Issue 50

A. Kostina et alii, Frattura ed Integrità Strutturale, 50 (2019) 667-683; DOI: 10.3221/IGF-ESIS.50.57 670 The numerical simulation was carried out with the finite-element software COMSOL Multiphysics®. The plate was heated by a square pulse with the amplitude o Q equal to 4·10 5 W/m 2 . The descending part of the pulse was smoothed to simulate gradual decrease of the incident heat flux. The temperature was registered for a time interval of 2 seconds with a step size of 0.01 s. The following boundary conditions were applied to the specimen: (3)-(5) to the front surface and (4)- (5) to the lateral and rear surfaces. To simulate non-uniform heating of the front surface induced by the convexity of the heating source, the incident heat flux was multiplied by the piecewise function which scales the amplitude o Q from 0.88 o Q to 1.03 o Q along the width of the specimen. Subsurface defects were represented as parts of the specimen filled with air. Continuity conditions were applied at the interface between steel and air. Physical properties as well as values of parameters used in boundary and initial conditions are given in Tab. 1. The modelled specimen was discretized by tetrahedral finite elements with various sizes. A more refined mesh was used in defective zones of the sample. The convergence analysis has shown that the optimal size of the elements in areas adjacent to the defects is equal to 0.6 mm. The maximum size of the elements in the finite-element model was 8 mm. The complete mesh consisted of 1250000 elements. The mesh is presented in Fig. 1 (b). Property Value Unit Density of steel 7990 kg/m 3 Thermal conductivity of steel 15.5 W/(m·K) Heat capacity of steel 500 J/(kg·K) Density of air 1.125 kg/m 3 Thermal conductivity of air 0.026 W/(m·K) Heat capacity of air 1005 J/(kg·K) Amplitude of heating 4·10 5 W/m 2 Initial temperature 298 K Convective heat transfer coefficient 10 W/(K·m 2 ) Surface emissivity 0.95 - Time interval 2 s Table 1 : Thermophysical properties of air, steel and parameters of heating. (a) (b) Figure 1 : (a) Schematic representation of the specimen. All dimensions are in mm. (b) Finite-element model of the specimen. Fig. 2 shows evolution of the temperature contrast for the considered specimen obtained with the use of the model (1)- (5). It can be seen that maximum values of the temperature contrast have defects located at the depth of 0.4 mm (the