PSI - Issue 81

V.S. Kravets et al. / Procedia Structural Integrity 81 (2026) 102–108

103

Nomenclature a

half-length of filled central part of the crack central half-thickness of crack-like defect

c

average shear stiffness of orthotropic material for longitudinal shear

3 с

relative stress intensity factor (SIF) Mode III

III F 0 G

shear modulus of the injection isotropic material 13 23 , G G shear modulus of the orthotropic body material h ( x ) variable half-thickness of crack-like defect Н ( х ) Heaviside function III c K Mode III crack growth resistance of material in the direction of crack propagation l half-length of rectilinear crack q longitudinal shear load at infinity q c critical shear load (CSL) q c 0 critical shear load with an unhealed crack u z ( x ) z -component of displacements at Ox axis  inclination angle of orthotropy axes of the body material relative to the axis Ox 3  orthotropy level parameter for longitudinal shear , xz yz   shear stresses along the Oz axis

In modern designs, along with isotropic materials, various composite materials are widely used, which are mostly modelled by anisotropic media (Lekhnitskii (1963), Bozhidarnik et al. (2007), Savruk and Kazberuk (2017)). Solution methods for the corresponding problems of the theory of elasticity and fracture mechanics of anisotropic bodies with various defects, such as cracks, are developed quite fully (Sih at al. (1965), Ioakimidis and Theocaris (1977), Serensen and Zaitsev (1982), Ting (1996), Bozhidarnik et al. (2007), Sylovanyuk at al. (2015), Savruk and Kazberuk (2017)). The influence of the filling volumes of the crack surfaces on changes in the stress intensity factors (SIF) Mode III and critical shear loads (CSL) of the anisotropic body is determined below, based on numerical solutions of problems of the mathematical cracks ’ theory. The obtained results coincide with the known analytical solutions for completely filled crack-type defects in the form of an oblate ellipse Sylovanyuk and Ivantyshyn (2022). 2. Рroblem formulation and solution method An infinite anisotropic body S with a tunnel along the Oz axis crack-like defect of length 2 l and variable thickness 2 h ( x ) along the Ox axis in the introduced Cartesian coordinate system Oxyz is considered (Fig. 1). The body is in a state of antiplane deformation – at infinity is sheared by a stress q along the Oz axis in the plane xOz ( , 0 yz xz q       ). It was assumed that the injection material fills only the central part of the crack-like defect on the segment [ – a , a ] and after its hardening (as a thin walled inclusion) at the interface of the materials we have an ideal mechanical contact.

Fig. 1. Longitudinal shear of an anisotropic body with a partially filled crack-like defect.

For a given body load the isotropic injection material S 0 is imaginary removed from the crack-like defect, and its action on the body is replaced by shear stresses along the Oz axis, according to the Winkler basis model (Panasyuk et al. (2014), Sylovanyuk and Ivantyshyn (2022)):

( ) W W xz y x x a x a       , ( ) 0,

* z x G u x h x    0 ( ) ( ) / 2 ( )

W

(1)

,



yz



