NANOFIBER NANOCOMPOSITE FOR STRENGTHENING NOBLE LIGHTWEIGHT SPACE STRUCTURES N.M. Awlad Hossain Assistant Professor Department of Engineering and Design EASTERN WASHINGTON UNIVERSITY Cheney, WA 99004 Email: nhossain@ewu.edu Phone: 509-359-2871-1 -
ABSTRACT Structural weight reduction to minimize the launching cost is one of the desired outcomes of all space missions. One way to achieve this objective is through the replacement of metallic structures with advanced composites. Currently, composite materials are widely used in many engineering applications because of their lightweight, novel multifunctional properties and low cost. The primary focus of this research was to examine the effects of fiber geometry to improve the strength of composites, and to pursue the possible advantages of using nanofibers instead of conventional fibers. First, a theoretical background was established to determine that the nanofiber composite contains significantly more surface area of fiber over the conventional composite keeping the same fiber volume fraction. The increased surface area of fiber can help to compensate the imperfect bonding between the fiber-matrix interphase. Then, extensive numerical simulation was performed through analyzing three different RVE models where the fiber volume fraction kept constant using reduced fiber diameter. Therefore, the surface area of fiber was increased gradually in each RVE model. The effects of fiber geometry were studied by comparing axial and shear stresses in the fiber region. As the cross sectional area of fiber remained the same in all RVE models, the axial stress of fiber was found relatively unchanged. On the other hand, the surface area of fiber was found to play an important role in shear stress distribution. The shear stress of fiber was found to be reduced significantly with increasing its surface area. Numerical simulation was then repeated with changing the boundary conditions. In all cases, an RVE model with the highest surface area of fiber was found to offer the lowest shear stress compared to the other RVE models. Therefore, if the composite strength depends on surface area of fiber, then a composite consisting of nanofibers will be stronger than a conventional composite prepared with same volume fraction, or conversely will be lighter at the same strength. - 2 -
TABLE OF CONTENTS Topics Page Number I. Introduction 5 II. Theoretical Background 7 III. Analysis 9 A. Numerical Models 9 B. Boundary Conditions and Loading 11 C. Materials Properties 12 IV. Results and Discussions 12 V. Conclusions... 24 VI. Future Work 25 VII. References 26-3 -
LIST OF FIGURES 1. Simplified concept of composite materials and the Representative Volume Element (RVE).. 6 2. Illustration of RVE of conventional and nanofiber composites. 8 3. Illustration of different RVE model with increased fiber surface area while keeping the same fiber volume fraction.. 10 4. Quarter symmetric models of conventional and nanofiber composites used in the numerical analysis. 10 5. 3D view of the conventional composite model... 11 6. Axial stress (z-direction) distribution along the fiber axis between conventional and nanofiber composite models... 13 7. Shear stress distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between the conventional and nanofiber composite models. 14 8. A closer view of shear stress (yz-direction) distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between the conventional and nanofiber composite models.. 14 9. Axial stress (z-direction) distribution along a nodal path coincident to the fiber axis between the conventional and two other nanofiber composites.. 15 10. Shear stress distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between the conventional and two other nanofiber composites. 16 11. A closer view of shear stress (yz-direction) distribution along a nodal path on the topmost fiber layer between the conventional and nanofiber composite, RVE-3. 17 12. A closer view of shear stress (yz-direction) distribution along a nodal path on the topmost fiber layer between two nanofiber composites RVE-2 and RVE-3. 17 13. Contour plot of axial displacement profile of (a) conventional and (b) nanofiber composite, RVE-2 for boundary displacement of 0.5 micron. 18 14. Contour plot of major principal stress distribution for (a) conventional and (b) nanofiber composite, RVE-2. 19 15. Contour plot of shear stress (τ yz ) distribution for (a) conventional and (b) nanofibers composite models... 19 16. Axial stress (z-direction) distribution along a nodal path coincident to the fiber axis between the conventional and nanofibers composite models. 20 17. Shear stress (yz-direction) distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between conventional and nanofiber composite models. 21 18. Contour plot of major principal stress distribution for (a) conventional and (b) nanofibers composite models. 22 19. Contour plot of shear stress (τ yz ) distribution for (a) conventional and (b) nanofibers composite models.. 22 20. Axial stress distribution along the fiber axis between conventional and two nanofiber composite models.. 23 21. Shear stress (yz-direction) distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between conventional and two nanofiber composite models.. 23-4 -
I. Introduction Structural weight reduction to minimize the launching cost is one of the targeted outcomes of NASA s space missions. One way to achieve this objective is through the replacement of metallic structures with advanced composites. Currently, lightweight composite materials are used in a variety of space applications including solar sails, sun shields, space mirrors & telescopes, lunar habitats, scientific balloons, and inflatable antennas. The primary focus of this research is to examine the effects of fiber geometry to improve the strength of composite materials. The proposed research will investigate the possible advantages of using nanofibers (diameters 10-9 meter) instead of conventional fibers (diameters 10-6 meters). Mathematically, it can be shown that the nanofiber composite contains significantly more surface area over the conventional composite at no cost of volume fraction. The increased surface area can help to compensate for the imperfect bonding between the fiber-matrix interphase. Therefore, composite materials consisting of nanofibers are expected to offer higher strength than a conventional composite prepared with the same volume fraction. Composite materials (or composites for short) are engineered materials made from two or more constituent materials with significantly different physical or chemical properties, and remain separate and distinct on a microscopic level within the finished structure. The two constituent materials are matrix and fiber (or reinforcement). The matrix material surrounds and supports the fiber materials by maintaining their relative positions. The fibers impart their special mechanical and physical properties to enhance the matrix properties. A synergism produces material properties unavailable from the individual constituent materials, while the wide variety of matrix and fiber materials allows the designer of the product or structure to choose an - 5 -
optimum combination. Figure 1(a) represents a simplified concept of composite material with fiber and matrix constituents. Figure 1(b) depicts the Representative Volume Element (RVE) the smallest cell, as shown by dotted line, to describe the individual composite constituents. The RVE is then divided into four subcells, as shown in Figure 1(c), all of rectangular geometry. Fig. 1: Simplified concept of composite materials and the Representative Volume Element (RVE). In a series of papers documented by Dr. Jacob Aboudi [1, 2], the overall behavior of composite materials was explored through micromechanical analysis. The analysis was performed using an RVE approach to predict the elastic, thermoelastic, viscoelastic and viscoplastic responses of composites. The composite material was assumed homogeneously anisotropic (properties depend on the direction) continuum without considering the interaction effects between fibers and matrix. Goh et al. [3] developed an analytical solution describing the average fiber stress (σ f ), where the fiber was surrounded by an elastic matrix. The model proposed in [3] consists of a differential equation whose solution provided the distribution of fiber stress (σ f ) and shear stress between fiber and matrix (τ) as a function of length. Expressions for (σ f ) and (τ) were derived without considering the effect of fiber geometry and fiber-fiber - 6 -
interaction. According to the micromechanics theory, an increase in strength cannot be obtained from scaling fiber size while maintaining the same fiber volume fraction. Assuming a unit depth, volume fraction (V f ) of fiber for the RVE model is defined as follows: 2 V FiberVolume h1 = = f 2 Total Volume ( h + (1) h ) 1 2 It can be seen that if the volume fraction is maintained while scaling h 1 down, this will directly affect the value of h 2. Consequently, the ratio h 1 /h 2 in the micromechanics equation will remain the same, and therefore not affect the strength at all. In conclusion, higher strength to weight ratios cannot be obtained from scaling fiber size down at constant volume fraction. II. Theoretical Background One of the focal points of the proposed research is to determine the strength of composites by creating a more effective RVE model that will incorporate the interaction effects of fibers and matrix. It has been suggested through other studies that the surface area (A s ) of fibers plays an important role in strength of the composites. An advantage of using nanofibers is to increase the surface area, which can help to compensate for imperfect bonding. It can be mathematically shown that the nanofibers composite contains significantly more surface area over the conventional composite at no cost to volume fraction. Figure 2 illustrates the concept of maintaining the same fiber cross-sectional area while increasing fiber surface area. Fig. 2: (a) Illustration of RVE of conventional composite with single unidirectional fiber. (b) Illustration of RVE of modified nanocomposite with many unidirectional fibers. - 7 -
Assuming the same depth dimension, the two fiber scenarios, as shown in Figure 2, represent the following definitions for cross sectional area: π 2 A x, c = * h1, c, (2) 4 π 2 A x, n = * h1, n, (3) 4 Where A x denotes cross-sectional area, subscripts with n and c refer to the nanofiber composite and the conventional composite respectively, and h 1 is the fiber diameter. The cross-sectional area of the conventional composite (A x,c ) can be considered as some multiple, N, of the individual nanofiber cross-sectional area as such: A = N A. (4) x, c * x, n Substituting the definition for A x,c and A x,n simplifies the results in the following relationship: h1, h = c 1, n. N (5) Next, the following two relations assess the total surface areas for each unit cell: A A s, n s, c ~ N * π * h ~ π * h 1, c, 1, n, (6) Where A s is shown as proportional as the depth dimension is omitted. Considering the surface area of nanofiber composite and substitute the relationship as found in Equation 5, the following proportionality is obtained - 8 -
A s, n A A A ~ N * π * h s, n s, n s, n 1, n h1, c ~ N * π * N ~ N * ~ N * A. ( π * h ) s, c 1, c (7) So, mathematically it can be proved that the surface area of fiber in nanofiber composite will be higher than that of conventional composite by a factor of N, where N represents the total number of nano fibers. Therefore, if the composite strength depends on fiber surface area, then a composite consisting of nanofibers will be stronger than a conventional composite prepared with same volume fraction. However, this strength advantage is not apparent in Aboudi s micromechanics theory. The primary purpose of this research will be to examine the effects of fiber geometry, and pursuing the possible advantages of utilizing nanofibers within composite materials using the RVE approach. A. Numerical Models III. Analysis Numerical models of conventional and nanofiber composites were developed using nonlinear finite element code ABAQUS and ANSYS. First, three different RVE models were developed as shown in Figure 3. For simplicity in the following sections, these numerical models are called RVE-1, RVE-2, and RVE-3. Note that all dimensions are in micrometer (μm). RVE-1, as shown in Figure 3(a), represents a conventional composite with one complete fiber connected with matrix. RVE-2, as shown in Figure 3(b) represents a nanofiber composite, with two nano fibers (one complete + four quarters) connected with matrix. Similarly, RVE-3, as shown in Figure 3(c), also represents a nanofiber composite with four nano fibers (one complete + 4 halves+ 4 quarters). In RVE-2 and RVE-3, the fiber size was scaled down from radial - 9 -
dimension 5 micron to 3.5 micron and 2.5 micron, respectively. All RVE models have the same volume fraction of fiber (20%). The surface area of fiber in RVE-2 and RVE-3 was increased by 40% and 100%, respectively compared to the RVE-1. For analysis simplicity and to minimize the computational time, quarter symmetric models of the conventional and nanofiber composites, as shown in Figure 4, were used. Fig. 3: Illustration of different RVE model with increased fiber surface area while keeping the same fiber volume fraction. Fig. 4: Quarter symmetric models of conventional and nanofiber composites used in the numerical analysis. - 10 -
B. Boundary Conditions and Loading Numerical analyses were performed with combining different types of boundary conditions and loadings. For better understanding, a 3D view of the quarter symmetric conventional composite model is shown in Figure 5. Two different boundary conditions were considered, as mentioned below. a. The entire back surface (z = 0), which contains both fiber and matrix nodes, was constrained in its normal direction. b. Only the fiber nodes located at the back surface (z = 0) were constrained in the normal direction. Fig. 5: 3D view of the conventional composite model. For each case, symmetric boundary conditions were applied. In addition, to constrain the rotational motion, two adjacent sides (x = 10, and y = 10) were also constrained to their normal directions. Also, one node point on the back surface was pinned to prevent translation in the global x- and y- directions. For each boundary condition, boundary displacement loading was assigned to the matrix nodes of the front surface. - 11 -
The fiber surface was connected by ties to all correlated matrix surface. The numerical model did not consider any interphase zone. The other quarter symmetric models, as shown in Figure 4, were also analyzed using the same boundary conditions and loading as discussed above. C. Material Properties The materials properties are simply elastic and include Young s modulus and Poisson s ratio. Standard mechanical properties of E-glass and Epoxy were used to mimic the fiber and matrix, respectively. IV. Results and Discussions The following results were obtained when the entire back surface was constrained to its normal direction, and the boundary displacement was applied to matrix at the front surface. All three quarter symmetric models, as shown in Figure 4, were analyzed. For each case, axial and shear stress distribution of the fiber was studied. As the matrix region of nanofiber composite models has different geometry compared to conventional composite, boundary displacement assigned to nanofiber composites was tuned until they offered the same reaction force found for the conventional composite model. First, we compared the stress distribution between RVE-1 and RVE-2. The axial stress distribution along a nodal path coincident with the fiber axis (x = 0 and y = 0) is shown in Figure 6. The cross sectional area of fiber remains the same between the conventional and nanofiber composite models. Therefore, the axial stress distribution was found to be fairly unchanged. The axial stress was found higher near the fixed end and gradually decreased near the free end where load was applied. - 12 -
Fig. 6: Axial stress (z-direction) distribution along the fiber axis between conventional and nanofiber composite models. The shear stress distribution along a nodal path (at angular orientation θ = 90 degree, as called 12 o clock section) on the topmost fiber layer is shown in Figure 7. The surface area of fiber was increased by 40% in RVE-2 compared to RVE-1. Therefore, the shear stress distribution in RVE-2, representing a nanofiber composite, was found significantly reduced. A closer observation of the shear stress distribution, up to nondimensional length (z/l) equal to 0.5, is shown in Figure 8. Shear stress in RVE-2 was found to be reduced by approximately 50% compared to RVE-1. Shear stress was also found to be smaller near the fixed end and increased exponentially towards the free end. - 13 -
Fig. 7: Shear stress distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between the conventional and nanofiber composite models. Fig. 8: A closer view of shear stress (yz-direction) distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between the conventional and nanofiber composite. - 14 -
The axial stress distribution along the fiber axis of all three different RVE models is shown in Figure 9. As the fiber cross sectional area is the same in each RVE model, the axial stress was found almost unchanged up to the nondimensional length (z/l) equal to 0.75. Some discrepancies were observed near the free end where boundary displacement was applied. Fig. 9: Axial stress (z-direction) distribution along a nodal path coincident to the fiber axis between the conventional and two other nanofiber composites. On the other hand, the shear stress distribution of the topmost fiber layer of all three different RVE models is shown in Figure 10. The shear stress in the RVE-2 and RVE-3, representing nanofiber composites, was found to be reduced more with increasing the fiber surface area. The surface area of fiber in RVE-3 is 60% more compared to RVE-2. Subsequently, the shear stress in RVE-3 was found much smaller compared to RVE-2. - 15 -
Fig. 10: Shear stress distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between the conventional and two other nanofiber composites. For closer observation, the shear stress distribution of RVE-3, up to nondimensional length (z/l) equal to 0.50, is plotted separately with RVE-1 and RVE-2. These results are shown in Figures 11 and 12, respectively. The surface area of fiber in RVE-3 is increased by 100% compared to the RVE-1, and by 60% compared to RVE-2. Shear stress of the topmost fiber layer, as shown in Figures 11 and 12, is expected to decrease more with the additional increment of the surface area of fiber. - 16 -
Fig. 11: A closer view of shear stress (yz-direction) distribution along a nodal path on the topmost fiber layer between the conventional and nanofiber composite, RVE-3. Fig. 12: A closer view of shear stress (yz-direction) distribution along a nodal path on the topmost fiber layer between two nanofiber composites RVE-2 and RVE-3. - 17 -
Numerical simulation of the above three RVE models was then repeated with changing the boundary condition as follows. Instead of constraining the entire back surface, only the fiber nodes on the back surface were constrained to their normal z-direction. Therefore, matrix nodes on the back surface were released to translate along the global z-direction. Boundary displacement was assigned to the matrix nodes of the front surface, as used before. First, RVE-1 and RVE-2 were analyzed and the axial displacement profile is shown in Figure 13. For simplicity, only the fiber displacement is shown. Note that the fiber diameter in RVE-2 was reduced by 30% keeping the same fiber volume fraction, and the surface area of fiber was increased by 41%. Figure 13: Contour plot of axial displacement profile of (a) conventional and (b) nanofiber composite, RVE-2 for boundary displacement of 0.5 micron. Figure 14 shows the contour plot of major principal stress, developed in the fiber region, of RVE-1 and RVE-2. The maximum stress was found to be 6.177 GPa and 4.82 GPa in RVE-1 and RVE-2, respectively. Therefore, the principal stress was found to be reduced by 22% in RVE-2 compared to the RVE-1 (conventional composite). - 18 -
Figure 14: Contour plot of major principal stress distribution for (a) conventional and (b) nanofiber composite, RVE-2. Figure 15 shows the shear stress (τ yz ) distribution for RVE-1 and RVE-2 models. The maximum shear stress was found to be 2.479 GPa and 1.795 GPa for RVE-1 and RVE-2 models, respectively. Therefore, the maximum shear stress was found to be reduced by 28% in the nanofiber composite RVE-2 compared to the conventional composite RVE-1. Figure 15: Contour plot of shear stress (τ yz ) distribution for (a) conventional and (b) nanofibers composite models. - 19 -
It was evident from these contour plots that both axial and shear stress were found to be reduced by 22% and 28%, respectively when the surface area of fiber was increased by 41% in the nanofibers composite model. The axial stress distribution along the fiber axis (x = 0, and y = 0) of the two different models, RVE-1 and RVE-2, is shown in Figure 16. Boundary displacement was also tuned to RVE-2 to receive the same reaction force at the fiber nodes as found in RVE-1. The axial stress distribution was expected to remain unchanged because of having the same fiber cross sectional area in each RVE model. Some difference was observed near the front surface, where boundary displacement was applied. The stress distribution pattern looks very similar to Figure 6. Fig. 16: Axial stress (z-direction) distribution along a nodal path coincident to the fiber axis between the conventional and nanofibers composite models. The shear stress distribution along a nodal path on the topmost fiber layer is shown in Figure 17. Due to change in boundary condition, the shear stress distribution observed in Figure - 20 -
17 is significantly different from Figure 7. Shear stress was also found to be smaller near the mid section and increased exponentially towards the fixed and free ends. As the surface area of fiber was increased in RVE-2 compared to RVE-1, the shear stress in RVE-2 was found significantly reduced. Fig. 17: Shear stress (yz-direction) distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between conventional and nanofiber composite models. The computational analysis was then advanced by replacing the conventional composite (i.e., RVE-1) with four nanofibers (i.e., RVE-3) keeping the fiber volume fraction same. Here, the fiber diameter was reduced by 50% and the surface area was increased by 100%. Consistency in results was expected as the fiber diameter was further reduced in the nanofibers composite model. The contour plots of principal stress and shear stress of RVE-3 model is shown in Figures 18 and 19, respectively. The maximum stress values were found to be 4.143 GPa and 1.671 GPa, - 21 -
respectively. Both of the stresses were found to be reduced by 33% compared to the conventional composite model RVE-1. Figure 18: Contour plot of major principal stress distribution for (a) conventional and (b) nanofibers composite models. Figure 19: Contour plot of shear stress (τ yz ) distribution for (a) conventional and (b) nanofibers composite models. The axial stress distribution along the fiber axis (x = 0 and y = 0) of three different RVE models is shown in Figure 20. No significant different was observed between them as the fiber cross sectional area was the same. The shear stress is also plotted for the topmost fiber layer at an angular orientation θ = 90 degree for the three different RVE models as shown in Figure 21. An RVE model with higher surface area of fiber was found to offer reduced shear stress. Therefore, - 22 -
the RVE-3 with the highest surface area of fiber was found to offer the least shear stress. The shear stress distribution pattern in Figure 21 has similar trend as shown in Figure 17. Fig. 20: Axial stress distribution along the fiber axis between conventional and two nanofiber composite models. Fig. 21: Shear stress (yz-direction) distribution along a nodal path (on 12 o clock section) on the topmost fiber layer between conventional and two nanofiber composite models. - 23 -
V. Conclusions The primary purpose of this research was to examine the effects of fiber geometry, and pursuing the possible advantages of utilizing nanofibers within composite materials using the representative volume element (RVE) approach. Mathematically, it was shown that nanofibers composite contains higher surface area over the conventional composite at no cost of volume fraction. Three different RVE models were analyzed where the surface area of fiber was increased gradually, keeping the fiber volume fraction constant. The effects of increased surface area were investigated by comparing the axial and shear stresses of fiber region. As the cross sectional area of fiber remained the same in all RVE models, the axial stress along the fiber axis was found almost unchanged. Therefore nanofiber or the fiber geometry was found to be neutral on the axial strength. The axial stress was found to be the highest near the fixed end and gradually decrease towards the free end. This increased surface area of fiber was found to play an important role in shear stress distribution. The shear stress of fiber was found to be reduced significantly with increasing its surface area. Therefore, an RVE model with the highest surface area of fiber was found to offer the least shear stress compared to the other RVE models. Numerical simulations were repeated with changing the boundary conditions, and consistencies in results were observed. In all cases, an RVE model with increase surface area of fiber was found to offer reduced shear stress. Therefore, on the basis of shear stress, developed in the fiber region, a composite consisting of nanofibers will be stronger than a conventional composite prepared with same volume fraction, or conversely will be lighter at the same strength. It is anticipated that the nanofibers composite is not only beneficial to reduce the shear stress but also helps to compensate for imperfect fiber-matrix bonding. - 24 -
VI. Future Work Additional research work is essential to explore the detailed micromechanical behavior of nanofibers composite. In particular, the following items deserved to be potential candidate for further investigation: 1. Currently, the effect of nanofibers on composite strength has been studied by using the RVE approach. To make the research outcomes robust, the nanofibers composite needs to be analyzed using the unit cell approach too. A unit cell has similar concept like the RVE has. The basic difference is that the unit cell s dependence on geometric symmetry that creates a repeatable structure. A unit cell must be symmetrical such that multiple cells combined at any space dimension will eventually build the actual structure of the material. 2. In this current research, the geometry of nanofibers has been found to be neutral on axial strength but has significant impact on shear strength of composite material. The axial stress along the fiber axis was found almost unchanged for the nanofibers composite compared to the conventional composite. However, it is anticipated that the nanofibers composite plays an important role in case of surface defects. Most of the composites fail under tensile loading by fiber breakage. After a fiber break, the fiber can no longer sustain the load it originally endured, and so must transfer the load to the nearest fiber. The length of fiber needed to transfer 90 percent of the original load to the next nearest fiber is considered the ineffective fiber length. It is worth to investigate whether the nanofibers composite offers shorter ineffective fiber length compared to the conventional composites. Shorter ineffective fiber length is desired for better composite strength. 3. Additional research is also essential to simulate the details of broken fiber scenario in composite material. It is important to know how the stress distribution, both axial and shear, will change and vary in a particular fiber when the other nearest fiber is broken. - 25 -
References [1] Aboudi, J., Micromechanical Analysis of Composites by the Method of Cells, ASME, 1989. [2] Aboudi, J., Micromechanics Prediction of Fatigue Failure of Composite Materials, Journal of Reinforced Plastic Composites, 1989. [3] Goh, K.L., Aspden, R.M., and Hukins, D.W.L., Shear Lag Models for Stress Transfer from an Elastic Matrix to a Fiber in a Composite Materials, Int. J. Materials and Structural Integrity, Vol. 1, Nos. 1/2/3, 2007. - 26 -