MDME: MANUFACTURING, DESIGN, MECHANICAL ENGINEERING

# PROPERTIES OF MATERIALS

A PROPERTY of a material is the same anywhere on the material, regardless of size or shape. Examples of properties: color, density, strength. Examples of NON-properties: mass, length.

 Image Video Lesson Description and Link Duration Date Download Mechanical Properties 24:49 min 20140723 Mechanical Properties-Fatigue 20:16 min 20140723

## Introduction

When a material is subject to forces (loads), they will deform (elongate, compress, twist) by some amount. It may be a small amount, but never zero. Engineers calculate these forces in order to predict the behaviour of the materials.

Materials scientists learn about these mechanical properties by testing materials. Results from the tests depend on the size and shape of material to be tested (specimen), how it is held, and the way of performing the test. That is why we use common procedures, or standards, such as NATA.

What is a Property?
A property is something that will be measured the same regardless of the size of a piece of material. For example, density is a property, but mass is not.

Important Properties for Engineering
There are many material properties used for all sorts of things, like how well the material conducts heat, or magnetism, or resists electricity or how much it expands with heat etc etc. (Thermal conductivity, Magnetic permeability, Resistivity, Coefficient of thermal expansion etc)
Mechanical properties are more focussed on how the material behaves under stress. Here are the key properties;

#### Elasticity

The ability of the material to return to its original size (or shape) after being deformed. (stretched, compressed, twisted, bent etc) Rubber is elastic, so is glass and spring steel

#### Plasticity

The ability of the material to be deformed and stay like that after load is removed. (Opposite of elasticity)  Lead is quite plastic.
There are some specific types of plasticity.
Ductility = tensile plasticity. A material that can be stretched. (Like chewing gum - it stretches when you pull it). Good examples are copper, and plastics like polypropylene.
Malleability = compressive plasticity. A material that can be compressed or hammered. (Like wet clay - it squashes when you press it, but doesn't stretch much). Engineering example; lead. Most  plastic materials show a bit of both - ductile and malleable.

#### Stress

The intensity of force inside a solid material. It is just like pressure except that it has a set direction (wheras pressure is in every direction). Stress acts through a cross-section of the material where the forces are applied on EACH SIDE of that cross-sectional area. So there is a SET of 2 forces  - when they are pulling it is tensile, if they push towards each other it is compressive. Definition of Stress f = F / A    where f  is the average stress, also called engineering or nominal stress, and F  is the force acting over the area - and perpendicular to it. The SI unit for stress is the pascal (symbol Pa), which is a shorthand name for one newton (Force) per square metre (Unit Area). The unit for stress is the same as that of pressure, which is also a measure of Force per unit area. Engineering quantities are usually measured in megapascals (MPa) or gigapascals (GPa). We always work in Newtons (N) and mm, which gives the stress in MPa, because 1 MPa = 1N / 1mm2. Example: In the diagram at left, assume a force of 2000N up and 2000N down. The area of cross-section is 50 square mm.   Stress = 2000 / 50 = 40 MPa

Strength: The amount of Stress a material can 'take'. Where 'take' might be before it breaks, before it deforms permanently, etc
Yield Strength: The stress that makes the material begin to have some plasticity.
Ultimate Strength. The highest stress the material can get to - any more and it will break.
Tensile Strength. Pulling - yield or ultimate.
Compressive Strength: Compressing strength
Shear Strength: Sliding or distorting, twisting. Yield or ultimate.
Fatigue Strength: The stress the material can handle when applied on and off many times.

#### Strain

The relative stretch of a material. It the material started with a length L, the amount of change (deformation) is x as a result of a tensile or compressive stress. This is not a property because it depends on how long the object is, so we have a property Strain,  e,  where

e = x/L

#### The Stress/Strain Curve

Elastic deformation. When the stress is removed, the material returns to the dimension it had before the load was applied. Valid for small strains (except the case of rubbers).
Deformation is reversible, non permanent.
Plastic deformation. When the stress is removed, the material does not return to its previous dimension but there is a permanent (irreversible) deformation. The following animation shows a lattice of atoms (such as in a metal). There are only 2 ways to distort the atoms - axial (tension and compression) and shear (sideways).

#### Stiffness

In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's law:
E=f/e E is the slope of the stress-strain curve, called Young's modulus or modulus of elasticity. In some cases (especially plastics and high speed loadings), the relationship is not linear so that E can be defined alternatively as the local slope:  E = df/de

Shear stresses also produce strains according to:  G=f/e
where G is the shear modulus.

Elastic moduli measure the stiffness of the material. They are related to the second derivative of the interatomic potential, or the first derivative of the force vs. internuclear distance. By examining these curves we can tell which material has a higher modulus. Due to thermal vibrations the elastic modulus decreases with temperature. E is large for ceramics (stronger ionic bond) and small for polymers (weak covalent bond). Since the interatomic distances depend on direction in the crystal, E depends on direction (i.e., it is anisotropic) for single crystals. For randomly oriented policrystals, E is isotropic.

Anelasticity

Here the behavior is elastic but not the stress-strain curve is not immediately reversible. It takes a while for the strain to return to zero. The effect is normally small for metals but can be significant for polymers. This is a type of friction effect and is sensitive to the speed of loading.

Poisson's Ratio (lateral shrinking)

Materials subject to tension shrink laterally. Those subject to compression, bulge. The ratio of lateral and axial strains is called the Poisson's ratio n.  n = elateral/eaxial

The elastic modulus, shear modulus and Poisson's ratio are related by E = 2G(1+n), so Poisson's ratio can be worked out from measurements of G and E.
Tensile Properties Yield point. If the stress is too large, the strain deviates from being proportional to the stress. The point at which this happens is the yield point because there the material yields, deforming permanently (plastically) Yield stress. Hooke's law is not valid beyond the yield point. The stress at the yield point is called yield stress, and is an important measure of the mechanical properties of materials. In practice, the yield stress is chosen as that causing a permanent strain of 0.002 (strain offset, Fig. 6.9.) The yield stress measures the resistance to plastic deformation

Plastic deformation:
The reason for plastic deformation, in normal materials, is not that the atomic bond is stretched beyond repair, but the motion of dislocations, which involves breaking and reforming bonds. Plastic deformation is caused by the motion of dislocations.
Tensile strength. When stress continues in the plastic regime, the stress-strain passes through a maximum, called the tensile strength (sTS) , and then falls as the material starts to develop a neck and it finally breaks at the fracture point (Fig. 6.10).  Note that it is called strength, not stress, but the units are the same, MPa. So strength is a certain stress a material can take.For structural applications, the yield stress is usually a more important property than the tensile strength, since once the it is passed, the structure has deformed beyond acceptable limits.
Ductility. Tensile Plasticity. The ability to deform before braking. It is the opposite of brittleness. Ductility can be given either as percent maximum elongation emax or maximum area reduction.  %EL = emax x 100 %,   %AR = (A0 - Af)/A0   These are measured after fracture (repositioning the two pieces back together).
Malleability. Compressive Plasticity.
Toughness. Ability to absorb energy up to fracture. The energy per unit volume is the total area under the strain-stress curve. It is also measured by an impact test.
Resilience. Capacity to absorb energy elastically. The energy per unit volume is the area under the strain-stress curve in the elastic region.

True Stress and Strain. When one applies a constant tensile force the material will break after reaching the tensile strength. The material starts necking (the transverse area decreases) but the stress cannot increase beyond sTS. The ratio of the force to the initial area, what we normally do, is called the engineering stress. If the ratio is to the actual area (that changes with stress) one obtains the true stress.

Elastic Recovery During Plastic Deformation.
If a material is taken beyond the yield point (it is deformed plastically) and the stress is then released, the material ends up with a permanent strain. If the stress is reapplied, the material again responds elastically at the beginning up to a new yield point that is higher than the original yield point (strain hardening, Ch. 7.10). The amount of elastic strain that it will take before reaching the yield point is called elastic strain recovery

Compressive, Shear, and Torsional Deformation.
Compressive and shear stresses give similar behavior to tensile stresses, but in the case of compressive stresses there is no maximum in the s-e curve, since no necking occurs.

Hardness. Hardness is the resistance to plastic deformation (e.g., a local dent or scratch). Thus, it is a measure of plastic deformation, as is the tensile strength, so they are well correlated. Historically, it was measured on an empirically scale, determined by the ability of a material to scratch another, diamond being the hardest and talc the softer. Now we use standard tests, where a ball, or point is pressed into a material and the size of the dent is measured. There are a few different hardness tests: Rockwell, Brinell, Vickers, etc. They are popular because they are easy and non-destructive (except for the small dent).

Variability of Material Properties.
Tests do not produce exactly the same result because of variations in the test equipment, procedures, operator bias, specimen fabrication, etc. But, even if all those parameters are controlled within strict limits, a variation remains in the materials, due to uncontrolled variations during fabrication, non homogenous composition and structure, etc. The measured mechanical properties will show scatter, which is often distributed in a Gaussian curve (bell-shaped), that is characterized by the mean value and the standard deviation (width).

Design/Safety Factors. To take into account variability of properties, designers use, instead of an average value of, say, the tensile strength, the probability that the yield strength is above the minimum value tolerable. This leads to the use of a safety factor N > 1 (typ. 1.2 - 4). Thus, a working value for the tensile strength would be sW = sTS / N.

Grades are stamped into the head of the bolt (for high strength bolts). The larger the number, the stronger the bolt. The first number is the ultimate tensile strength (UTS)  in 100 x MPa. The second number (if shown) is the yield strength (YS) as a proportion of UTS.  So, for 8.8 bolt, UTS=800MPa, YS = 0.8x800 = 640MPa.  More details given below

 Grade Nominal Size Proof Stress YS UTS Hardness R (core) Min. Max. 4.6 M5-M100 225 240 400 B67 B95 4.8 M1.6-M16 310 340 420 B71 B95 5.8 M5-M24 380 420 520 B82 B95 8.8 M16-M72 600 660 830 C23 C34 9.8 M1.6-M16 650 720 900 C27 C36 10.9 M5-M100 830 940 1040 C33 C39 12.9 M1.6-M100 970 1100 1220 C38 C44

### Fatigue

If stress is cycled on and off, the material can fail at a much lower stress than the yield or ultimate strength. This is due to fatigue - the slow growth of a crack each time the load is re-applied. If stresses are low, and the number of cycles is high, we use the S-N diagram, or Wohler diagram. (High = 100,000 or more) The S-N diagram plots stress S versus cycles to failure N.  The graph is usually displayed on a log-log plot, with the actual S-N line representing the mean of the data from several tests.

Endurance Limit: (Material A) Some materials have a fatigue limit or endurance limit  - the stress level below which the material never fails. This is characteristic of steel and titanium in benign environmental conditions.

Many non-ferrous metals and alloys, such as aluminum, magnesium, and copper alloys, do not exhibit well-defined endurance limits.  These materials instead display a continuously decreasing S-N response, similar to Curve B above.  In such cases a  fatigue strength Sf for a given number of cycles must be specified.  An effective endurance limit for these materials is sometimes defined as the stress that causes failure at 1E8 or 5E8 loading cycles.

The concept of an endurance limit is used in infinite-life or safe stress designs. It is due to interstitial elements (such as carbon or nitrogen in iron) that pin dislocations, thus preventing the slip mechanism that leads to the formation of microcracks.  Care must be taken when using an endurance limit in design applications because it can disappear due to:
• Corrosive environments (due to fatigue corrosion interaction)
• High temperatures (mobilize dislocations)
The endurance limit is not a true property of a material, since other significant influences such as surface finish cannot be entirely eliminated.  However, a test values (Se') obtained from polished specimens provide a baseline to which other factors can be applied. Influences that can affect (i.e. decrease) the endurance limit include:
• Surface Finish (rough)
• Temperature (higher)
• Stress Concentrations (geometry that increases stress)
• Size (larger)
Fatigue usually begins from a stress concentration at the surface. The fatigue cracks grow slowly and usually leaves a striated pattern that looks like a smooth sea shell. Then, when the crack has gone far enough, the object will break suddenly due to the stress in the small remaining area exceeding the ultimate strength. This sudden fracture will usually look different - rough or torn looking. #### Creep

Creep is the slow stretching of a material over time - especially at "high temperature".  Boilers, gas turbine engines, and ovens are some of the systems that have components that experience creep. For some materials "high temperature" could be room temperature - like lead. Many plastics is also very prone to creep. Failures involving creep usually involves deformation, but failures may appear ductile or brittle. In a creep test a constant load is applied to a tensile specimen maintained at a constant temperature.  Strain is then measured over a period of time.  The slope of the curve, identified in the above figure, is the strain rate of the test during stage II or the creep rate of the material.

Primary creep, Stage I, is a period of decreasing creep rate.  Primary creep is a period of primarily transient creep.  During this period deformation takes place and the resistance to creep increases until stage II.  Secondary creep, Stage II, is a period of roughly constant creep rate.  Stage II is referred to as steady state creep.  Tertiary creep, Stage III, occurs when there is a reduction in cross sectional area due to necking or effective reduction in area due to internal void formation.

## Quiz Study: (Multiple choice questions)

1. Ability of a material to be deformed and then return to its original size after removing the load.
2. Ability of a material to resist indentation or abrasion.
3. Ability of a material to sustain a high load for its size.
4. A material that requires a high stress to deform a small amount is...
5. Ultimate Tensile Strength is a measure of the ........ a material can take.
6. A material that takes a lot of energy to break has a high level of...
7. A tough material will exhibit both...
8. The ability of a material to absorb energy without permanent deformation.
9. Percentage elongation is a measure of a material's...
10. The rate of creep is higher when you increase ...
11. Which of the following would most likely be a CREEP problem?
12. Deformation that increases gradually is likely to be due to...
13. A crack which grows gradually through a shaft is likely to be due to...
14. Shot peening of springs is used to...
15. How does shot peening work?
16. What is a Fatigue Strength?
17. What is the Endurance Limit?
18. Which of the following would most likely be a FATIGUE problem?
19. Which graph indicates Mild Steel?
20. Which is FALSE?
21. The slope of the curve up to the yield point tells you the ...
22. The area under the entire stress-strain curve is an indication of a material's ...
23. Yield Point: Which is ... F A L S E ?
24. A bolt has 12.9 stamped on the head. This means it has maximum strength of ...
25. Comparison between a 25x1 spring steel ruler and 25x1 mild steel strip under bending. If the yield point of MS is 250MPa and SS is 400MPa, which is TRUE?
26. A Mild Steel beam deflects 0.3mm under load and springs back on removal. Which is FALSE?
27. A bent nail is an example of going beyond the .................
28. A new chain broke while attempting to drag a large fallen tree. This is an example of going beyond the .................
29. If the stress was between the Yield point and UTS then...
30. If the stress was below the Yield point then...
31. If the stress was above the UTS then...
32. Which is stiffer, mild steel or high tensile steel? (Up to yield point)
33. Which is stronger, Mild steel or High tensile steel?
34. Steel has a Modulus of Elasticity of about;
35. A 10m steel rod is stretched by 1cm. What is the Strain?
36. An electrical wire (cross section = 1 square mm) holds 12 N weight. The stress is;
37. How much will a 100m fence wire stretch if it is tensioned to 100MPa?
38. You are designing an aluminium crank for a bicycle. Which entry is most relevant to ensure it does not crack?

## Whiteboard Photos      #### Questions:

Assignment:

• Review Test #10101.
• Do a practice test 10101cp
##### Relevant pages in MDME
• Mechanical Properties practice test: 10101cp