Materials Selection and Design - Practical Examples
Chosen practical example:
1. Load-limited design – wire ropes 2. Energy-limited design – spring in pegs 3. Deflection-limited design – paperclips
1. Load-limited design – wire ropes
Wire ropes function as a tie. Hence the constraint is to withstand a certain tensile stress before failing by fracture.
σ_f=(CK_1c)/√(πa_c )
If the objective to maximize the allowable stress, then, the material indices is simply
M=K_1c
CES (Cambridge Engineering Selector) is utilized to plot a diagram of fracture toughness vs. Young’s modulus. In this plot, only material with K1c >15MPam0.5 are considered. The same plot is used to solve part b) and c). For part a), material of highest K1c is to be chosen. According to the plot, the best material for wire ropes is low alloy steel.
2. Energy-limited design – spring in pegs
The torsion springs in clothes pegs store energy that is pre-applied to them. The energy they are able to store determines how much force they can apply to the wooden part of the pegs and hence how firm they can hold the clothes. Therefore, function of the material is to store and release elastic energy. Meanwhile, objective is to maximize the elastic energy stored. In addition, the material also has to fulfill the constraint
U_e^max=C^2/(3πa_c ) (K_1c^2)/E
To maximize the stored elastic energy, material indices for this problem is then
M=(K_1c^2)/E
Material that lies on the top left corner of slope 0.5 in the K1c vs. E plot is then the best choice. Applying the constraint of K1c >15MPam0.5, the optimum material obtained from CES for this problem is low alloy steel.
3. Deflection-limited design – paperclip
Paperclips often fail by fracture due to over deflection. Function of the material is to deflect elastically. The objective is then to maximize allowable strain. This is constrained by fracture toughness of the material.
σ_f=(CK_1c)/√(πa_c )
which determines the allowable stress and related to the allowable
1. Load-limited design – wire ropes 2. Energy-limited design – spring in pegs 3. Deflection-limited design – paperclips
1. Load-limited design – wire ropes
Wire ropes function as a tie. Hence the constraint is to withstand a certain tensile stress before failing by fracture.
σ_f=(CK_1c)/√(πa_c )
If the objective to maximize the allowable stress, then, the material indices is simply
M=K_1c
CES (Cambridge Engineering Selector) is utilized to plot a diagram of fracture toughness vs. Young’s modulus. In this plot, only material with K1c >15MPam0.5 are considered. The same plot is used to solve part b) and c). For part a), material of highest K1c is to be chosen. According to the plot, the best material for wire ropes is low alloy steel.
2. Energy-limited design – spring in pegs
The torsion springs in clothes pegs store energy that is pre-applied to them. The energy they are able to store determines how much force they can apply to the wooden part of the pegs and hence how firm they can hold the clothes. Therefore, function of the material is to store and release elastic energy. Meanwhile, objective is to maximize the elastic energy stored. In addition, the material also has to fulfill the constraint
U_e^max=C^2/(3πa_c ) (K_1c^2)/E
To maximize the stored elastic energy, material indices for this problem is then
M=(K_1c^2)/E
Material that lies on the top left corner of slope 0.5 in the K1c vs. E plot is then the best choice. Applying the constraint of K1c >15MPam0.5, the optimum material obtained from CES for this problem is low alloy steel.
3. Deflection-limited design – paperclip
Paperclips often fail by fracture due to over deflection. Function of the material is to deflect elastically. The objective is then to maximize allowable strain. This is constrained by fracture toughness of the material.
σ_f=(CK_1c)/√(πa_c )
which determines the allowable stress and related to the allowable