A unified interpretation of the power laws in fatigue and the analytical correlations between cyclic properties of engineering materials

A phenomenological description of the fatigue life of engineering components can be given either by plotting the applied stress range as a function of the total number of cycles to failure, i.e., according to the Wohler’s curve, or, after the advent of fracture mechanics, by plotting the crack growth rate in terms of the stress-intensity factor range, i.e., using the Paris’ curve. In this work, an analytical approach is proposed for the study of the relationships existing between the Wohler’s and the Paris’ representations of fatigue. According to dimensional analysis and the concepts of complete and incomplete self-similarity, generalized Wohler and Paris equations are determined, which provide a rational interpretation to a majority of empirical power-law criteria used in fatigue. Then, by integration of the generalized Paris’ law, the relationship between the aforementioned generalized representations of fatigue is established, providing the link between the cumulative fatigue damage and the fatigue crack propagation approaches. Moreover, paying attention to the limit points defining the range of validity of the classical Wohler and Paris power-law relationships, whose co-ordinates are referred to as cyclic or fatigue properties, alternative expressions for the classical laws of fatigue are proposed. Finally, the correlations between such fatigue properties are determined according to theoretical arguments, giving an interpretation of the empirical trends observed in the material property charts.

[1]  I-Wei Chen,et al.  Fatigue of Yttria‐Stabilized Zirconia: I, Fatigue Damage, Fracture Origins, and Lifetime Prediction , 1991 .

[2]  Alberto Carpinteri,et al.  Strength and toughness in disordered materials: complete and incomplete similarity , 1994 .

[3]  F. Erdogan,et al.  The Effect of Mean Stress on Fatigue Crack Propagation in Plates Under Extension and Bending , 1967 .

[4]  R. Forman,et al.  Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures , 1967 .

[5]  K. J. Miller,et al.  What is fatigue damage? A view point from the observation of low cycle fatigue process , 2005 .

[6]  Alberto Carpinteri,et al.  Notch sensitivity in fracture testing of aggregative materials , 1982 .

[7]  K. Miller.  THE SHORT CRACK PROBLEM , 1982 .

[8]  Kwai S. Chan.  A scaling law for fatigue crack initiation in steels , 1995 .

[9]  Alberto Carpinteri,et al.  Static and energetic fracture parameters for rocks and concretes , 1981 .

[10]  Paul C. Paris,et al.  Service load fatigue damage — a historical perspective , 1999 .

[11]  N. Riley,et al.  Scaling, self-similarity, and intermediate asymptotics , 1998 .

[12]  O. Basquin.  The exponential law of endurance tests , 1910 .

[13]  Alberto Carpinteri,et al.  Fractal nature of material microstructure and size effects on apparent mechanical properties , 1994 .

[14]  Andrea Spagnoli,et al.  Self-similarity and fractals in the Paris range of fatigue crack growth , 2005 .

[15]  M. Ciavarella,et al.  A generalized Paris' law for fatigue crack growth , 2006 .

[16]  Michael F. Ashby,et al.  Overview no. 112: The cyclic properties of engineering materials , 1994 .

[17]  A. Carpinteri,et al.  On the stress singularities at multimaterial interfaces and related analogies with fluid dynamics and diffusion , 2008 .

[18]  K. Tanaka,et al.  A correlation of ΔKth-value with the exponent, m, in the equation of fatigue crack growth for various steels , 1979 .

[19]  M. E. Haddad,et al.  Prediction of non propagating cracks , 1979 .

[20]  R. Ritchie,et al.  Propagation of short fatigue cracks , 1984 .

[21]  G. I. Barenblatt,et al.  INCOMPLETE SELF‐SIMILARITY OF FATIGUE IN THE LINEAR RANGE OF CRACK GROWTH , 1980 .

[22]  J. C. Newman,et al.  Crack-growth calculations in 7075-T7351 aluminum alloy under various load spectra using an improved crack-closure model , 2004 .

[23]  V. M. Radhakrishnan,et al.  Parameter representation of fatigue crack growth , 1979 .

[24]  Michele Ciavarella,et al.  On the possible generalizations of the Kitagawa–Takahashi diagram and of the El Haddad equation to finite life , 2006 .

[25]  Sonalisa Ray,et al.  Fatigue Crack Propagation Models for Plain Concrete Using Self Similarity Concepts , 2008 .

[26]  J. Newman,et al.  Fatigue-life prediction methodology using small-crack theory , 1999 .

[27]  Alberto Carpinteri,et al.  Self-similarity and crack growth instability in the correlation between the Paris’ constants , 2007 .

[28]  Ali Fatemi,et al.  Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials , 1998 .

[29]  Masaki Hojo,et al.  Effect of stress ratio on near-threshold propagation of delimination fatigue cracks in unidirectional CFRP , 1987 .

[30]  Alberto Carpinteri,et al.  Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue , 2009 .

[31]  P. Paris.  A rational analytic theory of fatigue , 1961 .

[32]  Alberto Carpinteri,et al.  Plastic flow collapse vs. separation collapse (fracture) in elastic-plastic strain-hardening structures , 1983 .

[33]  H. Kitagawa,et al.  Fracture Mechanical Approach to Very Small Fatigue Crack Growth and to the Threshold Condition , 1979 .

[34]  Edward F. O'Neil,et al.  CRACK PROPAGATION IN FLEXURAL FATIGUE OF CONCRETE , 2000 .

[35]  Andrea Spagnoli,et al.  Fractality in the threshold condition of fatigue crack growth: an interpretation of the Kitagawa diagram , 2004 .

[36]  M. Klesnil,et al.  Effect of stress cycle asymmetry on fatigue crack growth , 1972 .

[37]  D. S. Dugdale,et al.  The propagation of fatigue cracks in sheet specimens , 1958 .

[38]  L. Molent,et al.  Recent developments in fatigue crack growth assessment , 2006 .

[39]  K. Chan,et al.  Scaling laws for fatigue crack , 1993, Metallurgical and Materials Transactions A.

[40]  Weicheng Cui,et al.  A state-of-the-art review on fatigue life prediction methods for metal structures , 2002 .

[41]  Alberto Carpinteri,et al.  Size effect in fracture toughness testing: a dimensional analysis approach , 1980 .

[42]  L. Molent,et al.  Crack growth of physically small cracks , 2007 .

[43]  Michele Ciavarella,et al.  One, no one, and one hundred thousand crack propagation laws: A generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth , 2008 .

[44]  B. R. Seshadri,et al.  The Effect of the Laboratory Specimen on Fatigue Crack Growth Rate , 2006 .

[45]  Ali Fatemi,et al.  Cumulative fatigue damage mechanisms and quantifying parameters : A literature review , 1998 .

[46]  Paolo Lazzarin,et al.  Fatigue Strength Assessments of Welded Joints: from the Integration of Paris’ Law to a Synthesis Based on the Notch Stress Intensity Factors of the Uncracked Geometries , 2008, CP 2013.

[47]  G. I. Barenblatt,et al.  Scaling Phenomena in Fatigue and Fracture , 2004 .

[48]  P. C. Paris,et al.  A Critical Analysis of Crack Propagation Laws , 1963 .

[49]  Masahiro Endo,et al.  Effects of hardness and crack geometry on .DELTA.Kth of small cracks. , 1986 .

[50]  A. J. Mcevily,et al.  Prediction of the behavior of small fatigue cracks , 2007 .

[51]  Pietro Cornetti,et al.  New unified laws in fatigue: From the Wohler's to the Paris' regime , 2007 .