Twisted composite structures made by 4D printing method

Journal Pre-proofs Twisted composite structures made by 4D printing method Suong V. Hoa, Xiao Cai PII: DOI: Reference:

S0263-8223(19)34623-9 https://doi.org/10.1016/j.compstruct.2020.111883 COST 111883

To appear in:

Composite Structures

Received Date: Accepted Date:

5 December 2019 3 January 2020

Please cite this article as: Hoa, S.V., Cai, X., Twisted composite structures made by 4D printing method, Composite Structures (2020), doi: https://doi.org/10.1016/j.compstruct.2020.111883

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Twisted composite structures made by 4D printing method Suong V. Hoa and Xiao Cai Concordia Center for Composites Department of Mechanical, Industrial and Aerospace Engineering Concordia University Center for Research in Polymers and Composites (CREPEC) Montreal, Quebec, Canada H3G 1M8 Abstract: This paper presents the determination of the configurations of twisted laminates made by 4D printing of composites (4DPC) method. Flat stacks of composite prepregs are laid onto a flat mold. Upon curing and cooling to room temperature, the flat stack becomes curved and twisted. The configurations of the twisted laminate are determined using both calculated method (FEM) and experimental measurement. Reasonable agreement is obtained. Keywords: 4D printing of composites, Mouldless composites manufacturing, Finite element method, Twisted composite structures. Introduction: 4D printing is a manufacturing technique where structures of complex geometries can be made without the need to have molds of complex geometries [1, 2, 3, 4, 5,6, 7]. The materials used in this method are usually soft polymer materials with low stiffness and strength (elastic modulus varies from about 0.5 MPa to 2.0 GPa). 4D printing of composites (4DPC) utilizes similar concept like 4D printing except that the materials are long continuous fiber composites that have been used to make major engineering structures such as those of aircrafts, automobiles and wind turbine blades. The composite materials used in 4DPC have very high stiffness (about 180 GPa) and strength (about 100 MPa along the fiber direction). The mechanism that provides the change in shape in 4DPC depends on the strategic position of materials possessing different properties along different directions, at different locations within the structure. The mechanism responsible for the shape reconfiguration in 4DPC depends on the anisotropy of the laminae that constitute the laminate of the structure. The stacking sequence of the different laminae plays a very important role in the shape reconfiguration in 4DPC [8] It has been shown that composite springs with good strength, good stiffness, and long fatigue lives can be made using 4DPC [9]. The concept of 4DPC can be extended to manufacture twisted composite structures. The twisted composite structure is made from flat laminate of prepregs consisting of stack of composite layers with fiber orientation that create un-symmetry. Upon curing and cooling, this unsymmetric arrangement provides the residual stresses that make the reconfiguration of the structure. Potential applications for 4D printing of composites include blades for hockey sticks (figure 1a) and blades for vertical wind mills (figure 1b). These are usually curved and twisted

structures. Moulds for the manufacturing of these structures can be quite complex and costly. By using 4DPC, only flat moulds are used and this can represent significant savings in time and cost.

(a)

(b)

Figure 1: Two potential applications for 4DPC. (Right image taken from amgpowersolutions.com) As a preliminary investigation, simple twisted composite laminates made of [0/30] and [0/45] lay up sequences are made. Figure 2 shows the final configuration of a [0/45] laminate made of carbon/epoxy. The laminate exhibits both bending and twisting curvatures. This paper examines the configurations of the laminate using both experimental measurement and calculation techniques.

Figure 2: Final configuration of laminate made of lay up sequence [0/45] Determination of configurations of the deformed laminate using measurement method: CYCOM 977-2-35-12K HTS-145 composite material was used. The material properties are shown in Table. 1. Flat stacks of prepregs (CYCOM 977-2-35-12K HTS-145) of dimensions 12 inch x 3.0 inch ( 304.8mm x 76.2 mm) and lay up sequences [0/30] and [0/45] were made. Grid points were marked on the surface of the laminate as shown in figure 2 for measurement using a laser coordinate measuring sensor.

Table 1: Material properties Longitudinal modulus E1 (GPa) Transverse modulus E2 (GPa) Shear modulus G12 (GPa) Poisson ratio ν12 Longitudinal coefficient of thermal expansion α1 (10-6/C) Transverse coefficient of thermal expansion α2(10-6/C) Ptn_3

Ptn_6

Ptn_9

Ptn_12

Ptn_15 25

128.9 6.3 4.4 [12] 0.33 -0.018 [12] 29.37

Ptn_18

Ptn_21

Ptn_24

Ptn_27

Ptn_17

Ptn_20

Ptn_23

Ptn_26

z (mm)

12.5 Ptn_2

Ptn_5

-100

Ptn_8

Ptn_11

-50

Ptn_14 0 0

50

100

-12.5 Ptn_1

Ptn_4

Ptn_7

Ptn_10

Ptn_13 -25

Ptn_16

Ptn_19

Ptn_22

Ptn_25

x (mm)

Figure 3: Positions of points in the initial position in the x-y plane Measurement of the deformed configuration: A combination of a laser distance sensor and an X-Y table was used to measure the coordinates of the grid points. The set up is as shown in figure 4. The laser sensor is located on the top and the sample is attached to an X-Y table. There are marks on the surface of the sample which are used as points to focus the laser points for measurement.

Figure 4: Set up for laser coordinate measurement (laser sensor on top- Sample on bottom). Table 2 shows the x,y,z coordinates for the grid points made by the laser displacement sensor for the undeformed shape and for the deformed shape for the [0/30] laminate. Table 3 shows those for the [0/45] laminate. Incremental finite element method: The finite element method was used to determine the deformed configuration of the laminate as it cools from cure temperature to room temperature. The laminate was modeled with 576 fully integrated shell elements with a mesh size of 0.25 inch in Abaqus. The material properties are shown in Table 1. The center of the laminate was fixed. Since the deformation is large, incremental analysis needs to be used. For the range of temperature from 177 oC to 20 oC, the analysis was carried out in the implicit non-linear FEA solver. For example, a first increment of 10 oC (from 177 oC to 167 oC) was first imposed on the flat configuration. The analysis is carried

out to determine the deformed configuration. This deformed configuration was then used as input for the next increment of thermal loading. The unsymmetric laminate [0/45] can exhibit many modes of deformation. When the laminate is cooled from cure temperature, these modes of deformation may compete with each other for dominance. Depending on the lay up sequence, geometry of the part, and possible defects existing in the laminate, when the temperature is lowered below a certain value, one of the competing modes of deformation may take over the other mode(s) to become the dominant mode of deformation. This is illustrated through two case studies below. Competing and dominant mode of deformation- [0/90] laminates: Consider a square laminate made of lay up sequence [0/90]. Laminate theory predicts that for the final laminate (the one that is already cooled to room temperature) there are two curvatures of equal magnitude but of opposite signs (Kx and Ky) [8]. This should give rise to a saddle configuration. Finite element analysis also predicts a similar shape. Figure 5 shows the configuration of this laminate at room temperature. The two vertical edges bend convex out while the two horizontal edges bend convex in.

Figure 5: Final configuration of a square laminate (12 in x 12 in) and [0/90] as predicted from finite element However in reality, a circular shape is obtained as shown in figure 6.

Figure 6: Final configuration of a [0/90] square laminate- Only 1 bending curvature exists [8]. The reason for this is due to the competition for and gaining dominance for deformation (in bending) in the two different directions. Perfectly, the bending stiffness along the two directions ExIx and EyIy have same magnitude but opposite in direction. This is due to the [0/90] lay up sequence and the equal lengths of both sides. If the two quantities keep being the same throughout the cooling process, then the configuration as shown in figure 5 should result. However in real structure, there are variations in material properties from location to location. If one quantity (say ExIx) is slightly larger than the other, then bending will be preferred in the y direction. Once bending is more along the y direction, the additional deformation would increase the difference between the two stiffness values and one direction for bending would become more definitely favored. This favorable selection is demonstrated below. Consider the case of a rectangular laminate of dimensions 12 in x 6 in with the lay up sequence [0/90]. Let the long direction be x and the short direction be y. For this, Ix = (1/12)by h3 and Iy = (1/12) bx h3. Since bx =2 by, Iy = 2 Ix. Finite element analysis was performed on this laminate as the temperature is cooled from cure temperature (177 oC) to room temperature (20 oC). The finite element analysis was done in increments of temperature of 1% each time. This means that in the first step, a reduction from 177 oC to 175.43 oC (difference of 1.57 oC which is 1% of 157 oC) is made. The deformed configuration at the end of this increment is used as input condition for the configuration of the laminate for the next increment of thermal loading. Figure 7 shows the configuration after 1% thermal loading. Figure 8 shows the configuration after 2% thermal loading and figure 9 shows the configuration at 100% thermal loading. It can be seen that at the beginning of the thermal loading process (figure 7), there are two curvatures along the two directions. Even though the curvature along the long direction is weaker than that along the short direction, but it is there. The blue region at the center of the laminate has and hourglass shape. As the loading is increased to 2%, the blue region becomes more of a rectangle indicating that bending along the short direction is gaining more dominance. As the loading is 100%, the dominance of bending along the short direction is complete and there is only a very slight showing of curvature along the long direction at the edges.

Figure 7: Configuration after 1% loading (12 in x 6 in and [0/90] laminate)

Figure 8: Configuration after 2% loading (12 in x 6 in and [0/90] laminate)

Figure 9: Configuration after 100% loading (12 in x 6 in and [0/90] laminate) Due to this competition of bending along the two directions, the curvature of the final piece at room temperature is not quite uniform along the length of the laminate. In figure 9, the blue region (center length) has a curvature of 101.5 mm while the brown red region (edge) has a curvature of 115.2 mm. Figure 10 shows the variation of the curvature radii along the length of the laminate. It can be seen that the curvature radius varies a lot at the edge of the laminate and becomes stabilized at the mid length section. The reason for the variation at the edges is due to the competition between the two curvatures. The center region is subjected to more constraints and only one curvature becomes dominant. 125

Curvature Radius (mm)

120

115

110

105

100

0

50

100 150 200 Cumulative Curve Length (mm)

250

300

Figure 10: Variation of the curvature radius along the length of the laminate

Competing and dominant mode of deformation- [0/45] laminates: For the twisted laminate of [0/45] lay up sequence, the progression of the deformed shape for a rectangular piece of 12 inch by 3 inch is shown in figures 11 to 13.

Figure 11: Deformation configuration of [0/45] laminate (12 x 3) at 1% thermal loading

Figure 12: Deformation configuration of [0/45] laminate (12 x 3) at 2% thermal loading

Figure 13: Deformation configuration of [0/45] laminate (12 x 3) at 100% thermal loading For this laminate, there are three curvatures, Kx, Ky and Kxy. At 100% loading (room temperature), there appear to be only two curvatures, bending along a certain direction and twist. At 1% thermal loading (figure 11), the two bending curvatures are competing. The dominance of one mode of bending over the other is gaining at 2% loading and finally complete dominance occurs at 100%. There is a transition level of thermal loading where complete dominance occurs and this can be much less than 100% (less or equal to 10%). This transition level depends on the difference in bending stiffness along the competing directions. This stiffness is contained in the EI term and this depends on the properties E and the shape of the structure. For example, for the [0/90] square piece, there is no dominance if there is no spatial variation of the properties of the material. For a 12 x 1 laminate with [0/90] sequence, the transition level is 5%. For a 12 x 2 laminate with [0/90] sequence, the transition level is 10%. For a structure such as that of a laminate of [0/45] stacking sequence, a slight push on the laminate can transform one curvature to the other. This is what is called morphing process, indicated by Dano and Hyer [10, 11]. They showed that upon cooling from the cure temperature, first there is a competition between the two curvatures. When the temperature drops below a certain point (before reaching room temperature), one curvature is preferred over the other.

Table 2: Coordinates of the different points as shown in figure 3 in the initial and final configurations- dimensions in inch. (unit in inch) for [0/30]T laminate. Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

Undeformed Shape x -117.467 -117.467 -117.467 -117.467 -117.467 -93.974 -93.974 -93.974 -93.974 -93.974 -70.480 -70.480 -70.480 -70.480 -70.480 -46.987 -46.987 -46.987 -46.987 -46.987 -23.493 -23.493 -23.493 -23.493 -23.493 0.000 0.000 0.000 0.000 0.000 23.493 23.493 23.493 23.493 23.493 46.987 46.987 46.987 46.987 46.987 70.480 70.480 70.480 70.480 70.480 93.974 93.974 93.974 93.974 93.974 117.467 117.467 117.467 117.467 117.467

y -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492 -28.492 -14.246 0.000 14.246 28.492

z 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Finite Element x y -113.422 -23.958 -114.548 -10.958 -115.447 2.286 -116.149 15.741 -116.672 29.391 -91.551 -25.729 -92.343 -12.368 -92.944 1.194 -93.387 14.929 -93.686 28.820 -69.171 -26.951 -69.689 -13.297 -70.053 0.523 -70.292 14.477 -70.430 28.543 -46.383 -27.735 -46.683 -13.845 -46.866 0.170 -46.966 14.276 -47.007 28.447 -23.278 -28.176 -23.417 -14.112 -23.483 0.031 -23.506 14.220 -23.515 28.426 0.054 -28.371 0.012 -14.201 0.000 0.000 -0.012 14.201 -0.054 28.371 23.515 -28.426 23.506 -14.220 23.483 -0.031 23.417 14.112 23.278 28.176 47.007 -28.447 46.966 -14.276 46.866 -0.170 46.683 13.845 46.383 27.735 70.430 -28.543 70.292 -14.477 70.053 -0.523 69.689 13.297 69.171 26.951 93.686 -28.820 93.387 -14.929 92.944 -1.194 92.343 12.368 91.551 25.729 116.672 -29.391 116.149 -15.741 115.447 -2.286 114.548 10.958 113.422 23.958

Deformed Shape Laser Displacement Sensor z x y z 29.408 -114.006 -24.377 26.670 23.795 -115.048 -11.618 20.811 18.738 -115.873 1.852 15.422 14.241 -116.474 15.751 10.717 10.343 -116.852 28.926 7.046 21.012 -92.897 -26.085 19.023 16.251 -93.617 -12.936 14.121 12.072 -94.152 0.901 9.763 8.474 -94.514 15.080 6.127 5.517 -94.723 28.458 3.435 13.971 -70.152 -27.278 12.407 10.089 -70.572 -13.784 8.598 6.825 -70.860 0.351 5.349 4.179 -71.040 14.718 2.780 2.195 -71.137 28.208 1.001 8.309 -46.981 -27.981 7.319 5.350 -47.202 -14.236 4.558 3.044 -47.336 0.102 2.354 1.376 -47.404 14.572 0.796 0.383 -47.433 28.107 -0.091 4.077 -23.548 -28.351 3.675 2.085 -23.645 -14.451 1.829 0.762 -23.688 0.013 0.577 0.088 -23.698 14.528 -0.010 0.097 -23.701 28.063 0.026 1.332 0.014 -28.515 1.316 0.325 -0.005 -14.528 0.341 0.000 0.000 0.000 0.000 0.325 0.005 14.505 0.336 1.332 -0.012 27.996 1.244 0.097 23.744 -28.571 0.107 0.088 23.740 -14.551 -0.039 0.762 23.731 -0.010 0.519 2.085 23.690 14.433 1.780 4.077 23.601 27.829 3.567 0.383 47.443 -28.589 0.070 1.376 47.437 -14.594 0.761 3.044 47.382 -0.102 2.245 5.350 47.250 14.217 4.461 8.309 47.035 27.462 7.152 2.195 71.117 -28.638 1.321 4.179 71.046 -14.744 2.971 6.825 70.878 -0.385 5.443 10.089 70.588 13.729 8.622 13.971 70.185 26.756 12.198 5.517 94.685 -28.814 3.928 8.474 94.478 -15.102 6.592 12.072 94.124 -0.964 10.091 16.251 93.602 12.860 14.270 21.012 92.934 25.577 18.785 10.343 117.099 -29.198 7.693 14.241 116.680 -15.736 11.366 18.738 116.067 -1.894 15.887 23.795 115.244 11.558 21.050 29.408 114.248 23.889 26.486

% of Error x -1.19 -1.02 -0.87 -0.66 -0.37 -2.73 -2.59 -2.46 -2.29 -2.11 -1.99 -1.79 -1.64 -1.52 -1.44 -1.21 -1.06 -0.96 -0.89 -0.87 -0.55 -0.46 -0.42 -0.39 -0.38 -0.08 -0.04 0.00 0.04 0.09 0.46 0.48 0.50 0.56 0.66 0.89 0.96 1.05 1.15 1.32 1.39 1.53 1.68 1.83 2.06 2.03 2.22 2.40 2.56 2.81 0.87 1.08 1.26 1.41 1.68

y -0.85 -1.34 -0.88 0.02 -0.94 -0.72 -1.15 -0.60 0.31 -0.74 -0.66 -0.99 -0.35 0.49 -0.68 -0.50 -0.79 -0.14 0.60 -0.69 -0.36 -0.69 -0.04 0.63 -0.74 -0.29 -0.66 0.00 0.62 -0.76 -0.30 -0.67 0.04 0.65 -0.70 -0.29 -0.64 0.14 0.76 -0.56 -0.19 -0.54 0.28 0.88 -0.40 0.01 -0.35 0.47 1.00 -0.31 0.39 0.01 0.80 1.22 -0.14

z -5.56 -6.07 -6.74 -7.16 -6.70 -4.04 -4.33 -4.69 -4.77 -4.23 -3.18 -3.03 -3.00 -2.84 -2.43 -2.01 -1.61 -1.40 -1.18 -0.96 -0.82 -0.52 -0.38 -0.20 -0.15 -0.03 0.03 0.00 0.02 -0.18 0.02 -0.26 -0.50 -0.62 -1.04 -0.64 -1.25 -1.62 -1.81 -2.35 -1.78 -2.45 -2.81 -2.98 -3.60 -3.23 -3.83 -4.03 -4.03 -4.52 -5.39 -5.84 -5.79 -5.58 -5.94

Table 3: Coordinates of the different points as shown in figure 3 in the initial and final configurations- dimensions in inch. (unit in inch) for [0/45]T laminate. Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

Undeformed Shape x -101.910 -101.910 -101.910 -101.910 -101.910 -81.528 -81.528 -81.528 -81.528 -81.528 -61.146 -61.146 -61.146 -61.146 -61.146 -40.764 -40.764 -40.764 -40.764 -40.764 -20.382 -20.382 -20.382 -20.382 -20.382 0.000 0.000 0.000 0.000 0.000 20.382 20.382 20.382 20.382 20.382 40.764 40.764 40.764 40.764 40.764 61.146 61.146 61.146 61.146 61.146 81.528 81.528 81.528 81.528 81.528 101.910 101.910 101.910 101.910 101.910

y -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158 -27.158 -13.579 0.000 13.579 27.158

z 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Finite Element x y -93.729 -21.414 -95.517 -9.303 -97.112 3.488 -98.481 16.537 -99.595 29.040 -77.494 -23.868 -78.723 -11.340 -79.790 1.827 -80.674 15.187 -81.367 27.890 -59.293 -25.615 -60.059 -12.743 -60.681 0.744 -61.152 14.376 -61.480 27.253 -40.112 -26.658 -40.523 -13.507 -40.823 0.224 -41.021 14.046 -41.135 27.014 -20.248 -27.201 -20.430 -13.864 -20.529 0.030 -20.564 13.968 -20.566 26.962 0.039 -27.408 0.005 -13.966 0.000 0.000 -0.005 13.966 -0.038 26.908 20.578 -27.444 20.571 -13.972 20.538 -0.026 20.449 13.871 20.289 26.681 41.133 -27.482 41.043 -14.052 40.874 -0.206 40.593 13.534 40.202 26.118 61.478 -27.695 61.196 -14.385 60.766 -0.730 60.157 12.752 59.402 25.013 81.384 -28.262 80.772 -15.163 79.940 -1.799 78.867 11.321 77.634 23.166 99.716 -29.286 98.677 -16.461 97.345 -3.456 95.715 9.234 93.927 20.599

Deformed Shape Laser Displacement Sensor z x y z 37.257 -93.045 -20.769 38.594 31.686 -94.956 -8.557 33.042 26.256 -96.584 3.855 27.853 21.163 -97.946 16.453 23.053 16.672 -99.063 29.226 18.665 26.529 -76.373 -23.403 27.173 21.837 -77.703 -10.781 22.425 17.338 -78.789 2.012 18.091 13.205 -79.656 14.959 14.188 9.655 -80.326 28.046 10.737 17.079 -58.507 -25.196 17.535 13.308 -59.348 -12.230 13.686 9.820 -59.995 0.872 10.292 6.772 -60.472 14.094 7.363 4.326 -60.805 27.419 4.918 9.692 -39.655 -26.295 9.871 6.921 -40.115 -13.059 6.999 4.505 -40.431 0.275 4.611 2.567 -40.634 13.691 2.714 1.199 -40.747 27.170 1.320 4.375 -20.052 -26.864 4.330 2.543 -20.242 -13.439 2.493 1.181 -20.347 0.045 1.158 0.382 -20.394 13.570 0.329 0.153 -20.410 27.118 0.011 1.146 0.056 -27.077 1.022 0.300 0.014 -13.548 0.254 0.000 0.000 0.000 0.000 0.305 -0.014 13.548 0.254 1.136 -0.056 27.077 1.022 0.003 20.410 -27.118 0.011 0.264 20.394 -13.570 0.329 1.057 20.347 -0.045 1.158 2.406 20.242 13.439 2.493 4.163 20.052 26.864 4.330 0.912 40.747 -27.170 1.320 2.236 40.634 -13.691 2.714 4.116 40.431 -0.275 4.611 6.539 40.115 13.059 6.999 9.276 39.655 26.295 9.871 3.937 60.805 -27.419 4.918 6.319 60.472 -14.094 7.363 9.299 59.995 -0.872 10.292 12.815 59.348 12.230 13.686 16.538 58.507 25.196 17.535 9.109 80.326 -28.046 10.737 12.572 79.656 -14.959 14.188 16.651 78.789 -2.012 18.091 21.228 77.703 10.781 22.425 25.874 76.373 23.403 27.173 15.923 99.063 -29.226 18.665 20.366 97.946 -16.453 23.053 25.436 96.584 -3.855 27.853 30.966 94.956 8.557 33.042 36.433 93.045 20.769 38.594

% of Error x 0.87 0.71 0.67 0.68 0.67 1.42 1.29 1.27 1.29 1.32 1.00 0.90 0.87 0.86 0.85 0.58 0.52 0.50 0.49 0.49 0.25 0.24 0.23 0.22 0.20 0.02 0.01 0.00 -0.01 -0.02 -0.21 -0.22 -0.24 -0.26 -0.30 -0.49 -0.52 -0.56 -0.61 -0.69 -0.85 -0.92 -0.98 -1.02 -1.13 -1.34 -1.41 -1.46 -1.47 -1.60 -0.83 -0.93 -0.96 -0.96 -1.12

y 0.82 0.95 0.46 -0.11 0.23 0.59 0.71 0.23 -0.29 0.20 0.53 0.65 0.16 -0.36 0.21 0.46 0.57 0.07 -0.45 0.20 0.43 0.54 0.02 -0.50 0.20 0.42 0.53 0.00 -0.53 0.21 0.41 0.51 -0.02 -0.55 0.23 0.40 0.46 -0.09 -0.60 0.22 0.35 0.37 -0.18 -0.66 0.23 0.27 0.26 -0.27 -0.68 0.30 0.08 0.01 -0.51 -0.86 0.22

z 1.69 1.72 2.02 2.39 2.52 0.82 0.74 0.95 1.24 1.37 0.58 0.48 0.60 0.75 0.75 0.23 0.10 0.14 0.19 0.15 -0.06 -0.06 -0.03 -0.07 -0.18 -0.16 -0.06 0.00 -0.06 -0.14 0.01 0.08 0.13 0.11 0.21 0.52 0.61 0.63 0.58 0.75 1.24 1.32 1.26 1.10 1.26 2.06 2.05 1.82 1.52 1.65 3.47 3.40 3.06 2.63 2.74

Comparison of the results from calculation and from experiment: Tables 2 and 3 list the out-of-plane deformation for the two laminates [0/30] and [0/45] as obtained from both experimental measurement and incremental FEM method. Figure 14 shows the 3D plot. Figure 15 shows the 2D plots for laminate made of [0/30] stacking sequence, along three lines (middle, half width and at the edge of the laminate). It can be seen that there is good agreement between experimental measurement and incremental FEM. Figure 16 shows similar comparison for the [0/45] laminate. Again good agreement is obtained between measurement values and those obtained from incremental FEM.

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Figure 15: 2D plots for deformed lines for laminates made of [0/30] lay up sequence. a) at y = -25 mm, b) at y = 0 and c) at y = 25 mm

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Figure 16: 2D plots for deformed lines for laminates made of [0/45] lay up sequence. a) at y = -25 mm, b) at y = 0 and c) at y = 25 mm

Figure 17 shows the comparison of deformation for the [0/30] and [0/45] laminates at three different values of the y coordinate. From figures 14 and 17, It can be seen that the [0/45] laminate shows larger deformation than the [0/30] laminate.

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Figure 17: Comparison of deformed lines between laminate made of [0/30] and [0/45] lay up sequences. a) at y = w/2, b) at y = 0, c) y = w. Discussion: The results presented above show that finite element method can provide good prediction for the deformed configuration for the unsymmetric laminates made of [0/θ] lay up sequences. This gives confidence in the method and it may be used for the prediction of deformation of other laminates with different lay up sequence. However caution needs to be taken for the prediction of the deformed configuration for the situation of square laminates with lay up sequence having the same number of layers in conjugate directions, for example, [0/90], [02/902] or [0m/90m]. This is because for this type of geometry and lay up sequence, theoretically, the two sides should have equivalent deformation, giving rise to a saddle configuration, as shown in figure 5. However in reality, only one curvature exists as shown in figure 6. The reason for this is that in reality, there may be un-uniform spatial distribution of the properties of the material in the laminate. This can make one direction weaker (or stronger) than the other direction. Once an initiation begins, the following action would favor one direction over the other giving rise to the final configuration as shown in figure 6. This issue can not be addressed using analytical technique, which does not take into account the variability in the material properties. Conclusions: Curved and twisted composite laminates can be made using the method of 4D printing of composites (4DPC). The deformed configurations of laminates made using the lay up sequences [0/30] and [0/45] have been determined using both theoretical calculations and measurement methods. Good agreement was obtained. This gives confidence to the calculation method to predict the final configuration of the laminates.

Laminates with combination of bending and twist curvatures can have applications in the low cost manufacturing of hockey stick blades, turbine blades, solar energy concentrators, actuators, medical devices etc. Acknowledgement: Financial support from the Natural Sciences and Engineering Research Council of Canada is appreciated. The manufacturing of the samples by Dr. Daniel Iosif Rosca, and the CMM measurement using the laser sensor by Mr. Heng Wang are appreciated. Data availability: The data for this paper are available upon request. References: 1. Tibbits S., “The emergence of 4D printing”, TED conference, 2013. 2. Farhang Momeni, Seyed M. Mehdi, Hasani N., Xun Liu, and Jun Ni, “A review of 4D printing”, Materials and Design, 122, 2017, pp. 42-79. 3. Mitchell A., Lafont U., Holynska M., Semprimoschnig C., “Additive Manufacturing,- A review of 4D printing and future applications”, Additive Manufacturing, 24, 2018, pp. 606-626. 4. Minkyu Kang, Youngjun Pyo, Joon young Jang, Yunchan Park, Yeon-Ho Son, MyungChan Choi, Joo wan Ha, Young-Wook Chang, Caroline Sunyong Lee, “Design of a shape memory composite (SMC) using 4D printing technology, Sensors and Actuators A: Physical, 283, 2018, pp. 187-195. 5. Farhang Memoni and Jun Ni, “Nature-inspired smart solar concentrators by 4D printing”, Renewable energy, 122, 2018, pp. 35-44. 6. Anna B. Baker, Simon R.G. Bates, Thomas M. Llewellyn-Jones, Laurie P.B. Valori, Michael P.M. Dicker, Richard S. Trask, “4D printing with robust thermoplastic polylurethane hydrogel-elastomer layers”, Materials and Design, 163, 2019, 107544. 7. Mohd Javad and Abid Haleem, “4D printing applications in medical field: A brief review”, Clinical epidemiology and global health, https://doi.org/10.1016/j.cegh.2018.09.007. 8. Hoa Suong Van, “Factors affecting the properties of composites made by 4D printing (moldless composite manufacturing)”, Advanced Manufacturing: Polymer & Composites Science, Vol. 3, No. 3, 2017, pp. 101-109. 9. Hoa Suong Van, “ Development of composite springs using 4D printing method”, Composite Structures, 210, 2019, pp. 869-876. 10. Dano M. L. and Hyer M.W., “Thermally induced deformation behavior of unsymmetric laminates”, Int. J. Solids Structures, Vol. 35, No. 17, 1998, pp. 2101-2120. 11.Hyer M. W., “Some observations on the cured shape of thin unsymmetric laminates”, J. Composite Materials, Vol. 15, March 1981, pp. 175-194. 12. Hyer M., Stress analysis of fiber reinforced composite materials, Destech Publications, 2009.