xi INTRODUCTION TO THE WORK OF ESIS TC 4 J.G. WILLIAMS HISTORICAL INTRODUCTION Technical Committee 4 of the then European Group on Fracture (now ESIS) started with the decision to form an activity in Polymers and Composites at the ECF conference in Portugal in 1984. Professor Kausch of EPFL (Lausanne) and myself were asked to chair it and we had the opportunity to have a discussion of interested parties at the Churchill College Conference* in April 1985. There was enthusiastic support for the idea and we decided to hold the first meeting in Les Diablerets, Switzerland in October 1985. The venue arose from my involvement with the village and the proximity to Lausanne. The venue and pattern of the meetings, ie 2 1/2 days held in May and October, became established and has continued without interruption. Two major areas were identified as appropriate for the activity. Firstly there was an urgent need for standard, fracture mechanics based, test methods to be designed for polymers and composites. A good deal of academic work had been done, but the usefulness to industry was limited by the lack of agreed standards. Secondly there was a perceived need to explore the use of such data in the design of plastic parts. Some modest efforts were made in early meetings to explore this, but little progress was made. In contrast things moved along briskly in the standards work and this has dominated the activity for the last fourteen years. The design issue remains a future goal. The development of standards has a poor reputation in some academic circles. The importance is conceded, but the task is perceived as being of a low academic level. This analysis is quite untrue. Producing a test protocol that gives reliable and meaningful results requires a deep understanding of the physics, and weakness in this regard is soon exposed by poor results. We developed a method, based somewhat on ASTM procedures, of evolving protocols via our regular meeting. An initial version is prepared by the project leader and one or more of the industrial members agreed to supply material. At the next meeting each participant describes their results and experience via presentation. The protocol is then modified in the light of this and the process repeated. About six iterations, ie three years, seems to be necessary to produce a satisfactory result. We have learnt a great deal about topics we felt we understood beforehand by this process. One's experience is multiplied many times by listening to others who have been through the same process. Several PhD students gained a good grounding in their subject via the group. This book is an overview of our activities over the last fifteen years. A wide range of tests is described and the numerous authors is a reflection of the wide and enthusiastic support we have had. It has been my privilege to act as co-chairman first with Henning Kausch and subsequently with Andrea Pavan, to such a talented and devoted group. *Yield, Deformation and Fracture of Polymers, Institute of Materials INTRODUCTION TO LINEAR ELASTIC FRACTURE MECHANICS J.G. WILLIAMS 1. INTRODUCTION Linear Elastic Fracture Mechanics (LEFM) is the basic scheme used for most of the protocols described here. It has a secure theoretical basis in that all energy dissipation is associated with the fracture process and the deformation which occurs is linear elastic. This turns out to be true for many of the situations covered here, i.e. brittle failures in polymers, impact tests, fatigue, delamination of composites and failure of adhesive joints. This is a great benefit since useful and simple methods can be developed in contrast to metals testing, for example, where plasticity and non-linear effects are important in most tests. Such phenomena can be important in polymers and will be described later, but the main emphasis will initially be on LEFM. 2. TOUGHNESS DEFINITIONS LEFM assumes that a linear elastic body contains a sharp crack and then describes the energy change which occurs when such a body undergoes an increase in crack area. (It should be noted that it is the growth of an already existing crack, or flaw, which is described and nothing is said about the generation of flaws in otherwise perfect bodies.) The parameter of most fundamental importance is theEnergy Release Rate, G, which is defined as the rate of energy released by the crack growth, dU G = (1) dA where dU is the energy change anddA is the area increase, Ad is taken as positive for crack growth, and a positive dU and hence G implies a positive energy release. It is this energy release which is available to drive the crack growth and overcomes the fracture resistance, .oG Therefore, at fracture dU G =~ =G (2) Bda c where a is the crack length for a uniform thickness B. G is determined by the loading and geometry of the cracked body while G c is a material property and is the energy per unit area necessary to create the new surface area of the crack. As such it may include the effects of many micro-mechanisms occurring in the region of the crack tip. Usually the cracks propagate in the opening, or mode I, in which the crack faces move apart with the displacement being normal to the crack faces. The toughness for this mode is designated G~c. In composites and adhesives it is possible to propagate cracks such that the displacements are parallel to the crack faces giving shear or mode II propagation and 4 .G.d SMAILLIW a toughness G,c. Mixed mode tests are combinations of these and loci of ~G for the degree of mode mix are determined. Out of plane sliding, or mode III, is possible, bat is not discussed here. An important aspect of fracture resistance is that it may vary as the crack grows such that cG is a function of the crack growth, Aa. Thus we may have a curve of G c versus Aa, which usually rises, and is termed the resistance or 'R' curve as sketched in Figule .1 This curve is a complete description of the fracture toughness of a material and some tests have its determination as the goal (e.g. delamination of composites). Some however, concentrate on the initiation value, i.e. when Aa = 0. This is usually the lowest value and is thus judged to be most critical. It may also be so regarded on the basis that once fracture has initiated, then a component has failed. Such arguments are valid, but lead to many practical difficulties of definition. Initiation may be defined via dJrect visual observation but this is difficult to achieve. Indirect, but more reprodutible methods are therefore employed, such as the onset of non-linearity in linear dao~ deflection curves, or the occurrence of a specific (5%) reduction in the slope of the toad deflection line. These schemes are a good example of where practicalities have required that exact definitions be replaced with something definable, but only indirectly related to the real phenomena. Many 'R' curves tend to level out to give a plateau value which can be a useful upper limit for cG although the definition is somewhat arbitrary. The special case, as shown by a broken line in Figure ,1 of a constant ~G is often observed. It is worth noting that LEFM conditions require linear load-deflection behaviour and thus very localised deformation at the crack tip. The stress state of this local deformation zone is however, not determined by the LEFM condition. The local nature of the deformation requires that the zone of deformation is small, compared with the in-plane dimensions of the body including the crack length. The stress state however, is determined by the size of the zone compared to the out-of-plane thickness. In many cases the zone is small compared to the thickness and is thus constrained transversely leading to the highly constrained, plane strain condition. In many situations plane strain will occur if the out- of-plane thickness, B, satisfies the condition: B> j (3) Where E is Young's modulus and tr c is the local critical stress and is usually takea as the shear yield stress. Testing under such conditions is of practical importance because this highly constrained condition is often assumed to provide a minimum toughness value. The same parameter is taken to define all the in-plane dimensions also, oGE ~ (4) i.e. a, W-a>2. tr: ) Introduction ot Linear Elastic Fracture Mechanics 5 where a is the crack length and W is the width. If both conditions are met we have plane strain and LEFM and this is most commonly sought. However if equation (4) is met, but equation (3) is not then lower degrees of constraint are possible, generally giving higher values of G c with an upper limit at the plane stress state. Plateau ~G Initiation > 0 i i aA Figure .1 Resistance or 'R' curve These criteria have been developed for homogeneous materials and will be discussed in the protocols for these later. For delamination in composites and for cracks in adhesive joints the proximity of stiff layers enhances constraint and tends to give plane strain conditions though the situation is often complex giving, for example, toughness variations with adhesive layer thickness. 3. CALIBRATION PROCEDURES In all the protocols to be described various specimen geometries are used and each must be calibrated so that load or energy measurements at fracture may be converted to G .c Two schemes are used for effecting this calibration. For many specimens, which are beams in one form or another, it is possible to measure their stiffness, or more conveniently compliance C (= (stiffness) l) as a function of crack length. For all loading systems, G may be defined as G = dUex' ~Ud dUk - dUd (5) dA dA dA dA 6 J.G. WILLIAMS where t,,eU is the external work U s is the strain energy U k is the kinetic energy U d is the dissipated energy and dA = Bda, the change in crack area for a uniform thickness, B. For low rate testing U k = 0 and if all the energy dissipation is local to the crack tip then U d = 0. For LEFM the load deflection lines are as shown in Figure 2 in which the compliance increases as a increases to a + da . The energy changes are, d U,~, = P du and sU = 1_ Pu 2 ie dU e =-~ 1 (Pdu + udP) . 1 (Pdu udP) (6) Thus G= 2B~ da da and G is the energy change represented by the shaded area in Figure 2. We may now invoke compliance, i.e. u = C.P and du = CdP + PdC and substituting in equation (6) we have, p2 dC Pu 1 dC u 2 1 dC (7) G -- 2.B ......da ..- .2B . . .C . da ~ 2B . .C . .2 . . da Thus if C (a) is known dC/da may be found and hence G calculated from either h~ad, load and displacement or energy, and displacement alone. These forms are all used in the various protocols described later. Introduction to Linear Elastic Fracture Mechanics 7 I I Load, P I I I I I I I I I I a+da I I I I I I I I I I I I 0 Deflection, u Figure 2. Load-deflection curves for LEFM The delamination tests on composites generally give stable crack growth using double cantilever beam (DCB) specimens so that P and u are recorded as a increases thus giving C (a). This can then be empirically curve fitted by a power law. C = A.a" which is termed the Berry Method resulting in, o n( u / 7" a )8( from the second of equations (7). This form is generally preferable because P, u and a may be used directly and only n is required. The protocols also employ beam theory to determine C which has the advantage of giving a value of Young's modulus which serves as a useful cross check. In most cases simple beam theory has to be corrected for shear deformation and rotation at the end of the crack. The corrected results given are from this corrected beam theory (CBT). The adhesives tests also employ DCB specimens, but in addition use contoured beams which are designed to give a constant dCI da so that a constant load gives a constant G. The peel test protocol also uses this approach for analysis though it is somewhat more direct. For peeling a strip with a force P at an angle 0 the rate of external work may be found directly and is given by: dU,,# :P(1-cosO) Bda B 8 J.G. WILLIAMS There are only minor changes in U, but plastic bending can give significant U d vaues. These can be computed and must be deducted from the external work to give G. Some geometries of practical interest do not lend themselves well to analysis via compliance measurements. Plates in tension and bending are examples and although equations (7) are still correct it is very difficult to find dC Ida experimentally. A raore accurate method is to consider the local stress field around the crack tip which has the form K "o = 2,~r. f (0), f (0)= I (9) where r is the distance from the crack tip and 0 is the angle measured from the c:ack line. The stresses are singular as r ~ 0 but the product tr~r remains finite and is characterised by K, the Stress Intensity Factor. Two relationships for K are impo1~ant in calibrating specimens. Firstly, K is related to G via, )0I( K 2 = EG and for the generic case of a large plate containing a central crack of length 2a subjected to a uniform stress ,~c K 2 = ar/2"0 (11) aff2.O i.e. G =----- (12) E t7 is the calibration factor for this case and noting that cr = P~ BW, where W is the width, then from equation (7) we have, dC 2~ a ~da ~ m , EB .ct, ot = W-- For other geometries the calibration factor tz is a function of a and these factors nave been derived in great detail both via analysis and computation. The general forra is expressed as, P K = f(ct) B.fW" (13) and for the large plate case f (a)= ~,~. This form is used in several of the protocols to give the critical K at fracture, K c . This is used in engineering design because it requires no knowledge of E to determine loads at fracture since, from equation (13), if f (a) is noitcudortnI ot Linear Elastic erutcar~l scinahceM 9 known by measuring P at fracture, then ~K can be found. Thus in any other geometry if f (ot) is known, a critical P value may be found without resort to G c . In general we are more concerned with characterisation here and hence finding G c . This may be done via cK and use of equation (10) when E is determined. This process may be included in the same test by finding ~G via the energy route using the second of equations (7). Thus, ~G = ~ ~ C dot ) BW~(ot) (14) The calibration factor r (ot) can be deduced from f (ot) if the compliance at ct = ,O C o , can be estimated since, 2 112, dot = EB. f 2 and r ~C o +o f The f (a) andr (ot) values and functions are given in the protocols for three point bend and compact tension specimens, which are used for slow rate and l m/s impact tests to determine K c and Go. The value of E from equation (10) is compared with that deduced from compliance measurements since, E= 2 f2 2 ~2 )51( dC =BC " f dot and is used as a cross check on accuracy. All the protocols are quasi-static in that U k = 0 is assumed except for the higher rate impact test. Here the loads cannot be measured and the test is conducted at a constant speed, V and timed to give the displacement at fracture. The static value of ~K is then found by deducing the load from, p= u Vtf _~-____ ,, , C C Where t I is the fracture time giving a static value of K. 1 o J.G. WILLIAMS E (Vt,) (16) K, = .~" 20.f A correction is made for kinetic energy effects via an experimentally or computed correction factor, kd, such that: K~ = K~.k a. (17) Kc AND Gc AT SLOW SPEEDS FOR POLYMERS J.G. WILLIAMS .1 INTRODUCTION A linear elastic fracture mechanics (LEFM) protocol for determining cK and cG for plastics is reproduced as the appendix to this paper. This was the first protocol developed by TC4 and was chosen as a starting point because many members had experience of the test method and it was felt to be of practical importance. The basic method was that developed by ASTM for K c testing of metals [ I] but with significant changes to make it suitable for polymers and to include ~G determination. The version in the appendix is the final form produced by TC4 and was the basis used for the ASTM version ]2[ and subsequently the ISO version [3]. These latter contain changes made to conform to the style and practices of those bodies, but none of substance occurred. 2. BACKGROUND TO THE TECHNICAL ISSUES The major technical issues addressed in the protocol are notching and the definition of initiation. The method requires that a natural sharp crack is first grown and then the conditions for its re-initiation used to define cK and .~G Great skill and care is required to produce these initial cracks and the results are critically dependent on their quality. Different techniques are required for different materials ranging from razor blade tapping in hard materials to blade sliding for soft materials. Initiation is defined as either the maximum load or the load which gives a 5% increase in compliance. Neither is true initiation but represents a reproducible value for a small amount of crack growth. The size criteria for validity are designed to ensure both LEFM and plane strain and a further restriction, that the maximum load should be no more than 10% greater than that for the 5% compliance change, is a guarantee on linearity and hence LEFM conditions. It is also worth noting that the energy result used to find G c requires a compliance correction for load point indentation, a notion which arises in several protocols. 3. RESULTS OBTAINED USING THE PROTOCOL An example of a set of data, in this case a nylon, is given below. Nine groups performed the tests and it can be seen that the average standard deviation are 5% for clK Gtc. and 12% for The agreement between the two values of E is generally good with differences of less than %1 for five sets of data and only one of up to 10%. The data sets do show the common characteristic of such exercises in that some values are wildly out suggesting an error which is usually difficult to identify. Nylon is given as an example because it is not among those materials which are ~e .... notch (e.g. epoxies, PMMA), nor is it amongst those which are rather dit