Analytical and semi-analytical solutions for underclad crack problems
Increasing requirements for the safe operation of nuclear power facilities along with the lifetime extension of nuclear power plant (NPP) equipment and pipelines requires the development of modern methods for strength justification. One of the basic emergency failure mechanisms of the safety-critical elements of NPP equipment and pipelines is unstable crack growth starting after the critical crack size has been achieved. Therefore development of models, criteria and methods for calculation of the brittle fracture resistance acquire a important role in the strength justification. A characteristic feature of modern WWER pressure vessel is the presence of anticorrosion cladding, i.e. interface between dissimilar materials. In present day Standards there are no recommendations for the stress intensity factors (SIF) evaluation for underclad cracks reaching the base metal-cladding interface. Currently SIF calculation for crack front lying in the base metal as well as on the interface between materials is done by the direct finite element crack modeling. The implementation of this approach is highly resource- and labor-intensive. Thus obtaining analytical solutions or approximations based on numerically evaluated SIF results for such cracks has become relevant.
On the basis of the complex variable technique the singular integral equation (SIE) has been derived for a two-dimensional problem on a finite crack reaching at a right angle the interface between materials with different elastic properties. Therefore explicit expressions in elementary functions were developed for SIF evaluation in dependence on the following parameters: elastic modulus ratio of the base metal and the cladding, crack length, stress distribution along the crack line.
A semi-analytical method of SIE solving was developed. It is based on the collocation method with explicit account for the solution singularity at crack tips. This semi-analytical approach can be used for verification of the derived approximate analytical expressions and assessment of their application range as well as for analysis of more complex geometry of bimetallic bodies with crack (cracks) including the case when the mixed loading occurs.
Presented analytical and semi-analytical results are the part of a comprehensive research aimed at enhancement of methodological bases on evaluation of the brittle fracture resistance for cladded WWER pressure vessels.Full version (russian)