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

1120

4

In such a case, the numerical I n -integral not only changes with the material properties described by the strain hardening exponent n but also changes with mixed mode parameter M p and the relative crack length ( a/w ) and the specimen or structure element configuration. In modern ductility-based crack growth models under elastic – plastic and creep conditions, damage accumulation is taken to be dependent on the ratio h of hydrostatic stress σ m to the equivalent von Mises stress σ e . Henry and Luxmoore (1997) proposed the local fracture parameter of the crack-tip constraint in the form of a stress triaxiality parameter: equation:     ij ij kk s s h r z , ,   (4) where  kk and s ij are the hydrostatic and deviatoric stresses, respectively. Being a function of both the first invariant of the stress tensor and the second invariant of the stress deviator, the stress triaxiality parameter is a local measure of the in-plane and out-of-plane constraint that is independent of any reference field. The algorithm proposed by Lee and Liebowitz (1977) for numerical determination of the J-integral under large scale yielding conditions is the basis of our calculations for considered specimens in the full range of mixed mode loading.      2 3 3 where Γ is a curve that surrounds the crack tip, starting from the lower crack flank, traversing counterclockwise, and ending on the upper crack flank; S is the arc length; n j is the outward unit vector normal to the curve; u ij is the dimensionless displacement, σ ij is stress tensor, Wdy – strain energy density. All nonlinear fracture resistance parameters mentioned above were calculated on the base of FE analysis of near the crack tip stress-strain fields for cruciform specimens of two configurations and compact tension-shear specimen in the full range of mixed mode loading. 4. Nonlinear mixed mode fracture resistance parameters As a result of numerical analysis of test specimens considered in this study distributions of the governing parameter of the elastic – plastic crack-tip stress field In-integral, the local fracture parameter the stress triaxiality h and J-integral were obtained. All results are presented as a function of both plastic mixity parameter M p and elastic – plastic material properties, described by strain hardening exponent n . Figure 3 shows the distributions of the governing parameter of the plastic stress field I n -integral for all considered test specimen configurations as a function of mode mixity M P ranging from 0 to 1. J E J w FEM 2 0   where       n u dS Wdy J j x i ij ,  (5)

a) c ) Fig. 3. Distribution of the I n -integral in the CTS (a), CS-1 (b) and CS-2 (c) as a function of mixity parameter. b)