Mode I Stress Intensity Factors for triangular corner crack nearby intersecting of cylindrical holes

E. Salvati, P. Livieri, R. Tovo


The paper deals with the Stress Intensity Factor assessment of cracks at the intersection of holes
loaded by internal pressure.
Triangular flaws are considered at the intersection of two holes inside a specific specimen. The research
examines the influence of hole diameter ratio D1/D2 and the angle between their axes ?. Numerical analysis is
performed to determine the Stress Intensity Factors (SIF) of mode I in many different geometric
The actual shape of a real crack nucleated at the intersection of two cylindrical holes is subject to variable
internal pressure and is usually geometrically complex. The Stress Intensity Factor changes along the crack
contour and the crack shape development is controlled by its local value, e.g. during a fatigue loading. In
general, the estimation of the Stress Intensity Factors of cracks with a complex shape is made by means of
numerical methods since closed form solutions in literature are limited. However, in order to solve the problem
of crack propagation more quickly, in the case of a crack corner at the intersection between two cylindrical
holes, we can assume, in agreement with scientific literature, a symmetrical triangular crack shape and the Stress
Intensity Factor are only calculated at the middle of the crack. Obviously, this is a strong approximation, but
this allows a reduction in the computation effort for crack growth rate assessments and safety evaluation.
In this paper, the weight function technique is used by integrating the actual stress field evaluated in the uncracked
model. The method of the weight function is of general validity and the weight function is related to the
displacement components close to the crack front, as proposed by Bueckner and Rice. From a computational
point of view, the use of the three-dimensional weight function is complex and in scientific literature a weight
function of general validity is not available. Nevertheless, thanks to the work conducted by Petroski and
Achenbach, Shen and Glinka, an efficient generalised weight function has been adopted and then developed by
Sha and Yang [9], which considers a series expansion of non-singular terms. In this way, the integration of the
weight function, multiplied by a nominal stress, is made along a line and not in a two-dimensional domain.
In this preliminary work, according to Herz et al., we consider a weight function with three terms by assuming a
priori the coefficients of the second and third non-singular terms. This contribution is essentially an extension
of a previous paper by Herz et al. They only considered the case of D1/D2=1 and ?=90° (Di are the diameters
of the two cylindrical holes and a is the angle between their axis). Here, we extend the analysis to D1/D2 equal
to 2, 4 and 8 with an ? of 60 and 45 degrees. 

With the aid of three-dimensional modelling, an accurate FE model of a triangular corner crack at different
crack depths has been made. Subsequently, by using ANSYS finite element software, it is possible to employ the
command KCAL that evaluates the Stress Intensity Factors in the middle of the crack. Subsequently, a
comparison between numerical FE results and the analytical results, giving the values of the unknown
coefficients of the weight function (the unknown coefficient is indicated in the paper as M1).
As reported in the tables, the accuracy of the weight functions in SIF predictions is about 5% despite the strong
simplification previously introduced in the model. This result is considerable because it is possible to determine
the Stress Intensity Factor of a triangular shaped crack by a line integral of a stress profile in a model without
considering the crack.

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