3.4.2 mechanical properties of matter

previously Hooke’s Law applies to the straight line section of the curve. Force (F)  Extension (x) F = -kx F is the force causing the extension in the spring. –kx is negative as it indicates that it is a restoring force. © Pearson Education Ltd 2008 This document may have been altered from the original

Straight-line graph of tension against extension The area under this graph is equal to the work done to stretch the spring © Pearson Education Ltd 2008 This document may have been altered from the original

The work done in stretching the object is stored in it as elastic potential energy E. E = work done in acheiving the stretch E = average force x extension Average force = F/2 so E = (F/2)x E = (kx/2)x E = 1/2 kx2 E = 1/2 k x2 & E = 1/2Fx Total work done W = Fx , so where has the other half of the energy gone? © Pearson Education Ltd 2008 This document may have been altered from the original

Stress (Pa) = Force (N) / Area (m2) Key terms Ductility - A material is said to be ductile if it can be permanently stretched. Brittleness - A material is said to be brittle if it cannot be permanently stretched. It will break soon after it has passed its elastic limit (point beyond which it will not return to its original shape / length). Strain - The extension per unit length. This has no unit. Stress - A measure of the force per unit cross sectional area applied to a material. Stress (Pa) = Force (N) / Area (m2)  = F / A

PAG 2

Young’s modulus – a measure of stiffness We know that stress is a measure of the force per unit cross sectional area applied to a material and that strain is the extension per unit length. Therefore; Young’s Modulus (E) E = stress / strain E = (F/A) / (L/L) E = FL AL The units of Young’s Modulus are……. PA

 8mm Permanent extension Strain is the percentage extension. Stress is the Force per unit cross sectional area. If the wire tested here was 1m long how much permanent extension was there? Permanent extension  8mm © Pearson Education Ltd 2008 This document may have been altered from the original

Stress / Pa Strain (0,0) Brittle material breaks here. Ductile material stretches permanently beyond its elastic limit. Release of stress. Permanent Deformation. If a material is stiff, it produces little strain so will have a steeper gradient.

Using pencils to stretch a copper wire When you do this you can feel a change in the way the copper wire stretches. You should be able to feel what is going on in the graph on the next slide. This should also be the shape of the graph achieved when the wire was stretched in the Young’s Modulus experiment. © Pearson Education Ltd 2008 This document may have been altered from the original

Stress-strain graph for a ductile material Limit of Proportionality Yield Point Elastic Limit Permanent Deformation © Pearson Education Ltd 2008 This document may have been altered from the original

Stress-strain graph for a brittle material eg cast iron or glass © Pearson Education Ltd 2008 This document may have been altered from the original

Stress-strain graph for a rubber band Graph shows an increase in the force needed to try and stretch the band as it stretches. It “goes solid like string”. Also the band shows a very large amount of extension relative to it’s length – strain axes very long! © Pearson Education Ltd 2008 This document may have been altered from the original

Hysteresis Here it matters if you are loading or unloading Stress / 109 Pa Strain (0,0) 0.5 1 Stress / 109 Pa Strain (0,0) 6 1 Polythene Rubber

Factsheet 27 Materials Support S&C Scaling up Calculation sheet 6 Calculation sheet 6.2 Practical 6.3 – Strawberry laces Practical 6.4 – Determining YM