PSI - Issue 42

V. Shlyannikov et al. / Procedia Structural Integrity 42 (2022) 714–721 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

716

3

Huang et al. (2004) presented a simplified theory of Gao et al. (1999), justifying and excluding from its high order terms associated with rotational components, and naming the formulation the conventional mechanism-based strain gradient (CMSG) plasticity theory. In CMSG theory, the gradient of plastic deformation appears only in the constitutional model of the behavior of the medium, and the equilibrium equations and boundary conditions coincide with the conventional theories of continuum mechanics. Recently Martínez-Pañeda (2015) and Shlyannikov et.al (2020) implemented this lower-order scheme to evaluate gradient effects, since it does not experience convergence problems in numerically solving complex problems of fracture mechanics, unlike the higher-order model (MSG). Also, the authors of Martínez-Pañeda et al. (2016, 2017) and Shlyannikov et al. (2020, 2021) quantified the relationship between the properties of the material and the characteristic size at which the gradient effects noticeably increase the true stresses in the crack tip region. 2. Experimental study The subject of the numerical and experimental study is a compact tension shear specimen (Fig. 1) manufactured from steel, aluminum and titanium alloys. The CTS specimen has in-plane sizes of 80×136 mm, and the relative crack length a/w after precracking varies in the range of 0.53 – 0.54.

Fig. 1. CTS specimen. Pure Mode I conditions are given by  = 90  while pure Mode II conditions are given by  = 0  .

The known standard tensile properties for all tested materials are listed in Table 1. In this table, E , σ 0 , n , and N denote the Young’s modulus, monotonic tensil e yield stress and plastic strain hardening exponent (where N = 1/ n ), respectively.

Table 1. Main mechanical properties for tested materials. Material E (GPa) σ 0 (MPa) n

N

σ 0 /E

Steel P2M

226.90

362.4 471.6 885.5

4.13

0.242 0.092 0.079

0.001597 0.006683 0.007504

Al-alloy 7050

70.57 118.0

10.85 12.59

Ti-6Al-4V

Table 2. Specimen sizes and loading conditions. Material Applied force F, kN

Applied force angle α, degree

Specimen thickness t, mm

Mode I

Mode II

Mode I

Mode II

Mode I

Mode II

Steel P2M

7.0

14.0 11.0 17.0

90 90 90

0 0 0

4.83 4.85

4.51 5.01 5.02

Al-alloy 7050 3.0

Ti-6Al-4V

11.0

5.0