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Lecture7-Sept16

Lecture7-Sept16

MSE200 Lecture 7 (CH. 6.2-6.4) Mechanical Properties I Instructor: Yuntian Zhu

• Objectives/outcomes: You will learn the following: •Stresses and strains in . •Normal and shear stresses. •Elastic and . •The tensile test and the engineering -strain curves. •Young’s modulus, the strength, the ultimate tensile strength, the percent elongation and percent reduction in area. •True stress and true strain. and hardness testing

http://www.mse.ncsu.edu/zhu Science & Engineering Elastic and Plastic Deformation in

• Elastic deformation: returns to its original dimension after the is removed.

• Plastic deformation: The metal is deformed to such an extent such that it cannot return to its original dimension after the load is removed

http://www.mse.ncsu.edu/zhu & Engineering Engineering Stress and Strain – under tension/

Engineering stress σ =

2 A0 Δl Units of Stress are N/m (Pascals, or Pa) or PSI  A

 0 Engineering strain = є  0  −  Δ € = 0 =   € 0 0

Force F (N) For elastic deformation: σ = E є

E is the€ Young’s modulus

http://www.mse.ncsu.edu/zhu Materials Science & Engineering Poissons Ratio

. є (lateral) єy Poissons ratio = ν = − = − є є (longitudinal) z z w − w y ν = − 0 w0 w €  −  0  0 

Usually poissons ratio ranges from 0.25 to 0.4.

Example: Stainless 0.28 0.33

http://www.mse.ncsu.edu/zhu Materials Science & Engineering and Shear Strain S (Shear force) Shear stress τ = A (Area of shear force application)

Tensile

Shear

Amount of shear displacement Shear strain γ = Distance ‘h’ over which shear acts G = τ / γ http://www.mse.ncsu.edu/zhu Materials Science & Engineering Tensile test/The most common test

• can be tested by pulling the metal to failure.

Load Cell

Specimen Extensometer Force data is obtained from Load cell Strain data is obtained from Extensometer.

http://video.google.com/videosearch?q=tensile+testing&hl=en&emb=0&aq=0&oq=tensile+test# http://www.mse.ncsu.edu/zhu Materials Science & Engineering Tensile Test (Cont)

Round bar sample Flat sheet sample

Commonly used Test specimen

ASTM standard gives more information

Typical Stress-strain curve

http://www.mse.ncsu.edu/zhu Materials Science & Engineering Young’s Modulus • Young’s Modulus (E) : Stress and strain are linearly related in elastic region. (Hooke’s law) Linear portion of the Stress stress strain curve Δσ E = E = Δ Δσ є

Δє

• The higher the bonding strength, Strain The higher the modulus of • Largely determined by composition • Insensitive to the grain size

http://www.mse.ncsu.edu/zhu Materials Science & Engineering Yield Strength

• 0.2% offset yield strength is that strength at which 0.2% plastic deformation takes place.

• Construction line, starting at 0.2% strain and parallel to elastic region is drawn to find 0.2% offset yield strength.

http://www.mse.ncsu.edu/zhu Materials Science & Engineering Ultimate tensile strength

• Ultimate tensile strength (UTS) is the maximum strength reached by the engineering stress strain curve. • Necking starts after UTS is reached. Al 2024-Tempered S T Necking Point • More ductile the metal is, more R E is the necking before failure. S S Al 2024-Annealed • True stress level at necking section? MPa

Eng. Strain Engineering Stress strain curves of Al 2024 With two different heat treatments. Ductile annealed sample necks more http://www.mse.ncsu.edu/zhu Materials Science & Engineering Percent Elongation/

• Percent elongation (elongation to failure) is a measure of ductility of a . • It is the elongation of the metal before expressed as percentage of original length.

% Elongation to failure =

lf − l0 i.e. Ductility (єf) = l0

€ http://www.mse.ncsu.edu/zhu Materials Science & Engineering Percent Reduction in Area

• Percent reduction area is also a measure of ductility.

% Reduction Initial area – Final area = Area Initial area Ductile Brittle

• Percent reduction in area in metals decreases in case of presence of porosity.

http://www.mse.ncsu.edu/zhu Materials Science & Engineering True Stress – True Strain • True stress and true strain are based upon instantaneous cross-sectional area and length. F • True Stress = σ = t Ai (instantaneous area)

li A0 • True Strain = εt = Ln = Ln l0 Ai

σt = σ (1+ є) € εt = ln (1+ є)

http://www.mse.ncsu.edu/zhu Materials Science & Engineering Hardness and Hardness Testing http://video.google.com/videosearch?q=hardness+testing&hl=en&emb=0&aq=1&oq=hardness# • Hardness is a measure of the resistance of a metal to permanent (plastic) deformation.

• A quick way to estimate the yield strength: σ0.2 ≈Hardness/3 • General procedure: Press the indenter that is harder than the metal Into metal surface.

Withdraw the indenter

Measure hardness by measuring depth or Rockwell hardness width of indentation. tester http://www.mse.ncsu.edu/zhu Materials Science & Engineering Home work

• Example Problems: 6.4, 6.5, 6.6, 6.7, 6.8, • Regular Problems, Chapter 6: download from web • Reading assignment: section 6.5-6.8

http://www.mse.ncsu.edu/zhu Materials Science & Engineering

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