Ultimate Strength vs. Young's modulus

[AJKing]

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

 

[SteamKing]

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.

 

[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?

 

[SteamKing]

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

 

[PJC01]

Young's modulus and ultimate strength are both important properties in materials science that describe a material's ability to resist deformation and failure under stress. However, they represent different aspects of a material's mechanical behavior and cannot be directly compared.

Young's modulus, also known as the elastic modulus, is a measure of a material's stiffness or how much it will deform under a given amount of stress. It is defined as the ratio of stress to strain within the elastic limit of a material. This means that Young's modulus is applicable only within the linear elastic range of a material, where the material will return to its original shape once the stress is removed.

On the other hand, ultimate strength is a measure of a material's maximum stress before it fails or breaks. It is also known as the tensile strength or yield strength. Unlike Young's modulus, ultimate strength is applicable at the point of failure, where the material has reached its maximum stress and can no longer resist deformation.

There is no specific threshold where Young's modulus stops being applicable and ultimate strength becomes relevant. Instead, these properties are both important and relevant in different scenarios. For example, in designing structures or machines, both Young's modulus and ultimate strength are considered to ensure the material can withstand the expected stress and deformation without failure.

In summary, Young's modulus and ultimate strength are both important properties in materials science, but they represent different aspects of a material's mechanical behavior and cannot be directly compared.