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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a) c ) Fig. 2. FEM meshes of flat the CS-1 (a) and CTS (b) geometries and 3D FEM mesh of the CS-2 specimen. For elastic – plastic hardening material behaviour in numerical calculations is the Ramberg – Osgood equation is used: n E E    0       (1) where - ε – strain, σ – stress, σ 0 – yield stress, E – Yong’s modulus, n – strain hardening exponent and α – strain hardening coefficient of the Ramberg-Osgood model. FEM numerical solutions have been obtained for a large number of different values of the inclina tion angle α and nominal stresses σ n in considered test specimen geometries. 3. Nonlinear mixed mode fracture resistance parameters The main feature of this study is determination of the governing parameter of the elastic – plastic crack-tip stress field I n -integral, the stress triaxiality parameter and J-integral as a function of both mode mixity and elastic – plastic material properties, described by strain hardening exponent. Different degrees of mode mixity from pure Mode I to pure Mode can be expressed by a near-field mixity parameter. Shih (1974) introduced for mixed-made small-scale yielding problem mixity parameter in the following form:     0 ~ 0 ~ 2 tan 1           p M (2) to pure Mode II and pure Mode I is realized when M p = 1 In the classical first-term singular HRR solution, the most important role belongs to the numerical governing parameter of the crack-tip elastic-plastic stress-strain field in the form of the I n -integral. Shlyannikov and Tumanov (2014) suggested a numerical procedure for calculating I n - integral for different cracked bodies via the elastic – plastic FE-analysis of the stress – strain fields near the crack tip:                                                      d u u d du u d du u n n n a w M I FEM FEM r FEM r FEM rr FEM FEM r FEM r FEM r FEM FEM rr n FEM e p FEM n . cos ~ ~ ~ ~ 1 sin ~ ~ ~ ~ ~ ~ cos ~ 1 ) ( , , ( / ), 1 (3) b)      0  r where – θ – polar angle,     r ~ , ~ – dimensionless functions of stresses. It should be noted that M p = 0 corresponds  

      

      

n

1



ij i u  ~ , ~ – dimensionless functions of stresses and displacements.

where – θ – polar angle,