Prediction of unstable crack length in aluminium alloys

ian.1961

TECHNISCHE HOGESCHOOL DELFT v

VLIEGTUIG30UWKUNDE

Michiel ét Ruyferweg 10 - DELFT ^ o A N o t e No. 109

THE COLLEGE OF AERONAUTICS

CRANFIELD

PREDICTION OF UNSTABLE CRACK LENGTH IN

ALUMINIUM ALLOYS

by

NOTE NO. 109 October, 1960.

T H E C O L L E G E OF A E R O N A U T I C S

C R A N F I E L D

Prediction of Unstable Crack Length in Aluminium Alloys b y

-R. H. Ryder, D . A . E .

SUMMARY

A method was set down for predicting the unstable length of a crack in a flat sheet of aluminium alloy subjected to a steady tensile s t r e s s .

The basis of the method was to take the work done to failure in the 'neck' region of a tensile test specimen and apply it, with a

suitable constraint factor, to the flat sheet to give the work rate required to propagate the crack.

CONTENTS Page Summa ry 1. Procedure 1 2. Experimental 'vVork 3 3. References 3 Figs. 1 - 5

1 -1. P r o c e d u r e T e n s i l e t e s t s w e r e f i r s t c a r r i e d o u t , l o a d a n d d e f l e c t i o n b e i n g r e c o r d e d r i g h t t o f a i l u r e . T h i s p r o d u c e d a s t r e s s - s t r a i n c u r v e of t h e f o r m of F i g . 1. T h e u s u a l t y p e of s p e c i m e n i s g i v e n i n F i g . 2. T h e t o t a l w o r k d o n e i n t h e r e g i o n of t h e n e c k w a s c o m p o s e d of two p a r t s , v i z . t h a t p r i o r t o c o m n r i e n c e m e n t of n e c k i n g , V p , a n d t h a t a f t e r n e c k i n g , V . In F i g . 1. , OA.CDF r e p r e s e n t s t h e b a s i c s t r e s s - s t r a i n c u r v e of t h e m a t e r i a l a t t h i c k n e s s t o X B C D F r e p r e s e n t s t h e s t r e s s - s t r a i n c u r v e of t h e m a t e r i a l ( b a s e d o n t ^ ) a f t e r s o m e p r e - s t r a i n i n g . A r e a X B C D F A p r e - s t r a i n p a r a m e t e r H i s d e f i n e d a s "T OA.'^DF * V-T m a y b e c a l c u l a t e d f r o m , (Ref. 1 ) , n£ - L g . e.^ V = t o C X ( A r e a X B F ) , w h e r e C = "^T"—^""^i P ( 1 + Cp) w h e r e tQ = i n i t i a l t h i c k n e s s of S i j e c i m e n

Cj^ = OF (or XF for a prestrained mate rial)(Fig. 1) nf = final length of neck

e^ = OE (or ZE for a prestrained material)(Fig. 1) V may be calculated as follows : -_n

V^ = r L^ t^ X (Area ECG)1 + pt Lg t^ ——™ x (Area JCG) 1

w

+ ["21. t ..JL X ( A r e a J C G )

t s " Wj

where L^, Lg, L,, L , w, , w, are defined in Fig. 2

+ L . to X (Area GCDF).

The areas refer to Fig. 1.

The terms in square brackets come from the elastic energy released to the neck by the bulk of the specimen, the remaining term being the work done by the loading machine after necking commenced. It was assumed that after point C no further v/ork is done on the specimen other than in the neck.

(2 + y'* )

^ = ( 2 ^ 7 ^ : y-» ) (Reference 2)

t = sheet t h i c k n e s s E = Young's Modulus The condition for i n s t a b i l i t y is

dV dW

dl ^ di

T h e r e f o r e we have 2

3

-2, Experimental Work .

Tests have been carried out on specimens approximately 21" long by 7" wide in unclad materials generally conforming to specifications L, 70, L. 71 and DTD. 687. Each specimen was subjected to a measured degree of plastic strain before the initial (artificial) crack was

introduced in the centre of the sheet.

The application of this formula to the experimental results is given in Figs. 3, 4 and 5, where both sides of the last equation are plotted against the p r e - s t r a i n p a r a m e t e r , H.

Values of k were chosen to give lines passing through the experimental points. The results showed good agreement for the slope of the lines

indicating that the effect of V had been correctly estimated.

The values of k found should be related to the amount of strain achieved during necking. This was not true for these t e s t s , indicating probable e r r o r s in m.easurement of the final portion of the s t r e s s

-strain curve.

Further experimental work is required to investigate this latter point.

3. References

1. Ryder, R. FI. The effect of vv^ork hardening on the static crack propagation properties of some aluminium alloys.

College of Aeronautics Thesis. June I960. 2. Greenspan, M. Axial rigidity of perforated structural

m e m b e r s .

National Bureau of Standards, Vol. 31, 1943.

3. _{Griffith, A. A. Phil. Trans. Royal Soc. , A. Vol.221, 1921,}

V T *

„ 7-7—7-7—?—7-r

- » , < >

b j _

FIG.2. TENSILE SPEQMEN REGIONS (Lq--2")

STRAIN e NB. CJ PARALLEL

TO AO

FIG.I. TYPICAL STRESS-STRAIN CURVE FOR ALUMINIUM ALLOY

1 0 %\ & - ^ ; " ^ . 'fi

1^

l'

FIG.3. EXPERIMENTAL RESULTS. MATERIAL-L70 FIG.4. EXPERIMENTAL RESULTS. MATERIAL-L7I

u|fc \ 3 ^ - - • ' 8 ^ X ,

1