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Why Material Test Data After Necking is Not Replicated in the Solver Material Data?

User: "altair_fukuoka"
Altair Employee
Updated by AltairLiz
Introduction

This article is translated from the following one:

Assume we obtain some test data, as shown in the following figure. After some necking point in the curve, the stress drops significantly. Here is my question: Should we apply the stress drop to the material property? The answer is no. This is the geometry property but not material property. Through this article, we will address this issue in depth.

image.png

Stress in material property in reality does not drop, but stress can often be seen to drop after necking in a 'stress/strain' plot.

The header title is slightly misleading. Obviously, it is wrong. But, indeed, strangely, it is also true.

To explain: we do the following material tensile test:

image.png

We use /MAT/LAW2,

https://help.altair.com/hwsolvers/rad/topics/solvers/rad/mat_law2_plas_johns_starter_r.htm

Here is the yield stress formulation: σ: yield stress, εp: plastic strain, and we assume a=90MPa, b=223MPa and n=0.368 as aluminium. The most important point of this formulation is that the stress always increases when the plastic strain increases.

image.png

This figure shows the image of the above material formulation. The stress keeps increasing. If in doubt, you can calculate it in Excel or a similar tool.

image.png

And, this is the result of our tensile test simulation. This shows the force-stroke curve. We can see the force drop after stroke=30mm.

image.png

Why does it happen?

The answer is necking. When necking occurs, the section becomes narrower and then the object cannot react against an increasing force anymore.

Untitled Image

However, of course, the stress in the necking area keeps increasing during the simulation.

image.png

We now understand the behavior from the necking causing the force to drop. But, why do we see stress also dropping when clearly it should still be increasing?

Indeed, it comes from a traditional methodology of testing. When we do a tensile test, we express the value that we divide the force by, as the coupon initial section area, Force/initial_Area as "Stress".

This is the cause of the plot leading us to wrongly think that "the stress drops after necking".

image.png

We may obtain some Stress-Strain curves from material test engineers. It is a good idea to check how they defined stress and strain before we apply the Stress Strain curve to our material model.

Is it unfair that we treat the test data as stress before necking?

It might feel unfair as the header title. However, I cannot say "absolutely", it is almost always OK.

To understand this, we check the stress triaxiality. When the stress field is one axial tensile field, the triaxiality should be 1/3. We can see the beautiful 1/3 field in a wide area before necking.

image.png

And the magnitude of the stress is also uniform.

image.png

The stress field has the same orientation and the same magnitude. Thus, all elements in the uniform area have the same stress value that we obtain by dividing force by the initial coupon section area, Force/initial_Area. We can say that the test data and the material property are close enough to identical.

However, after necking, the triaxiality and the stress field becomes varying. What we really should know is the stress and the strain relationship for every element. Even though we can calculate Force/Area_initial, to which element we should apply the value? It is impossible to figure out the material property from this stress field.

image.png image.png

Download the example

The example Radioss data above: radioss_model.7z

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    @altair_fukuoka I have asked a Radioss expert to do an editorial review of this discussion before it is published. Apparently, there is a regular Tuesday meeting to discuss Community questions and Pierre Christophe Masson will bring the editorial review up at that time.

    Hello, please remind that I am also the one of the Radioss expert.

    User: "PaulAltair"
    Altair Employee

    Title:
    Material Test Data after necking is not replicated in the material data

    Assume we obtain some test data, as shown in the following figure. After some necking point in the curve, the stress drops significantly. Here is my question. Should we apply the stress drop to the material property? The answer is no. This is the geometry property but not material property. Through this article, we will address this issue in depth.

    image.png

    Stress in material property in reality does not drop, but stress can often be seen to drop after necking in a 'stress/strain' plot.

    The header title is slightly misleading. Obviously, it is wrong. But, indeed, strangely, it is also true.

    To explain: we do the following material tensile test,

    image.png

    We use /MAT/LAW2,

    https://community.altair.com/home/leaving?allowTrusted=1&target=https%3A%2F%2Fhelp.altair.com%2Fhwsolvers%2Frad%2Ftopics%2Fsolvers%2Frad%2Fmat_law2_plas_johns_starter_r.htm

    Here is the yield stress formulation. σ: yield stress, εp: plastic strain, and we assume a=90MPa, b=223MPa and n=0.368 as aluminium. The most important point of this formulation is that the stress always increases when the plastic strain increases.

    image.png

    This figure shows the image of the above material formulation. The stress keeps increasing. If you still have doubt, you can calculate it in Excel or similar tools.

    image.png

    And, this is the result of our tensile test simulation. This shows the force-stroke curve. We can see the force drop after stroke=30mm.

    image.png

    Why does this happen!?

    The answer is necking. When necking occurs the section becomes narrower. And then, the object cannot react against an increasing force anymore.

    Untitled Image

    However of course, the stress in the necking area keeps increasing during the simulation.

    image.png

    Ok, we now totally understand the behavior from the necking causing the force to be dropping. But, why do we see stress also dropping when clearly it should still be increasing? Indeed, it comes from a traditional methodology of testing. When we do a tensile test, we express the value that we divide the force by, as the coupon initial section area, Force/Area_initial as "Stress".

    This is the cause of the plot leading us to wrongly think that "the stress drops after necking".

    image.png

    We may obtain some Stress Strain curves from material test engineers. It is a good idea to check how they defined stress and strain before we apply the Stress Strain curve to our material model.

    Is it unfair that we treat the test data as stress before necking?

    You might feel unfair as the header title. However, I cannot say "absolutely", it is almost always OK.

    To understand this, we check the stress triaxiality. When the stress field is one axial tensile field, the triaxiality should be 1/3. We can see the beautiful 1/3 field in a wide area before necking.

    image.png

    And the magnitude of the stress is also uniform.

    image.png

    The stress field has the same orientation and the same magnitude. Thus, all elements in the uniform area have the same stress value that we obtain by dividing force by the initial coupon section area, Force/Area_initial. We can say that the test data and the material property are close enough to identical.

    However, after necking, the triaxiality and the stress field becomes varying. What we really should know is the stress and the strain relationship for every element. Even though we can calculate Force/Area_initial, to which element we should apply the value? It is impossible to figure out the material property from this stress field.

    image.png image.png

    Download the example

    The example Radioss data above: radioss_model.7z