Material Properties: Stress, Strain, Elasticity, Plasticity, Hooke's Law, Young's Modulus, Lecture notes of Architecture

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“Mechanical Properties”

September 2016

Materials Properties

Mechanical Properties

 Compressive force: a ‘pressing’ force tending to cause a member to shorten.  Tensile force: a ‘pulling’ force tending to cause a member to lengthen.

Mechanical Properties

 Elasticity: it is the property of a material that enables it to return to its original shape and size, after undergoing deformation as a result of the application of a stress.  Plasticity: it is the property of a material that allows it to be deformed without the ability to return to its original shape and size.

Hooke’s Law

 Hooke’s Law – For an elastic material, the change in length is directly proportional to the applied force provided that the material is in the elastic state.

Young’s Modulus

 Young’s Modulus (E): E-value is a constant for a given material and is a measure of how stiff a material is. It is defined as the ratio of tensile (or compressive) stress to tensile (or compressive) strain. E-value = Stress/Strain  The greater the value of E, the more difficult it is to cause shortening or lengthening of the material, i.e. strong material  The E-value is important to tell us the strength of the material. Rubber deforms easily and has a very low E-value. Steel has a very high E-value and does not deform easily.

Stress-Strain Test

Stress  The formula where se = engineering stress, MPa F = applied force, N A 0 = original area of the specimen, mm^2 A 0 F s e 

Stress-Strain Test

Strain calculation  The formula: (no unit) Typical Stress-Strain Graph 0 0 L L L e   Elastic deformation Plastic deformation Strain (e) Stress (

s

e

Maximum load Y Yield stress TS Tensile stress Necking

Stress-Strain Relationship

 In the elastic deformation zone  The specimen will return to original shape after the force is removed.  The formula (the Hooke’s law)  se = Ee  where E = modulus of elasticity or Young’s modulus  In plastic deformation zone  The specimen will not return to the original shape after the force is removed.  Necking is when localized material deformation occurs.

Stress-Strain Behaviour of Materials

Other Terminologies

 Factor of safety: it is defined as the ratio between the yield stress and the allowable or working stress. Safety Factor = Yield Stress/Allowable Stress  The allowable stress shall be less than yield stress  The safety factor is usually between 1 and 2.

Other Terminologies

 Poisson’s ratio: When a body is subjected to an axial stress (tensile or compressive), deformation takes place not only in the axial direction but also in other directions perpendicular to the axis. The ratio of lateral strain to axial strain is called Poisson’s ratio.  For most substances, its value lies between 0.2 and 0.4.

Other Terminologies

 Malleability: it is the ability of a material to undergo deformation in all directions, usually cold deformation by hammering.

Other Terminologies

 Hardness: it is resistance to surface deformation under stress.