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Mechanical Properties of Metals How do metals respond to external loads?
Stress and Strain ¾ Tension ¾ Compression ¾ Shear ¾ Torsion Elastic deformation
Plastic Deformation ¾ Yield Strength ¾ Tensile Strength ¾ Ductility ¾ Toughness ¾ Hardness
Chapter Outline
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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To understand and describe how materials deform (elongate, compress, twist) or break as a function of applied load, time, temperature, and other conditions we need first to discuss standard test methods and standard language for mechanical properties of materials.
Introduction
Stress,
σ
(MPa)
Strain, ε (mm / mm)
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Types of Loading
Tensile Compressive
Shear
Torsion
F
F
F
F
l l 0 l 0 l
A (^0)
A (^0)
F
F
A (^0) τ
τ
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Concepts of Stress and Strain (tension and compression)
To compare specimens of different sizes, the load is calculated per unit area.
Engineering stress: σ = F / Ao
F is load applied perpendicular to specimen cross- section; A 0 is cross-sectional area (perpendicular to the force) before application of the load.
Engineering strain: ε = ∆ l / l o ( × 100 %)
∆l is change in length, l (^) o is the original length.
These definitions of stress and strain allow one to compare test results for specimens of different cross- sectional area A 0 and of different length l 0.
Stress and strain are positive for tensile loads, negative for compressive loads
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Stress-Strain Behavior: Elastic deformation
E is Young's modulus or modulus of elasticity , has the same units as σ, N/m^2 or Pa
In tensile tests, if the deformation is elastic, the stress- strain relationship is called Hooke's law:
Stress
Strain
Load
Slope = modulus of elasticity E
Unload
σ = E ε
Higher E → higher “stiffness”
0 0
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Geometric Considerations of the
Stress State
σ
σ
θ
Α 0
θ
σ’ τ’
A’
σ ’= σ cos 2 θ
τ ’= σ sin θ cos θ
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Elastic Deformation: Nonlinear elastic behavior
In some materials (many polymers, concrete...), elastic deformation is not linear, but it is still reversible.
Definitions of E
∆σ / ∆ε = tangent modulus at σ 2
∆σ/∆ε = secant modulus between origin and σ 1
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Elastic Deformation: Atomic scale picture
Chapter 2: the force-separation curve for interacting atoms
High modulus
Low modulus
E ~ (dF/dr) at r (^) o (r 0 – equilibrium separation)
Separation, r
Weakly bonded
Strongly bonded
Force, F
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Elastic Deformation: Shear Modulus
Zo
∆ y
τ
Unloaded
Loaded
Relationship of shear stress to shear strain: τ = G γ, where: γ = tan θ = ∆y / zo G is Shear Modulus (Units: N/m^2 ) For isotropic material: E = 2G(1+ υ ) → G ~ 0.4E (Note: most materials are elastically anisotropic: the elastic behavior varies with crystallographic direction, see Chapter 3)
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Stress-Strain Behavior: Plastic deformation
Plastic deformation :
- stress and strain are not proportional
- the deformation is not reversible
- deformation occurs by breaking and re-arrangement of atomic bonds (in crystalline materials primarily by motion of dislocations, Chapter 7)
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Tensile properties: Yielding
Elastic Plastic
Stress
Strain
Yield strength σy - is chosen as that causing a permanent strain of 0.
Yield point P - the strain deviates from being proportional to the stress (the proportional limit)
The yield stress is a measure of resistance to plastic deformation
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Tensile properties: Yielding
Stress
Strain
For a low-carbon steel, the stress vs. strain curve includes both an upper and lower yield point. The yield strength is defined in this case as the average stress at the lower yield point.
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Typical mechanical properties of metals
The yield strength and tensile strength vary with prior thermal and mechanical treatment, impurity levels, etc. This variability is related to the behavior of dislocations in the material, Chapter 7. But elastic moduli are relatively insensitive to these effects.
The yield and tensile strengths and modulus of elasticity decrease with increasing temperature, ductility increases with temperature.
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Toughness
Toughness = the ability to absorb energy up to fracture = the total area under the strain-stress curve up to fracture
Units: the energy per unit volume, e.g. J/m^3
Can be measured by an impact test (Chapter 8).
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True Stress and Strain
True stress = load divided by actual area in the necked-down region, continues to rise to the point of fracture, in contrast to the engineering stress.
σ = F/Ao ε = (l (^) i-l (^) o/l (^) o)
σT = F/Ai ε = ln(l (^) i/l (^) o)
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Elastic Recovery During Plastic Deformation
If a material is deformed plastically and the stress is then released, the material ends up with a permanent strain.
If the stress is reapplied, the material again responds elastically at the beginning up to a new yield point that is higher than the original yield point.
The amount of elastic strain that it will take before reaching the yield point is called elastic strain recovery.
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Hardness
Knoop hardness Rockwell B
Rockwell C
Diamond
Corrundum or sapphire Topaz Quartz Orthoclase Apatite
Fluorite Calcite
Gypsum
Talc Mohs hardness
Brinell hardness
Easily machined steels
Brasses and aluminum alloys
Most plastics
Nitrided steels Cutting tools File hard
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Hardness (II)
Both tensile strength and hardness may be regarded as degree of resistance to plastic deformation. Hardness is proportional to the tensile strength - but note that the proportionality constant is different for different materials.
Tensile strength (MPa) Tensile strength (
3 psi)
Brinell hardness number
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What are the limits of “safe” deformation?
Design stress : σd = N’σc where σc = maximum anticipated stress, N’ is the “design factor” > 1. Want to make sure that σd < σy
Safe or working stress : σw = σy/N where N is “factor of safety” > 1.
For practical engineering design, the yield strength is usually the important parameter
Strain
Stress
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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Take Home Messages
- Make sure you understand
- Language: (Elastic, plastic, stress, strain, modulus, tension, compression, shear, torsion, anelasticity, yield strength, tensile strength, fracture strength, ductility, resilience, toughness, hardness)
- Stress-strain relationships
- Elastic constants: Young’s modulus, shear modulus, Poisson ratio
- Geometries: tension, compression, shear, torsion
- Elastic vs. plastic deformation
- Measures of deformation: yield strength, tensile strength, fracture strength, ductility, toughness, hardness
