Using a UMM-XFEM technics to predict the damage in CFRP bi-graded with glass-epoxy materials of notched plate under quasi-static loading

Abstract

Composite materials, with their remarkable advantages in various industrial sectors, have increasingly broadened their applications, particularly in the reinforcement of notched structures. These still attract the intention of many researchers to analyze them is to improve them. Indeed, the study of their reinforcements can only be done by studying their damage. Depending on the proposed reinforcement, it can take several images; such as geometric or material, total or partial at the stat of the notch. Through a numerical prediction, our objective in this work consists in a total reinforcement of the structure by proposed materials called CFRP bi-graded with glass-epoxy. Following the proposed graduation design, these three different fiber qualities pooled a single quality in the middle for each design case. This is possible provided that these fibers are housed in the same matrix in epoxy quality and with the same volume in volume fraction. The parameters of rigidity and the graded damage in the structure are homogenized according to the thickness by volume fraction introduced by finite elements using technique UMM-XFEM. For this, a special mesh is used. Where the parameters evaluated such as the type and the density of finite elements as well as the architecture of mesh and the adequacy with the criterion of the damage and these parameters introduced, all showed an effect on the determined results. The linear constitutive law of our model agrees with the equivalent stress flow theory of Von Mises. The composite used in this work in CFRP is of quality IM7/8552. The evaluation under the effect of the graduation parameters is made on the response of the structure and its resistance capacity using the tensile separation curves. The study showed that the proposed concept, in the case where the strongest fiber is in the middle of the plate, a symmetrical stress with respect to the thickness of the structure and an overcapacity in its resistance. This resistance overcapacity becomes significant due to the effect of the graduation volume fraction index ($\beta$) chosen. The coupling of the XFEM technique with that of UMM has effectively shown the separation of the structure after crack initiation in structures with graded materials. Where It is also shown that the critical length which corresponds to the total failure of the proposed composite material is the average of the critical lengths of the graded layers. The damage under the effect of different concepts was highlighted in this work.

Keywords:

• CFRP (carbon fiber reinforced polymer)
• FGM (functional graded materials)
• UMM (user mesh method)
• XFEM (extend finite element method)
• CZM (cohesive zone modeling)

Disclosure statement

The authors declare that they have no conflict of interest.

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.