ANALYSIS OF FAILURE BEHAVIOR OF A PLATE USING LAW - 1,LAW - 2,LAW - 27, AND LAW - 36 MATERIAL MODELS AND JOHNSON-COOK FAILURE CARD IN RADIOSS.

Introduction:

In any FEA non-linear simulation, material modeling is a very complex step where you need to capture the plasticity of the material accurately and their failure. This experiment will use model different material laws like LAW-1 Elastic, Law-2 Elasto-Plastic, LAW-27 Brittle and Law-36 Elastoplastic to understand the modeling techniques and their failure with a Johncock failure card. We will also use the XFEM failure formulation to understand the crack propagation effect in the brittle materials. For all the above experiments Aluminum is taken as the material.

Boundary Condition:

The plate is made to have a impact through a rigid sphere with a velocity of 10mm/ms.

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 material card is changed with the same rho, E, and nu values.

CASE – 1:

The model has both Johnson Failure card as well as EPS_p_max value, with XFEM value as 0.

EPS_p_max = 0.151.

So the elements fail when the stress reaches 15% of plastic strain.

In Johnson Failure card,

Ifail_sh = 2

For Shell elements, in each integration point, the stress in the layer is set to Zero. When the stress reaches the last layer the element gets deleted.

Xfem = 0

The elements are delete when the strain reaches 15%.

Total number of cycles: 49480

Time for the simulation: 1min 51sec.

CASE – 2:

The model has both Johnson Failure card as well as EPS_p_max value, with XFEM value as 1.

EPS_p_max = 0.151.

So the elements fail when the stress causes 15% of plastic strain.

In Johnson Failure card,

Ifail_sh = 1

For Shell elements, when the stress reaches the one integration point, the element gets deleted.

Xfem = 1

The elements are cracked when the strain reaches 15% of plastic strain.

Total number of cycles: 49391

Time for the simulation: 1min 45sec.

OBSERVATIONS & REASONS

CASE – 1 VS 2:

A.The elements are DELETED(CASE_1) B. The elements are CRACKED(CASE_2)

From the above images of CASE – 1 & 2, the deletion and the cracking of the element is seen clearly.

• The elements in the case-1 fail rapidly when compared to the elements in the case-2 is because of the XFEM crack formulation.
• In CASE – 1, the shattering of the element is because of plastic strain failure.
• In CASE – 2 the energy is dissipated through the cracks.( at the last element row)

• The internal energy of the plate increases linearly due to the absorption of the kinetic energy from the impacting sphere.
• The Hourglass and the Contact energy remains zero because of the Physical stabilization of the hourglass.

• Since the shattering of the element with high velocity in case­­_1, there is a hike in the Kinetic energy curve. When compared with case_1, in case_2 because of cracking of the elements the graph is a bit smoother as well deletion of a big chunk of elements is the reason for the spike.

CASE – 3:

The model has only EPS_p_max value and no Johnson failure card.

EPS_p_max = 0.151.

So the elements fail and get deleted when stress causes 15% of plastic strain.

Total number of cycles: 49405

Time for the simulation: 1min 49sec.

CASE – 4:

The model has no EPS_p_max value but only a Johnson failure card.

The elements get deleted when the plate gets the maximum stress from the impact.

Ifail_sh = 2

For Shell elements, in each integration point, the stress in the layer is set to Zero. When the stress reaches the last layer the element gets deleted.

Xfem = 0

The elements are deleted when the plastic stress reaches the maximum value.

Total number of cycles: 49304

Time for the simulation: 1min 39sec.

OBSERVATIONS AND REASONS:

CASE – 3 VS CASE – 4

• The elements in the CASE-3 get deleted when they reach the failure of plastic strain to one integration point.
• The elements in CASE-4 are deleted when they reach the maximum stress to the last integration point due to the impact.
• Since the Ifail_sh=2, the elements are deleted when the plastic strain reaches all the integration points.
• There is a lag in the element deletion in CASE-4 when compared to CASE-3 is because of the stress reaching is biased through the integration point layers.

• The internal energy of the plate increases linearly due to the absorption of the kinetic energy from the impacting sphere.
• The Hourglass and the Contact energy remains zero because of the Physical stabilization of the hourglass.

• There is a noise in the graph because of elements getting deleted, also a big chunk of element got deleted from the system is the reason for the hike in the graph is.
• In CASE – 4 the Kinetic Energy is gradually increasing because the elements are deleted gradually during the impact.

CASE – 5:

The model has material LAW – 1 (elastic material).

Time for the Simulation: 1.28

No. of cycles: 48850

OBSERVATIONS AND REASONS:

• During the simulation the plate behaves perfectly elastic with no plastic strain, it stretches completely when the load is applied and returns back when the load is removed.

• The Hourglass and the Contact energy remains zero because of the Physical stabilization of the hourglass.
• The internal energy of the plate increases linearly due to the absorption of the kinetic energy from the impacting sphere and drops down once the plate returns to the original shape.

• The kinetic energy gradually increases as the plate is stretched to the maximum for the applied load.

CASE – 6:

The material card is changed to Law-36, i.e Plas_Tab. This material card uses the True stress-strain curve function. The failure criteria in this material card are,

Epmax = 0.16 (Failure Plastic strain)

EPS_t = 0.1 (Tensile failure strain where the stress starts to reduce)

EPS_m = 0.11 (Maximum failure strain, where the element strain is set to zero)

Total number of cycles: 46896

Time for the simulation: 1:27s.

OBSERVATIONS AND REASONS:

• There is a gradual deletion of elements as the Plastic strain in the elements reaches 0.16.

• The Internal Energy of the plate increases linearly since the Kinetic Energy from the sphere is transferred to it through the impact between them.
• The Hourglass and the Contact energy remains zero because of the Physical stabilization of the hourglass.

• There are a few noises and spike in the Kinetic Energy curve because the elements are deleted together.

CASE – 7:

The model has the Material card has LAW – 27 (Brittle material) with no Failure card.

The failure criteria are given in the material card are,

EPS_t1= EPS_t2= 0.14(the tensile failure strain starts reducing)

EPS_m1= EPS_m2= 0.15(the tensile failure strain reaches zero)

EPS_f1= EPS_f2= 0.151(the plastic strain at which the elements get deleted)

Damage factor (Dmax) = 0.999.

Total number of cycles: 49541

Time for the simulation: 01:32s.

• The elements starting to fail when the EPS_f value reaches one integration point. There is a slight elasticity seen in the plate before the failure takes place.

• The Hourglass and the Contact energy remains zero because of the Physical stabilization of the hourglass.
• The internal energy of the plate increases linearly due to the absorption of the kinetic energy from the impacting sphere.

• Since the elements are getting deleted there is a noise in the graph, as well there is a hike in the graph due to the deletion of a big chunk of elements.

Conclusion

The best case for on-field scenario totally depends upon the scenario i.e. if the elastic material has to be studied then Law-1 is best suitable.

If the brittle material has to be studied then Law-27 is the best.

On the other situation like the ductile material (Law-2) along with XFEM formulation i.e. the Case-2 is suitable because of the crack formulation, which is more relatable with the real-time scenario.