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Young S Modulus
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.
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.
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.
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.
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)
Plastic Strains (when material behave elastically)
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
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.
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.
Mild steel car bodies
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.