Engineering Materials Ch.E 311 Lecture 2 Assignment • Give an Industrial Example of any Engineering Material from the groups: • Composites • Advanced Materials Mechanical Properties of Materials • Many materials, when in service, are subjected to forces or loads; examples include: • The aluminum alloy from which an airplane wing is constructed • The steel in an automobile axle • In such situations it is necessary to know the characteristics of the material and to design the member from which it is made such that any resulting deformation will not be excessive and fracture will not occur. • The mechanical behavior of a material reflects the relationship between its response or deformation to an applied load or force. • Important mechanical properties are: • • • • Strength Hardness Ductility Stiffness Introduction to Testing • Testing of materials are necessary for many reasons, and the subject of materials testing is very broad one. Some of the purpose for the testing of materials are: 1. To determine the quality of a material. This may be one aspect of process control in production plant. 2. To determine properties such as strength, hardness, and ductility. 3. To check for the flaws within a material or in a finished component. 4. To assess the performance of the material. • Consequently, it is imperative that there be some consistency in the manner in which tests are conducted and in the interpretation of their results. This consistency is accomplished by using standardized testing techniques. • The most active organization is the American Society for Testing and Materials (ASTM) Standards. Concepts of Stress and Strain • There are three principal ways in which a load may be applied: namely, • Tension • Compression • Shear • In engineering practice many loads are torsional rather than pure shear. Types of Stress Tensile Stress • A force which points away from its point of application. Compressive Stress • The force which points towards its point of application. Tensile & Compressive stress Shear Stress • The force which acts parallel to the cross sectional area. Shear stress Mechanical Stress • There are two types of mechanical stress, 1. Elastic Stress 2. Viscous Stress • Elastic stress is related to the solid object and Viscous stress is related to the fluids. Strain • Strain is defined as “deformation of a solid due to stress”. It is the amount of deformation which an object experiences compared to its original size and shape. πΏπ π π = = ππ πΈ where • ε = unitless measure of engineering strain • δl= change of length (m, in) • lo = initial length (m, in) • E = Young's modulus (Modulus of Elasticity) (Pa, psi) Types of Strain 1. 2. 3. 4. 5. Tensile Strain (a) Compression strain (b) Shear strain (c) Homogeneous strain (d) Non-Homogeneous strain (e) (d) (e) Hooke's Law • Hooke's law of elasticity is an approximation that states: stress and strain are proportional to each other through the relationship π = ππΈ • This is known as Hooke’s law, and the constant of proportionality E is the modulus of elasticity, or Young’s modulus. Elasticity and Plasticity • A material is said to be perfectly elastic, If deformation produced in the object due to the application of external load disappears completely with the removal of the load/stress. • A material is said to be plastic, If deformation is retained after removing the applied stress. • The point of transition from elastic to plastic is termed Elastic limit or yield point. • Measured at an offset strain of 0.2% as this point is difficult to measure. • The yield point, *alternatively called the elastic limit*, marks the end of elastic behavior and the beginning of plastic behavior. Elastic and Plastic Deformation Modulus of Elasticity • Within an elastic limit, stress is directly proportional to strain. ππ‘πππ π ∝ ππ‘ππππ ππ‘πππ π = π ππππ π‘πππ‘ ππ‘ππππ • This constant is known as Coefficient of Elasticity or Modulus of Elasticity. Young’s Modulus • It is defined as a ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. ππππ πππ ππ‘πππ π πΆππππππ π ππ£π ππ‘πππ π πΈ= = ππππ πππ ππ‘ππππ πΆππππππ π ππ£π ππ‘ππππ πΈ= ππ‘ ππ = ππ‘ ππ πΉ πΈ= πΈ= δπ π΄π ππ πΉππ π΄π δπΏ Shear Modulus (Modulus of Rigidity) • The ratio of shear stress and shear strain. π πΊ= ππ Bulk Modulus • The ratio of normal stress and volumetric strain. Or • Pressure applied/Fractional change in volume of an object. Stress-Strain Curve Example Tensile /Tension Tests • If a load is applied uniformly over a cross section or surface of a sample, the mechanical behavior may be determined by a simple stress–strain test. • A tensile testing machine is used. • The main principle of the tensile test denotes the resistance of a material to a tensile load applied axially to a specimen. Tensile testing machine • The gauge length (L0) is the length over which the elongation of the specimen is measured. • The minimum parallel length (Lc) is the minimum length over which the specimen must maintain a constant cross-sectional area before the test load is applied. Typical progress of a tensile test: (1) beginning of test, no load; (2) uniform elongation and reduction of cross-sectional area; (3) continued elongation, maximum load reached; (4) necking begins, load begins to decrease; and (5) fracture. If pieces are put back together as in (6), final length can be measured. Tensile Testing Outcome • The output of such a tensile test is recorded (usually on a computer) as load or force versus elongation. • These load–deformation characteristics are dependent on the specimen size. For example, it will require twice the load to produce the same elongation if the cross-sectional area of the specimen is doubled. • To minimize these geometrical factors, load and elongation are normalized to the respective parameters of engineering stress and engineering strain. • Engineering Stress • F is the instantaneous load applied perpendicular to the specimen cross section, in units of newtons (N) or pounds force , and Ao is the original cross sectional area before any load is applied (m2 or in2.). The units of engineering stress (referred to subsequently as just stress) are megapascals, MPa (SI) (where 1 MPa N/m2), and pounds force per square inch, psi (Customary U.S.)2 • Engineering strain • lo is the original length before any load is applied, and li is the instantaneous length. Sometimes the quantity is denoted as Δl and is the deformation elongation or change in length at some instant, as referenced to the original length. • Engineering strain (subsequently called just strain) is unitless, but meters per meter or inches per inch are often used; the value of strain is obviously independent of the unit system. Sometimes strain is also expressed as a percentage, in which the strain value is multiplied by 100. Stress-Strain curve Tensile Properties • EL = Elastic limit, up to which Hook’s Law (Stress proportional to Strain) is valid. The material comes back to original shape when the load is released. • The proportional limit, PL, the load at which the curve deviates from linearity, is taken as the elastic portion. • The slope of the linear region is the Young’s Modulus or Elastic Modulus (E). • Loading beyond PL produces permanent or plastic deformation. The onset point of plastic deformation is known as Yield stress (YS). • In many other metals and alloys the yield point is not distinct (Curve 2, Fig. b). In such cases, a line parallel to the linear region is drawn at a strain = 0.002 (0.2%) and its intercept on the plastic region is taken as the yield stress (Fig. b). This is called 0.2% Proof stress. • The stress at the maximum load is called ultimate tensile strength (UTS). • The strain up to UTS is the uniform plastic strain. Beyond this the cross sectional area reduces and necking takes place. • The fracture strain Ef = (Lf - Lo)/Lo, where Lf is the length after fracture, is taken as the measure of Ductility. Ductile Vs. Brittle Fracture • The fracture strain • The reduction of area at fracture, is taken as the measure of Ductility. • A ductile material exhibits high fracture strain, that is, it undergoes significant plastic deformation before fracture. • A brittle material is the one which exhibits little or no plastic deformation before fracture. Resilience The ability of a material to absorb energy in the elastic region. This is given by the strain energy per unit volume, which is the area of the elastic region. Thus, resilient materials are those having high yield strengths and low moduli of elasticity. • High resilience is a property required in spring steels whereas structural steels have high toughness but lower resilience. Toughness • Toughness is a mechanical term that is used in several contexts; loosely speaking, it is a measure of the ability of a material to absorb energy up to fracture. • Specimen geometry as well as the manner of load application are important in toughness determinations. True Stress and Strain Poisson’s Ratio A tensile stress imposed on a metal specimen in the x direction that produces an extension along that axis, while it produces contraction along the transverse y and z axis. • A tensile stress imposed on a metal specimen in the x direction that produces an extension along that axis, while it produces contraction along the transverse y and z axis. • The ratio of the lateral to axial strain is the Poisson's ratio. • For many metals and other alloys, values of Poisson’s ratio range between 0.25 and 0.35. • Figure: Axial (z) elongation (positive strain) and lateral (x and y) contractions (negative strains) in response to an imposed tensile stress. Solid lines represent dimensions after stress application; dashed lines, before. True stress–true strain relationship in plastic region of deformation • The true stress–strain curve from the onset of plastic deformation to the point at which necking begins is known by: • In this expression, K and n are constants; K is is the strength coefficient and n is known as strain-hardening exponent. • The values of K and n vary from alloy to alloy and will also depend on the condition of the material (i.e., whether it has been plastically deformed, heattreated, etc.). • Value of n varies from 0-1, n = 0, perfectly plastic solid, n = 1, elastic solid For most metals n = 0.1 – 0.5 Problem to solve • A rod of aluminum 6061-T6 has a square cross section measuring 6mm by 6mm. Using the yield stress as the failure stress, find the maximum tensile load that the rod can sustain. The yield stress of aluminum 6061-T6 is 240 MPa. Reference • Chapter 6, Mechanical Properties of Metals • Material Science And Engineering - An Introduction By William D. Callister.
