1 Modeling Fatigue Life of Structural Alloys Under Block Asymmetric Loading
3
require a large amount of experimental data and are valid only for a narrow range of
loading conditions within the available basic experimental data (Kollinz 1984).
Some new on damage modeling can be found in (Placidi 2015; Placidi et al. 2018,
2019). There are also works on damage and plasticity for granular materials (Misra
and Poorsolhjouy 2015; Misra and Singh 2015; Zhao et al. 2018). Information about
generalized continuum theories can be found in (Alibert et al. 2003; dell’Isola et al.
2012; Auffray et al. 2013; dell’Isola et al. 2015; Abali et al. 2017; dell’Isola et al.
2017). The most fascinating application of theories is in designing new artificial
microstructured metamaterials (Del Vescovo and Giorgio, 2014; Placidi et al. 2016;
Barchiesi et al. 2018; dell’Isola et al. 2019).
In recent years, a new scientific direction of mechanics of damaged media (MDM)
for solving such problems has been successfully developed (Murakami 1983; Volkov
and Igumnov, 2017). The current practice of using MDM equations for different
mechanisms of worked out service life suggests that this approach is efficient enough
for practical applications and quite accurate in evaluating the process of working
out of service life of structural elements and components of load-bearing structures
(Mitenkov et al. 2007; Volkov and Korotkikh 2008; Volkov and Igumnov 2017).
In the present paper, a mathematical model of mechanics of damaged media
(Volkov and Korotkikh 2008; Volkov and Igumnov 2017) is developed, which
describes the processes of plastic deformation and fatigue accumulation in structural
steels (SS304, 12X18H9) under block-type non-stationary asymmetric low-cycle
loading. The obtained numerical results are compared with the data of full-scale
experiments and with numerical results, obtained by other researchers (Guozheng
et al. 2002).
1.2 Constitutive Equations of MDM
The model of damaged media developed in (Volkov and Korotkikh 2008; Volkov
and Igumnov 2017) consists of three interrelated parts as follows:
• equations describing thermoplastic behavior of materials, taking into account its
dependence on the failure process;
• evolutionary equations describing the kinetics of damage accumulation;
• strength criterion of the damaged material.
1.2.1 Constitutive Equations in Plasticity
Constitutive equations in plasticity are based on the following main assumptions
(Mitenkov et al. 2007; Volkov and Korotkikh 2008; Volkov and Igumnov 2017):
3
require a large amount of experimental data and are valid only for a narrow range of
loading conditions within the available basic experimental data (Kollinz 1984).
Some new on damage modeling can be found in (Placidi 2015; Placidi et al. 2018,
2019). There are also works on damage and plasticity for granular materials (Misra
and Poorsolhjouy 2015; Misra and Singh 2015; Zhao et al. 2018). Information about
generalized continuum theories can be found in (Alibert et al. 2003; dell’Isola et al.
2012; Auffray et al. 2013; dell’Isola et al. 2015; Abali et al. 2017; dell’Isola et al.
2017). The most fascinating application of theories is in designing new artificial
microstructured metamaterials (Del Vescovo and Giorgio, 2014; Placidi et al. 2016;
Barchiesi et al. 2018; dell’Isola et al. 2019).
In recent years, a new scientific direction of mechanics of damaged media (MDM)
for solving such problems has been successfully developed (Murakami 1983; Volkov
and Igumnov, 2017). The current practice of using MDM equations for different
mechanisms of worked out service life suggests that this approach is efficient enough
for practical applications and quite accurate in evaluating the process of working
out of service life of structural elements and components of load-bearing structures
(Mitenkov et al. 2007; Volkov and Korotkikh 2008; Volkov and Igumnov 2017).
In the present paper, a mathematical model of mechanics of damaged media
(Volkov and Korotkikh 2008; Volkov and Igumnov 2017) is developed, which
describes the processes of plastic deformation and fatigue accumulation in structural
steels (SS304, 12X18H9) under block-type non-stationary asymmetric low-cycle
loading. The obtained numerical results are compared with the data of full-scale
experiments and with numerical results, obtained by other researchers (Guozheng
et al. 2002).
1.2 Constitutive Equations of MDM
The model of damaged media developed in (Volkov and Korotkikh 2008; Volkov
and Igumnov 2017) consists of three interrelated parts as follows:
• equations describing thermoplastic behavior of materials, taking into account its
dependence on the failure process;
• evolutionary equations describing the kinetics of damage accumulation;
• strength criterion of the damaged material.
1.2.1 Constitutive Equations in Plasticity
Constitutive equations in plasticity are based on the following main assumptions
(Mitenkov et al. 2007; Volkov and Korotkikh 2008; Volkov and Igumnov 2017):