Finite element method analysis of fibremetal laminates considering different approaches to material model
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Abstract
In this work, different approaches to fibremetal laminates modelling are presented. Micromechanical, mesomechanical and macromechanical models are discussed. The application of these approaches for exemplary fibremetal laminate made of aluminium and epoxy resin/glass fibre layers are shown. The classical laminate theory was used to obtain engineering constants for the macroscopic solid model and Puck criterion to obtain material data about epoxy resin/glass fibre layer. Various simulations using different simulation techniques were carried out in Simulia ABAQUS environment and results were compared with experimental data found in the literature. In conclusions, described approaches from the viewpoint of numerical simulation and experiment were evaluate. Research proves that mesoscopic (with distinguished layers of material) approach along with solid model gives the best results.
Keywords
Fibremetal laminates FML FEM Composites Laminates1 Introduction
Fibremetal laminates (labelled often as FML) are a relatively new group of materials. FMLs are structural composites that have the form of a laminate. The key characteristic of this material is the fact that this is composed of both metal and composite layers, which is the reason why they are often called hybrid composites. In present aluminium and ordinary composites materials (i.e. matrix reinforced with fibres) can be used in constructions instead of steels for cost and weight reduction purposes. However, the use of these materials also has some disadvantages such as poor fatigue strength in aluminium, low impact strength, and low residual strength. To minimize these disadvantages, it was proposed to use both materials at the same time. Researchers from Delft University of Technology showed that the rate of crack growth is lower in the material formed by bonded layers than in a homogeneous material [1].
Fibremetal laminates as relatively new materials are not yet widely used in all branches of industry. The main obstacle is the high price and technical difficulties in processing, which is the reason why they are currently only used on a larger scale in the aviation industry. In the Airbus A380 version, 800 large sections of the plating are made of a fibremetal laminate called Glare [1] [2]. Other FML material called ARALL was used in Boeing C17 Cargo and Fokker 27 constructions [1] [3].
Initially, research in aircraft industry was conducted i.e. [4]. In the last few years, an increasing number of research projects in the area of fibremetal laminates can be observed. Papers are focused on various issues i.e. delamination process [5], lowvelocity impact behaviour [6] or fatigue [7].
2 Approaches to modelling fibremetal laminates in simulation using the finite element method

Micromechanical—in this approach individual materials are differentiated in the model including fibres and matrix. This is the most complex approach of all described. Potentially, it is the most realistic as well, but it requires partitioning model into a lot of very small parts. This can be unfavourable so it is usually better to consider the next two approaches.

Mesomechanical—in this approach a laminate was considered as a system of independent layers with specific mechanical properties. Similar to the previous approach there is some simplification in skipping the issue of layers boundary. But in fact, we don’t consider it until delamination process occurs, so within the scope of the application, it is not a critical problem. The criteria of decohesion is another important issue in describing fibremetal laminates and will be the subject of future works.

Macromechanical—in this approach it was described the laminate as a homogeneous body with anisotropic mechanical properties. This approach can be described as a generalization. A very simple model of material is generated—whole fibremetal laminate is described using a few engineering constants.
The mesomechanical model can be realised in ABAQUS in various ways. For thin objects, it is possible to use the shell model. In such a model structure of laminate is represented by Composite Layup. In this layup, there are defined all layers and their parameters such as orientation, thickness, material data, and relative location. Another possibility is to use a solid model. Using partitioning tool separated layers were extracted and all material data was defined for each of these layers separately. Regardless of the model choice, it is crucial to define local material orientation.
3 Classical laminate theory

Perfect joint with no thickness between layers,

No interlayer shear effect,

No slip between layers,
 Meeting the assumptions of the thin plate theory, i.e.:

No length and deformation change of the central plane,

Points contained in the normal direction to the plane also contained in this direction after deformation,


Stresses in the normal direction to the central plane are insignificantly smaller compared to inpane stresses.

In the plane of this layer determined by the directions x, y, i.e. tensile or compressive forces \(\left( {N_{x} , N_{y} } \right)\) and shearing forces \(\left( {N_{xy} } \right)\),

Bending (moments \(M_{x} , M_{y}\)) and twisting (\(M_{xy}\)).

Matrix A—stiffness tensile matrix, it is the only one having nonzero components when the material is in the membrane state of stress. The definition of its components is given in the formula (4). Summation by layers (with thickness denoted as \(z_{k}\)) makes it possible to reproduce the structure of the material;

Matrix B—connection stiffness matrix or Coupling Stiffness Matrix. It allows determining the mutual influence of tensioning (compression) and bending. Components of this matrix are zero when there is no bending at perfect stretching. This is possible for objects that are symmetrical in relation to their central plane both in geometry and material. The definition of its components is given by formula (5);

Matrix D—bending matrix. It is the only one that has nonzero components when the material is loaded with only bending and torsional moments. The definition of its components is given by the formula (6).
The assignation of engineering constants enables the presentation of a laminar material in the form of a homogeneous material with anisotropic properties defined by these constants.
4 Numerical analysis of threepoint bending of fibremetal laminates
In this article, there are presented different approaches that vary in complexity and accuracy. To present the difference between these approaches numerical simulations in Abaqus Simulia environment were conducted. In the work of Ostapiuk et al. [11] results of threepoint bending experiments are presented. The subject of this research was fibremetal laminates based on aluminium (2024 T3) and carbon fibre in epoxy resin. It was chosen the same material, so results of numerical simulations using different methods can be compared with the experimental one.
Mechanical properties of used material
Chemical composition of 2024 T3 alloy [14]
Component  Al  Cu  Mg  Mn  Si  Fe  Zn  Ti  Cr 

\(W_{t} \left[ \% \right]\)  90.7–94.7  3.8–4.9  1.2–1.8  0.3–0.9  max. 0.5  max. 0.5  max. 0.25  max. 0.15  max. 0.1 
Matrix ABD of laminate \([{\mathbf{Al}} 2024 {\mathbf{T}}30_{2}^{{\varvec{CFRP}}} ]_{\varvec{s}}\) with a thickness of aluminium layer equal to 0.3 mm
Reverse matrix to matrix ABD of laminate \([{\mathbf{Al}} 2024 {\mathbf{T}}30_{2}^{{\varvec{CFRP}}} ]_{\varvec{s}}\) with a thickness of aluminium layer equal to 0.3 mm
Mechanical properties of the homogeneous model
\(E_{1}\) (MPa)  \(E_{2}\) (MPa)  \(G_{12}\) (MPa)  \(\vartheta_{12}\) (–)  \(\vartheta_{21}\) (–)  

\([{\mathbf{Al}} 2024 {\mathbf{T}}30_{2}^{{\varvec{CFRP}}} ]_{\varvec{s}}  Al 3mm\)  76,417  64,482  23,460  0.345  0.295 
\([{\mathbf{Al}} 2024 {\mathbf{T}}30_{2}^{{\varvec{CFRP}}} ]_{\varvec{s}}  Al 5mm\)  71,743  67,097  24,662  0.35  0.327 
5 Results and discussion
Numerical simulations were conducted for the mediumfine mesh. Minimum 4 elements in case of thin layer and minimum 2 elements in case of thick layer were used. In the case of shell models, 5 integration points in each layer were used. It was researched that in this case using more fined mesh gives only slightly more smooth curves and no apparent difference in results. Results were acquired every 0.05 mm displacement of the stamp.
6 Conclusions
Different methods of fibremetal laminates modelling in the numerical environment were shown in this article. The mesoscopic approach gives better results (i.e. more convergent with experimental results) than the macroscopic approach. However, both of these methods are in good compliance with real measurement in the elastic range, so in the area of applicability of described materials. In some cases, proposed models become divergent with experimental results in case of large displacement of the stamp. It is caused by a decohesion process which occurs in the real specimen—especially delamination process. The issue of modelling destruction process will be examined by authors in future works.
Notes
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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