Fibre Break Failure Processes in Unidirectional Composites. Part 3: Unidirectional Plies Included in Laminates

This paper follows on from the earlier studies (Part 1 and Part 2) which considered the kinetics of fibre breakage in unidirectional composites. The first paper considered monotically increasing tensile loads at speeds which enabled any viscoelastic effects to be ignored (Part 1). Such unidirectional composite plies make up structures such as can be found in filament wound pipes and pressure vessels. This type of structure is often used under load over periods of decades and the time dependent behaviour of the matrix can lead to progressive damage. It is this which was considered in Part 2. The whole study has been organised in three distinct parts (Part 1, Part 2, Part 3). Each part of this series is described in a separate paper making therefore a suite of 3 coherent papers.

This paper (Part 3) considers complex stratifications containing unidirectional plies. More precisely, cross-plied and angle-plied laminates made up of stacks of unidirectional plies arranged at various angles to one another are considered. It will be shown that some of the most important conclusions obtained for the unidirectional composite plates in Part 1 and Part 2 can be extended to more complex lay-ups in which unidirectional plies nevertheless control ultimate failure. The loading conditions which will be considered in this third paper are those which have been analysed in the two earlier papers; monotonic tensile loading (ML) for which the viscoelastic properties of the matrix of the composite can be neglected, and (ML-H) in which the H represents a speed high enough for the viscoelastic nature of the matrix to be inconsequential. In addition monotonically increasing then sustained tensile load tests (SL) are also considered for which the effects of the viscoelastic properties of the matrix must be considered. This paper considers the damage accumulation in the unidirectional plies of the proposed stacking sequences.

Failure processes at the scale of individual fibres are difficult to observe experimentally and so have been studied through simulations. The F E ² model of \((0^{\circ }_{36})\) laminates which has been used, has been described in detail in the first paper of this trilogy (Part 1) and is the continuation of earlier studies [2, 3, 4, 5, 6, 7, 8, 9, 11, 16]. A Monte-Carlo process has been used to build a fibre strength distribution based on experimentally obtained data from tests on individual carbon fibres. This distribution assigns strength values to the fibres. It is clear that this random choice of fibre strengths could modify, more or less the conclusions reached. It is for this reason that the results presented in Part 1 correspond to those for which the probability of failure for the composite under high rate monotonic loading (ML-H) has been taken as equal to 0.5. Also, this distribution of local fibre strength is that which has been used to illustrate the results in this third paper (and was the same for the second paper). In this way the observed effects concerning the phenomena of fibre breaks were due to the type of loading applied rather than any perturbation due to the statistical analysis.

Terminology of the all the vocabulary and abbreviations used in these papers and defined in Part 1 is given in Section 5.

For all the lamina, in all the loading situations considered, the high order i-plets (32-plets) are the key parameters of the failure of the unidirectional material, as was seen for the unidirectional composites treated in Parts 1 and 2.

Equally when the laminates were loaded with SL type loads, for which the viscosity of the matrix must be considered because of the time effects involved in such loadings the values of the I and J points for the populations of fibre failures and of high order i-plets (32-plets) were very similar to the unidirectional case (Table 6). It is most significant that the clustering of fibre breaks effect was again seen in the laminate specimens, just as was seen for the unidirectional plates, which again raised the question of how to define the critical state of damage in these materials.

The above considerations have allowed the conclusions concerning the behaviour and failure of unidirectional plates to be extended to laminates consisting of unidirectional plies, either in one thick layer or separated into several plies by plies of different orientations. These simulations allow conclusions to be drawn on the effect of the confinement of the plies. In particular it allows the desirability or not of grouping plies of one fibre orientation 0^∘ into a single thick layer or sandwiching fractions of this orientation within the laminate to create several thinner plies of the same orientation to be examined. This question has been studied using three angle-ply laminates designated as AP_1_36, AP_2_18 et AP_4_9 (Table 1).

Secondly it is convenient to define the magnitude of values having the same significance in each laminate and especially that which determines the point of instability J and others, such as secant rigidity, which will be used to reveal any effect of confinement. The point of failure of the composite has to be indicated by the variation of the longitudinal strain. As can be seen from Table 4 the secant rigidity of the structure increases as the plie thicknesses are reduced. This is explained as when the 0^∘ plies are thick the off-axis plies are less constrained by them so that the value of < ε ₁₁> also increases. This means that in order to correctly analyse the effects of confinement it is necessary to correlate the variations (notably that of the population of 32-plets) not as a function of < ε ₁₁>, but with the average longitudinal strain over all the 0^∘ plies in the laminate < ε ₁₁>₀. The result of this analysis is that it is seen that, for the three laminates considered, the value is always the same (Fig. 1) except for after the point of instability which, in any case, is only accessible through the numerical analysis and has no physical signification.

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In the case of ML loadings, the effect of confinement is insignificant on the value of failure stress (Table 2): it should be highlighted that delamination was not considered in the modelling; in reality, the thinner-ply configurations should present higher delamination strength than the thicker-ply case. However there is a marked effect on the populations of high order i-plets (32-plets) at the point of instability J (Table 3) (although less obvious at the point of start of instability I): the more the 0^∘ plies are thin the smaller is the population of fibre breaks and of the population of 32-plets although the value of the failure stress does not change. It should also be mentioned that Sihn et al. [17] observed experimentally an increase in initial stiffness in thin-ply specimens as has been numerically observed in this study (Table 4), which supports the different strains to failure in (Table 2). Another possible advantage of thin plies may be a reduction of porosity induced during manufacture.

In the case of SL loadings the effect of confinement becomes obvious on the time to failure (Table 5): the time to failure becomes longer as the 0^∘ plies are increasingly confined. However the increase is particularly obvious if the steady applied load is small. That is to say that the confinement effect increases if the effects of the viscosity of the matrix has the time to have an effect: approximately 2% is gained on the lifetime for a steady load at 0.96×F _{M L} however an increase of approximately 13% is seen for a steady load of 0.90×F _{M L} . The populations of fibre breaks and of the development of 32-plets, are greatest at the point of instability when the plies are confined (Table 6). This seems to contradict the effects of confinement however the populations of fibre breaks and of 32-plets at the point of instability J are higher when the plies are confined as the times to failure are longer. If, however, the same loading durations are considered (Fig. 2, Fig. 3), these populations are always more numerous when the plies at 0^∘ are thicker. This shows clearly the effect of confinement: the development of clusters of fibre breaks in the thin plies is hindered by the adjacent plies whereas they can develop more easily when in thicker plies, where they are less inhibited.

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Table 5

Characteristics points in the < ε ₁₁> versus t curve (SL conditions). (*): see Part 2

Stacking sequence	F S L	Point I		Point J
F S L	(MPa)	t S I N S T (s)	ε S I N S T	t S L (s)	ε S L
0.90×F M L
UD_1_36 (*)	2610	2000000	0.0202	2164610	0.0227
CP_1_36	1413	3832000	0.0215	4287310	0.0230
AP_1_36	1425	3357400	0.0215	3807670	0.0231
AP_2_18	1425	3201000	0.0201	4239970	0.0220
AP_4_9	1425	3119300	0.0198	4346020	0.0216
0.96×F M L
UD_1_36 (*)	2790	18000	0.0209	20429	0.0240
CP_1_36	1507	23717	0.0220	25096	0.0222
AP_1_36	1520	21604	0.0221	22328	0.0232
AP_2_18	1520	22052	0.0210	22533	0.0223
AP_4_9	1520	22200	0.0207	22800	0.0225

Table 6

Damage state at characteristics points of the < ε ₁₁> versus t curve (SL conditions). (*): see Part 2

Stacking sequence	Point I		Point J
F S L	Fibre breaks (%)	32-plets (%)	Fibre breaks (%)	32-plets (%)
0.90×F M L
UD_1_36 (*)	15.03	13.97	28.90	23.50
CP_1_36	19.37	17.76	26.88	23.29
AP_1_36	19.96	18.23	28.11	23.68
AP_2_18	16.27	15.12	27.23	23.59
AP_4_9	15.62	14.54	26.72	23.35
0.96×F M L
UD_1_36 (*)	9.63	7.98	19.51	13.41
CP_1_36	11.27	9.54	12.60	10.79
AP_1_36	11.94	10.13	18.40	13.96
AP_2_18	11.34	9.63	17.66	14.20
AP_4_9	11.63	9.98	20.63	16.91

It can be seen that correlating the effects of confinement on the populations of 32-plets with < ε ₁₁> rather than < ε ₁₁>₀ would have led to the wrong conclusion. It could have been erroneously concluded that less damage would be observed, with fewer fibre breaks, with the layup AP_4_9 (with respect tothe sequence AP_1_36 for example) as the strain < ε ₁₁> was less (with respect to the sequence AP_1_36 for example) as fewere fibre breaks were induced and therefore the reduction in damage is due to the reduction of < ε ₁₁>. In reality the strain seen by the 0^∘ plies is the same in all the sequences. It is therefore the effect of confinement which causes the reduction in damage.

To resume, whatever the type of loading ML-H or SL, the conclusions are identical: the finer the layers at 0^∘ the greater is the restriction of clustering. This result has already been experimentally demonstrated by Sihn et al. [17] and Wisnom et al. [24]. Once again, the model is confirmed by experimental results.

In this third and last part of this study we have examined the damage of the unidirectional plies within a cross-plied laminate, including the cases in which the plies were separated by off-axis layers, but for which failure was controlled by the failure of the unidirectional plies. The choice of lay-up reflected the fibre arrangement in filament wound pressure vessels. This behaviour was exactly analogous to the the single unidirectional plies subjected to a continuously increasing load considered in Part 1 or under steady loading until failure as in Part 2. In this paper the unidirectional plies were part of a stratified laminate and were surrounded by off-axis composite plies, however the loading patterns were the same.

The simulation has also allowed the mute point of whether it is best to group all the plies of one orientation into one thick layer or to spread them throughout the thickness in several thinner plies 0^∘ or if this is no importance. Whatever the type of loading ML-H or SL, the conclusions are identical: the finer the layers at 0^∘ the greater the effect of clustering is restricted. In the case of loading of the type SL, the time to failure with the same number of plies (same number of off-axis plies; same number of plies at 0^∘) increases in proportion to the number of plies at 0^∘ spread throughout the thickness of the laminate as thin plies. However in the case of ML-H loading there is no difference in failure load but the high order i-plets are reduced if the plies at 0^∘ are thinner.

In the future, the next step of the study has to take into account the variability of the local volume fraction and the matrix cracking phenomenon [1, 14, 19, 20, 21, 23] which appears in these materials and to confirm or not the conclusions of the present study.

Nevertheless these variables should not modify the main conclusions described above. The cracking of the matrix should have only an effect on the load transfer between fibres in those plies which are susceptible to cracking which is to say the off-axis plies. The effect of local variations of fibre volume fraction could lead to variations in damage states but this does not change the principal mechanism governing damage, especially under sustained loads, which is the viscosity of the matrix.

The results given in this three papers are solidly based on earlier studies (some of the oldest are Rosen [15], Cox [12], Zweben [25]) of which many have been cited in the list of references (Part 1). The present study owes much to earlier researchers who have described the physically based processes governing composite behaviour beginning with analytical techniques. These earlier studies based as they were on a logical examination of mechanical processes at the level of reinforcements, have allowed a general understanding of the phenomena governing composite behaviour and ultimately failure. The increasing computation power of computers has allowed the present authors to develop models based on the understanding of the phenomena in a earlier studies [2, 3, 4, 5, 6, 7]. It is now possible, with a reasonable computational time and by using multi-scale approach [13, 18, 22], for a detailed simulation of those physical phenomena involved in composite behaviour to be made. A comparison between the simulated behaviour of composites and the results obtained experimentally [16] shows close agreement and justifies the use of this model in the understanding of composite structures, such as pressure vessels [10]. It also allows a closer examination of processes which are very difficult or impossible to observe experimentally, such as the critical effect of clustering of fibre breaks, which is more or less important depending on the loading conditions.