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Stress strain curve
ESO202A: Mechanics of Solids
Uni-axial loading So far we had
studied the cases of three rods made of the same material.
Uni-axial loading The bars were
loaded by forces applied at the ends and we were interested in the relative motion between the points of application of forces
Uni-axial loading & Deformation We define : Stress = Load/ Initial Area Strain = Change in length per unit length
With this definition, we get identical stress versus strain curves for bars 1,2 and 3.
Uni-axial loading & Deformation
For small strains, we observed that the stress and strain are linearly related. We defined:
Modulus of elasticity = Stress/Strain
(We use E to denote the modulus of elasticity).
Typical E for steel = 200 X 109 N/m2
Typical values of modulus of elasticity
Material E (GPa) 1 Pa = 1 N/m2
1 GPa = 109 N/m2
Steel & Iron 194-205
Cast Iron 69-138
Soft Rubber .0014-.005
Tensile test The most
important test of a material’s mechanical response is the tensile test.
Tensile test In a tensile
test, one end of a rod or flat specimen is clamped in a loading frame and the other subjected to a controlled displacement or load.
Tensile test A displacement transducer connected in series with the specimen gives an indication of the change in length between two gage marks
Specimen grips Attaching displacement transducer
Tensile test Figure shows the two gage marks and the change in length between the two gage marks
Tensile test In general, axial
extension is accompanied by a decrease in cross sectional dimensions.
Engineering stress and strain The Engineering stress and strain are defined on the basis of the initial specimen cross-sectional area A0 and gage length L0 .
Engineering stress and strain Engineering Stress σe = Load / A0 Engineering Strain εe = Change in length / L0
True stress and strain The specimen cross-sectional area A and
gage length L keep changing as the load is applied. These changes have a negligible effect except during the final stages of the test.
True Stress σtrue = Load / A True Strain εtrue = Change in length / L
Tensile testing machine
Tensile testing machine- grips
Tensile testing machine- Attaching displacement transducer
Tensile testing machine- Chart recorder
Tensile testing of Aluminum specimen
Specimen after failure
Specimen after failure
Load displacement (stress strain curve)
Engineering stress-strain curve The initial
portion (up to proportionali ty limit) is a straight line.