# Prediction of the Crack Front Shape of the Corner Interface Crack
Notably, their findings reveal intriguing insights into the maximum energy release rate (ERR) associated with each of these front shapes [21]. Their findings provided valuable insights into optimizing the design strategies and materials to mitigate delamination risks in electronic packaging and related applications. In a noteworthy exploration, [PERSON] et al. (2011) conducted an in-depth investigation into the application of the cohesive zone model (CZM) to elucidate the complex phenomenon of interface crack initiation within nanoscale components. They derived a unified criterion for the crack initiation at the edge of the interface, leveraging two pivotal CZM parameters. It was discerned that as the cohesive energy increased, the critical lateral force needed for crack initiation also increased [22]. [PERSON], [PERSON], and [PERSON] (2012) employed their previously established numerical method involving the M\({}_{1}\)-integral to thoroughly evaluate stress intensity factors for three-dimensional interface cracks existing between dissimilar anisotropic materials. Their methodology encompassed a comprehensive investigation, ranging from analyzing double edge cracks in jointed dissimilar isotropic semi-infinite plates under uniform cooling, to external circular interface cracks subjected to uniform changes in temperature and a uniform temperature gradient [23]. In a parallel research endeavor, [PERSON] et al. (2012) meticulously examined the effect of residual stresses on the propagation of interface cracks within dissimilar brittle (ceramic) materials. They investigated the influence of anti-plane mode on interface crack propagation and critically evaluated the validity of the 2D models, as well as the effects of mixed loading, incorporating both thermal and mechanical stresses. The authors underscored the prominent role of the anti-plane mode, particularly near the edges, and the Mode I contribution in causing an increase in ERR [24]. In a different way of inquiry, [PERSON] and [PERSON] (2013) directed their focus towards modeling the shape of the interface crack front and determining the critical stress for steady-state crack propagation, involving a rigorous estimation of the strain energy release rate, crack front profiles, and 3D mode mixity along the interface crack front. Their results contributed to a deeper understanding of the aspects of crack propagation at interfaces under specific stress conditions, aiding in the assessment of crack stability and growth in bonded materials [25]. [PERSON] et al. (2015) have proposed a method to derive the SIFs for the 3D cracks with the curved crack front, which is a combination of the direct integration method and the X-FEM (extended finite element method) localized multigrid approach. They applied the three-grid method, since the third grid provides an increased accuracy in determination of the SIFs. The authors stated that the proposed method can be easily adapted for solving other 3D crack problems [26]. In a significant study, [PERSON] et al. (2019) conducted a detailed analysis concerning the relationship between the stress intensity factor (SIF) of a circumferential crack and adhesive thickness in a bonded round bar. They concluded that the dimensionless SIFs for a small interface crack and a small edge crack, both located near the interface in a butt jointed plate, remained constant, regardless of the adhesive thickness [27]. Expanding on this research, [PERSON] et al. (2019, 2020) delved into a comprehensive analysis focusing on the propagation of a corner crack within two long plates made of dissimilar materials. Their research encompassed a thorough examination of various crack front shapes and presented results detailing the normalized stress intensity factors and energy release rate variations for the three crack propagation modes. Notably, they scrutinized how these factors varied concerning the angle measuring the distance from the symmetry plane [28; 29].