RD-E: 5502 Rotating Fan Blade Ice Impact and Failure

Two hailstone ice balls are added to the model from RD-E: 5501 Fan Blade Rotation Initialization to study the deformation and failure of the blades when impacted.

The stress in the blades, due to rotation is accounted for by using Radioss state files, /STATE. A Johnson-Cook Failure model, /FAIL/JOHNSON, is applied to the blade elements to take into account material failure.

Options and Keywords Used

Centrifugal force pre-load in rotating structures
State files used to apply pre-load stress in a new simulation (/STATE)
Implicit simulation options (Implicit Solution)
Centrifugal force field (/LOAD/CENTRI)
Rotational velocity about an axis (/INIV/AXIS/Z/1)
Boundary Condition remove in Engine file (/BCSR)
Johnson-Cook failure model (/FAIL/JOHNSON)

The stress state caused by the rotating blades, can be saved to a Radioss State file, RUNAME_0001.sta, (/STATE/* keywords) and then applied to future analysis. This saves having to rerun the Radioss implicit pre-load step every time a design change would be made to the rest of the structure. The *.sta file contains the deformed nodal coordinates, elements definition, and initial stress state for the shell elements requested.

Note: To make it easier to include the State file into the impact analysis, the nodes and elements of the parts in the State file are put into an include file, blade_nodes_elements.inc in RD-E: 5501 Fan Blade Rotation Initialization. Now to use the stress State file directly in a second analysis, replace the blade_nodes_elements.inc file by the State file (*.sta) from the implicit pre-load simulation.

To create the State file, add the following commands to the end of the pre-load step from the first Engine file from RD-E: 5501 Fan Blade Rotation Initialization and run the implicit pre-load simulation.

# To save the full stress use these 3 STATE SHELL options
/STATE/SHELL/STRESS/FULL
/STATE/SHELL/AUX/FULL 
/STATE/SHELL/STRAIN/FULL        
# time to write state file and which part 
/STATE/DT
0.1 0.1
1

Now the hailstone ice ball model and the stress State file from the implicit simulation are included in the full simulation. The initial rotational velocity on the blades is included in the Engine file (/INIV/AXIS/Z/1) but could have also been be added Starter file using /INIVEL/AXIS. The ice impact simulation is ran for 0.08 seconds.

Input Files

Before you begin, copy the file(s) used in this example to your working directory.

RD-E-5502_Rotating.zip

Model Description

Four fan blades are rotating at 1000 RPM in a steady state condition inside a simplified case. The base of each blade is attached to a rigid body which is constrained in all directions except rotation about the z axis. The rotating blades impact two 3.07 kg hailstone ice balls which cause the blades to fail and then impact the case. The blades are assumed to be made of titanium with a constant 5mm thickness. The case is made of steel with varying thickness.

Figure 1. Blades with Case and Hail Ice Balls

Units: mm, s, Mg, N, and MPa

/MAT/PLAS_JOHNS, isotropic elasto-plastic material using the Johnson-Cook material model and Johnson-Cook failure model. ^¹

Blade Titanium Material Properties: Value
Density: $4.43 e - 9 \frac{M g}{m m^{3}}$
Young's modulus: 113400 $[MPa]$
Poisson's ratio: 0.342
Yield stress: 1098 $[MPa]$
Plastic hardening parameter: 1092 $[MPa]$
Plastic hardening exponent: 0.93

/FAIL/JOHNSON, Johnson-Cook ductile failure material.

Failure Material Properties: Value
D₁: -0.09
D₂: 0.25
D₃: -0.05
D₄: 0.014
I_{fail_sh}: 1; Shell is deleted when Damage > 1 for any integration point in the shell.

Case Steel Material Properties: Value
Density: $7.9 e - 9 \frac{M g}{m m^{3}}$
Young's modulus: 210000 $[MPa]$
Poisson's ratio: 0.3
Yield stress: 200 $[MPa]$
Plastic hardening parameter: 450 $[MPa]$
Plastic hardening exponent: 0.5
Maximum stress: 425 $[MPa]$

/MAT/HYD_JCOOK, isotropic elasto-plastic material using the Hydrodynamic Johnson-Cook material.

Ice Ball Material Properties: Value
Density: $9.167 e - 10 \frac{M g}{m m^{3}}$
Young's modulus: 8304 $[MPa]$
Poisson's ratio: 0.2
Yield stress: 10.3 $[MPa]$

/EOS/POLYNOMIAL, a polynomial equation of state.

Ice Ball Material Properties: Value
Plastic hardening parameter: 2500 $[MPa]$
Plastic hardening exponent: $C_{0} = C_{2} = C_{3} = C_{4} = C_{5} = 0$

Boundary conditions:

Blade Center constrained all directions, except Rz
Imposed Rotational Speed = 1000 = 104.72 $[\frac{rad}{s}]$
Edges of case are fully constrained in X, Y, Z directions

Model Method

This simulation builds on the results in RD-E: 5501 Fan Blade Rotation Initialization. The blades are impacted by two 3.07 kg hailstone ice balls with a radius of ~ 85 mm. A Johnson-Cook Failure model is added to the blade material to demonstrate how material failure can be modeled. The Johnson-Cook failure model relates plastic failure strain as a function of stress triaxiality (normalized mean stress). Additional details can be found in Materials of the Radioss User Guide, /FAIL/JOHNSON and /FAIL/TAB1.

Results

Figure 2, shows the blade stress at t=0.0 and that the initial pre-load stress in the state file was correctly included in the simulation.

Figure 2. Initial Stress on Blade at t=0.0

Conclusion

The stress in the blades from steady state rotation can be correctly accounted by including stress state files from a separate simulation. This saves time since it is not necessary to rerun the pre-load simulation for every design change of the case. The Johnson-Cook failure model accounts for the material failure of the blades due to their impact with hailstone ice balls.

¹ Don Lesuer, Experimental Investigations of Material Models for Ti-6AL4V and 2024-T3, Lawrence Livermore National Laboratory, May 3, 1999