Analysing thermally induced macro-scale residual stresses in tailored morphing composite laminates
Post on 07-Apr-2017
Composite Structures 117 (2014) 4050Contents lists available at ScienceDirect
journal homepage: www.elsevier .com/locate /compstructAnalysing thermally induced macro-scale residual stresses in tailoredmorphing composite laminateshttp://dx.doi.org/10.1016/j.compstruct.2014.06.0130263-8223/ 2014 Elsevier Ltd. All rights reserved.
Corresponding author. Tel.: +353 (0) 61 20 2531.E-mail address: firstname.lastname@example.org (T.M. Young).R. Telford a, K.B. Katnamb, T.M. Young a,a Irish Centre for Composites Research (IComp), Materials and Surface Science Institute (MSSI), University of Limerick, Irelandb School of Mechanical, Aerospace and Civil Engineering, University of Manchester, UK
a r t i c l e i n f oArticle history:Available online 24 June 2014
Keywords:Tailored laminatesResidual stressesMulti-stable behavioura b s t r a c t
An approach for predicting and extracting through-thickness residual stresses in tailored compositelaminates (i.e. laminates with local variations in lay-up sequence and/or thickness) is presented. Tailoredcomposite laminate configurations can be explored in some novel structural applications (e.g. morphinglaminates) by incorporating unsymmetric laminate lay-up sequences. In such cases, the presence of andvariation in through-thickness (i.e. macro-scale) residual stresses can considerably influence the struc-tural geometry, strength and multi-stable behaviour of these laminates, and thus require considerationat a design stage. In this context, a combined numerical-experimental approach was used to analyseresidual stresses in tailored laminates. Laminates with local unsymmetric cross-ply lay-ups and/or vary-ing thicknesses were manufactured at elevated temperatures and experimental measurements (of curedshapes at room temperature) were used to develop laminate-level finite element models. The curedlaminate shapes were measured using a full-field non-contact technique. The numerical models werecalibrated and subsequently used to extract through-thickness residual stresses in the laminates. Itwas shown that the current approach can be successfully applied to predict the cured shapes of andthe through-thickness residual stresses in tailored laminates.
2014 Elsevier Ltd. All rights reserved.1. Introduction
It is known that uni-directional fibrematrix composites withunsymmetric lay-up sequences become warped following thecool-down from elevated cure temperature to room temperature.This is due to a mismatch in the coefficients of thermal expansion(CTE) between transverse and longitudinal plies, which, whenstacked adjacently, introduce residual stresses . This warping fol-lowing cure is generally undesirable in structural applications andthus laminates with unsymmetric lay-up sequences are largelyavoided in conventional designs. However, it is possible to useunsymmetric laminates beneficially, such as in stiffness tailoring or in morphing applications (e.g. aeronautical or wind turbine). In the case ofmorphing technologies, a likely solution to inte-grate a multi-stable laminate into a structure entails the use of tai-lored lay-ups, whereby the orientations of individual plies withinthe laminate are discontinuous, resulting in a changing ply lay-upsequence along the length or width of the laminate [8,9]. This couldbe done, for example, to couple the multi-stable laminate into thesurrounding structure  or to maximise the multi-stable configu-rations available [5,8]. In addition, laminate asymmetry may occuras a consequence of geometric requirements, such as ply-drop offcases where plies are prematurely cut short at discrete locationsleading a taper being formed, which in turn can lead to local asym-metry in the lay-up sequence [10,11].
The change in lay-up sequence will introduce through-thicknessresidual stress variation along the length of the laminate. This caninfluence the laminate shape, multi-stable behaviour and structuralperformance. An approach is thus required to correctly predictresidual stresses through-out the transition in lay-ups. The curva-tures developed by unsymmetrical composite laminates have beenpreviously used to measure macro-scale residual stresses by usingclassical laminate theory . However, such analytical techniquesto predict and analyse cured shapes become challenging and timeconsuming when complex laminate lay-ups and geometries areconsidered. Numerical modelling (using the finite elementmethod)offers flexibility in this regard and has been used in the past tocharacterise multi-stable laminate behaviour, particularly withthe use of shell models . When a detailed analysis is sought(e.g. when studying the interactions with local structures andactuating systems, or damage) it can be advantageous to use a solid
Fig. 1. Typical configuration of manufactured tailored laminates, featuring partitionalong the x-axis. In all cases, l = 200 mm, m = 100 mm. Only cross-ply (0 or 90) plyorientations were used.
R. Telford et al. / Composite Structures 117 (2014) 4050 41continuum approach. Additionally, complex environmental factorsthat influence residual stresses (such as moisture absorption) canrequire a transient analysis, to which a continuum approach lendsitself by use of the analogy between heat transfer/thermal expan-sion and moisture diffusion/moisture-induced swelling .
This work aims to build upon a previously developed experi-mentalnumerical approach to predict dry and saturatedthrough-thickness residual stresses (and thus the shapes) ofunsymmetric laminates  by expanding it to predict tailoredlay-up laminate shapes, and subsequently extract and analysemacro-scale through-thickness residual stresses. A number of dif-ferent laminate configurations are explored with varying laminatethickness and discontinuous ply orientations (with the transitionbeing both normal to the laminate thickness and tapered). Thechanges in through-thickness residual stresses due to the tailoredlaminate configuration were analysed at both the centre of lay-up partitions and at the boundary between changing lay-ups. Theeffectiveness of the numerical model in predicting cured laminateshapes is described in more detail by means of a full-field study ofthe variations.
Tailored laminates were manufactured from uni-directionalpre-preg (carbon fibres with epoxy resin) material. The lay-upsfeatured sections with both unsymmetric and symmetric lay-upsequences, and at least one multi-stable region. Numerical modelsof the laminates were then developed, and the cool-down fromcure temperature to room temperature was simulated toreproduce the warped laminate shapes. The orthotropic materialexpansion coefficients used in the numerical models were then cal-ibrated to reproduce the experimentally observed laminate shapes.Equivalent CTE values were employed to eliminate the need to pre-cisely account for individual contributors to residual stresses (suchas imperfections or manufacturing effects ), which canhave an effect on thin composites panels . Subsequently, theability of the present technique to correctly predict the curedlaminate shapes was investigated by means of a detailed shapecomparison. The through-thickness residual stresses at differentpositions of the tailored laminates were then extracted from themodels and analysed to gain insight into the effect of tailoredlaminate configuration on residual stresses.
2. Materials, manufacturing and testing
2.1. Manufacturing of tailored laminates
A range of tailored laminates were manufactured featuring dif-ferent tailored lay-ups. The material used was Hexply HTA 6376(uni-directional carbon fibre with impregnated epoxy resin). Handlay-up techniqueswere used, followed by autoclave (TC1000LHTHP,LBBC, UK) curing at 178 C temperature under 7 bar pressure. Fivedifferent lay-up configurationsweremanufactured. Each configura-tion featured partitions along the length (x-direction) of the lami-nate (see Fig. 1, showing a single partition). The cross-section ofeach laminate is presented in Fig. 2(a)(e) along with the corre-sponding cured shape. For convenience, each lay-up configurationwill be referred to by the corresponding numbers given in Fig. 2(i.e. Laminate15). As all the laminates featured amulti-stableprop-erty, with two or more stable shapes being obtainable, only theshapes depicted in Fig. 2 are analysed in this work.
2.2. Recording laminate shapes
In order to make detailed comparisons against numerical mod-els, a full-field non-contact shape measuring technique wasrequired. Optical methods, based on the fringe projection tech-nique, have been used is the past to record shapes of unsymmetricallaminates . As no contact is involved, distortion of the laminateduringmeasurement is eliminated. Additionally no assumptions onthe measured displacement fields are needed . This is impor-tant as the cured shapes of the laminates used feature varying cur-vature along their lengths, due to their tailored nature. In this work,laser scanning was used to measure laminate shapes. A flat laserline was swept over the laminate, and a camera was then used inconjunction with specialist software (David-Laserscanner 3.9.1) torecord the distortion of the laser line as it sweeps over the laminate.The experimental set-up used in this study is shown in Fig. 3. A fulldescription of the technique can be found in . Following a scanof the laminates surface, a point cloud of co-ordinates describingthe surface was obtained. The accuracy of this technique is statedto be 0.5% of the object size. To determine the accuracy of the exper-imental set-up used in this work, a calibration platewith patterns ofknown dimensions (item (e) in Fig. 3) was scanned. The plate wasmanufactured using identical methods and materials to those ofthe laminates, so as to give an identical scanning surface. The platewas scanned and a point cloud obtained. Using this point cloud, thedimensions of the patterns were compared against the actualdimensions. It was found (due to the resolution of the point cloud)that an error of 2 mm is possible when calculating in-plane dis-tances, depending upon the point cloud spacing. However, theimportant metric required in this work is the accuracy of the coor-dinates (specifically, in the out-of-plane direction) of each point inthe point cloud. As the calibration plate was flat (save for a slightwarping), the variation in the measured out-of-plane co-ordinateswas checked. The maximum variation was between +1.4/1.8 mm. This was deemed acceptable as: (a) the calibration platewas not completely flat and (b) the advantages of this technique(simplicity, full-field, non-contact) made it the most attractiveshape measuring technique.
3. Numerical modelling
The thermal deformation of each laminate following the curecycle was modelled using the finite element software Abaqus (ver-sion 6.11). Themodels incorporated the temperature drop followingcure, which induces thermal deformation in the model due to thematerials orthotropic CTEs. The models were developed as flatthree-dimensional solids to the nominal dimensions of themanufactured laminates (l = 200 mm, w = 100 mm, ply thick-ness = 0.125 mm). The models were then partitioned to create eachply as well as the tailored sections. A local material orientation wasthen assigned to each ply according to the ply stacking sequence forthat laminate. Orthotropic and linear-elastic material propertieswere used to represent the HTA 6376 material, as in Table 1 .The materials longitudinal CTE (aL) was deliberately left undefinedat this stage, and was later used as a calibration parameter to
Fig. 2. Cross-section of laminates manufactured showing tailored lay-up sequences used and cured laminate shapes. In all cases, l = 200 mm, laminate width = 100 mm andnominal ply thickness = 0.125 mm.
42 R. Telford et al. / Composite Structures 117 (2014) 4050reproduce as closely as possible the curvatures of themanufacturedlaminates. It is important tonote that this shouldbe consideredas anequivalent CTE value only, and not a directmeasure of thematerialsCTE value.
A static general step was used to apply a temperature change of158 C (corresponding to the difference between the cure temper-ature and room temperature when the laminate shapes wererecorded) to the models using predefined fields. Three-dimensionalcontinuum elements (C3D20R) were used. The bending stiffnessof the models was found to be critical in this analysis; otherwisethe correct laminate configuration would not be predicted. Thus,reduced integration quadratic elements were used (coupled withthe nlgeom feature). Three elements were used in the through-thickness direction of each ply in order to accurately capture thethrough-thickness residual stresses. A structured mesh comprisingelements with a fixed element aspect ratio (AR) of 60:1 (length/width to thickness ratio) was used to alleviate the solution frombeing overly stiff, while maintaining an element count that doesnot result in an overly computationally expensive analysis. Asensitivity checkwas conducted by comparing extracted stress pro-files (using Laminate 1) with AR values of 40:1, 60:1 and 80:1.Although a change was noted when reducing the AR from 80:1 to60:1, no further change was noted when reducing it from 60:1 to40:1 (see Fig. 4). Thus, an AR of 60:1 was chosen. This results inelement dimensions of 2.5 mm (length,width) and 0.0417 mm(thickness).
As all the laminates featured a multi-stable property, it wasfound that the solution may need to be biased to produce the shapeconfigurations depicted in Fig. 2. In such cases, an additional stepwas added to the solution whereby certain plies were cooled
Fig. 3. Laser scanning experimental setup, depicting: (a) computer system with David-Laserscanner software; (b) hand-held, flat-line laser; (c) Trust HD webcam; (d)scanning background; and (e) object being scanned. Note: Laser is shown clamped for illustrative purposes. During scanning, the laser is swept by hand.
Table 1Experimentally measured ply properties of HexPly HTA 6376 .
Parameter E11 (GPa) E22 (GPa) m12 G12 (GPa) aT (K1)
Magnitude 135.64 10.14 0.29 5.86 2.86 105
R. Telford et al. / Composite Structures 117 (2014) 4050 43before others, coaxing the solution to a particular shape. Finally,the materials longitudinal CTE (aL) was calibrated to reproducethe cured laminate shape. This was done separately for each lam-inate configuration. Using the coords field-output, the co-ordinatesof the nodes comprising the bottom surface of the laminate in thedeformed configuration were exported, resulting in a three-dimensional point cloud. This was then compared against the pointcloud obtained from laser scanning.
Following calibration, the through-thickness residual stressprofiles can be obtained. In this study, element integration pointswere used to directly obtain the stress components (r11 and r22)required to produce the through-thickness stress profiles. Thiswas possible due to the structured mesh scheme used in model-ling. With each element containing two integration points in thethrough-thickness direction, and with three elements being usedFig. 4. Sensitivity of through-thickness residual stresses to element Aspect Ratio (AR) forups refer to the two partitions of Laminate 1.per ply thickness, this results in six integration points per ply beingavailable to extract stresses. These stresses can then be plotted as afunction of laminate thickness to identify the through-thicknessstress profiles. Finally, depending on the ply orientation, thestresses may need to be transformed from the local materialorientation system to the global laminate orientation system.
4. Comparison of measured and predicted laminate shapes
The comparison between experimentally measured shapes andnumerical models was undertaken by subtracting the out-of-planeco-ordinates of the numerical models from those of the experimen-tally measured shapes to obtain the variation between the two. Theprocess for this is described in Fig. 5. The raw shapes (i.e. asextracted directly from experiments and models) were first trans-formed to a common coordinate system for comparison, using themathematical analysis software Matlab (see experimental andnumerical shapes, Fig. 5). A fine grid comprising x and y coordi-nates was then superimposed on both the experimental andnumerical shapes. From this, an out-of-plane z-coordinate waslinearly interpolated from surrounding points in the point cloud.Laminate 1: (a) along the x-axis; (b) along the y-axis. Note: [02/902] and [01/903] lay-
Fig. 5. Calculation of variation between measured and predicted laminate shapes. Note: Distorted areas highlighted with circles result from the supporting mechanism usedin experiments being included in measurements.
44 R. Telford et al. / Composite Structures 117 (2014) 4050The purpose of this step was to have identical x and y positions forthe experimental and numerical shapes at which out-of-planedeflections can be compared. At this stage, the outer 5 mm of thelaminates was ignored, so as to remove any edge effects that resultfrom laser scanning. The z-coordinates of the numericallypredicted shape (wn) were then subtracted from those of theexperimentally measured shape (we), giving a full field view ofthe out-of-plane variation between the two shapes. The variationis presented as a percentage of the maximum out-of-planedeflection measured for each of the experimental laminates(w in Eq. (1)). The full field variation (in terms of w) was thenplotted, as shown in Fig. 5.
w we wnwe;max
The calibration process then involved minimising the difference(or variation) between experimentally observed and numericallypredicted shapes. The materials aL value used in modelling wasthen altered to minimise the variation between plots. The resultof this process was a calibrated equivalent CTE value for aL. It isimportant to note that this equivalent CTE value should not beregarded as an actual CTE value for aL. It serves only to reproducethe curvature of the laminates without needing to preciselyaccount for each contributor to residual stresses, such as manufac-turing effects and imperfections. Following calibration, the equiva-lent CTE values for aL used in numerical models is given in Table 2.
In order to support the laminates during laser scanning, a smallfixture was used which allowed the laminates to stand upright,without being distorted due to clamping. This fixture was scannedduring the shape measurement process, and included in thescanned shapes of the laminates. This is responsible for the dis-torted areas highlighted by circles in Fig. 5. Similar features arepresent in all variation plots to follow and should be ignored.
5. Results and discussions
Two separate aspects are presented in this section. Firstly, adetailed comparison of the numerical/experimental shapes is pro-vided by plotting the full field measurements (see Fig. 6). Secondly,through-thickness stresses (parallel to the x- and y-axes) are pre-sented (see Figs. 711). The through-thickness residual stress pro-files for the laminates were extracted at certain discrete locationswithin each laminate (either at the middle of a partitioned sectionTable 2Calibrated equivalent aL used in numerical models.
Laminate 1 2 3 4 5
aL (106) K1 6.5 1 12 7.2 6or near a boundary between two different lay-ups). These aremarked in each of the cross-sectional figures and are taken atpoints in the middle of the laminate width. The stresses obtainedare along both the laminate length (x-axis, i.e. rxx) and the laminatewidth (y-axis, i.e. ryy).
For example, Fig. 7(a) shows the cross-section of the laminate,and the points (numbered 14) at which the through-thicknessstresses are extracted. The partition length p refers to the lengthof the sections with different lay-up configurations, which remainsconstant for each laminate. The variation (Fig. 6(a)) describes theover/under prediction of numerical models compared to experi-ments. Along the x-axis, the numerical model initially under pre-dicts the out-of-plane deflection. At an x location of 50 mm, thevariation becomes positive as the numerical model changes to overpredicting the out-of-plane deflection. The maximum variation(w) observed is 6.7/+14.5% of the maximum experimentallyobserved out-of-plane deflection. The through-thickness residualstress profiles depicting rxx stresses (Fig. 7(c)) and ryy stresses(Fig. 7(d)) are shown. Four locations are used to extract the residualstresses. Locations 1 and 4 are at the middle of the first and secondlay-up sections respectively, and thus represent steady-statestresses away from edge-effects on lay-up boundaries. Locations2 and 3 are on either side (by one element length of 2.5 mm) ofthe boundary, and are used to show the transition in stresses fromone lay-up configuration to the next. Finally, a view of thedeformed FE solution is given in Fig. 7(b) for comparison to thecured laminate shape shown in Fig. 2(a)
5.1. Correlation between predicted and measured laminate shapes
In all cases, the numerical models were able to predict the cor-rect tailored laminate shape configuration; that is, the correct cur-vature orientation for each of the tailored segments. However, ofparticular interest is the ability of the model to correctly predictthe complete profile of the laminates, such as where the laminateover/under predicts the out-of-plane curvature. The largest varia-tion range for all the laminates investigated in this work was foundto be 6.6/+24.9 for Laminate 3 (Fig. 6(c)). While it is possible toreduce this further by means of further calibration of the aL valueused, it is clear that entirely eliminating the variation will not beachievable by this means. Indeed, this is apparent for all the lami-nates investigated. One reason for this is that the laminates manu-factured were thin in nature (maximum of four plies thick, 0.5 mm)and thus are very susceptible to manufacturing effects and imper-fections . It is known from experience that the manufacturingmethod used to create the laminates introduces a warp in thinlaminates, bowing away from the tool plate. As the manufacturedlaminates featured relatively small out-of-plane deflections, themanufacturing effects become more pronounced in the cured
Fig. 6. Variation between experimentally measured and numerically predicted shapes. Note: Values on w axis highlight minimum and maximum values of w.
Fig. 7. Extracted through-thickness stresses for Laminate 1: (a) Locations at which through-thickness stresses are extracted; (b) deformed FE solution; (c) extracted through-thickness stresses along the x-axis; (d) extracted through-thickness stresses along the y-axis.
R. Telford et al. / Composite Structures 117 (2014) 4050 45
Fig. 8. Extracted through-thickness stresses for Laminate 2: (a) Locations at which through-thickness stresses are extracted; (b) deformed FE solution; (c) extracted through-thickness stresses along the x-axis; (d) extracted through-thickness stresses along the y-axis.
Fig. 9. Extracted through-thickness stresses for Laminate 3: (a) Locations at which through-thickness stresses are extracted; (b) deformed FE solution; (c) extracted through-thickness stresses along the x-axis; (d) extracted through-thickness stresses along the y-axis.
46 R. Telford et al. / Composite Structures 117 (2014) 4050laminate shapes. While the calibrated CTE is intended to minimisethe need to account for manufacturing effects individually in mod-elling, it becomes less effective when dealing with laminates whichfeature large opposing curvatures, such as laminates 4, or very thinlaminates such as Laminate 5. In the case of Laminate 4, a curva-ture exists along the x axis, which transitions to an inverse curva-ture along the y axis. The effect due to manufacturing tends towarp the laminate away from the tool-plate, and thus will increaseone of those curvatures, and decrease the other (something whicha calibrated CTE value does not take into account). Therefore, it isexpected that this laminate in particular will feature variation withrespect to the experimentally measured shape. The way in whichmanufacturing affects each laminate differently is further demon-strated by the fact that a range of equivalent CTE values wasrequired to numerically reproduce the laminate shapes (Table 2).
The variation between Laminate 1 and Laminate 3 are both verysimilar. Initially, the numerically predicted out-of-plane deforma-tion is under-estimated along the x axis. Mid-way through the firstpartition ([01/903] for Laminate 1 and [02/902] for Laminate 3) theout-of-plane deflection is subsequently over-predicted. It appearsthat the first partition is acting overly stiff in models (i.e. anincrease in curvature is required in this region). Doing this (by
Fig. 10. Extracted through-thickness stresses for Laminate 4: (a) Locations at which through-thickness stresses are extracted; (b) deformed FE solution; (c) extractedthrough-thickness stresses along the x-axis; (d) extracted through-thickness stresses along the y-axis.
Fig. 11. Extracted through-thickness stresses for Laminate 5: (a) Locations at which through-thickness stresses are extracted; (b) deformed FE solution; (c) extractedthrough-thickness stresses along the x-axis; (d) extracted through-thickness stresses along the y-axis.
R. Telford et al. / Composite Structures 117 (2014) 4050 47decreasing the equivalent CTE value) would, however, degrade thecorrelation for the second partition of the laminate. This behaviourmay be due to the manufacturing effects already noted in this sec-tion. A possible solution to increase the accuracy of predictedshapes would be to use separate equivalent CTE values for eachpartitioned section, thus separating manufacturing effects andincluding them in two separate calibrated values of aL.
Overall, the maximum variation is between +14.55/6.7% forLaminate 1 and +24.9/6.6% for Laminate 3. As this study is limitedto cross-ply laminates, no twist curvature is developed innumerical models. Close examination of the manufactured shapeacross the width of Laminate 1 (parallel to the y-axis) shows thatthe laminate is slightly twisted, a consequence of manufacturingimperfections that is hard to avoid. This leads to an increase inthe minimum/maximum variation. However, the curvature acrossthe y-axis appears to be well captured.
The profile of Laminate 2 also shows signs of manufacturingimperfections (see Fig. 6(b)). As the laminate is symmetrical aboutthe y-axis, it is expect that the variation would be mirrored aboutthe centre of the laminate. Instead, the variation is greater on the
48 R. Telford et al. / Composite Structures 117 (2014) 4050right hand side of the laminate than on the left. In addition, thissection is curved, showing that the manufactured laminate fea-tured a curvature in this (symmetrical) lay-up section. However,when considering the low out-of-plane deflection of this laminate,the overall variation is low (0.4/+12.5). The curvature of the cen-tre [02/902] section is marginally underestimated, as shown by thecurved section in the variation plot. Further calibration (by reduc-ing aL) would improve the correlation between experiments andthe numerical prediction.
The variation of Laminate 4 shows a range of 0.6/+22.2. Ini-tially, the longitudinal out-of-plane deflection is slightly underesti-mated. This area corresponds to the [01/903] lay-up. The bi-stableregion exists in the second partition, with a [02/902] lay-up. Alongthis section is where the curvature alternates between being gen-erated parallel to the y axis to parallel to the x axis. This was aregion that was particularly sensitive to overall stiffness of themodel; otherwise, only the other multi-stable shape (where thecurvature generated in this section remained parallel to the y axis)could be obtained. The largest variation appears at the right-handmost edge of the laminate, with the curvature being under pre-dicted in this section. Further calibration of the equivalent aL valueused may improve overall correlation, but it is clear that all varia-tion will not be removed by this means. This may be due to man-ufacturing induced warping increasing the curvature generatedalong the y axis while decreasing the curvature generate alongthe x axis, as previously described.
Being only two plies thick over most of the laminate, Laminate 5is particularly flexible and very sensitive to residual stresses. Thetwo sections of symmetrical lay-up () are reacting to residualstresses imposed due to the tailored laminate configuration andany manufacturing imposed residual stresses. At the first section, the laminate is largely deforming under the effect of the[02/902] lay-up which neighbours it. Subsequently, the [02/902] isin a multi-stable configuration whereby a cylinder along the x axisis formed. Coupled with the last partition ([0/90]) these partitionscontrol the shape of the laminate. The curvatures along these twopartitions appear to be captured well. However, the laminate didfeature multiple buckling modes, with the first partition featuringa twist curvature. This is shown by the raised corner at the bottomleft corner of Fig. 6(e). This behaviour was not captured in numer-ical models (due to the inherent symmetry) and thus appears as acontributor to the variation.
It is worth noting that this particular tailored configuration fea-tures a large number of snap-through configurations available, dueto the bi-stable region being able to alternate shape in two sepa-rate steps. It is possible to snap one half of the region through tothe second shape obtainable, with the first half remaining in theoriginal configuration (similar to what has been reported in ).
5.2. Through-thickness residual stresses
The effect of the tailored laminate configuration on residualstresses will be discussed by observing changes in the stress pro-files due to neighbouring lay-up partitions. The profiles themselvesare typical of what has been already observed and described in aprevious work  and thus will not be described in detail. Bystudying the stress profiles of the laminates it is evident that a tai-lored laminate configuration impacts upon the residual stresses ofa partition comprising a certain lay-up. For example, laminates 1and 3 feature a similar construction, with a [02/902] partitionneighbouring a [01/903] partition (Laminate 1) and a [0/90]s parti-tion (Laminate 3). The rxx profiles show that the peak stresses inthe [02/902] partition is higher for Laminate 1 than for Laminate3 (see Fig. 7(c) and Fig. 9(c) respectively, positions 4 and 1). The dif-ference between the two laminates can be reduced to the substitu-tion of a transverse ply for a longitudinal ply in the partitionneighbouring the [02/902] section. As the longitudinal ply willnot thermally contract to the same extent as the transverse ply,it therefore reduces the thermal straining of the bordering ply. Thiscan be seen directly in the reduced stresses in the lower half (i.e.transverse plies) of the stress profiles, which causes a reductionin the stresses counteracted by the longitudinal plies. Extendingthe comparison between the [02/902] partition of Laminates 1and 3 to the ryy stresses, it can be seen that the tailored configura-tion impacts upon these stresses as well. The peak stresses inLaminate 1 (Fig. 7(d), position 4) are much higher than those inLaminate 3 (Fig. 9(d), position 1). However, this particular observa-tion is a consequence of the laminate geometries investigated inthis work. Along the y axis, there are no changes in lay-upconfiguration and changes in residual stresses. The curvaturesdeveloped along neighbouring partitions directly influence eachother. Therefore, it is expected that a change in the neighbouringlay-up will have a large effect on the [02/902] partition, particularlywhen going from a symmetrical (Laminate 3, where no anti-clasticcurvature is imposed upon the [02/902] section) to an unsymmet-rical (Laminate 1) lay-up.
The boundary between two different lay-ups will, of course,involve a transition from one stress state to another. This wasexamined by extracting through-thickness stresses at points oneither side of the boundary between the two lay-ups. This wasdone for Laminates 13 (Figs. 79 respectively, positions 2 and3). These were extracted from numerical models, by selectingone element (2.5 mm) to either side of the boundary betweentwo lay-ups. In the cases of Laminate 1 and Laminate 3 the changesin rxx stresses across the boundary are almost imperceptible whencompared to the steady-state stresses, taken from the middle ofeach partition. It appears, therefore, that the transition zone fromone stress state to the next is shorter than one element length. Itis possible that a denser mesh in this region could lead to a differ-ent result as well as additional locations closer to the boundaryfrom which to extract stresses, giving a clearer view of thetransition in stresses. Laminate 2 however shows a much largertransition effect between the partition boundaries. In the [0/90/0]section, the stresses close to the boundary (position 2, Fig. 8(c))feature a higher compressive stress compared to the steady statestresses (position 1, Fig. 8(c)), with a change from 19 MPa to65 MPa predicted. The profiles of the stresses changes as well,with the top ply transitioning from compressive to tensile stresses.A large change can also be seen in the stresses of the [02/902] sec-tion, with a change in peak stresses (from 37 MPa to 60 MPa,positions 4 and 3, respectively), along with a change in the stressprofiles which now show signs of non-linearity through thelaminate thickness (position 3). In the top ply, this non-linearbehaviour may be a consequence of the laminate adjusting to thechange in thickness at the partition.
The changes to ryy stresses close to the boundary appear to bemore significant for all laminates, with a large change in stressesobservable when compared to the steady-state stresses. The tran-sition from one lay-up to the other introduces a net change instress (either compressive or tensile) along the longitudinal plies.In laminates 1 the stresses close to the partition boundary in thelongitudinal plies (position 3, Fig. 7(d)) experience an additionaltensile stress, when compared to the steady-state stresses (shownby position 4). Conversely, the stresses in the neighbouring parti-tion [01/903] lay-up experience a net compressive change instresses, as shown by the stresses at position 1 and 2. A similarobservation can be made with Laminate 2, Fig. 8(d). The stressesin the longitudinal plies of the [02/902] partition change (a netcompressive stress this time), while the stresses in the longitudinalply of the neighbouring [0/90]s section experience a net tensilechange in stresses. These changes appear to show the stressesadjusting to those in the neighbouring partition. The reason for this
R. Telford et al. / Composite Structures 117 (2014) 4050 49behaviour is not immediately obvious, but the consequenceremains significant (a change in peak stresses of 27% from33.7 MPa to 24.9 MPa in Laminate 1).
It must be remembered that these stresses are extracted at themiddle of the laminate width. It stands to reason that thesechanges (which are only observed in the longitudinal plies andthus not balanced by the transverse plies) are reacted by otherstresses when moving away from the middle of the laminate alongthe y axis. A similar effect may be seen in the stress profile of Lam-inate 5 at locations 1 and 3 (Fig. 11(c)). Close examination of therxx stress profiles at these positions show a slight non-linearityin the top ply. These stresses are not balanced through the lami-nate thickness at positions 1 and 3. Rather, the imbalanced stressesat position 1 are balanced by those at position 3. This behaviourappears to be confined to the stress profiles orthogonal to thestresses generating the primary curvature in the laminates (ryyin Fig. 11(d)). The interaction of residual stresses amongst differentlay-up partitions can be further demonstrated by examining thestresses induced in unidirectional partitions (e.g. Laminate 4 witha 4 partition, position 4 Fig. 10 (c) and (d)). This symmetricalregion is forced to curve due to neighbouring partitions. Thisresults in an induced (quasi-externally applied) stress profile. Thestiffness of this partition has therefore affected the residual stressprofiles of other lay-up partitions.
Laminate 4 features a staggered change in lay-up, similar towhat may occur in some scarf repairs. Additionally, a bi-stableregion exists which allows for the curvature to transition frombeing along the x-axis to the y-axis. The large changes in residualstresses due to the tailored lay-up can be seen here. The [02/902]partition is snapped through to change curvature from being gen-erated along the x axis (first partition) to being generated along they axis (the other snap through configuration leads to the curvaturein the first partition being continued). As such, the stresses in thispartition become very close to being mirrored along the x and yaxis, with no dominating curvature being formed.
It is interesting to note that the stress profiles are significantlyaffected by the tailored laminate configuration. This can be seendirectly from the stresses in the [02/902] region of each laminate.Each laminate features a [02/902] section which is influenced dif-ferently by surrounding lay-ups. The peak residual stresses varydrastically among the laminates (for example, from rxx = +74/110 MPa in Laminate 1, to rxx = +55/83 MPa in Laminate 3). Thisseems obvious, in that each tailored configuration has differentcurvatures, resulting from different residual stresses. The implica-tions of this though are significant. In design cases where residualstresses are critical (such as morphing parts, which depend uponresidual stresses for their multi-stable property), the interactionbetween the laminate and the surrounding lay-ups/structure canhave a significant impact upon residual stresses.
5.3. Sensitivity of residual stresses to modelling parameters
Comparisons between numerical and experimentally measuredshapes show that a degree of variation between the twowill alwaysbe evident, regardless of calibration. This can be due, in part, to dif-ferences between the numerical model and the manufactured lam-inate. In general, most of the material properties required fornumerical modelling (Youngs modulus, Poissons ratio, etc.) arereadily available from manufacturers data sheets or experiments.The equivalent aL value however is calibrated as part of thisapproach to match the experimentally observed laminate shapes.In addition, with hand lay-up techniques being used in the manu-facture of the laminates, a degree of ply misalignment is expected.Both these parameters (aL and fibre alignment) may influence theextracted residual stress profiles. As such, the sensitivity of residualstresses to changes in the aL value and fibre orientation wasexplored. This was done by using themodel of Laminate 1 as a base-line, and altering the value of aL used, as well as introducing a plymisalignment. The changes to the residual stresses caused by thesealtered parameters could then be assessed.
In the case of aL, two separate simulations were carried out.Firstly, the value of aL used was reduced from 6.5 106 to6.0 106. This increased the difference between aT and aL, result-ing in greater residual stresses. The change in residual stresses wasrelatively small, with the largest change observed being a 2.5 MPaincrease in the peak rxx value in the [02/902] partition.
Secondly, both the values of aL and aT were altered, with the dif-ference between the two (aT aL) being kept identical to that ofthe baseline case. The revised values were 6.0 106 for aL and2.81 105 for aT. Comparisons against the baseline case showedthat there were no changes in the extracted stress profiles. It wouldappear, therefore, that the difference between the two values isparticularly critical when using this approach to extract through-thickness residual stresses.
To take fibre misalignment into account, a third simulation wascarried out where a + 5 ply misalignment was introduced into thelongitudinally oriented plies (to produce a [51/903], [52/902] tai-lored laminate). The misalignment is in the region of what maybe expected with hand lay-up techniques . The change in resid-ual stresses caused by the misalignment was low, in the order of1 MPa. However, the variation in shape showed the significanceof ply imperfections, with the variation going from +14.5%/6.7%in the baseline case, to +9.4%/11.2% in the misaligned ply case.As the variation between shapes is used as a calibration parameter,such an imperfection in the manufactured laminate could result infurther calibration in the equivalent aL value, which would, asshown previously, result in different stress profiles beingextracted.
5.4. Some remarks
The approach developed was used to predict residual stresses intailored laminates (by means of a detailed shape comparison),which allows for an understanding of the residual stresses inmorphing structural applications. But the numerical model usedis relatively simple and could allow the analysis of more generalcomposite structural situations (e.g. co-cured composite laminateassemblies, laminates with ply-drop conditions, etc.). The use ofhomogenised orthotropic material properties aids in the simplicityof the approach, but should of course be used with caution indetermining absolute residual stress values, as fibre-resin interac-tion are not considered (i.e. only macro-scale stresses were consid-ered). Additionally, the laminates investigated in this study featurevery high length/width-to-thickness ratios, and as such can be con-sidered to be thin-plates. Solid continuum elements can be overlystiff in these instances (due, for example, to shear-locking effects).Indeed, when linear elements (C3D8R) were used, the solution wasfound to be stiff for Laminate 4, and would not accurately predictthe change in curvature along the length of the laminate. As such,an effort needs to be made to reduce the element aspect ratio asmuch as possible, while keeping computational effort down. Also,it has been noted that some through-thickness residual stress pro-files taken at discrete locations show evidence of stress imbalance.A summation of the forces through cross-sections, describing thelength and width of the laminate, shows that the stresses areindeed in equilibrium. Locally, however, a through-thicknesssection may be in a net state of tension/compression, which iscounteracted by other elements along the same cross-section.
The need for a range of equivalent aL values demonstrates thedifficulty in predicting the cured shapes of complex tailoredlaminates when considering the stresses developed between themiss-match in the materials CTE values only. For further
50 R. Telford et al. / Composite Structures 117 (2014) 4050validation, the measure and comparison of in-plane strains can beconsidered. Though not done in this study, the numerical model iscapable of extracting full-field strains. Experimentally measuredlocal strain values (obtained, for example, through embedded opti-cal fibres or strain gauges) could be compared against those pre-dicted numerically to further validate the model and the stressesextracted. However, measuring strains developed during cure canlead to additional complexities. For example, should embeddedstrain sensors be used, the thermal behaviour of the interactionbetween the sensor and the surrounding material may need carefulconsideration. Additionally, measuring strains near the partitionbetween different lay-ups may be challenging when using sensors,as stress gradients exist over a potentially small distance.Consequently, the use of a non-contact, optical based measure-ment technique allows for the full-field macro-scale stresses tobe predicted in a non-intrusive manner with a relatively simpleexperimental set-up.
An approach to numerically predict the cured shapes of tailoredcomposite laminates has been presented, along with a detailedcomparison of these shapes against experimentally measuredshapes. From numerical models, through-thickness residual stressprofiles have been extracted and analysed. The approach involvescalibrating numerical models (by means of the materials longitu-dinal expansion coefficient) to reproduce the cured laminateshapes following a simulated cool-down from cure temperature.Although experimentally measured in-plane strains can be usedwith the numerical approach proposed, the cured laminate shapes(out-of-plane displacements) were used for calibrating the numer-ical models in order to simplify the experiments. It was found thatthis technique is capable of predicting the complex shapes (includ-ing multi-stable sections) of tailored laminates, using (in someinstances) a controlled cool-down of certain plies when necessaryto coax the solution to the desired multi-stable shape. The use ofthree-dimensional laser scanning allowed for a non-contact full-field recording of the manufactured laminates, enabling a detailedcomparison of predicted shapes to experimentally observedshapes. This comparison revealed that, while the variationbetween numerical/experimental shapes could be further mini-mised (through continued calibration), some variation betweenthe two will still exist. In part, it is believed that this is due to man-ufacturing imperfections which affect the different lay-up sectionsof the tailored laminates to different extents. This has led to a largerange of calibrated equivalent CTE values (from 1e6 to 12e6 K1)being required to reproduce the experimentally observed laminateshapes. Finally, the extracted through-thickness residual stressprofiles indicate that the tailored laminate configuration impactsupon the residual stresses of a particular lay-up sequence. Depend-ing upon the bordering lay-ups, the [02/902] sections used in tai-lored laminates in this work featured peak stresses ranging from+74/110 MPa to +55/83 MPa. Applications which are sensitiveto the residual stress state (e.g. morphing structures utilisingmulti-stable laminates or ply drop-off cases) can therefore beaffected by the tailored laminate configuration. For two of thelaminate configurations explored, the transition length of the rxxstresses, (i.e. length across a lay-up boundary along whichthrough-thickness stresses change from one stress state to thenext) was found to be less than two element lengths (5 mm, or