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A Thermodynamic Framework for Rapid Prediction of S-N Curves Using Temperature Rise at Steady-State

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Abstract

Background

Building S-N curves for materials traditionally involves conducting numerous fatigue tests, resulting in a time-consuming and expensive experimental procedure that can span several weeks. Thus, there is a need for a more efficient approach to extract the S-N curves.

Objective

The primary purpose of this research is to propose a reliable approach in the framework of thermodynamics for the rapid prediction of fatigue failure at different stress levels. The proposed method aims to offer a simple and efficient means of extracting the S-N curve of a material.

Methods

In this paper, a method is introduced based on the principles of thermodynamics. It uses the fracture fatigue entropy (FFE) threshold to estimate the fatigue life by conducting a limited number of cycles at each stress level and measuring the temperature rise during the steady-state stage of fatigue.

Results

An extensive set of experimental results with carbon steel 1018 and SS 316 are conducted to illustrate the utility of the approach. Also, the efficacy of the approach in characterizing the fatigue in axial and bending loadings of SAE 1045 and SS304 specimens is presented. It successfully predicts fatigue life and creates the S-N curves.

Conclusion

The effectiveness of the approach is evaluated successfully for different materials under different loading types. The results show that the temperature rise is an indicator of the severity of fatigue and can be used to predict life.

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Abbreviations

\(A\) :

Conjugated force of internal variable

\({A}_{cond}\) :

Cross-sectional area

\({A}_{surf}\) :

Surface area

\({c}_{p}\) :

Specific heat capacity

e :

Specific internal energy

\({\dot{E}}_{diss}\) :

Rate of dissipated energy

\({\dot{E}}_{gen}\) :

Rate of internal energy generation

\({\dot{E}}_{in}\) :

Rate of energy entering the material

FFE:

Fracture fatigue entropy

h :

Heat transfer coefficient

\(k\) :

Thermal conductivity

m :

Material Constant

\({N}_{f}\) :

Number of cycles to failure

\(\overrightarrow{q}\) :

Heat flux across the boundary

\({R}_{\theta }\) :

Rate of temperature rise at the beginning of the fatigue process

s :

Specific entropy

t :

Time

T :

Temperature

\({T}_{s}\) :

Steady-state temperature

V :

Volume of the gauge section

\({V}_{k}\) :

Internal variable

\({W}_{P}\) :

Mechanical dissipation due to plastic deformation

\({\dot{W}}_{t}\) :

Rate of total energy generation

\(\gamma\) :

Non-negative entropy generation

\({\gamma }_{f}\) :

Entropy generation up to fracture

\(\dot{\varepsilon }\) :

Total strain rate

\({\varepsilon }^{e}\) :

Elastic strain

\({\varepsilon }^{p}\) :

Plastic strain

\(\rho\) :

Density

\(\sigma\) :

Symmetric stress tensor

\(\psi\) :

Helmholtz free energy

\(\theta\) :

Temperature rise of gauge section (The difference between gauge section and remote area)

\({\theta }^{d}\) :

Temperature rise due to damaging energies

\({\theta }^{nd}\) :

Temperature rise due to non-damaging energies

\(\Delta z\) :

Distance between gauge section and grips

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Funding

This work is supported in part by the members of the Center for Innovations in Structural Integrity Assurance (CISIA) under the US National Science Foundation award number 2052810. Also, the lead author (A.M.) wishes to acknowledge that the research was supported in part by the Louisiana Experimental Program to Stimulate Competitive Research (EPSCoR), funded by the National Science Foundation and the Board of Regents Support Fund under Cooperative Agreement Number OIA-1946231 (CFDA # 47.083).

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA, USA

    A. Mahmoudi & M.M. Khonsari

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  1. A. Mahmoudi
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Correspondence to M.M. Khonsari.

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Mahmoudi, A., Khonsari, M. A Thermodynamic Framework for Rapid Prediction of S-N Curves Using Temperature Rise at Steady-State. Exp Mech 64, 167–180 (2024). https://doi.org/10.1007/s11340-023-01016-y

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