PSI - Issue 18

Vedernikova A. et al. / Procedia Structural Integrity 18 (2019) 639–644 Author name / Structural Integrity Procedia 00 (2019) 000–000

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parameter  is determined by the additional experiment procedure of specimen cooling after pulse point heating (Iziumova et al. (2016)) and  equal 3.65·10 4 and 1.4 ·10 4 for Grade 2 and Ti-1Al-1Mn, corresponding. By assuming, that the elastic strains are negligible compared to the plastic strains, the part of the loading diagram reflecting the elastic behavior of the material is not analyzed. The final stages of loading are not taken into consideration, since properties of materials may be different from the properties at the beginning tests. Therefore, it is not possible to estimate the heat sources based on the heat equation used with the given constants. The some of the irreversible plastic work contributes to heat generation, but the remainder is stored in the metal as the energy of crystal defects accompanying plastic deformation, known as the stored energy of cold work (Ravichandran et al. (2002)). For plane specimens the plastic work can be defined as a function of strain rate V and loading force   F t :

 

  ,

(5)

p W t

F t V 

The directly measurement of the stored energy presents considerable experimental difficulties. We determined the energy stored in materials as the difference between the mechanical work expended and the heat evolved (Fig. 2b). (a) (b)

Fig. 2. (a) IR image of the specimen from titanium alloy Grade 2 under quasistatic tensile loading; (b) Time dependence of heat dissipation and stored energy for Grade 2 (Eq. 4). In paper Meneghetti (2007) the algorithm allowing on the basis of the energy balance equation to estimate transfer of heat to the surroundings by means of three main mechanisms: convection, conduction and radiation:       2 4 4 , cv ir ij ij cv n ir p V V S S V T d dV TdV T T dS T T dS c E dV t                                  (6) where  is the thermal conductivity of the material,  is the heat transfer coefficient by convection,  is the surface emissivity,  is the density, c is the specific heat, n  is the Stephan–Boltzmann constant equal to 5.67∙10 8 W/(m 2 K 4 ), p E  is rate of variation of the stored energy, T  is the room temperature and ( , , z, ) T x y t is the time-dependent temperature field, cv S , cd S , ir S - parts of surface S of the control volume V through which the heat Q is transferred to the surroundings by convection, conduction and radiation, respectively. The parameter Q and p E  can be derived by means of Eq. (6) from experimental measurements of the surface temperature along the specimen and of the room temperature if heat transfer coefficient  and the emissivity  are known. In our case, the emissivity coefficient was taken to be 0.92 (because a thin layer of amorphous carbon coated