Issue 40

Z. Zhang et alii, Frattura ed Integrità Strutturale, 40 (2017) 149-161; DOI: 10.3221/IGF-ESIS.40.13 152 damage in structure, so the temperature field during the fatigue process is closely related with the microstructure configuration and its nonlinear interaction with the local damage effect. As a consequence, the fatigue energy dissipation is in accordance with the regularity of thermal energy dissipation, which means that the temperature evolution could reflect the energy dissipation characteristics during the fatigue process. During the fatigue loading process, the mechanical energy, elastic strain energy, plastic energy and anelasticity damping energy are involved. . Specifically, the input energy from outside belongs to mechanical energy, which includes elastic strain energy, plastic strain energy and anelasticity damping energy. Elastic energy corresponds to the recoverable deformation of material crystal, which has no influence on damage accumulation. Anelasticity damping energy is time-related and conditionally reversible, which plays a significant role for high cycle fatigue, but it has very little influence on the total energy dissipation since plastic strain energy is the most important reason that causes damage. Energy balance law During the cyclic loading process, most of mechanical energy is dissipated as thermal energy into the surroundings, part of energy will stay in the material and is reflected as the transformation of microstructures. The energy balance law is shown below according to first law of thermodynamics                    0 K W t D t Q t E t E t (9) In which    W t is the increment of total input energy during cyclic loading process,    D t and    Q t are the increment of total storage energy and dissipation energy, respectively,    K E t is increment of kinetic energy, which is zero under cyclic load,    0 E t is the energy dissipation increment in other forms, which is relatively very small when compared with    D t and    Q t . Thermal energy dissipation and plastic strain energy during the cyclic loading process will be discussed in the following parts Characteristics of thermal energy Most of the mechanical energy will be transferred to thermal energy. This is the typical phenomenon of irreversibility in thermodynamics. Many researches have shown that massive thermal energy would be produced during the fatigue process. The thermal energy dissipation is caused by viscosity or interior friction, which is due to the shear deformation of crystals, specifically. Also, dislocation movement of atoms during the plastic deformation period would convert most energy into thermal energy. Thus, the temperature field caused by fatigue damage evlolution will change due to damage distribution and difference of motion for different atoms, also is partially because the thermal energy is different for different material elements. Although the ratio of thermal energy dissipation to total strain energy may be different in different cases, it is certain that thermal energy dissipation is the most important part, which plays a key role during the energy exchange of fatigue process. The thermal energy increment during the cyclic loading is shown below:            q h Q t Q t Q t (10)         q Q t CV T t (11)        h Q t hA T t (12) In which    q Q t is the increment of total interior energy of dampers at time t,    h Q t is the convection thermal energy dissipation at time t ,    T t is the average temperature rise of dampers,  is density, V is the working region volume, C is the specific heat, h is convection coefficient, A is the surface area of damper working zone. This paper assumes that the heat conduction between damper and loading system is negligible, the material of damper is Q235 steel, the material properties are shown in Tab. 1. ρ, kg/m 3 E , MPa v C , Jkg -1 K -1 h, Jm -2 s -1 K -1 σ b , MPa σ y , MPa σ f , MPa 7860 2.06E5 0.3 504 12.1 406 235 178 Table 1 : Physical and mechanical properties of Q235 steel.