PSI - Issue 32

A.Yu. Iziumova et al. / Procedia Structural Integrity 32 (2021) 93–100 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

96 4

Fig. 3 illustrates the typical hysteresis loop at the initial stage of deformation (black line), at the point indicated by circles in Fig. 2 and near the fracture moment (blue line). The hysteresis loop area (hence plastic work) increases during cyclic deformation and fatigue crack evolution.

Fig. 3. Hysteresis loop at the different moment of deformation.

Experimental data of heat flux, displacements of points near the notch and applied loading were recorded discretely. The estimation of the integral value of the plastic work ( A ) and heat dissipation ( Q ) was carried out by the trapezoidal method with the replacement of the integration operation by the summation:

1 n F ( x ) F ( x ) i i   cyc cyc

b

A





cyc F ( x )dx

1 x x , i i  





 



(2)

2

1

i

a

t

 H(t ) H(t ) t t 2    i i 1 i

n

1



Q H( t )dt 

 

0 t 

(3)

,

i 1 

i 1 

where t is time (s), Fcyc(t) is applied loading (N), x(t) is displacement (m), H(t) is heat flux (W). Fig. 4 shows evolution of the integral stored energy per cycle depends on the crack length. Circle markers indicate the time moment when the heat flux begins to deviate from a constant value (see Fig. 2b).

Fig. 4. Crack length dependence of stored energy per cycle.

The value of stored energy per cycle increases steadily as the crack length increases. At the final stage of deformation with a significant crack length, the stored energy reaches a value of almost 0.065 J/cycle for both values of loading. The main idea of the thermodynamic theory of strength is that the critical value of the stored energy (close to the fracture moment) is comparable to the enthalpy of material melting. Schipachev A.M. (2018) and