## 1. Introduction

Material selection is a crucial step in the process of engineering design. Optimal selection of the material can significantly reduce the possibility of failures, along with understanding the nature and stress intensity that occurs in a designed structure. Engineering practices usually distinguishes one or few causes of failure: excessive force and/or temperature-induced elastic deformation, yielding, fatigue, corrosion, creep, etc. Selection of improper materials may have a negative effect on operational lifetime cycle and result in flaw appearance, which can cause structural failure.

A successful material-selection process implies reconciling requirements, such as appropriate strength of a material, sufficient level of rigidity, heat resistance, etc. For structures susceptible to crack growth, it is necessary to ensure that the material has been selected on the basis of fracture mechanics parameters.

Considering shaft design, the fracture mechanics approach must be used in order to account for high stresses and harsh operating conditions. Implementation of the fracture mechanics approach has the benefit of reducing potential failures, such as the fatigue induced fracture presented in a study of marine main engine crankshaft failure [

1]. The agitator steel shaft failed due to an inadequate design, which was incapable of withstanding torsional-bending fatigue during operation [

2]. The gearbox shaft failure occurred due to high stress concentrations at the corners of the wobbler of the shaft, causing fatigue crack initiation [

3]. Improved design and machining practice suggested that this would help to prolong service life of the component. A forklift collapsed due to failure of axle shaft, caused by material inclusions and poor heat treatment [

4].

Most of the mentioned failures occurred on steels typically used in the manufacturing of shafts intended for use in harsh environments, where a higher corrosion resistance is necessary. To be able to properly choose a suitable material for such an environment, characterization of a material is essential.

Fracture mechanics parameters that define material resistance to crack propagation are usually determined through experimental investigations of the material under consideration. Fracture behavior is usually estimated using some of the well-established fracture parameters, such as stress intensity factor (

K),

J-integral, or crack tip opening displacement (CTOD).

J-integral is appropriate for quantifying material resistance to crack extension when dealing with ductile fracture of metallic materials, which includes nucleation, growth, and coalescence of voids [

5]. For a growing crack,

J-integral values can be determined for a range of crack extensions (Δ

a) and can be presented in the form of the

J-resistance curve. This curve is usually obtained experimentally following standardized procedures, but it can be successfully complemented or even substituted by numerical methods, e.g., the finite element (FE) method. Some of the recent articles on this topic include discussion on the accuracy of

J-integral obtained by experiments, two-dimensional (2D) FE analysis, three-dimensional (3D) FE analysis, or the Electric Power Research Institute method [

6].

J-integral and CTOD are related through plastic constraint factors evaluated using 3D FE analyses of a clamped, single-edge tension specimen [

7]. Methodology to evaluate 3D

J-integral for finite strain elastic-plastic solid using FE analysis is proposed [

8]. Stress intensity factors and T-stress of 3D interface cracks and notches are computed using the scaled boundary FE method [

9].

This paper presents a comparison of numerically predicted J-values taken from the measure of crack driving force for two types of steel commonly used in shaft manufacturing, steels 1.4305 and 1.7225. Obtained material data may help designers to find the best solution in appropriate material selection.

## Acknowledgments

This work has been financially supported by the Croatian Science Foundation under the project 6876, and by the University of Rijeka under the projects 13.09.1.1.01 and 13.07.2.2.04. Funds for covering the costs to publish in open access publications have been provided.

## Author Contributions

Goran Vukelic and Josip Brnic conceived the idea of the research; Josip Brnic performed the experiments; Goran Vukelic analyzed the data; Goran Vukelic performed numerical analysis; Goran Vukelic and Josip Brnic wrote the paper.

## Conflicts of Interest

The authors declare no conflicts of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

## Abbreviations

The following abbreviations are used in this manuscript:

FE | Finite Element |

DCT | Disc Compact Tension |

SENB | Single Edge Notched Bend |

CVN | Charpy V-notch |

## References

- Fonte, M.; de Freitas, M. Marine main engine crankshaft failure analysis: A case study. Eng. Fail. Anal.
**2009**, 16, 1940–1947. [Google Scholar] [CrossRef] - Zangeneh, Sh.; Ketabchi, M.; Kalaki, A. Fracture failure analysis of AISI 304L stainless steel shaft. Eng. Fail. Anal.
**2014**, 36, 155–165. [Google Scholar] [CrossRef] - Moolwan, C.; Netpu, S. Failure analysis of a two high gearbox shaft. Procedia Soc. Behav. Sci.
**2013**, 88, 154–163. [Google Scholar] [CrossRef] - Das, S.; Mukhopadhyay, G.; Bhattacharyya, S. Failure analysis of axle shaft of a fork lift. Case Stud. Eng. Fail. Anal.
**2015**, 3, 46–51. [Google Scholar] [CrossRef] - Kossakowski, P.G. Simulation of ductile fracture of S235JR steel using computational cells with microstructurally-based length scales. J. Theor. Appl. Mech.
**2012**, 50, 589–607. [Google Scholar] - Dai, Q.; Zhou, C.; Peng, J.; He, X. Experiment, finite element analysis and EPRI solution for J-integral of commercially pure titanium. Rare Metal. Mat. Eng.
**2014**, 42, 257–263. [Google Scholar] - Huang, Y.; Zhou, W. J-CTOD relationship for clamped SE(T) specimens based on three-dimensional finite element analyses. Eng. Fract. Mech.
**2014**, 131, 643–655. [Google Scholar] [CrossRef] - Koshima, T.; Okada, H. Three-dimensional J-integral evaluation for finite strain elastic-plastic solid using the quadratic tetrahedral finite element and automatic meshing methodology. Eng. Fract. Mech.
**2015**, 135, 34–63. [Google Scholar] [CrossRef] - Saputra, A.A.; Birk, C.; Song, C. Computation of three-dimensional fracture parameters at interface cracks and notches by the scaled boundary finite element method. Eng. Fract. Mech.
**2015**, 148, 213–242. [Google Scholar] [CrossRef] - Zambrano, O.A.; Coronado, J.J.; Rodríguez, S.A. Failure analysis of a bridge crane shaft. Case Stud. Eng. Fail. Anal.
**2014**, 2, 25–32. [Google Scholar] [CrossRef] - Fonte, M.; Duarte, P.; Anes, V.; Freitas, M.; Reis, L. On the assessment of fatigue life of marine diesel engine crankshafts. Eng. Fail. Anal.
**2015**, 56, 51–57. [Google Scholar] [CrossRef] - Tawancy, H.M.; Al-Hadhrami, L.M. Failure of a rear axle shaft of an automobile due to improper heat treatment. J. Fail. Anal. Prev.
**2013**, 13, 353–358. [Google Scholar] [CrossRef] - Bai, S.Z.; Hu, Y.P.; Zhang, H.L.; Zhou, S.W.; Jia, Y.J.; Li, G.X. Failure analysis of commercial vehicle crankshaft: A case study. Appl. Mech. Mater.
**2012**, 192, 78–82. [Google Scholar] [CrossRef] - Fuller, R.W.; Ehrgott, J.Q., Jr.; Heard, W.F.; Robert, S.D.; Stinson, R.D.; Solanki, K.; Horstemeyer, M.F. Failure analysis of AISI 304 stainless steel shaft. Eng. Fail. Anal.
**2008**, 15, 835–846. [Google Scholar] [CrossRef] - American Society for Testing and Materials (ASTM International). Metals Test Methods and Analytical Procedures; Annual BOOK of ASTM Standards; ASTM International: Baltimore, Maryland, MD, USA, 2005; Volume 03.01. [Google Scholar]
- Brnic, J.; Turkalj, G.; Canadija, M.; Lanc, D.; Krscanski, S. Responses of austenitic stainless steel American iron and steel institute (AISI) 303 (1.4305) subjected to different environmental conditions. J. Test. Eval.
**2012**, 40, 319–328. [Google Scholar] [CrossRef] - Brnic, J.; Turkalj, G.; Canadija, M.; Lanc, D.; Brcic, M. Study of the effects of high temperatures on the engineering properties of steel 42CrMo4. High Temp. Mater. Proc.
**2015**, 34, 27–34. [Google Scholar] [CrossRef] - Roberts, R.; Newton, C. Interpretive Report on Small Scale Test Correlations with K
_{Ic} Data; Welding Research Council Bulletin: New York, NY, USA, 1981; pp. 1–16. [Google Scholar] - Rice, J.R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech.
**1968**, 35, 379–386. [Google Scholar] [CrossRef] - Cherepanov, G.P. The propagation of cracks in a continuous medium. J. Appl. Math. Mech.
**1967**, 31, 503–512. [Google Scholar] [CrossRef] - Mohammadi, S. Extended finite element method; Blackwell Publishing: Singapore, 2008; pp. 56–58. [Google Scholar]
- Vukelic, G.; Brnic, J. Prediction of fracture behavior of 20MnCr5 and S275JR steel based on numerical crack driving force assessment. J. Mater. Civ. Eng.
**2015**, 27, 14132–14132(6). [Google Scholar] [CrossRef] - Narasaiah, N.; Tarafder, S.; Sivaprasad, S. Effect of crack depth on fracture toughness of 20MnMoNi55 pressure vessel steel. Mater. Sci. Eng. A
**2010**, 527, 2408–2411. [Google Scholar] [CrossRef]

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).