Fatigue life

Nguyen Van Chuong, Ul Rizwan Hassan1 School of Mechanical Engineering, Chung-Ang University, Heukseok-ro 84, Dongjak-gu, Seoul, South Korea, 156-756

(Manuscript Received 000 0, 2009; Revised 000 0, 2009; Accepted 000 0, 2009)

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AbstractIn this we will examine about fatigue life and how to determind fatigue life by using different methods. Fatigue behaviour of magne-

sium castings has been investigated with (Mg-Nd-Zn-Zr) alloys and other magnesium alloys. Multi-scale fatigue (MSF) life models have been adapted to estimate fatigue lives of the magnesium castings studied. Fatigue failure of magnesimu alloys with few casting defects is dominated by crack initiation within a grain close to the free surface. Magnesium alloy castings are increasingly used in cyclically-loaded structural application for light weighting and better performance. [12]

Keywords: Machining; Microhardness, Residual stress,

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1. Introduction

Fatigue is the weakenging of a material caused by repeat-edly applied loads. Fatigue occurs when a material is subjectd to repeat loading and unloading [1]. The fatigue behavior of engineering materials is substantially different depending on whether or not the material contains a pre-existing crack [2]. We therefore discuss fatigue in two categories. Fatigue fail-ures occur when metal is subjected to a repetitive or fluctuat-ing stress and will fail at a stress much lower than its tensile strength. Fatigue failures occur without any plastic deforma-tion (no warning). [3] Fatigue surface appears as a smooth region, showing beach mark or origin of fatigue crack.

Fig. 1. Fatigue types

Factor causing fatigue failure are : A maximum tensile stress of sufficiently high value, a large amount of aviation or

fluctuation in the applied stress, a sufficiently large number of cycles of the applied stress and some additonal factor like stress concentration, corrosion, temperrature, overload, met-alurgical, residual stress, combined stress.

2. The fatigue process [3]

Crack nucleation, fatigue cracks are normally initiated at a free surface. Slip lines are formed during the first few thou-sand cycles of stress. Back and forth fine slip movements of fatigue could build up notches or ridges at the surface.

Fig. 2. Model for fatigue initiation.

Small crack growth in an elastic-plastic stress field (stage I crack growth) the fatigue crack tends to propagate initially along slip planes planes (extrusion and intrusion of persistent slip bands) and later take the direction normal to the maximum tensile stress (stage II). The crack propagation rate in stage I is generally

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very low on the order of nm/cycles. Crack growth on planes of high tensile stress: growth of well-defined crack in direction normal to maximum tensile stress (stage II crack propagation) the fracture surface of stage II crack propagation fre-quently shows a pattern of ripples or fatigue.

Fig. 3. Fatigue striations

And the final step is final fracture.

3. Fatigue life [1]

ASTM defines fatigue life, Nf, as the number of stress cy-cles of a specified character hat a specimen sustains be-fore failure of a specified nature occurs. Engineers have used any of three methods to determine the fatigue life of a mate-rial: the stress-life method, the strain-life method, and the lin-ear-elastic fracture mechanics method.

3.1 The stress-life method [6], [7]

To determine the strength of materials under the action of fatigue loads, specimens are subjected to repeated or varying forces of specified magnitudes while the cycles or stress rever-sals are counted to destruction. The ordinate of the S-N dia-gram is called the fatigue strength. The fatigue strength (Sf’) and the endurance limit (Se’) for some materials can be found (refer to text appendices) or can be estimated from the follow-ing relations: The fatigue strength or endurance limit are typi-cally determined from the standard material tests (e.g. rotating beam test).

Fig. 4. S-N diagram

Fig. 5. The fatigue strength or endurance limit

However, they must be appropriately modified to account for the physical and environmental differences.

Between the test specimen and the actual part being ana-lyzed:

Sf (or Se) = ksurfaceksizekloadktemperaturekreliabilitySf’ (or Se’)Sf (or Se) – Corrected strength Sf’ (or Se’) – Strength deter-

mined from standardized test in fatigue testing, the applied stress, σ a, is typically described by the stress amplitude of the loading cycle and is defined as:

σa = ( σmax - σmin )/2 = Δσ/2The stress amplitude is generally plotted against the number

of cycles to failure on a linear-log scale. S-N plots Tests per-formed on unnoticed specimens Constant amplitude Cycles to failure (Nf) monitored for each stress amplitude level (S) Plot-ted linear-log Basquin eq: σa = σf’(Nf )b Endurance limit: 107 cycles (no failures).3.2 The strain-life method [8]

The method takes into account the actual stress-strain re-sponse of the material due to cyclic loading. Plastic strain, and the mechanism that leads to crack initiation, is accurately modeled. This method can model the effect of the residual mean stresses resulting from the sequence effect in load histo-ries and the manufacturing residual stresses. This allows for more accurate damage accumulation under variable amplitude cyclic loading. The ε-N method can be more easily extrapo-lated to situations involving complicated geometries. This method can be used in high temperature applications where fatigue-creep interaction is critical. In situations where it is important, this method can incorporate transient material be-havior. This method can be used for both low cycle (high strains) and high cycle fatigue (low strains) There is only one essential empirical element in the method, i.e. the correction for the mean stress effect.

G. Bell et al. / Journal of Mechanical Science and Technology 23 (2009) 1261~1269 1263

Fig. 6. Strain-Life Curve

Fig. 7. The Strain-life and the Cyclic Stress-Strain Curve Obtained from Smooth Cylindrical Specimens Tested Under Strain Control.

4. Conclusions

Machining process can be defined as process of removing material in form of the chips. By removing the chips form the workpiece, the residual stress are occurred. The residual play a key role, because residual stress and micro hardness are rele-vant to failure.

It is well known that tensile residual stress can be negative af-fect for fatigue life. So to improve fatigue resistance we try to have compressive residual stress and avoid tensile residual stress. The residual tress depth, sign, magnitude, and surface finish are dependent upon cutting velocity, feed rate, depth of cut, cutting tool geometry, and work piece material property.

The residual stresses may be determined analytically, compu-tationally with finite element analysis, and experimen-tally. The magnitude and distribution of residual stresses are most com-monly obtained using experimental methods.

References

[1] Henriksen, E.K., Residual Stresses in Machined Surfaces. American Society of Mechanical Engineers -- Transactions, 1951. 73(1): p. 69-76.

[2] Xie, Q., et al. A Study on Residual Stresses and Tool Wear Induced by the Machining Process. in NAMRC XVII. 1989: SME

[3] Sadat, A.B., Surface Region Damage of Machined Inconel-718 Nickel-Based Superalloy Using Natural and Controlled

Contact Length Tools. Wear, 1987. 119(2): p. 225-35.[4] Liu, C.R. and M.M. Barash, Variables Governing Patterns of

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[5] Sadat, A.B. and J.A. Bailey, Residual Stresses in Turned AISI 4340 Steel. Experimental Mechanics, 1987. 27(1): p. 80-85.

[6] Jin, Du, et al. "Influence of cutting speed on surface integrity for powder metallurgy nickel-based superalloy FGH95." The International Journal of Advanced Manufacturing Technol-ogy 56.5-8 (2011): 553-559.

[7] Fuchs, Henry Otten, and I. Stephens. "Metal fatigue in engi-neering." JOHN WILEY & SONS, NY. 1980. (1980).

[8] Kenda, Jani, Franci Pusavec, and Janez Kopac. "Analysis of residual stresses in sustainable cryogenic machining of nickel based alloy—Inconel 718."Journal of manufacturing science and engineering 133.4 (2011): 041009.

[9] Capello, Edoardo. "Residual stresses in turning: Part I: Influ-ence of process parameters." Journal of Materials Process-ing Technology 160.2 (2005): 221-228.

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