PSI - Issue 18

A.P. Zakharov et al. / Procedia Structural Integrity 18 (2019) 749–756 A.P. Zakharov / Structural Integrity Procedia 00 (2019) 000 – 000

752

4

stress intensity factor can be rewritten as:

1

n         f n J I

2

w

0 

1

FEM

FEM

K

J

J

,





(8)

P

f

f

E

In the present study all nonlinear fracture resistance parameters mentioned above were calculated on the base of small- and large-scale yielding FE analysis of near the crack tip stress-strain fields. 3. Small-and large-scale yielding analysis of central cracked plate under biaxial loading In this paper the plastic SIF is employed to study the coupling between loading biaxiality effects and crack tip configuration in both the small- and large-scale yielding ranges by means of the plane strain and 3D nonlinear FE analyses. To this end, the Mode I central cracked plate (CCP) subjected to of biaxial loading was used. Two types of crack tip configuration in CCP FE model were considered as it shown in Fig.1. The plane strain FE analysis was performed for CCP with mathematical notch crack tip (Fig.1.a) as well as the 3D full-field FEA was concerned with CCP with finite radius crack tip (Fig.1.b). The finite radius of the curvature at the crack tip was ρ/a = 0.0 1. In the case of plane strain problem the 2D eight-node isoparametric elements were used to CCP FE model. The twenty node quadrilateral brick isoparametric three-dimensional solid elements were used to model for the 3D CCP with finite radius crack tip.

Fig. 1. FE-mesh detail for (a) mathematical type crack tip and (b) crack tip with finite radius.

The Ti6Al4V titanium alloy was identified as a material of CCP. The main mechanical properties were determined for the Ti6Al4V alloy, namely, the Young’s modulus E = 118000 MPa; the Poisson’s ratio  = 0.3; the yield stress  0 = 885 MPa; the ultimate stress  u = 1289 MPa; the strain hardening exponent n = 12.59 and strain hardening coefficient  = 1.225. Numerical calculations for CCP were carried out in the full range of nominal stress biaxial ratio from equibiaxial tension ( η = +1) up to equibiaxial tension-compression ( η = -1). As a result, the J integral, the governing parameter of the elastic – plastic crack-tip stress field I n -integral and the plastic SIF were calculated as functions of loading biaxiality and applied stress levels. Fig.2 shows the numerical results of J -integral calculations for CCP from titanium alloy Ti6Al4V under different types of biaxial loading as a function of applied stress levels. As it follows from these results J -integral is almost unchanged for both crack-tip configurations when applied stress level σ/σ 0 ≤ 0.15. However, in the case of applied stress level when σ/σ 0 is more than 0.15 the J -integral distributions differ increasingly as a function of biaxial stress ratio. It should be noted that in the case of CCP with finite radius crack tip (Fig.2.b) the influence of the type of biaxial loading on the J -integral distributions is more significant. Moreover, the contrary trends of biaxiality effects on J -integral behaviour were established depending on crack tip configuration.