# Solid Mechanics - Stress-Strain diagram - absorbed energy

• Feodalherren
In summary, the conversation discusses determining the maximum energy that can be absorbed by a steel alloy without sustaining permanent deformation and prior to fracturing. The attempt at a solution involves using estimates and the 0.2% offset method to find the yield strength of the material, but the solution claims the energy is only the first part of the area under the graph. The concept of modulus of resilience is also mentioned, but it is not clear how it relates to yield strength and elastic limit.
Feodalherren

## Homework Statement

1.The maximum energy (per unit volume) that can be absorbed by the steel alloy without
sustaining permanent deformation is _______ lb/in^2

1.4. The maximum energy (per unit volume) that can be absorbed bythe steel prior to fracturing is _______ kip/in^2.

.

## The Attempt at a Solution

If I remember correctly, stored energy is the area under the graph.
Since I don't know the equation I will work with estimates.

First, I used the 0.2 % offset method to find the Yield strength of the material and I found the yield strength to be about 65 ksi.
The area under the straight line is (1/2)(.002)(60E3)=60
I estimate the rest of the area as a rectangle: (0.002)(60)=120
which gives a grand total of 180 lb/in^2.

Yet the solution, which is not worked out, claims that the energy is only the first part, namely 60 lb/in^2. I thought a material wouldn't be deformed before it gets to the point of yield strength, and in the previous step I found the yield strength correctly. I'm thinking they did something wrong because the solution even goes on to say "Modulus of resilience"=60PSI.

1.4 should just be the same thing, total area under curve?

Feodalherren said:

## Homework Statement

1.The maximum energy (per unit volume) that can be absorbed by the steel alloy without
sustaining permanent deformation is _______ lb/in^2

1.4. The maximum energy (per unit volume) that can be absorbed bythe steel prior to fracturing is _______ kip/in^2.

.

## The Attempt at a Solution

If I remember correctly, stored energy is the area under the graph.
Since I don't know the equation I will work with estimates.

First, I used the 0.2 % offset method to find the Yield strength of the material and I found the yield strength to be about 65 ksi.
The area under the straight line is (1/2)(.002)(60E3)=60
I estimate the rest of the area as a rectangle: (0.002)(60)=120
which gives a grand total of 180 lb/in^2.

Yet the solution, which is not worked out, claims that the energy is only the first part, namely 60 lb/in^2. I thought a material wouldn't be deformed before it gets to the point of yield strength, and in the previous step I found the yield strength correctly. I'm thinking they did something wrong because the solution even goes on to say "Modulus of resilience"=60PSI.

1.4 should just be the same thing, total area under curve?

IDK why you are using the 0.2% offset method to determine yield strength, IIRC, 0.2% offset is used for various non-ferrous metals and alloys (like aluminum) which don't exhibit a clear linear stress-strain relationship in the stress-strain curve.

For the test results shown in the graph, there is clearly a linear stress-strain relationship up to a stress of approx. 60 ksi.

http://en.wikipedia.org/wiki/Yield_(engineering)

Once the material is stressed beyond yield, there will be a permanent set (it's kinda the definition of what yield is.)

http://en.wikipedia.org/wiki/Resilience_(materials_science)

Feodalherren
So now I'm thoroughly confused as to what the difference between yield strength and elastic limit is... And if I don't use the .2 % method, then how am I supposed to know where the yield point is? It's not given to me in the problem.

Nevermind, the information was in the wikipedia article, thanks.

## What is solid mechanics?

Solid mechanics is a branch of mechanics that deals with the behavior of solid materials under external forces.

## What is a stress-strain diagram?

A stress-strain diagram is a graph that shows the relationship between stress (the force applied to a material) and strain (the resulting deformation) for a given material.

## What is absorbed energy in solid mechanics?

Absorbed energy refers to the amount of energy that a material can absorb before it fails or breaks. This is an important factor to consider in designing structures or materials that need to withstand external forces.

## How is absorbed energy measured?

Absorbed energy is typically measured by conducting a tensile test on a material. This involves applying a gradually increasing force to a material until it breaks, and measuring the amount of energy required for the material to reach its breaking point.

## Why is understanding stress-strain behavior and absorbed energy important in engineering?

Understanding the stress-strain behavior and absorbed energy of materials is crucial in engineering because it allows for the selection of appropriate materials for a given application, and helps predict how these materials will behave under different external forces. This information is essential in ensuring the safety and reliability of structures and materials.

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