ANALYSIS THE CIRCULAR PLATE WITH DIFFERENT MATERIAL CARD AND COMPARE THE RESULTS WITH DIFFERENT MATERIAL LAWS.

Objective:

• To Analysis the circular plate with a different material card by using Hypermesh as a pre-processor and Radioss as a Post-processor(Solver), Compare the results with the Law2, Failue mode and Law27.

Procedure:

Slide 1:

Model setup

• First we have to import the Failure_johnson_0000.rad by using solver deck and as shown below.

• After Importing the file run the model as it is by using Radioss as we completed simulation we get rigid sphere on a plate with finer mesh flow as shown below.

• The above model having the following Material Properties:
  • Material = Aluminium
  • Young's Modulus (E) = 71000 `(N)/(mm^2)`
  • Poission Ration (nu) = 0.33
  • Density (rho) = 0.0028 `(g)/(mm^3)`
  • Yeild Stress (a) = 290 `(N)/(mm^2)`
  • Hardening Modulus(b) = 562.3 `(N)/(mm^2)`
  • Hardening Exponent(n) = 0.63

• As we set up the model now we move on to the analysis and compare the different material card by Applying the different Laws i,e Law1, Failure mode and Law27.

Slide 2:

Case 1: Law 2_Epsmax_failure

• 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.
• Equation given by:
  • `sigma = (a+b*epsilonundersetp^n)*1+c*ln*epsilon/(epsilonunderset0)*(1-T^m)`Where,
    • a = Yeild Stress
    • b = Hardening Modulus
    • n = Hardening Exponent
• Change element properties into recommonded properties for better results.
• eps_p_max = 0.151 or 15.1% Maximum Strain Value.
• SIG_max0 = 425.0 Maximum Stress value.
• Now we Run the model by using Radioss Solver and as shown below.

Von-misses Stress:

Maximum Stress = 287.6 Mpa

• Above figure shows von-misses stress and it is ploted by using hyperview.
• Failure of the element happens when 1 integration point reaches εpmax.
• Here we have Maximum plastic strain of 15% upto which the element failure will not happen.

Elapsed Time & Total Number of Cycles:

Elapsed Time = 190.73 sec

Total Number of Cycles = 49,480

Energy Error & Mass Error:

Energy Error = -0.1%

Mass Error = 0.00

Kinetic Energy, Internal Energy and Total Energy:

• Total energy is the sum of internal energy, kinetic energy, contact energy, hourglass energy.etc in the model. For a typical crash analysis energy plot based on the external works, the total energy must remain constant or can decrease slightly.

• During a crash scenario due to the external forces applied there will be change in internal energy, kinetic energy, contact energy....etc and all these constitutes to the total energy of the model. When work is done by external forces, the total energy of the object may be altered.

• As we Observe in the above graph there is little KE will develop as compared to the IE because work is done by the Sphere on the circular plate that’s why the IE is on higher side all KE develop in the plate is observe by the sphere as shown in the above graph.
• Here the Maximum IE is 27,500 joules.

Case 2: Law 2_Epsmax_Crack

• In the case 2 we have to modify the Failure_JOHNSON Card with the following values.
  • Ifail_sh = 1 (Default) Shell is deleted or cracked.
  • Dadv = 1.0
  • Ixfem = 1 XFEM Formulation. and as shown in below figure

• Now the case set up is ready and to run the model by using radioss solver.

Von-Misses stress:

Maximum Stress = 294.7 Mpa

• When we changed those values (Ixfem & Dadv) in the Failure_JOHNSON Card Crack formulation better than the previous case 1 and as shown in the above figure.
• As we compare the stress in both cases are little bit same but only difference in the crack formation and also Maximum plastic strain given in this failure model as 15.1% when material reach this state it will gets cracked.
• Maximum stress generated in this case is 294.7 Mpa which is the maximum stress absorbed by the shell.

Number of Cycles and Elasped time:

Elapsed Time = 155.33 sec

Total Number of Cycles = 49397

Energy Error & Mass Error:

Energy Error = 3.1%

Mass Error = 0.00

Kinetic Energy, Internal Energy and Hourglass Energy:

• For a typical crash analysis energy plot based on the external works.
• As we Observe in the above graph there is little KE will develop as compared to the IE because work is done by the Sphere on the circular plate that’s why the IE is on higher side all KE develop in the plate is observe by the sphere as shown in the above graph.
• Here the Maximum IE is 29000 joules.
• The Hourglass energy is zero because we have use Ishell = 24 which is control the hourglass energy.

Case 3 : Law2_Epmax_Nofail:

• As given in the Assignment Epmax_Nofail we have to deleted the Failure card and Run the model and compare the results with above cases.

Von-Misses Stress:

• Maximum stress generated in this case is 270 Mpa which is the maximum stress absorbed by the shell.
• Here we deleted the failure card the matrial gets crack when the maximum plastic strain value reaches 15.1% and maximum stress reaches 425.0 Mpa.
• As we compare with the case 1 crack formualtion is same because here there is no values (Ixfem & Dadv) given in the failure card and failure card gets deleted.

Number of Cycles and Elasped time:

Elapsed Time = 162.27 sec

Total Number of Cycles = 49405

Energy Error & Mass Error:

Energy Error = 0.2%

Mass Error = 0.00

Kinetic Energy, Internal Energy and Hourglass Energy:

• For a typical crash analysis energy plot based on the external works.
• As we Observe in the above graph there is little KE will develop as compared to the IE because work is done by the Sphere on the circular plate that’s why the IE is on higher side all KE develop in the plate is observe by the sphere as shown in the above graph.
• Here the Maximum IE is 27500 joules.
• The Hourglass energy is zero because we have use Ishell = 24 which is control the hourglass energy.

Case 4: Law 2_delete the Epmax value_nofail:

• In this case Epmax value (40%) is deleted and solver takes default value i,e 10^30 as a maximum plastic strain, the material will not fail under epmax case because this value is very high.

• Here the material will gets cracked under only maximum stress condition i,e 425 Mpa.
• At this stress the material will never gets crack and all the stress generated in the material aboserb by the shell only if we further increases in the stress for that value the material will gets cracked.
• The material behaves like elastic and it reagins its orginal shape and size after removal of external load.

Von-Misses Stress:

The above figure shows there is a small penetration of sphere on the circular plate but there is no crack formulation.

Number of Cycles and Elasped time:

Elapsed Time = 149.27 sec

Total Number of Cycles = 48737

Energy Error & Mass Error:

Energy Error = 0.2%

Mass Error = 0.00

Kinetic Energy, Internal Energy and Hourglass Energy:

There is a higher value for the IE but our time limit 5ms hence the maximum energy is 66000 joules as shown in the above graph if we increase in simulation time may be we get end value of the IE.

• The Hourglass energy is zero because we have use Ishell = 24 which is control the hourglass energy.

Case 5: Convert this material model into Law 1 (Elastic):

Here we convert the material model into law 1 with the same values of rho, nu and E.

Von-Misses Stress:

In this case there is no failure card, no epmax value, no maximum stress value and hence the maximum stress generated is 1086Mpa and as compared to other cases (case 2) stress was better Absorption. For this model there is failure occure beacuse it behaves like a elastic material and when the load was removed it gets its origional shape and size with zero stress strain values.

Number of Cycles and Elasped time:

Elapsed Time = 148.86 sec

Total Number of Cycles = 47969

Energy Error & Mass Error:

Energy Error = 0.2%

Mass Error = 0.00

Kinetic Energy, Internal Energy and Hourglass Energy:

There is a higher value for the IE but our time limit 5ms hence the maximum energy is 8.12E+05 joules as shown in the above graph if we increase in simulation time may be we get end value of the IE.

• The Hourglass energy is zero because we have use Ishell = 24 which is control the hourglass energy.

Slide 3:

Case 1: Law27

• 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.
• Yield surface definition same as Johnson-Cook (Law2) Damage and rupture defined with 4 parameters for each principal direction:
  • et = Strain at the beginning of tensile failure
  • em = Maximum tensile strain at which the stress in the element is set to a value dependent on dmax1
  • dmax = Maximum damage factor
  • ef = Maximum tensile strain for element deletion