An introduction to fracture mechanics for engineers

An introduction to fracture mechanics for engineers Part III: Elastic/plastic fracture mechanics and energy methods R. A. S M I T H Cambridge University Engineering Department, Trumping/on Street, Cambridge CB2 IPZ This concluding paper of a three part series concentrates on elastic/plastic fracture mechanics. The C O D parameter is introduced as an extension of the stress intensity factor concept (Mats. in Eng. Appl 1, 2, pp 121-128, 1978 and 1, 4, pp227-235, 1979). The energy balance approach to crack extension is then discussed in order to show how the J-integral can be used as a measure of energy changes in cracked bodies with non-linear stress/strain response.

e m p l o y e d in a l a r g e r s t r u c t u r a l application where the plasticity would be more limited.

Applied stress

,.Y/

Io' Introduction The most obvious limitation to the use of Linear Elastic F r a c t u r e Mechanics ( L E F M ) is that resulting from the requirement of a minimum thickness to achieve plane strain conditions and, hence, valid Kic measurements. This was discussed in Part I1 of this series where we saw that the need for thickness greater than 2.5(K,c~ 2

\Oy ] would, in the case of a typical low yield, high toughness pressure vessel steel, imply specimens some 0 " 5 m thick. R e m e m b e r also that this requirement also defined a remaining ligament size, i.e. the distance from the crack tip to the back face of the specimen. Clearly, the capacities of available testing machines limit specimen sizes to much less than this, say to 0.04 m, so that for a wide range of practical structural steels some alternative fracture criterion is needed which will enable toughness measurements to be made in small size specimens, where plasticity might be extensive, and then subsequently used to predict fracture in the same material

316

Io CJ'ock length

Fig. 1. Simplified conditions for yield and

occurred, continued increase of applied stress causes little increase in the near crack tip stress levels, but leads to large increases in strain which cause the crack tip to 'round-off' or blunt. Wells made the suggestion that the crack would advance on attaining a critical level of crack tip strain, characteristic of a given material. The separating displacement, 6, of opposing crack surfaces adjacent to the crack tip can be used as a measure of this strain. The critical value for fracture is denoted by 6 c. The further assumption is then made that the same value of tSc controls crack advances in an application of the

fracture

I

Fig. 1 illustrates our difficulties. Consider a cracked structure with a crack length to width ratio of a/w. A simple estimate of the stress to cause net section yield (a path of plastically deformed material extending from the crack tip to the specimen boundary) can be made by setting W-a

o

_[ r-I I

7

I t

oW Onet =

L.

(7

= O'y,

I I

the yield stress.

This relationship, the dashed falling line on Fig. I, falls below the stress levels required to cause fracture, KI = O t o v / ~ :

Kic I.~rge ~ructure

for small values of crack length. Moreover, for a material with a higher fracture toughness, K]c, the whole fracture curve will move upwards, implying that even for long cracks yield failure will occur at lower stress levels than those required for rapid fracture. The Crack Opening Displacement (COD) c o n c e p t When net section, or general, yield has

Small specimen[ FAILURE[ test for ~c I e;jsc I Fig. 2. COD as an indirect determination of Kc

MATERIALS IN ENGINEERING APPLICATIONS, Vol. 1, December 1979

theoretical studies gives values of /3 ranging from Y2 in plain strain to 1 in plane stress. The fracture criterion for the large component therefore reduces to

same material where the plasticity might be less extensive. The methodology is illustrated and developed in Fig. 2. Consider a small test piece removed from the crack tip region of a large structure (the application). This test piece has a small crack length and extensive plasticity, the situation of crack length a' in Fig. I. We use this small specimen for an experimental determination of the critical C O D , 6 c. The structure has however a large crack with limited plasticity, surrounded by an elastic field. We may relate the C O D for this 'quasi-elastic' crack by using our familiar L E F M concepts in the following way:

/3KI 2

(2)

Eoy thus retaining the attractive quantitative elements of L E F M , since all the terms on the right of equation (2) are known for the quasi-elastic crack. We note in passing that for the purely elastic case the criterion,

on substitution into Equ" (2) verifies the

Y

otional crack tip C.O.D. X

O

/

Plastic

rt ~

- [

ZONe

Fig. 3. The 'Quasi-Elastic' crack Fig. 3 shows the detail of the plastically blunted crack tip region. As a reasonable approximation we consider the crack surfaces of the blunted profile to be due to a crack of length (a + q) where q is the radius of the plastic zone due to a crack of length a. We calculated this radius (Part I, Equation 7) to be, 1 K(~__~y~)2 rI ~

--

2rr

Now the COD, 6 is simply twice the y direction displacement measured at the original crack tip position. We may evaluate this from the displacement field of the shifted crack tip evaluated at 0 = rr and r = q, the result 6 =

4/3'K~ U E N/27r

fracture criterion, 6 c = constant. This approach serves to emphasise the C O D as an extension of L E F M and its use as an indirect method of toughness determ i n a t i o n b y p a s s i n g the s t a n d a r d specimen requirements. Some further extension of the C O D concept to more extensive plasticity can be made by employing more sophisticated analyses for 6. For the high toughness materials typified by the upper curve of Fig. 1, we lose the advantages of quantitative predictions and the use of C O D is reduced merely to the role of a comparative toughness parameter, which ranks higher toughness materials with a higher critical C O D , 6 c.

(1)

follows the elastic stress field solutions to the general crack problem presented in Part 1. The notation of Part 1 is maintained,/3, is a constant which depends on stress state (determined by thickness) at the crack tip. Combining these equations and absorbing the constants into a new constant/3, we find

/3 Kle 6-Eoy

The consensus of many experimental and

S o m e features of experimental C O D testing It is not the purpose o f this i n t r o d u c t o r y

article to acquaint the readers with all the experimental details of C O D testing their curiosity will be sated by the references given at the end but mention must be made of the difficulties arising from the somewhat loose definition of COD. In particular, where do we measure it'? And what steps do we take to deal with any small stable crack tearing which might precede fast fracture'?

MATERIALS IN ENGINEERING APPLICATIONS, Vol. 1, December 1979

As an indication of relative values the critical C O D , 6 c for a weld metal might be 40~tm increasing to, say, I mm in aluminium alloys. Early experiments relied on paddle wheel type displacement gauges which could fit into machined slots. Once fatigue cracks come into use as sharper crack starters, clip gauges with strain gauged sprung arms were fitted away from the crack tip. This led to the need for some calibration between this remote reading and the crack tip displacements. Even today this has not yet been achieved in an entirely satisfactory way. More recently crack tips have been infiltrated with hardening plastics which can be removed to allow subsequent examination of the replicated crack profile. The problem of identifying the critical event in the C O D test remains a matter of active controversy. While the value of C O D at the initiation of a stable tear at the crack tip is a reproducible 'material property', many authorities have produced evidence to show that its use in design can be very conservative. The inherent disadvantage of C O D is that the crack tip is a region of uncertainty, but our fracture criterion requires both direct analysis and experimental measurements in this area. We therefore seek some alternative measure which allows us to view this area of doubt from a safe distance this is the function of the so called J-integral. Before we can understand the physical meaning of this new concept we need to consider, as a rather long aside, the historically much older view of fracture as an energy controlled process.

T h e r m o d y n a m i c energy approach to fracture Consider the energy changes in a cracked body as the crack increases its area by an amount 6A. Work 6W, supplied by the movement of the external forces, is stored as elastic strain energy, 6El, and absorbed, at a rate proportional to the crack area increase, as the work required to advance the crack. If G c is the work required per unit area, the crack tip work absorbed is Gc6A. If the difference between the work supplied and the stored energy is less than the crack tip work, further energy must be supplied to continue the crack area increase. Critical conditions occur when the net energy supplied just balances the energy required. The equilibrium becomes unstable as soon as the net energy exceeds the crack tip energy required, i.e. 6W

6 E I ~ Gc6A

(3)

This is the essence of the thermodynamic requirement for fracture developed by

317

"////////////////

,'/////////////,

7/

6a

'&

6a a

//////

1°

\ X\\\\\\\\\\\\\

Fixed

IP

grip

Constant load

Fig. 4. 'Fixed grip' and 'Constant load' cracked plates Griffith in the 1930's. To fix ideas consider the extension 6a of a crack of length a in a linear elastic body of unit thickness loaded in the two ways illustrated in Fig. 4. In the first an extension u is imposed and the ends clamped. In the second, the same extension is applied by a constant load P. These are known respectively as the fixed grip and constant load cases. The body containing the longer crack (a + 6a) is more flexible and has a less steep load/displacement response as shown in Fig. 5.

all the shaded areas of Fig. 5. Thus Equation (3) becomes P6u

1/2P6u > Gc6a l//2P6u > Gc6a

(5)

Now for a linear elastic body, the relationship between load and displacement can be written in terms of the compliance C, a constant whilst the crack length is constant,

Thus

Y2--~' rra2B where rra2t is the cylindrical volume in which the stresses have been removed. Remembering there are two crack tips the strain energy release rate, with respect to crack area, becomes,

both Equation (4) and (5) reduce to

__a

N °

aa

i

Extension Fig. 5. Elastic load/extension curves for cracked plates For the fixed grip case, the crack extension is accompanied by a decrease in load, 6P and a decrease in the amount of stored elastic energy of (y2(P - 6P)u - y2Pu) = -Y2u(~P,

the singly shaded area on Fig. 5. Since the displacement is fixed, the external work is zero, hence Equation (3) reduces to -(-Y2u6P) > Gc6a

(4)

The constant load case is slightly more complicated in that the external work done is P6u, whilst the stored energy increases by an amount (y2P(u + 3u) - Y2Pu) = y2Pau,

318

by the crack of length 2a is 0 2

u=CP ~u Y2uaP = 72CP"u = I/2Pt~u, L

~p

--- I~~1 i

Fig. 6. Approximate 'stress flow' round crack of length 2a

(yxPu) > Gc

(6)

The LHS of this classical energy based fracture criterion is often written as G and termed, erroneously as the above derivation shows, the strain energy release rate. A better term might be the available energy rate. Note that the rate is with respect to crack area, for convenience of notation we have used unit thickness. The RHS is the critical strain energy release rate, Gc,which must be exceeded for fracture to occur. For any particular configuration the energy release rate of Equn (6) can be calculated from the stress/strain distribution in the cracked body. Griffith used an exact stress solution due to Inglis to calculate the energy changes to the presence of a central crack in a fixed grip infinite plate of thickness, B. By employing the flow analogy of stress, we can see, Fig. 6, that the crack relieves the stresses and hence removes the strain energy in an approximately circular zone encompassing the ends of the crack. As a crude approximation therefore, if the applied stress is o, then the energy per unit 1 02

J

~..(rro2a2B~

2B a a \ 2

E ] = %--E

which is correct in form but four times less than Griffith's more accurate calculation. He associated the fracture work with the surface energy, y. Since there are two surfaces at each crack tip, G c = 4% The situation as a function of crack Energy

• lease rate)

q(Absorption rote) Crltico I stable

Crack length, o

Fig. 7. Energy changes as a function of 'Griffith' crack length length is illustrated in Fig. 7. The surface energy absorption is independent of crack length, whilst the strain energy release rate increases proportionally to crack length. The critical condition, Equation (6), reduces to

2rro2a

volume is - - - . and the energy released 2E

rro2a

E

= 4"y

MATERIALS IN ENGINEERING APPLICATIONS, Vol. 1, December 1979

which on reorganisation yields ~x/~

= (2vE)~/2

(7)

has remarkable similarity to our previous fracture criterion K = aox/'-~'----

Klc,

(ce = 1 for the central crack in an infinite plate) in both cases the R H S is a material constant which measures the material's resistance to fracture. Griffith's approach worked extremely well for very brittle materials (classically glass), but his association of the fracture work with the surface energy was many orders of magnitude too small for materials (e.g. steels) w h i c h suffer c o n s i d e r a b l e plastic deformation near the crack tip. Modern usage therefore employs the energy criterion, Equation (6), without associating the critical energy release rate Gc with any particular mechanism of crack tip energy absorption. Rather G c, as Ktc, is measured experimentally. G cis also a function of specimen thickness, the minimum plane strain value, for thick plates, is designated Gl~. Since the calculation of G for a cracked elastic body depends only on the elastic stress distribution, which also uniquely defines the stress intensity factor, K, the two p a r a m e t e r s must be r e l a t e d . Appendix 1 shows in detail how the relationships: K2 G -- T - ( p l a n e stress) K2 G ----- - ( I E

v 2) (plane strain)

are derived. These results, combined with

the definitions of G, Equ n (6), and compliance, arm us with an experimental technique for measuring stress intensity factors, see Appendix 2. An important distinction must however be drawn between these two elastic fracture criteria. The Klc criterion automatically guarantees the presence of high tensile stresses near the crack tip which can operate the mechanisms required to separate the adjacent material. The criterion is therefore both necessary and sufficient. On the other hand the G~, criterion, whilst necessary, need not be sufficient the shear crack in Fig. 8 illustrates this point. The shear load causes zones of both compression and tension near the crack tip. The directions which provide maximum strain energy release are symmetric about the line of the crack at about 70 ° inclination. The energy criterion is unable to distinguish these two directions but our intuition and the K~c criterion tell us failure must occur along the direction pulled open by tensile stresses. Equipped with this information about the energy view of fracture, we can now return to our main task and introduce the J-integral parameter as a measure of energy changes during crack extension in a non-linear elastic body.

Lood

Potentialenergy U=W - E J ~ ~

J

Displacement

!,

Fig. 9. Non-linear elastic load/extension curves the crack tip and quantify the mechanical crack tip environment with a 'remote' measure, so we seek a parameter to do the same job for cracks surrounded by extensive plasticity. The J-integral is at the present time the most favoured candidate for this task. Although the J-integral was introduced by Rice as a path independent energy line integral surrounding the crack tip (see Appendix 3), it is more easily understood as a measure of the potential energy difference between two identically loaded non-linear elastic bodies containing cracks of slightly different lengths, Fig. 9,

The J-integral

9u

As previously stated, the maj or drawback of the C O D criterion is that it is both theoretically defined and must be experimentally measured adjacent to the crack tip, the very area about which we are most uncertain. Just as K in the elastic case allowed us to step back from the detail of

J --

IqQf

70 °

70 °

TENSION

/ Fig. 8. Tension and compression near a shear loaded crack

MATERIALS IN ENGINEERING APPLICATIONS, Vol. 1, December 1979

(8)

The potential energy change, 6U, is the difference between the external work done and the stored elastic strain energy, 6W-6E1 in our previous notation. The potential energy is therefore the area above the load/displacement curve. Thus for crack extension, 6a, in a body of thickness, B, the decrease in potential energy, Uca)

COMPRESSION

~a

U(a+aa) = -6U = JB6a

(9)

is represented by the shaded area between the two load extension curves of Fig. 9. The potential energy is available as the crack driving force. As previously we consider that a critical amount of this energy is needed to overcome the material's resistances to cracking. The corresponding fracture criterion is therefore written J---- Jc

(10)

Two limiting cases are of interest. For small extensions, the load/displacement curves near the origin tend to straight lines (Fig. 9) and the value of J approaches that of G, the elastic strain energy release rate, Fig. 5. Now consider the plastic collapse (limit) loads for the cracked plate of Fig. 10. If we assume a perfectly plastic solid where the strain can

319

(~) Differentiate to obtain J

Load and measure areas [potential energy)

Pylo+,t a }

Load Load

I

~

u

lal

i••

J

/~o, //I l

j~

j =-'T~'= 6U

o2

I

'.

la3

Ul

U2

U3

Displacement

Fig. ]0. Limit loads for perfectly plastic cracked plate

I U2 ~I U3 I

Displacement

Displacement

increase indefinitely after yield, then the yield load is Py(a) : ( W - a)O'y

gl|

-

(1l)

for a crack of length a, and Py(a+6a) ----(W - a - (~a)Oy

(12)

for a crack of length (a + 8a). Thus for unit thickness J~a =

[Py(a)- Py(a+~a) ]

Potential energy

U

is" obtained from Equation 9, which on substitution of the limit loads, Equations (11) and (12), becomes J = ayU

U

Oyt~¢

.2'

320

I

al

,,-----+, u2 lI I t

Q2

Crack length

(13)

We have therefore demonstrated that J has the properties of G for the elastic ease and COD for a plastic solid, whilst for intermediate situations we can regard J as a measure of the intensity of deformation near the tip. Experimentally, we can generate the relationship between J and displacement, by measuring the potential energy changes in a series of tests of identical specimens with different crack lengths, see the sequence of Fig. 11. From a fracture test, a critical displacement can be associated with a critical crack length and the value J¢ obtained by interpolation. This is obviously a laborious task and introduces many possibilities of error. The valuable role of the analytic approach to J is to produce accurate J c a l i b r a t i o n s w i t h o u t r e c o u r s e to experiment. However the elastic/plastic analyses required are much more difficult than the purely elastic analyses needed for K calibrations, and no general solutions to this problem have been presented. Finite element methods are however producing useful results. Finally, we identify the uses of J as being similar to those of COD - ranking the toughness of materials with extensive crack tip plasticity and indirect toughness determinations on small scale laboratory

U3

JB ~

Now for the critical (fracture) value, the displacement is simply equal to the critical COD, hence J¢ =

(~) Fracture test. Measure critical displacement and crack length Interpolate above plot to obtain Jc.

I

I

a3

(~) Plot against crack length

_/ Fig. I I. Experimental J calibration and testing specimens. Experimental evidence has been presented which supports these roles. Experimentally the determination of Jc is easier and less ambiguous than the measurement of ~c. Some difficulties associated with the definition of J for a non-linear elastic material do however remain - - a real material after yield does not, of course, unload down its stressstrain curve, but follows an essentially elastic unloading path leaving some permanent elongation. This obviously presents problems if unloading due to stable crack extension precedes rapid fracture, or if we attempt to apply J concepts to repeated loading cycles such as fatigue.

Closing

remarks

and summary

The purpose of this review was to introduce the reader to the thinking which lies behind the theory of two parameters, COD and J, which have been proposed to describe fracture in the presence of extensive plasticity. In the simplifying process much mathematical rigour has

been lost, but no apologies are made; reference to the literature will more t h a n satisfy most needs. Nevertheless, it should be clear that elastic/plastic fracture mechanics is much less well developed than its elastic counterpart. Neither of the two parameters described has, as yet, achieved universal acceptance, although the J-integral appears to be overtaking the older COD. The use of these ideas as quantitative design tools is only just beginning in the most advanced type of calculation, although because of increasing pressures for more effective utilisation of materials and weight saving, their use is bound to spread. We may summarise the position as follows: 1. The crack opening displacement, ~, reaches a critical value, (5c, for rapid crack advances. For small scale yielding (the quasi-elastic crack), we may relate (~ to the stress intensity factor K, 3Kl 2 Eoy 2. Critical fracture conditions may be

MATERIALS IN ENGINEERING APPLICATIONS, Vol. 1, December 1979

The corresponding release in elastic energy is therefore

regarded as an energy balance. For an

elastic body crack advance occurs when the strain energy release rate, G, exceeds the energy absorption capability-of the material, Gc, G>

I/~ovdx

(upper and lower displacements are symmetrical)

Gc

3. The J-integral measures the energy available for crack extension in a nonlinear body. Again, for fracture, a critical energy rate must be exceeded, J>

f:

6El =

y,x

rrE

J~

On substituting x = 6a sin2w, this integral can be evaluated as

Q

4. We may regard J as aglobal parameter which is a measure of local crack tip deformation. We have demonstrated that J has the properties of G for an elastic body and COD for a perfectly plastic solid.

K2( 1-~,2)6a 6El -or as (ra

E

,O, ~E1 ---

K2( I u-~) z

-

-

Oa

J

E

F r o m our definitions, Equations (3) and

(6) in the text,

Further reading COD was introduced by A.A. Wells in 1961, Crack Propagation Symposium Proceedings, 1, pp 210-230, Cranfield College of Aeronautics, Cranfield, England. Rather than treating a 'pseudo-elastic' crack, B.A. Bilby, A.H. Cottrell and K. H. Swinden developed the stress fields near yielded crack tips by considering arrays of dislocations. The J-integral appeared in a paper by J. R. Rice (1968), Trans. ASME, J. App. Mech. 35, pp 379 386. Its use as a fracture criterion was investigated by J. A. Begley and J. D. Landes in ASTM, STP 514, Philadelphia, Pa. USA. The energy approach was the brain child of A. A. Griffith, Phil. Trans. Roy. Soc. A 221, pp 163-198, ( 1921). Some errors in this paper were corrected in Proc. I st Int. Congress App. Mech., Delft, (1924). This seminal work went largely ignored for some twenty years. G.R. Irwin (1957), Trans. ASME, J. Appl, Mech., 24, pp 341- 364, related the energy and stress approaches to fracture. The development of elastic/plastic fracture theory can be followed in ASTM, STP 536, Progress in Flaw Growth and Fracture Toughness Testing, ASTM, STP 632, Developments in Fracture Mechanics Test Methods Standardization, ASTM, STP 668, Elastic/Plastic Fracture. A readable and critical discussion of the concepts of fracture theory has been given by F. A. Nichols, Eng. Fract. Mech. 12, pp 307-316, (1979). D. G. H. Latzko (Ed), Post-Yield Fracture Mechanics, Applied Science, London, (1979), gives an up-to-date review, whilst the whole field of fracture mechanics is covered in a book which aims to cover what the title implies

~w

OEl

G-----~a Fig. 1.1 Crack tip closure energy calculation

Oa

~w

~El

but for fixed grip - - ~ = 0 and - ~ - is the elastic energy stored.

'Fracture Mechanics - Current Status, Future Prospects'. R.A. Smith (Ed), Pergamon, Oxford, (1979).

Appendix 1 The relationship between stress intensity factor, K, and strain energy release rate, G. We need the results arising from the elastic near crack tip stress field introduced in Part I: Kl 1 OyyJ 0 = 0 -- (2rrr)l/2 and the y direction displacement, v

I

0=rr

E

for plane strain (thick plates). Consider a crack of length, a, in a body of unit thickness loaded by fixed grips, Fig. 1.1. Let the tip of the crack advance from a to (a+3a). If we apply a stress distribution equal but opposite to the opening stresses ahead of the original length, the crack surfaces will be kept just in contact and the elastic energy of the system will be unchanged. The closing stresses are thus = --Oyy

0~'0

-K) (2rr r)1/2

If these stresses are now relaxed to zero, the crack opens to a profile of a crack of length (a+6a), or neglecting second order terms, to a profile of a crack of length a with its tip at (a+Sa). Hence 4(l-u z) (ra-x~V2 v-- ~ K ' \ 2~. ]

MATERIALS IN ENGINEERING APPLICATIONS, Vol. 1, December 1979

K2 (1 u2) G =-(plane strain). E Similar considerations give the plane stress result Therefore

K2 G=--

E

Appendix 2 Stress intensity determination by compliance testing From our Equation (6) and the above G

K2 (l-v2) E

~(IX~Pu) (plane strain).

For a series of tests of varying crack lengths stressed to constant displacement

~P G= V2u-9a But from the definition of compliance. u = CP. 8 u = 0 = C r P + PrC Thus G --- GCP

~a

2 ~a

The same result can be obtained from the same starting point by considering the conslant load case. Thus by increasing the crack length in a series of tests on identical specimens, we can measure the compliance as a function of crack length. (The compliance will decrease, longer crack, weaker spring.) On differentiating this data we obtain ( ~ C / ~ a ) as a function of crack length and hence the variation of either G or K with crack length. Note that for plane stress the term

321

(I-u 2) is dropped from our starting equation and that for specimens of thickness, B, instead of unit thickness, the energy changes are simply divided by B. This experimental technique is useful for small laboratory test pieces where the displacements between the loading points can be accurately measured. It is of no use for large structures. Errors due to the .differentiation of the compliance/crack length curve tend to be high. The method can however be used in conjunction with finite element analyses to compute stress intensity factors without the need for detailed knowledge of the stress/strain field near the crack tip and the consequent need for a fine mesh of elements in that vicinity.

Appendix 3 The representation of J as a line integral

~Y

Rice formulated J as a path independent line integral for a non-Bnear elastic solid, For any path I" surrounding the crack tip and for unit thickness J=fp

Fig. 3.1. J-integral definition

[Wdy-Te

(dd~xU) ds 1

where W is the strain energy density'f is a traction vector normal to the integral path, u is the displacement vector and s is the arc length anti-clockwise around P. The fact that J is path independent means that the most convenient path for evaluation can be followed. For example, the boundaries of a cracked sheet are often chosen in finite element determination of J. Many of the terms in the general line integral above are then either known to be of constant value or disappear. Whilst this mathematical formulation is not important for an elementary physical understanding of J, its use in computing theoretical value of J for test pieces is of considerable importance.

INTERNATIONAL CONFERENCE "THE IMPLICATION OF MATERIALS SELECTION ON PRODUCT LIABILITY"

The proceedings of this conference held in September 1979 will be published shortly by Scientific & Technical Press and will be price £30. The following papers will be presented:

!. The current and potential legal requirements for product liability in UK, Europe and USA. B. D. Monk. MBG Management Consultants Ltd. 2. Product failure due to bad material choice and processing. N. A. Waterman, Fulmer Research Institute. 3. Safety in chemical process plant. Cambridge University. 4. The implications of equipment materials selection on product liability in food processing. C. D. Marriott, Unilever Research Lahoratoo', Co/worth House, BedJord. 5. Product quality, product liability and oil products. R. Lindsay, Shell UK Ltd. 6. Testing for product liability. D. B. S. Berry, Yarsley Technical Centre, Trowers Way, Redhill, Surrey. 7. Materials selection for durability. P. Watson, GKN Group Technology Centre, Birmingham New Road, Wolverhampton. 8. Materials used in manufacture of consumer goods. D. J. Unwin, Consumers" Association. Research Division

322

Laboratories, Haq~enden Rise Laboratory, Harpenden, Herts. 9. D.I.Y. Products. Black and Decker (Ireland) Ltd., Naas, Republic c?[ Ireland. 10. Elastomer ageing and product liability. J. N. Havers and D. Norhuo', Dunlop Ltd., Research Centre, Kingshuo' Road, Birmingham. 1 !. Contribution of condition monitoring to the elimination of failure in service. M. J. Neale, Michael Neale & Associates, 43 Downing Street, Farnham, Surrey. 12. The insurance of product liability. P. Sherman, Royal Insurance Company Ltd., P.O. Box 144, New Hall Place, l.iverpool.

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MATERIALS IN ENGINEERING APPLICATIONS, Vol. 1, December 1979