ANALYSIS OF A FAILURE ALUMINIUM PLATE USING MATERIAL MODELS (LAW_1,LAW_2,LAW_27,LAW_36) AND JOHNSON FAILURE CARD IN RADIOSS

OBJECTIVE: It is very important to define properly the plasticity of material and failure accurately when modeling FEA. This project involves the experimental analysis and comparison of certain material laws and failure to analyse their differences and how accurate their failure and results are in terms of certain engineering quantities. Their failures Below are the material laws and failures to be compared

1. LAW_1 (ELASTIC)
2. LAW_2 (ELASTO-PLASTIC)
3. LAW_27 (BRITTLE)
4. LAW_36 (ELASTO-PLASTIC WITH USER DEFINED FUNCTION)

PROCEDURE

Unit : mm g ms

A plate is impacted by a rigid ball with a velocity of 10mm/ms. An aluminium plate is used with shell and material properties below

MATERIAL (ELASTO-PLASTIC )

• Card image = M2_PLAS_JOHNS_ZERIL
• Initial density (rho) = 0.0028g/mm3
• Young Modulus (E) = 71000Mpa
• Poisson ratio (u) = 0.3
• True yield stress (a) = 290Mpa
• Hardening Modulus (UTS) (b) = 562.3
• Hardening Exponent (n) = 0.63
• Maximum plastic strain for failure (EPS_p_max) = 0.151
• Maximum stress (sig_max0) = 425Mpa

SHELL PROPERTIES

• CARD IMAGE = P1_SHELL
• Ishell = QEPH shell formulation
• Ismstr = Full geometric nonlinearity with possible small strain formulation
• Ish3n = 2
• Ithick = 1
• Iplast = 2

CASE_1

FAILURE CARD	JOHNSON FAILURE CARD
EPS_p_max	0.151
XFEM	0

JOHNSON FAILURE CARD

ifail_sh	2
D1,D2,D3	0.11,0.8,-1.5
Xfem	0 <elements are deleted when strain reaches 15%>
Time of simulation	01m:51s
Total number cycle	49480

CASE_2

Using the same material and shell properties the only differece from case_1 is seen below

JOHNSON FAILURE CARD

ifail_sh	1
D1,D2,D3	0.11,0.8,-1.5
Dadv	1
Xfem	1 <elements are cracked when strain reaches 15%>
Total number cycle	49397
Time of simulation	01:42

RESULTS OF COMPARISON BETWEEN CASE_1 AND CASE_2

Case_1(left) it can be seen how the elements are deleted due to XFEM set to 0.

Case_2(right) it can be seen how the elements are cracked due to XFEM set to 1

Case_1(left) it can be seen how the elements are shattered and deleted at 15% plastic strain.

Case_2(right) it can be seen how the elements are cracked at 15% plastic strain and energy is dissipated through cracks.

KINETIC ENERGY

Case_1(left) it can be seen at 4ms there is the maximum kinetic energy which occurs when more elements are shattered and deleted.

Case_2(right) it can be seen that at 4ms more kinetic energy low compared to case_1 but it increases at 4.4ms where the kinetic energy increase due to the cracking and energy is dissipated.

For both cases, the internal energy is increasing linearly as the ball crushes the plate. So is the total energy. The hourglass and contact energy remains constant at 0 due to its high stability

The kinetic energy is the only difference and was explained above.

CASE	MASS ERROR	ENERGY ERROR <Less than is acceptable 15% GOOD>
1	0.00	0.2
2	0.00	4.0

CASE_3

FAILURE CARD	NA without failure card, the material is not able to simulate compression under forces .
EPS_p_max	0.151 (elements fail at 15% plastic strain)

Total number cycle	49405
Time of simulation	01:47

Case_3 all material and property remains the same except this time Johnson failure card is removed.

CASE_4

Case_4 there is no specified maximum plastic strain value so the material is not going to be deleted at 15% plastic strain.

FAILURE CARD	JOHNSON FAILURE
EPS_p_max	0

XFEM	0 (elements deleted at maximum plastic stress
Ifail_sh	2 (The shell is deleted or cracked when for all integration points or layers.

Total number cycle	49304
Time of simulation	01:46

CASE_3 ABOVE

CASE_4 ABOVE

RESULTS OF COMPARISON BETWEEN CASE_3 AND CASE_4

Elements in case_3 can be seen that elements are deleted very early at the same time compared to case_4.That means that the elements in case_3 are deleted at 15% maximum plastic strain, whereas case_4 at the same time element cannot be deleted because eps_p_max was not specified .But case_4 element are deleted after the maximum stress value is reached at the very last integration point because ifail_sh =2 .

KINETIC ENERGY

Case_3(left) it can be seen at 4ms there is the maximum kinetic energy which occurs when more elements are shattered and deleted.

Case_4(right) it can be seen that the kinetic energy low compared to case_3 because less elements are deleted at certain compared times and the elemnts are being deleted slowly and gradually. More plastic strain occurs in case_4.

For both cases, the internal energy is increasing linearly as the ball crushes the plate. So is the total energy. The hourglass and contact energy remains constant at 0 due to its high physical stabilisation.

The kinetic energy is the only difference and was explained above.

CASE	MASS ERROR	ENERGY ERROR <Less than is acceptable 15% GOOD>
3	0.00	0.8
4	0.00	1.1

CASE_5

MATERIAL CARD	LAW_1 (Elastic)
Initial density (rho)	0.0028g/mm3
Poisson ratio (u)	0.3
Time of simulation	01:46
Young Modulus (E)	71000Mpa
Total number cycle	47949
Mass error	0.00
Energy error	1.8%

Case_5 simulation shows a perfect elastic material with no plastic deformation. This is due to the material law_1 selected.

Kinetic energy shows the fluctuating curves or noise due to the elastic nature of the material. Energy is absorbed and not dissipated so there is a resistance which decelerates the ball little as the kinetic energy is increasing. Due to the elastic nature of the material without plastic deformation it is expected that the kinetic energy absorbed would be conserved and thus the material would return to its starting position.

The internal energy is increasing linearly as the ball crushes the plate. So is the total energy. The hourglass and contact energy remains constant at 0 due to its high physical stability

CASE_6

This is an elasto-plastic Johnson-cook material model with an orthotropic brittle failure model.

MATERIAL CARD	LAW_27 (plast_BRIT)
Eps_t1	0.14 Tensile failure strain at which stress starts to reduce
Eps_m1	0.15 (The end of tensile damage the stress value is 0)
Eps_f	0.151 (Plastic strain value where the element is deleted)
Damage Factor (Dmax)	0.999 Stress is reduced by the value of the damage factor
Time of simulation	01:24
Total number cycle	49349
Mass error	0.00
Energy error	1.0

At one integration point the plate fails when the strain reaches EPS_f and a slight brittle behaviour is seen in the simulation before failure.

Kinetic energy spiky curves indicate the gradua

l element deletion when the the 0.151 plastic strain is reached

CASE_7

This material card is an isotropic elasto-plastic material using user defined function for work-hardening portion of stress strain curve.

MATERIAL CARD : LAW_36

Below it can be seen that a custom the stress-strain curve (Plastic_True_Stress_Strain) was computed for this law to be simulated.

Time of simulation	01:29
Total number cycle	51660
Mass error	0.00
Energy error	0.9%

Stress values ar very large this is due to the custon function curve and the eps_max value

Kinetic energy spiky curves indicate the gradual element deletion when the the 0.16 plastic strain is reached

The internal energy is increasing linearly as the ball crushes the plate. So is the total energy. The hourglass and contact energy remains constant at 0 due to its high physical stability

CONCLUSION

Per the simulation made ,the best case on field scenario depends on the situation.

Law_1 is good for elastic material

Law_27 is good for brittle material

Law_2 with Xfem formulation is accurate for ductile materials. The case_2 in this case is more suitable for realistic scenario because of the crack formulation