LECTURE 9.1

LECTURE OUTLINE Weekly Deadlines Weekly Deadlines Stress and Strain Stress and Strain

STRESS AND STRAIN The Three Stages in the Deformation of a Material The Three Stages in the Deformation of a Material The “Atomic Spring Model” The “Atomic Spring Model” Stress and Strain, Calculations Stress and Strain, Calculations The Stress-Strain Curve The Stress-Strain Curve The Meaning of Young’s Modulus The Meaning of Young’s Modulus

THE THREE STAGES OF DEFORMATION

HOOKE’S LAW

ATOMIC SPRINGS I

ATOMIC SPRINGS II

STRESS AND STRAIN Stress = Load/Area Strain = Elongation/Original Length Young’s Modulus = Stress/Strain

STRESS AND STRAIN CALCULATIONS I

STRESS AND STRAIN CALCULATIONS II a) A square metal bar of length 1,000 mm and width 40 mm is loaded in tension and begins to yield at 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/mm 2 Strain = 1, ,000/1,000 = 10 = 0.01

STRESS AND STRAIN CALCULATIONS III 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 long. At what stress will this second bar yield, and at what elongation? Stress = Load, 10/Area = Load/20 x 50 Load = 10,000 kg Strain = Elongation 0.01/Original Length = ?/ 1,500 Elongation = 1500 x 0.01 = 15mm

STRESS AND STRAIN CALCULATIONS IV What is the Young’s Modulus of the Material? Young’s Modulus = Stress/Strain Young’s Modulus = 10/0.01 = 1,000 kg/mm2

THE STRESS-STRAIN CURVE

YOUNG’S MODULUS: CERAMICS, METALS, AND POLYMERS

STRESS-STRAIN CURVE OF A STAINLESS STEEL I

STRESS-STRAIN CURVE OF A STAINLESS STEEL II

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