Elastic properties of materials

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ELASTIC PROPERTIES OF SOLIDS

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Presentation transcript:

Elastic properties of materials Stress (outside forces on material) Strain (response of material to stress) Modulus: “stiffness” of a material: Strength of a material: maximum stress before material fails. figure from hyperphysics.com

New unit of F/A figure from hyperphysics.com

Strain proportional to stress in “elastic” region (Hooke’s law) D L/L slope: stiffness (modulus) = stress/strain

Correction to text Strength is not the same as stiffness. When the text uses the phrase "tensile strength", they mean "tensile stiffness". Stiffness is a measure of elasticity. Strength is a prediction of when things will break.

Young’s Modulus : Stiffness against change in length If the tensile strength of steel in a cable is 400 MPa, how wide must a wire cable be to lift a Toyota Camry which weighs 12000 N? How much will the cable stretch if it is 10 m long and Young’s modulus (stiffness) is 200 GPa?

Bulk Modulus: Stiffness against change in volume with uniform pressure

Shear Modulus: Stiffness against shape change due to shear forces DL Lo Shear strength is important in fastening parts. Shear is not the same as bending, as the text incorrectly suggests.

Bending: compression and tension in the same object Figure from HowStuffWorks.com

Why concrete bridges and driveways must have steel buried inside (rebar) Concrete’s tensile strength is very low! Steel’s tensile strength very high.

Thermal expansion Lengths all change by the same tiny fraction per degree Demo: bimetallic strip

Why do almost all material EXPAND when heated? Atomic bonds act like imperfect springs that get weaker as thermal vibration amplitude increases, and the atoms move farther apart. P1. You heat a disc with a hole in it. Will the hole expand or shrink, or stay the same? Shrink Stay the same Expand

A dentist heats to 130 C a steel circular band of cross sectional area 1mm2 and circumference 1cm. It expands and fits around a tooth. What is the tension in the band when it cools to 30 C in the mouth?

P2. You are building a musical instrument, and find that a wire “string” under tension breaks at a tension of 100 N. If you double the diameter of the wire, it will now support up to 50 N 100 N c) 200 N d) 400 N e) 800 N P3. Scissors work by overcoming a material’s a) tensile strength b) shear strength c) bulk modulus