High Speed Ice Impact Modelling with RADIOSS

Dr. Rene ROYANH Structure Co., Ltd

2017.09.15Seoul, South Korea

RADIOSS를이용한 Ice Modeling 기법연구

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COMPANY INTRODUCTION

About Us

ANH STRUCTURE supplies outstanding & accountable solutions in aerospace, automobile, off-shore plant and shipbuilding industries based on stress, design, test and production via core engineering technology.

Shipbuilding & Offshore Plant Business Division

Sinseon-ro 365, Nam-gu, Busan

Headquarter & R&D Center

Business Support Center, Jinju-daero501, Jinju-si, Gyeongsangnam-do, Korea

Tel +82 (0) 55 752 1090Fax +82 (0) 55 752 1091

Manufacturing Center

Bangji-ro 80, Sanam-myeon, Sacheon-si, Gyeongsangnam-do, Korea

R&D Center

Unam-ro 10, Deokjin-gu, Jeonju-si, Jeollabuk-do

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COMPANY INTRODUCTION

Structural Design

• Aerospace• Automotive and general

machinery• Shipbuilding and offshore

plants

Structural Analysis

• Linear static and buckling• Non-linear and dynamic• Fatigue and damage

tolerance• Impact resistance and

seismic analysis

Test Evaluation

• Metallic and composite coupon test

• Sub-component test• Test correlation

Prototype and Software Development

• Precise air supply system• Unmanned GPS paramotor• MR flight simulator• Composite structural analysis

software

Main Business Area

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COMPANY INTRODUCTION

Financial Highlights Customers

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OUTLINE

1. Introduction to ice impact events

2. Ice material properties

3. Physics of ice impact

4. Ice material models

5. Ice material model for RADIOSS

6. Ice model benchmarking

7. Model for ice impact on aircraft wing

8. Wing impact results and effect of parameters

9. Conclusion and observations

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1. Introduction to ice impact events

ICE IMPACT EXAMPLES

- Impact velocity on helicopter rotor blade: 150~300 m/s

- Impact velocity on aircraft turbofan blade: 400~600 m/s

- Maximum hail size: D=75mm, p=10% in 10 years

- Hail size at 30,000ft: D≥43mm, p=0.1% for 200-mile route

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2. Ice material properties

2. Strain rate effect

1. Typical properties- Density (ρ) ~ 0.92 g/cc- Elastic modulus (E) ~ 9.4 GPa- Poisson ratio (ν) ~ 0.33- Static compressive strength (σc) ~ 10 MPa- Static tensile strength (σt) ~ 1 MPa- Static shear strength (σs) ~ 1 MPa

Ice compressive strength versus strain rateReference: Pernas-Sanchez et al. 2012, Tippmann et al. 2013.

1- Essentially brittle behavior above ἑ=10-3 sec-1

2- Ice parameters (crystallinity, porosity, grain size)

3- For our case we consider properties at -10°C

4- Tensile strain rate effect data is limited, we

consider it the same as in compression

5- After failure ice is considered fluid-like (G=0)

6- After failure only compressive stress possible

3. Key Features

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3. Physics of ice impact

Hailstone impact test, 4.36g at 365 m/s (ref. Hammetter et al., 2017) 477g at 208 m/s (ref. Kuznetsova, 2011)

2DOF model(ref. Sun et al., 2015)107g at 61.8 m/s (ref. Tippmann et al., 2013) Hydrodynamic impact process (ref. Grimaldi, 2011)

1- Initial impact (p) 2- Pressure decay (pr)

3- Steady flow (ps) 4- Flow termination

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4. Ice material models

1. Carney et al., 2006Hydrostatic pressure equation of state, LS-DYNA

𝑃"#$ = 𝐶'𝜀) + 𝛾𝑇-𝜀)𝐸with𝜀) = 𝑙𝑛 𝑉𝑉78

𝑃 = min 𝑃"#$, 𝑃<=>?@AA

2. Tippmann et al., 2013Elastic-plastic behavior, ABAQUS/Explicit

𝐹𝑎𝑖𝑙𝑢𝑟𝑒 → 𝐺 = 0, −∞ ≤ 𝑃NOP ≤ 𝜎>

3. Pernas-Sanchez et al., 2012Drucker-Prager plasticity criteria, LS-DYNA

4. Ortiz et al., 2015Mazars damage model, EUROPLEXUS code

Damagevariables:𝑑] plasticstrain , 𝑑` pressure

Elasticzone:𝜎e = 𝐶: 𝑑]

Inelasticzone: 𝑓 = 𝜎h − 𝜎7O + 3𝛼𝑝 (Drucker-Prager yield function)

𝑑l = λ̇32𝐬𝜎h + 𝛼Ѱ𝟏

(plastic flow rule)𝜎h = 328 𝐬: 𝐬

�(equ. stress)

𝜎 = 𝐸 1 − 𝐷< 𝜀 𝜎 = 𝐸 1 − 𝐷> 𝜀(or)

𝐷 = 𝛼>𝐷> + 𝛼<𝐷< = 𝑓 𝜀̃, 𝜀w̃xy_7, 𝐴>, 𝐵>, 𝐴<, 𝐵<The compressive yield strength is strain rate dependent

σC is strain rate dependent

Pcut-off is strain rate dependent (compression)

Strength is strain rate dependent in compression and tension

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5. Ice material model for RADIOSS

1. MAT options

- MAT4, hydrodynamic Johnson-Cook: strain rate, similar in tension-compression

- MAT66, visco-elastic plastic: strain rate, tension and compression parameters

- MAT6, hydrodynamic viscous fluid: P = C1μ + C2μ2 +… (C1 = bulk modulus), kinematic viscosity (ν)

- EOS/POLYNOMIAL, pressure/volumetric strain relation: P = C1μ + C2μ2 +… (C1 = bulk modulus)

1- SPALLING, spalling and Johnson-Cook: Pmin failure then G=0 and compressive pressure only (Ifail_so = 1)

2- SPALLING, spalling and Johnson-Cook: εp_max failure then G=0 (Ifail_so = 3)

3- TENSSTRAIN, maximum strain failure: used to delete highly strained elements (Eps_t1 = 0.45, Eps_t2 = 0.50)

Johnson-Cook plastic model with strain rate effect (LAW4) : 𝜎O = 𝑎 + 𝑏𝜀l~ � 1 + 𝑐 � 𝑙𝑛𝜀̇𝜀7̇

(semi-log strain rate relation)

semi-log log-log

2. FAIL options

𝑃��� =𝜎<3 MPa

𝑃��~ = −𝜎>3 MPa

In compression:

In tension:

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6. Ice model benchmarking

𝑝 = 𝜌�𝑐�𝑣� = {535, 749}MPa

2- Initial upstream shock pressure (1D theory)

𝑐�<],l =𝐸 1 − ν

ρ 1 + ν 1 − 2ν�

= 3920m/sec

1- Sound pressure wave speed in solids

(rigid)

𝑝 = 𝜌�𝑐�𝑣�𝜌>𝑐>

𝜌�𝑐� + 𝜌>𝑐>= {497,696}MPa (compliant)

𝑐�>]]�,l =𝐸 1 − ν

ρ 1 + ν 1 − 2ν�

= 5843m/sec

3- Radial pressure distribution at t=0 (2D, v=213)

Ice impact case (ref. Pernas-Sanchez et al., 2012)

Impact target set-up (ref. Carney et al., 2006)

vi={152,213}m/sec

mt=474g

mi=9.1g

𝑝 𝑟 = 𝑝��� 𝑒?���� >

= 696 � 𝑒?�7��7.7���

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6. Ice model benchmarking

Ice model parameters: 1-Lagrange, 2-SPH, 3-Hail, 4-Bird (units: MPa, N, mm, ton, sec).

1- Ice LAW4 Lagrange 2- Ice LAW4 SPH 3- Hail LAW4 SPH 4- Bird LAW6 SPH (0.9)

MAT

E,K,nu,ν = E = 9310, nu = 0.33 E = 9310, nu = 0.33 E = 8996, nu = 0.3 K = 2150, ν = 1.6rho = 9.00E-10 9.00E-10 9.00E-10 9.00E-10

a = 10.976 10.976 10.3 ─b = 0.0 0.0 6890 ─n = 1.0 1.0 1.0 ─c = 0.192 0.192 0.0 ─

eps_0 = 1.0 1.0 0.0 ─EPS_max = 1.0E+30 1.0E+30 0.0035 ─

Pmin = -0.573 -0.573 -4.0 -0.01

PROP/SPRING

K1 = 330000 330000 330000 330000C1 = 0.0001 0.0001 0.0001 0.0001m1 = 1.0E-12 1.0E-12 1.0E-12 1.0E-12K2 = 3750000 3750000 3750000 3750000C2 = 0.0001 0.0001 0.0001 0.0001m2 = 1.0E-12 1.0E-12 1.0E-12 1.0E-12

INTER/TYPE7Stfac = 1.0 1.0 1.0 1.0Fric = 0.05 0.05 0.05 0.05

GapMin = 0.05 0.05 0.05 0.05

FAIL/SPALLINGD1 = 1.0E-08 1.0E-08 0.0035 ─

P_min = -0.573, -1E+30 -0.573, -1E+30 -4.0 ─Ifail_so = 1 , 3 1 , 3 1 ─

FAIL/TENSSTRAINEps1 = 0.45 0.45 0.45 0.45Eps2 = 0.50 0.50 0.50 0.50

PROP/SPHqa = ─ 1.0E-20 1.0E-20 1.0E-20qb = ─ 2.0E-20 2.0E-20 2.0E-20h = ─ 1.1271 1.1271 1.1271

PROP/SOLIDLambda = 0.00025 ─ ─ ─

Mu = 0.00025 ─ ─ ─EOS C1 = ─ ─ 8990 ─

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6. Ice model benchmarking

Ice impact verification 152 m/sec (ref. Pernas-Sanchez et al., 2012) Ice impact verification 213 m/sec (ref. Pernas-Sanchez et al., 2012)

Simulation Results

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6. Ice model benchmarking

1- Initial upstream shock pressure

2- Stress shock wave

SPH ice impact verification 152 m/sec with published spring rates

SPH ice impact verification 213 m/sec with published spring rates

pmax = 473 MPa pmax = 665 MPa

V = 152 m/sec V = 213 m/sec

Lagrange mesh, V = 152 m/sec SPH, V = 213 m/sec

vwave » 3750 m/sec vwave » 3820 m/sec

Theoretical Verifications

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7. Model for ice impact on aircraft wing

Ice impact on rear horizontal stabilizer

FEM model: equivalent beam with rigid element.

Ice 2 kg

9.4 m

Software HyperWorks/RADIOSS version 2017.01

Ice dimensions D = 100 mm, L = {212, 283, 354} mm

Ice mass {1.5, 2.0, 2.5} kg

Ice velocity {200, 225, 250} m/sec

Impact angle {0.0, 2.5, 5.0} deg

Laminate [ AL / CF02 / CF452 / CF90 / CFm452 / CF02 ], t = 5.5 mm

Leading edge core Rohacell 110 foam

Material models MAT25 (laminate), MAT2 (foam), MAT4 (ice)

Failure models Composite: MAT25 Ioff=6. Foam: FAIL/TENS eps=0.5.Ice: FAIL/SPAL Ifail_so={1,3}, FAIL/TENS eps=0.5.

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8. Wing impact results and effect of parameters

Speed{200, 225, 250} m/sec

Mass = 2.0 kgAngle= 0.0 deg

Mass{1.5, 2.0, 2.5} kg

Speed = 225 m/secAngle = 0.0 deg

Angle{0.0, 2.5, 5.0} deg

Speed = 225 m/secMass = 2.0 kg

Ek = 51 kJ, σmax = 50 MPaEk = 40 kJ, σmax = 36 MPa Ek = 63 kJ, σmax = 1215 MPa

Ek = 51 kJ, σmax = 50 MPaEk = 38 kJ, σmax = 69 MPa Ek = 63 kJ, σmax = 421 MPa

Ek = 51 kJ, σmax = 50 MPa Ek = 51 kJ, σmax = 371 MPa Ek = 51 kJ, σmax = 479 MPa

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9. Conclusion and observations

─ Thank you for the opportunity ─

1. Conclusions

- MAT4 or MAT6 material models gave reasonable results

- Initial peak pressure and shock wave speed tendencies verified theory

- Ice impact angle and velocity have a great effect on blade damage

2. Observations

- Evaluate using MAT66 and Drucker-Prager models (MAT10, MAT21, MAT81)

- Motivation to make a user defined failure law

- Investigate the test target natural frequencies or use other test data