Assignment 4

MATERIAL LAWS IN RADIOSS

Objective: To study the different material laws and their parameters through a case by case comparison by varying the different parameters.

Observations:

Case-1 (Law2_epsmax_failure)

It represents the Johnson Cook material model, with a failure card. The model was simulated as downloaded without any changes.

Fig: Johnson Cook model (with Eps_max and failure card specified) and Material card

Case-2 (Law2_epsmax_crack)

It represents the Johnson Cook material model with the failure card changed (IXFEM changed to 1and I_failsh=1). This results in the cracking of the element first when failure criterion is met and then subsequent deletion of the element when there is a second crack. Setting I_failsh=1, ensures that element deletion occurs suddenly as soon as the second crack forms on the element without making the stress tensor zero.

Fig: Johnson Cook model with crack propagation and Failure card

The above image shows the occurrence of crack as the element fails initially.

Case-3 (Law2_epsmax_nofail)

This represents the Johnson cook material model without a failure card, thus the failure strain is not specified. But it behaves like the first case were deletion of element takes place once strain in the element reaches the eps_max value.

Fig: Johnson Cook (material model with No failure card) and Material card

Case-4 (Law2)

It is Johnson cook material model with eps_max=0 (default value 10³⁰). Here failure occurs through the failure card specified. Eps_f value is specified through the failure model and as the strain in the element reaches the eps_f value, stress tensor in the element turns zero and element deletion occurs.

Fig: Johnson Cook model with default Eps_max

Thus, it is observed from the above four cases that element failure occurs either through the failure criterion set by the failure card or after reaching the eps_max values set in the material card.

Case-5 (Law1)

It is elastic material model. Here, the material doesn’t fail as no failure criterion is specified. Thus the material undergoes large elastic strain and regains shape after removal of the load.

Fig: Elastic Deformation (Law 1) simulation and Material Card

As can be seen above, large scale deformation without failure.

Case-6 (Law27)

It is known as PLAS_BRIT material law. It essentially meant for elasto-plastic brittle material with Johnson cook material model and damage . Failure can occur along two principal strain directions and failure occur only due to tension and not combined loading.

Fig: Law 27 and Material card

As can be seen in the above image, element deletion happens initially at the center and over a period of time the entire component fails as it split into several parts.

Case-7(Law36)

It is also known as PLAS_TAB. It serves as an elasto-plastic material model. The material is created from the experimental values given in the question by specifying material law36 and adding curve to it. It can be used to model complex materials which cannot be found in the material library, while also accounting for the strain rates that occur in real time conditions. The mechanism of failure and the failure criterion being the same as Johnson Cook material model as per this question.

Fig: Law 36 simulation and Material card

Results:

The following table represents the comparison of the cases based on parameters asked in the question. The values were obtained from the corresponding output files.

Case	Total cycles	Energy error	Simulation time (ms)	Mass error
1	49384	0.8%	5.010	0.00
2	49407	3.7%	5.010	0.00
3	49405	0.8%	5.010	0.00
4	49304	1.1%	5.010	0.00
5	47969	0.3%	5.010	0.00
6	49356	1.1%	5.010	0.00
7	53181	-1.2%	5.010	0.00

The mass error across cases remain zero as there is no mass added for time step control. The energy error for all cases are under the accepted limits. However, in Case-2 there is a significantly positive value of energy error this is due to the delayed element failure due to crack initiation and propagation, which has resulted in additional internal energy to pile up over the same time interval.

Energy graphs:

Case-1 Case-2

In Case-2 due to crack initiation and propagation, element failure happens slowly compared to Case-1. This results in greater internal energy stored in the material over the same time.

Case-3 Case-4

Case-3 behaves in a similar manner as Case-1. Case-4 undergoes larger strain as eps_max from material model is not specified (default value) and failure occurs at a failure plastic strain calculated from the failure card.

Case-5

With large strains occurring without failure, very high internal energy (of the order of 10⁵⁾ gets stored in the material as can be seen from the graph.

Case-6

In brittle materials, with similar failure strain value as that of the 1^st three cases (eps_max=0.151), higher stresses are encountered which result in relatively higher internal energy stored compared to Johnson cook material model.

Fig: Material Stress-Strain curve

Case-7

The material is created by plotting the experimental data and is applied through the PLAS_TAB material model. The failure strain is set to (eps_max=0.161) which is relatively larger than other cases and as a result greater internal energy is stored as can be seen in the plot.

Conclusions:

• Thus, through this exercise several material laws were studied and the influence of several material parameters on the results could be inferred. It gave an understanding of the kind of materials laws to be applied to different applications.
• Based on the cases above and the problem given,

Case-2 (Johnson Cook model with Crack initiation and propagation) is most suitable for the given problem statement.

• Case-1 (Johnson Cook with failure card and eps_max specified) can be useful for large component where crack propagation cannot be monitored.
• Case-6 (PLAS_BRIT Law 27) is most suitable for modelling brittle materials.
• Case-7 (PLAS_TAB Law 36) can be used to model complex material curves obtained experimentally for different strain rates depending on the application, making it more versatile.
• Case-1 (Law 1 Elastic) is most suited for elastic materials.