Issue 50

O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01 4 (a) (b) Figure 1 : Plastic strain (η=0, component ε 22 ): (a) numerical simulation; (b) analytic solution by Eqn. (4). (a) (b) Figure 2 : Plastic strain (η=1, component ε i ): (a) numerical simulation; (b) analytic solution by Eqn. (4). The analysis of data presented in Fig. 3 allows us to conclude that the maximum relative error of Eqn. (1) is less than 20 percent. As a result, we can expect qualitative description of energy dissipation process at fatigue crack based on the simple hypothesis (4). E XPERIMENTAL STUDY OF STRAIN FIELD AT THE CRACK TIP series of samples made of Grade 2 titanium alloy were tested using servo-hydraulic biaxial testing system Biss BI- 00-502, located in Kazan Scientific Center of Russian Academy of Sciences. The photo of the experimental setup is presented in Fig. 4. The geometry of the samples is shown in Fig. 5. During tests the samples were subjected to cyclic loading of 10 Hz with constant stress amplitude, different biaxial coefficient η=Px/Py (1, 0.7, 0.5, 0) and stress ratio R (0.1, 0.3, 0.5). The crack length was measured by an optic method. The strain field was measured by digital image correlation method based on StrainMaster system and Lavision software. Surface of the sample near the crack tip was polished and covered with a black matte paint before the experiment. Then, the white paint was sprayed over the black paint to obtain a high contrast image. A macro lens and an elevated Led lamp were used for recording of material displacement at the crack tip. To restore the deformation field at the crack tip area, each frame was subjected to additional processing: calibration to level distortions caused by distortion of the lens, motion compensation, regulation of the illumination with digital filters. The spatial resolution of the strain field near the crack tip was 3e-6 m. Fig. 6 shows the characteristic result of measurements for the case of uniaxial loading. The deformation field is asymmetric due to the influence of the relative direction of the crack. Fig. 7 shows the shape of the plastic area boundary and characteristic sizes which have been used for the comparison of the experimental and numerical data. Tab. 1 gives a quantitative comparison of the obtained data. A