Journal of Materials Engineering and Performance

, Volume 26, Issue 8, pp 3784–3793 | Cite as

High Load Ratio Fatigue Strength and Mean Stress Evolution of Quenched and Tempered 42CrMo4 Steel

  • Leonardo Bertini
  • Luca Le Bone
  • Ciro Santus
  • Francesco Chiesi
  • Leonardo Tognarelli


The fatigue strength at a high number of cycles with initial elastic–plastic behavior was experimentally investigated on quenched and tempered 42CrMo4 steel. Fatigue tests on unnotched specimens were performed both under load and strain controls, by imposing various levels of amplitude and with several high load ratios. Different ratcheting and relaxation trends, with significant effects on fatigue, are observed and discussed, and then reported in the Haigh diagram, highlighting a clear correlation with the Smith–Watson–Topper model. High load ratio tests were also conducted on notched specimens with C (blunt) and V (sharp) geometries. A Chaboche model with three parameter couples was proposed by fitting plain specimen cyclic and relaxation tests, and then finite element analyses were performed to simulate the notched specimen test results. A significant stress relaxation at the notch root became clearly evident by reporting the numerical results in the Haigh diagram, thus explaining the low mean stress sensitivity of the notched specimens.


42CrMo4+QT steel Chaboche kinematic hardening model Haigh diagram high load ratio fatigue mean stress relaxation strain ratcheting 



Finite element


Smith–Watson–Topper (model)


Load (or stress) ratio


Theoretical stress concentration factor


Yield strength


Ultimate tensile strength


Fracture strength


Fatigue limit


True fracture strength


Mean stress


Alternating stress


Mean strain during ratcheting tests


Range of alternating strain


Range of alternating stress


Maximum stress


Minimum stress

K, n

Ramberg–Osgood parameters

\(\sigma_{ \hbox{max} }^{\text{e}}\)

Maximum elastic stress

\(\sigma_{ \hbox{min} }^{\text{e}}\)

Minimum elastic stress


Mean elastic stress


Stress tensor


Deviatoric stress tensor


Backstress tensor


Deviatoric backstress tensor


Size of the yield surface


Yield function


Plastic strain tensor


Uniaxial plastic strain component


Accumulated plastic strain


Uniaxial stress component


Uniaxial backstress component

Ci, γi

Chaboche model parameters

\(\sigma^{\bmod } (\varepsilon_{i} )\)

Model cyclic stress for the Chaboche parameter optimization

\(\sigma^{\exp } (\varepsilon_{i} )\)

Experimental cyclic stress for the Chaboche parameter optimization

\(\sigma_{\text{m}}^{\bmod } (i)\)

Model relaxation mean stress for the Chaboche parameter optimization

\(\sigma_{\text{m}}^{\exp } (i)\)

Experimental relaxation mean stress for the Chaboche parameter optimization

M, N

Number of sample points for the objective functions

w1, w2

Relative weights for the Chaboche parameter optimization


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Copyright information

© ASM International 2017

Authors and Affiliations

  1. 1.DICI - Department of Civil and Industrial EngineeringUniversity of PisaPisaItaly
  2. 2.General Electric Oil & Gas, Nuovo PignoneFlorenceItaly

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