Mechanical Properties: 1 Eyres: MSC101

Chapter Learning Objectives Identify the key features of the uniaxial stress-strain curve (elastic modulus, yield stress, ultimate tensile strength, necking, etc.) Construct a stress-strain curve given load and displacement data and calculate the ductility of the sample Calculate engineering and true stress and strain and explain why two systems of stress and strain exist Predict how the mechanical properties of a material will change when a material is subjected to different temperatures and strain rates Calculate the flexural strength and flexural modulus for a material subjected to a bend test Define the materials property of hardness and explain how it is measured at various length scales © 2014 Cengage Learning Engineering. All Rights Reserved.

Terminology for Mechanical Properties Stress: Force acting per unit area over which the force is applied Strain: Change in dimension per unit length Elastic strain: Fully recoverable strain resulting from applied stress Young’s Modulus or modulus of elasticity (E): Slope of linear section of tensile stress-strain curve Shear modulus (G): Slope of the linear part of the shear stress- strain curve © 2014 Cengage Learning Engineering. All Rights Reserved.

Definitions and units Stress: S= 𝐹 𝐴 0 Units are: 𝑁 𝑚 2 =𝑃𝑎 Strain: 𝑒= ∆𝑙 𝑙 0 Units are: 𝑚 𝑚 =dimensionless or unitless Young’s Modulus or modulus of elasticity: 𝐸= ∆𝑆 ∆𝑒 Units are: 𝑃𝑎 1 =𝑃𝑎 © 2014 Cengage Learning Engineering. All Rights Reserved.

Illustration of Stresses and Strains © 2014 Cengage Learning Engineering. All Rights Reserved.

The Tensile Test: Use of the Stress-Strain Diagram In a tensile test, a specimen is placed in the testing machine and a force, called the load, is applied slowly A strain gauge or extensometer is used to measure the amount that the specimen stretches between the gauge marks Thus, the applied load is known and the change in length Δl is measured with respect to the original length l0 © 2014 Cengage Learning Engineering. All Rights Reserved.

Properties Obtained from the Tensile Test The critical stress value needed to initiate plastic deformation is defined as the elastic limit of the material The proportional limit is defined as the as the level of stress above which the relationship between stress and strain is not linear Since neither limit can be determined precisely, they are defined at an offset strain value (typically 0.2%) The corresponding stress value is defined as the offset yield strength, also sometimes known as just yield strength © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Elastic vs. Plastic Elastic strain: Fully recoverable strain resulting from applied stress Plastic deformation, which is permanent, in a material is known as plastic strain © 2014 Cengage Learning Engineering. All Rights Reserved.

Tensile Strength and Elastic Properties The stress obtained at the highest applied force is the tensile strength, or ultimate tensile strength At some point in a tensile test, specimens undergo necking, which is a large local decrease in cross-sectional area The relationship between stress and strain is given by Hooke’s Law, which relates stress and strain linearly through Young’s modulus E Poisson’s ratio ν relates the longitudinal deformation and lateral deformation that occur simultaneously © 2014 Cengage Learning Engineering. All Rights Reserved.

Tensile Toughness, Ductility, and Temperature Effects The energy absorbed by a material prior to fracture is known as tensile toughness, the area under the true stress-strain curve Ductility is the ability of a material to be permanently deformed without breaking when a force is applied There are two common ways of measuring ductility, percent elongation and percent reduction, and both are described by the equations below Mechanical properties depend on temperature. Yield strength, tensile strength, and modulus of elasticity decrease at higher temperatures, whereas ductility commonly increases © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Question Modulus of Elasticity is defined as both 𝐸= 𝑆 𝑒 and 𝐸= ∆𝑆 ∆𝑒 Can you Explain? © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Table 6-1: The results of a tensile test of a 1.263 cm diameter aluminum alloy test bar, initial length (l0) = 5 cm. © 2014 Cengage Learning Engineering. All Rights Reserved.

Load (N) Change L (cm) Strain Stress (MPa) 0.0000 4450 0.0025 0.0005 35.52 13350 0.0075 0.0015 106.56 22240 0.0125 177.52 31150 0.0175 0.0035 248.63 33360 0.075 0.0150 266.27 35150 0.2 0.0400 280.56 35580 0.3 0.0600 283.99 35360 0.1 0.0200 282.24 33800 0.5125 0.1025 269.79

© 2014 Cengage Learning Engineering. All Rights Reserved. Identify the important values and terms in the problem statement and their connection to the diagram. © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Strain Rates Strain vs Time graphs When materials are subjected to high strain rates, we refer to the type of loading as impact loading © 2014 Cengage Learning Engineering. All Rights Reserved.

Viscous material A viscous material: strain develops over a period of time; material does not return to its original shape after the stress is removed A viscoelastic material: a response between that of viscous and elastic materials Viscoelastic materials under constant strain: level of stress decreases over time. This is known as stress relaxation (tennis racket example) Can you show Strain Recovery on the diagram?

True Stress and True Strain The decrease in engineering stress beyond the tensile strength on an engineering stress-strain curve is related to the definition of engineering stress We used the original area A0, but this is not precise since that area changes. © 2014 Cengage Learning Engineering. All Rights Reserved.

True Stress and True Strain Assuming constant volume, we can convert between definitions using the following equations 𝑒= ∆𝑙 𝑙 0 = 𝑙− 𝑙 0 𝑙 0 = 𝑙 𝑙 0 −1 𝑨𝒍= 𝑨 𝟎 𝒍 𝟎 © 2014 Cengage Learning Engineering. All Rights Reserved.

The Bend Test for Brittle Materials In many brittle materials, the normal tensile test cannot be performed because of the presence of flaws at the surface These materials are tested using the bend test By applying load at three points and causing bending, a tensile force acts on the material opposite the midpoint. Fracture begins at this location The flexural strength σbend describes a materials strength The flexural modulus Ebend is the modulus of elasticity in bending © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Hardness of Materials The hardness test measures the resistance to penetration of the surface of a material by a hard object Most common are Rockwell test and Brinell Test Force steel balls (though in some Rockwell test cases, it is a diamond cone) into the surface of a material Brinell test measures the diameter of the impression while the Rockwell test measures its depth Both tests produce a hardness number for qualitative comparison Knoop test, is a microhardness test, microscope for measurement © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Nanoindentation Microhardness Nanoindentation Dimensions of millimeters or microns Quick, easy, and inexpensive Only for macroscale samples Hardness is the only materials property that can be directly measured Nanometer length scale Small diamond tip Measure both hardness and elastic modulus at much smaller length scales © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved.