Poisons Ratio Poisons ratio = . w0 w Usually poisons ratio ranges from υ ( nu) Poisons ratio = . w0 w Usually poisons ratio ranges from 0.25 to 0.4. Example: Stainless steel 0.28 Copper 0.33 A longitudinal elastic deformation of a metal produces an accompanying lateral dimensional change. A tensile stress segma produces an axial strain and lateral contraction of and 1 1

Table 6.1

Mechanical Property obtained from the Engineering Tensile Test Modulus of elasticity Yield strength at 0.2 percent offset Ultimate tensile strength Percent elongation at fracture Percent reduction in area at fracture

Physical Properties Stiffness - a measure of the resistance offered by an elastic body to elastic deformation Elastic – determine how much a material will compress under a given amount of pressure without undergoing deformation Strength – is the ability to withstand an applied stress without failure Toughness - used to describe combination of strong and ductile

Malleable - a material that can be Straighten without fructure Ductility - a measure of degree of plastic deformation that has been sustained at fracture Malleable - a material that can be Straighten without fructure Strain – the amount of deformation Brittle – a material that experience very little or no plastic deformation upon fracture

Sample Problem 6.25. The following engineering stress-strain data were obtained for a 0.2% C plain-carbon steel (a) Plot the engineering stress-strain curve. (b) Determine the tensile elastic modulus of this steel (c ) Elastic limit (d ) Determine the 0.2 percent offset yield strength for this steel (e) Ultimate tensile strength of the alloy (c) Determine the percent elongation at fracture

Stress Strain 30 0.001 55 0.002 60 0.005 68 0.01 72 0.02 74 0.04 75 0.06 76 0.08 0.1 73 0.12 69 0.14 65 0.16 56 0.18 51 0.19

Stress and Strain in metals Engineering Stress-Strain Diagram Experimental plot of engineering stress (σ) Versus Engineering strain (ε); σ is normally plotted as the y axis and ε as the x axis.

Mechanical properties of metals Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram 1. Modulus of Elasticity (E) The linear elastic region (OP): linear means that the relationship between stress and strain obeys the uniaxial Hook’s law. σ=E ε E (modulus of elasticity) can be determine by measuring the slope of the curve in this region. E= σ/ε Units of psi or Pa

Higher the bonding strength, higher is the modulus of elasticity. 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 10 10

Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram 2. The Elastic Limit (E) Upon continued loading past point P, a transition to a new region takes place. In this region (PE), the relationship between stress and strain is no longer linear but the behavior is still elastic. Point E called the elastic limit. Up to point E, if one removes the load, the specimen will regain its original shape and dimensions.

3. Yield Strength (point) (Y) Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram 3. Yield Strength (point) (Y) With additional loading applied to the specimen, past point E, the material reaches the yield point (Y). The deformation experienced by the material past point Y is permanent and is called plastic deformation.

3. Yield Strength (point) (Y) Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram 3. Yield Strength (point) (Y) The stress at which yield occurs, is called the yield strength of the material. In order to have a unified standard, the 0.2 % offset yield strength is used. Engineers often design various components to protect against yield. Calculation method of the yield strength

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. 15 15

4. Ultimate Tensile strength (UTS) Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram 4. Ultimate Tensile strength (UTS) With continued loading past the yield point (Y), the specimen undergoes severe plastic deformation. Although the specimen becomes longer and thinner in this region, it retains its cylindrical shape up to point U. The stress corresponding to point U is called ultimate strength of the metal. It represents the largest stress or the peak point in the stress-strain diagram.

4. Ultimate Tensile strength (UTS) Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram 4. Ultimate Tensile strength (UTS) In region YU, as the metal plastically deforms, it becomes stronger, i.e, one needs to apply larger loads to cause the same level of deformation. This phenomenon is called strain hardening). Also in this region (YU), as the length increases, the cross-sectional area of the specimen becomes smaller. This is called Poissons effect.

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. 18 18

Tensile Test (Cont) Commonly used Test specimen Typical Stress-strain curve 19 19

Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram Necking This is the point at which the specimen undergoes extensive necking; where the diameter drops sharply in an unstable manner. Necking occurs at point U.

Mechanical properties of metals Stress and Strain in metals

Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram 5. Percent Elongation The amount of elongation that a tensile specimen undergoes during testing provides a value for the ductility of a metal. Ductility of metals is most commonly expressed as percent elongation. Percent elongation is a measure of the ductility of the metal and is also an index of quality of the metal.

Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram 6. Percent reduction in area The ductility of a metal or alloy can also be expressed in terms of the percent reduction in area. Percent reduction in area is a measure of the ductility of the metal and is also an index of quality.

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. Initial area – Final area % Reduction Area = Final area Stress-strain curves of different metals 24 24

Seatwork : Mechanical Properties of Metal The following engineering stress-strain data were obtained at the beginning of a tensile test for a 0.2% C plain-carbon steel. (a) Plot the engineering stress-strain curve for these data. (b) Determine the modulus of elasticity of this steel (c) Determine the 0.2 percent offset yield strength for this steel (d ) Elastic limit (e) Ultimate tensile strength

Problems 1 A cylindrical aluminum specimen of diameter 1.28 cm and length 10 cm is loaded in tension to 10,000N. The yield strength of the metal is given to be 250 MPa and the modulus of elasticity is given to be 70 GPa. Under the action of this force, compute for the stress and the strain in the specimen.

Problems 2 A cylinder metal specimen 15.0 mm in diameter and 150 mm long is to be subjected to a tensile stress of 50 MPa; at this stress level the resulting deformation will be totally elastic. If the elongation must be less than 0.072 mm, which of the metals in the Table 6.1 below are suitable candidates ? Why ?