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Damage mechanics of top-hat stiffeners used in FRP ship construction
Marine Structures 12 (1999) 1}19
Damage mechanics of top-hat sti!eners used in FRP ship construction H.J. Phillips , R.A. Shenoi *, C.E. Moss Hamworthy Marine Technology Ltd., Poole, UK Department of Ship Science, University of Southampton, Southampton, Highxeld, Hants SO17 1BJ, UK B.M.T. (Defence Services) Ltd., Bath, UK Received 29 May 1997; received in revised form 14 January 1999; accepted 18 January 1999
Abstract This paper is concerned with the assessment of damage tolerance of a top-hat sti!ener to plate connection in FRP marine structures. The subject is addressed in two parallel schemes, using stress-based and fracture-dependent criteria. Numerical modelling is used to determine the internal load transfer characteristics and failure mechanisms in top-hat sti!eners under typical loadings seen in practice. The "nite element models are benchmarked against published test results, which include phenomena such as delaminations. The models are then extended to include crack elements, which are employed to calculate the strain energy release rates in the form of G values. The result from this modelling is compared against typical experimentally derived data pertaining to G values for the materials in question. Finally, an attempt is made to compare the results of the studies using the two approaches and to judge the overlap. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Fibre-reinforced plastic (FRP); Ship structures; Top-hat sti!eners; Finite element analysis; Delamination; Strain energy release rates; Damage tolerance
1. Introduction The sti!ness of large unsupported panels constructed of "bre-reinforced plastic (FRP) materials is inherently low. Thus, it is necessary to sti!en such panels by a
* Corresponding author. Tel.: #1-44-1703-592316; fax: #1-44-1703-593299. E-mail address: [email protected] (R.A. Shenoi) 0951-8339/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 1 - 8 3 3 9 ( 9 9 ) 0 0 0 0 3 - 9
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Fig. 1. A typical top-hat sti!ener.
suitable method. The most prevalent form is the use of top-hat sti!eners. A typical con"guration of the sti!ener is shown in Fig. 1. The present fabrication method starts with the laying-up of the unsti!ened base plate panel. Rigid foam cores are then laid on these panels in the locations where the extra sti!ness is desired. Then, an adequate amount of "lleting resin is injected into the recess between the foam and the plate panel and the required radius is scraped out. Next, a resin-impregnated cloth, or overlaminate, is laid across the crown (or table), down the web and around the "llet onto the base plate. A similar cloth run is carried out for the opposite side. The process of overlaminating is repeated a number of times, frequently with as many as 24 plies, to achieve the desired sti!ness. Occasionally, a limited number of unidirectional plies may be applied to the crown to obtain extra sti!ness. The reinforcement material for the web, #ange and overlaminate is E-Glass woven roving and chopped strand mat; the resin matrix is isophthalic polyester resin. Although top-hats are a critical part of the ship's structure, it has received surprisingly little attention in the open literature. Early reported work [1,2] was in connection with the development of the "rst GRP minehunter and dealt mainly with the gross problems of qualifying design concepts with regard to a speci"c application. This was extended to develop a more fundamental understanding of the top-hat behaviour through theoretical modelling [3,4]. Such early modelling attempts were necessarily restricted because of the relatively immature nature of the available "nite element types. There was also some fundamental work on the use of novel "lleting materials, with large strain to failure capability, and their application to marine joints
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and top-hat sti!ening purposes [5]. E!ort was also now being directed towards various failure scenarios. One of the principal cases involved overall panel instability and sti!ener-plate interaction under compressive loading [4,6]. The second approach focused on the transfer of load at the top-hat sti!ener to plate connection through the orthogonal or out-of-plane direction under static loading conditions [7,8]. Guidance on this subject in existing design regulations is minimal [9}11]. This is all the more important because many ships have now been in operation for over 20 years and are seeing sustained damage at the roots of the joints in the form of delaminations. It is thus essential that a systematic study is carried out with regard to the localised behaviour of a top-hat sti!ener to plate connection and its response under the presence of cracks or delaminations. The purpose of this paper is three-fold: (a) to understand the behaviour of a top-hat sti!ener under static loading and the mechanisms of load transfer and failure; (b) to study the in#uence of delamination cracks on strain energy release rates; and (c) to propose a uni"ed approach to categorise damage tolerance levels in FRP structures in the regions of top-hat sti!eners.
2. Strength-based assessment 2.1. Purpose of analysis The main aim of this analysis is to identify how the load is transferred from an in-plane direction in the base panel to an orthogonal direction in the plane of the web. The transfer is achieved through the overlamination and "lleting material. It is essential to categorise the stress states within the di!erent constituent elements of the joint. These stresses can then be used to assess the likely causes of failure in the joints. The three main possibilities are delamination in the overlaminate, cracking of the "lleting resin and braking of the "bre plies in the overlaminate. 2.2. Physical characterisation of joint behaviour Three load con"gurations were adopted for the test programme [12]; these were the three-point bend, reverse bend and straight pull-o!, as shown schematically in Fig. 2. Both the three-point and reverse bend tests aim to simulate gross panel deformation and its e!ect on the top-hat connection. The pull-o! test is designed to simulate inertial loadings on the sti!ener under impact and explosion loadings. In all cases the load-de#ection plots were linear up until failure. The structural sti!nesses in the three cases are listed in Table 1. In case of the three-point bend test, specimens "rst showed damage at about 13.5 kN when the "llet-to-overlaminate interfaces failed. Subsequent loading caused progressive through-thickness delamination in the inner region of the overlaminate and the onset of cracking along the overlaminate-to-#ange joints from the cracks in the "llet. Final failure occurred by #exural failure on the tension surface under the top of the top-hat (see Fig. 3a).
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Fig. 2. Loading con"gurations for the experiments: (a) three-point bend; (b) reverse bend; (c) pull-o!.
H.J. Phillips et al. / Marine Structures 12 (1999) 1}19 Table 1 Experimental failure loads and de#ections Loading con"guration
Three-point bend Reverse bend Pull-o!
Sti!ness
(kN/mm)
Experimental
FEA
909 600 952
750 458 667
Fig. 3. Experimental failure modes: (a) three-point bend; (b) reverse bend; (c) pull-o!.
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In the reverse bend tests, "rst signs of damage were observed at a load of 5 kN at which point cracks appeared in the "llets on both sides. Final failure occurred at a load of 14 kN due to tensile action on the inner surface at the centre of the #ange, as shown in Fig. 3b. In the pull-o! tests, cracks appeared at the #ange-to-"llet interface at a load of about 5.5 kN. These cracks extended and joined together with increased load, until at a load of 7 kN overlaminate was severed completely from the #ange on one side (see Fig. 3c). 2.3. Features of the FE models A series of models was generated in the ANSYS "nite element analysis package using two dimensional solid elements (which possess three translational degrees of freedom at each node); see Fig. 4 for a typical model. Each of the 12 layers in the overlaminate was represented by one element through the thickness. The #ange plate of the top-hat sti!ener has been represented by one element through the thickness. Conditions of plain strain have been assumed throughout. The loads applied to the structural model attempt to mimic those in the experimental investigation. For each of the three test con"gurations, stress distributions have been computed (i) at the load at which initial damage was noted and (ii) at the failure load of the sti!ener. The material properties used in the FE model generation were obtained from previous work at Southampton [8] and from parallel work at DERA Rosyth [12]; the relevant properties are given in Table 2. 2.4. Stiwness characterisation The "rst step is to validate the FE models by comparing the model sti!ness with that of the equivalent tested specimen. The FE model and experimental initial
Fig. 4. A typical "nite element model for strength calculations.
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Table 2 Material properties used in the FE modelling Material
Location
Property
Value
Polyester/woven roving glass
Sti!ener, #ange and overlaminate
Ex
13,060 MPa
Ey nuxy Ex Ey nuxy Ex Gxy nuxy
7770 MPa 0.25 1500 MPa 1500 MPa 0.25 10\ MPa 10\ MPa 0.25
Urethane acrylate
Fillet
Core material
Table 3 Comparison of sti!nesses } experimental versus FEA Three point bending (3PB)
Reverse bending (RB)
Straight pull o! (PO)
FE (N/mm)
Expt. (N/mm)
FE (N/mm)
Expt. (N/mm)
FE (N/mm)
Expt. (N/mm)
731.2
696.8
713.0
384.6
930.0
1000
sti!nesses of the top-hat under each of the three loading con"gurations are shown in Table 3. It is evident that for the three-point bend and the straight pull-o! tests there is quite good correlation between the two sets of values. There is however a discrepancy as far as the reverse bend results are concerned. 2.5. Stress patterns The stress distributions of interest are the "llet principal stress, overlaminate through-thickness and in-plane stresses, #ange plate through-thickness and in-plane stresses. It is also necessary to compare the load transfer mechanisms predicted from the FE models with some experimentally derived failure modes. Table 4 shows the value and location of the maximum stress for each load level and load con"guration for the top-hat sti!ener. 2.5.1. Three-point bending The most signi"cant stress patterns for the top-hat at the experimental initial load of 13.5 kN are shown in Fig. 5a for the overlaminate through-thickness stresses and Fig. 5b for the #ange in-plane stresses. The magnitude of the "llet principal stress is the greatest in the central region in the "llet as shown in Table 4 but is less than the
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Fig. 5. Stress distributions in three-point bend con"guration: (a) overlaminate through-thickness stress; (b) #ange in-plane stress.
Table 4 Locations and values of maximum stresses
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ultimate value. Thus, the "llet is unlikely to fail at this load. The region under the greatest in-plane stress in the #ange is in the inner central part below the core; this however is unlikely to cause failure. The region of the #ange under the highest through-thickness stress is in the outer central part as shown in Table 4. The region of the overlaminate which is subject to both the highest in-plane and through-thickness stresses is the outer region in the curved part above the "llet as shown in Fig. 5a. Delaminations are likely to form here due to high through-thickness stresses. The value of the maximum principal stress in the "llet at the sti!ener experimental failure load of 16.5 kN is 18.09 MPa. The ultimate tensile strength (UTS) of the "llet material in the literature [13] is quoted at about 26 MPa, so the "llet would remain intact at this load. This corresponds to the failure mode in the experiments in which the "llet itself did not crack. The initial damage was seen along the interface of the "llet with the overlaminate. The through-thickness stress at the initial failure load of 13.5 kN, however, is greater than the quoted interlaminar tensile strength (ILTS) of 7 MPa for the woven roving/polyester [14]. Hence, the FE model predicts that delaminations would occur near to the outer surface of the overlaminate at 13.5 kN due to through-thickness stresses greater than the ILTS of the material. This exactly matches the experimental "ndings. A similar match is obtained for the #ange failure cause. At 16.5 kN the in-plane stress in the #ange is 208 MPa which is greater than the UTS of the material. The FE model predicts that the #ange plate would fail in the centre of the upper surface at a load of 16.5 kN, which again mirrors the experimental "ndings.
2.5.2. Reverse bending At a load of 5 kN, the "llet principal stress is 4.8 MPa which is much less than the UTS of 26 MPa. The FE model, therefore, does not predict "llet failure at this load level. The initial failure mode in the experiments, however, was that of "llet cracking. The presence of voids within the "llet would cause higher stresses which could have caused premature failure. This indicates that large voids may have been present in the "llets prior to loading which opened out due to the nature of the load but did not cause any further damage within the "llets. The experimental load/de#ection curve showed no sudden loss of sti!ness and an FE model containing a void in the resin exhibits an almost identical value of sti!ness as the model not containing voids. Thus, it seems likely that the cracks in the "llet were due to the voids opening out under load with no loss of top-hat sti!ness. The in-plane stresses in the overlaminate are lower than the in-plane failure stress but the through-thickness stresses in the overlaminate predicted by the FE model are 21 MPa along the interface of the overlaminate and the "llet. This is about three times the ILTS so delaminations would be predicted in this location. No delaminations, however, were visible in the experiments in this location. The high through-thickness stresses may have caused a debond between the overlaminate and the "llet which in turn caused the "llet crack. The FE model predicts maximum in-plane and throughthickness stresses in the #ange plate which are not high enough to cause failure at a load of 5 kN. This is consistent with the experimental initial failure mode at 5 kN.
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2.5.3. Straight pull-ow The maximum values of stress for the "llet principal stress, overlaminate in-plane and through-thickness and #ange in-plane and through-thickness stresses are given in the lower two rows of Table 4. The "llet maximum principal stress at the sti!ener experimental failure load of 7 kN is 7.8 MPa. This is much lower than the UTS of the "llet material of 26 MPa. The FE model would not, therefore, predict "llet failure at this load. This corresponds to the experimental failure mode in which no "llet cracks were visible. The maximum in-plane stresses in the overlaminate and in the #ange are less than the UTS (in-plane) stress of 207 MPa at a load of 7 kN. Therefore, no failure is predicted at this load from the FE model as a result of high in-plane stresses. The maximum through-thickness stress of 2.8 MPa in the #ange is lower than 7 MPa which is the ILTS. The maximum through-thickness stress in the overlaminate, however, is higher than the ILTS. The FE model predicts delamination of the overlaminate in the curved region close to the "llet due to high through-thickness stresses.
3. Energy-based assessment 3.1. Fracture mechanics criteria used in the approach Two dimensional linear elastic fracture mechanics (LEFM) models have been used to calculate mode I and mode II stress intensity factors which, in turn, have been used to evaluate strain energy release rates, G. The theoretical basis is outlined in Appendix A. The load}de#ection characteristics of the top-hat sti!ener under the three modes of loading discussed in the previous section are almost linear. Furthermore, in the previous section, it was shown that the curved region of the overlaminate is one of the most sensitive areas prone to delamination. The material in this location is linear elastic up to failure. For this reason, there is no need to evaluate non-linear parameters such as the J-integral: only the strain energy release rate has been calculated in each case. 3.2. Modelling details The FE model used in the strength analyses has been adapted so as to include a region containing cracks. The crack elements are six-noded triangular elements with their mid-side nodes at the quarter point. The general scheme was similar to the pattern shown in Fig. 4 except for the region containing the crack; this is shown in Fig. 6. Investigations showed that under certain conditions the two crack faces crossed over each other, i.e. under a tensile load, the vertical displacement of the top crack face was in fact less than the vertical displacement of the lower crack face. The problem of crack faces overlapping has been discussed in the literature [15,16]. Four methods exist which can be used to overcome this problem: (a) application of displacement
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Fig. 6. Finite element detail in the region of cracks.
constraints on the crack face nodes, (b) application of nodal loads on the crack face, (c) application of gap elements at the crack interface or (d) to assume that the overlapping e!ect is negligible. In this particular case, a number of gap elements were inserted along the crack face. The gap elements behave as linear springs in compression but in tension their sti!ness drops to zero thus not inhibiting the crack face should it open. In addition, the unloaded crack face is generated using nodes at the same location since the gap element allows connection of two nodes which are initially coincident. A check has been made to con"rm that the presence of the gap elements does not a!ect the calculated values of the strain energy release rate. This has been done by comparing the results from two models with and without the gap elements present. The two sets of results are identical indicating that the presence of the gap elements has no e!ect on the calculations. 3.3. Loads, material properties and boundary conditions The material properties used in the "nite element model are given in Table 2. Boundary conditions chosen were consistent with the strength analyses for the three cases of three-point bend, reverse bend and straight pull-o!. The applied load in each case is chosen as 10 kN. The signi"cance of this load is that it is below any
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delamination damage which occurred in the three-point bend and reverse bend tests, implying that any cracks simulating delaminations observed in the tests and appropriately inserted in the model should be stable at this load. Additionally, since the strain energy release rates are proportional to the square of the applied load, it is simple to interpolate values for di!erent load values. 3.4. Results The study focused on cracks in the overlaminate region only, despite the fact that the limited tests showed up some ultimate failures within the #ange laminate. This is because the strength analysis showed the region of high stresses is in the curved portion of the overlaminate, as indicated in Table 4. It was argued earlier that some of the discrepancy in the static test results could have been due to fabrication variations. Furthermore, parallel work on tee joints [17] shows that it is the curved region that is crucial to the crack propagation tendency. Hence the focus of the fracture studies is the overlaminate region. Two types of crack variations for each of the three load cases were studied } in#uence on crack depth and in#uence of crack length. 3.4.1. Crack depth Fig. 7 shows the variation of G with crack depth. In Fig. 7a, pertaining to the three-point bend, it can be noted that there is a peak value of G which corresponds to a crack depth of 4 mm. Cracks which are deeper than 4 mm give rise to lower values of G. It is anticipated that the reason why the value of G calculated for the crack at 2 mm depth is lower than expected is due to the proximity of the crack to the surface. Cracks close to the surface are more di$cult to model than those deeper within the overlaminate due to the limited area available to mesh with elements. This problem can be avoided to a degree, by re"ning the mesh close to the surface. All the values of G are, however, less than the critical value of 0.5 kJ/m [18]. This indicates that none of these cracks under the three-point bend would propagate. The trend does, however, suggest that under three-point bending, cracks which are deeper within the overlaminate are less likely to propagate than those nearer the surface. Similar trends can be observed for the reverse bend and straight pull-o! load cases as well, see Fig. 7b and 7c, respectively. The strain energy release rates are of similar orders of magnitude as in the three-point bend case. 3.4.2. Crack length Fig. 8 shows the variation of G with crack length. Each crack is at a depth of 6 mm from the outer surface of the overlaminate. From Fig. 8a for the three-point bend case, it can be noted that the values of G increase at a steady rate as the crack length increases. From the trends, it can be concluded that cracks greater than 38 mm in length at a depth of 6 mm under these loading conditions are likely to propagate. For the reverse bend condition, whose e!ect is shown in Fig. 8b, the G values are relatively low indicating that this mode of loading is not as critical as the previous case. The most severe condition in this respect is the straight pull-o!; the trends are indicated in
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Fig. 7. Variation of G with crack depth: (a) three-point bend; (b) reverse bend; (c) pull-o!.
H.J. Phillips et al. / Marine Structures 12 (1999) 1}19
Fig. 8. Variation of G with crack length: (a) three-point bend; (b) reverse bend; (c) pull-o!.
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Fig. 8c. The nature of the curve is similar to that in the three-point bend condition. However, it can be seen that the fracture toughness value is exceeded at crack lengths of about 30 mm.
4. Discussion The results of the "nite element strength models are in good agreement with the experimental results, particularly in the case of the three-point bending load. The results have shown that the damage prone areas are (i) in the curved region of the overlaminate and (ii) in the central region of the #ange plate. This is indicated by the presence of high through-thickness stresses in the curved region of the overlaminate and also the presence of high in-plane stresses in the #ange. The stress results have shown that the dominant failure modes of the top-hat sti!eners under the three modes of loading include delamination in the overlaminate, "llet-to-#ange interface cracking, "llet-to-overlaminate cracking, "llet cracking and #exural failure in the #ange. In the case of damage tolerance calculations, it is the initial failure mode which must be predicted since it is at this point when the structure's load-bearing capabilities are gradually reducing. Thus, it is the initial failure mode which is considered to be the most important in this case. In the case of the three-point bending, the initial failure mode was in the form of delaminations in the overlaminate. Damage in the #ange plate was also visible in both the three-point bending and reverse bending cases but this was a "nal failure mode and is, therefore, less signi"cant from a damage tolerance aspect. For these reasons, the delaminations which have been modelled in the energy-based assessment which followed are those within the curved part of the overlaminate. The results of the strength and fracture approaches give similar results. For example, the strength-based model of the three-point bending load shows that the highest through-thickness stresses occur in the outer layers of the overlaminate. This is shown in Fig. 5a. The energy-based approach shows that straight cracks which are close to the outer surface of the overlaminate are more likely to propagate than those which are deep. This is shown in Fig. 7a where greater values of G are obtained for shallow cracks (not including the value at a crack depth of 2 mm). Also, the graph showing the e!ect of crack length, shown in Fig. 8a shows that cracks which extend into the curved part of the overlaminate are more likely to propagate than shorter cracks which are contained within the #at portion of the overlaminate.
5. Conclusions It has been shown that the delamination prone areas in top-hat sti!eners are located in the curved region of the overlaminate close to the outer surface. The delaminations are likely to be due to excessive through-thickness stresses. The damage which occurs in the #ange is likely to be due to excessive in-plane stresses in the case of
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three-point bending loads and due to excessive through-thickness stresses in the case of reverse bending loads. Calculation of fracture parameters with regard to delaminations in the top-hat overlaminates, have shown that curved delaminations are most likely to propagate under a straight pull-o! load. They are next likely to propagate under a three-point bending load and are most stable under a reverse bending load. Also, delaminations close to the surface are more likely to propagate than deep delaminations in the case of all three loading scenarios. Results from the strength-based approach and the energy-based approach are comparable and similar trends have been found.
Acknowledgements The work presented in this paper was funded by the EPSRC/MoD. 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.
Appendix A. Fracture mechanics criteria for damage modelling A.1. Elastic stress xeld approach Irwin [19] 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 Eq. (A.1) depends upon the magnitude of the applied stress, p, the length of the crack, 2a, and a parameter which depends upon the crack and specimen geometry, f (a/=) where = is the specimen width: K"p(pa f
a . =
(A.1)
Irwin proved that the achievement of a critical stress intensity factor, K , is exactly ! equivalent to the Gri$th}Irwin balance approach. This requires that the achievement of a stored elastic strain is equal to the critical strain energy release rate, G [20]. For ! tensile loading, the relationship between K and G is given in Eq. (A.2) for plane ! ! stress, K G " ! plane stress. ! E
(A.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.
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A.2. 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 Eq. (A.2) and with f (a/=) in Eq. (A.1) being equal to ' unity (i.e. an in"nitely long plate) as K G " ' plane stress. ' E
(A.3)
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: (K#K )(i#1) K '' G" ' # ''', 8k 2k
(A.4)
where K is the mode I stress intensity factor, K is the mode II stress intensity factor, ' '' K is the mode III stress intensity factor, k is the material shear modulus, i is the ''' conversion factor between conditions of plane strain and plane stress, and is equal to (3!4t) for plane strain conditions and t is the material Poisson's ratio. For the case where only modes I and II are applicable, mode III is assumed to give a negligible contribution to the strain energy release rate and hence the second term in Eq. (A.4) can be neglected.
References [1] Dixon RH, Ramsey BW, Usher PJ. Design and build of the GRP hull of HMS Wilton. Proceeding of the Symposium on GRP Ship Construction, RINA, London, 1972;1}32. [2] Smith CS. Structural problems in the design of GRP Ships, Proceedings of the Symposium on GRP Ship Construction, RINA, London, 1972;33}56. [3] Clark MA. Stress analysis of a frame-skin connection in the MCMV. NCRE Report No. NCRE/L8/76, March 1976. [4] Smith CS. Design of marine structures in composite materials. Amsterdam: Elsevier, 1990. [5] Green AK, Bowyer WH. The development of improved attachment methods for sti!ening frames on large GRP panels. Composites, 1981;12:49}58. [6] Smith CS, Dow RS. Interactive buckling e!ects in sti!ened FRP panels. In: Marshall IH (Ed.), Composite Structures Amsterdam: Elsevier, 1987;122}134. [7] Shenoi RA, Hawkins GL. An investigation into the performance characteristics of top-hat sti!ener to shell plating joints. Compos. Struct 1995;30:109}121. [8] Dodkins AR, Shenoi RA, Hawkins GL. Design of joints and attachments of FRP Ships' structures. Marine Struct 1994;7:365}98. [9] Rules for Yachts and Small Craft, Lloyds Register of Shipping, London, 1983. [10] Rules for Building and Classing Reinforced Plastic Vessels, American Bureau of Shipping, New York, 1978. [11] Rules for Classi"cation of High Speed and Light Craft, Det Norske Veritas, 1991. [12] Elliott DM. Mechanical testing of composite joints } Interim Report. DRA/AW/AWS/TR94212, April 1994. [13] Shenoi RA, Hawkins GL. In#uence of material and geometry variations on the behaviour of bonded Tee connections in FRP Ships. Composites, 1992;23:335}345.
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[14] Bird J, Allan RC. The determination of the interlaminar strength of ship type laminates. in: Proceedings of the 7th International Conference Experimental Stress Analysis, Haifa, 1982:91}104. [15] Pavier MJ, Clark MP. A specialised composite plate element for problems of delamination buckling and growth. Composite Struct 1996;34:43}53. [16] Tian Z, Swanson SR. E!ect of delamination face overlapping on strain energy release rate calculations. Composite Struct 1992;21:195}204. [17] Phillips HJ. Assessment of damage tolerance levels in FRP Ships' structures. PhD thesis, University of Southampton, March 1997. [18] Court R. Fracture toughness of woven glass reinforced composites. Interim Report DRA/SMC/CR943111, December 1994. [19] Irwin GR, Kies JA. Critical energy rate analysis of fracture strength. Welding J Res Suppl 1954;193s}198s. [20] Ewalds HL, Wanhill RJH. Fracture mechanics. Publs. Arnold & DUM, 1986. ISBN 0 7131 3515 8.
Damage mechanics of top-hat sti!eners used in FRP ship construction H.J. Phillips , R.A. Shenoi *, C.E. Moss Hamworthy Marine Technology Ltd., Poole, UK Department of Ship Science, University of Southampton, Southampton, Highxeld, Hants SO17 1BJ, UK B.M.T. (Defence Services) Ltd., Bath, UK Received 29 May 1997; received in revised form 14 January 1999; accepted 18 January 1999
Abstract This paper is concerned with the assessment of damage tolerance of a top-hat sti!ener to plate connection in FRP marine structures. The subject is addressed in two parallel schemes, using stress-based and fracture-dependent criteria. Numerical modelling is used to determine the internal load transfer characteristics and failure mechanisms in top-hat sti!eners under typical loadings seen in practice. The "nite element models are benchmarked against published test results, which include phenomena such as delaminations. The models are then extended to include crack elements, which are employed to calculate the strain energy release rates in the form of G values. The result from this modelling is compared against typical experimentally derived data pertaining to G values for the materials in question. Finally, an attempt is made to compare the results of the studies using the two approaches and to judge the overlap. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Fibre-reinforced plastic (FRP); Ship structures; Top-hat sti!eners; Finite element analysis; Delamination; Strain energy release rates; Damage tolerance
1. Introduction The sti!ness of large unsupported panels constructed of "bre-reinforced plastic (FRP) materials is inherently low. Thus, it is necessary to sti!en such panels by a
* Corresponding author. Tel.: #1-44-1703-592316; fax: #1-44-1703-593299. E-mail address: [email protected] (R.A. Shenoi) 0951-8339/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 1 - 8 3 3 9 ( 9 9 ) 0 0 0 0 3 - 9
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Fig. 1. A typical top-hat sti!ener.
suitable method. The most prevalent form is the use of top-hat sti!eners. A typical con"guration of the sti!ener is shown in Fig. 1. The present fabrication method starts with the laying-up of the unsti!ened base plate panel. Rigid foam cores are then laid on these panels in the locations where the extra sti!ness is desired. Then, an adequate amount of "lleting resin is injected into the recess between the foam and the plate panel and the required radius is scraped out. Next, a resin-impregnated cloth, or overlaminate, is laid across the crown (or table), down the web and around the "llet onto the base plate. A similar cloth run is carried out for the opposite side. The process of overlaminating is repeated a number of times, frequently with as many as 24 plies, to achieve the desired sti!ness. Occasionally, a limited number of unidirectional plies may be applied to the crown to obtain extra sti!ness. The reinforcement material for the web, #ange and overlaminate is E-Glass woven roving and chopped strand mat; the resin matrix is isophthalic polyester resin. Although top-hats are a critical part of the ship's structure, it has received surprisingly little attention in the open literature. Early reported work [1,2] was in connection with the development of the "rst GRP minehunter and dealt mainly with the gross problems of qualifying design concepts with regard to a speci"c application. This was extended to develop a more fundamental understanding of the top-hat behaviour through theoretical modelling [3,4]. Such early modelling attempts were necessarily restricted because of the relatively immature nature of the available "nite element types. There was also some fundamental work on the use of novel "lleting materials, with large strain to failure capability, and their application to marine joints
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and top-hat sti!ening purposes [5]. E!ort was also now being directed towards various failure scenarios. One of the principal cases involved overall panel instability and sti!ener-plate interaction under compressive loading [4,6]. The second approach focused on the transfer of load at the top-hat sti!ener to plate connection through the orthogonal or out-of-plane direction under static loading conditions [7,8]. Guidance on this subject in existing design regulations is minimal [9}11]. This is all the more important because many ships have now been in operation for over 20 years and are seeing sustained damage at the roots of the joints in the form of delaminations. It is thus essential that a systematic study is carried out with regard to the localised behaviour of a top-hat sti!ener to plate connection and its response under the presence of cracks or delaminations. The purpose of this paper is three-fold: (a) to understand the behaviour of a top-hat sti!ener under static loading and the mechanisms of load transfer and failure; (b) to study the in#uence of delamination cracks on strain energy release rates; and (c) to propose a uni"ed approach to categorise damage tolerance levels in FRP structures in the regions of top-hat sti!eners.
2. Strength-based assessment 2.1. Purpose of analysis The main aim of this analysis is to identify how the load is transferred from an in-plane direction in the base panel to an orthogonal direction in the plane of the web. The transfer is achieved through the overlamination and "lleting material. It is essential to categorise the stress states within the di!erent constituent elements of the joint. These stresses can then be used to assess the likely causes of failure in the joints. The three main possibilities are delamination in the overlaminate, cracking of the "lleting resin and braking of the "bre plies in the overlaminate. 2.2. Physical characterisation of joint behaviour Three load con"gurations were adopted for the test programme [12]; these were the three-point bend, reverse bend and straight pull-o!, as shown schematically in Fig. 2. Both the three-point and reverse bend tests aim to simulate gross panel deformation and its e!ect on the top-hat connection. The pull-o! test is designed to simulate inertial loadings on the sti!ener under impact and explosion loadings. In all cases the load-de#ection plots were linear up until failure. The structural sti!nesses in the three cases are listed in Table 1. In case of the three-point bend test, specimens "rst showed damage at about 13.5 kN when the "llet-to-overlaminate interfaces failed. Subsequent loading caused progressive through-thickness delamination in the inner region of the overlaminate and the onset of cracking along the overlaminate-to-#ange joints from the cracks in the "llet. Final failure occurred by #exural failure on the tension surface under the top of the top-hat (see Fig. 3a).
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Fig. 2. Loading con"gurations for the experiments: (a) three-point bend; (b) reverse bend; (c) pull-o!.
H.J. Phillips et al. / Marine Structures 12 (1999) 1}19 Table 1 Experimental failure loads and de#ections Loading con"guration
Three-point bend Reverse bend Pull-o!
Sti!ness
(kN/mm)
Experimental
FEA
909 600 952
750 458 667
Fig. 3. Experimental failure modes: (a) three-point bend; (b) reverse bend; (c) pull-o!.
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In the reverse bend tests, "rst signs of damage were observed at a load of 5 kN at which point cracks appeared in the "llets on both sides. Final failure occurred at a load of 14 kN due to tensile action on the inner surface at the centre of the #ange, as shown in Fig. 3b. In the pull-o! tests, cracks appeared at the #ange-to-"llet interface at a load of about 5.5 kN. These cracks extended and joined together with increased load, until at a load of 7 kN overlaminate was severed completely from the #ange on one side (see Fig. 3c). 2.3. Features of the FE models A series of models was generated in the ANSYS "nite element analysis package using two dimensional solid elements (which possess three translational degrees of freedom at each node); see Fig. 4 for a typical model. Each of the 12 layers in the overlaminate was represented by one element through the thickness. The #ange plate of the top-hat sti!ener has been represented by one element through the thickness. Conditions of plain strain have been assumed throughout. The loads applied to the structural model attempt to mimic those in the experimental investigation. For each of the three test con"gurations, stress distributions have been computed (i) at the load at which initial damage was noted and (ii) at the failure load of the sti!ener. The material properties used in the FE model generation were obtained from previous work at Southampton [8] and from parallel work at DERA Rosyth [12]; the relevant properties are given in Table 2. 2.4. Stiwness characterisation The "rst step is to validate the FE models by comparing the model sti!ness with that of the equivalent tested specimen. The FE model and experimental initial
Fig. 4. A typical "nite element model for strength calculations.
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Table 2 Material properties used in the FE modelling Material
Location
Property
Value
Polyester/woven roving glass
Sti!ener, #ange and overlaminate
Ex
13,060 MPa
Ey nuxy Ex Ey nuxy Ex Gxy nuxy
7770 MPa 0.25 1500 MPa 1500 MPa 0.25 10\ MPa 10\ MPa 0.25
Urethane acrylate
Fillet
Core material
Table 3 Comparison of sti!nesses } experimental versus FEA Three point bending (3PB)
Reverse bending (RB)
Straight pull o! (PO)
FE (N/mm)
Expt. (N/mm)
FE (N/mm)
Expt. (N/mm)
FE (N/mm)
Expt. (N/mm)
731.2
696.8
713.0
384.6
930.0
1000
sti!nesses of the top-hat under each of the three loading con"gurations are shown in Table 3. It is evident that for the three-point bend and the straight pull-o! tests there is quite good correlation between the two sets of values. There is however a discrepancy as far as the reverse bend results are concerned. 2.5. Stress patterns The stress distributions of interest are the "llet principal stress, overlaminate through-thickness and in-plane stresses, #ange plate through-thickness and in-plane stresses. It is also necessary to compare the load transfer mechanisms predicted from the FE models with some experimentally derived failure modes. Table 4 shows the value and location of the maximum stress for each load level and load con"guration for the top-hat sti!ener. 2.5.1. Three-point bending The most signi"cant stress patterns for the top-hat at the experimental initial load of 13.5 kN are shown in Fig. 5a for the overlaminate through-thickness stresses and Fig. 5b for the #ange in-plane stresses. The magnitude of the "llet principal stress is the greatest in the central region in the "llet as shown in Table 4 but is less than the
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Fig. 5. Stress distributions in three-point bend con"guration: (a) overlaminate through-thickness stress; (b) #ange in-plane stress.
Table 4 Locations and values of maximum stresses
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ultimate value. Thus, the "llet is unlikely to fail at this load. The region under the greatest in-plane stress in the #ange is in the inner central part below the core; this however is unlikely to cause failure. The region of the #ange under the highest through-thickness stress is in the outer central part as shown in Table 4. The region of the overlaminate which is subject to both the highest in-plane and through-thickness stresses is the outer region in the curved part above the "llet as shown in Fig. 5a. Delaminations are likely to form here due to high through-thickness stresses. The value of the maximum principal stress in the "llet at the sti!ener experimental failure load of 16.5 kN is 18.09 MPa. The ultimate tensile strength (UTS) of the "llet material in the literature [13] is quoted at about 26 MPa, so the "llet would remain intact at this load. This corresponds to the failure mode in the experiments in which the "llet itself did not crack. The initial damage was seen along the interface of the "llet with the overlaminate. The through-thickness stress at the initial failure load of 13.5 kN, however, is greater than the quoted interlaminar tensile strength (ILTS) of 7 MPa for the woven roving/polyester [14]. Hence, the FE model predicts that delaminations would occur near to the outer surface of the overlaminate at 13.5 kN due to through-thickness stresses greater than the ILTS of the material. This exactly matches the experimental "ndings. A similar match is obtained for the #ange failure cause. At 16.5 kN the in-plane stress in the #ange is 208 MPa which is greater than the UTS of the material. The FE model predicts that the #ange plate would fail in the centre of the upper surface at a load of 16.5 kN, which again mirrors the experimental "ndings.
2.5.2. Reverse bending At a load of 5 kN, the "llet principal stress is 4.8 MPa which is much less than the UTS of 26 MPa. The FE model, therefore, does not predict "llet failure at this load level. The initial failure mode in the experiments, however, was that of "llet cracking. The presence of voids within the "llet would cause higher stresses which could have caused premature failure. This indicates that large voids may have been present in the "llets prior to loading which opened out due to the nature of the load but did not cause any further damage within the "llets. The experimental load/de#ection curve showed no sudden loss of sti!ness and an FE model containing a void in the resin exhibits an almost identical value of sti!ness as the model not containing voids. Thus, it seems likely that the cracks in the "llet were due to the voids opening out under load with no loss of top-hat sti!ness. The in-plane stresses in the overlaminate are lower than the in-plane failure stress but the through-thickness stresses in the overlaminate predicted by the FE model are 21 MPa along the interface of the overlaminate and the "llet. This is about three times the ILTS so delaminations would be predicted in this location. No delaminations, however, were visible in the experiments in this location. The high through-thickness stresses may have caused a debond between the overlaminate and the "llet which in turn caused the "llet crack. The FE model predicts maximum in-plane and throughthickness stresses in the #ange plate which are not high enough to cause failure at a load of 5 kN. This is consistent with the experimental initial failure mode at 5 kN.
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2.5.3. Straight pull-ow The maximum values of stress for the "llet principal stress, overlaminate in-plane and through-thickness and #ange in-plane and through-thickness stresses are given in the lower two rows of Table 4. The "llet maximum principal stress at the sti!ener experimental failure load of 7 kN is 7.8 MPa. This is much lower than the UTS of the "llet material of 26 MPa. The FE model would not, therefore, predict "llet failure at this load. This corresponds to the experimental failure mode in which no "llet cracks were visible. The maximum in-plane stresses in the overlaminate and in the #ange are less than the UTS (in-plane) stress of 207 MPa at a load of 7 kN. Therefore, no failure is predicted at this load from the FE model as a result of high in-plane stresses. The maximum through-thickness stress of 2.8 MPa in the #ange is lower than 7 MPa which is the ILTS. The maximum through-thickness stress in the overlaminate, however, is higher than the ILTS. The FE model predicts delamination of the overlaminate in the curved region close to the "llet due to high through-thickness stresses.
3. Energy-based assessment 3.1. Fracture mechanics criteria used in the approach Two dimensional linear elastic fracture mechanics (LEFM) models have been used to calculate mode I and mode II stress intensity factors which, in turn, have been used to evaluate strain energy release rates, G. The theoretical basis is outlined in Appendix A. The load}de#ection characteristics of the top-hat sti!ener under the three modes of loading discussed in the previous section are almost linear. Furthermore, in the previous section, it was shown that the curved region of the overlaminate is one of the most sensitive areas prone to delamination. The material in this location is linear elastic up to failure. For this reason, there is no need to evaluate non-linear parameters such as the J-integral: only the strain energy release rate has been calculated in each case. 3.2. Modelling details The FE model used in the strength analyses has been adapted so as to include a region containing cracks. The crack elements are six-noded triangular elements with their mid-side nodes at the quarter point. The general scheme was similar to the pattern shown in Fig. 4 except for the region containing the crack; this is shown in Fig. 6. Investigations showed that under certain conditions the two crack faces crossed over each other, i.e. under a tensile load, the vertical displacement of the top crack face was in fact less than the vertical displacement of the lower crack face. The problem of crack faces overlapping has been discussed in the literature [15,16]. Four methods exist which can be used to overcome this problem: (a) application of displacement
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Fig. 6. Finite element detail in the region of cracks.
constraints on the crack face nodes, (b) application of nodal loads on the crack face, (c) application of gap elements at the crack interface or (d) to assume that the overlapping e!ect is negligible. In this particular case, a number of gap elements were inserted along the crack face. The gap elements behave as linear springs in compression but in tension their sti!ness drops to zero thus not inhibiting the crack face should it open. In addition, the unloaded crack face is generated using nodes at the same location since the gap element allows connection of two nodes which are initially coincident. A check has been made to con"rm that the presence of the gap elements does not a!ect the calculated values of the strain energy release rate. This has been done by comparing the results from two models with and without the gap elements present. The two sets of results are identical indicating that the presence of the gap elements has no e!ect on the calculations. 3.3. Loads, material properties and boundary conditions The material properties used in the "nite element model are given in Table 2. Boundary conditions chosen were consistent with the strength analyses for the three cases of three-point bend, reverse bend and straight pull-o!. The applied load in each case is chosen as 10 kN. The signi"cance of this load is that it is below any
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delamination damage which occurred in the three-point bend and reverse bend tests, implying that any cracks simulating delaminations observed in the tests and appropriately inserted in the model should be stable at this load. Additionally, since the strain energy release rates are proportional to the square of the applied load, it is simple to interpolate values for di!erent load values. 3.4. Results The study focused on cracks in the overlaminate region only, despite the fact that the limited tests showed up some ultimate failures within the #ange laminate. This is because the strength analysis showed the region of high stresses is in the curved portion of the overlaminate, as indicated in Table 4. It was argued earlier that some of the discrepancy in the static test results could have been due to fabrication variations. Furthermore, parallel work on tee joints [17] shows that it is the curved region that is crucial to the crack propagation tendency. Hence the focus of the fracture studies is the overlaminate region. Two types of crack variations for each of the three load cases were studied } in#uence on crack depth and in#uence of crack length. 3.4.1. Crack depth Fig. 7 shows the variation of G with crack depth. In Fig. 7a, pertaining to the three-point bend, it can be noted that there is a peak value of G which corresponds to a crack depth of 4 mm. Cracks which are deeper than 4 mm give rise to lower values of G. It is anticipated that the reason why the value of G calculated for the crack at 2 mm depth is lower than expected is due to the proximity of the crack to the surface. Cracks close to the surface are more di$cult to model than those deeper within the overlaminate due to the limited area available to mesh with elements. This problem can be avoided to a degree, by re"ning the mesh close to the surface. All the values of G are, however, less than the critical value of 0.5 kJ/m [18]. This indicates that none of these cracks under the three-point bend would propagate. The trend does, however, suggest that under three-point bending, cracks which are deeper within the overlaminate are less likely to propagate than those nearer the surface. Similar trends can be observed for the reverse bend and straight pull-o! load cases as well, see Fig. 7b and 7c, respectively. The strain energy release rates are of similar orders of magnitude as in the three-point bend case. 3.4.2. Crack length Fig. 8 shows the variation of G with crack length. Each crack is at a depth of 6 mm from the outer surface of the overlaminate. From Fig. 8a for the three-point bend case, it can be noted that the values of G increase at a steady rate as the crack length increases. From the trends, it can be concluded that cracks greater than 38 mm in length at a depth of 6 mm under these loading conditions are likely to propagate. For the reverse bend condition, whose e!ect is shown in Fig. 8b, the G values are relatively low indicating that this mode of loading is not as critical as the previous case. The most severe condition in this respect is the straight pull-o!; the trends are indicated in
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Fig. 7. Variation of G with crack depth: (a) three-point bend; (b) reverse bend; (c) pull-o!.
H.J. Phillips et al. / Marine Structures 12 (1999) 1}19
Fig. 8. Variation of G with crack length: (a) three-point bend; (b) reverse bend; (c) pull-o!.
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Fig. 8c. The nature of the curve is similar to that in the three-point bend condition. However, it can be seen that the fracture toughness value is exceeded at crack lengths of about 30 mm.
4. Discussion The results of the "nite element strength models are in good agreement with the experimental results, particularly in the case of the three-point bending load. The results have shown that the damage prone areas are (i) in the curved region of the overlaminate and (ii) in the central region of the #ange plate. This is indicated by the presence of high through-thickness stresses in the curved region of the overlaminate and also the presence of high in-plane stresses in the #ange. The stress results have shown that the dominant failure modes of the top-hat sti!eners under the three modes of loading include delamination in the overlaminate, "llet-to-#ange interface cracking, "llet-to-overlaminate cracking, "llet cracking and #exural failure in the #ange. In the case of damage tolerance calculations, it is the initial failure mode which must be predicted since it is at this point when the structure's load-bearing capabilities are gradually reducing. Thus, it is the initial failure mode which is considered to be the most important in this case. In the case of the three-point bending, the initial failure mode was in the form of delaminations in the overlaminate. Damage in the #ange plate was also visible in both the three-point bending and reverse bending cases but this was a "nal failure mode and is, therefore, less signi"cant from a damage tolerance aspect. For these reasons, the delaminations which have been modelled in the energy-based assessment which followed are those within the curved part of the overlaminate. The results of the strength and fracture approaches give similar results. For example, the strength-based model of the three-point bending load shows that the highest through-thickness stresses occur in the outer layers of the overlaminate. This is shown in Fig. 5a. The energy-based approach shows that straight cracks which are close to the outer surface of the overlaminate are more likely to propagate than those which are deep. This is shown in Fig. 7a where greater values of G are obtained for shallow cracks (not including the value at a crack depth of 2 mm). Also, the graph showing the e!ect of crack length, shown in Fig. 8a shows that cracks which extend into the curved part of the overlaminate are more likely to propagate than shorter cracks which are contained within the #at portion of the overlaminate.
5. Conclusions It has been shown that the delamination prone areas in top-hat sti!eners are located in the curved region of the overlaminate close to the outer surface. The delaminations are likely to be due to excessive through-thickness stresses. The damage which occurs in the #ange is likely to be due to excessive in-plane stresses in the case of
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three-point bending loads and due to excessive through-thickness stresses in the case of reverse bending loads. Calculation of fracture parameters with regard to delaminations in the top-hat overlaminates, have shown that curved delaminations are most likely to propagate under a straight pull-o! load. They are next likely to propagate under a three-point bending load and are most stable under a reverse bending load. Also, delaminations close to the surface are more likely to propagate than deep delaminations in the case of all three loading scenarios. Results from the strength-based approach and the energy-based approach are comparable and similar trends have been found.
Acknowledgements The work presented in this paper was funded by the EPSRC/MoD. 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.
Appendix A. Fracture mechanics criteria for damage modelling A.1. Elastic stress xeld approach Irwin [19] 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 Eq. (A.1) depends upon the magnitude of the applied stress, p, the length of the crack, 2a, and a parameter which depends upon the crack and specimen geometry, f (a/=) where = is the specimen width: K"p(pa f
a . =
(A.1)
Irwin proved that the achievement of a critical stress intensity factor, K , is exactly ! equivalent to the Gri$th}Irwin balance approach. This requires that the achievement of a stored elastic strain is equal to the critical strain energy release rate, G [20]. For ! tensile loading, the relationship between K and G is given in Eq. (A.2) for plane ! ! stress, K G " ! plane stress. ! E
(A.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.
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A.2. 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 Eq. (A.2) and with f (a/=) in Eq. (A.1) being equal to ' unity (i.e. an in"nitely long plate) as K G " ' plane stress. ' E
(A.3)
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: (K#K )(i#1) K '' G" ' # ''', 8k 2k
(A.4)
where K is the mode I stress intensity factor, K is the mode II stress intensity factor, ' '' K is the mode III stress intensity factor, k is the material shear modulus, i is the ''' conversion factor between conditions of plane strain and plane stress, and is equal to (3!4t) for plane strain conditions and t is the material Poisson's ratio. For the case where only modes I and II are applicable, mode III is assumed to give a negligible contribution to the strain energy release rate and hence the second term in Eq. (A.4) can be neglected.
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[14] Bird J, Allan RC. The determination of the interlaminar strength of ship type laminates. in: Proceedings of the 7th International Conference Experimental Stress Analysis, Haifa, 1982:91}104. [15] Pavier MJ, Clark MP. A specialised composite plate element for problems of delamination buckling and growth. Composite Struct 1996;34:43}53. [16] Tian Z, Swanson SR. E!ect of delamination face overlapping on strain energy release rate calculations. Composite Struct 1992;21:195}204. [17] Phillips HJ. Assessment of damage tolerance levels in FRP Ships' structures. PhD thesis, University of Southampton, March 1997. [18] Court R. Fracture toughness of woven glass reinforced composites. Interim Report DRA/SMC/CR943111, December 1994. [19] Irwin GR, Kies JA. Critical energy rate analysis of fracture strength. Welding J Res Suppl 1954;193s}198s. [20] Ewalds HL, Wanhill RJH. Fracture mechanics. Publs. Arnold & DUM, 1986. ISBN 0 7131 3515 8.