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An in-depth analysis of material strength and failure, focusing on static load, yield and ultimate strength, ductility, maximum shear stress and distortion energy theories. It covers the concepts of static load, failure, material strength, ductility, brittle materials, and elastic and distortion energy. The document also includes equations and design equations for calculating yield and ultimate strengths, as well as safety factors and failure envelopes.
Typology: Lecture notes
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magnitude and direction
A part has been separated into two or more pieces.
A ductile material deforms significantly before fracturing. Ductility is measured by % elongation at the fracture point. Materials with 5% or more elongation are considered ductile. Brittle material yields very little before fracturing, the yield strength is approximately the same as the ultimate strength in tension. The ultimate strength in compression is much larger than the ultimate strength in tension.
yield point → failure
The area under the curve in the elastic region is called the Elastic Strain Energy. Strain energy
3D case
E
E
E
E
E
E
E
E
Stress-strain relationship E
2
2
2
Strain energy from a tension test at the yield point σ 1 = S y and σ 2 = σ 3 = 0 (^) Substitute in equation (2)
1 + v
2 Utest = To avoid failure, Ud < Utest (σ 1 – σ 2 ) 2
< S y
1 + v (σ 1 – σ 2 ) 2
2
2
y
Where σ′ is von Mises stress
y
Design equation
2
2
2
y
y
y
Distortion energy theory Maximum shear stress theory
y
u
One of the characteristics of a brittle material is that the ultimate strength in compression is much larger than ultimate strength in tension.
Mohr’s circles for compression and tension tests. Compression test S uc Failure envelope The component is safe if the state of stress falls inside the failure envelope.
Tension test
σ 3 Stress σ 1 S ut state
σ 1 S ut S uc S ut S uc Safe Safe Safe Safe -S ut Cast iron data
σ 1 σ 3 or σ 2 S ut S ut S uc -S ut
Three design zones σ 3 or σ 2
