ENGR 225 Section 3.1 - 3.8

49
ENGR 225 Section 3.1 - 3.8

description

ENGR 225 Section 3.1 - 3.8. Relation between Stress and Strain. Load increase –> stress increase. Deformation increase –> strain increase. Tension Test. Standard test specimen. Universal Testing Machine (UTM). Tension Test. http://www.youtube.com/watch?v=9suShuEwc7I&feature=related. - PowerPoint PPT Presentation

Transcript of ENGR 225 Section 3.1 - 3.8

Page 1: ENGR 225 Section 3.1 - 3.8

ENGR 225Section 3.1 - 3.8

Page 2: ENGR 225 Section 3.1 - 3.8

Load increase –> stress increase.

Deformation increase –> strain increase.

Relation between Stress and Strain.

Page 3: ENGR 225 Section 3.1 - 3.8

Tension Test

Standard test specimen

Page 4: ENGR 225 Section 3.1 - 3.8

Universal Testing Machine (UTM)

Page 5: ENGR 225 Section 3.1 - 3.8

Tension Test

http://www.youtube.com/watch?v=9suShuEwc7I&feature=related

Page 6: ENGR 225 Section 3.1 - 3.8

Nominal Stress: σ = P/A0

Where A0 is original cross section

Nominal Strain: ε = δ/L0

Where L0 is the original gauge length and δ is the change in gauge length

No two stress-strain diagrams for a particular material will be exactly the same since the results depend on:

material’s compositionmicroscopic imperfections,way material is manufacturedrate of loadingtemperature

Stress-Strain Diagrams

Page 7: ENGR 225 Section 3.1 - 3.8

Stress-Strain Diagrams

Page 8: ENGR 225 Section 3.1 - 3.8

Stress is proportional to strain

(within proportional limit)

in most Solids

Not so for fluids !!

Page 9: ENGR 225 Section 3.1 - 3.8

Mild Steel

y = 25 pl

Page 10: ENGR 225 Section 3.1 - 3.8

Ductility

• The extent of plastic deformation that a material undergoes before fracture.

Page 11: ENGR 225 Section 3.1 - 3.8

Ductile Material– A material that can be subjected to large strains before it ruptures.

– Ductility can be measured by percent elongation or percent reduction in area at the time of fracture.

– Mild Steel : 38%

– Mild Steel : 60%

%)100(ElongationPercent o

of

L

LL

%)100(Areain Reduction Percent o

of

A

AA

Page 12: ENGR 225 Section 3.1 - 3.8

Ductility• Why use ductile materials?

– Capable of absorbing shock or energy– When overloaded, usually exhibit large deformation before failing.

Page 13: ENGR 225 Section 3.1 - 3.8

Aluminum

Page 14: ENGR 225 Section 3.1 - 3.8

Yield Strength• Yield Strength is not a physical property of the material.

• We will use approach that – Yield strength– Yield point– Elastic limit– Proportional limit

• All coincide unless otherwise stated

Page 15: ENGR 225 Section 3.1 - 3.8

Natural Rubber(Nonlinear Elastic Behavior)

Page 16: ENGR 225 Section 3.1 - 3.8

Brittle Material

– A material that exhibits little of no yielding before failure. It fractures suddenly under tension.

Page 17: ENGR 225 Section 3.1 - 3.8

Grey Cast Iron

Page 18: ENGR 225 Section 3.1 - 3.8

Concrete

Page 19: ENGR 225 Section 3.1 - 3.8

Modulus of Elasticity

E = Stress / Strain

Hooke’s Law

= E

Page 20: ENGR 225 Section 3.1 - 3.8

Modulus of Elasticity• Modulus of Elasticity (E) indicates stiffness of a material.

If material is stiff, E is large

(for steel, E = 200 GPa)

If material is spongy, E is small

(for vulcanized rubber, E = 0.70 MPa)

Page 21: ENGR 225 Section 3.1 - 3.8

• Strength• Ductility• Brittleness• Stiffness• Resilience• Toughness• Endurance• Rigidity

Material Properties

Page 22: ENGR 225 Section 3.1 - 3.8

Strain Hardening

• Strain hardening is used to establish a higher yield point for a material

• The modulus of elasticity stays the same.

• The ductility decreases.

Page 23: ENGR 225 Section 3.1 - 3.8

Chapter 3 Lecture Example 1

A tension test for a steel alloy results in the stress-strain diagram shown. Calculate the modulus of elasticity and the yield strength based on a 0.2% offset. Identify on the graph the ultimate stress and the fracture stress.

Page 24: ENGR 225 Section 3.1 - 3.8

Strain Energy

• Energy stored in a material due to deformation

Page 25: ENGR 225 Section 3.1 - 3.8

Modulus of Resilience

Page 26: ENGR 225 Section 3.1 - 3.8

Chapter 3 Lecture Example 2

The stress-strain diagram for an aluminum alloy that is used for making aircraft parts is shown. If a specimen of this material is stressed to 600 MPa, determine the permanent strain that remains in the specimen when the load is released. Also, find the modulus of resilience both before and after the load application.

Page 27: ENGR 225 Section 3.1 - 3.8

Toughness

• The area under the stress-strain curve

• The amount of energy per unit volume that the material dissipates prior to fracture.

Page 28: ENGR 225 Section 3.1 - 3.8

Modulus of Toughness

Page 29: ENGR 225 Section 3.1 - 3.8

Strength, Toughness and Ductility

• Strength ~ related to the height of the curve

• Ductility ~ related to the width of the curve

• Toughness ~ related to area under the curve

Page 30: ENGR 225 Section 3.1 - 3.8

Poisson’s Ratio

Page 31: ENGR 225 Section 3.1 - 3.8

Poisson’s Ratio

Page 32: ENGR 225 Section 3.1 - 3.8

Poisson’s Ratio

• When a deformable body is subjected to a tensile force, not only does it elongate, but it also contracts.

• Longitudinal is in the direction of the tensile force.

long

lat

French mathematician Simeon Denis Poisson

Page 33: ENGR 225 Section 3.1 - 3.8

• Value of is positive

• Value of same in tension and compression

• Range of 0.25 to 0.35

• constant only in the elastic range

• Maximum possible value of is 0.5 (Section 10.6)

• Only Longitudinal force is acting to cause the lateral strain.

Poisson’s Ratio

Page 34: ENGR 225 Section 3.1 - 3.8

Shear Stress –Strain Diagram

Page 35: ENGR 225 Section 3.1 - 3.8

Shear Stress –Strain Diagram

G

Page 36: ENGR 225 Section 3.1 - 3.8

Modulus of Rigidity

G)1(2 v

EG

Derivation of this equation in section 10.6

Page 37: ENGR 225 Section 3.1 - 3.8

Chapter 3 Lecture Example 3

This is a titanium alloy. Determine the shear modulus, G, the proportional limit, and the ultimate shear stress. Find the maximum d where the material behaves elastically. What is the magnitude of V to cause d?

Page 38: ENGR 225 Section 3.1 - 3.8

Failure of turbine blade due to creep

Failure of steam pipe due to creep

Page 39: ENGR 225 Section 3.1 - 3.8

Creep• Creep is the time-related deformation of a

material for which temperature and stress play an important role.

• Creep results from sustained loading below the measured yield point.

• Members are designed to resist the effects of creep based on their creep strength, which is the highest amount of stress a member can withstand during a specified amount of time without experiencing creep strain.

Page 40: ENGR 225 Section 3.1 - 3.8

Creep

Page 41: ENGR 225 Section 3.1 - 3.8

Fatigue

• Fatigue occurs in metals when stress or strain is cycled. It causes a brittle fracture to occur.

• Members are design to resist fatigue by ensuring that the stress in the member does not exceed its endurance limit.

• This the maximum stress member can resist when enduring a specified number of cycles.

Page 42: ENGR 225 Section 3.1 - 3.8

Concept Questions

• How would you explain strain to one of your engineering classmates?

– Strain is a linear deformation due to stress– Percent increase in length under tension or

compression

Page 43: ENGR 225 Section 3.1 - 3.8

Concept Questions

• How would you characterize a ductile material? Give several examples.

– A material that can be subjected to large strains before it ruptures.

– Steel, wood, natural rubber, brass, copper, gold, aluminum

Page 44: ENGR 225 Section 3.1 - 3.8

Concept Questions

• How would you characterize a brittle material? Give several examples.

– A material that exhibits little or no yielding before failure.

– Cast iron, concrete, glass, ceramics

Page 45: ENGR 225 Section 3.1 - 3.8

Concept Questions

• What is the difference between engineering stress and true stress?

– Engineering stress assumes a constant cross sectional area during elongation.

Page 46: ENGR 225 Section 3.1 - 3.8

A tale of two cities• How can you explain Elasticity?

– Property of material by which it returns to original dimensions on unloading.

• How can you explain Plasticity?

– Characteristic of material by which it cannot return to original dimensions on unloading and undergoes permanent deformation.

Page 47: ENGR 225 Section 3.1 - 3.8

Strength – Capacity to resist loads – yield stress. Higher y, higher strength.

Resilience – Measure of energy absorbed without permanent damage .

Toughness – Measure of energy absorbed before fracturing.

Ductility – Property of material which allows large deformation before fracture.

Brittleness – Property of material which allows little or no yielding before fracture.

Endurance – Ability to sustain cyclic loads.

Stiffness – Mechanical property indicated by E. Higher E means stiff material. Steeper slope in the Stress – Strain diagram.

Rigidity - Mechanical property of material indicated by G.

Material Properties

Page 48: ENGR 225 Section 3.1 - 3.8

3.7 (a) A structural member in a nuclear reactor is made of Zirconium alloy. If an axial load of 4 kip is to be supported by the member, determine the required cross sectional area. Yield stress for Zirconium is 57.5 ksi. Factor of safety 3.

(b) What value of load would cause an elongation of 0.02 inch in this member if length of member is 3 ft. Ezr = 14 x 103 ksi.

Page 49: ENGR 225 Section 3.1 - 3.8

3.26 A short cylindrical block of 2014-T6 Aluminum having an original diameter of 0.5 in and an original length of 1.5 in is placed in the smooth jaws of a vise and a compressive force of 800 lb is applied. Determine

(a) The decrease in length.(b) The new diameter.