PSI - Issue 13

V.N. Shlyannikov et al. / Procedia Structural Integrity 13 (2018) 1117–1122 Boychenko N.V. / Structural Integrity Procedia 00 (2018) 000 – 000

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mode III and 2D- as well as 3D mixed mode deformation combinations. Ayatollahi and Saboori (2015) analysed T stress effects for such complex types of mixed mode I/II/III loading conditions. Shlyannikov and Zakharov (2017) calculated elastic-plastic parameters for three test specimen geometries subjected to the full range of mode mixity and compared with the analytical solution for an infinite centre-cracked plate. The main aim of this study is the evaluation of coupling mode mixity and elastic-plastic material properties effects on the behavior of I n -integral, the stress triaxiality h and J-integral. 2. Specimen geometry and material properties In the present study, test specimens of various configurations subjected to uniaxial and biaxial mixed mode loading by using a finite element method are analyzed. Plane strain and full-field elastic – plastic FE analyses are performed using ANSYS Code for a flat cruciform specimen (CS-1), a cruciform specimen with thinned working area (CS-2) and a compact tension – shear specimen (CTS). Specimen configurations are presented in Fig.1. ranging from 0 to 1.

a) c) Fig. 1. Specimen configurations: (a) flat cruciform specimen, (b) cruciform specimen with thinned working area, (c) compact tension-shear specimen. b)

Different degrees of mode mixity from pure Mode I to pure Mode II are obtained in all specimens by combinations of the nominal stress level σ n , remote biaxial stress ratio η=σ xx /σ yy and the initial crack angle α with respect to the loading direction. For the biaxial loaded cruciform specimens, α = 90°, correspond to pure Mode I, whereas pure Mode II can be realised when α = 45° and η = -1. In the CTS α = 90° corresponds to pure Mode I, and pure Mode II can be achieved when α = 0°. The main mechanical properties of the considered materials are listed in Table 1, where E is Young’s modulus, σ 0 is the yield stress, σ u is the ultimate tensile stress, and α and n are strain hardening coefficient and the strain hardening exponent of the Ramberg – Osgood constitutive equation, respectively.

Table 1. The main mechanical properties. Material E [GPa]

σ u [MPa]

σ 0 [MPa]

n

α

Steel P2M

226.9

362.4 714.4 471.6 885.5

1190.0 1260.4

4.131 7.889

4.141 0.529 1.570 1.225

Steel 34XH3MA

216.21

Al 7050 Ti6Al4V

70.57

701.0

10.851 12.588

118.01

1289.6

The elastic – plastic FE calculations were performed using FE meshes of the cruciform and compact tension – shear specimen configurations considered (Fig. 2) to determine the crack-tip stress – strain distributions under different mixed-mode loading conditions. To this end, two-dimensional (2D) plane strain eightnode isoparametric elements have been used for the 2D flat CTS and CS-1 configurations, and twenty-node quadrilateral brick isoparametric three-dimensional (3D) solid elements have been used to model the 3D biaxially loaded CS-2 in its thin central part. ranging from 0 to 1.