When design a racing car chassis or any other composite material made structure, there is a book that literally tells how this is made, this is the ply book. One of the information described on it is the stack-up and lay-up ones. These are extremely important and is carefully defined in the beginning of the design phase of any chassis. To understand the reason behind the these informations it is necessary to have a complete comprehension of the length scales. This article provides a summary about the multi-scale approach and its impact on the mathematical models developed to describe the composite material.

Multi-scale approach

In the material engineering, the length scale means a magnification len to look at the material and at the components. There are several length scales applied in general designing processes. The power of the magnification lens that are being used defines what can be obtained from the material. If it is being considered a length scale of the real world (in meters), it is possible to observe the behaviour of the components. For instance, the oscillations of an airplane wings due to turbulence, flutter or airfoil loads. However, if the length scale is improved to an order of centimetre (cm), this is something that allows to observe the behaviour of a thick laminate or a sandwich panel. These are a kind of a composite or mixed material structure. In the case of a sandwich panel, this is considered a structure, because from the point of view of the length scale, it behaves according to some mathematical rules used for plates. In other words, it is not being considered what is happening inside the honeycomb or the skins. Actually, this length scale is focused on the behaviour of the panel. In order to observe the behaviour inside the laminate, the length scale should be increased again, to the order of millimetre.

The length scale is where there is a section that allows to identify the number of plies and their orientations. A laminate is considered as a material if the plies are laminated in order to manufacture a specimen to test material properties, the ply properties in particular. This means that, the laminate is a rather border line between what is a structure and what is a material. If it is necessary to understand the behaviour inside a laminate, it is possible to increase the length scale even more to the level of a lamina. The lamina is just the assembly of fibers and matrix, which is considered as a homogeneous material. This is not an isotropic one, sometimes it is considered anisotropic or orthotropic one. A homogenous material is the one that, the properties are the same at every part of the lamina. These can be different regarding the direction, which is the orthotropic case, but it is even across the laminate. If the length scale is increased, it is possible to observe the heterogeneity of the material, thus how properties vary from point-to-point inside the ply. This is the smallest length scale observed for engineering purposes. The fibers can be at the order of micrometer. Therefore, the length scale of this fiber-matrix interface is of the same order of micrometers. In the case of the ply, the length scale is in the order of tenths of millimeter (Figure 1). Therefore, it is possible to observe what is occurring in a different length scale depending of what is required from the design guidelines. Considering a deep knowledge on materials, it is possible to determine or figure out the properties of the ply starting from the properties of the fibers and the matrix.

The different mathematic models allow to obtain some results from inputs for different length scales. Each of these has a different problem to be faced in terms of the stresses that have to be determined. For example, considering the microscale, the local stress in each face will be the target (Figure 1). In the case of the ply scale, the target is the average stress in the ply, which is the average stress in each phase. The laminate scale is used to calculate the average in each ply of the laminate. Above this scale, but below the structure one, it is observed the laminate as a whole. This allows to calculate the average stress in the entire laminate. Above this length scale, everything is transposed into the average stress into the structure. This is normally done by numerical methods, that allow to scale-up from small structures, as sandwich panels, to a larger ones, as a laminate. Each of these length scales has its own identification problems. For microscales, these are the statistical variations of the size and the properties of the constituents. In laboratory analysis of microstructure, what can be obtained is a regularly shaped n-size structure. This reflexes on the variability of the properties of the following scales. Hence, the strength of a ply will be affected by the statistical variation of the constituents at the microscale. When the plies are stacked-up, the stack-up sequence affects the laminate properties. The problem of the laminate is the selection of the experimentation of the identification route in order to determine the properties of the laminate. For an analysis that goes from the material scale to the structure scale, there is always the problem to find the behavioural modal for the structure made out of materials which have a quite complex behaviour. The reason is that, composite materials and also honeycombs are not very well homogeneous and isotropic materials. Actually, these are very heterogenous and anisotropic materials. Hence, for each length scale, there is a proper experimental method and mathematical model to be adopted.

References

• Mallick, P. K. Fiber-Reinforced Composites: Materials, manufacturing and design;
• Antunes Galli, C. Caracterização das Propriedades Mecânicas de Compósitos de Matriz de Epóxi com Fibras de Carbono Unidirecionais. Dissertaçao de Graduaçao – Universidade Federal do Rio de Janeiro (UFRJ). Rio de Janeiro, pg 6-9.