Retracted: Fracture investigation of U‐notch made of tungsten–copper functionally graded materials by means of strain energy density

Abstract

The averaged strain energy density over a well‐defined control volume was employed to assess the fracture of U‐notched specimens made of tungsten–copper functionally graded materials under prevalent mode II loading. The boundary of control volume was evaluated by using a numerical method. Power law function was employed to describe the mechanical properties (elasticity modulus, Poisson's ratio, fracture toughness and ultimate tensile stress) through the specimen width. The effect of notch tip radius and notch depth on notch stress intensity factors and mode mixity parameter χ were assessed. In addition, a comparison based on fracture load between functionally graded and homogeneous W–Cu was made. Furthermore, in this research, it was shown that the mean value of the strain energy density over the control volume can be accurately determined using coarse meshes for functionally graded materials.

Ductile Failure Prediction of U-Notched Bainitic Functionally Graded Steel Specimens Using the Equivalent Material Concept Combined with the Averaged Strain Energy Density Criterion

“…The mentioned criterion has been used in different investigations to predict the fracture of notched specimens made of functionally graded materials [32,33,31,[27][28][29][30]. However, in this study, as the notch root has been located in a very ductile region, the mentioned criterion cannot give reasonably accurate results.…”

“…Unlike homogeneous materials, in FGMs due to a gradual change in material properties, the outer boundary of control volume is no longer a circular arc, but rather an oval arc is assumed. This notion has been used in a number of previous studies on fracture of notched specimens made of FGMs [32,31,39,[27][28][29][30]. For a U-notched FGM specimen with a material variation in the xdirection under mode I, the outer boundary can be determined by a numerical approach using the following equations.…”

“…Recently, the averaged SED criterion was employed to predict the fracture of notched specimens made of different types of materials such as Polyurethane (PUR) [25,26], tungsten-copper functionally graded material [27][28][29][30][31] and functionally graded steels [32][33][34].…”

“…To predict the fracture of notched specimens made of FGMs by the averaged SED criterion, unlike homogeneous materials for which the outer boundary of the control volume is a circular arc, the strain energy density is averaged over a well-defined control volume which its outer boundary is an oval arc [27][28][29][30][31][32][33][34]. In these works, the notch depth was in brittle or semi-brittle region.…”