Issue 62

Frattura ed Integrità Strutturale (Fracture and Structural Integrity): issue 62 (October 2022)

Frattura ed Integrità Strutturale, 62 (2022); International Journal of the Italian Group of Fracture

Table of Contents

V. Shlyannikov, A. Tumanov, N. Boychenko Elastic and nonlinear crack tip solutions comparison with respect to failure probability ………... 1-13 B. Kebaili, M. Benzerara, S. Menadi, N. Kouider, R. Belouettar Effect of parent concrete strength on recycled concrete performance …………………..……….. 14-25 H. Guedaoura, Y. Hadidane, M. J. Altaee Numerical investigation on strengthening steel beams with web openings using GFRP ………… 26-53 Investigation of the effect of yarn waste fibers and cocamide diethanolamide chemical on the strength of hot mix asphalt ……………………………...………………………...…... 54-63 A. Brotzu, B. De Filippo, S. Natali, L. Zortea Corrosion behavior of Shape Memory Alloy in NaCl environment and deformation recovery maintenance in Cu-Zn-Al system …………………………………………………….... 64-74 D. D’Andrea, G. Risitano, M. Raffaele, F. Cucinotta, D. Santonocito Damage assessment of different FDM-processed materials adopting Infrared Thermography …… 75-90 Y. Boulmaali-Hacene Chaouche, N. Kouider, K. Djeghaba, B. Kebaili Numerical study of the plasticity effect on the behavior of short steel columns filled with concrete loaded axially ………………………………………………………………………. 91-106 F. Slimani, M. Benzerara, M. Saidani Experimental and numerical investigation of gap K-joints of rectangular hollow section trusses ...... 107-125 M. Baruah, A. Borah Impact behaviour and fractography of 6061 alloy with trace addition of Sn ………………….. 126-133 M. Saltan, G. Kaçaro ğ lu, Ö. Karada ğ


Fracture and Structural Integrity, 62 (2022); ISSN 1971-9883

G.B. Veeresh Kumar, P. S. Shivakumar Gouda, R. Pramod, N.D. Prasanna, H.S. Balasubramanya, S.M. Aradhya Fabrication, mechanical and wear properties of Aluminum (Al6061)-silicon carbide-graphite Hybrid Metal Matrix Composites …………………………………………………….. 134-149 M. S. Shaari, S. D. Urai, A. Takahashi, M. A. M. Romlay Predicting fatigue crack growth behavior of coalesced cracks using the global-local superimposed technique …………………………………………………………………………… 150-167 K.C. Anil, J. Kumarswamy, M. Reddy, B. Prakash Mechanical behavior and fractured surface analysis of bauxite residue and graphite reinforced aluminum hybrid composites …………………………………………………………... 168-179 A.S. Yankin, A.V. Lykova, A.I. Mugatarov, V.E. Wildemann, A.V. Ilinykh Influence of additional static stresses on biaxial low-cycle fatigue of 2024 aluminum alloy ……... 180-193 A. A. Maaty, F. M. Kamel, A.A. ELShami Microstructure characterization of sustainable light weight concrete using trapped air additions …. 194-211 N. E. Tenaglia, D. O. Fernandino, A. D. Basso Effect of Ti addition and cast part size on solidification structure and mechanical properties of medium carbon, low alloy cast steel …………………………………………………….. 212-224 Y. Biskri, M. Benzerara, L. Babouri, O. Dehas, R. Belouettar Valorization and recycling of packaging belts and post-consumer PET bottles in the manufacture of sand concrete ..…………………………………………………………………….. 225-239 Y. S. Rao, B. Shivamurthy, N. S. Mohan, N. Shetty Influence of hBN and MoS 2 fillers on toughness and thermal stability of carbon fabric-epoxy composites …………………………………………………………………………... 240-260 N. Ab Razak, C. M. Davies Numerical simulation of creep notched bar of P91 steel ……………...……………………. 261-270 M. M. Pazdi, F. A. Ghazali Evaluation on fatigue behaviour of spot-welded joint under low blow impact treatment ……….... 271-278


Frattura ed Integrità Strutturale, 62 (2022); International Journal of the Italian Group of Fracture

J. C. Toledo, F. V. Díaz, M.E. Peralta, D. O. Fernandino High-quality nodule analysis in spheroidal graphite cast iron using X-ray micro-computed tomography …………………………………………………………………............... 279-288 M.A. Fauthan, S. Abdullah, M.F. Abdullah, I.F. Mohamed Multiple linear regression parameters for determining fatigue-based entropy characterisation of magnesium alloy …………………………………………………………………….. 289-303 D. C. Safa, N. Kaddouri, M. ElAjrami, M. Belhouari, K. Madani Use of combined CZM and XFEM techniques for the patch shape performance analysis on the behavior of a 2024-T3 Aluminum structure reinforced with a composite patch ………………. 304-325 T. Tahar, D. Djeghader, B. Redjel Mechanical properties and statistical analysis of the Charpy impact test using the Weibull distribution in jute-polyester and glass-polyester composites ………………………………… 326-335 T. Mohsein, S. Lakhdar, G. Belhi, K. Meftah On the use of the stepped isostress method in the prediction of creep behavior of polyamide 6 …..... 336-348 J. C. Santos, M. V. G. de Morais, M. R. Machado, R. Silva , E. U. L. Palechor , W. V. Silva Beam-like damage detection methodology using wavelet damage ratio and additional roving mass .. 349-363 D. Wang Seismic vulnerability analysis of reinforced concrete frame with infill walls considering in-plane and out-of-plane interactions ……………………………..………………………………... 364-384 G. Veeresha, B. Manjunatha, V. Bharath, M. Nagaral, V. Auradi Synthesis, microstructural characterization, mechanical, fractographic and wear behavior of micro B 4 C particles reinforced Al2618 alloy aerospace composites ……………………………….. 385-407 S. S. E. Ahmad, M. M. Elmesiri, M. Fawzy Ahmed, M. Bneni, A.A. ELShami Experimentally evaluation of high-performance concrete mixes used for tunnels and containing silica fume and polypropylene fiber after exposed to high temperatures ……………………….. 408-425 R. J. Bright, P. Hariharasakthisudhan Mechanical characterization and analysis of tensile fracture modes of ultrasonically stir cast Al6082 composites reinforced with Cu powder premixed Metakaolin particles ………………. 426-438


Fracture and Structural Integrity, 62 (2022); ISSN 1971-9883

M. Ravikumar, R. Naik Impact of nano sized SiC and Gr on mechanical properties of aerospace grade Al7075 composites 439-447 A. Mishra, A. Dasgupta Optimization of the tensile strength of friction stir welded heat treatable aluminum alloy by using bio-inspired artificial intelligence algorithms ……………………………………………... 448-459 P. Ghannadi, S. S. Kourehli, S. Mirjalili The application of PSO in structural damage detection: an analysis of the previously released publications (2005–2020) ………………………………………………………....…. 460-489 F. Cantaboni, P. S. Ginestra, M. Tocci, A. Avanzini, E. Ceretti, A. Pola Compressive behavior of Co-Cr-Mo radially graded porous structures under as-built and heat treated conditions ……………………………………………………………………. 490-504 D. Santonocito, D. Milone Deep Learning algorithm for the assessment of the first damage initiation monitoring the energy release of materials …………………...……………………………………………… 505-515 A. Iziumova, A. Vshivkov, A. Prokhorov, E. Gachegova, D. Davydov Heat dissipation and fatigue crack kinetic features of titanium alloy Grade 2 after laser shock peening …...……………………………………………………………………….... 516-526 E.V. Lomakin, B.N. Fedulov, A.N. Fedorenko Influence of manufacturing shrinkage and microstructural features on the strength properties of carbon fibers/PEEK composite material ……………………………………………….. 527-540 Yu. G. Matvienko, V.S. Pisarev, S. I. Eleonsky, I. N. Odintsev Quantitative description of low-cycle fatigue damage accumulation in contact interaction zone by local strain evolution …………………………………………………...…………….. 541-560 I. Shardakov, A. Shestakov, I. Glot, V. Epin, G. Gusev, R. Tsvetkov Estimation of nonlinear dependence of fiber Bragg grating readings on temperature and strain using experimental data ……………………………………………………………… 561-572 Y. U. Chapke, D. N. Kamble Effect of friction-welding parameters on the tensile strength of AA6063 with dissimilar joints …. 573-584


Frattura ed Integrità Strutturale, 62 (2022); International Journal of the Italian Group of Fracture

A. Baryakh, A. Tsayukov Justification of fracture criteria for salt rocks …………………………………………….. 585-601 R. Andreotti, A. Casaroli, M. Quercia, M.V. Boniardi A simplified formula to estimate the load history due to ballistic impacts with bullet splash. Development and validation for finite element simulation of 9x21mm full metal jacket bullets …. 602-612 H. Samir A. Mondal, D. Pilone, A. Brotzu, F. Felli Effect of composition and heat treatment on the mechanical properties of Fe Mn Al steels ……... 624-633 S. Bouhiyadi, L. Souinida, Y. El hassouani Failure analysis of compressed earth block using numerical plastic damage model …………....... 634-659 The P-h 2 relationship as a function of (h f /h m ) in indentation ……………….………..…….. 613-623


Fracture and Structural Integrity, 62 (2022); ISSN 1971-9883

Editorial Team

Editor-in-Chief Francesco Iacoviello

(Università di Cassino e del Lazio Meridionale, Italy)

Co-Editor in Chief Filippo Berto

(Università di Roma “La Sapienza”, Italy; Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

Sabrina Vantadori

(Università di Parma, Italy)

Jianying He

(Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

Section Editors Sara Bagherifard

(Politecnico di Milano, Italy) (Politecnico di Milano, Italy) (University of Porto, Portugal) (University of Belgrade, Serbia)

Marco Boniardi

José A.F.O. Correia

Milos Djukic

Stavros Kourkoulis

(National Technical University of Athens, Greece) (University Politehnica Timisoara, Romania)

Liviu Marsavina Pedro Moreira

(INEGI, University of Porto, Portugal) (Chinese Academy of Sciences, China)

Guian Qian

Aleksandar Sedmak

(University of Belgrade, Serbia)

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) (Politecnico di Torino, Italy)

Leslie Banks-Sills Alberto Carpinteri Andrea Carpinteri Giuseppe Ferro

Donato Firrao

Emmanuel Gdoutos

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

Youshi Hong M. Neil James Gary Marquis

(University of Plymouth, UK)

(Helsinki University of Technology, Finland)

(Ecole Nationale Supérieure d'Arts et Métiers | ENSAM · Institute of Mechanics and Mechanical Engineering (I2M) – Bordeaux, France)

Thierry Palin-Luc Robert O. Ritchie Ashok Saxena Darrell F. Socie

(University of California, USA)

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

(University of Illinois at Urbana-Champaign, USA)

Shouwen Yu

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

Cetin Morris Sonsino

Ramesh Talreja David Taylor John Yates Shouwen Yu

(The Engineering Integrity Society; Sheffield Fracture Mechanics, UK)

(Tsinghua University, China)

Regional Editorial Board Nicola Bonora

(Università di Cassino e del Lazio Meridionale, Italy)

Raj Das

(RMIT University, Aerospace and Aviation department, Australia)

Dorota Koca ń da

(Military University of Technology, Poland)


Frattura ed Integrità Strutturale, 62 (2022); International Journal of the Italian Group of Fracture

Stavros Kourkoulis Carlo Mapelli Liviu Marsavina

(National Technical University of Athens, Greece)

(Politecnico di Milano, Italy)

(University of Timisoara, Romania) (Tecnun Universidad de Navarra, Spain)

Antonio Martin-Meizoso Mohammed Hadj Meliani

(LPTPM , Hassiba Benbouali University of Chlef. Algeria) (Indian Institute of Technology/Madras in Chennai, India)

Raghu Prakash

Luis Reis Elio Sacco

(Instituto Superior Técnico, Portugal) (Università di Napoli "Federico II", Italy)

Aleksandar Sedmak

(University of Belgrade, Serbia)

Dov Sherman Karel Sláme č ka

(Tel-Aviv University, Tel-Aviv, Israel)

(Brno University of Technology, Brno, Czech Republic) (Middle East Technical University (METU), Turkey)

Tuncay Yalcinkaya

Editorial Board Jafar Albinmousa Mohammad Azadi Nagamani Jaya Balila

(King Fahd University of Petroleum & Minerals, Saudi Arabia) ( Faculty of Mechanical Engineering, Semnan University, Iran)

(Indian Institute of Technology Bombay, India) (Indian Institute of Technology Kanpur, India)

Sumit Basu

Stefano Beretta Filippo Berto K. N. Bharath

(Politecnico di Milano, Italy)

(Norwegian University of Science and Technology, Norway) (GM Institute of Technology, Dept. Of Mechanical Engg., India)

Elisabeth Bowman

(University of Sheffield)

Alfonso Fernández-Canteli

(University of Oviedo, Spain) (Università di Parma, Italy)

Luca Collini

Antonio Corbo Esposito

(Università di Cassino e del Lazio Meridionale, Italy)

Mauro Corrado

(Politecnico di Torino, Italy)

Dan Mihai Constantinescu

(University Politehnica of Bucharest, Romania)

Manuel de Freitas Abílio de Jesus Vittorio Di Cocco Andrei Dumitrescu Devid Falliano Riccardo Fincato Eugenio Giner Milos Djukic

(EDAM MIT, Portugal)

(University of Porto, Portugal)

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Belgrade, Serbia)

(Petroleum-Gas University of Ploiesti, Romania)

(Dipartimento di Ingegneria Strutturale, Edile e Geotecnica, Politecnico di Torino, Italy)

(Osaka University, Japan)

(Universitat Politecnica de Valencia, Spain) (Université-MCM- Souk Ahras, Algeria) (Middle East Technical University, Turkey) (Hassiba Benbouali University of Chlef, Algeria)

Abdelmoumene Guedri

Ercan Gürses

Abdelkader Hocine

Ali Javili

(Bilkent University, Turkey) (University of Piraeus, Greece)

Dimitris Karalekas Sergiy Kotrechko Grzegorz Lesiuk

(G.V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine, Ukraine)

(Wroclaw University of Science and Technology, Poland)

Paolo Lonetti

(Università della Calabria, Italy)

Tomasz Machniewicz

(AGH University of Science and Technology) (Università Politecnica delle Marche, Italy)

Erica Magagnini Carmine Maletta

(Università della Calabria, Italy)

Fatima Majid Sonia Marfia

(University Chouaib Doukkali, El jadida, Morocco) (Università di Cassino e del Lazio Meridionale, Italy)

Lucas Filipe Martins da Silva

(University of Porto, Portugal) (Kyushu University, Japan)

Hisao Matsunaga Milos Milosevic Pedro Moreira

(Innovation centre of Faculty of Mechanical Engineering in Belgrade, Serbia)

(University of Porto, Portugal)


Fracture and Structural Integrity, 62 (2022); ISSN 1971-9883

Mahmoud Mostafavi Vasile Nastasescu

(University of Bristol, UK)

(Military Technical Academy, Bucharest; Technical Science Academy of Romania)

Stefano Natali Andrzej Neimitz

(Università di Roma “La Sapienza”, Italy) (Kielce University of Technology, Poland)

(Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Ukraine)

Hryhoriy Nykyforchyn

Pavlos Nomikos

(National Technical University of Athens) (IMT Institute for Advanced Studies Lucca, Italy)

Marco Paggi Hiralal Patil Oleg Plekhov

(GIDC Degree Engineering College, Abrama-Navsari, Gujarat, India) (Russian Academy of Sciences, Ural Section, Moscow Russian Federation)

Alessandro Pirondi Maria Cristina Porcu Zoran Radakovi ć D. Mallikarjuna Reddy

(Università di Parma, Italy) (Università di Cagliari, Italy)

(University of Belgrade, Faculty of Mechanical Engineering, Serbia) (School of Mechanical Engineering, Vellore Institute of Technology, India)

Luciana Restuccia Giacomo Risitano Mauro Ricotta Roberto Roberti

(Politecnico di Torino, Italy) (Università di Messina, Italy) (Università di Padova, Italy) (Università di Brescia, Italy)

Elio Sacco

(Università di Napoli "Federico II")

Hossam El-Din M. Sallam

(Jazan University, Kingdom of Saudi Arabia) (Università di Roma "Tor Vergata", Italy)

Pietro Salvini Mauro Sassu

(University of Cagliari, Italy) (Università di Parma, Italy)

Andrea Spagnoli Ilias Stavrakas Marta S ł owik Cihan Teko ğ lu Dimos Triantis

(University of West Attica, Greece) (Lublin University of Technology)

(TOBB University of Economics and Technology, Ankara, Turkey

(University of West Attica, Greece)

Paolo Sebastiano Valvo Natalya D. Vaysfel'd

(Università di Pisa, Italy)

(Odessa National Mechnikov University, Ukraine)

Charles V. White Shun-Peng Zhu

(Kettering University, Michigan,USA)

(University of Electronic Science and Technology of China, China)

Special Issue Salvinder Singh Shahrum Abdullah Roberto Capozuzza

Failure Analysis of Materials and Structures

(Universiti Kebangsaan, Malaysia) (Universiti Kebangsaan, Malaysia)

(Polytechnic University of Marche, Italy)

Special Issue

Russian mechanics contributions for Structural Integrity (Mechanical Engineering Research Institute of the Russian Academy of Sciences, Russia) (Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Russia)

Valerii Pavlovich Matveenko

Oleg Plekhov


Frattura ed Integrità Strutturale, 62 (2022); International Journal of the Italian Group of Fracture

Frattura ed Integrità Strutturale is an Open Access journal affiliated with ESIS

Sister Associations help the journal managing Algeria: Algerian Association on Fracture Mechanics and Energy -AGFME Australia: Australian Fracture Group – AFG Czech Rep.: Asociace Strojních Inženýr ů (Association of Mechanical Engineers) Greece: Greek Society of Experimental Mechanics of Materials - GSEMM India: Indian Structural Integrity Society - InSIS Israel: Israel Structural Integrity Group - ISIG Italy: Associazione Italiana di Metallurgia - AIM Italy: Associazione Italiana di Meccanica Teorica ed Applicata - AIMETA Italy:

Società Scientifica Italiana di Progettazione Meccanica e Costruzione di Macchine - AIAS Group of Fatigue and Fracture Mechanics of Materials and Structures


Portugal: Portuguese Structural Integrity Society - APFIE Romania: Asociatia Romana de Mecanica Ruperii - ARMR Serbia:

Structural Integrity and Life Society "Prof. Stojan Sedmak" - DIVK Grupo Espanol de Fractura - Sociedad Espanola de Integridad Estructural – GEF

Spain: Turkey: Ukraine:

Turkish Solid Mechanics Group

Ukrainian Society on Fracture Mechanics of Materials (USFMM)


Fracture and Structural Integrity, 62 (2022); 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 (January, April, July, October). 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 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) 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)


Frattura ed Integrità Strutturale, 62 (2022); International Journal of the Italian Group of Fracture

FIS news


ear friends, this time we have some news concerning the journal website. In order to improve the journal website readability, especially using mobile devices, we modified the home page as follows: - “Online first” papers are now available in a dedicated page (the link is available in the main menu). - It is possible to be forwarded to the Visual Abstracts YouTube channel using the dedicated link in the column on the right side of the screen. - The users reports are now collected in a dedicated page of the web site (the link is available in the column on the right side of the screen) - The “Most Read Articles” section now offers the most read 15 papers in the last 365 days. Results are updated every 15 days. I wish to remember to all the members of our community that the next IGF conference ( IGF27, the 27th International Conference on Fracture and Structural Integrity; will be held in Rome and on web, (February 22-24, 2023). I wish to underline the 100% of the fees will be used for the: - event organisation; - publication of the dedicated Procedia Structural Integrity issue; - publication of the IGF journal Frattura ed Integrità Strutturale ; - all the other IGF activities (e.g., the website publication). If you love Frattura ed Integrità Strutturale, and you appreciate it as a good Diamond Open Access journal (no APC), you have only to: - participate to the IGF27; - consider Frattura ed Integrità Strutturale for your refs, if you find papers of your interest! Looking forward to meeting you in Rome!

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief


V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 62 (2022) 1-13; DOI: 10.3221/IGF-ESIS.62.01

Elastic and nonlinear crack tip solutions comparison with respect to failure probability

Valery Shlyannikov, Andrey Tumanov, Natalia Boychenko FRC Kazan Scientific Center of Russian Academy of Sciences, Russia,,

A BSTRACT . This study represents a methodology to assess the probability of failure based on three the driving force formulations defined by the corresponding brittle and ductile fracture criteria for compact and bending specimens made of 34XH3MA and S55C steels. The elastic stress intensity factor (SIF) and two types of the non-linear plastic SIFs were considered as the driving force or generalized parameter (GP) to determine the probability of failure assuming a three-parameter Weibull distribution. The elastic SIF were experimentally obtained for studied materials and specimen geometries whereas the plastic SIFs were numerically calculated for the same material properties, specimen configurations and loading conditions according to classical J 2 and strain gradient plasticity theories. Different specimen types with varying relative crack lengths and thicknesses were investigated. Proposed the normalized generalized parameter accounting for brittle or ductile fracture can be used as a suitable failure variable that is confirmed by comparison of the obtained failure cumulative distribution functions based on the three studied GPs. K EYWORDS . Failure probability; Weibull distributions; Nonlinear stress intensity factors; Generalized parameters.

Citation: Shlyannikov, V., Tumanov, A., Boychenko, N., Elastic and nonlinear crack tip solutions comparison with respect to failure probability, Frattura ed Integrità Strutturale, 61 (2022) 1-13.

Received: 10.07.2022 Accepted: 19.07.2022 Online first: 20.07.2022 Published: 01.10.2022

Copyright: © 2022 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.


he main objective of experimental studies in fracture mechanics is to determine the critical value of a parameter characterizing the failure of a material. In most cases, the results of experimental studies must be evaluated statistically owing to the scatter of the critical fracture resistance parameter. If the fracture parameter is chosen correctly and the measuring instruments provide the required accuracy, the dispersion density corresponds to the normal Gaussian–Laplace distribution [1]. To evaluate the fracture resistance parameters and probability of failure, it is convenient T


V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 62 (2022) 1-13; DOI: 10.3221/IGF-ESIS.62.01

to use the Weibull distribution function [2]. The analysis of the Weibull parameters suggests that the studied characteristic is applicable as a fracture criterion. The generalized probabilistic local approach (GPLA), developed by Muniz-Calvente et al. [3–7], allows the primary failure cumulative distribution function (PFCDF) owning to a certain failure type to be determined for a given material from experimental data and used subsequently for probabilistic design. Such approach introduce a realistic safety boundary provided that the failure criterion represented by an adequate generalized parameter (GP) and the corresponding failure criterion is properly recognized as a reference variable to be considered in the failure assessment. The authors [3] supposed that the three-parameter Weibull distribution could be extended to any type of failure using the driving force ( X c ) defined by the corresponding fracture criterion. This methodology is feasible to apply for any kind of failure provided the experimental results for this specific failure are available and the corresponding reference driving force controlling such a failure is recognized. The reference driving force is characterized by the different Weibull distribution obtained, which influences the resulting predictions for brittle and ductile type of failure. The authors [3] draw attention to the need to apply the statistical technique denoted confounded data [8,9]. This approach allows the cumulative distribution functions (CDF) for any of the flaw populations to be separately achieved without neglecting the mutual statistical interference between several distributions. In the present study, an extension of such a probabilistic failure approach is presented allowing the consideration of different constitutive equation of the material behavior, as well as the influence of scale effects, when specimens of different size are tested. The results are compared for states when the most suitable failure generalized parameter to determine the probability of failure is identified among three alternatives, namely, elastic solution, classical J 2 theory of plasticity and strain gradient plasticity theory.



he model for a probability–statistical assessment used in this study is based on a generalized local model, described in [3–7]. This generalized probabilistic local approach (GPLA) allows a direct relationship to be found between the critical reference variable, as defined by the fracture criterion, and the failure probability. The relationship, known as primary failure cumulative distribution function (PFCDF) can be expressed by means of a three parameter Weibull cumulative distribution function (CDF) [10]. Accordingly, the failure probability P fail of an element subjected to a certain critical factor X c uniformly distributed on the element can be represented as follows

 

   

   

 

 



1 exp    


 


where λ , β and δ are, respectively, the location parameter, the shape parameter and the scale parameter associated with the selected reference area. Generalized parameter GP in Eq.1 is determined in terms of the driving force for accepted either brittle or ductile failure criterion. The following is the iterative procedure applied to achieve fitting of the optimal primary distribution function from an experimental data set exhibiting three different failure types. It implies estimation of the nine Weibull parameters, three for any of the failure mechanisms. Fig. 1 shows a flaw chart that describes the iterative procedure applied consisting in the following steps:  In an experimental program, failure tests are carried out and the corresponding results for the critical parameter determined.  The loading process up to failure for any test is simulated by means of a finite element code. In this way, the type and value of the driving force at failure for any element are known.  The failure results are ranked in increasing order according to the value of the driving force reached by any specimen at failure. Subsequently, using Bernard’s expression [11]:





, fail i



the accumulated failure probability is provided for any population individually referred to the specific specimen size and failure type obtained. In Eq.2 i = 1 , ..., N , and N is the number of cases studied.


V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 62 (2022) 1-13; DOI: 10.3221/IGF-ESIS.62.01

 The Weibull parameter are estimated by applying Eq.1 to the generalized parameter and the failure probability as obtained for any test. Once fitting is accomplished, the value of the nine Weibull parameters are estimated for the iteration being.  With the aim of assessing the convergence of the procedure, the parameter values obtained at any iteration are compared with those found in the preceding iteration until the summation of the variations in the values of each of them is less than a prescribed threshold value ε :

1 i i                 1 1 i i i i


When this occurs, the parameter values obtained in the last iteration are considered to be the final solution.

Figure 1: Flow-chart representing the iterative procedure applied for data fitting.

As can be observed, the procedure proposed is implemented by merely mentioning without specifying the “failure criterion” bound to the driving force being considered. This allows the approach to be applicable to any specific failure problem handled irrespective of its complexity provided the weakest link principle is applicable referred to either brittle or ductile failure.


n this section we will consider both elastic and nonlinear formulations for the generalized parameter which characterizes the fractures of the tested specimens according to brittle and ductile failure criteria. Three GPs were analyzed in this study, related to the following fracture parameters: elastic stress intensity factor (SIF) K 1 ( GP K1 ), plastic stress intensity factor K p ( GP Kp ) based on the classical J 2 Hutchinson-Rice-Rosengren (HRR) solution, and plastic SIF K SGP ( GP Ksgp ) backgrounded on strain gradient plasticity theory. I


V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 62 (2022) 1-13; DOI: 10.3221/IGF-ESIS.62.01



he values of the elastic SIF K 1 were obtained in accordance with standard ASTM E399 [12] by the following equations. For the compact tension C(T) configuration:

q P

a      


1 Y B W W





   

   

a W

2 

a       W

a      

a      

a      

a      

0.886 4.64 










a W

1 /

and for the single-edge-notched bend (SENB) configuration:

1 3 2 1 q P L a Y BW W

     






a       W

a      

a      

a      

a      


 


1.93 3.07







where a is the crack length, B is the specimen thickness, W is the specimen width, L 1 is the span of the bending specimen, and Y 1 is the geometry-dependent SIF correction factor. The values of the P Q loads were obtained using the typical load versus load-line crack opening displacement curves for the C(T) and SENB configurations.



he classical HRR singular solution [13,14] for an infinite size cracked body of a strain-hardening material was completed by Shlyannikov and Tumanov as numerical method [15] for plastic stress intensity factor determination applied to mixed mode plane strain/plane stress problems and general three-dimensional (3D) structural element configurations. According to this method, the plastic SIF K p can be expressed directly in terms of the corresponding elastic SIF K 1 :     1 1 2 2 1 n K a      

yn    I

W      

0        

 





where α and n are the strain hardening parameters,  yn is the nominal stress,  0 is the yield stress, and I n is the governing parameter of the elastic–plastic stress–strain fields in the form of dimensionless factor:

 

  n a w d

    



( , , 

n I

n a w

, ,

  

   



  

  

  

  

du 

du 


  1 n e   


 





rr     

r  

n a w

u 

u 

, ,









1 

FEM FEM FEM FEM rr r r u u         





V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 62 (2022) 1-13; DOI: 10.3221/IGF-ESIS.62.01

In this case, the numerical integral of the crack-tip field I n changes not only with the strain-hardening exponent n , but also with the relative crack length a/W and specimen configuration. Numerical results regarding the behavior of the I n -integral in the most common experimental configurations for test specimens in fracture mechanics can be found in Refs. [16–18].



he third generalized parameter is presented in the form of a plastic stress intensity factor based on the strain gradient plasticity (SGP) theory. In this case the aim of the conventional mechanism-based strain gradient plasticity theory [19-21] is to capture the role of geometrically necessary dislocation (GND) density in the mechanics of crack initiation and growth. The advantage of SGP plasticity theory, which grounded on the Taylor’s dislocation model [22], is sensitivity to the intrinsic material plastic length parameter ℓ . According to SGP theory, the tensile flow stress is related to a reference stress σ ref , the equivalent plastic strain ε p and the effective plastic strain gradient η p :   2 P P flow ref f l       (8)


 2

2 18

  





Here, ā is an empirical coefficient that is assumed to be equal to 0.5, μ is the shear modulus and b is the Burgers vector length. The first-order version of the conventional mechanism-based strain gradient (CMSG) plasticity model is implemented in the computation of the material Jacobian and, consequently, of the rate of the stress tensor:

   

   


  


ij  



2           kk ij ij K ij

 

  

  




where ij    is the deviatoric strain rate tensor. As with other continuum strain gradient plasticity models, the CMSG theory is intended to model a collective behaviour of dislocations and is therefore not applicable at scales smaller than the dislocation spacing. Taking into account the singular nature of the stress distribution at the crack tip for the CMSG plasticity theory of plasticity Eqs.8-10, Shlyannikov et al. [23-25] introduced a new plastic stress intensity factor in the following form:     ˆ , , FEM FEM FEM e SGP e r K r r       (11)       ˆ , , , FEM FEM FEM P ij ij A r r r       (12) where r r l  is the normalized distance to the crack tip, and  is the power of the stress singularity. In Eq.11, the angular distributions of the dimensionless stress component   ˆ , FEM ij r   are normalized, such that   1 2 ,max max ˆ 3 2 1 FEM FEM FEM e ij ij S S    and FEM FEM ij ij Y     . In the further presentation of numerical and experimental results, we will use the following notation for plastic SIF FEM SGP SGP K K  . In this study, tested compact and bending specimens made of 34XH3MA and S55C steels are considered as a subject for application of the conventional elasticity, the classical J2 and CMSG plasticity theories. The implementation of a mechanism FEM FEM SGP P K A r   (13)


V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 62 (2022) 1-13; DOI: 10.3221/IGF-ESIS.62.01

based SGP theory in ANSYS [26] using a user material subroutine USERMAT has been described in more detail by the authors [23-25].



he algorithm described in Section 2 was used for the probabilistic assessment based on the experimental data. Several experiments and corresponding numerical calculations were performed on CT and SENB specimen configurations produced from steels 34XH3MA and JS55C. The fracture toughness tests were performed in accordance with ASTM E399 [12]. The experimental data for the fracture toughness characteristics of the SENB specimens of JS55C steel were obtained from Meshii et al. [27]. The main mechanical properties of the analyzed materials are listed in Tab. 1, where Е is the Young’s modulus, σ 0 is the yield stress, σ f is the tensile strength, σ u is the true ultimate tensile stress, α is the strain hardening coefficient, and n is the strain hardening exponent.




E, GPa

σ 0 , MPa

σ f , MPa

σ u , MPa















Table 1: Main mechanical properties of the steels.

a) b) Figure 2: SENB (a) and C(T) (b) specimen configuration.

The loading configuration and specimen geometry are shown in Fig. 2. The relative crack length a/W and relative thickness B/W were varied for each specimen configuration. The relative crack length a/W was varied in the range of 0.245–0.645. Three types of C(T) specimens with B/W ratios of 0.125, 0.25, and 0.5 and four types of SENB specimens with B/W ratios of 0.25, 0.5, 1.0, and 1.5 were used. The specimen sizes and crack lengths are listed in Tab. 2. A full-field 3D finite-element analysis was performed using the experimental set of P q loads for each tested specimen to determine the elastic–plastic stress fields along the through-thickness crack front in the SENB and C(T) specimens subjected to bending and tension loadings. In all numerical calculations for a strain-hardening material with a pure power-law behavior, the Ramberg–Osgood constitutive relationship with n , a , and  0 constants, listed in Tab. 1, was used. The numerical calculations for the conventional mechanism-based strain gradient plasticity model according to the constitutive Eqs.8-10 were performed for the value of the intrinsic material plastic length parameter ℓ = 5 μ m. To accurately characterize the strain gradient effect, a high-density FE mesh was formed near the crack tip and along crack front in SENB and C(T) specimens. The FE-mesh sensitivity parametric study shown that a quadrilateral brick element size less than 0.15 μ m provided mesh-independent results. For the elastic-plastic analysis of both specimen FE models, the initial crack tip was assigned a radius of curvature ρ = 0.87 μ m. A typical FE mesh for the C(T) specimen configuration has 9,625,812 nodes, while for the SENB specimen has 17,903,812 nodes. The ANSYS [26] finite-element code was applied to obtain the distribution of stresses along the crack front for the tested specimen, which were used to determine both the elastic and nonlinear stress intensity factors. The obtained GPs in the form of elastic and plastic SIFs for all specimen configurations are listed in Tab. 2.


V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 62 (2022) 1-13; DOI: 10.3221/IGF-ESIS.62.01



n this work, the method of confounded data is employed to the consideration of the cumulative distribution functions (cdf) for three flaw populations, characterized by corresponding the generalized parameters, namely, elastic K 1 and two types of plastic K P and K SGP stress intensity factors. The first of them represent brittle material behavior, while the second and third parameters are related to ductile fracture. The maximum elastic or plastic stress intensity factor is considered to be the critical parameter (GP) under static failure conditions. Recall that, the method of confounded data allows the cumulative distribution functions for any of the flaw populations to be separately achieved.

W , mm

B , mm

a , mm

Specimen type



K 1









0.350 0.350 0.625 0.645 0.380 0.425 0.475 0.487 0.380 0.358 0.475 0.245 0.250 0.445 0.445 0.610 0.615 0.605 0.620 0.507 0.501 0.499 0.503 0.500 0.500 0.504 0.497 0.498 0.502 0.497 0.494 0.502 0.499 0.501 0.4625 0.5008 0.5028 0.5016

14.0 14.0 25.0 25.8 15.2 17.0 19.0 19.5 15.2 15.4 18.5 19.0

66.012 63.343

0.6965 0.6864 0.6860 0.6965 0.7209 0.7245 0.7188 0.7140 0.7071 0.7021 0.6995 0.7945 0.7629 0.7659 0.7576 0.7525 0.7289 0.7328 0.682 0.745

1.301 1.308 1.302 1.342 1.401 1.441 1.490 1.399 1.332 1.269 1.330 1.326 1.288 1.272 1.289 1.310 1.285 1.238 1.232 1.258 1.985 2.442 1.872 2.232 2.323 1.891 2.329 1.983 2.120 2.104 1.943 1.935 2.149 2.064 1.897 2.031 2.132 2.039


68.152 77.563









60.67 70.17 69.44 68.12 57.24 64.35






4.9 5.0 8.9 8.9


12.2 12.3 12.1 12.4

55.25 57.53



52.146 55.964 58.112 67.492






12.67 12.53 12.47 12.58 12.51 12.49 12.61 12.52 12.57 12.54 12.43 12.45 12.54 12.43 12.35 12.56 12.48 12.53



58.12 65.81 67.79


0.732 0.744 0.699 0.733 0.725 0.722 0.722 0.715 0.741 0.735 0.723 0.733 0.749 0.71



55.214 63.259 56.896


61.359 59.295










64.635 61.516


Table 2: Generalized parameters for tested specimens.


V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 62 (2022) 1-13; DOI: 10.3221/IGF-ESIS.62.01



n order to illustrate the methodology applied for checking the suitability of the failure criterion, as represented by an adequate generalized parameter (GP), taking into account the critical parameter distribution and the size of the specimen tested the following examples are exposed. Three experimental programs consisting of SENB and C(T) specimen tests with different sizes (Tab. 2) are simulated. For each of the considered generalized parameter, we distinguish three separate populations: SENB specimen from JS55C steel, SENB specimen from 34XH3MA steel and C(T) specimen from 34XH3MA steel. Thus, we will consider the behavior of two different materials that are implemented on test samples of two configurations.

K 1



JS55C SENB 55.697 7.782 1.456


34XH3M C(T)

JS55C SENB 0.643 0.089 6.079


34XH3M C(T)

JS55C SENB 1.835 0.277 1.481


34XH3M C(T)

λ δ β

51.103 8.395 1.359

57.030 15.019 1.986

0.707 0.054 2.459

0.668 0.039 2.477

1.220 0.060 1.595

1.256 0.109 1.479

Table 3: The resulting three-parameter Weibull distribution characteristics for tested steels.

Test data are simulated assuming that N=18 SENB specimens from JS55C, N=8 SENB specimens from 34XH3MA and N=12 C(T) specimens from 34XH3MA are loaded up to failure, which may caused by three different initiating failure mechanisms related to elasticity, classical and strain gradient plasticity. In this experimental program, the values of the failure load for each test is registered from which the corresponding driving force (in this case, stress intensity factors) distribution at failure is determined using a finite element code. Thereafter, the FEM results are used for estimating the three sets of Weibull parameters corresponding to any failure type following the steps as indicated above. Making use of the data numerically simulated, nine cdfs are fitted separately. The Weibull parameters being found in this procedure are listed in Tab. 3, from which the adequacy of the fitting performed is apparent, provided a sufficient number of experimental data results are at disposal.

a) c) Figure 3: Probabilities of failure for (a) elastic, (b) plastic K P and (c) K SGP SIFs for SENB JS55C steel specimens. b)

Figs. 3-5 represent the experimental failure cumulative distribution function (EFCDF) for each test type and their fitting by Eq.1. As shown in Figs. 3-5, the PFCDF leads to a satisfactory adjustment of the experimental results for each experimental programs have been implemented on SENB and C(T) test samples produced from JS55C and 34XH3MA steels, which would not be possible if the failure criterion were unsuitable. However, as can be observed, the primary failure cumulative distribution function, based on the nonlinear generalized parameters (plastic SIFs K P and K SGP ), give more uniform behavior with respect to the GP related with elastic SIF K 1 . The use of the material property PFCDF (Figs. 3-5) in combination with the Weibull parameters (Tab. 3) generated for each experiment permits us to conclude that the division into three external ( K 1 , K P and K SGP ) and three internal (SENB-JS55C, SENB-34XH3MA and C(T)-34XH3MA) populations was justified.


Made with FlippingBook PDF to HTML5