Chapter Objectives Understand how to measure the stress and strain through experiments Correlate the behavior of some engineering materials to the stress-strain diagram. Copyright © 2011 Pearson Education South Asia Pte Ltd

1. Reading QuizReading Quiz 2. ApplicationsApplications 3. Stress-Strain diagramStress-Strain diagram 4. Strength parametersStrength parameters 5. Poisson’s ratioPoisson’s ratio 6. Shear Stress-strain diagramShear Stress-strain diagram 7. Concept QuizConcept Quiz In-class Activities Copyright © 2011 Pearson Education South Asia Pte Ltd

TENSION AND COMPRESSION TEST Copyright © 2011 Pearson Education South Asia Pte Ltd

READING QUIZ 1)The modulus of elasticity E is a measure of the linear relationship between stress and strain. The common unit is: a)kN/mm 2 b)MPa c)GPa d)All of them Copyright © 2011 Pearson Education South Asia Pte Ltd

READING QUIZ (cont) 2) The Poisson’s ratio, v of common engineering materials lies in the range: a)0 ≤ v ≤ 1 b)0 ≤ v ≤ 0.5 c)-1 ≤ v ≤ 1 d)-0.5 ≤ v ≤ 0.5 Copyright © 2011 Pearson Education South Asia Pte Ltd

APPLICATIONS Copyright © 2011 Pearson Education South Asia Pte Ltd

APPLICATIONS (cont) Copyright © 2011 Pearson Education South Asia Pte Ltd

STRESS STRAIN DIAGRAM Copyright © 2011 Pearson Education South Asia Pte Ltd Note the critical status for strength specification  proportional limit  elastic limit  yield stress  ultimate stress  fracture stress

STRENGTH PARAMETERS Copyright © 2011 Pearson Education South Asia Pte Ltd Modulus of elasticity (Hooke’s Law) Modulus of Resistance Modulus of Toughness –It measures the entire area under the stress-strain diagram

EXAMPLE 1 Copyright © 2011 Pearson Education South Asia Pte Ltd The stress–strain diagram for an aluminum alloy that is used for making aircraft parts is shown in Fig. 3–19. 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.

EXAMPLE 1 (cont) Copyright © 2011 Pearson Education South Asia Pte Ltd When the specimen is subjected to the load, the strain is approximately mm/mm. The slope of line OA is the modulus of elasticity, From triangle CBD, Solution

EXAMPLE 1 (cont) Copyright © 2011 Pearson Education South Asia Pte Ltd This strain represents the amount of recovered elastic strain. The permanent strain is Computing the modulus of resilience, Note that the SI system of units is measured in joules, where 1 J = 1 N m. Solution

POISSON’S RATIO Copyright © 2011 Pearson Education South Asia Pte Ltd Please refer to the website for the animation: Poisson’s Ratio

EXAMPLE 2 Copyright © 2011 Pearson Education South Asia Pte Ltd A bar made of A-36 steel has the dimensions shown in Fig. 3–22. If an axial force of P = 80 kN is applied to the bar, determine the change in its length and the change in the dimensions of its cross section after applying the load. The material behaves elastically.

EXAMPLE 2 (cont) Copyright © 2011 Pearson Education South Asia Pte Ltd The normal stress in the bar is From the table for A-36 steel, E st = 200 GPa The axial elongation of the bar is therefore Solution

EXAMPLE 2 (cont) Copyright © 2011 Pearson Education South Asia Pte Ltd The contraction strains in both the x and y directions are The changes in the dimensions of the cross section are Solution

SHEAR STRESS-STRAIN DIAGRAM Copyright © 2011 Pearson Education South Asia Pte Ltd Strength parameter G – Shear modulus of elasticity or the modules of rigidity G is related to the modulus of elasticity E and Poisson’s ratio v.

EXAMPLE 3 Copyright © 2011 Pearson Education South Asia Pte Ltd A specimen of titanium alloy is tested in torsion and the shear stress– strain diagram is shown in Fig. 3–25a. Determine the shear modulus G, the proportional limit, and the ultimate shear stress. Also, determine the maximum distance d that the top of a block of this material, shown in Fig. 3– 25b, could be displaced horizontally if the material behaves elastically when acted upon by a shear force V. What is the magnitude of V necessary to cause this displacement?

EXAMPLE 3 (cont) Copyright © 2011 Pearson Education South Asia Pte Ltd By inspection, the graph ceases to be linear at point A. Thus, the proportional limit is This value represents the maximum shear stress, point B. Thus the ultimate stress is Since the angle is small, the top of the block will be displaced horizontally by Solution

EXAMPLE 3 (cont) Copyright © 2011 Pearson Education South Asia Pte Ltd The shear force V needed to cause the displacement is Solution

CONCEPT QUIZ 1)The head H is connected to the cylinder of a compressor using six steel bolts. If the clamping force in each bolt is 4000 N, determine the normal strain in the bolts. Each bolt has a diameter of 5 mm. If σ y = 280 MPa and E st = 210 GPa, what is the strain in each bolt when the nut is unscrewed so that the clamping force is released? Copyright © 2011 Pearson Education South Asia Pte Ltd

CONCEPT QUIZ (cont) a)0.970 b)0.203 c)0.970(10 -3 ) d)Insufficient information to determine because the stress is beyond yield point Copyright © 2011 Pearson Education South Asia Pte Ltd