Summary

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Failure of a circular plate subjected to the impact of an infinite rigid sphere is studied. Material models, with or without a dedicated failure criteria, are compared. The new failure criteria available adds to the simple rupture models existing in such material laws as Law 2 and Law 27. The study is divided into three parts:

The sensitivity of the results for the different failure models is demonstrated.

 

Overview

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Aim of the Problem

The purpose of this example is to model the perforation of a thick plate using a rigid sphere. The simulations are performed using different failure models:

Numerical results are not compared with experimental data. However, this example proposes different approaches to take account of failure.

Physical Problem Description

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.

Fig 1: Problem description.

The material undergoes an isotropic elasto-plastic behavior which can be reproduced by a Johnson-Cook model, independently of the failure model: .

Material properties are:

The maximum stress and the failure plastic strain are considered in the failure modeling section. The strain rate effect is not taken into account in this example.

Analysis, Assumptions and Modeling Description

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Modeling Methodology

The plate is meshed with 4-node shell elements.

The shell properties (Type 1) are:

Fig 2: Mesh of the metallic plate with the initial rigid sphere position.

RADIOSS Options Used

A sphere with non-zero mass is considered as a rigid body, modeled by a rigid sphere of 12.7 mm diameter. Slave nodes include the plate part.

Here in this example, non-zero mass (5g) in /RWALL will keep energy balance. If mass =0, then 99% energy error is received. This is because you have external work done by the rigid wall and this external work is proportional to the mass of the rigid wall. But if the mass is zero, then the external works is also zero. The loss of external work will lead to bad energy balance.

A constant imposed velocity of -1.0 ms-1 in the Z-direction is applied on the rigid sphere via the ID 4067 master node. Its displacement is proportionally linked to time.

Boundaries of the plate are clamped, as shown in Fig 3.

Fig 3: Side fixed in X, Y, Z translations and X, Y, Z rotations.

Failure Modeling

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Law 27: Elasto-plastic Material Law using a Damage Model

Law 27 is used to simulate material damage following a Johnson-Cook plasticity law. Thus, a damage model is incorporated into the material law to take into account the damage evolution with stress decreasing up to element rupture.

The damage parameters are:

Fig 4: Stress/strain curve for damage affected material (with i=1,2)

 

The maximum stress and the failure plastic strain are activated:

The element is removed if one layer (one integration point) of the element reaches the failure tensile strain.

For further information about this law, refer to the RADIOSS Theory Manual and RADIOSS User's Guide.

 

Johnson-Cook Failure Model

The elasto-plastic behavior of the material is defined using the Johnson-Cook law (/MAT/LAW2), with or without damage (max and max).  The failure model is independent from the material law and the hardening model.

The Johnson-Cook failure model is defined using /FAIL/JOHNSON in the input deck.

The model uses cumulative damage to compute failure.

where,

D refers to the current damage (failure if D = 1)

is the normalized mean stress

is the increment of plastic strain during the loading increment

D1, D2 and D3 are the first three parameters

The strain rate and thermo-plastic effects are not taken into account in this example. Therefore, only three parameters are required (D1, D2 and D3).

Two cases are considered:

Two failure approaches are also investigated:

Therefore, the four simulations performed are shown in the following table:

 

For further information about this failure model, refer to the RADIOSS Theory Manual and the RADIOSS User's Guide.

 

FLD Failure Model (Forming Limit Diagram)

This failure model uses the generic forming limit diagram, defined for the given material. The curve is expressed in the area of principal strains (max and mini strains) and defines the failure zone.

An input curve and the flag Ifail_sh (same as Johnson-Cook model) are required. However, the results obtained using Ifail_sh = 1 and Ifail_sh = 2 are very similar and only if Ifail_sh = 1 is presented.

Two failure modes can be simulated by adjusting the diagram. Shells elements are deleted if one layer is in the failure zone.

For further information about this failure model, see the RADIOSS User's Guide.

Simulation Results and Conclusions

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The failure simulations considered in the example are:

Engine file:

In the /DEF_SHELL option defined in the input desk, the Istrain flag must be set to 1 for computing strains in view of post-processing.

During simulation, failure of the elements can be checked in the output file runname_0001.out.

[…]

 3869  0.5145      0.1330E-03 SHELL      159   0.0%   2451.      0.1692       2.336      0.0000E+00  0.0000E+00

 3870  0.5147      0.1330E-03 SHELL      159   0.0%   2452.      0.1697       2.335      0.0000E+00  0.0000E+00

-- RUPTURE OF SHELL ELEMENT NUMBER      151

-- RUPTURE OF SHELL ELEMENT NUMBER      151

 3871  0.5148      0.1330E-03 SHELL      159   0.0%   2453.      0.1694       2.361      0.0000E+00  0.0000E+00

 3872  0.5149      0.1330E-03 SHELL      159   0.0%   2452.      0.7397       3.424      0.0000E+00  0.0000E+00

 3873  0.5151      0.1330E-03 SHELL      159   0.0%   2446.        3.288       6.740      0.0000E+00  0.0000E+00

 3874  0.5152      0.1330E-03 SHELL      159   0.0%   2443.        5.818       8.481      0.0000E+00  0.0000E+00

-- RUPTURE OF SHELL ELEMENT NUMBER      169

-- RUPTURE OF SHELL ELEMENT NUMBER      169

-- RUPTURE OF SHELL ELEMENT NUMBER      192

-- RUPTURE OF SHELL ELEMENT NUMBER      192

 3875  0.5153      0.1330E-03 SHELL      159   0.0%   2443.       6.888       8.419      0.0000E+00  0.0000E+00

 3876  0.5155      0.1330E-03 SHELL      159   0.0%   2443.       7.988       8.214      0.0000E+00  0.0000E+00

 3877  0.5156      0.1330E-03 SHELL      159   0.0%   2437.       12.35       9.924      0.0000E+00  0.0000E+00

 3878  0.5157      0.1330E-03 SHELL      159   0.0%   2430.       17.44       11.89      0.0000E+00  0.0000E+00

 3879  0.5159      0.1329E-03 SHELL      159   0.0%   2425.       21.28       13.40      0.0000E+00  0.0000E+00

 3880  0.5160      0.1329E-03 SHELL      159   0.0%   2421.       23.82       14.56      0.0000E+00  0.0000E+00

-- RUPTURE OF SHELL ELEMENT NUMBER      153

-- RUPTURE OF SHELL ELEMENT NUMBER      153

 3881  0.5161      0.1329E-03 SHELL      159   0.0%   2419.       25.85       15.13      0.0000E+00  0.0000E+00

[…]

Fig 6: Perforation of the plate by the rigid sphere at 5 ms (case: Johnson-Cook failure model without failure plastic strain, Ifail_sh=2).

The following table compares the results provided by simulations in terms of plate deformation, hole dimension, residual shells, etc.

Conclusion

The rupture of a circular plate, due to the impact of a rigid sphere was studied and several failure models with different simulation parameters were compared. The results obtained highlight the sensitivity of the numerical models to simulate the failure.

Laws 2 and 27, with or without the failure models were compared. The comparison shows that the results are quite similar when coherent simulation parameters are used.