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138
Edson Denner Leonel & Wilson Sergio Venturini
strains and then one use the Hooke’s law to obtain the integral representation in terms of stress.
Finally, multiplication by the director cosines of the normal to crack surfaces at the collocation point
leads to the traction representation, as follow:
1
P ( f) + η ⋅ S ( f, c) u ( c) dΓ = η D ( f, c) P ( c)
dΓ
(8)
∫
2 j k kj k k kj k
Γ Γ
∫
where ∫ is the principal value integral of Hadamard, terms S kj and D kj contain the derivatives of P ij
*
and u ij * , respectively, following Portela et al. (1992). In the present investigation, only linear boundary
elements are used. The singular integrals are evaluated in numerical form, using the sub-element
procedure, while the hyper-singular integrals are calculated by analytical expressions. This procedure
is efficient and sufficiently accurate in the solution of arbitrary crack growth problems.
3 DEVELOPMENT
This paper shows results of a model developed to analyze crack propagation under fatigue. The
proposed model is able to simulate crack growth process with a simple crack or multiple cracks inside a
2D domain using the theories already described.
4 RESULTS
The model proposed is able to simulate the crack growth process in 2D domains. Fig. (1) shows
this process in a perforated plate with multiple cracks. In each hole one have two cracks which ones
grow according the fatigue cycle loads. The model gives accurate results to crack growth trajectory and
to structural life prediction.
Figure 1 – Crack growth process with multiple cracks.
5 CONCLUSIONS
The BEM formulation to deal with crack propagation under fatigue has been studied. The model
proposed has shown good agreement with analytical and experimental results in terms of structural life
prediction and crack growth trajectory. The BEM model is also able to simulate coalescence and then
is possible to considerer localization problems.
Cadernos de Engenharia de Estruturas, São Carlos, v. 11, n. 53, p. 135-139, 2009