Crack tip asymptotic fields in anisotropic planes: Importance of higher order terms

On brittle fracture of two‐dimensional lattices with material anisotropies

“…This agrees with the previous works demonstrating the significant role of T-stress in fracture behavior and fatigue crack growth in anisotropic domains. 44,67,75 Indeed, the developed theoretical/computational framework and numerical analyses performed in the current work can be further validated against experimental data. Moreover, the proposed framework can be employed as part of a larger structural optimization framework to design for optimized fracture toughness in periodic cellular structures against various loading conditions.…”

“…Then, given the boundary conditions and the calculated macroscopic stiffness tensor, the stress field coefficients K I , K II , and T are obtained numerically for the homogenized domain in every increment of the crack growth. In the current work, these coefficients are computed using the finite element overdeterministic (FEOD) approach which has been used widely in the past by Mirsayar and co-workers 44,57,[59][60][61][62][63][64] and other researcher [65][66][67] for various material systems, loading conditions, and specimen geometries. Finally, the crack propagation angle and onset of mixed-mode fracture can be predicted using the O-MPS criterion in every increment for any specimen geometry and loading conditions.…”

Crack tip fields in anisotropic planes: a review

“…Thereafter, Lee (2016Lee ( , 2018 continued their previous study (Lee et al 1996) and analysed the propagating crack in an anisotropic medium, with stress and displacement fields given along with a generic solution for all the crack parameters in dynamic fracture. More recently, Ghouli et al (2020); Nejati et al (2021b) suggested infinite series solutions for stress, strain and displacement fields in cracked anisotropic planes, while decomposing fracture modes according to a stress-based definition. These authors also devised exact analytical solutions for all crack tip coefficients in centrally cracked infinite anisotropic plates.…”

“…Now, consider a crack parallel to the x-axis with the crack tip positioned at z 0 in plane P. For any points in the planes P j , the coordinates with respect to the crack tip are given by z j − z 0 = r (cos θ + μ j sin θ), where r and θ (0 < r , −π < θ ≤ π ) are the components The material orientation is assumed to make an angle β with respect to the crack bisector of the polar coordinate system centred at the crack tip. Nejati et al (2021b) proposed the potential functions j (z j ) in accordance with a stress-based definition of loading modes in anisotropic planes (at θ = 0 • , τ xy = 0 for pure mode I, and σ y = 0 for pure mode II) as…”

“…Here, the coefficients of mode I and mode II terms are designated by A n and B n , respectively, with both sets of parameters being real valued that satisfy the tractionfree boundary conditions of the crack faces (Nejati et al 2021b). Within this formulation, the crack tip stress intensity factors can be obtained through the relations…”