Subscribe Now Subscribe Today
Research Article
 

Simulating Fatigue Propagation Life of Martensitic Steel



O.O. Ajayi and J. Ikotun
 
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail
ABSTRACT

The linear elastic fracture mechanics equation together with that for stress intensity factor range ΔK, was used to develop a fatigue propagation life model, after substituting parameters of material constants. The model was then employed in creating simulation software which can be used at any time to generate data, make design consideration and predict response to variable loading. This became useful in predicting the life of metal from the point of crack initiation; investigate behaviour to changes in crack sizes and also determine adequate damage tolerance for the metal.

Services
Related Articles in ASCI
Search in Google Scholar
View Citation
Report Citation

 
  How to cite this article:

O.O. Ajayi and J. Ikotun, 2009. Simulating Fatigue Propagation Life of Martensitic Steel. Trends in Applied Sciences Research, 4: 62-67.

DOI: 10.3923/tasr.2009.62.67

URL: https://scialert.net/abstract/?doi=tasr.2009.62.67
 

INTRODUCTION

Fracture is the fragmentation of a solid into two or more parts under the action of stress (Dieter, 1988). Its process can be considered to be made up of crack initiation and growth and can be classified into two broad headings namely ductile and brittle fracture. While ductile fracture is characterized by appreciable amount of plastic deformation prior to and during the propagation of crack, with an amount of gross deformation present at the crack surface, brittle fracture is characterized by a rapid rate of crack propagation, without gross deformation but little micro deformation (Dieter, 1988; Shaffer et al., 1999). It occurs in engineering structures and can be costly in terms of human and/ or property damage (Benham et al., 1996; Odukwe et al., 2007).

Many researchers have reviewed some structural damages, beginning from the late 1800s (Dieter, 1988; Benham et al., 1996; Odukwe et al., 2007), when members of the British Iron and Steel Institute reported the mysterious cracking of steel in a brittle manner. Investigation shows that the most failures were initiated in welds that are defective. Later discoveries also reveal that crack initiation and growth in structures resulted in sudden failures (Anderson, 1995). However, in spite of design improvements, increased use of crack arresters, use of quality materials and so on, brittle fractures still occurs in ships within the 1950s. This occurrence continued up to 1988 when the fuselage of a 19 year old Boeing 737 airline ripped open in flight (Chau and Chan, 2002). The cause was found to be due to fatigue crack propagation from a rivet hole in the fuselage of the jet. In real sense, most cracks nucleate in areas of increased stress concentration and propagate unnoticed within the microstructure of the material (Courtney, 2000; Dieter, 2000). Fracture mechanics have shown that because of the interrelations among materials, design, fabrication and loading, fatigue failure cannot be eliminated merely by using materials with improved notch toughness (Tomkins et al., 1981; Anderson, 1995; Miller and Akid, 1996). The failures still occurs today. Moreover, materials subjected to fluctuating stresses can fail at stresses much lower than their yield stress (Odukwe et al., 2007).

Reliability studies had shown that structural members contain pre-existing cracks which may have resulted during fabrication (Tomkins et al., 1981; Dieter, 1988, 2000; Odukwe et al., 2007). These cracks are assumed to be known and therefore, efforts are geared towards determining the remaining number of cycle of loading to failure (Dieter, 2000). The number of these cycles from the point of crack initiation to failure is the fatigue propagation life of the material, which depends on when and how a crack initiates and the rate at which it grows through the microstructure (Tomkins et al., 1981). Most fatigue failure have been discovered to be caused by cracks, which initiates unnoticed and grows at a fast rate through the structural member, it is easily the most common type of failure of engineering structures in service and difficult to foresee, because conditions causing it are frequently not easily recognizable (Sobczyk, 1987; Odukwe et al., 2007).

More over, advances in fatigue design had shown that relationship exist between the rate of crack growth da/dN and the stress intensity factor range ΔK, obtained by plotting a log-log graph of da/dN on the ordinate against ΔK on the abscissa. The resulting plot is a sigmoid curve which can be divided into regions I-III (Dieter, 1988, 2000; Courtney, 2000; Ashby and Jones, 2005). Region I is called the non-propagating crack region, II is the linear elastic fracture mechanics range and III is the accelerated crack growth region that is followed by failure respectively. The region II is represented by the power law as (Benham et al., 1996; Courtney, 2000):

Image for - Simulating Fatigue Propagation Life of Martensitic Steel
(1)

where, A, M are material constants determined by experimental procedures.

Further study on Eq. 1 was carried out by Odukwe et al. (2007), which analyzed experimental conclusion on high yield strength (σy = 100 Ksi (689 MN m-2), critical stress intensity factor (Kc) = 150 Ksi [in]1/2 (165 MN mm-2)) Martensitic steel in air environment. It was discovered that ΔK explains about 99.85% of the changes in da/dN and that as a result of experimental analysis A = 7.244x10-9 and M = 2.22 for Martensitic steel. When crack growth and stress intensity factor are correlated, it is possible to use data generated under constant amplitude loading to determine the fatigue life of a component (Dieter, 2000; Odukwe et al., 2007). The knowledge of when a material will fail and the required number of cycles to failure will aid in knowing the rate of changeability and maintenance of such material, therefore, researchers must look into the problem of structural failures with a view to bring ideas and develop new packages, which can be used to generate data and evolve new design considerations, so that the problem of catastrophic failure will be a forgone issue. This can be achieved by developing interactive software which can be used on the field and at any time to determine design consideration and loading parameters. This research focused on achieving this, by using Eq. 1 together with the stress intensity factor range to develop a simple model and therefore carry-out the simulation process for Martensitic steel. It is also sort to extend such simulation to include other metals.

MATERIALS AND METHODS

The linear elastic fracture mechanics equation, represented by Eq. 1 was employed with the relation for ΔK presented as Eq. 2. Constant amplitude stresses, σ of 15 Ksi (103.43 MPa), 20 Ksi (137.90 MPa) and 25 Ksi (172.38 MPa), together with values of material constants A and M developed by Odukwe et al. (2007) were used to develop a possible fatigue life model of Martensitic steel containing edge and surface cracks as follows:

Image for - Simulating Fatigue Propagation Life of Martensitic Steel
(2)

Where:

C = Constant for edge and surface cracks = 1.12 (Odukwe et al., 2007)
a = Average crack size

Putting (2) into (1) gives:

Image for - Simulating Fatigue Propagation Life of Martensitic Steel
(3)

Integrating from No to Nf gives:

Image for - Simulating Fatigue Propagation Life of Martensitic Steel
(4)

Substituting values of A, M and C given earlier gives:

Image for - Simulating Fatigue Propagation Life of Martensitic Steel
(5)

The Eq. 5 above is therefore the constant amplitude fatigue life model of Martensitic steel containing edge and surface crack. This is employed to develop a simulation that can be used at any time to generate data for design consideration, change and modify design parameter, predict and determine safe operating conditions or damage tolerance for the metal. The simulation is Fig. 1.

where, A = Are you working on Martensitic steel? And B = Do you have more data?

RESULTS AND DISCUSSION

Simulation Result
The result of the number of cycles corresponding to the crack sizes from 0.2 inches (5.08 mm) and above is shown in Table 1. This is obtained from the simulation software after the desired crack sizes are inputted.

Table 1 show that a pre-existing crack size of 0.2 inches (5.08 mm) was assumed present. Crack sizes were pre-suggested and the corresponding numbers of crack propagation cycles were then determined by employing the software developed from the simulation (Fig. 1). The plot of Fig. 2 reveals that the constant amplitude stress is inversely related to the number of cycles but directly to the crack size. This is expected because, as the stress builds up, the energy release rate required to propagate the crack on a pre-cracked surface increases and thus, crack increment occurs when the increase in the energy release rate is at least equal to the energy required to create a new crack surface (Dieter, 1988; Anderson, 1995; Miller and Akid, 1996), thereby, lowering the number of crack propagation cycles required to create the new crack length. Thus, inferring that, as the constant amplitude stress increases, the required surface energy of the cracked surface increases, the material resistance to crack extension reduces and thus, crack growth takes place with reduced number of cycles of loading (Pascual and Meeker, 1999). The findings of many researchers (Benham et al., 1996; Felbeck and Atkins, 1996; Shaffer et al., 1999; Courtney, 2000; Dieter, 2000; Shigley et al., 2004; Smith and Hashemi, 2004) further support this. More so, at a constant amplitude stress value, the number of cycles increases with increasing crack lengths. This is the basis for the linear elastic fracture mechanics which relates the rate of crack growth to the average crack length at constant amplitude stress (Benham et al., 1996; Courtney, 2000). In addition, Fig. 2 reveals the following: that, at constant crack size, the number of cycles decreases with increasing stress values and also that, at constant number of cycles, crack sizes increases with increasing stresses. These information can be used adequately in mechanical reliability design of machine parts, where the designer may wish to know the behaviour of such part under different loading conditions, when it is desired that crack size or number of cycles are to be kept constant. This would aid in gaining quick access to valid information and also determine safe operating conditions. Moreover, the use of the simulation software, if employed in design, will create flexibility, as design parameters can be changed at ease and corresponding predictive response can easily be determined without recourse to rigorous and expensive experimentation.


Table 1: The number of cycles of loading corresponding to desired crack sizes, obtained from simulation software
Image for - Simulating Fatigue Propagation Life of Martensitic Steel

Image for - Simulating Fatigue Propagation Life of Martensitic Steel
Fig. 1: Simulation flowchart representing fatigue propagation life of Martensitic Steel, extended to include other metals

Image for - Simulating Fatigue Propagation Life of Martensitic Steel
Fig. 2: Plot of desired crack sizes against corresponding number of crack propagation cycles, determined from the simulation software

CONCLUSION

The simulation of the fatigue propagation life of Martensitic steel has been done. A model developed from the linear elastic fracture mechanics equation together with the relation for the stress intensity factor range was employed in the modeling and simulation work. The resulting simulation software was then used to investigate the behaviour of the metal to different constant amplitude loading stresses and found to be adequate, as result obtained agreed with previous findings. This became useful in predicting the life of the metal from the point of crack initiation and to investigate its behaviour to changes in crack sizes and also determine adequate damage tolerance for the metal. Thus, removing the cumbersome computational and repetitive processes involved in data generation and adds pleasantness and speed to design.

REFERENCES

1:  Anderson, T.L., 1995. Fracture Mechanics: Fundamentals and Application. 2nd Edn., CRC Press, Florida, ISBN: 0849342600

2:  Ashby, M.F. and D.R.H. Jones, 2005. Engineering Materials 1: An Introduction to Properties Application and Design. 3rd Edn., Elsevier, Oxford, ISBN: 0750663804

3:  Benham, P.P., R.J. Crawford and C.G. Armstrong, 1996. Mechanics of Engineering Materials. 2nd Edn., Longman, England, ISBN: 0582251648

4:  Chau, K.T. and S.L. Chan, 2002. Failure of a Steel Plate Containing a Circular Rivet Hole With an Emanating Crack. In: Advances in Steel Structures, Chan, S.L., J.G. Teng and K.F. Chung (Eds.). Elsevier, Oxford, ISBN: 0080440177, pp: 1017-1024

5:  Courtney, T.H., 2000. Mechanical Behaviour of Materials. 2nd Edn., McGraw-Hill, New York, ISBN: 0071161716

6:  Dieter, G.E., 1988. Mechanical Metallurgy. 1st Edn., McGraw-Hill, New York, ISBN: 0071004068

7:  Dieter, G.E., 2000. Engineering Design: A Materials and Processing Approach. 3rd Edn., McGraw-Hill, New York, ISBN: 0071162046

8:  Felbeck, D.K. and A.G. Atkins, 1996. Strength and Fracture of Engineering Solids. 2nd Edn., Prentice Hall, New Jersey, ISBN: 0138561133

9:  Miller, K.J. and R. Akid, 1996. The application of microstructural fracture mechanics to various metal surface states. Proceedings of the Mathematical, Physical and Engineering Sciences, June 8, 1996, Royal Society, pp: 1411-1432
Direct Link  |  

10:  Odukwe, O.A., O.O. Ajayi and G.O. Oluwadare, 2007. Simulation of crack growth rate in martensitic steel. J. Applied Sci., 7: 302-305.
CrossRef  |  Direct Link  |  

11:  Pascual, F.G., Q. William and Meeker, 1999. Estimating fatigue curves with the random fatigue-limit model. Technometrics, 41: 277-290.
Direct Link  |  

12:  Shaffer, J.P., A. Saxena, S.D. Antolovich, T.H. Sandars and S.B. Warner, 1999. The Science and Design of Engineering Materials. 2nd Edn., McGraw-Hill, New York, ISBN: 0256247668, pp: 749-763

13:  Shigley, J.E., C.R. Mischke and R.G. Budynas, 2004. Mechanical Engineering Design. 7th Edn., McGraw Hill, New York, ISBN 978-0072520361
Direct Link  |  

14:  Smith, W.F. and J. Hashemi, 2004. Foundation of Materials Science and Engineering. 3rd Edn., McGraw-Hill, New York, ISBN: 0071122729

15:  Sobczyk, K., 1987. Stochastic models for fracture damage of materials. Adv. Applied Probabil., 19: 652-673.
Direct Link  |  

16:  Tomkins, B., H.K. Grover and T.G.F. Gray, 1981. Subcritical crack growth: Fatigue, creep and stress corrosion cracking. Philosophical Trans. Royal Soc. London Series A Math. Physical Sci., 299: 31-44.
Direct Link  |  

©  2021 Science Alert. All Rights Reserved