Bài giảng Mechanics of Composite Material_9_2015

Introduction to composite materialsMechanical behaviors of composite materials Elastic behaviour of unidirectional composite materials Elastic behaviour of orthotropic composite Off-axis

Assoc Prof Dr Nguyen Trung Kien Email: kiennt@hcmute.edu.vn , https://fceam.hcmute.edu.vn

Faculty of Civil engineering and Applied mechanics HCMC University of Technology and Education

1 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Vietnam

September 2015

Materials

Introduction to composite materials

Mechanical behaviors of composite materials

Elastic behaviour of unidirectional composite materials Elastic behaviour of orthotropic composite

Off-axis behaviour of composite materials

Fracture and damage of composite materials

Modeling of mechanical behaviours of laminated plates Homogenization of composite materials

Jean-Marie Berthelot, Composite Materials–Mechanical behavior and Structural analysis, Springer, 1999

J N Reddy, Mechanics of laminated composite plates and shells–Theory and Analysis, CRC Press, 2004

Autar K Kaw, Mechanics of Composite Materials, Taylor & Francis, NewYork, 2006

S LI, Introduction to micromechanics and nanomechanics, Lecture notes.

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Investigation of characteristics of the constituent and composite materials

Introduction to composite materials

Mechanical behaviors of composite materials

Elastic behavior of unidirectional composite materials Elastic behavior of orthotropic composite

Off-axis behavior of composite materials

Fracture and damage of composite materials

Modeling of mechanical behaviors of laminated plates Homogenization of composite materials

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Composite materials

o Matrix materials

o Fibers

o Architecture of composite materials

o Study the mechanical behavior of composite

materials

Application of composite materials

Old and new aspects of

composites

o Human body, plants

o Early 1960s (fibrous composites)

Definition:

“Composite” means "made of two or

more different parts heterogeneous

All materials may be considered

heterogeneous if the scale of interest is

sufficiently small

Fibrous composites (Fiber-Reinforced

Composites) are materials in which one

phase acts as a reinforcement of a second

phase

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Organic matrix composites

Metallic matrix composites

Mineral matrix composites

Continuous phase (matrix)

Dispersed phase (reinforcement)interphase

Particle composite

Fiber composite

Classification by class of constituents

Fiber Reinforcement Matrix Composite

Mechanical properties of composites

nature of the constituents

proportions of the constituents

orientation of the fibers

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Low-medium performance composites

The reinforcement provides stiffening and local strengthening of the materials (short fiber)

The matrix is the main load bearing constituent governing the mechanical properties

High performance composites

The reinforcement is the backbone of the materials (continuous fiber)

The matrix provides protection and support for the sensitive fiber The interphase controls the failure mechanisms

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Nonhomogeneous anisotropic No conventional method

Structural analysis tool for composites required

Polymer Metal (higher use temperature) Ceramics (very high use temperature)

Matrix: a resin (polyester, epoxide, etc.) and fillers which

is to improve the characteristics of the resin:

o Thermosetting Resins:

Polyester Resins Condensation Resins Epoxide Resins

1 Good mechanical properties

2 Good adhesive properties

3 Good toughness properties

4 Good resistance to environmental degradation

Any resin system for use in a composite material

will require the following properties:

Epoxide Resins:

Advantages of epoxide resins are the following:

good mechanical properties (tension, bending, compression, shock, etc.) superior to those of polyesters

good behavior at high temperatures: up to 150-190°C in continuous use excellent chemical resistance

low shrinkage in molding process and during cure (from 0.5-1 %)

very good wettability of reinforcements

excellent adhesion to metallic materials

Disadvantages:

High cost, manufacture, sensibility to cracking

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Polypropylene, polyamide:

Advantages of epoxide resins are the following:

low cost, fabrication

Disadvantages:

mechanical and thermomechanical properties : low

Limited development

Thermostable Resins: Bismaleimide Resins, Polyimide Resins

Thermal performance developed especially in the aviation and space

Fillers and additives: function of improving the mechanical and

physical characteristics of the finished product or making their manufacture easier

Fillers: Reinforcing Fillers, Nonreinforcing Fillers

o Reinforcing Fillers : improve the mechanical properties of a resin

Spherical fillers: diameter usually lying between 10 and 150 µ m They can be glass, carbon, or organic (epoxide, phenolic, polystirene, etc.),

Nonspherical fillers: mica used most (dimension: 100-500 µ m, thickness: 1-20

µ m)

o Nonreinforcing Fillers: reducing the cost of resins, preserving their

performance carbonates, silicates

Additives: pigments and colorants, antishrinkage agents,

antiultraviolet agents

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Improve mechanical characteristics: stiffness,strength, hardness, etcImprove certain of the physical properties: thermal properties, fire

resistance, resistance to abrasion, electrical properties

Reinforcements origins: vegetable, mineral, artificial, synthetic fiberslinear forms (strands, yarns, rovings, etc.)

surfacing tissues (woven fabrics, mats, etc.)

multidirectional forms (preforms, complex cloths, etc.)

Specific mechanical characteristics of materials, made

in the form of fibers

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Specific mechanical characteristics of materials, made

in the form of fibers

Architecture of composite materials

Laminates

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Architecture of composite materials

o Sandwich

Laminated composite materials

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Study the mechanical behavior of composite materials

"Further Possibility to Use CFRP parts

on Commercial Aircraft"

Airplane manufacturers now plan to expand use

of CFRP Airbus's A380s, the new wide-body

plane, and Boeing's Sonic Cruisers shall be the

state of the art examples Use of CFRP for

airplane parts will be developed further and

further toward the future.

Aircraft flooring panels

Aircraft/Aerospace:

In aerospace field, which demands material

light in weight and of high rigidity, the H-IIA

rocket adopts CFRP parts

Aircraft/Aerospace:

Composite materials can be used in a

number of applications within the

transportation market from exterior door

panels, radiators and ignition components

on passenger vehicles, to the side panels

on light- and heavy - duty trucks

The benefits of using composites include

greater fuel efficiency, corrosion resistance,

low weight and high strength

Transportation

McLaren Formula 3 bodywork

in carbon fiber Composite wings & boot

Glass/Phenolic Honeycomb

Sandwich Panels

Honeycomb sandwich panel

has superior flexural stiffness,

buckling resistance, and light

weight

Light Weight Interior

& Exterior Panels for

Rail Way Vehicles.

Composite materials can be used

in a variety of applications in the

marine market, including the materials

used in the construction, maintenance,

repair and equipping of powerboats,

sailboats and other crafts

Composites bring a myriad of benefits to

marine applications, including high strength,

reduced weight, corrosion resistance,

dimensional stability and design flexibility.

Marine

Baja Marine Manufactures composite high-performance powerboats, with Sophisticated In-gel graphics that have become the company’s trade mark.

Turbine blades(32-39m)

The Blade Factory in Nakskov, Denmark.

As reliable, cost effective, environmentally

friendly power source, wind energy provides

many benefits.

It's Not surprising that over the last decade

utilization of wind power has expanded at the

impressive rate of 20 percent per annum

Wind Energy

Composite applications for electrical and

electronics markets include light poles,

circuit boards, electrical junction boxes

and ladder rails

The benefits of using composites in these

applications include high strength, low weight,

dimensional stability, design flexibility, cost

performance and corrosion resistance.

Electrical/Electronic

Leisure/Sports

Increasingly, composites can be found in a variety

of consumer goods, particularly recreational and

sporting goods products

The benefits of using composites for consumer goods

include strength, low weight, resilience, flexibility and

Medical

At the medical worksite, CFRP is widely used

for X-ray inspection equipment making use of

its X-ray permeability

Furthermore, CFRP is used for surgical outfits such as artificial legs and

braces utilizing its mechanical features.

Features of CFRP, lightweight and easy to handle, increases its use for welfare

equipment such as wheel chairs, care beds and portable slope.

Many of today’s construction needs are being met with products that have

fiberglass yarns at the core

The ever growing needs of the construction market make fiberglass yarns

a natural choice for material selection and product development.

“Desert Flower” dome in composites

to respond to all situations

Uses of fiberglass yarns in the

construction market include the

following applications:

»Architectural fabric structures

»Roofing scrim

»Insect and solar screening

»Decorative wall covering

»Reinforced facings and foils

»Dry wall tape and patch

Architectural fabric structures

Roofing scrim

Air dome which is membrane structure has been

advanced very rapidly in USA from 1960th and

proven permanent structure to have durability

and non-flammability characteristics

Seoul World Cup Stadium

Gratings and planksStrong, lightweight structures

Walkway on purifying

plant Plank

Plank with quartz sand coating for optimum non-slip surfaces

Bridge over purifying plant

in glass fiber reinforced

Materials

Composite structure

of the West Mill Bridge(UK)

Europe’s First Composite Highway

Bridge Opens In Oxfordshire

Structural profile made from glass and carbreinforced polymer

on fiber

Aluminum Honeycomb

New external construction material

Heartwood honeycomb structure

Earthquake-Resistant Reinforcement of Piers

Using Carbon Fiber Sheet

Drinking Water & Aqua Duct

Industrial & Irrigation

Gravity Pipe/ Pressure Sewerage

Storm Water Pipe

Power Plant Circulation & Cooling

Aboveground Pipe & Irrigation

Chemical Sewer & Slurry Pipeline

Vessel Pipe Line

Pipeline & Undersea Tunnel

High Strength

Anti-Corrosive Multi Applicable

Compatibility

GRP Pipe

GRP Pipe Manufacturing Process & Installation

Introduction to composite materials

Mechanical behaviors of composite materials

Elastic behavior of unidirectional composite materials Elastic behavior of orthotropic composite

Off-axis behavior of composite materials

Fracture and damage of composite materials

Modeling of mechanical behaviors of laminated

plates

Homogenization of composite materials

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Linear elastic scheme

Elastic behavior of a unidirectional composite material Elastic behavior of an orthotropic composite material

Elastic behavior of composite materials outside of main axes

Strength failure theories

Linear elastic scheme

o Stiffness and compliance matrix

C, S 6x6-matrix is called the

stiffness matrix and compliance matrix having 21 independent

constants: S = C-1

Change of coordinate system

Rotation of a ɵ angle of coordinate

system around 3-axis

where

Vector:

Tensor:

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Mechanical behaviors of composite materials

Change of coordinate system

Rotation of a ɵ angle of coordinate

system around 3-axis

Change of coordinate system

Mechanical behaviors of composite materials

Engineering Matrix Notation

Stress:

Strains:

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Note that these constants can vary

from point to point if the material is

nonhomogeneous

Monoclinic material

Note:

A monoclinic material is a material that has a symmetry plane

13 independent elastic constants

1–2 symmetry plane of a monoclinic material

Orthotropic material

Note:

Three mutually perpendicular planes of material symmetry

9 independent elastic constants

Transverse isotropic material (Unidirectional material)

Note:

Orthotropic material having one axis of revolution

5 independent elastic constants

Isotropic material

Note:

Properties are independent of the choice of its reference axis

2 independent elastic constants

Exercise 1: In the case of a monoclinic material with the symmetry plane (1,2) show that the stiffness matrix has the form (a).

Exercise 2: The symmetry plane (1,3) is added to a monoclinic

material in order to obtain an orthotropic material Show that the stiffness matrix has the form (b)

Exercises 3: Consider a rotation through an angle e about the I-axis

of an orthotropic material Write the stiffness matrix in the new axes and deduce the form (a) of the stiffness matrix of a transverse

isotropic material.

Exercise 4: In case of isotropic material, show that the stiffness

matrix has the form (b)

C1 : Introduction to composite materials

C2 : Mechanical behaviors of composite materials

C3 : Elastic behavior of unidirectional composite materials

C4 : Elastic behavior of orthotropic composite

C5 : Off-axis behavior of composite materials

C6 : Fracture and damage of composite materials

C7 : Modeling of mechanical behaviors of laminated plates

C8 : Homogenization of composite materials

Effective moduli:

Microscopic scale : scale of constituents

Macroscopic scale of size δ : properties of the material can be averaged to a good approximation The properties measured in a sample of size δ are independent of the place (of the point)

Homogenized problems of designing structures can be solved by considering the average properties measured on the scale δ

Macroscopic homogeneity or statistical homogeneity Homogenization.

Microscopic ↔ Macroscopic

How to determine the homogenized properties

Phenomenological approach

Homogenization method

An element of volume V and size δ :

Basic equations of the average strain and stress field:

C: Effective stiffness matrixS: Effective compliance matrix

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Homogenization method: 3 main stages

• Representative Volume Element (RVE)

• Localization problem

• Homogenization

Localization problem of periodic composites

Resolution method of the elastic problem on a unit cell: FEM, Fourier

(Gusev, Kanit et al., Suquet et al., Mishneavsky, etc)

Strain energy:

Macroscopic constitutive equation:

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Unidirectional composite material

Engineering constants: Young's moduli (E), Poisson

Longitudinal Tensile Test

Stress and strain:

Elastic moduli:

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Transverse tensile test

Stress and strain:

Elastic moduli:

(ν21)(ν23)

Nota:

Longitudinal shear test

Stress and strain:

Lateral hydrostatic compression

Stress and strain:

Lateral compression modulus:

Moduli as functions of the stiffness

Only 5 independent moduli, practically: EL, ET, νLT, GLT, GTT'

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Moduli as functions of the stiffness

Stiffness as functions of Moduli

Different approach to the problem

Find 5 independent constants as functions of the mechanical and geometric properties of the constituents (engineering constants of the matrix and fibers, volume fraction of the fibers),…

Periodic fiber arrangements:

Random fiber arrangements:

How to estimate elastic constants ?

Estimation of elastic constants:

Bounds (upper and lower bounds) using energy variational

theorems (total potential energy theorem, Hashin-Shtrikman,…) : not accurate for high contrast of materials

Exact solutions: simple geometry

Numerical methods (FEM, Fourier)