Chapter 7. Mechanical properties
7.1. Introduction
7.2. Stress-strain concepts and behaviour 7.3. Mechanical behaviour of metals
7.4. Mechanical behaviour of ceramics 7.5. 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 testing techniques.
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 load
Torsional deformation
Important points
Standard sample configuration gauge length UTM, extensometer
Fast and destructive test
Permanently 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 to engineering 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.
A
0σ = F
0 0
0
l
∆l l
l ε l− =
= The engineering stress or stress
The engineering strain or strain
A
0= F
Shear stress
τ
Shear strain
γ = tanθ
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 the relationship of
σ = Eε
Hooke’s LawSome 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 viscoelastic
behaviour. 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 as the ratio of the lateral and axial strains.
For isotropic materials (inc
most of polycrystallines), shear and elastic moduli are related to Poisson ratio.
E = 2G (1+υ)
For anisotropic materials, the elastic behaviour varies with crystallographic direction.
z y z
x
ε ε ε
υ = − ε = −
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 transition A 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 l
%EL l
0 0
f
−
= x100%
A Af
%RA A
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.
ε d σ U
εy
0 r
= ∫
In the elastic region r
σ
yε
y2
U = 1
J/m3Materials 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-ε
curve 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
T
A
σ = F
and0 T
T l
ln l
ε =
σ =
TKε
TnSee 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 the porosity with an equation of:
E = E0 (1 – 1.9 P + 0.9 P2) where E and E0 are the moduli of 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 behaviour of 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 σw = σy
where σc is the maximum stress and N’ is the safety factor.
where σy is the yield stress and N is the safety factor.
