Issue 78

A. Zakharov et alii, Fracture and Structural Integrity, 78 (2026) 260-274; DOI: 10.3221/IGF-ESIS.78,16

It should be noted that the stress and the displacement components in Eqs. (15) and (19) were determined numerically via the FE analysis of the near crack tip fields.

P LANE STRAIN CENTER - CRACKED PLATE UNDER BIAXIAL LOADING

I

n the present study, for comparison between small-scale yielding and extensive plasticity conditions, a rectangular plate of width 2 w containing a central crack of length 2 a (Fig. 1a) was analyzed. The nonlinear fracture mechanics parameters, including the J-integral and the plastic SIF, were calculated using the finite element method (FEM). The CCP is subjected to biaxial remote loading, with stresses applied along the Y- and X-directions; the transverse stress is quantified by the biaxiality ratio

      / xx

yy .

(23)

Different degrees of biaxial nominal stress ratio were considered from equibiaxial tension (  =+1) up to equibiaxial tension compression (  =-1). The plane strain FE simulations were carried out using ANSYS [30] to examine the coupled effects of biaxial loading and applied stress level on the elastic-plastic crack-tip field.

(a) (b) Figure 1: Central cracked plate under biaxial loading finite elements at the crack tip region.

Fig. 1b illustrates the FE mesh details in the crack-tip region for both configurations. For the plane-strain analysis, 2D eight-node isoparametric elements were used. Due to high stress gradients, a refined focused mesh with a ring of elements around the crack front was used to ensure convergence. To this end, a focused mesh topology with a ring of elements surrounding the crack front was adopted to improve the convergence of the numerical solutions. In the circumferential direction around the crack tip, 40 equally sized elements were defined over the angular range from -  to + π . The radial size of each successive ring increases gradually with distance from the crack tip. The material considered for the CCP was a titanium alloy, and its mechanical properties are listed in Tab. 1.

Young’s modulus, E (MPa)

Yield stress, σ 0 (MPa)

Ultimate stress, σ f (MPa)

Strain hardening exponent, n

Strain hardening coefficient, α

Material

Ti6Al4V

118010

885.5

1289

12.588

1.225

Table 1: The main mechanical properties.

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