Answer:
Steel, Titanium and Tungsten
Explanation:
Given:-
- The diameter of the cylindrical specimen, d = 12.7 mm
- The length of the cylindrical specimen, L = 250 mm
- The tensile stress in the specimen, σ = 28 MPa
- Assume elastic deformation of the material up-to the specified tensile stress
Solution:-
- To determine or select suitable materials that are subjected to the given stress ( σ ) and an elongation constraint ( Δl ) or contraction of diameter ( Δd ). We need material intrinsic properties and relate them to our analysis.
- We studied two material intrinsic properties that is the Elastic Modulus ( E ) and Poisson ratio ( v ).
- Since, the question poses a constraint on the diameter. Note that the axis of stress applied ( axial ) and the contraction dimension are orthogonal to each other. In such case, we will determine the poisson ratio ( v ) of the suitable material as follows:
- We will first determine the permissible strain in the diametrical direction ( εx ). It is the ratio of allowable contraction of diameter ( Δd ) to the initial diameter ( d ):
εx = Δd / d
εx = ( -1.2*10^-3 ) / ( 12.7 )
εx = -0.00009
- The poisson ratio ( v ) of a material is defined as the negative ratio of the transversal strain ( εx ) to the axial strain ( εz ). The axial strain ( εz ) is determined as the ratio of elongation in length ( Δl ) to the initial length ( L ) of the specimen as follows:
εz = Δl / L
εz = ( 0.08 ) / ( 250 )
εz = 0.00032
- The poisson ratio ( v ) is expressed as:
v = - [ εx / εz ]
v = [ 0.00009 / 0.00032]
v = 0.2812
- Hooke's law gives us a linear relation between the applied stress ( σ ) and the engineering strain in the direction of applied stress. Since, the specimen is subjected to tensile stress and abides by the Hooke's law ( Elastic deformation ). The modulus of elasticity ( E ) is given as :
E = σ / εz
E = (28*10^6 ) / 0.00032
E = 87.5 GPa
- As per maximum elongation allowed the modulus of elasticity calculated above is the minimum value that must be satisfied by the selected material. We will use a list of materials ( ASTM ) standard and list a few that meet the elongation criteria as follows:
Copper, Nickel , Steel, Titanium , Tungsten
- From the above selected metals the most closely associated poisson ratio ( v ) calculated above would be:
Metals poisson ratio ( v ) range
Copper 0.33
Nickel 0.31
Steel 0.27–0.30
Titanium 0.265–0.34
Tungsten 0.27
- The suitable materials would be:
Steel, Titanium and Tungsten
