## General Mechanical

#### Bilinear/Multilinear curve fitting for plasticity modelling

• VJ0085
Subscriber

Hello, I have two questions here:

1. How should include plasticity model in Ansys for such a curve below?

2. Which model should I consider to capture the failure (isotropic/kinematic hardening)?

• Sandeep Medikonda
Ansys Employee

During plastic deformation, isotropic hardening causes a uniform increase in the size of the yield surface and results in an increase in the yield stress.This type of hardening can model the behavior of materials under monotonic loading and elastic unloading, but often does not give good results for structures that experience additional plastic deformation after a load reversal from a plastic state.

During plastic deformation, kinematic hardening causes a shift in the yield surface in stress space. In uniaxial tension, plastic deformation causes the tensile yield stress to increase and the magnitude of the compressive yield stress to decrease. This type of hardening can model the behavior of materials under either monotonic or cyclic loading and can be used to model phenomena such as the Bauschinger effect and plastic ratcheting.

So, it is hard to come to a conclusion based on just a uni-axial test and you would often need a cyclic test to determine which hardening behavior can be used. But in general, plastic materials such as polycarbonate often do experience ratcheting in my experience.

Note: The strain-strain data entered should be true stress-strain not engineering stress-strain data. Converting engineering data to true data might help. The slope of the stress-strain curve cannot be negative.

• peteroznewman
Subscriber

Watch the video closely and you can see that when the curve suddenly goes negative, necking of the material has begun. Necking is a localized deformation rather than the uniform stretching and contracting over the entire sample that was occurring up to that point.

You can't convert any Engineering Stress - Engineering Strain data from this plot into True Stress - True Stain after necking has begun. You can only do that up to the point where the necking begins.

The flat part of the curve is just the local necking behavior migrating from the initial site down the length of the sample.  Once necking has completed over the full length, there is some hardening behavior at the end before fracture.

• VJ0085
Subscriber

You are right Peter, the yield stress is appx 63 Mpa in this case. The formation of true stress-strain data comes into picture only after the yield stress point (plastic strain being zero and true stress being yield stress, both as first data point in multilinear iso hardening). So, if it's not possible in case of PC, I'm curious to know how some of the researchers are able to get it, for example this research here (Figure 4).

Thanks for the information.

• VJ0085
Subscriber

Thanks Sandeep for the information. I'm aware of using multilinear isotropic hardening parameters but as Peter informed one can't get such parameters once necking occurred, and if I have to simulate plasticity behaviour in Ansys we will certainly need it. How could we get/formulate one in such cases? Thanks.

• peteroznewman
Subscriber

You can simulate Necking by using a plasticity material model.

• peteroznewman
Subscriber

Hi vijimech, please use the big green New Discussion button and copy your question into that. Then you can delete the two posts from this discussion. The reason is you don't own this discussion so you won't be notified of new posts the way the original member who started this discussion gets emails about new posts.

• vijimech
Subscriber

ok sir, thank you