrovica, Kneza Milosa 7, Serbia Zijah Burzic Military Technical Institute, Rastka Resanovica 1, Belgrade, Serbia Aleksandar Sedmak Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade, Serbia asedmak@mas.bg.ac.rs Aleksandar Radovic Technical School Mihailo Petrovic Alas, Kosovska Mitrovica, Lole Ribara 29, Serbia

A BSTRACT . The influence of exploitation period and temperature on the fatigue crack growth parameters in different regions of a welded joint is analysed for new and exploited low-alloyed Cr-Mo steel A-387 Gr . B . The parent metal is a part of a reactor mantle which was exploited for over 40 years, and recently replaced with new material. Fatigue crack growth parameters, threshold value  K th , coefficient C and exponent m, have been determined, both at room and exploitation temperature. Based on testing results, fatigue crack growth resistance in different regions of welded joint is analysed in order to justify the selected welding procedure specification. K EY WORDS : Welded joint; Crack; Yield stress; Tensile strength; Permanent dynamic strength.

I NTRODUCTION

he reactor analysed here has a form of a vertical pressure vessel with a cylindrical mantle and two welded lids, made of Cr-Mo steel A-387 Gr. B , [1]. It is used for some of the most important processes in the motor gasoline production, including platforming in order to change the structure of hydrocarbon compounds and to achieve a higher octane rating. Long-time, high temperature exploitation of the reactor, caused siginficant damage in reactor mantle, requiring a thorough inspection and repair of damaged parts, including replacement of a part of reactor mantle. For designed exploitation parameters ( p= 35 bar, t =537 °C), the material is prone to decarbonization, reducing its strength as a consequence, [2]. Testing of high-cycle fatigue behaviour of new and exploited parent metal (PM), weld metal (WM) and heat affected zone (HAZ), at room and service temperature (540 °C) is necessary to get detailed insight in all parameters influencing fatigue crack growth resistance of Cr-Mo steel A-387 Gr. B . welded joints. T

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I. Camagic et alii, Frattura ed Integrità Strutturale, 36 (2016) 1-7; DOI: 10.3221/IGF-ESIS.36.01

T ESTING MATERIAL

B

oth new and exploited PM was steel A-387 Gr. B with thickness of 102 mm. Chemical composition and mechanical properties for both new and exploited PM are given in Tabs. 1 and 2.

% max

Specimen designation

C

Si

Mn

P

S

Cr

Mo

Cu

E N

0.15 0.13

0.31 0.23

0.56 0.46

0.007 0.006 0.009 0.006

0.89 0.85

0.47 0.51

0.027 0.035

Table 1 : Chemical composition of exploited (E) and new (N) PM specimens

Specimen designation

Yield stress, R p0.2 , MPa

Tensile strength R m , MPa

Elongation A, %

Impact energy, J

E N

320 325

450 495

34.0 35.0

155

165 Table 2 : Chemical composition of exploited (E) and new (N) PM specimens.

Welding of both new and exploited PM was performed in two stages, according to the following welding procedure specification:  Root pass by shielded metal arc welding, using LINCOLN S1 19G electrode, and  Filling passes by arc submerged arc welding, using LINCOLN LNS 150 wire and LINCOLN P230 flux. Chemical composition of the coated electrode LINCOLN S1 19G, and the wire LINCOLN LNS 150 according to the atest documentation is given in tab. 3, whereas their mechanical properties, also according to the atest documentation, are given in tab. 4.

% mas

Filler material

C

Si

Mn

P

S

Cr

Mo

LINCOLN S1 19G LINCOLN LNS 150

0.07 0.10

0.31 0.14

0.62 0.71

0.009 0.010 0.010 0.010

1.17 1.12

0.54 0.48

Table 3 : Chemical composition of filler materials.

Yield stress, R p0.2 , MPa

Tensile strength R m , MPa

Elongation A, %

Impact energy, J, 20°C

Filler material

LINCOLN S1 19G LINCOLN LNS 150

515 495

610 605

20 21

>60 >80

Table 4 : Mechanical properties of filler materials

F ATIGUE CRACK GROWTH PARAMETERS EVALUATION

F

atigue crack growth testing at room temperature was performed on three-point bending specimens, as defined by ASTM E399, [3], whereas tesitng at service temperature, 540  C, was performed on modified CT specimens, as defined by standard BS 7448 Part 1, [4]. The high-frequency resonant pulsator was used, in force control mode, with loading ratio R = 0.1 to obtain diagrams da/dN-  K for specimens with fatigue crack tip located in PM, WM and

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I. Camagic et alii, Frattura ed Integrità Strutturale, 36 (2016) 1-7; DOI: 10.3221/IGF-ESIS.36.01

HAZ, both new and expoloited material, at room and service temperature. Only two diagrams are shown here, as an illustration, whereas the others can be found in [1].

1.00E-05

1.00E-06

1.00E-07

da/dN, m/ciklus

1.00E-08

1.00E-09

1.00E-10

1

10

100

 K, MPa m 1/2

Figure 1 : Diagram da/dN-K for specimen PM-1-1n, 20°C.

1.00E-05

1.00E-06

1.00E-07

da/dN, m/ciklus

1.00E-08

1.00E-09

1.00E-10

1

10

100

 K, MPa m 1/2

Figure 2 : Diagram da/dN-K for specimen PM-2-1e, 540°C.

d C K dN    a

  m

Obtained values for parameters of Paris law, , i.e. coefficient C and exponent m , fatigue threshold  K th , and fatigue crack growth rate, da/dN , for  K = 10 MPa  m, are given in Tabs. 5-9 for new and exploited PM, for new WM, and for new and exloited HAZ, respectively.

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I. Camagic et alii, Frattura ed Integrità Strutturale, 36 (2016) 1-7; DOI: 10.3221/IGF-ESIS.36.01

Specimen

Coefficient C 5.70 · 10 -12 5.38 · 10 -12 6.23 · 10 -12 1.52 · 10 -10 2.08 · 10 -10 1.11 · 10 -10 Coefficient C 4.45 · 10 -12 3.89 · 10 -12 5.17 · 10 -12 1.48 · 10 -8 2.67 · 10 -8 1.25 · 10 -8 Coefficient C 2.14 · 10 -11 3.55 · 10 -11 1.98 · 10 -11 1.26 · 10 -9 1.78 · 10 -9 2.24 · 10 -9 Coefficient C 2.55 · 10 -11 2.97 · 10 -11 2.08 · 10 -11 9.61 · 10 -10 7.45 · 10 -10 8.85 · 10 -10 Coefficient C 1.54 · 10 -10 1.95 · 10 -10 2.35 · 10 -10 5.50 · 10 -9 4.67 · 10 -9 6.24 · 10 -9

Exponent m

da/dN. m/cycle ΔK = 10 MPa  m

Temperature °C

Fatigue threshold ΔK th

PM-1-1n PM-1-2n PM-1-3n PM-2-1n PM-2-2n PM-2-3n

5.9 5.6 5.8 5.2 5.1 5.0

2.98 3.02 2.83 2.94 2.88 2.99

5.44 · 10 -9 5.63 · 10 -9 4.21 · 10 -9 1.32 · 10 -7 1.58 · 10 -7 1.08 · 10 -7

20

540

Table 5 : Fatigue crack growth parameters for specimens with notches in new PM.

Specimen

Exponent m

da/dN. m/cycle ΔK = 10 MPa  m

Temperature °C

Fatigue threshold ΔK th

PM-1-1e PM-1-2e PM-1-3e PM-2-1e PM-2-2e PM-2-3e

5.2 5.1 5.2 4.7 4.6 4.7

3.76 3.87 3.71 1.80 1.68 1.84

2.56 · 10 -8 2.88 · 10 -8 2.65 · 10 -8 9.34 · 10 -7 1.28 · 10 -6 8.65 · 10 -7

20

540

Table 6 : Fatigue crack growth parameters for specimens with notches in exploited PM.

Specimen

Exponent m

da/dN. m/cycle ΔK = 10 MPa  m

Temperature °C

Fatigue threshold ΔK th

WM-1-1e WM-1-2e WM-1-3e WM-2-1e WM-2-2e WM-2-3e

6.8 6.9 6.7 5.8 5.6 5.5

2.53 2.38 2.56 2.51 2.47 2.21

7.25 · 10 -9 8.71 · 10 -9 7.19 · 10 -9 4.08 · 10 -7 5.25 · 10 -7 3.63 · 10 -7

20

540

Table 7 : Fatigue crack growth parameters for specimens with notches in WM.

Specimen

Exponent m

da/dN. m/cycle ΔK = 10 MPa  m

Temperature °C

Fatigue threshold ΔK th

HAZ-1-1n HAZ-1-2n HAZ-1-3n HAZ-2-1n HAZ-2-2n HAZ-2-3n

5.7 5.4 5.5 4.9 4.7 4.8

2.48 2.41 2.57 2.47 2.83 2.68

7.70 · 10 -9 7.63 · 10 -9 7.72 · 10 -9 2.84 · 10 -7 5.03 · 10 -7 4.24 · 10 -7

20

540

Table 8 : Fatigue crack growth parameters for specimens with notches in new HAZ.

Specimen

Exponent m

da/dN. m/cycle ΔK = 10 MPa  m

Temperature °C

Fatigue threshold ΔK th

HAZ-1-1e HAZ-1-2e HAZ-1-3e HAZ-2-1e HAZ-2-2e HAZ-2-3e

4.8 4.6 4.5 4.2 4.1 4.3

2.62 2.57 2.51 2.33 2.49 2.11

6.42 · 10 -8 7.24 · 10 -8 7.60 · 10 -8 1.18 · 10 -6 1.44 · 10 -6 8.04 · 10 -7

20

540

Table 9 : Fatigue crack growth parameters for specimens with notches in exploited HAZ.

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I. Camagic et alii, Frattura ed Integrità Strutturale, 36 (2016) 1-7; DOI: 10.3221/IGF-ESIS.36.01

Influence of testing temperature and exploitation period on the fatigue threshold  K th

is graphically presented in Fig. 3-5,

for PM, WM and HAZ, respectively.

9

▫  new PM ◦  exploited PM

6

Fatigue threshold,  K th , MPa√m 0 0 3

100

200

300

400

500

600

Temperature, 0 C

Figure 3 : Fatigue threshold ΔK th

vs. temperature in PM

9

6

Fatigue threshold,  K th , MPa√m 0 0 3

100

200

300

400

500

600

Temperature, 0 C

Figure 4 : Fatigue threshold ΔK th

vs. temperature in WM.

9

▫  new HAZ ◦  exploited HAZ

6

Fatigue threshold,  K th , MPa√m 0 0 3

100

200

300

400

500

600

700

Temperature, 0 C

Figure 5 : Fatigue threshold ΔK th

vs. temperature in HAZ.

The influence of testing temperature and exploitation period on the fatigue crack growth rate, da/dN, is graphically presented in Fig. 6-8, for PM, WM and HAZ, respectively.

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I. Camagic et alii, Frattura ed Integrità Strutturale, 36 (2016) 1-7; DOI: 10.3221/IGF-ESIS.36.01

10 -6

▫  new PM ◦  exploited PM

10 -7

10 -8

10 -9

da/dN, m/cycle

0 -10

0

100

200

300

400

500

600

Temperature, 0 C

Figure 6 : Fatigue crack growth rate, da/dN, vs. temperature for specimens with notches in PM.

10 -6

10 -7

10 -8

10 -9

da/dN, m/cycle

10 -10

0

100

200

300

400

500

600

Temperature, 0 C Figure 7 : Fatigue crack growth rate, da/dN, vs. temperature for specimens with notches in WM.

10 -6

▫  new HAZ ◦  exploited HAZ

10 -7

10 -8

10 -9

da/dN, m/cycle

10 -10

0

100

200

300

400

500

600

Temperature, 0 C

Figure 8 : Fatigue crack growth rate, da/dN, vs. temperature for specimens with notches in HAZ.

D ISCUSSION

alues obtained for PM fatigue threshold,  K th , are in the range 5.8 MPa  m (20  C) to 5.1 MPa  m (540  C), Tab. 5. Additional reduction for 10-15% is recorded due to exploition period 10-15%, since values for fatigue threshold,  K th , are in that case in the range 5.2 MPa  m (20  C) to 4.7 MPa  m (540  C), Tab. 6. Similar effects are noticed in HAZ, where values of fatigue threshold,  K th , obtained for new material, are in the range 5.5 MPa  m (20  C) to 4.8 MPa  m (540  C), i.e. from 4.6 MPa  m (20  C) to 4.2 MPa  m (540  C) for exploited material, Tabs. 8 and 9. V

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I. Camagic et alii, Frattura ed Integrità Strutturale, 36 (2016) 1-7; DOI: 10.3221/IGF-ESIS.36.01

The largest values of fatigue threshold,  K th

, are obtianed in WM, from 6.8 MPa  m (20  C) to 5.6 MPa  m (540  C), Tab.

7. Fatigue crack growth rate, da/dN, increases with temperature, being in the range 5.09  10 -9 m/cycle for new PM (20  C) to 1.33  10 -7 m/cycle (540  C), Tab. 5. Exploition period additionally increases fatigue crack growth rate, da/dN, from 2.70  10 -8 m/cycle (20  C) to 1.03  10 -6 m/cycle (540  C), Tab. 6. The same holds for HAZ, where values of fatigue crack growth rate, da/dN, are in the range 7.68  10 -9 m/cycle (20  C) to 4.04  10 -7 m/cycle (540  C) for new material, i.e. in the range 7.09  10 -8 m/cycle (20  C), to 1.14  10 -6 m/cycle (540  C) for exploited material, Tabs. 8 and 9, respectivley. One should notice significantly higher values for fatigue crack growth rate in HAZ as compared to PM. The values for WM are in between, in the range 7.72  10 -9 m/cycle (20  C) to 4.32  10 -7 m/cycle (540  C), Tab. 7. ased on the presented results, one can conclude the following:  Influence of material heterogeneity, as well as temperature and exploation effects, on fatigue threshold, da/dN, and crack growth rate, da/dN, is significant.  Fatigue threshold values are the lowest for WM, and lowest for HAZ, whereas crack growth rate values are highest for HAZ and lowest for PM. Therefore, generally speaking, the lowest fatigue crack resistance is in HAZ.  Higher temperature and longer exploitation peroids increase crack growth rates and decreases fatigue thresholds for both new and exploited materials in all regions of welded joint (PM, WM, HAZ). These effects are due to microstructural changes such as carbide formation and growth at grain boundaries and inside grains. [1] Čamagić, I., Investigation of the effects of exploitation conditions on the structural life and integrity assessment of pressure vessels for high temperatures (in Serbian), doctoral thesis, University of Pristina, Faculty of Technical Sciences with the seat in Kosovska Mitrovica, (2013). [2] Čamagić, I., Vasić, N., Jović, S., Burzić, Z., Sedmak, A., Influence of temperature and exploitation time on tensile properties and microstructure of specific welded joint zones, In: 5 th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, (2015). [3] ASTM E399-89, Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials, Annual Book of ASTM Standards, 03.01 (1986) 522. [4] BS 7448-Part 1, Fracture mechanics toughness tests-Method for determination of K Ic critical CTOD and critical J values of metallic materials, BSI, (1991). B C ONCLUSION R EFERENCES

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V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02

Focused on Fracture Mechanics in Central and East Europe

Modeling of edge cracks interaction

V. Petrova http://orcid.org/0000-0002-9131-2469 Voronezh State University and University of Stuttgart, Russia

veraep@gmail.com S. Schmauder University of Stuttgart, Germany siegfried.schmauder@imwf.uni-stuttgart.de A. Shashkin Voronezh State University, Russia shashkin@amm.vsu.ru

A BSTRACT . From experimental and theoretical investigations it is known that cracks are sensitive to geometry, e.g., to the inclination angle to the load. A small deviation of a crack from the normal direction to a tensile load causes mixed mode conditions near the crack tip which lead to deviation of the crack from its initial propagation direction. Besides, the presence of other cracks, inhomogeneities, surfaces and their interaction causes additional deformations and stresses which also have influence on the initiation of the crack propagation and on the direction of this propagation. The aim of this paper is to show the effects of the interaction of edge cracks on further crack formation. The main fracture characteristics, such as, stress intensity factors, fracture angles and critical loads are provided in this study. A series of illustrative examples is presented for different geometries of arbitrarily inclined edge cracks. K EYWORDS . Edge cracking; Stress intensity factors; Fracture criteria; Direction of crack propagation; Shielding- amplification effects. urface cracking is observed in many engineering structures, e.g., aircraft structures, turbine blades, engine components and many others, see [1, 2] for some examples and references. In everyday life we can see asphalt pavement cracking, called also as crocodile cracking [3]. The structures are subjected to different mechanical and thermal loading as well have to resist high temperature, wear and aggressive environments. Cracks can initiate from initial defects or microcracks appear during manufacturing or service. An example of multiple surface cracking is the fracture of thermal barrier coatings (TBCs), where the upper layer is usually a ceramic - the brittle material. Investigations of thermal barrier coatings show that heating and then subsequent cooling of the coating causes the surface to experience a tensile stress leading to surface cracking [4]. S I NTRODUCTION

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V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02

There is abundant experimental results (e.g., [4-6]) showing that when TBCs are subjected to thermal shock, multiple cracks occur at the ceramic surface. Besides, the crack patterns strongly depend on the microstructure of the materials and on the type of loading. Numerous investigations are devoted to different types of fracture including surface fracture. In previous papers of the authors [7-10] the fracture of FGM/homogeneous bimaterials (an infinite medium) under thermal and mechanical loadings were investigated, besides, in [11] some results for edge cracks in FGM/homogeneous structures (a semi-infinite medium) were obtained in the frame of the approach used in [7-10]. The results show that the fracture of materials (both composites and homogeneous) is significantly affected by a complex crack interaction mechanism, e.g., interacting cracks can enhance or suppress the propagation of each other. During further studying of the fracture of functionally graded coatings on a homogeneous substrate and the preparation of the results for the influence of material non-homogeneity on surface fracture it became clear that a classical problem for edge cracks interaction is still not well examined. Before presenting the results for more complicated cases of non- homogeneous materials (FGMs, bimaterials, and others), modeling of the interaction of edge cracks should be done for a homogeneous medium. From experimental and theoretical investigations it is known that cracks are sensitive to geometry, e.g., to the inclination angle to the load. A small deviation of a crack from the normal direction to a tensile load causes mixed mode conditions near the crack which lead to deviation of the crack from its initial propagation direction. Besides, the presence of other cracks, inhomogeneities, surfaces and their interaction causes additional deformations and stresses which are also influenced on the initiation of the crack propagation and on the direction of this propagation. That is, the picture of the fracture with respect to the crack pattern for a system of arbitrary inclined edge cracks will be different from the picture of regularly distributed cracks, e.g, for periodically distributed equal (and non-equal) cracks, this case was often studied, see [12-14]. The goal of this paper is to show the effects of the interaction of edge cracks on further fracture formation. The main fracture characteristics, such as, stress intensity factors, fracture angles and critical loads are provided for this study. A series of illustrative examples is presented for different geometries of arbitrarily inclined edge cracks.

P ROBLEM FORMULATION AND ASSUMPTIONS

T

he geometry of the problem is presented in Fig. 1 a. A homogeneous half-medium contains pre-existing edge cracks inclined arbitrarily on angles β n to the surface. A Cartesian coordinate system ( x, y ) has x -axis along the boundary of the half-plane, and local coordinate systems ( x k , y k ) are attached to each crack. The lengths of the cracks are 2 a n , and the midpoint coordinates are 0 0 0 n n n iy x z   ( 1  i is imaginary unity). The homogeneous medium is subjected to tension p applied parallel to the free surface.

(a)

(b)

Figure 1 : (a) Edge cracks inclined arbitrarily with an angle β n

to the surface of the medium. a n

– a half length of n -th crack,

z n 0 +i y n 0 – the crack midpoint coordinate. (b) The angle ϕ of crack deflection (the fracture angle). The problem is solved by using the method of singular integral equations. The cracks are modeled by displacement jumps on the crack faces and unknown functions in this formulation are the derivatives of displacement jumps 0 = x n

2 ) (  



 ] [ ] [

i   



x g

u

n vi

(1)

n

n



)1 ( x 

9

V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02



 E



) 1(2/  is the

Here [ u n

] and [ v n

] are shear and vertical displacement jumps, respectively, on the n -th crack line,





) 1/()    for 

shear modulus, E - Young’s modulus,  - Poisson’s ratio,



 43  for the plane strain state and

3(

the plane stress state. For arbitrary located cracks in a half-plane the system of singular integral equations is written as [15, 16]

a

a

N

n 

dt t g

n

k

)(

nk    k 

)] ,( )( ) ,( )( [ nk k    n



, ||), ( a x xp dt xt St g xt Rt g  n = 1,2, …, N (2)

n



x t

 

k

1



a

a

n

k

nk

An overbar   ... is the complex conjugate. N is number of cracks. The method of superposition was used in deriving of Eq. (2) where the loads at infinity are reduced to the corresponding loads on the crack faces. The functions p n in the right side of Eq. (2) are these loadings, and in the case of a homogeneous half-plane under tension p they are written as





2/))      (n = 1, 2, .., N ) 2 exp( i

n 

p

i

p

(3)

1(

n

n

n

   (see Fig. 1 a).

with

n

n

If a non-homogeneous medium is considered, e.g., a functionally graded structure with continuous gradation of the thermo-mechanical properties with the coordinate y , and this structure is cooled, then tensile residual stresses are arising due to mismatch in the coefficients of thermal expansion [4, 14]. The influence of this inhomogeneity can be accounted via continuously varying residual stresses p* which are written as follows [14]:

T xx

*







t 

t ] ) ( [ ) ( 0 

TE  

p

y

y

This function is added to the right side of Eq. (2). It should be noted, that in this case we also have the problem for a half- plane under tension.

N UMERICAL SOLUTION , STRESS INTENSITY FACTORS

he solution of singular integral equations (Eq. 2) is obtained by a numerical method which is based on Gauss- Chebyshev quadrature. The method is similar to the method presented by Erdogan and Gupta [17], but we will follow the version formulated in [15, 16]. The equations (2) are rewritten in dimensionless form with the non-dimensionless coordinates n k ax a t / and /     , where 2 a k is a length of the k -th crack. The unknown function ) (  n g  consists of a function ) (  n u (a bounded continuous function in the segment [-1,1]) and the weight function 2 1/1   , that is,

2 1/) (  



  n u



g

(4)

) (

n

n g 

)(  possess a singularity less than

  1/1 at the edge point

1  

For edge cracks the function

and this condition

is accounted as [15, 16]

0 )1( 

u

(5)

n

In spite of the exact singularity at the edge points is not taking into account, the numerical results have shown good accuracy [15, 16]. Using Gauss’s quadrature formulae for the regular and singular integrals the integral equations are reduced to the following system of NxM (N – number of cracks, M – number of nodes) algebraic equations

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V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02

 ), ( ) , ( ) ( p     

M

N

1

    1 1 k



) , ( ) (   



R u

S u

(6)

r n r m nk m k r m nk m k

M

m

M



m

1 2 tan) (

1    m

)1( u m







( n =1,2, …, N ; r =1,2,…, M -1)

0

(7)

m n

M

4

with

r





m

1 2 cos

cos 







r 

( m =1,2,…, M );

( r = 1, 2, …, M -1)

m

M

M

2

M is the total number of discrete points of the unknown functions within the interval (-1,1). Applying the conjugate operation to the system (6) additional NxM equations are obtained, i.e. 2 NxM equations should be solved, where N is the number of cracks. Eq. (7) is obtained from the condition (5) and the interpolation formula for the functions )(  n u : ) ( 1 ) ( ) ( ) ( 2 ) ( 0 1 0 1 m n M m r m r M r m n M m n u M T T u M u               . (8) Here T r are Chebyshev polynomials of the first kind. Inserting (8) into Eq. (4) the derivative of displacement jumps on the crack lines are obtained and then the displacement jumps can be derived by integrating the function (4) with (8). The stress intensity factors (SIFs) are calculated according to the following formula ) (  n u

)1(    n n IIn ua

iK K

In

M  



m

1

1 2 cot ) (

u )1( m









( n = 1, 2, …, N ).

M a p

(9)

n n

m n

M

4

m

1

C RITICAL LOADS , FRACTURE ANGLES

F

or general crack problems the stress intensity factors are both nonzero, i.e. mixed-mode conditions are in the vicinity of cracks. For this mixed-mode case the cracks deviate from their initial propagation direction. For the prediction of the crack growth and direction of this growth a fracture criterion should be applied. Using the maximum circumferential stress criterion (see [18] and for references [15, 16]) the direction of the initial crack propagation (Fig. 1 b) is evaluated as

    

 

  

2

II 2





  8

K K K K 4

(10)

arctan 2

I

I

II

and the critical stresses can be calculated from the expression      / )2/ tan( 3 )2/( cos 3 Ic II I K K K   .

(11)

Here K Ic

is the fracture toughness of the material. The critical stresses are given as   ])2/ tan( 3 )2/( /[cos 1 ) 2/ /( / 3 0    II I Ic cr cr cr k k a K P p P p     .

(12)

k ,

Here

are non-dimensional SIFs

II I

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V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02

0

0





a p K K K k 2

/

,

(15)

II I

II I

,

,

and p 0 = K Ic /(2π a ) 1/2 is critical load for a single crack in a material with the fracture toughness K Ic . For the system of cracks the fracture starts from the crack tip where P cr is minimal, i.e.

P k cr k

] / [min 0 ) ( p .

R ESULTS AND DISCUSSION

S

ome examples for edge crack interaction is investigated and presented here for homogeneous materials. The verification of the method and the numerical outcomes has been done in [11], where the results for some special cases were compared with the results for SIFs for a single inclined edge crack cited in [19] and with SIFs for periodic edge cracks cited in [20]. The tensile loading p is applied parallel to the boundary and on the crack lines we have the loading Eq. (3). The non- dimensional stress intensity factors Mode I and Mode II ( II I k , ) are defined by Eqs. (9) and (15). Non-dimensional k I for a single edge crack normal to the surface is equal to k I =1.12 and SIF k II is k II = 0. The non-dimensional distances ad d /ˆ  between the cracks are d = 1, 2, 4, 6, k k a a max  and we remind that 2 a k is the size of the k-th crack. After obtaining SIFs the fracture angles  are calculated by Eq. (10) and critical loads p cr by Eq. (12).

(a)

(b)

(c)

(d)

Figure 2 : Stress intensity factors k I of the edge cracks to the surface for different distances d between the cracks: (a) for crack 1 (60° ≤ β ≤ 120°), (b) for crack 2 (60° ≤ β ≤ 120°), (c) for crack 1 (15° ≤ β ≤ 90°), (d) for crack 2 (15° ≤ β ≤ 90°). Two equal edge cracks. and k II as functions of the inclination angle β=β n

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V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02

Two arbitrary inclined cracks Figs. 2, 5 and 8 show the SIFs k I,II

, Figs. 3, 6 and 9 – the fracture angles, and Figs. 4, 7 and 10 – the critical loads as

functions of inclination angles of the two edge cracks to the surface and for different distances d . It is observed that for all angles β SIF k I

increases with increasing the distance d between the cracks and k I = 0 at β = 90°. Besides, for all parameters of the problem the values for a single crack (Figs. 2, 5 and 8). That is, the shielding effect is observed, which is tends to the = 1.12 and k II

value for a single edge crack, e.g., to k I are smaller than the values of k I of k I

known for parallel cracks under tensile load normal to the crack lines. Figs. 2–4 present results for two equal edge cracks inclined arbitrarily to the surface with the same angle β=β n ( n =1, 2). Stress intensity factors k I and k II as functions of the inclination angle β are presented for the angles 60°≤ β ≤120° in Figs. 2 a, b and for 15°≤ β ≤90° in Figs. 2 c, d and for different distances d between the cracks. In the interval 60°≤ β ≤120° a small variation of the magnitude of k I with β is observed (Fig. 2 a, b), but in the interval 15°≤ β ≤60° for the small inclinations angles this variation is significant (Figs. 2 b, c). k I is increased from 0.2 to 0.99 for 15°≤ β ≤90° (for d =2) and then decreased for 90°≤ β ≤120°. SIFs k II are mostly nonzero, the absolute values of k II are greater than k I , and k II is monotonically decreased for 60°≤ β ≤120° (Fig. 2 a, b) and increased for 15°≤ β ≤45° (Figs. 2 b, c).

(a)

(b)

(c)

(d)

Figure 3 : Fracture angles ϕ 1) of the edge cracks to the surface for different distances d between the cracks: (a) for crack 1 (60° ≤ β ≤ 120°), (b) for crack 2 (60° ≤ β ≤ 120°), (c) for crack 1 (15° ≤ β ≤ 90°), (d) for crack 2 (15° ≤ β ≤ 90°). Two equal edge cracks. The fracture angles ϕ for two edge cracks are presented in Figs. 3, strong influence of the inclination angles β on the fracture angles ϕ is observed. For all β fracture angles ϕ are increased and changed the sign from negative to positive at β ≈103° (crack 1) and at β ≈77° (crack 2) for d =2, for larger distances d these points are shifted towards β ≈99° (crack 1) and β ≈81° (crack 2) for d =4 (Fig. 3 a, b). These changes of sign mean the changes of direction of the crack propagation. Fig. 4 shows results for the non-dimensional critical loads for crack 1 and for both cracks in Fig. 4 b (60°≤ β ≤120°) and 4 d (15°≤ β ≤90°). The larger the distance between the cracks – the less the p cr , i.e. the material becomes weaker with respect to fracture resistance. What crack starts to propagate first depends on the inclination angle, for 62°≤ β ≤90° p cr (1) < p cr (2) and the crack 1 propagates first and for 90°< β<118° the crack 2 will be starting first (Fig. 4 b). For small angles 15°≤ and ϕ (2) as functions of the inclination angle β=β n

13