"Calculating Stress-Strain Graph Homework

[TyErd]

Homework Statement

okay i have attached the question and what i simply have to do is plot the stress-strain graph.

Homework Equations

strain = extension/initial length
stress=force/area

The Attempt at a Solution

Okay, i calculated the strain by dividing each of the extensions by 30mm which is correct right??
But now i need to calculate the stress in order to plot the graph which is simply the force divided by the area however it says the diameter reduces down from 12mm to 11.74mm. at fracture. So then which one do i use to calculate the stress the 12 or 11.74. how do i know exactly at what force the diameter changes??or do i just ignore that and find the stress by dividing the force by 12mm---0.0012metres?

 

[PeterO]

Homework Statement

okay i have attached the question and what i simply have to do is plot the stress-strain graph.

Homework Equations

strain = extension/initial length
stress=force/area

The Attempt at a Solution

Okay, i calculated the strain by dividing each of the extensions by 30mm which is correct right??
But now i need to calculate the stress in order to plot the graph which is simply the force divided by the area however it says the diameter reduces down from 12mm to 11.74mm. at fracture. So then which one do i use to calculate the stress the 12 or 11.74. how do i know exactly at what force the diameter changes??or do i just ignore that and find the stress by dividing the force by 12mm---0.0012metres?

To calculate the stress I would ignore the diameter changes - but I would not divide by the diameter - I think you should be dividing by the cross-sectional area.

Your proposal from stress was correct.

 

[TyErd]

okay thankyou.

 

[TyErd]

okay i have another similar question to this except its given original diameter, diameter at maximum load and diameter at fracture. Would i still proceed to find stress by using original diameter??

 

[PeterO]

okay i have another similar question to this except its given original diameter, diameter at maximum load and diameter at fracture. Would i still proceed to find stress by using original diameter??

How much difference in the diameters?

When you say diameter at maximum load - was the maximum load near fracture or near the yield point?

Certainly in the last bit before a sample fails we see the applied force drop as the sample distorts - the stress of course remaining the same.

 

[TyErd]

well the diameters are:
original diameter-12.8mm
diameter at max load - 11.5mm
diameter at fracture - 7.21mm

the max load is near the fracture but I am not sure because i can't find what the yield point is without knowing which diameters to use to find stress. I've attached the table given.

 

[PeterO]

well the diameters are:
original diameter-12.8mm
diameter at max load - 11.5mm
diameter at fracture - 7.21mm

the max load is near the fracture but I am not sure because i can't find what the yield point is without knowing which diameters to use to find stress. I've attached the table given.

I would certainly use original diameter for all points up to the last two, then the stated diameter fro those two.

 

[TyErd]

okay thanks.