Polymer Engineering question related to Von Mises yield criterion

In summary, the conversation is about a proof question for extra credit on a final exam. The question involves finding values for A and B using two equations, one for uniaxial tension yielding and the other for uniaxial compression yielding. It is mentioned that A and B must have different values in order for the equation to make sense, and once they are found, the hydrostatic case can be solved for σ.
  • #1
kennyyip
1
0
It is a proof question. Does anyone can tell me how to do this question?question 22.2
it is the question for extra credit for my final exam.
thank you so much.
 

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  • #2
You can find A and B with two simultaneously equations.
For the first equation assume uniaxial tension yielding - i.e. take σ1 as fty and σ2=σ3=0.
For the second equation assume uniaxial compression yielding. This is a polymer so it makes sense that fty and fcy would be different values - and they have to be different values otherwise you'd find that A=0.

Once you have A and B, then consider the hydrostatic case - i.e. take σ1=σ2=σ3=σ. Solve for σ.
 

What is the Von Mises yield criterion?

The Von Mises yield criterion is a mathematical equation that predicts the onset of plastic deformation in materials subjected to complex stress states. It is based on the principle that a material will yield when the equivalent stress reaches a critical value.

How is the Von Mises yield criterion used in polymer engineering?

In polymer engineering, the Von Mises yield criterion is often used to predict the yield behavior of polymers under different loading conditions. This is important for designing polymer components that can withstand the stresses and strains of real-world applications.

What is the difference between the Von Mises yield criterion and the Tresca yield criterion?

While both the Von Mises and Tresca yield criteria are used to predict plastic deformation, they differ in their assumptions about the material's behavior. The Von Mises criterion is based on the concept of equivalent stress, while the Tresca criterion is based on the maximum shear stress.

What is the significance of the yield surface in polymer engineering?

The yield surface, also known as the plastic strain surface, is a graphical representation of the Von Mises yield criterion. It is used to visualize the yield behavior of a material under different stress states, and can help engineers determine the maximum allowable stress levels for a given material.

Can the Von Mises yield criterion be used for all types of polymers?

No, the Von Mises yield criterion is only applicable to ductile materials, such as thermoplastics and elastomers. For brittle materials, such as thermosets, other yield criteria, such as the Tresca or Mohr-Coulomb criterion, may be more appropriate.

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