Comparing Results of Ruptured Plate with different Material Card - Using Hypermesh Radioss

Objective : To Simulate Ruptured Plate using different Material Card and Comparing the results.

Case 1: Law 2-M2_Plas_Johns_Zeril – Elasto-plastic

Case 2 : Law 2 M2_Plas_Johns_Zeril with Fail_Johnson and with Ixfem (Crack Formation)

Case 3 : Law 2 M2_Plas_Johns_Zeril wihout Fail_Johnson

Case 4 : Law 2 M2_Plas_Johns_Zeril with Default eps_p_max value

Case 5 : Law 1- Elastic material

Case 6 : Law 36- Plas_tab material

Case 7 : Law 27- Plas_Brit material

Model :

A 3 mm thick plate is impacted at its midpoint by a 12.7 mm diameter sphere with an imposed velocity of 1 ms^-1.

Units: mm, ms, g, N, MPa.

Shell Properties

Material used:

• Material- Aluminium
• Density (ρ)- 0.0028 Kg/mm^2
• Young’s modulus (E)- 71000 N/mm^2
• Poisson ratio (μ)- 0.33
• Yields Stress (SigmaY)- 290 N/mm^2
  

Case 1 : LAW 2 (PLAS_JOHNS) Johnson-Cook Material

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

Once the simulation is over go to file FAILURE_JOHNSON_0001.out to the check the Energy Error Mass error , simulation Time and No of Cycles

Ouput File:

Number of Cycle	Simulation Time	Energy Error	Mass Error
49480	5.010ms	0.2%	0

Since Energy error is less than 15% The results is accepted.

Results :

Von Mises Stress

Max Stress: 2.876e+02

When EPS_S reaches the value of EPS_P_max in one integration point, The corresponding shell element is deleted., since the EPS_p_max values set as 0.15 when the strain energy in plate reaches 15% of total strain energy. the plate starts to rupture .

Energy Graph

since we knew energy error is 0.2% the hourglass energy will not be there we are going to plot only

Internal Energy, Kinetic Energy, and Total Energy

1. Till 4ms the internal Energy increases linearly as the kinetic energy remain constant but at 4ms the internal energy becomes constant
2. And there is slight increase in the kinetic energy and drops ,
3. Plate was able to absorbed the energy applied till 4ms but once it reaches the EPS_p_max values the plate cant absorb anymore energy and its crack and the internal energy become constant and when the crack is generated at that instant the kinetic energy increases and drop again

• Case 2 : Law 2 M2_Plas_Johns_Zeril with Fail_Johnson and with Ixfem (Crack Formation)

In this case, We are using Same LAW2 (PLAS_JOHNS) Johnson-Cook Material for simualtion but few parameters are added to visualize checking or braking down of elements with the help of 'Ixfem' option in Fail-Johnson failure model card.

The parameters for Failure johnson model card are set as

Ouput File:

Number of Cycle	Simulation Time	Energy Error	Mass Error
49397	5.010ms	4%	0

• Since Energy error is 4% which is less than 15% so The results is accepted

Results

Von Mises Stress

Max Stress: 2.913e+02

Since we have set Ixfem=1, this failure criteria will lead to element cracking instead of element or layer deletion.

• D_adv function is, element cracks,
• If the element has no failed neighbours and D > 1, then in this case, new crack initialization in element.
• If the element has failed neighbours and D > D_adv, then in this case, crack advanced and D_adv used for crack advancement. D_adv will be only used if existing crack arrives to a boundary of an element.
• Element deleted, if a second crack arrives to the same element.
• In this is case first cracking will take place first and then deleting of elements.

Energy Graph

The Max internal energy is higher in this cases so that plate is able to absorb more than and dissipate energy will be less , the plate were able to absorb the energy till 4.5 ms and After 4.5ms energy becomes almost constant it is because plate started rupturing. Since we used Ixfem & D_adv values. the no .of element were deleted is less they crack first and element gets deleted that why till 4.5 ms plate were able to absorb the energy. The slight increase in kinetic energy at 4.5ms show the plate is rupturing.

Case3 : Law 2 M2_Plas_Johns_Zeril wihout Fail_Johnson

This is case were going to delete the Fail_Johnson model card and use only LAW2 (PLAS_JOHNS) Johnson-Cook Material and check the results

Ouput File:

Number of Cycle	Simulation Time	Energy Error	Mass Error
49405	5.010ms	0.8%	0

Since Energy error is 0.8% which is less than 15% so The results is accepted

Results

Von Mises:

Max Stress: 2.705e+02

Since the We deleted Fail_Johnson model card the EPS_p_max is set to 0.151 & Ixfem=0 by default. which means the element gets deleted once the integration point reached the EPS_p_max value thast why the max stress is less than the case1 and case 2

Energy Graph

1. The internal & total energy goes on increasing with time because plate is resisting the punch force. Max value of both is 27000 J.
2. It can be seen that internal energy increases till 4ms it is because plate is able to absorb the force applied by punch. After 4ms energy becomes almost constant it is because plate started rupturing.
3. Tt the time of rupture starting the kinetic energy increase and drops again
4. Rupture starts early as compare to the case2 is because there is no Fail_Johnson model card which makes Ixfem=0 by default

Case 4 : Law 2 M2_Plas_Johns_Zeril with Default EPS_p_max value

In this case the EPS_p_max (which defines the maximum permitted plastic strain) is changed to '0' which input value of 10^3 as default. This makes the material to behave like Elastoplastic such that strain is computed but not failure due to plastic deformation beyond the limit is experienced

Ouput File:

Number of Cycle	Simulation Time	Energy Error	Mass Error
49304	5.010ms	1.1%	0

Since Energy error is 1.1% which is less than 15% so The results is accepted

Result

Von Mises Stress

Max Stress: 3.280e+02

Since the EPS_p_max value is set to 10^3 as default and still Fail_Johnson model card is there and Ifail_sh value =2 default which means for each integration point, the stress tensor is set to zero so that there is no rupture take place in the plate

Energy Graph

1. Since there is no rupture involved all energy is absorb during the simulation that's why the internal energy is keep on increases throughout the simulation
2. Kinetic energy is constant throughout the simulation
3. Max Energy is 37500J

Case 5 : Law 1- Elastic material

In this cases the material is elastic as an ideal elastic hooks law up to the elastic limit and when the goes a plastic stage throughout any stress no matters the magnitude.. Here no plasticity is expected from the component material.

Ouput File:

Number of Cycle	Simulation Time	Energy Error	Mass Error
47969	5.010ms	0.3%	0

Since Energy error is 0.3% which is less than 15% so The results is accepted

Results

Von Mises Stress

Max Stress : 1.099e+04

The stress induced is very higher compare to all the other case because we defined the material as the elastic behavior so whole deformation will take place in elastic region , so more strain results in more stress.There will be no ruptured or crack involved in the plate in simulation .

Energy Graph

1. The Internal Energy is increases exponentially because the energy is absorbed by the plate throughout the time
2. The kinetic energy is constant because there is no crack or rupture took place in the plate it behaved like elastic so no kinetic energy is there
3. Max Energy is 8.5e+05J

Case 6 : Law 36- Plas_tab material

Elastic Plastic Piecewise Linear Material ,This law models an isotropic elasto-plastic material using user-defined functions for the work-hardening portion of the stress-strain curve.

Once the card Image is set to Law 36 the required values for the materials are changed

• EPS_max/EPS_F- It is a value at which after whichever element crosses it gets deleted from the system.
• EPS_t- It is strain value at which strain damage of material starts & stress starts reducing.
• EPS_m- It is a value at which stress becomes completely zero.

User define stress strain curve is defined in Material Card

Output File:

Number of Cycle	Simulation Time	Energy Error	Mass Error
53181	5.010ms	-1.1%	0

Since Energy error is -1.1% which is less than 15% so The results is accepted

Results :

Von Mises Stress

Max Stress : 9.750e+02

The stress induced is 975MPa with is more than the ultimate stress 460MPa we mentioned in the Stress-Strain graph and EPS_max value is set as 0.16 when the strain energy in plate reaches 16% of total strain energy. the plate startes to rupture and element gets deleted

Energy Graph

1. That internal & total energy goes on increasing Linearly with time till 3 ms, at this point strain reaches EPS_t & value of stress starts reducing thus energy graph becomes constant after 3 ms.
2. At the point of rupture the there is slight increases in kinetic energy and drops become constant

Case 7 Law 27- Plas_Brit material

Elasto-plastic Material with Brittle Failure ,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.

• EPS_t1- It is a tensile failure strain at which stress starts to reduce.
• EPS_m1- Maximum tensile failure strain in principal strain direction 1 at which the stress in the element is set to a value dependent on d_max1
• D_max1- Maximum damage factor in principal strain direction 1 it controls the damage between EPS_f1 and EPS_t1.
• EPS_f1-Maximum tensile strain for element deletion in principal strain direction 1
• EPS_t2-ensile failure strain at which stress starts to reduce in the principal strain direction 2
• EPS_m2- Maximum tensile strain in principal strain direction 2 at which the stress in the element is set to a value dependent on d_max2
• D_max2- Maximum damage factor in principal strain direction 2 it controls the damage between EPS_f2 and EPS_t2.
• EPS_f2- Maximum tensile strain for element deletion in principal strain direction 2.

Ouput FIle

Number of Cycle	Simulation Time	Energy Error	Mass Error
49356	5.010ms	1.1%	0

Since Energy error is 0.3% which is less than 15% so The results is accepted

Results :

Von Mises Stress

Max Stress : 2.772e+02

The material shows the brittle failure of the element since the EPS_f1 is set to 0.151 strain energy in plate reaches 15% of total strain energy the element starts to delete.

Energy Graph

1. The internal energy and total energy keep on increases linearly till 4.3ms after that line reduces goes to constant because after the 4.3ms the element starts to fail and get deleted
2. Kinetic energy is constant throughout the time since no rupture is involved
3. Max Energy is 40000J

Conclusion :

Different Type of material card is tried out for this simulation setup

1. Law 2 M2_Plas_Johns_Zeril is most Commonly used material card we tried this material card with different parameter such as with and without failure model and by change EPS_p_max values
2. Law 36 Elastic Plastic Piecewise Linear Material - This law models an isotropic elasto-plastic material using user-defined stress- strain curve from physical testing
3. Law 1 Elastic material -This Material as an ideal elastic hooks law up to the elastic limit, no plasticity is expected
4. Law 27- Plas_Brit material -Elasto-plastic Material with Brittle Failure This law combines an isotropic elasto-plastic Johnson-Cook material model with an orthotropic brittle failure model. These can be should brittle materials

Model File :

https://drive.google.com/file/d/1RQWnd95pGT2ngyRCe1nlAn3Tsw9lHlSG/view