Chapter 7. Mechanical properties7.1. Introduction

7.2. Stress-strain concepts and behaviour7.3. Mechanical behaviour of metals

7.4. Mechanical behaviour of ceramics7.5. Mechanical behaviour of polymers

7.6. Other mechanical properties

7.7. Design and safety factor

7.1. Introduction

The mechanical behaviour of a material reflect the relationship between its response or deformation to an applied load or force.Important mechanical properties are strength, hardness, ductility and stiffness.

The mechanical properties of materials are determined by performing carefully designed lab experiments that replicate as nearly as possible the service condition.

The material users are very concerned with the material properties showing that the consistency of the values and the tests are conducted. This consistency is accomplished by using a standardized testingtechniques.

7.2. Stress – strain concepts

There are three ways in which a static load may be applied on a material; namely tension, compression and shear.

Tension load Compression load

Shear loadTorsionaldeformation

Important points

Standard sample configuration gauge lengthUTM, extensometerFast and destructive testPermanently deform and fracture

The out put of this type of test is load or force versus elongation. These load-deformation characteristics depend on specimen dimensions. To reduce experimental errors and to meet engineering needs, the load and the elongation are normalized toengineering strain and engineering stress respectively.

7.2.1. Tension test

Tensile test is the most common test in material testing because it is easy and quick to perform.

7.2.2. Compression test

The compression test is conducted in a similar method to the tensile test, except that the force is compressive. The compressive tests are used if the material is brittle and the materials will be used under a large and permanent strains.

0A

Fσ =

00

0

l

∆l

l

llε =

−=

The engineering stress or stress

The engineering strain or strain

0A

F=τShear stress

Shear strain tanθγ =

7.2.3. Shear and torsional test

Torsional tests are performed on cylindrical solid shaft or tubes and these materials will be used under twisted load.

A linear relationship of stress-strain plot is called the elastic deformation. Elastic deformation is nonpermanent, which means that when the applied load is released, the shape of the material returns to its original shape.The slope of this linear relationship is the modulus of elasticity.

Compare the modulus of elasticity of different materials.

where E is modulus of elasticity or Young’s modulus.

The stress and strain are proportional to each other through therelationship of

Eεσ = Hooke’s Law

Some materials have non-linear stress - strain curves. The modulus of elasticity cannot be determined from this curve.

tangent modulus or secant modulus.

The modulus of elasticity is proportional to the slope of a curve at the equilibrium interatomic separation (r0).

Modulus of elasticity depends on the material’s temperature

Elasticity is a time-independent phenomenon.

Anelasticity is a time-dependent behaviour. This behaviour can be clearly observed in polymers, which is called the viscoelasticbehaviour. In metals, this behaviour is relatively small and can be neglected.

The stress – strain curve of shear and torsional tests also shows an elastic behaviour.

τ = G γ

Where G is the shear modulus.

7.2.4. Poisson ratio

Poisson ratio (υ) is defined asthe ratio of the lateral and axial strains.

For isotropic materials (incmost of polycrystallines), shearand elastic moduli are related to Poisson ratio.

E = 2G (1+υ)

For anisotropic materials, theelastic behaviour varies with crystallographic direction.

z

y

z

x

ε

ε

ε

ευ −=−=

7.3.1. Tensile properties

7.3. Mechanical behaviour of metals

For most metallic materials, elastic deformation persists only to strains of about 0.005 (Hooke area).Beyond Hooke area, plastic deformation occurs, where permanent and nonrecoverable deformation occurs. Plastic deformation begins where yielding occurs.For most metals, proportional limit (P) can be shown in the transition of elastic-plastic. However, point P may not be determined precisely.

a convention to determine the elastic-plastic transitionA straight line is constructed parallel to the elastic portion of the

stress-strain curve at specific strain offset ( ε = 0.002 or 0.005)Yield strength (σy) is defined as the intersection of this line and the stress-strain curve as it bends over in the plastic region.For some metals, yield point phenomenon can be determined easily.

At the upper yield point, plastic deformation is initiated. Deformation fluctuated about some constant stress value, which is defined as lower yield point.

After yielding, the stress increases and achieves a maximum point (M). Tensile strength is the stress at the maximum on the engineering stress-strain curve.

Beyond point M, the deformation occurs uniformly throughout the narrow region of the tensile specimens and “necking” occurs, then fracture occurs on at the neck. The fracture strength relates to the fracture stress and fracture strain.Fracture strength are not normally specified for engineering design purposes.

Ductility is a degree of plastic deformation that has been sustained at fracture. Brittle material is a material that experiences very little or no plastic deformation upon fracture.

Ductility ≡ percent elongation or percent reduction area.

There are 2 important factors why ductility is important for an engineering design, they are:•Ductility indicates to a designer the degree to which the structure will deform plastically before fracture,•Ductility specifies the degree of allowable deformation during fabrication operations.

x100%l

ll%EL

0

0f

−= x100%

A

AfA%RA

0

0

−=

Where lf is the length of fracture and l0 is the original length of gauge length; Af is the cross-sectional area at the point of the fracture and A0

is the original cross-sectional area.

Table 7.2. === some tension properties of various materials

The tensile strength, yield strength and ductility depends strongly on prior deformation, the presence of impurities and heat treatment.

Resilience is the capacity of a material to absorb energy when it is deformed elastically, and then, upon unloading, to have the energy recovered.Modulus of resilience (Ur) is the strain energy per unit volume to stress a material from unloaded state up to the point of yielding.

εd σU

yε

0

r ∫=

In the elastic regionyyr εσ

2

1U = J/m3

Materials for spring application usually have high yield strength and low moduli of elasticity

Toughness is a measure of the ability of a material to absorb energy up to fracture. For a dynamic loading conditions (high strain rate), notched toughness is assessed using by an impact test.For a static loading conditions (low strain rate), toughness may be

obtained from tensile stress-strain tests the area under the σ-εcurve up to fracture.A tough material has both high strength and ductility. Ductile materials are usually tougher than brittle ones, even the brittle materials have higher tensile strength and yield.

In the neck region, the cross sectional area is decreasing rapidly.True stress – true strain scheme.

T

TA

Fσ = and

0

TT

l

llnε =

n

TT Kεσ =

See Table 7.3 for K

and n values

7.3.2. Compressive, shear and torsional deformation

Metals may experience plastic deformation under compressive, shear and torsional loads.

7.4. Mechanical behaviour of ceramics

Ceramics are brittle materials thus the behaviour is an opposite to metals.

7.4.1. Flexural properties

Ceramics fail after only about 0.1% strain so that tensile test is not suitable for ceramics. It is also difficult to prepare the ceramics for tensile test geometry. Therefore, flexural tests are more visible for ceramics. Three-point and four-point loadings are popular test for brittle materials. The important parameters from flexural test are flexural strength, modulus of rupture, fracture strength and bend strength.

The moduli of elasticity of ceramics are slightly higher than that of metal.Notice that there is no plasticity region before fracture.

Three-point loading

Ceramic material fabrication is made by compaction of powder particles into the desired shape, which means pores or void spaces will exist between the particles. Heat treatment eliminates the pore contents, however residual porosity will remain in the material.Both the strength and the modulus of most ceramics depend on theporosity with an equation of:

E = E0 (1 – 1.9 P + 0.9 P2)

where E and E0 are the moduliof elasticity of the porous and nonporous materials respectively,P is the porosity volume fraction.

Alumina silica at RT

7.5. Mechanical behaviour of polymers

Mechanical properties of polymers are highly sensitive to the rate of deformation (strain rate), the temperature, and the chemical nature of the environment. Modification of testing technique and specimen configuration are applied but most of the properties obtained from simple stress-strain tests as for metals.

thermosets

thermoplastics

elastomerics

The influence of temperature on the stress – strain behaviourof PMMA

σy TS

Slope = modulus of elasticity

Semicrystalline polymers:

Within the neck, the chain axes

become aligned parallel to the

elongation direction, which leads to

localized strengthening

7.6. Other mechanical properties

Hardness is a measure of a material’s resistance to localized plastic deformation (a dent of a scratch). Hardness test is more performed compared to other mechanical tests, because:

1. The test is simple and inexpensive,2. The test is nondestructive,3. Other mechanical properties are often estimated from hardness test.

Among the materials, the hardest materials are ceramics. Diamond has a Knoop hardness of 7000. Glass hardness is about 550 Knoop.

There are four hardness testing techniques (see Table 7.4)

Hardness conversion

Hardness conversion data have been determined experimentally and found to dependent on material types and characteristics.

7.6.1. Hardness and creep of ceramics

Among the materials, the hardest materials are ceramics. Diamond has a Knoop hardness of 7000. Glass hardness is about 550 Knoop.

The creep behaviour (time deformation) of ceramics is similar to metals but at elevated temperatures.

7.6.2. Hardness and tear strength of polymers

Polymers are softer than metals and ceramics. The hardness test are conducted by similar techniques to metals and ceramics. Rockwell is often used for polymer, followed by Durometer and Barcoll.

Tear strength is the energy required to tear apart a cut specimen that has a standard geometry. The magnitude of tensile and tear strengths are related.

7.7. Design and safety factor

The data collected from specimens of the same material are usually scattered even the procedure of the test is highly controlled.It is often desirable to specify to a typical value and a degree of scatter for some measured properties.

average value and standard deviation.

For particular application, it is determined the design stress (σd) or safe

stress (σw). For examples:

σd = N’ σc

N

σσ

y

w =

where σc is the maximum stress and N’ is the safety factor.

where σy is the yield stress and N is the safety factor.