MATERIALS: Clarifications and More on Stress Strain Curves

Transcription

1 A 3.0 m length of steel rod is going to be used in the construction of a bridge. The tension in the rod will be 10 kn and the rod must extend by no more than 1.0mm. Calculate the minimum cross-sectional area required for the rod. Young modulus of steel = Pa WARM UP QUESTION m 2 MATERIALS: Clarifications and More on Stress Strain Curves 1

2 BRITTLE AND DUCTILE CANDY BARS Brittle vs. Stiff Brittleness is the ability of a material to resist permanent deformations Stiffness is the ability of a material to resist elastic (nonpermanent) deformations. For example, wood, which can bend, is not stiff, but brittle because you cannot permanently bend wood without fracturing it. In comparison, steel is highly ductile because it can be bent or stretched under load without failure. It is also stiffer than wood, because it can not bend much without causing a permanent deformation. SOME CLARIFICATIONS 2

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4 SOME CLARIFICATIONS Yield point - where plastic deformation begins. A large increase in strain is seen for a small increase in stress. Upper and Lower yield points ANALOGOUS TO STATIC AND SLIDING FRICTION Upper yield point initiates yielding behavior Lower yield point - min load that is required to maintain yield Once UYP is reached, the grains start to flow (they rearrange themselves to fill any gap present between them). So stress relieves (stress value decreases) while deformation continues to happen (strain increases) DISLOCATIONS 4

5 KEY POINTS ON GRAPH Limit of Proportionality before this limit, Hooke s Law applies (stress and strain are directly proportional) Elastic Limit point at which elastic deformation ends and plastic deformation begins Yield Point point where the stress causes sudden deformation without any increase in the force Upper Yield Point dislocations freed and set in motion Lower Yield Point - Once dislocations have been freed, the stress needed for their motion drops abruptly and is called the lower yield point Ultimate Tensile Stress measure of strength. maximum material can withstand before fracturing Breaking Stress - the stress coordinate on the stress-strain curve at the point of rupture. STRAIN HARDENING Strain hardening, also known as work hardening or cold working, is the strengthening of a metal by plastic deformation. Higher stresses can be carried at the expense of large plastic strains This strengthening occurs because of dislocation movements and dislocation generation within the crystal structure of the material It means, it s more difficult to deform the metal as the strain increases and hence it s called strain hardening. 5

6 VOCABULARY Elastic deformation - When the stress is removed, the material returns original dimensions. Reversible Plastic deformation - When the stress is removed, the material does not return to its previous dimension but there is a permanent, irreversible deformation. Ductile - The ability to deform (strain) before breaking (maintains strength in plastic region) Brittle opposite of ductile. Brittle materials absorb relatively little energy before fracture. Stiffness - the rigidity of an object: the extent to which it resists deformation in response to an applied force. Opposite of flexibility. Young s Modulus measures stiffness. Strength maximum amount of stress material can take before fracture Toughness - ability of material to absorb energy before fracture takes place Resilience - ability of material to absorb energy when it's deformed elastically & release this energy when unloaded Hardness resistance to plastic deformation (e.g., a local dent or scratch) BRITTLE/DUCTILE 6

7 TOUGHNESS RESILIENCE 7

8 TRUE STRESS/ENGINEERING STRESS Engineering stress is the applied load divided by the original crosssectional area of a material. Also known as nominal stress. True stress is the applied load divided by the actual cross-sectional area (the changing area with respect to time) of the specimen at that load 8

9 NECKING Begins at ultimate tensile stress 9

10 NOW, SOME NEW INFORMATION 10

11 LOADING AND UNLOADING CURVES Metals loading and unloading curves are the same, provided elastic limit not exceeded - Past elastic limit, unloading line is parallel to loading line - Permanent extension (permanent set) occurs if unloading happens after the elastic limit LOADING AND UNLOADING CURVES Rubber very low limit of proportionality - for a given extension the loading force is greater than the unloading force - Hysteresis: it returns to its original shape, but does not follow the same load extension graph when being unloaded 11

12 LOADING AND UNLOADING CURVES Polythene low limit of proportionality - Permanent plastic deformation LOADING AND UNLOADING CURVES Metal Rubber Polythene 12

13 STRAIN ENERGY Area under force-extension graph is work done to stretch material Strain Energy work done to deform an object Provided the limit of proportionality is not exceeded, work done to stretch a metal wire is STRAIN ENERGY - METALS Because loading and unloading lines are the same, all energy stored in the wire can be recovered when the wire is unloaded 13

14 Work done to stretch the rubber band is the area under the loading curve Work done by the rubber band when it is unloaded is the area under the unloading curve Area between the curves represents the difference between energy stored in stretched rubber band and useful energy recovered when it is unstretched Difference occurs some of the stored energy becomes internal energy of molecules (heat) STRAIN ENERGY - RUBBER STRAIN ENERGY - POLYTHENE Area between loading and unloading curves represents work done to deform the material permanently 14

15 STRAIN ENERGY PRACTICE Complete Summary Questions on page