Quantitative Assessment and Analysis of Non-Masing Behavior of Materials under Fatigue


Quantitative assessment of non-Masing behavior is studied, and a new method is proposed for the estimation of cyclic plastic strain energy density and fatigue life. Low cycle fatigue tests were performed on 304L stainless steel employing strain amplitudes ranging from ±0.25% to ±1.0% at a strain rate of 3 × 10-3 s-1. The material exhibited Masing behavior at lower strain amplitudes and non-Masing behavior at higher strain amplitudes. Secondary hardening was observed at relatively higher strain amplitudes. Both the secondary hardening and non-Masing response were found to be associated with the deformation induced martensitic transformation. The master curve approach, which is generally used for the analysis of non-Masing response, could not be used as experimental data could not be represented in the form of a master curve. The proposed method of quantification of non-Masing response could estimate the cyclic plastic strain energy density of 304L stainless steel well within a scatter band of 1.2. The fatigue life of 304L stainless steel could also be predicted within a scatter band of 2. The proposed approach could also estimate the cyclic plastic strain energy density and fatigue life of materials of different grades within scatter factors of 1.2 and 2, respectively.

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Cyclic plastic strain energy density [ML-1T-2]


Degree of initial hardening [M0L0T0]


Degree of softening [M0L0T0]


Degree of secondary hardening [M0L0T0]

\(E_{exp}\) :

Cyclic plastic strain energy density of experimental hysteresis loop without any regard to the Masing or non-Masing behavior [ML-1T-2]

\(E_{f}\) :

Normalized cyclic plastic strain energy density difference [M0L0T0]

\(E_{m}\) :

Cyclic plastic strain energy density for Masing behavior [ML-1T-2]

\(E_{nm,exp}\) :

Experimental cyclic plastic strain energy density for non-Masing behavior [ML-1T-2]

\(E_{nm,pre}\) :

Predicted cyclic plastic strain energy density for non-Masing behavior [ML-1T-2]

\(K\) :

Cyclic strength coefficient for ideal Masing behavior [ML-1T-2]

\(K_{1}\) :

Material constant, the coefficient obtained from Eq. 11 [ML-1T-2]

\(n\) :

Cyclic strength exponent for ideal Masing behavior [M0L0T0]

\(n_{1}\) :

Material constant, the exponent obtained from Eq. 11 [M0L0T0]

\(n^{\prime}\) :

Cyclic hardening exponent of Master curve for non-Masing behavior [M0L0T0]

\(N_{f,exp}\) :

Experimental fatigue life of the material [M0L0T0]

\(N_{f,pre}\) :

Predicted fatigue life of the material [M0L0T0]

\(S_{1}\), \(S_{2}\) :

Material constants, obtained from Eq. 4. [M0L0T0]

\(S_{3}\), \(S_{4}\) :

Material constants, obtained from Eq. 9. [M0L0T0]

\(\Delta E\) :

Extra cyclic plastic strain energy density due to non-Masing behavior [ML-1T-2]

\(\Delta \varepsilon_{p}\) :

Plastic strain range [M0L0T0]

\(\Delta \varepsilon_{t}\) :

Total strain range [M0L0T0]

\(\delta \sigma_{0}\) :

Change in proportional limit due to non-Masing behavior [ML-1T-2]

\(\varepsilon_{t}\) :

Total strain amplitude [M0L0T0


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The authors would like to acknowledge the Department of Science and Technology, Government of India for financial assistance [DST/INSPIRE/04/2016/001402]. Authors are thankful to Dr. A. K. Bhaduri, Centre Director, and A. Nagesha, head, fatigue studies section, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu for allowing us to conduct experiments. A special thanks to Prof. Pravash Chandra Chakraborti from Jadavpur University for his support and motivation.

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Yadav, S.S., Roy, S.C., Veerababu, J. et al. Quantitative Assessment and Analysis of Non-Masing Behavior of Materials under Fatigue. J. of Materi Eng and Perform 30, 2102–2112 (2021). https://doi.org/10.1007/s11665-021-05494-w

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  • low cycle fatigue
  • Masing and non-Masing behavior
  • life prediction
  • strain energy density approach