The aim of this work is to model a functionally graded material layer (FGML) around U notches and to observe the effect of the FGML on stress distribution as well as the stress concentration factor (SCF) under far field tensile and in plane bending loads. The FGML is also optimized to obtain the minimum SCF near U notches. The Extended Finite Element Method (XFEM) is used for numerical analysis. XFEM offers advantages for modeling notches such as U notches efficiently, due to its nonconformal mesh and level set function based geometric and FGM layer description. A comparison between U shaped and elliptical shaped FGMLs is presented and it is found that the U shaped FGML yields slightly lower SCF values with the difference being more noticeable for sharper U notches. The UFGML is then optimized for FGM parameters over a range of notch sharpness (l/r) from 1 to 5 and normalized notch length (2l/W) from 0.05 to 0.5. The interaction effect of FGMLs is observed at higher notch lengths and low notch sharpness causing increased stress at the interface and leading to higher SCF. The FGM parameters are also tailored to reduce this interaction effect. The SCF around U notches can be significantly reduced by applying a linear UFGML with FGM thickness 1 and 1.5 times for in-plane bending and uniaxial tensile loading, respectively. A smaller power law coefficient for tensile loading and a thinner FGML for bending can be used to reduce or avoid the interaction effects of FGMLs.
Kumar et al. (Mon,) studied this question.