Tecnologia em Metalurgia, Materiais e Mineração
Tecnologia em Metalurgia, Materiais e Mineração
Artigo Original – Edição especial 75th ABM Annual Congress

Effect of R load ratio on fatigue crack growth resistance  of steels used in automotive applications: experimental  results and use of performance prediction models

Leonardo Barbosa Godefroid, Américo Tristão Bernardes, Tainan Ferreira Muniz, Jefferson José Vilela, Fabiano Alcântara Machado

Downloads: 1
Views: 254


This research consisted in comparing the fatigue crack growth (FCG) performance of four HSLA/ AHSS steels used in automotive applications and with different microstructures, and the application of some prediction models for the da/dN versus ΔK traditional sigmoidal curve as a function of the R load ratio. FCG tests were carried out on C(T) test specimens with R-ratios varying between 0.03 and 0.7. Using the original and empirical methodology proposed by Paris and Erdogan to describe the da/dN-ΔK relationship, the results showed significant differences in function of microstructure, and a deleterious effect of R-ratio increase on the crack growth rate. In order to check existing methodologies based on physical considerations for predicting the fatigue behavior of materials and the effect of the R-ratio mainly in the fatigue threshold ΔKth region, the well-known crack closure model proposed by Elber, an approach using two parameters as a driving force for the crack growth proposed by Vasudevan and co-authors and a combination of these two models recently proposed by Zhu and co-authors were compared. The manifestation of crack closure and its qualitatively expected dependence on the R-ratio were verified for the studied steels, but the Elber model was not able to provide a master curve that accurately summarized the effect of the R-ratio on the sigmoidal fatigue curve of steels. The combined use of two critical thresholds, ΔKth* and Kmax*, for predicting fatigue crack growth according to the Vasudevan model also did not provide accurate results in evaluating the effect of the R-ratio. Regardless of the verified dispersions, there is a connection between the two-parameter methodology and crack closure, hence the model by Zhu and co-authors could be a promising alternative. However, this model also showed significant dispersions and was unable to create a master curve to adequately predict the effect of R-ratio on crack growth. Thus, it can be concluded that this research topic is still open, requiring a more in-depth phenomenological knowledge to predict the effect of the R-ratio on FCG.


Fatigue crack growth; Load ratio; Crack closure; Driving force parameters; Steels for automotive industry


1 Keeler S, Kimchi M, Mconey PJ, editors. Advanced high-strength steels: application guidelines - version 6.0. Middletown: WorldAutoSteel; 2017.

2 Cooman BC, Findley K. Introduction to the mechanical behavior of steel. Warrendale: Association for Iron & Steel Technology; 2017.

3 Fonstein N. Advanced high strength sheet steels. Cham: Springer; 2015.

4 Suzuki H, McEvily AJ. Microstructural effects on fatigue crack growth in a low carbon steel. Metallurgical Transactions. 1979;10:475-481.

5 Minakawa K, Matsuo Y, McEvily AJ. The influence of a duplex microstructure in steels on fatigue crack growth in the near-threshold region. Metallurgical Transactions. 1982;13:439-445.

6 Dutta VB, Suresh S, Ritchie RO. Fatigue crack propagation in dual-phase steels. Metallurgical Transactions. 1984;15:1193-1207.

7 Wasynczuk JA, Ritchie RO, Thomas G. Effects of microstructure on fatigue crack growth in duplex ferritemartensite steels. Materials Science and Engineering. 1984;62:79-92.

8 Tzou JL, Ritchie RO. Fatigue crack propagation in a dual-phase plain-carbon steel. Scripta Metallurgica. 1985;19:751-755.

9 Ramage RM, Jata KV, Shiflet GJ, Starke EA. The effect of phase continuity on the fatigue and crack closure behavior of a dual-phase steel. Metallurgical Transactions. 1987;18:1291-1298.

10 Sun L, Li S, Zang Q, Wang Z. Dependence of fatigue crack closure behaviour on volume fraction of martensite in dual-phase steels. Scripta Metallurgica. 1995;32:517-521.

11 Sarwar M, Priestner R. Fatigue crack propagation behaviour in dual-phase steel. Journal of Materials Engineering and Performance. 1999;8:245-251.

12 Gritti JA, Melo TMF, Machado FA, Horta WS, Cândido LC, Godefroid LB. Influência da pré-deformação e do tratamento de “bake hardening” na tenacidade à fratura e na resistência à fadiga de dois aços bifásicos. In: Anais do 61º Congresso Anual da ABM; 2006; Rio de Janeiro, Brasil. São Paulo: ABM; 2006.

13 Cheng X, Petrov R, Zhao L, Janssen M. Fatigue crack growth in TRIP steel under positive R-ratios. Engineering Fracture Mechanics. 2008;75:739-749.

14 Gutz AE, Machado FA, Gritti JA, Melo TMF, Cândido LC, Godefroid LB. Tenacidade à fratura e resistência ao crescimento de trinca por fadiga de um aço bifásico da classe de 780MPa de resistência. In: Anais do 65º Congresso Anual da ABM; 2010; Rio de Janeiro, Brasil. São Paulo: ABM; 2010.

15 Godefroid LB, Andrade MS, Horta WS, Machado FA. Effect of prestrain and bake hardening heat treatment on fracture toughness and fatigue crack growth resistance of two dual-phase steels. In: Proceedings of the Materials Science and Technology Conference; 2011; Columbus OH, USA. Warrendale: Association for Iron & Steel Technology; 2011.

16 Idris R, Prawoto Y. Influence of ferrite fraction within martensite matrix on fatigue crack propagation: an experimental verification with dual phase steel. Materials Science and Engineering. 2012;A552:547-554.

17 Guan M, Yu H. Fatigue crack growth behaviors in hot-rolled low carbon steels: a comparison between ferrite–pearlite and ferrite-bainite microstructures. Materials Science and Engineering A. 2013;559:875-881.

18 Li S, Kang Y, Kuang S. Effects of microstructure on fatigue crack growth behavior in cold-rolled dual phase steels. Materials Science and Engineering. 2014;A612:153-161.

19 Godefroid LB, Lima APS, Vilela TCG, Martins CA, Fonstein N. Effect of Mo and Cr on the fracture toughness and fatigue crack growth resistance of a complex-phase Cr-Mn-V steel. In: Proceedings of the 23rd ABCM International Congress of Mechanical Engineering (COBEM); 2015; Rio de Janeiro, RJ, Brasil. Rio de Janeiro: ABCM; 2015.

20 Anderson TL. Fracture mechanics: fundamentals and applications. Boca Raton: CRC Press; 2017.

21 Paris PC, Erdogan F. A critical analysis of crack propagation laws. Journal of Basic Engineering. Transactions of the American Society of Mechanical Engineers. 1963;85:528-534.

22 Ritchie RO. Near-threshold fatigue-crack propagation in steels. International Metallurgical Reviews. 1979;24:205-230.

23 Liaw PK, Leax TR, Logsdon WA. Near-threshold fatigue crack growth behavior in metals. Acta Metallurgica. 1983;31:1581-1587.

24 El-Shabasy AB, Lewandowski JJ. Effects of load ratio R and temperature on fatigue crack growth of fully pearlitic eutectoid steel. International Journal of Fatigue. 2004;26:305-309.

25 Godefroid LB, Moreira LP, Vilela TCG, Faria GL, Candido LC, Pinto ES. Effect of chemical composition and microstructure on the fatigue crack growth resistance of pearlitic steels for railroad application. International Journal of Fatigue. 2019;120:241-253.

26 Stanzl-Tschegg SE, Plasser O, Tschegg EK, Vasudevan AK. Influence of microstructure and load ratio on fatigue threshold behavior in 7075 aluminum alloy. International Journal of Fatigue. 1991;21:255-262.

27 Godefroid LB, Barroso EKL, Al-Rubaie KS. Fatigue crack growth analysis of pre-strained 7475-T7351 aluminum alloy. International Journal of Fatigue. 2006;28:934-942.

28 Al-Rubaie KS, Barroso EKL, Godefroid LB. Statistical modeling of fatigue crack growth rate in pre-strained 7475-T7351 aluminium alloy. Materials Science and Engineering A. 2008;486:585-595.

29 Jones R, Molent L, Walker K. Fatigue crack growth in a diverse range of materials. International Journal of Fatigue. 2012;40:43-50.

30 Dubey S, Soboyejo ABO, Soboyejo WO. An investigation of the effects of stress ratio and crack closure on the micromechanisms of fatigue crack growth in Ti–6Al–4V. Acta Materialia. 1997;45:2777-2787.

31 Boyce BL, Ritchie RO. Effect of load ratio and maximum stress intensity on the fatigue threshold in Ti–6Al–4V. Engineering Fracture Mechanics. 2001;68:129-147.

32 Godefroid LB, Lopes J, Al-Rubaie KS. Statistical modeling of fatigue crack growth rate in Inconel alloy 600. International Journal of Fatigue. 2007;29:931-940.

33 Roy AK, Pal J, Hasan MH. Temperature and load ratio effects on crack-growth behavior of austenitic superalloys. Journal of Engineering Materials and Technology. 2010;132(1):1-7.

34 Zhihong Z, Yuefeng G, Osada T, Yong Y, Chuanyong C, Yokokawa T, et al. Fatigue crack growth characteristics of a new Ni–Co-base superalloy TMW-4M3: effects of temperature and load ratio. Journal of Materials Science. 2011;46:7573-7581.

35 Elber W. Fatigue crack closure under cyclic tension. Engineering Fracture Mechanics. 1970;2:37-45.

36 Elber W. The significance of fatigue crack closure. In: American Society for Testing and Materials – ASTM, editor. Damage tolerance in aircraft structures – ASTM STP 486. West Conshohocken: ASTM International; 1971. p. 230-242.

37 Hudak SJ, Davidson DL. The dependence of crack closure on fatigue loading variables. In: American Society for Testing and Materials – ASTM, editor. Mechanics of fatigue crack closure, ASTM STP 982. West Conshohocken: ASTM International; 1988. p. 121-138.

38 Vasudevan AK, Sadananda K, Louat N. A review of crack closure, fatigue crack threshold and related phenomena. Materials Science and Engineering A. 1994;188:1-22.

39 Sadananda K, Vasudevan AK, Holtz RL. Extension of the unified approach to fatigue crack growth to environmental interactions. International Journal of Fatigue. 2001;23:277-286.

40 Sadananda K, Vasudevan AK. Fatigue crack growth mechanisms in steels. International Journal of Fatigue. 2003;25:899-914.

41 Sadananda K, Vasudevan AK. Crack tip driving forces and crack growth representation under fatigue. International Journal of Fatigue. 2004;26(1):39-47.

42 Vasudevan AK, Sadananda K, Iyyer N. Fatigue damage analysis: Issues and challenges. International Journal of Fatigue. 2016;82:120-133.

43 Zhu ML, Xuan FZ, Tu ST. Interpreting load ratio dependence of near-threshold fatigue crack growth by a new crack closure model. International Journal of Pressure Vessels and Piping. 2013;110:9-13.

44 Zhu ML, Xuan FZ, Tu ST. Effect of load ratio on fatigue crack growth in the near-threshold regime: a literature review, and a combined crack closure and driving force approach. Engineering Fracture Mechanics. 2015;141:55-77.

45 De AK, Speer JG, Matlock DK. Color tint-etching of multi-phase steels. Advanced Materials & Processes. 2003;161(2):27-30.

46 American Society for Testing and Materials – ASTM. ASTM E112: standard test methods for determining average grain size. West Conshohocken: ASTM International; 2013.

47 American Society for Testing and Materials – ASTM. ASTM E8 M: standard test methods for tension testing of metallic materials. West Conshohocken: ASTM International; 2016.

48 American Society for Testing and Materials – ASTM. ASTM E 92: standard test methods for Vickers hardness and Knoop hardness of metallic materials. West Conshohocken: ASTM International; 2017.

49 American Society for Testing and Materials – ASTM. ASTM E647-15: standard test method for measurement of fatigue crack growth rates. West Conshohocken: ASTM International; 2016.

50 Klesnil M, Lukáš P. Fatigue of metallic materials. Prague: Elsevier Science; 1992.

51 Dasarathy C, Goodwin TJ. Recent developments in automotive steels. Metals and Materials. 1990;6:21-28.

52 Abdalla AJ, Hashimoto TM, Moura NCM, Pereira MS, Souza NS, Mendes FA. Alterações das propriedades mecânicas em aços 4340 e 300M através de tratamentos térmicos isotérmicos e intercríticos. In: Anais do 59º Congresso Anual da ABM; 2004; São Paulo, Brasil. São Paulo: ABM; 2004.

53 Klaus H, Friedrich H. Low carbon structural steels: the key to economic constructions. In: Proceedings of the Symposium on Low Carbon Steels for the 90’s; 1993; Pittsburg; USA. Warrendale: Metals & Mat. Soc.; 1993. p. 211-218.

54 Mecelis GR, Assis CLR. Gallego J. Relação de Hall-Petch em aços microligados produzidos como tiras a quente. In: Anais do 22º Congresso Brasileiro de Engenharia e Ciência dos Materiais; 2016; Natal, Brasil. São Paulo: Metallum Congressos Técnicos e Científicos; 2016. p. 4824-4833.

55 Podder AS, Pandit A, Murugaiyan A, Bhattacharjee D, Ray RK. Phase transformation behaviour in two C–Mn–Si based steels under different cooling rates. Ironmaking & Steelmaking. 2007;34(1):83-88.

56 Rigsbee JM, VanderArendt PJ. Laboratory studies of microstructures and structure-properties relationships in dualphase HSLA steels. In: Davenport AT, editor. Formable HSLA and dual-phase steels. Warrendale: AIME; 1979. p. 56-86.

57 Tanaka T, Nishida M, Hashiguchi K, Kato T. Formation and properties of ferrite plus martensite dual-phase structures. In: Structure and Properties of Dual-Phase Steels; 1979; New Orleans, LA. Warrendale: AIME; 1979. p. 221-241.

58 Rashid MS, Rao BVN. Tempering characteristics of a vanadium containing dual-phase steel. In: Proceedings of the Fundamentals of Dual-Phase Steels; 1981; Chicago, IL. Warrendale: AIME, 1981, p. 249-264.

59 Matlock DK, Zia-Ebrahimi F, Krauss G. Deformation, processing and structure. Materials Park: ASM; 1984. Structure, properties and strain hardening of dual-phase steels; p. 47-87.

60 Krauss G. Steels: processing, structure and performance. 2nd ed. Materials Park: ASM International; 2005. p. 250-256.

Submetido em:

Aceito em:

64401ba4a953955cf35f8a73 tmm Articles
Links & Downloads

Tecnol. Metal. Mater. Min.

Share this page
Page Sections