entropy invariance with respect to geometry and loading frequency. According to the
total accumulated entropy of metals, undergoing repeated cyclic load as it reaches
the point of fracture is a constant value, independent of load amplitude, geometry,
size of specimen, frequency, and stress state; Naderi et al. (2010) experimentally
validated invariance of experimental fatigue fracture entropy with respect to loading
path and displacement loading amplitude for Al 6061-T6.
Fracture fatigue entropy remains at about 4 MJ m
À3 K
À1 for both tensioncompression and bending fatigue. Displacement amplitude is varied from 25 to
50 mm. Filled square, tension-compression; filled circle, bending; filled star, torsion.
After Naderi et al. (2010).
Amiri and Khonsari (2012) and Jang and Khonsari (2018) also did extensive
experiments to show that fatigue fracture entropy remains constant independent of
loading condition, loading frequency, and sample geometry. Their samples were
AISI 1018 carbon steel and Al 7075-T6. Liakat and Khonsari (2015) measured
fatigue fracture entropy of un-notched and V-notched specimens. They observed that
fatigue fracture entropy remains constant.
Imanian and Modarres (2015, 2018) and Yun and Modarres (2019) experimentally proved the concept of using entropy as a degradation metric, and authors
discussed the entropic characterization of the corrosion-fatigue degradation mechanism. They proposed an entropy-based damage prognostics and health management
technique for integrity assessment and remaining useful life prediction of aluminum
7075-T651 specimens. Their experimental validations proved that using entropy as a
thermodynamic state function for damage characterization is an effective way of
handling the endurance threshold uncertainties for life prediction purposes. Authors
also derived the formulation of entropy generation during corrosion-fatigue.
Imanian and Modarres (2015, 2018) and Yun and Modarres (2019) also proved
experimentally that multiple entropic-damage tests show the evolution of corrosionfatigue volumetric entropy for different loading conditions. They measured the
cumulative final value of fracture corrosion-fatigue entropy. The final entropy
value is between 0.7 MJ m
À3 K
À1 and 1.5 MJ m
À3 K
À1 . Authors also observed
that there is a narrow band distribution of entropy to failure data points [fracture
entropies] irrespective of loading condition. They concluded that the entropy has the
ability to quantify the uncertainties associated with microstate variables. Furthermore, they stated that it reveals the independence of entropy to the loading condition
(i.e., failure path). Fracture entropy’s slim distribution can be interpreted due to
uncertainties, such as instrumental measurement errors, the legitimacy of the
assumptions considered in entropy evaluation, weak control of the experimental,
operational and environmental conditions, and human error.
Sosnovskiy and Sherbkov (2015, 2016) published a generalized theory of evolution based on the concept of tribo-fatigue entropy. The essence of the proposed
approach is that tribo-fatigue entropy is determined by the process of degradation of
any system due to thermodynamic mechanical effects causing the change in the state.
Sosnovskiy and Sherbkov (2016) provided a mathematical framework for law of
entropy increase in a general form. They also provided extensive experimental
validation for mechanothermodynamics theory. They stated, “It is shown that the
4.1 Literature Review of Use of Thermodynamics in Continuum Mechanics
129
total accumulated entropy of metals, undergoing repeated cyclic load as it reaches
the point of fracture is a constant value, independent of load amplitude, geometry,
size of specimen, frequency, and stress state; Naderi et al. (2010) experimentally
validated invariance of experimental fatigue fracture entropy with respect to loading
path and displacement loading amplitude for Al 6061-T6.
Fracture fatigue entropy remains at about 4 MJ m
À3 K
À1 for both tensioncompression and bending fatigue. Displacement amplitude is varied from 25 to
50 mm. Filled square, tension-compression; filled circle, bending; filled star, torsion.
After Naderi et al. (2010).
Amiri and Khonsari (2012) and Jang and Khonsari (2018) also did extensive
experiments to show that fatigue fracture entropy remains constant independent of
loading condition, loading frequency, and sample geometry. Their samples were
AISI 1018 carbon steel and Al 7075-T6. Liakat and Khonsari (2015) measured
fatigue fracture entropy of un-notched and V-notched specimens. They observed that
fatigue fracture entropy remains constant.
Imanian and Modarres (2015, 2018) and Yun and Modarres (2019) experimentally proved the concept of using entropy as a degradation metric, and authors
discussed the entropic characterization of the corrosion-fatigue degradation mechanism. They proposed an entropy-based damage prognostics and health management
technique for integrity assessment and remaining useful life prediction of aluminum
7075-T651 specimens. Their experimental validations proved that using entropy as a
thermodynamic state function for damage characterization is an effective way of
handling the endurance threshold uncertainties for life prediction purposes. Authors
also derived the formulation of entropy generation during corrosion-fatigue.
Imanian and Modarres (2015, 2018) and Yun and Modarres (2019) also proved
experimentally that multiple entropic-damage tests show the evolution of corrosionfatigue volumetric entropy for different loading conditions. They measured the
cumulative final value of fracture corrosion-fatigue entropy. The final entropy
value is between 0.7 MJ m
À3 K
À1 and 1.5 MJ m
À3 K
À1 . Authors also observed
that there is a narrow band distribution of entropy to failure data points [fracture
entropies] irrespective of loading condition. They concluded that the entropy has the
ability to quantify the uncertainties associated with microstate variables. Furthermore, they stated that it reveals the independence of entropy to the loading condition
(i.e., failure path). Fracture entropy’s slim distribution can be interpreted due to
uncertainties, such as instrumental measurement errors, the legitimacy of the
assumptions considered in entropy evaluation, weak control of the experimental,
operational and environmental conditions, and human error.
Sosnovskiy and Sherbkov (2015, 2016) published a generalized theory of evolution based on the concept of tribo-fatigue entropy. The essence of the proposed
approach is that tribo-fatigue entropy is determined by the process of degradation of
any system due to thermodynamic mechanical effects causing the change in the state.
Sosnovskiy and Sherbkov (2016) provided a mathematical framework for law of
entropy increase in a general form. They also provided extensive experimental
validation for mechanothermodynamics theory. They stated, “It is shown that the
4.1 Literature Review of Use of Thermodynamics in Continuum Mechanics
129