Modelling of Ice-Propeller Blade Impact Experiments

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Modelling of Ice-Propeller Blade Impact Experiments

R427

Natlonal Research Consell natlonal

I*

Research in recherche en Construction construction

Modelling of ice-Propeller Blade Impact

Experiments

M.

Internal Report No. 537 Date

of

ANALYZED

NRC

-

This is an internal report of the institute for Research in Construction. Although not intended for general distribution, it may be cited as a reference in other publications.

MODELLING OF ICE-PROPELLER BLADE IMPACT EXPERIMENTS M. Sayed G e o t e c h n i c a l S e c t i o n I n s t i t u t e f o r Research i n C o n s t r u c t i o n BACKGROUND T h i s r e p o r t b r i e f l y d e s c r i b e s a numerical s i m u l a t i o n o f l a b o r a t o r y e x p e r i m e n t s r e l a t e d t o i c e - p r o p e l l e r b l a d e impact. The a n a l y s i s i s based on t h e approach developed by V a r s t a (1983) t o model i c e impact problems. The f i n i t e element method i s used t o c a l c u l a t e l i n e a r e l a s t i c , t h r e e d i m e n s i o n a l s t r e s s e s i n i c e . Loads a r e determined by i n c o r p o r a t i n g an a n i s o t r o p i c

f a i l u r e c r i t e r i o n .

The experiments, performed e a r l i e r by J u s s i l a (1987), i n c l u d e d measurements o f f o r c e s on r i g i d sharp i n d e n t o r s as t h e y impact b l o c k s o f

B a l t i c Sea i c e .

The p r e s e n t work was conducted a t t h e Technical Research Centre o f F i n l a n d (VTT) d u r i n g a v i s i t t h a t t o o k p l a c e i n January 1987. The v i s i t was a p a r t o f t h e J o i n t Research P r o j e c t Agreement No. 1 ( I c e Load P e n e t r a t i o n Model ) between Canada and F i n l a n d .

ANALYSIS

1. Model

_-

A prism, 0.15 x 0.15 x 0.1 m, as shown i n F i g u r e 1, i s assumed t o

r e p r e s e n t t h e i c e b l o c k . A l i n e l o a d a c t s a t a d i s t a n c e o f 0.01 m from, and p a r a l l e l t o , t h e f r e e s i d e o f t h e p r i s m . The i n d e n t o r was s l i g h t l y i n c l i n e d t o t h e h o r i z o n t a l when i m p a c t i n g t h e t o p s i d e o f t h e i c e d u r i n g t h e

e x p e r i m e n t s . Therefore, t h e l i n e l o a d may n o t be u n i f o r m (e.g. t r i a n g u l a r ) .

The i c e i s assumed t o be l i n e a r l y e l a s t i c u n t i l f a i l u r e i s i n i t i a t e d . T e s t e d samples were c o l u m n a r - g r a i n e d and t h u s may be t r a n s v e r s e l y i s o t r o p i c . S t r e s s c a l c u l a t i o n s , however, a r e c a r r i e d o u t u s i n g i s o t r o p i c e l a s t i c

p r o p e r t i e s . T h i s i s c o n s i d e r e d adequate f o r a p r e l i m i n a r y q u a l i t a t i v e i n s i g h t i n t o t h e problem. The v a l u e s o f Young's modulus E and P o i s s o n ' s r a t i o v a r e chosen as:

F a i l u r e i s assumed t o be governed by t h e Tsai-Wu c r i t e r i o n . F o r t r a n s v e r s e l y i s o t r o p i c i c e , w i t h t h e l o n g axes of t h e columns p a r a l l e l t o t h e 3 - d i r e c t i o n , t h e f a i l u r e c r i t e r i o n i s w r i t t e n as

and

where 01, o 2 and u3 a r e t h e normal s t r e s s e s , and T12, T23 and

are

The f a i l u r e parameter A r e p r e s e n t s a measure o f t h e p r o x i m i t y o f t h e s t r e s s s t a t e t o t h e f a i l u r e envelope (A = 1 corresponds t o f a i l u r e ) . It i s g i v e n by

where AF c o n s i s t s o f t h e f i r s t two terms and

BG

2. C a l c u l a t i o n p r o c e d u r e s

The f i n i t e element program ADINA i s used t o d e t e r m i n e t h e t h r e e d i m e n s i o n a l s t r e s s d i s t r i b u t i o n . The element mesh i s shown i n F i g u r e 2. S o l i d , 20 node elements a r e used. Loading cases a r e as f o l l o w s :

1. U n i f o r m l i n e l o a d = 1 kN 2. T r i a n g u l a r l i n e l o a d = 1 kN

3. Uniform l i n e d i s o l a c e m e n t = 0.5 x l o m 5 m

These f o r c e and d i s p l a c e m e n t v a l u e s a r e chosen t o be c l o s e t o f a i l u r e l o a d s p r e d i c t e d by a p r e l i m i n a r y t e s t run.

The r e s u l t i n g s t r e s s e s ( a t each e l e m e n t ' s i n t e g r a t i o n p o i n t s ) a r e used as i n p u t f o r a program t h a t c a l c u l a t e s t h e f a i l u r e parameter A . R e s u l t s a r e o b t a i n e d f o r two cases c o n s i d e r i n g i c e columns t o be p a r a l l e l , and

p e r p e n d i c u l a r t o t h e l i n e l o a d .

RESULTS

S t r e s s d i s t r i b u t i o n s c o r r e s p o n d i n g t o l o a d i n g case 1 a t a v e r t i c a l p l a n e near t h e c e n t r e o f t h e i c e b l o c k a r e shown i n F i g u r e 3. As mentioned e a r l i e r , t h e s e s t r e s s e s a r e c a l c u l a t e d u s i n g i s o t r o p i c e l a s t i c p r o p e r t i e s . These a r e t y p i c a l o f a l l l o a d i n g cases. Values o f t h e shear s t r e s s e s ,T, and T~~ a r e n o t shown because t h e y a r e t o o s m a l l .

Contours o f t h e f a i l u r e parameter A ( i n a v e r t i c a l p l a n e near t h e

b l o c k ' s f r o n t ) f o r l o a d i n g case 2 and c o n s i d e r i n g i c e columns t o be p a r a l l e l t o t h e l o a d a r e shown i n F i g u r e 4a. The v a l u e o f A near t h e a p p l i e d l o a d

( a p p r o x i m a t e l y 1) i n d i c a t e s t h a t f a i l u r e i s i n i t i a t e d ; i .e. t h e l i m i t i n g l o a d i s equal t o t h e chosen v a l u e o f 1 kN. I f X was n o t equal t o 1, t h e n t h e l i m i t i n g l o a d would be equal t o t h e chosen v a l u e d i v i d e d by A .

The r e s u l t s a t a v e r t i c a l p l a n e near t h e c e n t r e o f t h e b l o c k a r e shown i n F i g u r e 4b; t h o s e a t a p l a n e near t h e edge, b u t c o n s i d e r i n g i c e columns t o be p e r p e n d i c u l a r t o t h e l i n e load, a r e shown i n F i g u r e 4c.

According t o F i g u r e 4a, f a i l u r e i n i c e w i t h columns p a r a l l e l t o t h e l i n e l o a d i s l i k e l y t o p r o g r e s s a l o n g a v e r t i c a l plane. I n s p e c t i o n o f t h e c o r r e s p o n d i n g s t r e s s d i s t r i b u t i o n r e v e a l s t h a t f a i l u r e i s p r i m a r i l y caused by t h e v e r t i c a l compressive normal s t r e s s . I f i c e columns a r e p e r p e n d i c u l a r t o t h e l o a d ( F i g u r e 4c), f a i l u r e would p r o g r e s s a l o n g a p l a n e i n c l i n e d a p p r o x i m a t e l y 30 degrees t o t h e v e r t i c a l , and would be caused by shear s t r e s s e s .

Both F i g u r e s 4a and 4c show t h a t X = 1 near t h e c o n c e n t r a t e d l o a d . Accuracy a t t h i s r e g i o n , however, i s l i m i t e d because o f t h e f i n i t e element d i s c r e t i z a t i o n . The parameter A ( f r o m F i g u r e 4a) i s p l o t t e d versus t h e v e r t i c a l d i s t a n c e from t h e l o a d i n F i g u r e 5 t o i l l u s t r a t e i t s s p a t i a l r a t e o f change. More t e s t runs a r e s t i l l needed t o examine mesh s i z e e f f e c t s .

R e s u l t s from l o a d i n g cases 1 ( u n i f o r m l i n e l o a d ) , and 3 ( u n i f o r m l i n e d i s p l a c e m e n t ) a r e shown i n F i g u r e s 6 and

7

CONCLUDING REMARKS

I n i t i a l r e s u l t s from an a n a l y t i c a l model o f i c e - p r o p e l l e r b l a d e

e x p e r i m e n t s were presented. Load p r e d i c t i o n s appear t o be reasonable. The s t u d y i n d i c a t e s t h a t t h e m o d e l l i n g approach developed by V a r s t a (1983) can be used t o t r e a t cases o f i c e i m p a c t w i t h sharp i n d e n t o r s .

ACKNOWLEDGEMENT

T h i s work was c a r r i e d o u t i n c o l l a b o r a t i o n w i t h c o l l e a g u e s f r o m VTT. Many c o n t r i b u t i o n s were made by K. Riska, P. K l i n g e and M. J u s s i l a , VTT, and by Dr. R. F r e d e r k i n g , NRCC. F i n a n c i a l s u p p o r t was p r o v i d e d by t h e Canadian Coast Guard.

REFERENCES

Varsta, P., 1983. On t h e mechanics o f i c e l o a d on s h i p s i n t h e B a l t i c Sea. Technical Research Centre o f F i n l a n d , P u b l i c a t i o n s 11.

F I X E D S I D E

NEGATIVE P O S I T I V E

( a ) SHEAR STRESS T ( k P a ) Y Z

( b ) VERTICAL NORElAL STRESS cZ ( k P a ) NEGATIVE (COMP. )

P O S I T I V E (TENSION)

0 . 0 4 M

FIGURE 3 : STRESS D I S T R I B U T I O N , LOADING CASE 1

( x

-

_I

I

I

I

I

I

I

I

v

L

----

NEGATIVE (COMPRESSION) P O S I T I V E (TENSION)

0.

( c ) HORIZONTAL NORMAL STRESS oy ( k P a )

NEGATIVE (COMPRESSION) P O S I T I V E (TENSION)

0 .

L

- - -

- - -

( a ) I C E COLUMNS PARALLEL TO THE L I N E LOAD, x = 0 . 0 8 4 m

( b ) I C E COLUMNS PARALLEL TO THE L I N E LOAD, x = 0 . 0 4 4 m

0 .01 . 0 2 . 0 3 . 0 4 . 0 5 VERTICAL DISTANCE FROM LOAD, M

FIGURE 5 : D I S T R I B U T I O N OF THE FAILURE PARAMETER X NEAR THE LOAD

( a ) I C E COLUMNS PARALLEL TO THE L I N E LOAD, x = 0 . 0 8 4 m

( b ) I C E COLUMNS PARALLEL TO THE L I N E LOAD, x = 0 . 0 4 4 n1

FIGURE 7: _{CONTOURS OF THE F A I L U R E PARAFIETER A,}

LOADING CASE 3

( I C E COLUMNS PARALLEL TO THE L I N E LOAD,

x