Lecture 40 –Failure theoriesweb.ics.purdue.edu/~gonza226/ME323/Lecture-40.pdf · 2021. 1. 15. ·...
Transcript of Lecture 40 –Failure theoriesweb.ics.purdue.edu/~gonza226/ME323/Lecture-40.pdf · 2021. 1. 15. ·...
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Lecture 40 – Failure theories
Instructor: Prof. Marcial Gonzalez
Spring, 2021ME 323 – Mechanics of Materials
Reading assignment: 12.3
Last modified: 1/14/21 7:23:57 PM
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Failure theories
Material properties from stress-strain diagrams (Lecture 3)- Tensile uniaxial test – two distinct failure mechanisms
- What is the criterion if the solid is under combined loads and the state of stress is triaxial?
Brittle vs. ductile materials
Brittle Ductile(yielding before fracture)
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Failure theories – Ductile materials
Failure criteria for ductile materials- Maximum-shear-stress theory
equivalentto
failure criterion (where is measured)
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Failure theories – Ductile materials
Failure criteria for ductile materials- Maximum-shear-stress theory
For plane stress, using in this analysis!)---
What are the conditionsfor each quadrant?
failure criterion (where is measured)
The failure envelope is a hexagon.+ inside: no failure+ outside: failure
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Failure theories – Ductile materials
Failure criteria for ductile materials- Maximum-distortion-energy theory
Total elastic energy = Change of volume + Distortion
Distortion energy:
Distortion energy at yielding point:
Misses equivalent stress
Failure criterion (for a triaxial state of stress)
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Failure theories – Ductile materials
Failure criteria for ductile materials- Maximum-distortion-energy theory
For plane stress, using in this analysis!)
Failure criterion (for a triaxial state of stress)
failure criterion
The failure envelope is an ellipsoid.+ inside: no failure+ outside: failure
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Problem 82 (from last class):
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Failure theories
Determine the principal stresses and the maximum shear stress at point A (i.e., the point on top of the wrench handle). The diameter of the circular crosssection is 12.5 mm. The material is ductile.The yield stress is 300 MPa.
MaximumDistortionEnergytheory
MaximumshearStresstheory
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Failure theories – Brittle materials
Failure criteria for brittle materials- Maximum-normal-stress theory
For plane stress, using in this analysis!)
failure criterion
Notice that this theory assumes that failure undertension and compression occur under the sameultimate stress (not true for most materials).
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Failure theories – Brittle materials
Failure criteria for brittle materials- Mohr’s failure criterion (it incorporates )
failure criterion
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Problem 83:
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Failure theories
Determine the principal stresses and the maximum shear stress at point A (i.e., the point on top of the wrench handle). The diameter of the circular crosssection is 12.5 mm. The material is brittle.The ultimate tensile stress is 300 MPa.
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Problem 84:
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Failure theories
Determine the principal stresses and the maximum shear stress at point A (i.e., the point on top of the wrench handle). The diameter of the circular crosssection is 12.5 mm. The material is brittle.The ultimate tensile stress is 300 MPa and the ultimate compressive stress is 500 MPa.
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Any questions?
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Failure theories