Tension and Compression Test: a standard shape and size of a material is made. Punch marks are created on the material to measure the length between them. The cross sectional area is also measured. A machine will compress or stretch the material slowly and at a constant rate until the material breaks(from stretching). δ = L - Lo this is the elongation of the material, L and Lo are distances between the marks after and before elongation.
Values from this test are graphed and is called the stress(σ)-strain(ε) diagram. Stress(σ) is calculated from σ = P / Ao where P is the applied load and Ao is the original cross sectional area.
Strain(ε) is calculated as ε = δ / Lo where δ is the elongation and Lo is the original length.
When the curve is plotted for a material there are 4 ways the material behaves
- Elastic behavior: this is a region of the curve that is linearly elastic, stress is proportional to the strain and looks like a straight line. The curve will then tend to flatten out at which point the proportional limit(σPl) is reached. Very close to this point is the elastic limit, at this point if the load were to be removed from the specimen it will return to its original shape.
- Yield: Beyond the elastic limit(stress increase) the material will start to breakdown and cause permanent deformation. This point is known as the yield point(σy). At this point the sample will elongate without an increase in load.'
- Strain Hardening: After yielding, an additional load can be applied until the sample reaches a ultimate stress(σu). From yielding the curve will increase and then flatten out and at the peak is the ultimate stress. All this time the sample is being stretched out and the cross sectional area is decreasing.
- Necking: After the ultimate stress is reached the sample will have a decrease in the cross sectional area in one specific location, instead of over the whole member. The curve on the diagram will decrease until stress fracture(σf).
Ductile Materials: A material that has a large plastic range. It is able to absorb shock and will show large deformation before failing when it is overloaded.
Specifying the ductility of a material:
- Percent Elongation = [(Lf - Lo) / Lo] *100% where Lf is the length at fracture and Lo is the original length
- Percent Reduction of Area = [(Ao - Af) / Ao] * 100% where Ao is the original cross sectional area, and Af is the cross sectional area at fracture
Brittle Materials: Materials that have a small plastic range and show little or no yielding(warning) before failure. However, these materials have a higher resistance to axial compression loads.
Properties of materials can change based on changing temperature. Materials will become more brittle and therefore harder when the temperature is lowered, and materials will become more ductile (softer) at higher temperatures.
For the stress-strain diagram the equation for the curve in the elastic range(up to the proportional limit) is given by Hooke's Law: σ = E ε where E is the modulus of elasticity(also the slope of the line)
Strain Hardening: A sample of a ductile material is loaded so that it's in the plastic region(on the diagram) then unloaded, the elastic strain is recoved as the sample is returing to its original state. Example: a paperclip, when bent, will recover a small amount when the force bending it is taken away.
Poisson's Ratio(ν): A deformable body contracts laterally as it's elongating when a axial tensile force is applied.
- εlong = δ / L
- εlateral = δ' / r where δ' is the change in radius, and r is the radius
ν = -εlat / εlong Poisson's ratio mostly between .25 and .33 but its maximum is .5
Shear Stress-Strain Diagram: similar to the tension test, a sample of material subjected to a shear force will behave linearly-elastic, and Hooke's law applies...
= G γ where G is the modulus of rigidity(and is also the slope on the diagram)
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