chapter 6: mechanical properties ii
TRANSCRIPT
Chapter 6 - 1
Chapter 6: Mechanical Properties II
Outline • Elastic recovery during plastic deformation • Compressive, shear, and torsional deformation • Hardness • Variability of material properties • Design/safety factors
Chapter 6 -
Concepts of stress and strain
• Tension tests – engineering stress
– engineering strain
• Compression tests
Chapter 6 - 3
Elastic means reversible!
Elastic Deformation 1. Initial 2. Small load 3. Unload
F
δ
bonds stretch
return to initial
F
δ
Linear- elastic
Non-Linear- elastic
Chapter 6 - 4
Plastic means permanent!
Plastic Deformation (Metals)
F
δ linear elastic
linear elastic
δ plastic
1. Initial 2. Small load 3. Unload
p lanes still sheared
F
δ elastic + plastic
bonds stretch & planes shear
δ plastic
Chapter 6 - 5
Elastic Strain Recovery
Adapted from Fig. 6.17, Callister 7e.
Chapter 6 - 6
• Elastic Shear modulus, G:
τ G
γ τ = G γ
Other Elastic Properties
simple torsion test
M
M
• Special relations for isotropic materials:
2(1 + ν) E G =
3(1 - 2ν) E K =
• Elastic Bulk modulus, K:
pressure test: Init. vol =Vo. Vol chg. = ΔV
P
P P P = - K
Δ V V o
P Δ V
K V o
Chapter 6 - 7
• Simple tension:
δ = FL o E A o
δ L = - ν Fw o
E A o
• Material, geometric, and loading parameters all contribute to deflection. • Larger elastic moduli minimize elastic deflection.
Useful Linear Elastic Relationships
F
A o δ /2
δ L /2
Lo w o
• Simple torsion:
α = 2 ML o π r o
4 G
M = moment α = angle of twist
2ro
Lo
Chapter 6 - 8
Hardness • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties.
e.g., 10 mm sphere
apply known force measure size of indent after removing load
d D Smaller indents mean larger hardness.
increasing hardness
most plastics
brasses Al alloys
easy to machine steels file hard
cutting tools
nitrided steels diamond
Chapter 6 - 9
Hardness: Measurement • Rockwell
– No major sample damage – Each scale runs to 130 but only useful in range
20-100. – Minor load 10 kg – Major load 60 (A), 100 (B) & 150 (C) kg
• A = diamond, B = 1/16 in. ball, C = diamond
• HB = Brinell Hardness – TS (psia) = 500 x HB – TS (MPa) = 3.45 x HB
Chapter 6 - 10
Hardness: Measurement Table 6.5
Chapter 6 -
Correlation between hardness and tensile strength
• Relations between hardness and tensile strength for steel, brass, and cast iron.
• For most steels: TS (MPa)=3.45xHB TS (psi)=500xHB
Chapter 6 -
Example
• Estimate the Brinell and Rockwell hardnesses for brass and carbon steel
Chapter 6 - 13
Variability in Material Properties • Elastic modulus is material property • Critical properties depend largely on sample flaws
(defects, etc.). Large sample to sample variability. • Statistics
– Mean
– Standard Deviation
where n is the number of data points
Chapter 6 -
Example
• Determine the average and standard deviation of tensile strength
Chapter 6 - 15
• Design uncertainties mean we do not push the limit. • Factor of safety, N Often N is
between 1.2 and 4
• Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5.
Design or Safety Factors
5
1045 plain carbon steel: σ y = 310 MPa TS = 565 MPa
F = 220,000N
d
L o
d = 0.067 m = 6.7 cm
Chapter 6 - 16
• Stress and strain: These are size-independent measures of load and displacement, respectively. • Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G).
• Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure.
Summary
• Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches σy.
• Hardness: Resistance to permanently indenting the surface. • Safety: Design uncertainties mean we do not push the limit