Determine the modulus of resilience, and estimate the modulus of toughness, assu
ID: 2088821 • Letter: D
Question
Determine the modulus of resilience, and estimate the modulus of toughness, assuming that the last data point corresponds to fracture. The diameter of the test specimen is 0.499 in. For the elastic state Pi(lb) /(in) 1000 0004 0006 2000 001 400 8800 9200 0.0013 0.0023 0.0028 0.0036 0.0089 For the plastic state Pi (lb) 8800 9200 8800 9200 100 13200 15200 17000 16400 14800 i (in 0.0036 0.0089 0.1984 0.1978 0.1963 01924 0.1875 0.1563 01307 0.1077 Determine the value of the 0.2% offset yield strength The value of yield strength iskpsiExplanation / Answer
The modulus of resilience is maximum energy (Ur )that can be absorbed per unit volume without creating a permanent distortion (within the elastic limit).
Maximum Strain energy which a body stores upto the Elastic limit is called Proof Resilience
Modulus of resilience = Proof resilience / Unit volume of the body
Ur = ?y X ?y / 2E
Where,
Ur - Modulus of resilience
?y - Yeild Stress
E- Youngs Modulus
The modulus of toughness is the work done per unit volume of material when the simple tensile load is increased from zero until the material ruptures.
The modulus of toughness is calculated as the area under the stress-strain curve up to the fracture point.
On the horizontal axis you have strain, and on the vertical axis you have stress. The stress-strain curve will be directly proportional under proportional limit,. i.e., the curve will be linear starting from the origin.
Now, you just have to measure the value of 0.2% of strain and mark it on the strain (horizontal) axis. Start drawing a line parallel to the stress-strain curve until it meets the curve at some point on the curve.
Draw a horizontal line from the meeting point until it meets the vertical (stress) axis.
Measure the value - that will be the yield point stress corresponding to 0.2% of strain.
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