Preface

The term analysis in engineering typically means the application of an acceptable analytical procedure to a design problem based on established engineering principles. One performs analysis to verify the structural or thermal integrity of a design. Sometimes this can be done using handbook formulas or analytical procedures for simple designs. More often, however, this analysis is being performed using numerical analysis and computers to predict structural or product performance. The predominate type of engineering software used in these analyses is based on the finite element method, and this type of analysis is termed finite element analysis (FEA).

What Are Composites?

The term composite, used here, refers to fiber-reinforced plastic (FRP), manufactured from fibers and resins. Composites consist of a reinforcing material (fibers, whiskers) supported in a binder or matrix material. Fibers are the reinforcing material that provides strength in a composite material. Typical fibers include glass, graphite, and boron. Matrices are the filler (resins or glues) that bind fibers together. Typical matrix materials are epoxy, metal, ceramic, and carbon. Composites are a series of lamina or plies of varying thickness and/or materials The lamina are stacked with various orientations of the fiber direction between lamina, to obtain a laminate which has the desired directional stiffness and strength properties required for an acceptable design. The reinforcing material is normally the load carrying medium of the material, and the matrix serves as a carrier, protector, and load splicing medium around the reinforcement.

Why Use Composites?

Composite fibers are deliberately oriented in a matrix in such a way as to increase the directional structural stiffness and strength of the material. Fibers typically have high static and fatigue strength. The plies are stacked with various orientations of the fiber direction between plies to obtain a laminate which as the desired stiffness and strength properties to handle the directional flow of forces through the structure or product. Because of the variety of combinations and arrangements of the fibers and matrices, combined with the concept of lamination, designers today have greatly increased opportunities of tailoring structures and/or materials to meet systems of forces and changing environments. The most efficient configuration for a unidirectional force system is a unidirectional composite oriented in the load path direction. If loads are such that unidirectional composites are inadequate and/or inefficient, than multi-directional laminates will be required. Basic purpose of using composites is to use the directional dependent properties of the laminate effectively to transfer forces. Composites are also typically lighter than traditional structural materials and offer versatility in the fabrication process.

Complexity Of Analysis/Design

Both micro-mechanics and macro-mechanics of composite materials are required in design of composite structures and products. Micro-mechanics establishes the relation between the properties of the constituents and those of the unit composite ply. Macro-mechanics (laminate plate theory) relies on measured ply data to establish optimum laminates for a structural application. The number of ply angles must be balanced between considerations of manufacturing and cost, and the requirements for directional stiffness and strength. Composite materials may be isotropic, orthotropic or anisotropic and either homogeneous or heterogeneous. Orthotropic material properties are normally required for analysis. Material properties may vary with temperature, time, and moisture content more so than traditional structural materials.

Ply stacking sequence is important to obtain the stiffness and strength properties of the an efficient laminate. Balanced and symmetric layers prevent warping during fabrication and service. One must determine in-plane and out-of-plane stiffness properties of the total ply stack. One must also be able to transfer stiffness and compliance characteristics between ply and laminate orientations. Constitutive matrices are developed for a laminate based upon ply properties, thicknesses, and orientations. Interlaminar shear stresses are important design considerations of laminate composites. These stresses develop because of the mismatch in material properties between ply layers. Delamination between layers is a direct result of interlaminar stresses and is of particular concern at the boundary layer along the free edges of a laminate composite. Even though geometry of a part may be symmetric, non-symmetric stacking introduces cross-coupling resulting in non-symmetric displacement and stress fields.

Failure Criteria

Failure criteria are used to guide design and material improvement. Failure criteria are typically developed empirically. Failure modes in a laminate depend on ply layup, ply material, and the history of loading. It is usually not feasible to obtain the strength data from literature for an entire laminate as each laminate is unique. To analyze the strength of a laminate, strength theories are required. Lamina strength is influenced by the presence of residual stresses, stress concentrations, and interlaminar stresses which manifest themselves at the free edge of a laminate. Progressive failure of a laminate takes place from first-ply-failure (fpf) to last-ply-failure (lpf). Laminate plate theory (macro-mechanics) is used to determine first-ply-failure. Typical first-ply-failure theories include maximum stress, maximum strain, and quadratic failure criteria such as Tsai-Wu, Hoffman, and Hill.

Environmental Considerations

A change in temperature or the absorption of fluids or gases from the environment will result in a dimensional change in the lamina. When an orthotropic material (lamina) is subjected to a change in temperature or absorption induced swelling (dilation), the constitutive equations must be modified to account for stress free expansion strains. In-plane and out-of-plane coupling, present in non-symmetric laminates, causes warping under in-plane loads, for example thermal induced expansion or contraction. With mid-plane symmetric laminates, thermal expansion/ contraction introduces mid-plane strains but do not introduce bending (in-plane and out-of-plane forces are uncoupled). Only balanced and symmetric laminates can sustain a volumetric strain without producing an out-of-plane deformation. Composites are typically resistant to chemicals and corrosion.

Composite Analysis/Design

Either specialized composite design and analysis programs can be used or general purpose analysis programs, with appropriate capabilities, can be used for design and analysis of composite structures and products. It is a specialized field where a dedicated analyst, rather than a design engineer, is required. Material identification, layer thicknesses, layer location, and ply angle must be specified. Constitutive relations may be established by assuming the laminae are homogeneous, orthotropic materials and are in a plane stress state. The constitutive relation for each individual lamina must be transformed to the laminate reference axis in order to determine the laminate constitutive relationship. The end result of building a laminate is to have one material property table that can be assigned to elements in the FEA model. After solving the composite problem, post-processing is required to interrogate the results of the analysis in terms of both laminate and ply orientations.

Sequence Of FEA Analysis

• Define material properties of plies used in the laminate.
• Define ply properties from material properties and micro-mechanic procedures.
• Build plies into laminate, define laminate layup.
  • Define stacking sequence, ply groups, and stack of ply groups. Symmetric, antisymmetric and repeat stacking.
  • Specify ply material orientation so that laminate constitutive matrix can be formed.
• Assign laminate properties to FEA model, assign laminate material property table to elements.
• Define boundary conditions, loads, constraints, etc.
• Perform FEA analysis using using either specific or general purpose finite element analysis computer program.
• Display and evaluate results.
  • Access ply-by-ply stress and strain results, interlaminar shear stresses, etc.
  • Evaluate failure criteria using Hill, Hoffman, Tsai-Wu, maximum strain, etc.

Design Considerations

• Low to moderate modulus of elasticity which may not be linear in the regions of interest.
• Core material may be used to increase dimensions, increasing stiffness and strength properties of the laminate.
• Susceptibleness to deformation under long term load.
• Adequate material property data may be difficult to obtain.
• Boundary conditions may be difficult to specify.
• Laminate code must be fully understood to prevent ply configuration errors.
• Must know how published orthotropic material properties are derived.
• Structural symmetry not usable if in-plane and out-of-plane coupling exits.
• Element size at material boundary must be small enough to accurately resolve interlaminar shear stresses.