Analysis of a rupture plate element by using different material laws in Altair Radioss and comparing the results of all the seven cases
OBJECTIVE :
Analysing different Material Law Properties in Altair Radioss solver by conducting 7 different cases os rupture plate simulation and deciding the best suitable material law based on the given simulation scenario.
7 Simulation Cases :
Case (1) - Run the model as it is with the name Law2_epsmax_failure_0000.rad
Case (2) - Run the model with the values Ifail_sh = 1 , Dadv = 1 , Ixfem = 1. Name the files as Law2_epsmax_crack_0000.rad
Case (3) - Delete the fail_JOHNSON card and run the model with the name Law2_epsmax_nofail_0000.rad
Case (4) - Input the value of EPS_p_max = 0 and run the model with the name Law2_0000.rad
Case (5) - Convert the material model to Law1 and run the model with name Law1_0000.rad
Case (6) - Open the Law27_0000.rad file and chnage the shell properties to recommended properties and then run the model with the name Law27_0000.rad
Case (7) - Change the material law to M36_PLAS_TAB and run the model with the file name law_36_0000.rad
Case (1) - Law2_epsmax_failure_0000.rad
/MAT/PLAS_JOHNS/ is used as the material model
This law represents an isotropic elasto-plastic material using the Johnson-Cook material model.
This model expresses material stress as a function of strain, strain rate and temperature. A built-in failure criterion based on the maximum plastic strain is available.
The rad file is imported in and the simulation is performed by selecting Analysis>Radioss in the bottom toolbar.
Once the simulation is done, the out file is opened for checking the energy error, mass error, number of cycles.
Here the energy error is less than +5% hence it is acceptable
ENERGY ERROR : 0.2%
MASS ERROR : 0.000
SIMULATION TIME : 5.010 ms
ELAPSED TIME : 171.91 s
CYCLES : 49479
The Von Mises stress,plastic-strain,displacement, thickness reduction plot are seen in Hyperview by opening the .h3d file
Von Mises stress plot
plastic-strain plot
displacement plot
thickness reduction plot
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in Hypergrpah2d.
In the internal energy graph the energy increases upto 4ms but after that due to Strain-hardening process the internal energy values oscillates
The Kinectic energy graph gives only small spikes which indicate that the elements are getting deleted on reaching the maximum Strain rate of 15%.
After 4ms the maximum strain rate is reached and the elements start to deleted and hence this movement of element causes increase in Kinetic energy
Since Ixfem = 0, elements are getting deleted on reaching maximum strain rate and their is no crack formation.
Due to usage of QEPH element formulation their is zero Hourglass energy.
Since the sphere is considered as a rigit body the kinetic energy of the rigid body is negelected and hence the total energy starts from zero for the plate alone
Total energy increases linearly till 4ms after that due to strain-hardening process the graph tends to flat.
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in a single sheet to get an overview.
Case (2) - Law2_epsmax_crack_0000.rad
/MAT/PLAS_JOHNS/ is used as the material model
Here these values used
Ifail_sh = 1
Dadv = 1
Ixfem = 1, since Ixfem = 1 crack is formed when maximum plastic strain is reached in any of the integration point of an element
The rad file is imported in and the simulation is performed by selecting Analysis>Radioss in the bottom toolbar.
Once the simulation is done, the out file is opened for checking the energy error, mass error, number of cycles.
Here the energy error is less than +5% hence it is acceptable
ENERGY ERROR : 4.0%
MASS ERROR : 0.000
SIMULATION TIME : 5.010 ms
ELAPSED TIME : 58.08 s
CYCLES : 49396
The Von Mises stress,plastic-strain,displacement, thickness reduction plot are seen in Hyperview by opening the .h3d file
Von Mises stress plot
plastic-strain plot
displacement plot
thickness reduction plot
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in Hypergrpah2d.
In the internal energy graph the energy increases upto 4ms but after that due to Strain-hardening process the internal energy values oscillates
The Kinectic energy graph gives only small spikes which indicate that the elements undergo crack formation on reaching the maximum Strain rate of 15%.
Since Ixfem = 1, their is crack formation once the elements reach maximum plastic strain value.
Thus when compared to case(1) the internal and kinetic energy are decreased due to crack formation.
Due to usage of QEPH element formulation their is zero Hourglass energy.
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in a single sheet to get an overview.
Case (3) - Law2_epsmax_nofail_0000.rad
The fail_JOHNSON card is deleted and the model is run by selecting Analysis>Radioss in the bottom toolbar.
Once the simulation is done, the out file is opened for checking the energy error, mass error, number of cycles.
Here the energy error is less than +5% hence it is acceptable
ENERGY ERROR : 0.8%
MASS ERROR : 0.000
SIMULATION TIME : 5.010 ms
ELAPSED TIME : 58.95 s
CYCLES : 49404
The Von Mises stress,plastic-strain,displacement, thickness reduction plot are seen in Hyperview by opening the .h3d file
Von Mises stress plot
plastic-strain plot
displacement plot
thickness reduction plot
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in Hypergrpah2d.
In the internal energy graph the energy increases upto 4ms but after that due to Strain-hardening process the internal energy values oscillates
The Kinectic energy graph gives only small spikes which indicate that the elements are getting deleted onve reaching the maximum Strain rate of 15%.
h
Due to usage of QEPH element formulation their is zero Hourglass energy.
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in a single sheet to get an overview.
Case (3) and case (1) are similar without any crack formation.
Case (4) - Law2_0000.rad
The fail_JOHNSON card is deleted and EPS_p_max is deleted
After that the simulation is performed by selecting Analysis>Radioss in the bottom toolbar.
Once the simulation is done, the out file is opened for checking the energy error, mass error, number of cycles.
Here the energy error is less than +5% hence it is acceptable
ENERGY ERROR : 3.0%
MASS ERROR : 0.000
SIMULATION TIME : 5.010 ms
ELAPSED TIME : 59.80 s
CYCLES : 48736
The Von Mises stress,plastic-strain,displacement, thickness reduction plot are seen in Hyperview by opening the .h3d file
Von Mises stress plot
plastic-strain plot
displacement plot
thickness reduction plot
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in Hypergrpah2d.
In the internal energy graph the energy increases in an exponential model because there is no EPS_p_max value.
Thus it shows that the elements keep on absorbing energy and they are getting streched.
The Kinectic energy graph gives only small values since no element is displaced due to any crack formation or deletion.
Due to usage of QEPH element formulation their is zero Hourglass energy.
The value of total energy keeps on increasing as the internal energy of the plate is increasing due to no EPS_p_max value.
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in a single sheet to get an overview.
Case(4) has no EPS_P_max value hence there are no element deletion happening and thus the elements are only streched when they are stressed under load conditions
Case(5)
Convert the material model to Law1 and run the model with name Law1_0000.rad
MATERIAL
RECOMMENDED SHELL PROPERTIES
The out file is viewed to get energy error, mass error, cycles, simulation time and run time
Here the energy error is less than +5% hence it is acceptable
ENERGY ERROR : 1.8%
MASS ERROR : 0.000
SIMULATION TIME : 5.010 ms
ELAPSED TIME : 56.44 s
CYCLES : 47948
The Von Mises stress,plastic-strain,displacement, thickness reduction plot are seen in Hyperview by opening the .h3d file
Von Mises stress plot
plastic-strain plot
Since law1 is used which is elasticity model, the plate behaves as a pure elastic material and the stress strain curve is always under Hooke's law. Because of this only there are no plastic strains in the material
displacement plot
thickness reduction plot
Case(5) is suitable for static analysis of beam or any other quasi-static analysis. But in a case of crash analysis entire event is dynamic and happens within 120ms so Law1 cannot be used.
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in Hypergrpah2d.
In the internal energy graph the energy increases in an exponential model because the stress-strain graph always lies within Hooke's law
Thus it shows that the elements keep on absorbing energy and they are getting streched.
The Kinectic energy graph gives only small values since no element is displaced due to any crack formation or deletion.
Due to usage of QEPH element formulation their is zero Hourglass energy.
The value of total energy keeps on increasing as the internal energy of the plate is increasing due to the elastic behaviour of the material
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in a single sheet to get an overview.
Case(5) has only elastic model behaviour hence there are no element deletion happening and thus the elements are only streched when they are stressed under load conditions
Case(6)
Open the Law27_0000.rad file and chnage the shell properties to recommended properties and then run the model with the name Law27_0000.rad
Law27 - M27_PLAS_BRIT
This law combines an isotropic elasto-plastic Johnson-Cook material model with an orthotropic brittle failure model. Material damage is accounted for prior to failure. Failure and damage occur only in tension. This law is applicable only for shells.
Material card
The simulation is donw by selecting Radioss under Analysis option.
Once the simulation is done it give out various output files such as .RST, .ABF, .OUT, .h3d and so on.
The OUT file is used to view the no of cycles, energy error , mass error, simulation time and run time
Here the energy error is less than +5% hence it is acceptable
ENERGY ERROR : 1.1%
MASS ERROR : 0.000
SIMULATION TIME : 5.010 ms
ELAPSED TIME : 175.21s
CYCLES : 49355
The Von Mises stress,plastic-strain,displacement, thickness reduction plot are seen in Hyperview by opening the .h3d file
Von Mises stress plot
In the stress plot it is seen that even before failue occurs some elemets on the outer edge are deleted, this is due to orthotropic brittle failure. It ensures the fact that in Law27 material damage is taken into account even before the failure occurs
plastic-strain plot
Since law1 is used which is elasticity model, the plate behaves as a pure elastic material and the stress strain curve is always under Hooke's law. Because of this only there are no plastic strains in the material
displacement plot
thickness reduction plot
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in Hypergrpah2d.
The Kinectic energy graph gives only small values since no element is displaced due to any crack formation or deletion.
Due to usage of QEPH element formulation their is zero Hourglass energy.
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in a single sheet to get an overview.
Case(6) gives total energy and internal energy curve which are almost same with minor differences, these minor differences are caused due to kinectic energy of elements of plate under impact of the Solid Sphere.
Case (7)
Change the material law to M36_PLAS_TAB and run the model with the file name law_36_0000.rad
This law models an isotropic elasto-plastic material using user-defined functions for the work-hardening portion of the stress-strain curve (for example, stress vs. plastic strain) for different strain rates.
The MAT36_PLAS_TAB can be used to define user-define functions for work-hardening portion of stress-strain curve.
In this case a user define curve is given for stress-strain curve.
The curve is named as 36
The curve is chosen under the N_funct tab
These values are defined
Fscale = 1.0
Eps_dot = 1.0
EPS_p_max = 0.16 Failure occurs when platic strain reaches 16%
EPS_t = 0.1 Tensile failure strain at which the stress start to reduce
EPS_m = 0.11 It is maximum tensile failure strain at which the stress in the element are set to zero.
The OUT file is opened to get energy error, mass error, cycles, simulation time and run time.
Here the energy error is less than +5% hence it is acceptable
ENERGY ERROR : -1.2%
MASS ERROR : 0.000
SIMULATION TIME : 5.010 ms
ELAPSED TIME : 64.20s
CYCLES : 53179
The Von Mises stress,plastic-strain,displacement, thickness reduction plot are seen in Hyperview by opening the .h3d file
Von Mises stress plot
In the stress plot it is clearly seen that stress value is much higher than all cases indicating that the material is absorbing more stress due to the elasto-plastic nature. In the plastic strain process the material absorbs a lot of strain thus reducing the impact of the load.
Plastic strain Plot
Displacement plot
Thickness reduction plot
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in Hypergrpah2d.
The Kinectic energy graph gives high value due ti the plasticity behaviour of the material
Due to usage of QEPH element formulation their is zero Hourglass energy.
The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in a single sheet to get an overview.
From the 7 cases the results are compared.
From analysing the result the case(2) is the best suited for rupture plate experiment.
case(1) can be also used for this experimernt
But case(4) and case(5) donot undergo any failure of elements thus they cannot be used
Case(6) can be used only if shell elements are used
Case(7) can be used for this rupture plate experiment but it has high Von Mises stress value of 975Mpa which is higher than Aluminium's Ultimate stress value 310Mpa, altering the Strain-hardening curve can reduce the induced stress values
CONCLUSION
This experiment gives an robust understanding of different material laws used in Radioss
Law1 - It gives perfect elastic model suitable only for static or quasi-static model analysis
Law2 - This law represents an isotropic elasto-plastic material using the Johnson-Cook material model. This model expresses material stress as a function of strain, strain rate and temperature. Best suitable for crash test analysis.
Law27 - Applicable only for shell properties and incorporates brittle nature with elasto-plastic Johnson-Cook material model.
Law36 - It is used when user defined values are needed to define stress-strain curve in the strain-hardening region
GOOGLE DRIVE LINK FOR THE FILES USED
https://drive.google.com/file/d/1dNP3xDbZQVQ3jvVNl4ctAlc4TrwvJt8Y/view?usp=sharing