Purpose: To create an effective in engineering strength calculation three-dimensional submodel
of the near crack tip region in solids for hi-fidelity analysis of their stress-strain state
by the finite element method.
Design/methodology/approach: To create a volume near the crack tip, regular threedimensional
20-node prismatic isoparametric elements and 15-node special elements with
edge length of 12.5 μm with shifted nodes in order to simulate the singularity of stress at the
crack tip were used. Using these two types of elements, a cylindrical fragment of diameter
of 100 μm was built. In its base is a 16-vertex polygon, and its axis is the crack front line. In
the radial direction the size of the elements was smoothly enlarged by creating of 5 circular
layers of elements, and in the axial direction 8 layers were created. For convenience of the
sub-model usage, the cylindrical fragment was completed by regular elements to a cubic
form with edge size 400 μm. For the sub-model approbation, the full-scale three-dimensional
models of standard specimens with cracks were built. The stress intensity factor K at normal
tension was calculated assuming small scale yielding conditions in a plane between 4th and
5th layers of special elements on the basis of analysis of displacement fields near the crack tip.
Findings: An effective three-dimensional sub-model of the near crack tip region is
proposed. The sub-model was used to obtain the dependence of the stress intensity factor
on the relative crack length at normal tension for four types of standard specimens. The
obtained dependences show excellent correlation with known analytical solutions.
Research limitations/implications: The concept of finite element meshing at threedimensional
modelling of the near crack tip region for high-fidelity stress-strain state
analysis was generalized. A sub-model of the near crack tip region was created and used to
determine the stress intensity factor at normal tension of four types of standard specimens.
It is shown that the proposed methodology is effective for precise analysis of the stressstrain
state of solids with cracks within the framework of linear fracture mechanics.
Practical implications: By applying the generalized approach and the proposed threedimensional
sub-model of the near crack tip region, one can determine the stress-strain
state of structure elements and machine parts when analysing their workability by the finite
element method.
Originality/value: An effective finite-element sub-model for the stress-strain state analysis
in the vicinity of the crack tip within the framework of the linear fracture mechanics is
proposed.
INFLUENCE OF THE HIGHER ORDER TERMS IN WILLIAMS’ SERIES EXPANSION OF THE STRESS FIELD ON THE STRESS-STRAIN STATE IN THE VICINITY OF THE CRACK TIP. PART II
