# Ultimate Strength vs. Young's modulus

1. May 30, 2013

### AJKing

What is the threshold where Young's modulus stops being applicable, and ultimate strength becomes relevant?

2. May 30, 2013

### SteamKing

Staff Emeritus
The limit on the applicability of Young's modulus is called the 'elastic limit' or the 'yield stress', sometimes the 'tensile yield stress'.

Generally, the ultimate strength is only used when trying to figure the load which produces complete failure of the material.

For most design purposes, it is desirable to keep stresses below the yield stress, divided by the factor of safety. There are some designs where the stresses are greater than yield, but these are evaluated using plastic analysis methods.

3. Jun 1, 2013

### AJKing

How do we describe the elastic limit?
Is that solely based on experimental results?

A.P French said, in Vibrations and Waves, that "Young's Modulus represents a stress corresponding to a 100% elongation a condition that is never approached in the actual stretching of a sample. Failure occurs [...] at strain values of between 0.1 and 1%."

I'm getting confused information.

From You and the internet, I understand:

• For every stress below the elastic limit there is an existing strain in linear proportion
• For stresses at or above the elastic limit, the material is plastic and there is no simple description for its deformation.
• The ultimate strength is the maximum point on the stress-strain curve - with no other significance.

From A.P. French, I understand that:

• Young's modulus is only applicable for lengths below ~1% of l0
• Ultimate strength is the description of the material at "failure" (fracture?)
• [strike]If strain is equal to (U / Y)%, then one may solve problems with ultimate strength[/strike]

How am I doing?

Last edited: Jun 1, 2013
4. Jun 1, 2013

### SteamKing

Staff Emeritus
Young's modulus is the slope of the stress-strain curve in the elastic region. The tensile limit for a particular material is determined by an experiment called a 'tensile test'. A carefully prepared sample of the material is put into a machine which is capable of pulling on both ends of the sample. The sample usually has the shape of a cylinder in the middle. As the sample is pulled, the pulling force is measured as is the elongation of the sample. Knowing the dimensions of the sample, the stress and the strain are calculated and plotted. The test continues until the sample is pulled apart. If the test is done correctly, the first portion of the plotted curve will be a straight line, which indicates elastic behavior.

The link gives more details: http://dolbow.cee.duke.edu/TENSILE/tutorial/node1.html