PSI - Issue 28

Carlos D.S. Souto et al. / Procedia Structural Integrity 28 (2020) 146–154

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Carlos D.S. Souto et al. / Structural Integrity Procedia 00 (2020) 000–000

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3.1. Modified virtual crack closure technique

The modified virtual crack closure technique was implemented in Omicron to calculate the stress intensity factor as a function of the crack’s length, K ( a ). To achieve this, the user must define a node path on which the crack’s length is allowed to increase. Omicron will then calculate K ( a ) assuming a new crack-tip at each of the path’s nodes. The crack’s length, a , is automatically updated by modifying the elemental connectivity of the mesh (in the case of a non-symmetric crack) or by modifying the boundary conditions (in the case of a symmetric crack).

3.2. J-integral

The procedure proposed by Monteiro (1984) to numerically determine stress intensity factors was implemented in Omicron as a post-processing option, where after a numerical simulation using a finite element model, the user just needs to select the integration contour by defining a node path. The J-integral is path-independent, however, due to the approximations and interpolations done by both the finite element method and by the proposed procedure, some variation of the value of J is expected, depending on the chosen contour.

4. Case study of a finite plate with a central crack

Consider the following case study of a plate with a central crack in the middle, subjected to an uniaxial tensile stress with σ y = 500 MPa. The material is considered to be under plane stress condition.

Fig. 4: Finite plate with a central crack.

Considered dimensions of the plate were: w = h = 50 mm, t = 1 mm; and the plate’s elastic material properties considered were: E = 210 GPa, ν = 0 . 35. The analytical solution for this problem, considering a << w , is already well known: K = σ y √ π a (10) However, the above solution is a good approximation when a << w . If this is not guaranteed, the following solution for a periodic repeating crack must be used instead: K = σ y w tan π a w (11)