PDT 153 Materials Structure And Properties Chapter 7: Introduction to Mechanical Properties of Materials Prepared by: Dr. Tan Soo Jin

Technological Significance Aircraft, such as the one shown here, makes use of aluminum alloys and carbon-fiber-reinforced composites. The materials used in sports equipment must be lightweight, stiff, tough, and impact resistant.

Terminology for Mechanical Properties Stress - Force or load per unit area of cross-section over which the force or load is acting. Strain - Elongation change in dimension per unit length. Young’s modulus - The slope of the linear part of the stress-strain curve in the elastic region, same as modulus of elasticity.

Stress and Strain in Metals Metals undergo deformation under uniaxial tensile force. Elastic deformation: Metal returns to its original dimension after tensile force is removed. Plastic deformation: The metal is deformed to such an extent such that it cannot return to its original dimension

Engineering Stress and Strain F (Average uniaxial tensile force) A0 (Original cross-sectional area) Units of Stress are PSI or N/m2 (Pascals) 1 PSI = 6.89 x 103 Pa Engineering strain = ε = Change in length Original length Units of strain are in/in or m/m.

Poisons’s Ratio Poisons ratio = Usually poisons ratio ranges from 0.25 to 0.4. Example: Stainless steel 0.28 Copper 0.33

Shear Stress and Shear Strain S (Shear force) τ = Shear stress = A (Area of shear force application) Elastic Modulus G = τ / γ Amount of shear displacement Shear strain γ = Distance ‘h’ over which shear acts.

Tensile test Strength of materials can be tested by pulling the metal to failure. Specimen Extensometer Force data is obtained from Load cell Strain data is obtained from Extensometer. Load Cell

Tensile test (Cont..) Commonly used Test specimen Typical Stress-strain curve

Tensile test (Cont..) (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. A unidirectional force is applied to a specimen in the tensile test by means of the moveable crosshead. The cross-head movement can be performed using screws or a hydraulic mechanism

Tensile test (Cont..) Tensile stress-strain curves for different materials. Note that these are qualitative

Stress-Strain Curve

Stress-Strain Curve (Cont..) The stress-strain curve for an aluminum alloy from Table 6.1

Mechanical Properties Modulus of elasticity (E) : Stress and strain are linearly related in elastic region. (Hooks law) Higher the bonding strength, higher is the modulus of elasticity. Examples: Modulus of Elasticity of steel is 207 Gpa. Modulus of elasticity of Aluminum is 76 Gpa E = σ (Stress) ε (Strain) Stress Strain Linear portion of the stress strain curve Δε Δσ

Yield Strength Yield strength is strength at which metal or alloy show significant amount of plastic deformation. 0.2% offset yield strength is that strength at which 0.2% plastic deformation takes place. Construction line, starting at 0.2% strain and parallel to elastic region is drawn to 0.2% offset yield strength.

Ultimate Tensile Strength Ultimate tensile strength (UTS) is the maximum strength reached by the engineering stress strain curve. Necking starts after UTS is reached. More ductile the metal is, more is the necking before failure. Stress increases till failure. Drop in stress strain curve is due to stress calculation based on original area.

Percent Elongation Percent elongation is a measure of ductility of a material. It is the elongation of the metal before fracture expressed as percentage of original length. % Elongation = Measured using a caliper fitting the fractured metal together. Example:- Percent elongation of pure aluminum is 35% For 7076-T6 aluminum alloy it is 11% Final length* – initial Length* Initial Length

Percent Reduction in Area Percent reduction area is also a measure of ductility. The diameter of fractured end of specimen is meas- ured using caliper. Percent reduction in area in metals decreases in case of presence of porosity. % Reduction Area = Initial area – Final area Final area

True Stress – True Strain True stress and true strain are based upon instantaneous cross-sectional area and length. True Stress = σt = True Strain = εt = True stress is always greater than engineering stress. F Ai (instantaneous area)

True Stress – True Strain (Cont..) True stress - The load divided by the actual cross-sectional area of the specimen at that load. True strain - The strain calculated using actual and not original dimensions, given by εt ln(l/l0). The relation between the true stress-true strain diagram and engineering stress-engineering strain diagram. The curves are identical to the yield point

Example 1: Young’s Modulus of Al Alloy From the data in Table 1, calculate the modulus of elasticity of the aluminum alloy. Use the modulus to determine the length after deformation of a bar of initial length of 50 in. Assume that a level of stress of 30,000 psi is applied. Solution:

Example 2: Ductility of an Al Alloy The aluminum alloy in Table 1 has a final length after failure of 2.195 in. and a final diameter of 0.398 in. at the fractured surface. Calculate the ductility of this alloy. Solution:

Example 3: True Stress and True Strain Calculation Compare engineering stress and strain with true stress and strain for the aluminum alloy in Table 6.1 at (a) the maximum load. The diameter at maximum load is 0.497 in. Solution: