LECTURE 9.1LECTURE 9.1

LECTURE OUTLINELECTURE OUTLINE

Weekly DeadlinesWeekly DeadlinesStress and StrainStress and Strain

Lesson# 9 Name Properties, Part 1: Mechanical Properties

Lectures Monday: Lecture 9.1 Stress and Strain

Wednesday: Lecture 9.2 Deformation and Dislocations

Required Book Reading 1 (For the End-of-Lesson Quiz)

Part E: The Materials Science Tetrahedron II: Properties Chapters 25, 26, and 27

Required Book Reading 2 (For the Lesson 10 Practice Quiz)

Part E: The Materials Science Tetrahedron II: Properties Chapters 28 and 29

Animations Ian Harrison: "Mechanical Properties" Biographies Mineral of the Week

Camera-Ready Review Article (CRRA)

None

Practice Quiz Practice quizzes (5 questions each) are available. There are also practice quizzes in Perception. Questions are similar to those in the main quiz database. A complete “prototype” end-of-lesson (practice) quiz is found in the Lesson 09 Lecture Notes folder.

End-of-Lesson Quiz Quiz 9 will consist of ~ 20 questions for a total of 50 points. Quizzes are “individualized” but questions are taken from a large database. The material covered will be the book reading and animations.

STRESS AND STRAINSTRESS AND STRAIN

The Three Stages in the Deformation of a The Three Stages in the Deformation of a MaterialMaterial

The “Atomic Spring Model”The “Atomic Spring Model”Stress and Strain, CalculationsStress and Strain, CalculationsThe Stress-Strain CurveThe Stress-Strain CurveThe Meaning of Young’s ModulusThe Meaning of Young’s Modulus

THE THREE STAGES OF THE THREE STAGES OF DEFORMATIONDEFORMATION

ELASTIC DEFORMATION

Is temporary (reversible) and involves bond stretching.

PLASTIC DEFORMATION

Is permanent (irreversible), and involves bond breaking.

FRACTURE IS CATASTROPHIC!

HOOKE’S LAWHOOKE’S LAW1234567

ATOMIC SPRINGS IATOMIC SPRINGS I

aa

P

PLlSample #1a)b)

P

P

4L4l

Sample #2

a)b)

ATOMIC SPRINGS IIATOMIC SPRINGS II

a

aaArea, A = a2L

P

Pa)

P

Pb)

STRESS AND STRAINSTRESS AND STRAIN

Stress = Load/AreaStress = Load/Area

Strain = Elongation/Original LengthStrain = Elongation/Original Length

Young’s Modulus = Stress/StrainYoung’s Modulus = Stress/Strain

STRESS AND STRAIN STRESS AND STRAIN CALCULATIONS ICALCULATIONS I

a

40mm40mm16000kg1000mm

1600kg1500mm20mm50mm

a) b)

STRESS AND STRAIN STRESS AND STRAIN CALCULATIONS IICALCULATIONS II

a) A square metal bar of length 1,000 mm and width a) A square metal bar of length 1,000 mm and width 40 mm is loaded in tension and begins to yield at 40 mm is loaded in tension and begins to yield at 16,000 kg. Its length is now 1,010 mm.16,000 kg. Its length is now 1,010 mm.

What is the yield stress?What is the yield stress? What is the strain at yield?What is the strain at yield?

Stress = 16,000/40 x 40 = 10kg/mmStress = 16,000/40 x 40 = 10kg/mm22

Strain = 1,010 - 1,000/1,000 = 10 = 0.01Strain = 1,010 - 1,000/1,000 = 10 = 0.01

STRESS AND STRAIN STRESS AND STRAIN CALCULATIONS IIICALCULATIONS III

Suppose that a second bar, of the same material and in the same Suppose that a second bar, of the same material and in the same condition, is 20 mm x 50 mm in cross-section and is 1,500 mm condition, is 20 mm x 50 mm in cross-section and is 1,500 mm long. At what stress will this second bar yield, and at what long. At what stress will this second bar yield, and at what elongation?elongation?

Stress = Load, 10/Area = Load/20 x 50Stress = Load, 10/Area = Load/20 x 50

Load = 10,000 kgLoad = 10,000 kg

Strain = Elongation 0.01/Original Length = ?/ 1,500Strain = Elongation 0.01/Original Length = ?/ 1,500

Elongation = 1500 x 0.01 = 15mmElongation = 1500 x 0.01 = 15mm

STRESS AND STRAIN STRESS AND STRAIN CALCULATIONS IVCALCULATIONS IV

What is the Young’s Modulus of the Material?What is the Young’s Modulus of the Material?

Young’s Modulus = Stress/StrainYoung’s Modulus = Stress/Strain

Young’s Modulus = 10/0.01 = 1,000 kg/mm2Young’s Modulus = 10/0.01 = 1,000 kg/mm2

THE STRESS-STRAIN CURVETHE STRESS-STRAIN CURVE

YOUNG’S MODULUS: YOUNG’S MODULUS: CERAMICS, METALS, AND CERAMICS, METALS, AND

POLYMERSPOLYMERS

STRESS-STRAIN CURVE OF A STRESS-STRAIN CURVE OF A STAINLESS STEEL ISTAINLESS STEEL I

STRESS-STRAIN CURVE OF A STRESS-STRAIN CURVE OF A STAINLESS STEEL IISTAINLESS STEEL II

ON STRENGTH AND ON STRENGTH AND STIFFNESSSTIFFNESS

Lest there be any possible, probable, shadow of Lest there be any possible, probable, shadow of doubt, strength is not, repeat not, the same thing as doubt, strength is not, repeat not, the same thing as stiffness. Stiffness, Young's modulus, is concerned stiffness. Stiffness, Young's modulus, is concerned with how stiff, flexible, springy or floppy a material with how stiff, flexible, springy or floppy a material is. Strength is the force or stress needed to break a is. Strength is the force or stress needed to break a thing. A biscuit is stiff but weak, steel is stiff and thing. A biscuit is stiff but weak, steel is stiff and strong, nylon is flexible but strong, raspberry jelly is strong, nylon is flexible but strong, raspberry jelly is flexible and weak. The two properties together flexible and weak. The two properties together describe a solid about as well as you can reasonably describe a solid about as well as you can reasonably expect two figures to do.expect two figures to do.

J. E. Gordon, J. E. Gordon, The New Science of Strong MaterialsThe New Science of Strong Materials