Please wait a minute...
Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

Postal Subscription Code 80-975

2018 Impact Factor: 0.989

Front. Mech. Eng.    2015, Vol. 10 Issue (3) : 255-262    https://doi.org/10.1007/s11465-015-0342-1
RESEARCH ARTICLE
Some remarks on the engineering application of the fatigue crack growth approach under nonzero mean loads
Jorge Alberto Rodriguez DURAN1,*(),Ronney Mancebo BOLOY2,Rafael Raider LEONI3
1. Mechanical Engineering Department, Federal Fluminense University, Volta Redonda 27255-125, Brazil
2. Mechanical Engineering Department, Federal Center of Technological Education, Angra dos Reis 23953-030, Brazil
3. Mechanical Engineer, Structural Data Acquisition & Fatigue Analysis Engineer, Resende 27511-970, Brazil
 Download: PDF(1069 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

The well-known fatigue crack growth (FCG) curves are two-parameter dependents. The range of the stress intensity factor ?K and the load ratio R are the parameters normally used for describing these curves. For engineering purposes, the mathematical representation of these curves should be integrated between the initial and final crack sizes in order to obtain the safety factors for stresses and life. First of all, it is necessary to reduce the dependence of the FCG curves to only one parameter. ?K is almost always selected and, in these conditions, considered as the crack driving force. Using experimental data from literature, the present paper shows how to perform multiple regression analyses using the traditional Walker approach and the more recent unified approach. The correlations so obtained are graphically analyzed in three dimensions. Numerical examples of crack growth analysis for cracks growing under nominal stresses of constant amplitude in smooth and notched geometries are performed, assuming an identical material component as that of the available experimental data. The resulting curves of crack size versus number of cycles (a vs. N) are then compared. The two models give approximately the same (a vs. N) curves in both geometries. Differences between the behaviors of the (a vs. N) curves in smooth and notched geometries are highlighted, and the reasons for these particular behaviors are discussed.

Keywords fatigue crack propagation modeling      life prediction      mean stress effects     
Corresponding Author(s): Jorge Alberto Rodriguez DURAN   
Online First Date: 30 July 2015    Issue Date: 23 September 2015
 Cite this article:   
Jorge Alberto Rodriguez DURAN,Ronney Mancebo BOLOY,Rafael Raider LEONI. Some remarks on the engineering application of the fatigue crack growth approach under nonzero mean loads[J]. Front. Mech. Eng., 2015, 10(3): 255-262.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-015-0342-1
https://academic.hep.com.cn/fme/EN/Y2015/V10/I3/255
Fig.1  Schematic representation of the constant FCG rates plotted in ΔK-Kmax coordinates, and the intrinsic thresholds according to the UA
Fig.2  Experimental FCG curves for the 2024 T3 aluminum alloy
Fig.3  Three-dimensional representation of elements of vectors x, y, and z (see Eqs. (9) and (10)), and the plane that best fits them using the (a) Walker and (b) unified approaches
Approach Coefficients Parameters
a0 a1 a2
Walker −10.97 −1.24 3.95=mw C0=1.06E−11 m/cycle/(MPa·m1/2 m w , γ=0.68
Unified −9.47 1.97=p 0.72=q A=1.06E−11 m/cycle/(MPa·m1/2)p+q
Tab.1  Coefficients and parameters of the Walker and unified approaches (Eqs. (5) and (7)), obtained after an MLR analysis of the experimental data.
Fig.4  Some constant FCG rates (in “m” and using Eq. (11) with parameters from Table 1) and the raw experimental FCG data in UA coordinates
Fig.5  SIF for a pair of cracks emanating from a circular hole in a wide plate under a nominal stress S, and variation of the Fλ(s) parameter
Fig.6  Calculated residual life versus the final value of the s-parameter for a crack growing between 2.5 and 40 mm from the circular hole of Fig. 5
Fig.7  Residual life Nif calculated for a plate
Geometry Smax/MPa Initial SIF/(MPa·m1/2) Final SIF/(MPa·m1/2)
1 28 3.4 6.6
2 28 3.6 11.8
Tab.2  Loading conditions for the FCG simulations in Geometries 1 and 2, with constant load ratio (R=0.4)
Fig.8  Comparison between normalized SIFs for cracks in notched and smooth components. The (a vs. Nif) curve of Fig. 7 corresponds to a smooth component, with width b that is four times the radius of the hole R0 of the notched component (Fig. 6)
a Crack size
A, C, m, γ, p, q Material parameters
da/dN fatigue crack growth rate
F(s) Geometric factor as a function of normalized crack size
Nf Total fatigue life to failure, in number of cycles
Ni Crack initiation life, in number of cycles
Nif Number of fatigue cycles spent in the propagation stage
P Load
R Ratio of the minimum to maximum load
R0 Radius of the hole
s Normalized crack size, a/b or a/(a+R0)
Ks or Kn Stress intensity factors, SIFs, for cracks in smooth and notched components, respectively
ΔK SIF range
S Nominal stress
Tab.3  Nomenclature
1 De Castro  J T P, Landim  R V, Leite  J C C, . Prediction of notch sensitivity effects in fatigue and in environmentally assisted cracking. Fatigue & Fracture of Engineering Materials & Structures, 2015, 38(2): 161–179
https://doi.org/10.1111/ffe.12156
2 Janssen  M M, Zuidema  J, Wanhill  R J H. Fracture Mechanics. 2nd ed. Delft: VSSD, 2006
3 Lazzarin  P, Tovo  R. A notch intensity factor approach to the stress analysis of welds. Fatigue & Fracture of Engineering Materials & Structures, 1998, 21(9): 1089–1103
https://doi.org/10.1046/j.1460-2695.1998.00097.x
4 Atzori  B, Lazzarin  G, Meneghetti  G. Fatigue strength assessment of welded joints: From the integration of Paris’ law to a synthesis based on the notch stress intensity factors of the uncracked geometries. Engineering Fracture Mechanics, 2008, 75(3−4): 364–378
https://doi.org/10.1016/j.engfracmech.2007.03.029
5 Witek  L. Crack propagation analysis of mechanically damaged compressor blades subjected to high cycle fatigue. Engineering Failure Analysis, 2011, 18(4): 1223–1232
https://doi.org/10.1016/j.engfailanal.2011.03.003
6 Luke  M, Varfolomeev  I, Lutkepohl  K, . Fatigue crack growth in railway axles: Assessment concept and validation tests. Engineering Fracture Mechanics, 2011, 78(5): 714–730
https://doi.org/10.1016/j.engfracmech.2010.11.024
7 Walker  K. The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum. In: Rosenfeld  M, ed. Effects of Environment and Complex Load History on Fatigue Life, ASTM STP 462. 1970, 1–14
8 Sadananda  K, Vasudevan  A K. Short crack growth and internal stresses. International Journal of Fatigue, 1997, 19(93): 99–108
https://doi.org/10.1016/S0142-1123(97)00057-1
9 Sadananda  K, Vasudevan  A K. Analysis of small crack growth behavior using unified approach. In: Ravichandran  K S, Murakami  Y, Ritchie  R, eds. Small fatigue cracks: Mechanics, Mechanisms and Applications. Elsevier, <?Pub Caret1?>1998
10 Dinda  S, Kujawski  D. Correlation and prediction of fatigue crack growth for different R-ratios using Kmax and ΔK+ parameters. Engineering Fracture Mechanics, 2004, 71(12): 1779–1790
https://doi.org/10.1016/j.engfracmech.2003.06.001
11 Sadananda  K, Vasudevan  A K. Fatigue crack growth mechanisms in steels. International Journal of Fatigue, 2003, 25(9−11): 899–914
https://doi.org/10.1016/S0142-1123(03)00128-2
12 Sadananda  K, Vasudevan  A K. Crack tip driving forces and crack growth representation under fatigue. International Journal of Fatigue, 2004, 26(1): 39–47
https://doi.org/10.1016/S0142-1123(03)00105-1
13 Dowling  N E. Mean stress effects in strain-life fatigue. Fatigue & Fracture of Engineering Materials & Structures, 2009, 32(12): 1004–1019
https://doi.org/10.1111/j.1460-2695.2009.01404.x
14 Miller  M S, Gallagher  J P. An analysis of several fatigue crack growth rate (FCGR) descriptions. In: Hudak  S J, Bucci  R J, eds. Fatigue Crack Growth Measurement and Data Analysis. ASTM, 1981, 205–251
15 Lipson  C, Narendra  J S. Statistical Design and Analysis of Engineering Experiments. New York: McGraw-Hill, 1973
16 Castro  J T P, Meggiolaro  M A. Fadiga: Técnicas e Práticas de Dimensionamento Estrutural sob Cargas Reais de Serviço, CreateSpace, 2009 (in Portuguese)
17 Tada  H, Paris  P C, Irwin  G R. The Stress Analysis of Cracks Handbook. 3nd ed. New York: ASME Press, 2000
[1] Zhihua ZHANG,Huichen YU,Chengli DONG. LCF behavior and life prediction method of a single crystal nickel-based superalloy at high temperature[J]. Front. Mech. Eng., 2015, 10(4): 418-423.
[2] Tahir MAHMOOD, Sangarapillai KANAPATHIPILLAI, Mahiuddin CHOWDHURY. A model for creep life prediction of thin tube using strain energy density as a function of stress triaxiality under quasi-static loading employing elastic-creep & elastic-plastic-creep deformation[J]. Front Mech Eng, 2013, 8(2): 181-186.
[3] SHANG De-guang, SUN Guo-qin, DENG Jing, YAN Chu-liang. Nonlinear cumulative damage model for multiaxial fatigue[J]. Front. Mech. Eng., 2006, 1(3): 265-269.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed