Mechanical Properties: Part One Chapter 6: Mechanical Properties: Part One Chapter 6: Mechanical Properties: Part One © 2011 Cengage Learning Engineering. All Rights Reserved.`

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Learning Objectives Technological significance Terminology for mechanical properties The tensile test: Use of the stress–strain diagram Properties obtained from the tensile test True stress and true strain The bend test for brittle materials Hardness of materials Nanoindentation 6 - 2 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Learning Objectives Strain rate effects and impact behavior Properties obtained from the impact test Bulk metallic glasses and their mechanical behavior Mechanical behavior at small length scales 6 - 3 © 2011 Cengage Learning Engineering. All Rights Reserved.

Technological Significance Chapter 6: Mechanical Properties: Part One Technological Significance Biocompatible titanium alloys used in bone implants must have enough strength and toughness to survive in the human body for many years without failure. Mechanical robustness of small devices fabricated using nanotechnology is important. Materials processing requires a detailed understanding of the mechanical properties of materials at different temperatures and conditions of loading. 6 - 4 © 2011 Cengage Learning Engineering. All Rights Reserved.

Terminology for Mechanical Properties Chapter 6: Mechanical Properties: Part One 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 an applied stress Young’s modulus or modulus of elasticity (E) The slope of a tensile stress-strain curve in the linear regime [Figure 6-1 (b)] Elastomers Materials that show large elastic deformations 6 - 5 © 2011 Cengage Learning Engineering. All Rights Reserved.

Terminology for Mechanical Properties Chapter 6: Mechanical Properties: Part One Terminology for Mechanical Properties Shear modulus (G) Slope of the linear part of the shear stress-shear strain curve Plastic deformation or strain Permanent deformation of a material when a load is applied and then removed Strain rate Rate at which strain develops in or is applied to a material Impact loading Type of loading when materials are subjected to high strain rates 6 - 6 © 2011 Cengage Learning Engineering. All Rights Reserved.

Terminology for Mechanical Properties Chapter 6: Mechanical Properties: Part One Terminology for Mechanical Properties Viscous material One in which the strain develops over a period of time and the material does not return to its original shape after the stress is removed Viscoelastic (or anelastic) material A material with a response between that of a viscous material and an elastic material Stress relaxation Decrease in stress for a material held under constant strain as a function of time, which is observed in viscoelastic materials Newtonian Materials in which the shear stress and shear strain rate are linearly related 6 - 7 © 2011 Cengage Learning Engineering. All Rights Reserved.

Terminology for Mechanical Properties Chapter 6: Mechanical Properties: Part One Terminology for Mechanical Properties Viscosity () Measure of the resistance to flow Viscosity is defined by Kinematic viscosity ()  =  / Non-Newtonian materials Materials with a nonlinear relationship between shear stress and shear strain rate Shear thinning Materials in which the apparent viscosity decreases with increasing rate of shear Shear thickening Materials in which the apparent viscosity increases with increasing rate of shear 6 - 8 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.1 (a) Tensile, compressive, and shear stresses. F is the applied force. (b) Illustration showing how Young’s modulus is defined for an elastic material. (c) For nonlinear materials, we use the slope of a tangent as a varying quantity that replaces the Young’s modulus. © 2011 Cengage Learning Engineering. All Rights Reserved. 6 - 9

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.3 Shear stress-shear strain rate relationships for Newtonian and non-Newtonian materials. 6 - 10 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.4 Apparent viscosity as a function of shear strain rate. (b) and (c) Illustration of a Bingham plastic. Note the horizontal axis in (b) is shear strain. Take the slope of the line obtained by joining the origin to any point on the curve, what we determine is the apparent viscosity. Apparent viscosity(app) - Viscosity obtained by dividing shear stress by the corresponding value of the shear-strain rate for that stress. 6 - 11 © 2011 Cengage Learning Engineering. All Rights Reserved.

Terminology for Mechanical Properties Chapter 6: Mechanical Properties: Part One Terminology for Mechanical Properties Bingham plastics Apparent yield strength Obtained by interpolating the shear stress-shear strain rate data to zero shear strain rate Thixotropic behavior Materials that show shear thinning and also an apparent viscosity that at a constant rate of shear decreases with time Rheopectic behavior Materials that show shear thickening and also an apparent viscosity that at a constant rate of shear increases with time 6 - 12 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.5 A unidirectional force is applied to a specimen in the tensile test by means of the moveable crosshead. The crosshead movement can be performed using screws or a hydraulic mechanism. 6 - 13 © 2011 Cengage Learning Engineering. All Rights Reserved.

The Tensile Test: Use of the Stress–Strain Chapter 6: Mechanical Properties: Part One The Tensile Test: Use of the Stress–Strain Diagram Load The force applied to a material during testing Strain gage or extensometer A device used for measuring strain Glass-transition temperature (Tg) Temperature below which a ductile material behaves as if it is brittle 6 - 14 © 2011 Cengage Learning Engineering. All Rights Reserved.

The Tensile Test: Use of the Stress–Strain Chapter 6: Mechanical Properties: Part One The Tensile Test: Use of the Stress–Strain Diagram Engineering stress (S) = F Ao Engineering strain (e) = Δl lo where Ao original cross-sectional area of the specimen before the test begins. lo original length between the gage marks. Δl change in the length after a force of F is applied Units Common units for stress are pounds per square inch (psi) and MegaPascals (MPa). Units for strain include inches/inches, m/m, and cm/cm or strain may be written as unitless Engineering stress - The applied load, or force, divided by the original area over which the load acts. Engineering strain - Elongation per unit length calculated using the original dimensions. 6 - 15 © 2011 Cengage Learning Engineering. All Rights Reserved.

Properties Obtained from the Tensile Test Chapter 6: Mechanical Properties: Part One Properties Obtained from the Tensile Test Yield strength Elastic limit The magnitude of stress at which plastic deformation commences. Proportional limit Level of stress above which the relationship between stress and strain is not linear. Offset strain value Value of strain (e.g., 0.002) used to obtain the offset yield stress value. 6 - 16 © 2011 Cengage Learning Engineering. All Rights Reserved.

Properties Obtained from the Tensile Test Chapter 6: Mechanical Properties: Part One Properties Obtained from the Tensile Test Offset yield strength Stress value obtained graphically that describes the stress that gives no more than a specified amount of plastic deformation (usually 0.002). Yield point phenomenon Abrupt transition from elastic deformation to plastic flow which occurs in some materials. 6 - 17 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.8 (a) Determining the 0.2% offset yield strength in gray cast iron, and (b) upper and lower yield point behavior in a low carbon steel. 6 - 18 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.9 The stress obtained at the highest applied force is the tensile strength (STS), which is the maximum stress on the engineering stress-strain curve. This value is commonly known as the ultimate tensile strength. At some point, one region deforms more than others and a large local decrease in the cross-sectional area occurs. The locally deformed region is called a “neck” and the phenomenon is called necking. Localized deformation of a ductile material during a tensile test produces a necked region. The micrograph shows a necked region in a fractured sample. 6 - 19 © 2011 Cengage Learning Engineering. All Rights Reserved.

Properties Obtained from the Tensile Test Chapter 6: Mechanical Properties: Part One Properties Obtained from the Tensile Test Elastic properties Hooke’s law The linear-relationship between stress and strain in the elastic portion of the stress-strain curve. It is denoted by the ratio E = S/e. Stiffness Measure of a material’s resistance to elastic deformation. Stiffness of a component is directly proportional to its Young’s modulus. 6 - 20 © 2011 Cengage Learning Engineering. All Rights Reserved.

Properties Obtained from the Tensile Test Chapter 6: Mechanical Properties: Part One Properties Obtained from the Tensile Test Poisson’s ratio () The negative of the ratio between the lateral and longitudinal strains in the elastic region. Denoted by the ratio  = - elateral / elongitudinal Modulus of resilience The maximum elastic energy absorbed by a material when a load is applied. 6 - 21 © 2011 Cengage Learning Engineering. All Rights Reserved.

The Tensile Test: Use of the Stress–Strain Chapter 6: Mechanical Properties: Part One The Tensile Test: Use of the Stress–Strain Diagram Tensile toughness Energy absorbed by a material prior to fracture. Sometimes measured as the area under the true stress- strain curve (also known as the work of fracture). Ductility: The ability of a material to be permanently deformed without breaking when a force is applied. 6 - 22 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.13 The effect of temperature (a) on the stress-strain curve and (b) on the tensile properties of an aluminum alloy. 6 - 23 © 2011 Cengage Learning Engineering. All Rights Reserved.

True Stress and True Strain Chapter 6: Mechanical Properties: Part One True Stress and True Strain where A instantaneous area over which the force F is applied. l instantaneous sample length. l0 initial length. After necking begins, Instantaneous area A is the cross-sectional area of the neck. © 2011 Cengage Learning Engineering. All Rights Reserved. 6 - 24

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.14 6 - 25 © 2011 Cengage Learning Engineering. All Rights Reserved.

The Bend Test for Brittle Materials Chapter 6: Mechanical Properties: Part One The Bend Test for Brittle Materials Flexural strength for a three-point bend test Flexural modulus The maximum stress or flexural stress for a four-point bend test Flexural strength [modulus of rupture] - The stress required to fracture a specimen in a bend test. Flexural modulus - The modulus of elasticity calculated from the results of a bend test; it is proportional to the slope of the stress-deflection curve. © 2011 Cengage Learning Engineering. All Rights Reserved. 6 - 26

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.18 Three-point bend test setup (b) Four-point bend test setup 6 - 27 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Hardness of Materials Hardness test: Measure of resistance to penetration of the surface of a material by a hard object. Bulk hardness of materials measured using loads > 2N. where F applied load in kilograms. D diameter of the indenter in millimeters. Di diameter of the impression in millimeters. © 2011 Cengage Learning Engineering. All Rights Reserved. 6 - 28

Figure 6.19 - Indenters for the Brinell and Rockwell Hardness Tests Chapter 6: Mechanical Properties: Part One Figure 6.19 - Indenters for the Brinell and Rockwell Hardness Tests In the Brinell hardness test, a hard steel sphere (usually 10 mm in diameter) is forced into the surface of the material. The Rockwell hardness test uses a small-diameter steel ball for soft materials and a diamond cone, or Brale, for harder materials. E.g.: Brinell hardness is related to the tensile strength of steel by approximation Tensile strength (psi) = 500HB where HB has units of kg/mm2 and 1 psi = 6.895  103 Pa. The Knoop hardness (HK) test is a microhardness test, forming small indentations that a microscope is required to obtain the measurement. 6 - 29 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Nanoindentation Nanoindention is hardness testing performed at the nanometer length scale. The reduced elastic modulus Er is related to the unloading stiffness S according to where  is a constant for the shape of the indenter ( = 1.034 for a Berkovich indenter) where E elastic modulus of the material being indented  Poisson’s ratio of the material being indented Ei elastic modulus of the indenter i Poisson’s ratio of the indenter 6 - 30 © 2011 Cengage Learning Engineering. All Rights Reserved.

Figure 6.20 - Indentation in a Bulk Metallic Glass Chapter 6: Mechanical Properties: Part One Figure 6.20 - Indentation in a Bulk Metallic Glass An indentation in a Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 bulk metallic glass made using a Berkovich tip in a nanoindenter. 6 - 31 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.21 6 - 32 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.23 The impact test: (a) the Charpy and Izod tests, and (b) dimensions of typical specimens. 6 - 33 © 2011 Cengage Learning Engineering. All Rights Reserved.

Strain Rate Effects and Impact Behavior Chapter 6: Mechanical Properties: Part One Strain Rate Effects and Impact Behavior Impact test Measures the ability of a material to absorb the sudden application of a load without breaking Impact energy Energy required to fracture a standard specimen when the load is applied suddenly Impact toughness Ability of a material to withstand an impact blow Tensile toughness Energy absorbed by a material subjected to tension prior to fracture Fracture toughness Resistance of a material to failure in the presence of a flaw 6 - 34 © 2011 Cengage Learning Engineering. All Rights Reserved.

Properties Obtained from the Impact Test Chapter 6: Mechanical Properties: Part One Properties Obtained from the Impact Test Ductile to brittle transition temperature (DBTT) Temperature below which a material behaves in a brittle manner in an impact test. Notch sensitivity Evaluated by comparing the absorbed energies of notched versus unnotched specimens. Use of impact properties Absorbed energy and the DBTT are very sensitive to loading conditions. 6 - 35 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.26 6 - 36 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.27 A schematic diagram of the compressive stress-strain behavior of various engineering materials including metallic glasses. Serrated flow is observed in the plastic region. 6 - 37 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Figure 6.29 A schematic diagram of a thin film on a substrate. The grains have diameters on the order of the film thickness. Note that thin films typically have thicknesses about 1/500th of the substrate thickness (some are far thinner), and so, this diagram is not drawn to scale. (b) Stress versus temperature for thermal cycling of a 0.5 m polycrystalline aluminum thin film on an oxidized silicon substrate during a wafer curvature experiment. 6 - 38 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Key Terms Stress Strain Elastic strain Young’s modulus or modulus of elasticity (E) Shear modulus (G) Plastic deformation Plastic strain Strain rate Impact loading Viscoelastic Stress relaxation Shear thinning Apparent viscosity Bingham plastics Yield strength Thixotropic behavior Rheopectic behavior Load Glass-transition temperature Engineering stress 6- 39 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Key Terms Engineering strain Elastic limit Proportional limit Offset strain value Offset yield strength Yield strength Plastic strain Yield point phenomenon Tensile strength Ultimate tensile strength Necking Hooke’s law Poisson’s ratio Modulus of resilience Tensile toughness or Work of fracture Ductility Percent elongation Percent reduction in area True stress True strain 6 - 40 © 2011 Cengage Learning Engineering. All Rights Reserved.

© 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 6: Mechanical Properties: Part One Key Terms Bend test Elastic limit Flexural strength or Modulus of rupture Flexural modulus Hardness test Macrohardness Impact energy Impact toughness Tensile toughness Fracture toughness Ductile to brittle transition temperature Notch sensitivity Modulus of resilience 6- 41 © 2011 Cengage Learning Engineering. All Rights Reserved.