How to calculate Young's modulus of layered cross section

In summary: Acharya, an engineering professor at the University of Utah, said the difficulty in arriving at a meaningful value arises from the fact that the bond between the layers can be either weak or strong.
  • #1
Bob Joey
3
0
Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of trying to find the modulus.
 
Engineering news on Phys.org
  • #2
If in the end you want to work out stresses and deflections a piecewise method is needed using the individual Young's moduli of the different layers .
 
  • #3
Bob Joey said:
Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of trying to find the modulus.
It depends on what you are trying to accomplish.

If you want to calculate the bending stresses in a beam made of this layered material, there is a way to calculate a weighted-modulus if you know the moduli of the individual components.

Other than this, we'll need further information.
 
  • #4
The end goal is to calculate the buckling load of the overall material. Given a specific list of materials and their elastic moduli, is it possible to mathematically set up a process to find the modulus of the overall structure?

I have looked into the Rule of Mixtures, but I am not sure if it is applicable here.
 
  • #5
An expression can be derived for a beam of specific dimensions and layer construction but there are difficulties in arriving at a truly meaningful value .

In a laminated beam the strength and flexibility of the bond between layers has to be included .
 
  • #6
Could someone please elaborate on the procedure and how someone should go about it?
 
  • #7
Bob Joey said:
Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of trying to find the modulus.
You assume that, since all the layers are glued together, they all experience the same in-plane strain. Once you know the strains, you can calculate the stresses in each layer, and average these to get the average modulii. If it is a uniaxial unconstrained deformation, you first solve for the strain that makes the average transverse stress zero, and then determine the average axial stress.

Information like this should be available in the Composite literature.

Chet
 

1. What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It describes how much a material will deform under a given amount of stress.

2. What is a layered cross section?

A layered cross section refers to a material that is composed of multiple layers, each with different properties and thicknesses. This can include materials such as composites, laminates, and layered metals.

3. How do you calculate Young's modulus of a layered cross section?

To calculate Young's modulus of a layered cross section, you will need to know the properties of each individual layer, including its thickness and Young's modulus. Then, you can use the rule of mixtures to determine the overall Young's modulus of the cross section.

4. What is the rule of mixtures?

The rule of mixtures is a formula used to calculate the overall properties of a composite material based on the properties of its individual components. For Young's modulus, the rule of mixtures is: E = ∑(V_i x E_i), where E is the overall Young's modulus, V_i is the volume fraction of each layer, and E_i is the Young's modulus of each individual layer.

5. Does the order of the layers impact the calculation of Young's modulus?

Yes, the order of the layers can impact the calculation of Young's modulus. This is because the layers may interact with each other and affect the overall stiffness of the material. It is important to consider the order of the layers when using the rule of mixtures to calculate Young's modulus.

Similar threads

Determining Young's Modulus of Aluminium from Tensile Test
    • Materials and Chemical Engineering
Replies
7
Views
4K
B Why is Young's modulus constant below the limit of proportionality?
    • Classical Physics
Replies
23
Views
3K
Young's modulus — Finding the change in the length of a metal bar under stress
    • Introductory Physics Homework Help
Replies
20
Views
2K
Ranking "by eye" bi-material cross sections for strength/stiffness
    • Aerospace Engineering
Replies
1
Views
1K
Anisotropic Modulus of elasticity and Poisson's ratio
    • Materials and Chemical Engineering
Replies
1
Views
2K
Young's modulus of rubber sheet using the inflation technique
    • Materials and Chemical Engineering
Replies
1
Views
5K
Engineering Analyzing Shear & Bending on Idealized Cross Section
    • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
Young's Modulus and the Poisson Ratio of Aluminium
    • Introductory Physics Homework Help
Replies
1
Views
1K
Difference Between Young's Modulus & Second Moment of Area
    • General Engineering
Replies
2
Views
4K
Magnetic field in a solenoid with rectangular cross-sectional area
    • Introductory Physics Homework Help
Replies
25
Views
1K

Hot Threads

Recent Insights

Back
Top