Recent Changes - Search:
  • Welcome 54.198.58.62

'We have 4 guest/s online'

Content Areas

Other Areas

Our Sites

Save to del.icio.us Save to LinkAGoGo Save to Ma.gnolia Save to Yahoo! My Web

edit SideBar

Young S Modulus

Introduction...

A nice introduction to the topic of stress/Strain

Young's Modulus is known as the measure of stiffness of a given material, usually given as a ratio of stress to strain.

9.1.1 Define Young’s modulus.

Young’s modulus
The stiffness of a material.

9.1.2 State that stress (load) is force per unit area acting on a body or system.

The load on a structural member divided by its cross-sectional area is called the “stress in the member”.

9.1.3 State that strain is the ratio of a change in dimension to the original value of that dimension.

The strain in a material is a measure of the relative change of shape it undergoes when subjected to a load. It is independent of the size of the structural member.

Tensile test

9.1.4 Draw and describe a stress/strain graph and identify the elastic region, plastic flow region, yield stress and ultimate tensile strength (UTS).

For most materials the elastic region is a straight line, which changes to a curved line (plastic region). Quantitative details of specific materials are not required.
The Stress Strain Graph and its regions Related to Ductility

Every material will perform differently under the application of stress and strain and therefore each material's graph will be different. We can identify and collect considerable amounts of information from a Stress-Strain graph. Some of the graph's most important aspects are outlined below.

A stress/strain graph with a comparison of brittle to ductile materials.

  • The elastic region
  • Yield stress
  • Plastic flow region
  • Ultimate stress (UTS)
  • For most materials the elastic region is illustrated by the initial straight line.
  • The plastic flow region is illustrated by the curved line that ends at the "rupture stress" point.
  • The ultimate tensile stress is the maximum stress recorded throughout the continued stress application.
  • The rupture stress is the maximum instantaneous stress at the breaking point of the material.
  • After the yield point, the curve will dip slightly then the stress will increase because of strain hardening. Finally, the graph will reach its ultimate tensile strength. Hence forth the material becomes unstable and fractures.
  • There are different materials varying from ductile to brittle. For example, steel usually has a very linear stress strain relationship and a well defined yield point. Other materials, which are brittle, like ceramics, do not have a yield point. Their rupture and ultimate strength is the same, so the curve has only the straight elastic region then the rupture.

9.1.5 Outline the importance of yield stress in materials.

This is the stress at the yield point on the stress/strain graph. Beyond the yield point, the material undergoes plastic deformation.

The Yield Stress differentiates the elastic region from the plastic flow region. In other words how well a material holds its shape integrity, doesn't deform too much but can return to its original shape.

9.1.6 Explain the difference between plastic and elastic strains.

When a material behaves elastically, if the stress on the material is released before it breaks, the extension (strain) relaxes and the material returns to its original length. Beyond the yield point, the material deforms plastically and does not return to its original length or shape.

This information is extremely useful for determining if a material is suitable for its design, as engineers/designers, can choose materials with enough yield to be able to return to their original position depending on how much elasticity is required.

Elastic Strains (when material behave elastically)

  • When material is bent (not reaching yield point) then relaxed, it reaches original position again

Plastic Strains (when material behave elastically)

  • When bent/deformed beyond yield and cannot change back to original shape.
  • It maintains the new shape or stretches/tears/breaks.
Plastic strain of ruler Elastic strain of ruler

In the straight portion of the stress/strain graph the material behaves elastically, ie if the stress on the material is released before it breaks, the extension (strain) relaxes and the material returns to its original length. However, when the material is brought past the yield stress it becomes plastically deformed, ie the material will not return to its original shape. We can determine whether the material will become plastically deformed or not before the application of the force. This can save time, money and effort in a design situation.

9.1.7 Calculate the Young’s modulus of a range of materials.

Young’s modulus = stress/strain

where

E is the Young's modulus (modulus of elasticity)
F is the force applied to the object;
A0 is the original cross-sectional area through which the force is applied;
ÄL is the amount by which the length of the object changes;
L0 is the original length of the object.
Material GPa lbf/in
(psi)
Rubber (small strain) 0.01-0.1 1,500-15,000
Teflon 0.5 75,000
Polypropylene 1.5-2 217,000-290,000
Nylon 2-4 290,000-580,000
Medium-density fibreboard 3.654 530,000
Pine wood (along grain)[ 8.963 1,300,000
Oak wood (along grain) 11 1,600,000
High-strength concrete (under compression) 30 4,350,000
Magnesium metal (Mg) 45 6,500,000
Aluminium 69 10,000,000
Glass 50-90
Mother-of-pearl 70 10,000,000
Tooth enamel 83 12,000,000
Brass and bronze 100-125 17,000,000
Titanium (Ti) 16,000,000
Copper (Cu) 117 17,000,000
Wrought iron 190–210
Steel 200 30,000,000
Diamond 1220 150,000,000-175,000,000

9.1.8 Explain how knowledge of the Young’s modulus of a material affects the selection of materials for particular design contexts.

Young’s modulus provides quantitative data relating to the relationship of strength and stiffness in structures.

Steel Bridges

  • stiff enough to resist bending
  • high tensile strength to carry the weight

Mild steel car bodies

  • ductile enough so can be easily and economically plastically deformed
  • Yet stiff enough to retain its shape or resist bending

Spring

  • can be stretched yet return to its original shape

References

Bulleted list and italicised paragraphs are excerpted from Design Technology: guide. Cardiff Wales, UK: International Baccalaureate Organization, 2007.

Images are clickable links to its location.

Edit - History - Print - Recent Changes - Search
Page last modified on September 11, 2012, at 12:39 AM