How Does Toughness Compare Between Martensite and Carbon Steel?

[temaire]

Homework Statement

[PLAIN]http://img20.imageshack.us/img20/2223/mateb.png

The Attempt at a Solution

Assuming that the guitar string is made of martensite and the metal chain link is made of carbon steel, I think that the metal chain link would have a higher toughness. My reasoning behind this is since martensite is very strong but not ductile, then the elastic region of its stress-strain curve would be steep and the plastic region would be very small before the string fails. On the other hand, the metal chain link is not as strong as the string but is a bit more ductile. The elastic region of its stress-strain curve would not be as steep, and the plastic region would last longer before failure. Therefore, the area under the stress-strain curve of the metal chain link would be greater than the area under the stress-strain curve of the string, as seen in the figure below.

[PLAIN]http://img413.imageshack.us/img413/3831/mate2.png

Also, looking at it from a design point of view, a metal chain link is obviously designed to withstand high tensile stresses, whereas a guitar string is only designed to withstand tensile stresses in the elastic region.

Is my understanding of the problem correct? Am I wrong with my choice?

 

[nvn]

temaire: Your answer is correct. By the way, please do not post wide images directly to the forum page. Just post a text link to wide images.

 

[tvavanasd]

...then the elastic region of its stress-strain curve would be steep and...
... The elastic region of its stress-strain curve would not be as steep...

This is not correct. The "steepness" or slope (Young's Modulus) of the elastic region would be approximately identical for the two steels.

 

[Astronuc]

Also, looking at it from a design point of view, a metal chain link is obviously designed to withstand high tensile stresses, whereas a guitar string is only designed to withstand tensile stresses in the elastic region.

Is my understanding of the problem correct? Am I wrong with my choice?

The key in the problem is found in the problem statement, "Basically, toughness is the amount of energy a material can withstand before it fails." The energy is measured by the area under the stress-strain curve, which gives the strain-energy density. As strength of a material increases (and total elongation decreases), the material is less tough, i.e., it absorbs less energy before failure.

Ductility is associated with the ability of a material to deform before failure. However, most metals are designed to operated well within the elastic region. Usually, permanent or plastic deformation is undesirable.

 

[DeeNos]

Your understanding of the problem is correct. Toughness is the ability of a material to absorb energy before it fractures, and it is measured by the area under the stress-strain curve. In this case, the metal chain link would have a higher toughness because it has a larger area under the curve, indicating that it can absorb more energy before failure. This is due to its higher ductility, as you mentioned. Additionally, as you pointed out, the design of the metal chain link is specifically for high tensile stresses, whereas the guitar string is not. Therefore, the metal chain link is a better choice for a material with high toughness in this scenario.