Damage tolerance of laminated tee joints in FRP structures

Composites Purr A 29A (1998) 465-478 6 1998 Elsevier Science Limited

PII: S1359-835X(97)00081-X

ELSEVIER

Printed in Great Britain. All rights reserved 1359-835X/98/$19.00

Damage tolerance of laminated tee joints in FRP structures

H. J. Phillips and R. A. Shenoi* Department of Ship Science, University of Southampton, Southampton SO17 ISJ, (Received 26 March 1997; revised 18 June 1997; accepted 1 August 7997)

UK

This paper is concerned with the damage tolerance of laminated tee connections in large fibre reinforced plastic (FRP) structures found in marine construction. Such connections represent a potential zone of weakness in ships and it is essential that their mechanical behaviour is well characterised. Previous work has focused on static as well as fatigue behaviour. There is growing evidence that delamination induced damage in the root of the tee is a potential source of catastrophic failure as well as being expensive in repair terms. The paper briefly outlines the load transfer mechanisms in single skin tee joints under representative boundary conditions and establishes the failure inception and damage progression under static loading. Numerical analyses are then presented to link the observed failure scenarios to stress levels in different parts of the tee. Lastly, a fracture mechanics approach is used to identify the seriousness of a particular delamination vis-a-vis ultimate failure. 0 1998 Elsevier Science Limited. All rights reserved. (Keywords: criteria)

B. damage tolerance;

C. finite element analysis

INTRODUCTION Large fibre reinforced plastic (FRP) structures, by necessity of design and production constraints, have a number of joints in their topologies. Such connections can be divided into two basic types; namely in-plane and out-of-plane joints. In-plane joints have been the subject of attention of many researchers”2, with attention being focused on analytical treatments”, numerical analyses4, experimental studies”, failure criteria6 and material aspects’. Arguably, the more difficult problem is the one that pertains to load transfer between two orthogonally placed members meeting at a joint. A typical joint is illustrated in Figure 1. The joint is formed by placing laminated strips of reinforcement cloth on both sides of the joint (boundary angle or overlaminate). The reinforcements are usually alternate layers of woven roving (WR) and chopped strand mat (CSM). The numbers of plies or laminae will depend on the required stiffness for the joint. The resulting gap formed between the cloth and plates is filled with an appropriate resin, i.e. one which is compatible with the cloth material and is generally one with a high yield strength. The weakness in this case is due to the lack of reinforcement across the connected surfaces and through the occurrence of stress concentrations associated with joint geometry and production considerations. There is now a growing body of literature on the

* Corresponding author

(FEA); E. joints/joining;

fibre reinforced

plastics; stress

behaviour of laminated tee joints. Early work concerned theoretical modelling using simple plane strain8 and plane stress’ approaches; these corresponded to marine and aircraft applications respectively. These efforts were rather restrictive owing to the relatively immature finite element analysis (FEA) capabilities at the time. More recent effort, incorporating layered (finite) elements and a variety of failure criteria, has successfully characterised through numerical analyses both single skin” and sandwich”,‘2 tee joints under representative static loadings. This work has been supplemented by experimental programmes studying failure mechanismsI and stress pattems14. The work has been extended to studying the long-term effects of such joints under repetitive, cyclic loadings l5 including inception and progression of failure as well as approaches to life modelling. All such work has formed the basis of writing a procedure for the synthesis of design variables for typical single skin tee joints in ship and civil construction’6. Such joints form an integral part of several ships some of which are now over 20 years old. There is growing evidence” that damage in such joints owing to ‘root whitening’ (caused by delaminations) is requiring larger efforts at repair. This is principally because the significance of the defects arising from delaminations is not fully documented and understood. In the case of laminates, there is extensive evidence of stress based criteria” and fracture mechanics based approachesl’ being used to map damage tolerance of structures. There is a need to extend such work to the case of more complex geometries such as tee joints.

465

Damage tolerance of laminated joints: H. J. Phillips and R. A. Shenoi

WEB z

shear and tensile loads between two orthogonal sets of plate panels meeting at a joint. Previous work” has shown that there are two principal modes of concern to naval architects. The first of these assumes a ‘worst case’ scenario with the side or bottom shell of the ship being punctured and one hold of the ship being flooded. This imposes a hydrostatic head, amplified by dynamic factors owing to roll, pitch and heave, on the bulkhead. The load transfer mechanism requires that the root of the bulkhead-to-bottom/ side-shell tee joint is capable of carrying vertical tensile loading as well as horizontal bending. This is best modelled as a 45” pull-off test, see Figure 2(a). The second scenario is more representative of normal ship operation with both sides of the bulkhead being subjected to similar loads in the holds and for the bottom and side shells to be subject to hydrostatic (and indeed dynamic) loadings. This can be modelled in laboratory as three point bend tests, see Figure 2(b). The justification for the loading modes is explored in more detail by Phillips2’. The mechanical properties of the materials used in the tee are given in Table 1.

1

OVERLAMINATE

FLANGE

GAP /

\

Figure

1

FILLET RESIN

A typical tee joint configuration

(a) 45 DEGREE PULL-OFF LOAD

I

1

-d

CONSTRAINTS .c

Degree pull-off tests lo I

f

THREEPOINT BENDING

Figure bend

2

Representative

load conditions:

LOAD

(a) 45” pull-off; (b) three point

The aim of this paper, therefore, is to propose an approach for evaluating damage tolerance of FRP structureszO in the critical regions of single skin tee joints. Specific objectives are: (a) to outline the sequence of failure inception and progression in tee joints under representative loadings and boundary conditions; (b) to characterise stress patterns in the joints under load and partial failure conditions; (c) to assess the significance of strain energy release rates (e.g. G- and J-integral) in establishing the structural integrity of tee joints with delaminations.

CHARACTERISTIC BEHAVIOUR OF TEE JOINTS UNDER REPRESENTATIVE LOADING Representative load conditions The primary function of a tee joint is to transmit flexural,

466

A typical load-deflection plot is shown in Figure 3(a). The figure shows that there is a significant drop in stiffness when the applied load reaches about 5 kN, indicating that delaminations have formed in the curved portion of the overlaminate. Further load application shows additional load carrying capability up to 11 kN resulting in further delamination and final failure at 15 kN. The sample failed initially by delamination in about the third ply from the inner surface of the boundary angle comer on the side in tension. The load carried by the joint dropped significantly. On applying further displacement (in this load-controlled test), it was found that the joint continued to carry load, with little reduction in stiffness. Final failure occurred when the remaining boundary angle plies delaminated and the fillet failed as a consequence. Figure 3(b) illustrates the final failure scenario.

Three point bending tests 22 A typical load-deflection plot is shown in Figure 4(a). The points marked A to D correspond to loads at which damage was observed in the tests, with details of these as follows. A at a load of about 5500 N a crack appeared in the fillet. ?? B at a load of 7500 N, the first delamination was seen in the boundary angle. ?? C between 10000 and 15 000 N, there was increasing delamination in different parts of the boundary angle. ?? D at a load of 19000 N there was final failure with complete debonding of the overlaminate/web and overlaminate/flange interfaces. ??

Figure 4(b) illustrates

the final failure scenario.

Damage

tolerance

of laminated

joints:

H. J. Phillips

and R. A. Shenoi

16

16 i

14 12

-

5

,-FEMODEL

10

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1’

FEMODEL2~

2;8

0

(a)

15

10

5

20

25

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10

5

DEFLECTION (mm) Figure 5 pull-off

Comparison

FILLET CRACK \

/

I

Figure 3 45” Pull-off: failure scenario

(a) experimental

load-deflection

11

plot; (b) final

18 16

’g

load-deflection

plot: 45”

ASSESSMENT

Element and modelling details

INITIAL DELAMINATION

1-r

20

of FE and experimental

STRENGTH-BASED

lh)

15

DEFLECTION(mm)

12

The theoretical modelling was carried out using the finite element analysis package ANSYS. The elements used to generate the models are four-noded structural solid elements with two translational degrees of freedom at each node23. Plane strain conditions are assumed to prevail since the joints on board ships can be considered wide in relation to the length and thickness. One element is modelled per layer of the overlaminate material which allows delaminations to be inserted, by separating manually two adjacent layers by a small gap. The boundary conditions are those of clamped (45” pull-off) and simple supports (three point bending). Linear analyses have been carried out in each case and the material properties are given in Table 1. Degree pull-off load

a’ 10

The stiffness and stress distributions of three FE models have been compared with published data obtained from similar tee joints”. The first model contains no inserted damage, the second contains a single delamination within the overlaminate on the tension side and the third model contains additional delamination in the overlaminate.

$8 6 4 2 0 0

(a)

5

10

15

20

25

30

35

DEFLECTION (mm)

/

\

’

DELAMINATIONS Ih'NNERPLIES OFO~~RL,~~~NATE

I

FILLET CRACKS

(b) I

Figure 4 Three point bend: (a) experimental final failure scenario

load-deflection

plot; (b)

Correlation with experimental load-deflection curve. Figure 5 shows a comparison of the first finite element model and experimental load/deflection plots. For an applied load of 5 kN, which is the load at which delaminations occurred in the experiments, the deflection calculated using Model 1 (representing the undamaged state) is equal to 3.48 mm. This corresponds very well with the equivalent value from the experimental load/deflection curve of about 4 mm. Using Model 2 (which incorporates the observed delamination) it can be seen that the deflection at a load of 11 kN is equal to 10 mm. This is less than the experimental value. A possible reason for this is that the delamination which was modelled did not truly represent the delamination which formed in the experiments. A greater value of deflection would be obtained if the

467

Damage tolerance of laminated joints: H. J. Phillips and R. A. Shenoi

Table 1

Material properties

used in the construction

Material Polyester/woven

roving glass

of single skin tee joints Location

Property

Value

Web, flange and overlaminate

E,

.___ 13 060 MPa 1710 MPa 0.25 207 MPa 6890 MPa 7770 MPa 0.25 I MPa 1500 MPa 1500 MPa 0.25 26 MPa 10000 MPa 0.25

E, Poisson ratio UTS PolyesterKSM

Overlaminate

Polyester/woven roving/CSM Urethane acrylate

Overlaminate Fillet resin

Cracked elements

Cracked region

EX EY Poisson ratio ILTS E* EY Poisson ratio UTS EX Poisson ratio

directly with the experimental findings for which delaminations occurred within the third ply from the inner surface of the overlaminate at a load of 5 kN. At a load of 11 kN, Model 2 gives rise to a maximum overlaminate throughthickness stress equal to 20 MPa in the inner regions of the overlaminate. This indicates that further delamination is likely at this load which corresponds with the experimental findings. At a load of 15 kN, Model 3 gives rise to a maximum overlaminate through-thickness stress equal to 6 MPa in the inner regions of the overlaminate which is not likely to cause further delamination. The maximum fillet principal stress, however, is equal to 30 MPa at this load, which is greater than the ultimate tensile strength (UTS) of the fillet of 26 MPa; This indicates that fillet cracking is likely at this load. This corresponds with the final failure seen in the experiments where there was no additional delamination but there was fillet cracking.

Three point bend load

Figure 6 Overlaminate pull-off load

through-thickness

stress distribution

under a 45”

delamination extends further around the radius of the overlaminate as this increases the flexibility of the joint. At a load of 15 kN, Model 3 (which includes additional delaminations in the overlaminate) gives a maximum deflection equal to 17 mm. This value is slightly less than the experimental value at this load indicating that the experimental damage may extend further around the radius than that modelled in the PEA. Comparison of finite element stress patterns with experimental damage. At a load of 5 kN, Model 1 gives a value of the maximum overlaminate through-thickness stress equal to 7.5 MPa in the inner regions of the overlaminate as shown in Figure 6. This value is larger than the quoted ILTS (or Interlaminar Tensile Strength) of 7 MPaZ4. In other words, from a stress-based view point, it is likely that the plies which have this high throughthickness stress will open out and separate, i.e. delamination is likely to occur. This theoretical prediction corresponds

46%

A total of six models, numbered l-6 have been generated to represent: (1) the undamaged tee joint; (2-5) the successive damage, A-D, noted in the experiments; and (6) a tee joint containing additional delamination. Correlation with experimental load-deflection curve. Figure 7 illustrates the comparison between the experimentally-derived load versus deflection (P/S) curve with points corresponding to each of the six models. It can be seen that the undamaged tee joint model (Model 1) gives very similar values of deflection and hence initial stiffness to those obtained from the linear section of the experimental load-deflection curve. From the values obtained for Models 2-5 respectively, it can be noted that there is gradual decrease in FE model stiffness. This is to be expected due to the increasing amounts of delamination which have been represented in the models. Although Model 5 represents similar damage to that of the experimental failure mode of the joint, the stiffness is significantly greater than the tested specimen, i.e. at a given load, the FE model gives rise to less deflection than the tested joint. Thus in an attempt to achieve similar deflections to those obtained from experiment, Model 6 has been analysed which contains the same damage as Model 5 but with further

Damage

tolerance

of laminated

joints:

H. J. Phillips

and R. A. Shenoi

16 i

[-

Experimental . FE MODEL 1~

. FE MODEL 2 j j x FEMODEL3~ i D FEMODEL4~ .

61

Figure 7 Comparison

of theoretical

FEMODEL5

+ FE MODEL 6

and experimental

load-deflection

plots: three point bending

delaminations along the web/overlaminate and flange/ overlaminate interfaces. This model gives values of deflection close to the experimental values although there is some difference, as can be seen from Figure 7. It is likely that there was internal damage which was not visible during the experiments. In addition, there may have been more delamination along the web/overlaminate and flange/overlaminate interfaces than was visible during the tests. This would account for the increased flexibility and hence deflection of the joint for a given load. To confirm this hypothesis, an FE model of the flange plate alone was generated and loaded in three point bending. The central deflection at a load of 19 kN equalled 27.7 mm which is within 0.8% of the experimental maximum deflection of the entire joint. This result shows that the tee joint behaviour is ultimately dictated by the stiffness of the flange plate. In addition, a finite element model has been generated to represent complete delamination along the entire overlaminate/flange interface. The fillet material elements, however, remained in contact with the flange. The value of the maximum deflection at the tip of the web for this model equalled 21.6 mm for an applied load of 19 kN. This suggests that there may have been substantially more delamination along the flange/overlaminate interface than could be observed from the experiments. Comparison of finite element stress patterns with experimental damage. The values of the maximum deflection, maximum fillet principal stress, maximum overlaminate in-plane stress and maximum overlaminate throughthickness stresses for the three point loading configuration are given in Table 2. Model 1. At a load of 5500 N the high principal stresses in the upper fillet corners indicate that damage is likely along the webioverlaminate interface. Figure 8(a) shows the principal stress distribution. The resulting stresses in

the fillet at a load of 5500 N equal to about 8.5 MPa would not be enough to cause failure of the fillet material which has a UTS of 26 MPa. It is possible that either an initial flaw or void was already present in the fillet due to fabrication processes. In order to check whether or not the presence of voids in the fillet gave rise to the experimental premature failure of the fillet, a finite element model containing voids in the fillet was generated. At a load of 5500 kN, the highest principal stress in the fillet was 14.3 MPa and the corresponding strain was 0.8%. Tests on small specimens of urethane acrylate resin25, which is the material used in the tee joint fillets, indicate that the ultimate tensile stress is about 16 MPa rather than the quoted value of UTS of 26 MPa (as given in Table I). Consequently, the presence of voids in the fillet and the fact that the UTS may be significantly less than the quoted value explain the premature fillet failure seen in the experiments. The maximum value of in-plane stress in the overlaminate occurs on its outer surface near the centre and is shown in Figure S(b). A value of 53 MPa is not enough to cause failure since the in-plane tensile strength of the overlaminate material is taken to be 207 MPa”. The highest value of through-thickness stress in the overlaminate is equal to 6.3 MPa and occurs in the inner three to four layers of the overlaminate in two distinct regions as shown in Figure 8(c). The value is approaching the ILTS of 7 MPa24 and indicates that at a load of approximately 6000 N, delamination is likely to occur. This is consistent with the location of the delaminations which were seen in the experiments. Model 2. At a load of 5500 N the principal stress in the fillet is lower than the fillet UTS of 26 MPa. In addition, the strains in the fillet were found to be of the order of 0.5% which is negligible when compared with the quoted elongation at break value of 100%. This result indicates that the fillet would not fail at this load. The through-thickness

469

Damage tolerance of laminated joints: H. J. Phillips and R. A. Shenoi

Table 2

Stress values for three point bending Models l-6

stress distribution at this load is similar to that for Model I at the corresponding load level and indicates that the delamination would progress. At a load of 7500 N at which the first signs of delamination were visible, high throughthickness overlaminate stresses occur near the lower fillet comer, indicating that there would be delamination along the flange/overlaminate interface. Model 3. At a load of 7500 N high regions of throughthickness overlaminate stresses occur in the central regions of the overlaminate where the delaminations are present indicating that further damage in these regions is likely. When the load is increased to 10 000 N, a much greater region of high through-thickness overlaminate stresses is present which is consistent with the observed failure at this load indicating numerous delaminations in this region.

470

Model 4. At loads of 10000 N and 19 000 N, regions of high through-thickness overlaminate stresses indicate that delaminations are likely along the web/overlaminate and flange/overlaminate interfaces. This is consistent with the experimental findings. Failure due to overlaminate in-plane stresses would not be predicted to occur at a load of 15 000 N since the maximum stress value is less than the ultimate tensile strength of 207 MPa. At a load of 19 000 N, however, the maximum in-plane stress in the overlaminate is greater than the ultimate stress and thus damage is predicted at this load. Model 5. At a load of 19 000 N stresses in the fillet are still low and not great enough to cause the experimentally observed failure. As indicated earlier, the fillet failure is likely to have been due to imperfections or

Damage

tolerance

of laminated

joints:

H. J. Phillips

and R. A. Shenoi

MAX. VALUE = 8.6 MPa

i (b)

6-4

I

Cc) Figure 8 Figure 8 Stress distributions thickness tensile stress in overlaminate

under three point bending:

(a) principal

flaws. Importantly, stress patterns in the overlaminate seem to mirror adequately the damage scenario seen in the experiments. The maximum values of the overlaminate throughthickness stress have reduced significantly indicating that further delamination is unlikely. The introduction of the delaminations into the model has the effect of relieving these stresses within the boundary angle. The in-plane stresses, however, are much greater than the ultimate stress level at loads above 1.5000 N. This would indicate damage on the outer surface of the boundary angle. ModeE 6. This model represents the damaged joint as observed from experiments

completely at the load

stress in fillet; (b) in-plane

direct stress in overlaminate;

(c) through-

of 19000 N as well as additional delamination along the web/overlaminate and flange/overlaminate interfaces. The stress distributions yielded from this analysis are similar to those generated for Model 5. The overlaminate in-plane and through-thickness stresses are lower than the equivalent ultimate values thus suggesting that no further damage or delamination is likely. Identijkation of delamination prone areas. The series of models has given an indication of the stiffness reduction due to the progressive delaminations within the joint. As a result of the stress analyses it has been possible to identify the regions which are most susceptible to damage. These are

471

Damage tolerance of laminated joints: H. J. Phillips and R. A. Shenoi

WEB -w_____

v

OVERLAMINATE

FLANGE FILLET RESIN

r

/I

I

Flat Region (seeFigure 10(b))

(a) (a) CRACK TIP

CRACK TIP +

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“1 (c) Figure 10 Typical FE models used in the fracture studies: (a) schematic of crack locations; (b) straight cracks; (c) curved cracks

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(c)

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6

7

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Node Position

Figure 9 Stress variations through overlaminate: (a) path location; (b) inplane direct stress; (c) through-thickness tensile stress

472

the curved regions of the overlaminate which are most prone to delamination. In order to understand fully the load transfer mechanisms within the joint, it is necessary to investigate the overlaminate in-plane direct stress and through-thickness stress distributions along a path as shown in Figure 9(a). The tee joint which has been investigated in this manner is the tee joint FE model (Model 1) under a three point bending load of 7.5 kN. This is the model representing the undamaged tee joint and the load level at which the first delamination occurred in the experiments. The overlaminate in-plane and through-thickness stresses at all the nodal locations along the path have been calculated. The in-plane stresses and through-thickness stresses calculated along the path are given in Figure 9(b) and (c). In the figures, ‘1’ is the innermost node defining the

Damage

tolerance

overlaminate and ’12’ is the outermost node of the overlaminate, at the outer surface. Figure 9(b) shows that the value of the in-plane stress is greatly dependent upon the type of material present in each layer. The values of the in-plane stress have been calculated at nodes along the path which are at the interface between two layers of the overlaminate with one element modelled per layer. The graph shows distinct peaks at the nodes which are at the interface between a layer of WR and a layer of CSM (nodes at positions 3, 4, 6, 7 and 9). This is due to the difference in the values of the in-plane stiffnesses of the WR and CSM layers. The nodes at positions 10, 11 and 12 are located between layers of WR. The outer regions of the overlaminate are under the highest in-plane stresses. Figure 9(c) shows that the through-thickness overlaminate stresses in the region close to the fillet are greater than the ILTS of 7 MPa. The node in position 1 is in the exact location of the maximum through-thickness stress at this load. The through-thickness stress gradually decreases towards the outer layers of the overlaminate. This corresponds with the experimental findings that a delamination occurred within approximately ply 3 of the overlaminate under a three point bending loadz2. It has been shown that the delaminations form in the inner regions of the overlaminate due to high throughthickness stresses. These delaminations have the effect of reducing the through-thickness stresses. On further loading the through-thickness stresses cause additional delaminations. There reaches a point when the through-thickness stresses have dropped significantly, even at high loads, and thus delamination due to through-thickness stresses ceases. However, the presence of the delaminations in the inner regions of the overlaminate causes an increase in the in-plane stresses in the outer regions of the overlaminate. Thus, damage is subsequently caused in these outer regions due to high in-plane stresses.

ENERGY-BASED

Model&g

ASSESSMENT

details

The FE model used to represent the undamaged tee joint (Model 1) has been adapted so as to include a region in which delaminations (or cracks) can be modelled. As shown in the previous section, most delaminations were observed in the overlaminate region of the joint. Therefore, all the models generated in this section contain cracks which are within the overlaminate region. Figure 10 shows locations of the two regions that have been meshed with crack elements. Figure IO(a) shows a schematic of a typical tee, with the zones defining the flat and curved regions used in the analysis. Figure IO(b) and (c) show the finite element mesh details of the flat region, where the overlaminate joins the ‘flange’ of the tee, and the curved region around the radius of the tee respectively. These regions contain the crack elements which are six-noded triangular elements with their mid-side nodes at the quarter point. Conditions of

of laminated

joints:

H. J. Phillips

and R. A. Shenoi

plane strain have been assumed since the tee joints are considered to be long in relation to their width. Gap elements have been included to prevent interpenetration of the two crack faces.

Loads, material properties

and boundary conditions

The applied load chosen in all cases is 10 kN which is the load at which a significant amount of delamination occurred in the tee joints when loaded under both three point bending and 45” pull-off configurations. Since the latter is more severe, that has been chosen as the relevant boundary value problem.

Calculation

of fracture parameters

Values of strain energy release rate, G, have been calculated in addition to values of the J-integral, J. Both have been estimated using routines pre-existing within the ANSYS suite. For the J-integral calculation, the users need to define a path along which the integral is evaluated. In order to prove convergence, several different paths were generated; it was confirmed that the value of J-integral was fairly consistent for the different paths. Since the tee joint behaviour is linear-elastic, the values of G are numerically equal to J and both can be compared to ensure consistency. Appendix A outlines the strain energy concepts used in this context.

Sensitivity studies The effects of crack depth and crack length have been investigated for both straight and curved cracks. Effect of crack depth. Figure 11 gives the values for the J-integral for the different crack configurations for both (a) straight and (b) curved cracks. The results indicate that for both types of crack, the J-integral values are greater for cracks close to the inner surface of the overlaminate, i.e. deep cracks are most likely to propagate. Efect qf crack length. In the case of a straight crack, the J-integral values for four different crack lengths have been calculated and are shown in Figure 12. The right hand crack tip (marked + in Figure IO(b)) in each case remained in the same location and the length of the crack has been determined by the position of the left hand crack tip. It can be noted from the graph that long straight cracks give rise to higher values of the J-integral than shorter cracks. In the case of curved cracks, a series of nine models have been generated containing cracks of different lengths at approximately the mid-depth of the overlaminate. The right hand crack tip (marked + in Figure IO(c)) remained in the same location. The other tip was moved to nine different locations around the radius of the overlaminate. It should be pointed out that the left tip of the longest crack extends into the vertical region of the overlaminate adjacent to the web. The dotted line in Figure 13 shows

473

Damage

tolerance of laminated

joints:

H. J. Phillips

and R. A. Shenoi

0.03

0.025

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0

5

IO

15

20

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ply depth (no.plies f?om outer surface)

crack length (mm)

Figure 12 Effect of crack length on J-integral (crack depth = 6 mm)

values for straight cracks

3.0

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” 2.0 E 3 Y a 1.5

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ply depth (no.plies ffom outersurface)

0: Figure 11 Effect of crack depth on J-integral

values: (a) straight crack (crack length = 10 mm); (b) curved crack (crack length = 36 mm)

the values of the J-integral calculated at the right hand crack tip, for each of the nine crack lengths. The results show that the maximum value of the J-integral at the right hand end occurs for a crack of length 35 mm. In this case the left hand crack tip is well into the curved portion of the overlaminate. The critical value of the strain energy release rate for the overlaminate material is quoted to be equal to 0.5 kJ m226. From the trends, it is evident that cracks longer than 16 mm are likely to propagate under these conditions. In order to calculate the values of the J-integral at the left hand crack tip, it has been necessary to generate additional finite element models with a linear crack face close to the left hand tip. Four models representing cracks of four different lengths have been generated and strain energy release rates and J-integral values calculated at the left hand crack tip. The dashed line in Figure 13 shows the J-integral values and strain energy release rate values calculated at the left hand tip, for cracks at approximately mid-depth. The results

474

0

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I

I

5

10

15

20

25

30

35

40

Distance around curve between Ih and rh crack tip (mm)

Figure 13 J-integral and strain energy release rate values calculated both crack tips for curved cracks (crack depth = 6 mm)

at

calculated at the left hand tip are higher than those at the right hand tip. This is to be expected, since the throughthickness stresses in the curved region of the overlaminate are much greater than those in the flat region of the overlaminate and consequently give rise to greater values of the mode I stress intensity factor. The curve for the left hand tip has a peak prior to that for the right hand tip. This indicates that the crack tips approaching the curved region are more likely to propagate than those in the flat region of the overlaminate. The critical strain energy release rate for the overlaminate material has been taken as 0.5 W/m’. Assuming this critical value, the critical crack length based on the values at the left hand tip can be calculated to be 8 m. This is half the critical crack length of 16 m based on the values at the right hand tip. This therefore indicates that the crack is more likely to propagate at the left hand tip into the curved region of the overlaminate.

Damage

Figure 14 assessment

Locations

of crack tips in the overlaminate

COMPARISON OF STRENGTH-BASED ENERGY-BASED APPROACHES

tolerance

for comparative

AND

Both the approaches discussed above have their merits and shortcomings. The strength-based assessment allows the locations of the highest stresses to be determined. Once a delamination has been inserted in the model in this high stress region, the stresses can again be calculated to determine additional regions under excessive stresses. The presence of the delamination in the model, without accurate interpretation, can cause misleading results due to stress singularities at the delamination tips. The energy-based approach gives accurate results for the strain energy release rates indicating the likelihood of crack propagation. These results, however, are calculated from a finite element model which involves certain limitations. For example, the material modelled in the cracked region of the overlaminate is assumed to be homogeneous. This is not actually the case. Thus, both the strength-based and energybased approaches have some unique peculiarities. In the analysis which follows, the two approaches are used in order to predict whether a delamination (or crack) in the curved region of the overlaminate would propagate under a 45” pull-off load of 10 kN. This loading configuration has been shown to be the most severe.

Strength-based

assessment

The material properties of the models are the same as those discussed previously and are given in Table 1. Two FE models have been generated to represent a tee joint containing a single delamination of two different lengths. Figure 14 shows the schematic of the two delaminations: A-A* and B-B*. The delamination in both cases has been modelled at a depth of six plies from the outer surface of the overlaminate on the tension side. The delamination extends from the flat region above the flange around the radius. The two crack tips are marked A and A* in one model and B and B* in the other model. The overlaminate in-plane and through-thickness stress distributions have been analysed and the maximum values recorded in both cases. In the case of crack A-A*, the maximum value of the overlaminate in-plane stress is 141.1 MPa in the outer plies of the overlaminate. The maximum value of the overlaminate through-thickness stress is 10 MPa at the tip

of laminated

joints:

H. J. Phillips

and R. A. Shenoi

marked A*. From this it can be concluded that under this load, the crack would propagate around the radius since the maximum through-thickness stress is greater than the ILTS value. see Table 1. The stress distributions for crack B-B* are similar to those for crack A-A* but the stress magnitudes are higher. The maximum overlaminate in-plane stress is 211 MPa and the maximum overlaminate through-thickness stress is 30 MPa at the tip marked B*. Damage would be expected due to the excessive in-plane stress which is greater then the UTS of the material of 207 MPa. The maximum through-thickness stress is greater than the ILTS (see Table I) and consequently, further delamination would be predicted. Values of through-thickness stress greater than the ILTS are also predicted at the tip marked B. Thus, further delamination would be predicted from both ends of the existing delamination.

Energy-based

assessment

Two FE models have been generated which contain a single curved crack in the same locations as the delaminations which have been modelled for the strength assessment above. For the short crack, A-A*, the value of the J-integral is calculated to be 0.2 kJ/m* at tip A and 0.7 kJ/m* at tip A*. Consequently, crack propagation would be predicted from the tip marked A* only. For the long crack, B-B*, the value of the J-integral is calculated to be 2.9 kJ/m’ at tip B and 3.4 kJ/m* at tip B*. Thus, crack propagation would be predicted from both crack tips at this load.

Comparison

qf results

The strength-based approach has shown that under a 10 kN 45” pull-off load, the short delamination would be expected to grow around the radius due to high throughthickness stresses. The energy-based approach is in direct correlation with this result, predicting that crack propagation would occur around the radius due to a value of the J-integral greater than the critical value. Also, both approaches suggest that further delamination is likely from both tips in the case of the longer delamination. Thus there seems to be a convergence of results in predicting the tolerance of a structure to delaminations using both stress and fracture criteria.

DISCUSSION The FE models containing delaminations can appropriately represent the stiffness reduction due to delamination which has been seen in three point bending experiments. In addition, the resulting internal stress distributions indicate regions of high through-thickness stresses within the overlaminate. These regions, which would be likely to delaminate, correspond with the regions of the tested tee joint overlaminate which contained delaminations. The reason why the finite element model did not correctly predict fillet failure is explained by the fact that

475

Damage

tolerance

of laminated

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H. J. Phillips

the experimental tee joints contained a significant number of voids which reduced the UTS of the fillet material. Finite element models containing voids in the fillet successfully predicted that premature failure would have occurred since the voids had the effect of increasing the fillet principal stresses. Under three point bending, the presence of the delaminations in the overlaminate has the effect of relieving the stress which enables the structure to continue sustaining load. On further loading, the through-thickness stresses increase again thus causing more delaminations. This damage continues as the load is increased. This is shown well by comparing the through-thickness stresses for Models 3 and 4 at a load of 10000 N shown in Table 2. For Model 3 the equivalent value is 10.7 MPa which would result in delaminations forming since it is greater than the ILTS. For Model 4, the maximum value of throughthickness stress is 5.5 MPa which does not indicate that delaminations are likely to form. As the load is again increased for Model 4, the through-thickness stresses increase above the ILTS and thus indicate the likely formation of delaminations. The in-plane stresses in the outer regions of the overlaminate increase as the amount of delamination increases in the inner regions. It can, therefore, be concluded that initially, the delaminations arise on the inner surface of the overlaminate due to the presence of high through-thickness stresses. As loading increases, the delaminations which form have the effect of relieving the through-thickness stresses but cause the in-plane stresses to increase and ultimately cause damage close to the outer surface of the overlaminate. The current modelling is restricted to stresses arising from mechanical loading only. It is well recognised that the structures have locked-in stresses generated from fabrication processes. Such cure-based, thermal stresses have not been incorporated in the present modelling. It is desirable that future work attempts to examine the influence of such production-related factors on the response and failure patterns. The fracture mechanics results show that deep cracks give greater values of the J-integral than surface cracks and long straight cracks give greater values of the J-integral than short straight cracks. In the case of the curved cracks, the critical length of a crack which will propagate under a 45” pull-off load with clamped boundaries subjected to a load of 10 kN is 8 mm for values calculated at the left hand tip and 16 mm for values at the right hand crack tip. The fracture analysis assumes that the cracks shall propagate along the existing line of the crack face, i.e. it does not take into account delaminations which are prone to jumping across interfaces. In addition, the FE models generated here assume that cracks have pre-existed in specific locations. In reality, cracks arise due to high through-thickness stresses or stress concentrations. For example, the formation of a delamination serves so as to relieve the local stress. As loads increase, however, they may cause the formation of a new delamination in an additional region of high stress rather than propagation

476

and R. A. Shenoi

of the initial crack. For these reasons, a crack extension analysis would give a more accurate estimation of the full extent of the damage tolerance of the tee joints. The method discussed here does, however, draw our attention to the most damage critical areas within the joint and also to those most prone to delamination damage. In addition, critical crack lengths can be calculated which determine the damage tolerance of the tee joints. A comparative study of stress- and fracture-based analysis showed that it is possible to achieve convergence of results for predicting damage tolerance in the two cases. The example presented, confirmed crack growth at a load of 10 kN, which is consistent with test results.

CONCLUSIONS The main conclusions are as follows:

(2)

(3)

(4)

(5)

(6)

which can be drawn from this work

The region of a tee joint which is most susceptible to damage under both 45” pull-off loads and three point bending loads is the curved region of the overlaminate. In the overlaminates, excessive in-plane stresses occur at the interface of the chopped strand mat layers and the woven roving layers. Hence, damage is likely in these locations. An iterative procedure has been used to character&e the damage which occurs in tee joints under a three point bending loading. Three important features have been brought out as a result. Firstly, the initial delaminations which form in the inner regions of the boundary angle are caused by excessive through-thickness stresses. Secondly, the delaminations which form have the effect of relieving the stresses and allowing further loading to take place. Thirdly, the subsequent damage which forms in the outer regions of the boundary angle is caused as a result of high in-plane stresses. The results from the energy-based approach show that curved cracks in the boundary angle are likely to propagate around the radius. This is consistent with the three point bending tests in which delamination damage occurred primarily in the curved region of the overlaminate. Deep cracks within the overlaminate are much more likely to propagate than cracks near the surface and must, therefore, be closely monitored in existing vessels. It has been shown that stress- and fracture-based criteria yield similar results in predicting damage tolerance of tee joints.

ACKNOWLEDGEMENTS The work presented in this paper was funded by the Mod/EPSRC. We are grateful to Lt Cdr. Mark Gray (MOD), Prof. John Sumpter, Richard Court, David Elliott, Philip Lay, Andrew Swift and Richard Trask (DRA) for their helpful discussions during the project.

Damage

tolerance

APPENDIX

of laminated

joints:

H. J. Phillips

and R. A. Shenoi

strain energy release rate and hence the strain energy release rate can be calculated from:

A. Fracture mechanics

criteria for damage modelling G=

(K,2 +Kh+ 1)

Irwin27 developed the stress intensity approach from linear elastic theory. In the region of the crack tip, the stress intensity factor, K, determines the magnitude of the elastic stresses. The value of K, shown in eqn (1) depends upon the magnitude of the applied stress, s, the length of the crack, 2a, and a parameter which depends upon the crack and specimen geometry, f(alW) where W is the specimen width. K=a&f

(

;

>

Irwin proved that the achievement of a critical stress intensity factor, Kc, is exactly equivalent to the Griffith-Irwin balance approach. This requires that the achievement of a stored elastic strain is equal to Gc. For tensile loading, the relationships between Kc and Gc is given in eqn (2) for plane stress. 7 G,. = s

c-3

8~

A 1. Elastic stress jield approach

plane stress

(2)

All stress systems in the vicinity of the crack may be derived from three modes of loading, (a) mode I which is the opening mode, (b) mode II which is the sliding mode, and (c) mode III which is the tearing mode. The mode I elastic stress field equations can be expressed in terms of principal stresses which are in turn written in polar coordinates2’. Similar expressions for modes II and III can also be written.

A3. The J-integral

The use of linear elastic fracture mechanics (LEFM) may not always be applicable, for example in the case of ductile materials where the crack tip plastic zone is too large. It is therefore necessary to identify alternative parameters to analyse elastic-plastic fracture mechanics (EPFM) problems. The J-integral 29 is based on an energy balance as with the strain energy release rate, G, in the case of LEFM. Eqn (4), given above, remains valid as long as the material behaviour remains elastic but it need not necessarily be linear. An important consequence of this is that this nonlinear elastic behaviour can be used to represent the plastic behaviour of a material. One restriction of its use, however, requires that no unloading occurs in any part of the body. This is because in actual plastic behaviour, the plastic part of the deformation is irrecoverable. Hence the non-linear equivalent to the LEFM parameter, G can be given as J, the J-integral. The J-integral is a path independent line integral which measures the magnitude of the singular stresses and strains near a crack tip:

A2. Energy balance approach

The mode I strain energy release rate, G,, can be written in terms of the mode I stress intensity factor, K,, from eqn (2), and eqn (1) for f(alW) = 1 (infinite plate) as shown in

where: G is any path surrounding the crack tip W is strain energy density (strain energy per unit volume) t, is the traction vector along the x-axis (uxnx + uTyny) t, is the traction vector along the y-axis (cvny + a+,) s is the component stress n is the unit outer normal vector to path G u is the displacement vector s is the distance along path G

eqn (3). 2

G, = $

plane stress

The strain energy release rate, G, can be considered to be the amount of energy which is available for crack extension and can be written in terms of the three stress intensity factors for mixed mode behaviour: G=

(K?+&(K+1) I K& 8P

2P

(4)

where: K, is the mode I stress intensity

factor; factor; K,,[ is the mode III stress intensity factor; p is the material shear modulus; K is the conversion factor between conditions of plane strain and plane stress (equal to 3-4~ for plane strain conditions); v is the material Poisson’s ratio. K,, is the mode II stress intensity

The J-integral approach may be used for nonlinear elastic materials and thus can be used in a wider variety of problems than the strain energy release rate, G, which is only valid in the case of linear elastic behaviour. For linear elastic materials, the J-integral is related to the stress intensity factors in a similar manner as the strain energy release rate (eqns (4) and (5)) i.e. for linear elastic materials, J = G. A crack will propagate if the calculated value of the strain energy release rate (or J-integral) is greater than or equal to the material critical strain energy release rate.

REFERENCES For the case where only modes I and II are applicable, mode III is assumed to give a negligible contribution to the

I.

Godwin. E.W. and Matthews,

F.L., Cmnposites,

1980, 11, 165

477

Damage tolerance of laminated joints: H. J. Phillips and R. A. Shenoi 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

478

Matthews, F.L., Kilty, P.F. and Godwin, E.W., Composites, 1982, 13, 29. Goland, M. and Reissner, E., J. Appl. Mech., 1944, 11, A-17. Harris, J.A. and Adams, R.D., ht. J. Adhesion andAdhesives, 1984, 4, 65. Tuzi, I. and Shimada, H., Bulletin JSME, 1964, 1, 263. Wooley, G.R. and Carver, D.R., J. Aircraft, October 1971, p. 817. Lees, W.A., Adhesives in Engineering Design. The Design Council, London, 1984. Smith, C.S. in Proc. Symp. GRP Ship Construction, R.I.N.A., London, October 1972, p. 33. Gillespie, J.W. and Byron-Pipes, R., J. Comp. Muter., 1978, 12,408. Shenoi, R.A. and Hawkins, G.L., Composites, 1992, 23, 335. Shenoi, R.A. and Violette, F.L.M., J. Comp. Muter., 1990,24,644. Theotokoglou, E.E. and Moan, T., J. Comp. Mater., 1996,30, 190. Hawkins, G.L., Holness, J.W., Dodkins, A.R. and Shenoi, R.A., Plastics, Rubber, Camp. Process. Applic., 1993, 19, 279. Dulieu-Smith, J.M., Shenoi, R.A., Read, P.J.C.L., Quinn, S. and Moy, S.S.J., J. Appl. Comp. Mater., 1997, 4, 283-303. Shenoi, R.A., Read, P.J.C.L. and Hawkins, G.L., ht. J. Fatigue, 1995, 17, 415. Clark, J.L. (ed.), Structural Design of Polymer Composites-

17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 21. 28. 29.

EUROCOMP Design Code and Handbook, E and FN Spon, London, 1996. Cable, C.W., Marine Technology, 1991, 28, ~91. Brewer, J.C. and Lagace, P.A., J. Camp. Mater., 1988,22, 1141. Partridge, C., Waechter, R.T., Williams, J.F. and Jones, R., Theor. and Appl. Fract. Mech., 1990, 13, 99. Phillips, H.J., Ph.D. Thesis, University of Southampton, 1997. Hawkins, G.L., Ph.D. Thesis, University of Southampton, 1994. Elliott, D.M., Mechanical Testing of Composite Joints, Report DRAlAWiAWSfTR94212, April 1994. ANSYS User’s Manual Version 5, Swanson Analysis Systems, Houston PA, 1992. Bird, J. and Allan, R.C., Proc. 7 th Int. Cof Exp.1 Stress Anal., Haifa, Israel, 1982, 91. Read, P.J.C.L., Ph.D. Thesis, University of Southampton, 1997. Court, R.S., Fracture Toughness of Woven Glass Reinforced Composites, Report DRA/SMC/CR943 111. December 1994. Irwin, G.R. and Kies, J.A., Welding J., Res. Suppl., April 1954, p. 193s. Ewalds, H.L. and Wanhill, R.J.H., Fracture Mechnnics, Arnold and DUM, 1986. Rice, J.R., J. Appl. Mech., 1968, 35, 379.