Analysis of Failure Mechanism of different material cards in Radioss under Impact Loading

Failure Mechanism of different material cards in Radioss under Impact Loading

Objective: To simulate a sphere under impact loading and study its failure mechanism under different material property cards and decide upon the most realistic scenario.

Geometry and Mesh Definition:

• The setup involves a sphere impacting a circular plate with a certain velocity. The time frame selected begins with the point of impact of the sphere with the plate. (as shown in image below)
• Since the scope of this study is to analyze the failure of the plate only, the sphere has been modeled as a rigid body.
• The circular plate has been meshed with shell elements with consideration for physical hourglass stabilization.
• The plate is provided with a displacement in the negative Z direction of the global coordinate system.

Material Definition: The plate is considered to be made of aluminium that has the following mechanicla properties:

Young’s Modulus (E) = 71000MPa

Initial density (rho) = 0.0028 g/mm3

Poisson’s Ratio (nu) = 0.33

For the above material different property cards are assigned to the plate:

Case 1.Law01-Isotropic Elastic Material

Law01 material card exhibits isotropic elastic property. Only three properties are required to define the material-

Young’s Modulus (E) = 71000MPa

Initial density (rho) = 0.0028 g/mm3

Poisson’s Ratio (nu) = 0.33

Case 2. Law02_epmax_fail

Law02 materials exhibit elasto-plastic properties i.e they exhibit elastic properties up to the yield point and then plastic behaviour for the rest of the stress-strain curve. The material model is defined by a number of parameters-

Young’s Modulus (E) = 71000MPa

Initial density (rho) = 0.0028 g/mm3

Poisson’s Ratio (nu) = 0.33

true yield stress (a) = 290MPa

Hardening Modulus or UTS (b) = 562.3

Hardening exponent (n) = 0.63

Maximum stress (sig_max0) = 425MPa

Maximum plastic strain for failure (EPS_p_max) = 0.151

Apart from the above material properties a Johnson Failure card is also included in the property tree as FAILURE_Johnson_1. The parameters of this card are left to their default values. Four stress-strain curves corresponding to different strain rates are also fed to the solver to compute the values of the parameters in the Johnson failure card. The purpose of using the Johnson-Cook failure card is to consider the effect of stress-triaxiality in the system.

Case 3. Law02_epmax_crack

This model uses the same material card Law02 along with the FAILURE_Johnson_1 failure card. The only difference here is that we change certain input parameters to take crack initiation and advancement into account.

The material properties are same as case 2 (Law02_epmax_fail). The failure card parameters are set to-

Parameter	Description
D1=0.11	1st Parameter
D2=0.08	2nd Parameter
D3=-1.5	3rd Parameter
Ifail_sh = 1	Shell gets cracked if Ixfem = 1, deleted if Ixfem = 0
Ifail_so = 1	Solid element is deleted, if D=∑Δεpεf≥1D=∑Δεpεf≥1 for one integration point.
Dadv = 1	Criterion for crack advancement
Ixfem = 1	Extented Fem is used to solve the model for better accuracy around cracks.

Case 4. Law02_epmax_nofail

This model uses the same material card Law02 with the same material properties as in Case2. The only difference here is the absence of a failure card. The FAILURE_Johnson_1 card from the property tree is deleted hence the Johnson-Cook failure criteria is not invoked here. This implies that the effect of stress triaxiality is not being taken into account in this simulation.

Case 5. Law02_noepmax

In this model the same material card Law02 is used to model the plate with the exception of the value of EPS_p_max which is set to zero. The material model is defined by a number of parameters-

Young’s Modulus (E) = 71000MPa

Initial density (rho) = 0.0028 g/mm3

Poisson’s Ratio (nu) = 0.33

true yield stress (a) = 290MPa

Hardening Modulus or UTS (b) = 562.3

Hardening exponent (n) = 0.63

Maximum stress (sig_max0) = 425MPa

Maximum plastic strain for failure (EPS_p_max) = 0.0

The parameters of FAILURE_Johnson_1 card are set to their default values i.e. without invoking XFEM method or crack advancement approach.

Ixfem = 0

Dadv = 0

Case 6. Law27- Elastoplastic Brittle

In this case the plate is modeled with Law27 card which exhibits typical behaviour of a brittle elastoplastic material. The material model is defined by a number of parameters-

Young’s Modulus (E) = 71000MPa

Initial density (rho) = 0.0028 g/mm3

Poisson’s Ratio (nu) = 0.33

true yield stress (a) = 290MPa

Hardening Modulus or UTS (b) = 562.3

Hardening exponent (n) = 0.63

Maximum stress (sig_max0) = 425MPa

Tensile failure strain at which stress starts to reduce = EPS_t1 = EPS_t2 = 0.14

Tensile failure strain at which stress becomes zero = EPS_m1 = EPS_m2 = 0.15

Plastic strain at which element is deleted = EPS_f1 = EPS_f2 = 0.151

Damage Factor = dmax1 = dmax2 = 0.999

where 1 = principle stress direction 1

2 = principle stress direction 2

With the above settings, the simulation is run for 5.01ms and the results are plotted.

Results: The reults obtained from the simulations are tabulated below

Sl No.	Material/ Parameter	No. of Cycles	E error(%)	M error(%)	Simulation Time (s)	Failure Type	1st element failure at (ms)	Property exhibited
1.	Law01	47969	0.3	0.0	41.67	None	NA	Elastic
2.	Law02_epmax_fail	49480	0.2	0.0	47.08	deletion	0.3494	ductile
3.	Law02_epmax_crack	49391	3.8	0.0	190.02	Crack	0.3297	ductile
4.	Law02_epmax_nofail	49405	0.8	0.0	44.95	deletion	0.3499	ductile
5.	Law02_noepmax	49304	1.1	0.0	48.18	Deletion	1.687	Ductile
6.	Law27	49541	1.2	0.0	49.89	Deletion without any rupture	0.5187	brittle

1. Law01: The positive energy error indicated energy created by the system due to the kinetic energy (of the elements) generated in excess of the energy imparted by the impacting sphere.

The kinetic energy of the system remains constant at 0 N-mm. All the energy of the impact is converted to internal energy (strain energy)of the plate which goes on increasing. The total energy of the system is only composed of the Internal energy. The contact and hourglass energies are zero.

Exhibiting typical isotropic elastic property, the material operates within the elastic region in accordance with Hooke’s Law and gets stretched like a rubber sheet right up to the termination of the simulation. Slight tear can be observed on some of the elements but no element undergoes failure.

2. Law02_epmax_fail: Failure in this case takes place when the value of strain of at least one integration point of any element exceeds the value of EPS_p_max that was fed as an input parameter. The elements get ruptured first and then get deleted as a whole. No crack formation takes place. A certain degree of elasticity is exhibited up to the yield stress value post which plastic deformation takes place.

Contact and hourglass energy remain constant at 0 N-mm due to physical hourglass stabilization properties. Internal energy of the system increases continuously from the point of impact as the all of the sphere’s kinetic energy is getting absorbed into the plate as strain energy. This increase is almost linear up to the point where the elements start break off from the parent body. This removal of elements from the plate increases the Kinetic energy of the system and subsequently decreases the internal energy of the plate.

3. Law02_epmax_crack: Failure in this case also takes place when the value of strain of at least one integration point of any element exceeds the value of EPS_p_max that was fed as an input parameter.

The only difference here is the elements crack before getting deleted. Element is cracked if the element has no failed neighbors and D > 1, then in this case, new crack initializes in element. If the element has failed neighbors and D > Dadv, then in this case, crack advanced and Dadvused for crack advancement. Dadvwill be used till existing crack arrives to a boundary of an element. Element deleted, if a second crack arrives to the same element.

The behaviour of energy distribution graph is the same as the previous case, with the only difference being an increase in the Kinetic Energy and Energy error.

4. Law02_epmax_nofail: The failure rate in this case though is much higher due to the absence of a stringent failure criteria. As can be seen from the image below, at the 4.0ms mark, a significant number of elements have already separated from the parent body. Due to the non-consideration of stress triaxiality, the overall stress in the system is quite high and failure takes place at a rapid rate. The elements get deleted post rupture.

It can be noticed here that the spike in KE and dip in IE takes place quite early, well before the 4.0ms mark, indicating the rapid dismantling of shell elements.

5. Law02_noepmax: In the absence of EPS_p_max value, the failure in this case depends on the maximum stress (SIG_max0) value which is 425MPa in this case. When the stress at any integration point in the element reaches or exceeds the value maximum stress value fed to the system, the element ruptures and then gets deleted. The failure propagation is quite uniform and takes place at perpendicular lines.

The behaviour of the energy curves in this case is different from most of the law02 cases. The internal energy here goes on increasing with time. All of the impact energy of the sphere is absorbed by the plate as strain energy. Since no elements break of from the plate, the kinetic energy of the system remains 0 N-mm. Hence, the total energy curve comprises only the values of internal energy.

6. Law27: Since there is no EPS_p_max value here, failure in this case takes place based on the EPS_f (plastic strain for failure) value. If the strain in one at least one of the integration points of the element reaches the failure strain value, the element gets deleted at once without exhibiting any signs of rupture. A certain degree of elasticity is exhibited before plastic brittle failure.

The internal energy here goes on increasing with time. All of the impact energy of the sphere is absorbed by the plate as strain energy. Since no elements break of from the plate, the kinetic energy of the system remains 0 N-mm.

Inference:

• The analysis of the six cases provides insight into the different types of mechanisms, associated with different material cards, that cause failure of the plate under the impact of the rigid sphere.
• If the subject under study had been an elastic membrane like a rubber sheet, case 1 i.e. Law01 would have been the ideal choice.
• If the subject under consideration would have been a brittle material like glass or cast grade steel or aluminium, case 6 i.e. Law27 would have been the ideal choice.
• Although selection of material cards differ with the requirements of the situation, the most ideal case that would represent an on field scenario with the highest degree of accuracy would be case 3 (Law02_epmax_crack) where the plate was modeled using a ductile material that accounted for crack propagation as well as the effects of stress triaxiality.

Comparison of deformation behaviour at 4.501ms