Islamic University of Gaza Mechanical Engineering Department Material Science Lab. (EIND3101) Experiment #3 Extension of Wires (Elasticity Modulus) Eng. Ibrahim A. Aljaish

Modulus of Elasticity ε : Percent Elongation or Strain (Dimensionless) Most engineering structures are designed to undergo relatively small deformations, involving only the straight-line portion of the corresponding stress-strain diagram. For that initial portion of the diagram (Fig. 1), the stress σ is directly proportional to the strain P, and we can write: Were : σ : Applied Stress (Pascal) E : Young’s Modulus (Pascal) ε : Percent Elongation or Strain (Dimensionless) σ = Eε

Modulus of Elasticity Cont. This relation is known as Hooke’s law. The coefficient E is called the modulus of elasticity of the material involved. The largest value of the stress for which Hooke’s law can be used for a given material is known as the proportional limit of that material. In the case of ductile materials possessing a well-defined yield point, as in Fig. 2.6a, the proportional limit almost coincides with the yield point. For other materials, the proportional limit cannot be defined as easily, since it is difficult to determine with accuracy the value of the stress for which the relation between σ and ε ceases to be linear. But from this very difficulty we can conclude for such materials that using Hooke’s law for values of the stress slightly larger than the actual proportional limit will not result in any significant error.

Objectives To understand the concept of modulus of elasticity. To verify that the modulus of elasticity is independent of wire Parameters . To verify that the modulus of elasticity depends on the type from material from which the wire is made.

Equipment: Top Wall Bracket. Bottom Wall Bracket Slide Housing. Vernier Slide. Wires of different materials and parameters.

0.85 Copper 1.29 1 steel Loading schedule for the wires Increments (N) Max. Load Diameter(mm) Material 5 100 0.85 Copper 10 200 1.29 20 500 1 steel

procedures Hang the wires on a wall using the brackets. Start adding loads to each wire and write down the loads and the respective elongation for each wire. Construct a graph representing the relation between the load (p) on the y-axis and the elongation (ΔL) on the x-axis for each wire separately. find the slope for each wire then calculate the modulus of elasticity using the following equation Compare the three values of E. E = stress/strain = P/A•L/ΔL = L/A × slope(elongation-load graph)

Extension ΔL (mm) Scale Reading Load P (N) Experiment results Table 1 Load/extension of a wire Material. Diameter. (mm): Test Length L (m): Extension ΔL (mm) Scale Reading Load P (N)