Two-Dimensional Finite Element Method for Modeling Edge Effects in Cross-Ply Laminates
DOI:
https://doi.org/10.48048/tis.2022.4584Keywords:
Finite element modeling and programing, Exponential shape functions, Cross-ply laminates, Edge effect, DelaminationAbstract
A 2-dimensional finite element (FE) method, based on an approximate analytical solution, is developed to define accurately stress fields and boundary layer width in symmetrically laminated composites. A better insight into the edge effect and delamination failure of cross-ply laminates is attained through a physical explanation of the mathematical FE solution. While some other solutions failed, the present FE solution obtains accurate results using a limited number of elements, and therefore reduces computer storage and computation time. A perturbation technique is employed to derive shape functions for the free edge boundary region, which properly describes the physics of sudden exponential growth of stress field in the vicinity of the edge. An original and comprehensive FE computer program is developed, using these specific shape functions, special numerical integration, and mesh generation algorithms. Results for bidirectional laminates under uniaxial extension are presented and compared with finite difference, FE, and approximate analytical solution.
HIGHLIGHTS
- Defining accurately stress field in free edge region is the main challenge
- Shape functions based on perturbation solution yield accurate results
- Boundary layer width is proportional to geometric ratio of laminates
- Finer mesh in boundary region is required for small geometric ratio laminates
- A huge number of finite elements are needed to determine narrow boundary width
GRAPHICAL ABSTRACT
Downloads
Metrics
References
M Islam and P Prabhakar. Modeling framework for free edge effects in laminates under thermo-mechanical loading. Compos. B. Eng. 2017; 116, 89-98.
D Cao, H Hu, Q Duan, P Song and S Li. Experimental and three-dimensional numerical investigation of matrix cracking and delamination interaction with edge effect of curved composite laminates. Compos. Struct. 2019; 225, 111154.
JJ Espadas-Escalante, NPV Dijk and P Isaksson. The effect of free-edges and layer shifting on intralaminar and interlaminar stresses in woven composites. Compos. Struct. 2018; 185, 212-20.
D Zhang, J Ye and HY Sheng. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos. Struct. 2006; 76, 314-25.
P Lecomte-Grosbras, B Paluch and M Brieu. Characterization of free edge effects: influence of mechanical properties, microstructure and structure effects. J. Compos. Mater. 2013; 47, 2823-34.
T Lorriot, H Wargnier, J Wahl, A Proust and L Lagunegrand. An experimental criterion to detect onset of delamination in real time. J. Compos. Mater. 2014; 48, 2175-89.
P Lecomte-Grosbras, J Réthoré, N Limodin, JF Witz and M Brieu. Three-dimensional investigation of free-edge effects in laminate composites using x-ray tomography and digital volume correlation. Exp. Mech. 2015; 55, 301-11.
DW Oplinger, BS Parker and FP Chiang. Edge-effect studies in fiber-reinforced laminates. Experimental Mechanics. 1974; 14, 347-54.
CT Herakovich, D Post, MB Buczek and R Czarnek. Free edge strain concentrations in real composite laminates: Experimental-theoretical correlation. J. Appl. Mech. 1985; 52, 787-93.
P Hsu and C Herakovich. A perturbation solution for interlaminar stresses in bidirectional laminates. In: J David (Ed.). Composite materials: Testing and design (fourth conference). American Society for Testing and Materials, Pennsylvania, USA, 1977, p. 526.
RB Pipes and NJ Pagano. Interlaminar stresses in composite laminates under uniform axial extension. J. Compos. Mater. 1970; 4, 538-48.
A Solis, S Sánchez-Sáez and E Barbero. Influence of ply orientation on free-edge effects in laminates subjected to in-plane loads. Compos. B. Eng. 2018; 153, 149-58.
N Pagano. Stress fields in composite laminates. Int. J. Solids Struct. 1978; 14, 385-400.
G Isakson A and Levy. Finite-element analysis of interlaminar shear in fibrous composites. J. Compos. Mater. 1971; 5, 273-6.
E Stanton, L Crain and T Neu. A parametric cubic modelling system for general solids of composite material. Int. J. Numer. Methods Eng. 1977; 11, 653-70.
A Wang and FW Crossman. Some new results on edge effect in symmetric composite laminates. J. Compos. Mater. 1977; 11, 92-106.
A Wang and FW Crossman. Calculation of edge stresses in multi-layer laminates by sub-structuring. J. Compos. Mater. 1978; 12, 76-83.
P Bar-Yoseph and J Avrashi. New variational-asymptotic formulations for interlaminar stress analysis in laminated plates. Z. Angew. Math. Phys. 1986; 37, 305-21.
R Barboni, R Carbonaro and P Gaudenzi. On the use of a multilayer higher-order theory for the stress analysis around a circular hole of laminates under tension. Compos. Struct. 1995; 32, 649-58.
JM Romera, MA Cantera, I Adarraga and F Mujika. Application of the submodeling technique to the analysis of the edge effects of composite laminates. J. Reinf. Plast. Compos. 2013; 32, 1099-11.
S Dölling, J Hahn, J Felger, S Bremm and W Becker. A scaled boundary finite element method model for interlaminar failure in composite laminates. Compos. Struct. 2020; 241, 111865.
CR Cater, X Xiao, RK Goldberg and X Gong. The influence of interlaminar microstructure on micro-cracking at laminate free edge. Compos. A: Appl. Sci. Manuf. 2018; 110, 217-26.
B Mohammadi and D Salimi-Majd. Investigation of delamination and damage due to free edge effects in composite laminates using cohesive interface elements. Eng. Solid Mech. 2014; 2, 101-18.
XX Li, D Tian and JH He. High energy surface as a receptor in electrospinning: A good switch for hydrophobicity to hydrophilicity. Therm. Sci. 2021; 25, 2205-12.
X Yao and JH He. On fabrication of nanoscale non-smooth fibers with high geometric potential and nanoparticle’s non-linear vibration. Therm. Sci. 2020; 24, 2491-7.
NB Peng and JH He. Insight into the wetting property of a nanofiber membrane by the geometrical potential. Recent Pat. Nanotechnol. 2020; 14, 64-70.
JH He. Seeing with a single scale is always unbelieving: From magic to two-scale fractal. Therm. Sci. 2021; 25, 1217-9.
X Li, Y Li, Y Li and J He. Gecko-like adhesion in the electrospinning process. Results Phys. 2020; 16, 102899.
JD Whitcomb and I Raju. Superposition method for analysis of free-edge stresses. J. Compos. Mater. 1983; 17, 492-507.
JT Wang and JN Dickson. Interlaminar stresses in symmetric composite laminates. J. Compos. Mater. 1978; 12, 390-402.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
