AIM: To analyze and compare the 7 cases of a spherical ball hitting the rupture plate simulations with different materials properties.

INTRODUCTION:

LAW 2: /MAT/LAW2 (PLAS_JOHNS)

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.

σ = (A + Bε n )(1 + C lnε˙ ∗ )(1 − T ∗m )

where,σ is the equivalent stress, and ε is the equivalent plastic strain. The material constants are A, B, n, C and m. A is the yield stress of the material under reference conditions, B is the strain hardening constant, n is the strain hardening coefficient, C is the strengthening coefficient of strain rate, and m is the thermal softening coefficient .

LAW 27: /MAT/LAW27 (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.

σ=(a+bεpn)(1+cln˙ε˙ε0)σ=(a+bεpn)(1+clnε˙ε˙0)

Where, εp is the plastic strain and ˙εε˙ is the strain rate.

The plasticity hardening exponent, n must be less than 1.

LAW 36: /MAT/LAW36 (PLAS_TAB)

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.It is used when user defined values are needed to define stress-strain curve in the strain-hardening region.

Material Property :(Elasto Plastic Material)

Initial density (rho) = 0.0028 g/mm3

Young’s Modulus (E) = 71000MPa

Poisson’s Ratio (nu) = 0.33

True yield stress (a) = 290MPa

Hardening Modulus or UTS (b) = 562.3

Hardening exponent (n) = 0.63

Maximum plastic strain for failure (EPS_p_max) = 0.151

Maximum stress (sig_max0) = 425MPa

The shell properties used for the model are:

Objective:

1. To run the simulation for the ball hitting a rupture plate with 7 different cases.
2. Compare the results obtained from the simulation, Total number of cycles, Energy error, mass error and simulation time.
3. Plot the curves of different energies.
4. Learning out comes and conclusion.

Procedure:

Case (1) - Law2_epsmax_failure_0000.rad

/MAT/PLAS_JOHNS/ is used as the material model

1. Import the FAILURE_JOHNSON_0000.rad file into hypermesh and radioss as solver.
2. Run the radioss analysis and save the file as Law2_epsmax_failure.
3. Now check whether the energy and mass error is less than 15% in .out.rad file.
4. Now open Hyperview and select .h3d file.
5. Select contour-von mises-simple method and click apply.
6. Now select multi-window and open .T01 file in Hypergraph to plot the graphs.

The images of the simulations are

The image of plot time vs contact energy, total energy, hour glass energy, kinetic energy,internal energy:

The Internal energy, Kinetic energy, Hourglass energy and Total energy graph are plotted in Hypergrpah2d.

After 4ms the maximum strain rate is reached and the elements start to deleted and hence this movement of element causes hike in Kinetic energy and due to shell element formulation there is no hour glass energy and contact energy is also zero .

Since Ixfem = 0, elements are getting deleted on reaching maximum strain rate and there is no crack formation.

Case (2)- Law2_epsmax_crack_0000.rad

/MAT/PLAS_JOHNS/ is used as the material model

1. Import the Law2_epsmax_failure_0000.rad file into hypermesh and radioss as solver..
2. In Failure Johnson card change Ifail_sh=1, Dadv=1, Ixfem=2.
3. Run the radioss analysis and name the file as Law2_epsmax_crack.
4. Now check whether the energy and mass error is less than 15%.
5. Now open Hyperview and select .h3d file.
6. Select contour-von mises-simple method and click apply.
7. Now select multi-window and open .T01 file in Hypergraph to plot the graphs.

NOTE: This model has both the failure card and epsmax value.

The images of the simulations are

The image of plot time vs contact energy, total energy, hour glass energy, kinetic energy,internal energy:

In this case the elements are first gets cracked and then then they start deleting this is due to the ixfem = 1.

Case (3) - Law2_epsmax_nofail_0000.rad

/MAT/PLAS_JOHNS/ is used as the material model

1. Import the Law2_epsmax_crack_0000.rad file into hypermesh and radioss as solver.
2. Delete the failure johnson card.
3. Run the radioss analysis and name the file as Law2_epsmax_nofail.
4. Now check whether the energy and mass error is less than 15%.
5. Now open Hyperview and select .h3d file.
6. Select contour-von mises-simple method and click apply.
7. Now select multi-window and open .T01 file in Hypergraph to plot the graphs.

NOTE: This model has no failure card.

The images of the simulations are

The image of plot time vs contact energy, total energy, hour glass energy, kinetic energy,internal energy:

In this case the elements start deleting when the plastic strain reaches maximum since there is no failure card the elements does not cracks.

Case (4) - Law2_0000.rad

/MAT/PLAS_JOHNS/ is used as the material model.

1. Import the Law2_epsmax_nofail_0000.rad file into hypermesh and radioss as solver.
2. Remove the EPS_p_max value.
3. Run the radioss analysis and name the file as Law2.
4. Now check whether the energy and mass error is less than 15%.
5. Now open Hyperview and select .h3d file.
6. Select contour-von mises-simple method and click apply.
7. Now select multi-window and open .T01 file in Hypergraph to plot the graphs.

NOTE: This model has no both the failure card and epsmax value.

The images of the simulations are

The image of plot time vs contact energy, total energy, hour glass energy, kinetic energy,internal energy:

In this case the element does not undergo failure because there is no eps_max value,hence the element strectches when it takes the load impact.

Case (5) - Law1_0000.rad

/MAT/M1_ELAST/ is used as the material model.

1. Import the Law2_0000.rad file into hypermesh and radioss as solver.
2. Change the card image to Law1 i.e, M1_ELAST and assign the material properties as recommended.
3. Run the radioss analysis and name the file as Law1.
4. Now check whether the energy and mass error is less than 15%.
5. Now open Hyperview and select .h3d file.
6. Select contour-von mises-simple method and click apply.
7. Now select multi-window and open .T01 file in Hypergraph to plot the graphs.

NOTE: This model has no both the failure card and epsmax value.

The images of the simulations are

The image of plot time vs contact energy, total energy, hour glass energy, kinetic energy,internal energy:

Since the material model is elastic the elements doesn't get deleted,but they strecthes when they experience the load impact.

Case (6) – Law27_0000.rad

/MAT/M27_PLAS_BRIT/ is used as the material model.

1. Open the Law27_0000.rad file.
2. Change the shell properties to recommended properties.
3. Run the radioss analysis and name the file as Law27.
4. Now check whether the energy and mass error is less than 15%.
5. Now open Hyperview and select .h3d file.
6. Select contour-von mises-simple method and click apply.
7. Now select multi-window and open .T01 file in Hypergraph to plot the graphs.

The images of the simulations are

The image of plot time vs contact energy, total energy, hour glass energy, kinetic energy,internal energy:

In this case the elements starting to fail when the EPS_f value reaches one integration point.

Case (7) – Law36_0000.rad

/MAT/M36_PLAS_TAB/ is used as the material model.

1. Open the Law1_0000.rad file.
2. Create Law36 card i.e, M36_PLAS_TAB and assign the properties as recommended.
3. Create a test curve with values as mentioned in the video.
4. Run the radioss analysis and name the file as Law36.
5. Now check whether the energy and mass error is less than 15%.
6. Now open Hyperview and select .h3d file.
7. Select contour-von mises-simple method and click apply.
8. Now select multi-window and open .T01 file in Hypergraph to plot the graphs.

The values of the test curve are:

The images of the test curve are

The images of the simulations are

The image of plot time vs contact energy, total energy, hour glass energy, kinetic energy,internal energy:

In this case the element gets deleted when the plastic strain reaches 0.16.

Compairing results of the simulations:

Cases	Failure card	Material card	Energy error(%)	Mass error(%)	Total no of cycles	Simulation time (seconds)	Vonmisile stress(mpa)	Remarks
Case 1	fail_jhonson	/MAT/PLAS_JOHNS/	0.2%	0	49480	140.55	328	The element gets deleted when it reaches the eps_max value.
Case 2	fail_jhonson	/MAT/PLAS_JOHNS/	4%	0	49397	163.82	294	The element gets Cracked first & then deleted due to changes in failure card.
Case 3	No failure card	/MAT/PLAS_JOHNS/	0.8%	0	49405	156.74	311	The element gets deleted when it reaches eps_max value.
Case 4	No failure card	/MAT/PLAS_JOHNS/	3%	0	48737	138.15	425	The elemnts gets neither cracked nor deleted due to no eps_max value
Case 5	No failure card	/MAT/M1_ELAST/	0.3%	0	47969	136.95	10900	The elements neither cracked nor deleted due to elastic property.
Case 6	No failure card	/MAT/M27_PLAS_BRIT/	0.9%	0	49442	164.06	286	The failure occurs when the elemnts reaches eps_f=0.15.
Case 7	No failure card	/MAT/M36_PLAS_TAB/	-1.2%	0	47969	165.5	797	The failure happens when it reaches the maximum strain rate.

The simulations of different cases in a single hyperview window:

Comparison of graphs plotted in different cases:

The internal energy vs time plot in different cases:

Case 1:/MAT/PLAS_JOHNS/

• With failure card and eps_max value,but Ixfem = 0.

Case 2:/MAT/PLAS_JOHNS/

• With failure card and eps_max value and Ixfem = 1.

Case 3:/MAT/PLAS_JOHNS/

• Without failure card.

Case 4:/MAT/PLAS_JOHNS/

• With out failure card and eps_max value.

Case 5:/MAT/M1_ELAST/

Case 6:/MAT/M27_PLAS_BRIT/

Case 7:/MAT/M36_PLAS_TAB/

• In case 1 the internal energy increases gradually upto 4ms and after that the strain rate reaches maximum and the kinetic energy increases the elements start deleting hence there is a disturbance in the graph.
• In case due to Ixfem = 1,the elements cracks first before getting deleted due to this the internal energy value is higher in case2 and kinetic energy is less when compared to case 1 and the disturbance in graph is created a way later when compared to case 1.
• The case 3 is similar to the case1 since it has no failure card the elements gets deleted with out cracking.So the graph increases gradually and has disturbance when the kinetic energy increases and strain rate reaches maximum.
• In case 4 the internal energy increases gradually with out any disturbance because it has no failure card and eps_max value,so the element gets stretches with out deleting or being cracked.
• The case 5 also similar to the case 4 the internal increases with out any disturbance because the material is elastic,but when compared to case 4 the magnitude of internal energy is higher in case 5 due its elastic material property card.
• In case 6 and case 7 the internal energy graph behaves depending on their material card.
• The hour glass energy and the contact energy are same in every case they remains zero.

Learning outcomes:

• We have learn how to create the material properties using material laws.
• We have also learn how to create the failure cards and also how to create the test curves.

Conclusion:

• The simulations for the ball hitting rupture plate with different material properties is completed.
• By comparing the results of the simulations the case that would represent the on-field scenario is case 2 since the ultimate tensile strength of alluminium is 310 MPa (45000 psi) .

link for the model files

https://drive.google.com/drive/folders/1af6gYOJYtO85dP1Baz9Yo-tptV-46xy4?usp=sharing