Analysis of failure behavior of a plate with 3 different materials using Hypermesh Radioss

OBJECTIVE

The main objective is to analyze and compare the failure behavior of a plate using different material models LAW-1, LAW-2, LAW-27 & LAW-36 along with Johnson-cook Failure card.

  • For LAW-2, Once use Johnson's Failure card along with some certain properties and second time run without Johnson's Failure card and third time change the Equivalent plastic strain(EPS_p_max) value to the default value and run the file.
  • For LAW-1, change card image to M1_ELAST keep EPS_p_max value to default.
  • For LAW-27, change the shell properties to recommended shell properties.
  • For LAW-36, use two different curves: one is a standard curve and one is the Test curve(according to given data).

1. The total number of cycles, Energy error, mass error and simulation time.
2. Notice the animation of all 7 cases and describe the animations in brief on the basis of whether the elements are being deleted or cracked.
3. Plot energies and notice any difference.
4. Based on all the results, which case would represent the on-field scenario.
5. List down case by case result and your conclusion as to why the failure happened.

PROCEDURE

#Material LAWs in Radioss which we use.

  • LAW1: Isotropic elasticity: Linear elastic material using Hook's Law. 
  • LAW2: Johnson-cook: Isotropic Elasto-Plastic: Von Mises hardening without damage. It expresses material stress as a function of strain, strain rate, and temperature.
  • LAW27: Elasto-Plastic material with Brittle failure.
  • LAW36: Isotropic Elasto-Plastic: Tabulated piecewise Linear

Run the file and see Animation into Hyperview with Von Mises simple average stress values and plot the Internal & kinetic Energy curve for that in Hypergraph 2D. HyperGraph minimizes the manual effort and time required to generate plots. Run the simulation for that and observe the results.

1. Case 1: Law2_epxmax_failure

Take our default file and change the name to Law2_epxmax_failure_0000 RAD file. Open it into Hypermesh see properties which are assigned to the plate and model also have failure card contains certain parameters:

  • Ifail_sh = 2 i.e. for each integration point stress tensor is set to Zero.
  • Dadv = 0 i.e. criterion for the crack advancement
  • Xfem = 0: Represents the crack over an element until now without using Ixfem treatment.

In material Properties file also carry EPS_p_max value = 0.151 which means elements will fail when the stress value is above 15% of plastic strain.

Case 2: Law2_epxmax_crack

In case 2 we have to change some failure card properties like:

  • Ifail_sh = 1 i.e. shell is deleted if there is one layer of failure zone. 
  • Dadv = 1 
  • Xfem = 1 means Ixfem formulation.

All other things keep the same for case 2.

So run that model and observe the difference between both the cases.

            Case 1 Law2_epxmax_failure                       Case 2 Law2_epxmax_crack

We can see that in case 1 stress generation is a little less comparing to the case 2 because of case 1: Xfem = 0 so if your material model needs to be very accurate and the way Ixfem treatment goes it dissipates little more energy because of that small propagation or very local deformation Ixfem could be the good method.

But if we want to see how the crack is propagated over a longer distance then Ixfem may not be a great idea.

Element in case 1 shattered rapidly as compared to the case 2.

Ifail_sh is 2 that means the shell is deleted if all layers in the failure zone.

            Case 1 Law2_epxmax_failure                  Case 2 Law2_epxmax_crack

Kinetic energy is more fluctuating because of more number of elements cracked in case 1 as compared to case 2. Elements did not crack more in case 2.

Internal energy is the same at starting but later on it became constant soon in case 1 and it keeps on increasing in case 2 because elements didn't crack and split more.

2. For Case 3 and Case 4

Here we compare the cases with and without Equivalent plastic strain i.e. EPS_p_max.

In case 3, the value of EPS_p_max = 0.151 i.e. element will fail when stress reaches to 15 % of plastic strain.

In Case 4 we delete the value of EPS_p_max that means it goes to its default value.

Simultaneously, we delete the Johnson failure card for both cases.

Run both the simulations and compare the results.

            Case 3 Law2_epxmax_nofail                                  Case 4 Law2

The plate gets rupture and elements crack and get deleted because we know the Eps_p_max value is 15% of plastic strain in case 3 and we delete in case 4.

We can see in the picture the maximum Von Mises stress value in case 3 is very less compared to case 4 because in case 4 plate doesn't rupture so strain keeps on increasing and simultaneously stress also increases continuously and we also delete Johnson's failure card that's why in case 4 elements not getting deleted.

             Case 3 Law2_epxmax_nofail                                  Case 4 Law2

In energy curves, we can see a clear difference between both kinetic and Internal energy.

Kinetic energy is equal to 19 and it little fluctuates and around 4 ms after that it suddenly hikes to very high value and after that, it fluctuates. This is because plate before rupture store good amount of internal energy and when plate suddenly breaks the elements get crack and move fastly.
With comparing to case 4 plate doesn't rupture so it continuously stores internal energy and gets deformed and with that kinetic energy is nearly equal to 2.05 around in the beginning and only little fluctuation and remains the same from where it starts.

3. For Case 5: We use LAW 1 which means Isotropic elasticity: Linear elastic material which follows Hook's Law. It is good for elastic materials, this law represents a linear relationship between stress and strain. The material stiffness is determined by only two values Young modulus and Poisson's ratio.
We change the Card Image to M1_ELAST and (Density) Rho_initial = 0.0028, Young modulus E = 71000 and Poisson's ratio = 0.33 remains the same. Shell properties are also the same as the recommended properties.

Here Von Mises Stress values hike too much because as it is elastic material it stores so much of strain and simultaneously stresses are generating.
There is no plastic material is involved in this case which gives us linear deformation only and Internal energy increases exponentially here as it is a perfectly elastic material.

We can see that kinetic energy is nearly equal to zero but as time increases it start to increase very slowly but at the end, it suddenly hikes because at that time so much of strain already stored.
LAW 1 should not be used for part undergoing large deformation.

4. For Case 6

We use LAW 27 (PLAS_BRIT) Elasto-Plastic material with brittle failure.

This law combines an isotropic Elasto-Plastic and Johnson cook material model with an orthotropic brittle failure model.

Open LAW 27 RAD File and change the shell properties to recommended shell properties.

Change the material card to the Aluminium material and now run that file and observe the simulation.

Here we can see that the whole plate will rupture bur elements didn't crack much.
Material damage is accounted for prior to failure. Failure and damage occur only in tension. This law is applicable only for shells. Yield surface definition is the same as LAW 2.

Damage and rupture defined with four parameters:
a) et = strain at the beginning of tensile failure
b) em = maximum tensile strain at which the stress in the element is set to a value which is dependent on dmax=1
c) dmax = Maximum damage factor
d) ef = Maximum tensile strain for element deletion 

Kinetic energy is fluctuating but near to zero but suddenly around 4ms it hikes and again decreases. at that point the whole plate gets rupture & split at that point internal energy goes to the constant curve at the end, initially it increases gradually w.r.t time.

LAW 27 is useful for modeling brittle failure of glass. Ex- safety glass.

5. For Case 7

LAW36: M36 PLAS_TAB: Isotropic Elasto-Plastic: Tabulated piecewise Linear

This law models an isotropic elastoplastic material using a user-defined function for the work-hardening portion of the stress-strain curve. Ex- Plastic strain vs stress for different strain rates.

In case 7, we use two curves for making our model and save the data in files.

The test curve we make by our given data and Standard curve is below.
         Strain                  Stress                             Strain                  Stress
 

Here we create new material and name it M36 Plas_tab. For understanding the concept of new material creating and assign the curve in that material.
EPS_p_max is 0.16, EPS_t = 0.1, EPS_m = 0.11 and F_smooth = 1

Assign the curve to the component and after that run the file.

                          Test curve                                                Standard curve

In the Test curve the plate rupture abruptly and crack elements get deleted after some instant but in the standard curve, 16% of equivalent plastic strain value the element should fail and achieved sooner. The Von Mises stress is also more in the test curve. 

                          Test curve                                                Standard curve

In the test curve, sudden increases in the value of kinetic energy after around 2 ms because before that it stores the internal energy by hitting of force and suddenly plate breaks down and elements distorted and kinetic energy fluctuates and decreases drastically.

But in the standard curve, If we see the scale of the Kinetic energy, it doesn't increase that much because before that the elements get deleted and another element will crack out so it fluctuates.

The table in which the number of cycles, energy error and mass error and simulation time is given for all cases.

CONCLUSION

  • We learned about all different laws, what is the use and work of each LAW.
  • We analyzed how the "plate" behaves after the crash for each case.
  • If we have Elastic material like rubber sheet: LAW 1 would be the better option.
  • If we are doing analysis on any brittle component like safety glass then LAW 27 is a better option.
  • For Isotropic Elasto-plastic we can use LAW 2 and LAW 36.
    We analyze that in LAW 2 if we give EPS_p_max value accordingly and our Johnson failure card would be proper and then according to it, case 2 would be the better option for our plate because we get the least maximum value of Von Mises stress.
  • LAW 36 is commonly used in industries because we can change the curve with the lab data curve which helps us to perform the simulation using lab data values.

 

Analysis of failure behavior of a plate with 3 different material using Hypermesh Radioss

Google drive link for all files:

https://drive.google.com/open?id=12Ememw9mQx7WIGnbMTd41_K9xAKwZdOC

 


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