Mechanical Properties Of Metals - I 6-1

Calculate the percent cold reduction after cold rolling 0 Calculate the percent cold reduction after cold rolling 0.040-in-thick aluminum sheet to 0.025 in. Solution:

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 6-10

Engineering Stress and Strain F (Average uniaxial tensile force) Engineering stress = σ = A0 (Original cross-sectional area) Engineering stress σ = F Units of Stress are PSI or N/M2 (Pascals) Δl A0 1 PSI = 6.89 x 103 Pa Change in length Engineering strain = ε = Original length A Units of strain are in/in or m/m. F 6-11

Calculate the engineering stress in SI units on a 2 Calculate the engineering stress in SI units on a 2.00-cm-diameter rod that is subjected to a load of 1300 kg.

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 σ (Stress) Δσ E = E = Strain Δε ε (Strain) Δσ Δε Stress Linear portion of the stress strain curve 6-17

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 fiend 0.2% offset yield strength. Figure 5.23 6-18

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. Al 2024-Tempered S T R E Mpa Necking Point Al 2024-Annealed Strain Stress strain curves of Al 2024 With two different heat treatments. Ductile annealed sample necks more 6-19

Tensile Strength Figure 7.11 Typical engineering stress-strain behavior to fracture, point F. The tensile strength is indicated at point M. Very familiar property and widely used for identification of a material. It is used for the purposes of specifications and for quality control of a product.

Ductility It is a measure of the degree of plastic deformation that has been sustained at fracture. A material that experiences very little or no plastic deformation upon fracture is termed brittle. Figure 7.13 Schematic representations of tensile stress-strain behavior for brittle and ductile materials loaded to fracture.

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 6-20

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 Stress-strain curves of different metals 6-21

True Stress – True Strain True stress and true strain are based upon instantaneous cross-sectional area and length. True Stress = σt = True Strain = εt = F Ai (instantaneous area) 6-22

Hardness and Hardness Testing Hardness is a measure of the resistance of a metal to permanent (plastic) deformation. General procedure: Press the indenter that is harder than the metal Into metal surface. Withdraw the indenter Measure hardness by measuring depth or width of indentation. Rockwell hardness tester Figure 5.27 6-27

Hardness Tests Table 5.2 6-28

Tensile Testing of Aluminum Alloy Example 1: Tensile Testing of Aluminum Alloy Convert the change in length data in Table 6-1 to engineering stress and strain and plot a stress-strain curve.

Example 1: SOLUTION

Young’s Modulus of Aluminum Alloy Example 2 : Young’s Modulus of Aluminum Alloy From the data in Example 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. Example :SOLUTION

Ductility of an Aluminum Alloy Example 3 : Ductility of an Aluminum Alloy The aluminum alloy in Example 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. Example 3 :SOLUTION

True Stress and True Strain Calculation Example 4: True Stress and True Strain Calculation Compare engineering stress and strain with true stress and strain for the aluminum alloy in Example 6.1 at (a) the maximum load and (b) fracture. The diameter at maximum load is 0.497 in. and at fracture is 0.398 in. Example 4: SOLUTION

Example 4 : SOLUTION (Continued)

Example Problem 5 A cylindrical specimen of steel having an original diameter of 12.8 mm is tensile tested to fracture and found to have an engineering fracture strength (σf) of 460 MPa. If its cross-sectional diameter at fracture is 10.7 mm, determine: (a) The ductility in terms of percent reduction in area (b) The true stress at fracture