Abstract An incremental model was developed so as to predict the growth of fatigue cracks under complex load spectra. It contains a crack propagation law (da/dt = α|dρ/dt|) and a cyclic elastic plastic constitutive law for the cracked structure d ρ / d t = f ( ϕ ∝ J , ϕ X c , ϕ th c , ϕ X m , ϕ th m ) . The crack growth rate da/dt is a rate of creation of cracked area per unit length of crack front. The plastic flow intensity factor rate dρ/dt is function of the loading level ϕ and of the thresholds for plastic deformation either within the monotonic or within the cyclic plastic zone. Two internal variables are introduced so as to define each threshold, the first one ϕX is associated with internal stresses, while the second one, ϕth, measures the effective threshold for plastic deformation in the crack tip region. The material parameters in the equations are determined using the finite element method. This identification was performed for a 0.48%C carbon steel. Then various fatigue crack growth experiments have been performed in order to validate the model, monotonic fatigue crack growth experiments at different stress ratios from R = −1 to R = 0.4, single overloads with overloads factor between 1.5 and 1.8, and bloc loads with X overloads every Y cycles, X and Y varying from one experiment to another. The predictions of the model reproduce well experimental results. Finally the model was applied to an industrial problem: the growth of a semi elliptical crack at the surface of a train wheel. For this purpose, load spectra were measured in situ on a train wheel, it came out that the model had to be extended to biaxial tension-compression and bending loading conditions, which was done.
[1]
Andrew H. Sherry,et al.
COMPENDIUM OF T‐STRESS SOLUTIONS FOR TWO AND THREE DIMENSIONAL CRACKED GEOMETRIES
,
1995
.
[2]
S. Pommier.
Cyclic plasticity and variable amplitude fatigue
,
2003
.
[3]
W. Elber.
The Significance of Fatigue Crack Closure
,
1971
.
[4]
R. Forman,et al.
Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures
,
1967
.
[5]
Sylvie Pommier,et al.
Time-derivative equations for fatigue crack growth in metals
,
2005
.
[6]
Xin Wang,et al.
Elastic T-stress solutions for semi-elliptical surface cracks in finite thickness plates
,
2003
.
[7]
J. Li,et al.
Edge dislocations emitted along inclined planes from a mode I crack
,
1988
.
[8]
M. de Freitas,et al.
Effect on fatigue crack growth of interactions between overloads
,
2002
.
[9]
James C. Newman,et al.
An empirical stress-intensity factor equation for the surface crack
,
1981
.
[10]
M. Skorupa,et al.
Load interaction effects during fatigue crack growth under variable amplitude loading—a literature review. Part II: qualitative interpretation
,
1999
.
[11]
Sylvie Pommier,et al.
Incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode I elastic–plastic displacement fields
,
2007
.
[12]
O. E. Wheeler.
Spectrum Loading and Crack Growth
,
1972
.
[13]
J. Schijve.
The Significance of Fractography for Investigations of Fatigue Crack Growth under Variable-Amplitude Loading
,
1999
.