TMM4175 Polymer Composites
Fibers¶
A fiber is simply a component that is significantly longer than it is wide and where the cross section dimensions are on the microscale. There is a vast amount of both natural fibers and synthetic fibers, many of them applicable for composites. The following overview is relatively comprehensive, yet not complete:
Natural fibers fall largely into two different groups: the ones base on cellulose (vegetable fibers) and the ones base on animal proteins. In the first group, we find significant fibers as Wood fibers, Hemp, Jute, Flax, Sisal and Cotton. Fibers from animals includes Wool, Hair and Fur broadly, Silk from silkworm and spider as well as Skin and Gut. The only naturally occurring inorganic fibers are the Asbestos.
Synthetic fibers are often categorized by the three main groups of materials: Metals, Ceramics and Polymers. Fibers of metals and ceramics are frequently called inorganic fibers, while polymer fibers are called organic fibers. Any metal and alloy that can be drawn into fibers (that is, most of the engineering metals) is principally a candidate for a metallic fiber, some of the significant being Steel, Copper, Nickel, Titanium and Aluminum alloys. Significant ceramic fibers includes Glass fibers, Alumina fibers, Silicon Carbide fibers, Basalt fibers and Boron fibers. Carbon and Graphite fibers are often included in this group although they do not follow the definition of ceramics consistently. A complete list of available polymer fibers would be extensive. Commercially important fibers for non-composite applications (textiles, ropes, etc.) include Polyesters, Polyamides, Polypropylene and Polyethylene. The number of significant polymer fibers for structural composites is however more limited, the Aramids (such as Kevlar) being the most important.
Glass fibers¶
Glass fibers are used extensively in commercial composite applications due to their combinations of low cost, high strength and chemical resistance. E-glass fiber is by far the most common and least expensive type, followed by S-glass fiber that comes with slightly higher stiffness and significant higher strength and cost. Glass fibers are brittle and their high strength depends on the absence of flaws and defects. Virgin glass filaments are very susceptible to degradation from exposure to environment and mechanical abrasion. Therefore, a protective sizing (i.e. coating) is applied immediately after manufacturing. The sizing also serves as a, usually required, coupling agent for fiber-matrix bonding.
The relatively wide tensile strength range of E-glass fiber given in Table-1 reflects primarily the different conditions under which the strengths were obtained. Freshly drawn fibers will typically show significantly higher strength than fibers exposed to environment and handling during subsequent composite manufacturing steps.
While the diameters of carbon and aramide fibers are found within a relatively narrow and consistent range, glass fibers show a much greater variaton, both between different batches and within individual batches. The case study fiber diameter distribution provide an example of a statistical representation of the variation.
Carbon and graphite fibers¶
Carbon and graphite fibers can be produced with a wide range of properties. They generally exhibit superior strength, have high moduli, excellent fatigue properties, and do not corrode. Although the terms are often used interchangeably, graphite fibers are graphitized at higher temperature then carbon fibers, graphite fibers have carbon contents greater than 99 percent and elastic moduli greater than 345 GPa, while carbon fibers have lower carbon contents (93 to 95 percent) [1] [2]. The P100S and possibly the M60 in Table-1 falls into the category graphite fibers while the other examples are carbon fibers by the definition.
For the remainder of this compendium, the general term carbon will be used for both carbon and graphite fibers.
Aramid fibers¶
Aramid fibers are organic fibers with stiffness and strength intermediate between those of glass and carbon. Kevlar fibers are the most prevalent. The structure of aramid fibers consists of highly crystalline, aligned polymer chains having aromatic rings that provide thermal stability. However, the bonds between the chains are relatively weak causing the compression strength to be much less the tensile strength. Due to their extreme toughness and ability to absorb large amounts of energy during fracturing, aramid fibers are often used for ballistic protection.
| Density (g/cm3) |
Diameter (um) |
Longitudinal modulus (GPa) |
Poisson's ratio |
Tensile strength (MPa) |
longitudinal CTE (10-6 /K) |
|
|---|---|---|---|---|---|---|
| E-glass [1-6] | 2.50-2.60 | 5-25 | 69-76 | 0.22 | 1700-3800 | 4.9-6.0 |
| S-glass [1-6] | 2.46-2.49 | 5-15 | 84-91 | 0.23 | 4400-4800 | 1.6-2.9 |
| Carbon, T300 [2][7] | 1.77 | 7-9 | 230 | 0.2 | 3600 | -0.5 |
| Carbon, AS4 [2][8] | 1.80 | 7-9 | 235 | 0.2 | 3600 | -0.5 |
| Carbon, IM6 [8] | 1.76 | 276 | 5600 | |||
| Carbon, T1100GC [7] | 1.79 | 324 | 7000 | |||
| Carbon, M60JB [7] | 1.93 | 588 | 3820 | |||
| Carbon, P100s [2] | 2.15 | 724 | 0.2 | 2200 | -1.0 | |
| Kevlar-29 [1] | 1.44 | 12 | 83 | 0.34 | 3000-3600 | -2.0 |
| Kevlar-49 [1] | 1.44 | 12 | 130 | 0.34 | 3000-3600 | -2.0 |
| Kevlar-149 [1] | 1.47 | 12 | 186 | 0.34 | 3000-3600 | -2.0 |
| Boron [2][6] | 2.4-2.6 | 33-140 | 365-440 | 0.21 | 2300-3800 | 8.3 |
| Bamboo [9] | 0.6-1.1 | 25-40 | 11-32 | 140-800 | ||
| Flax [9] | 1.4-1.5 | 12-600 | 27-103 | 343-2000 | ||
| Hemp [9] | 1.4-1.5 | 25-500 | 23-90 | 270-900 | ||
| Sisal [9] | 1.33-1.5 | 8-200 | 9-38 | 363-700 |
Table-1: Fiber properties
Natural fibers¶
Natural fibers are one of the abundant resources that exist in nature. They are easily decomposable, bio degradable, renewable and cost efficient and used as reinforcement material in polymers for the growth of natural-fiber composites. The renewable fibers have high potential due to low cost, high production volume, and their advantageous properties in other markets. However, one of the biggest disadvantages of natural fibers in structural composites is their variability in mechanical properties. This variability is typical for all natural fibers, and most data tables give a wide range of values for each property [9].
Fun fact¶
Boeing's 787 Dreamliner contains 20 ton carbon fibers . The diameter of a carbon fiber is approximatly 10 micrometer and the density is 1.8 g per cubic centimeter. The total length of fibers is:
rho, r, m = 1800 , 5E-6, 20E3 #density, radius, and mass (SI-units)
L = (m/rho)/(3.14*r**3)
print('Length = ',L, 'm')
print('The fiber can be stretched to the sun and back',round(L/(2*1.5E11)),'times.')
Specific stiffness and strength¶
The most cited advantage of fiber composites is high specific stiffness and strength compared to traditional engineering materials. These properties lead to improved performance and reduced energy consumption for most engineering structures. At the extremes, advanced fiber composites enables technological solutions that would have been impossible using traditional engineering materials.
Specific stiffness is simply the modulus divided by the mass density, while the specific strength is the tensile strength divided by the mass density. For the fibers in Table-1 we can explore these values using Python.
The first step is to create a list of dictionaries, each dictionary having the relevant fiber properties. The maximum values are used for all values, and steel and aluminum are added for comparison. Note that the assumed strength values of these metals are probably on the limit of, or beyond, achievable performance:
fibers=[]
fibers.append( {'name':'E-glass' , 'rho':2.60, 'E': 76, 'TS':3800} )
fibers.append( {'name':'S-glass' , 'rho':2.49, 'E': 91, 'TS':4800} )
fibers.append( {'name':'T300' , 'rho':1.77, 'E': 230, 'TS':3600} )
fibers.append( {'name':'IM6' , 'rho':1.76, 'E': 276, 'TS':5600} )
fibers.append( {'name':'T1100' , 'rho':1.79, 'E': 324, 'TS':7000} )
fibers.append( {'name':'M60' , 'rho':1.93, 'E': 588, 'TS':3820} )
fibers.append( {'name':'P100S' , 'rho':2.15, 'E': 724, 'TS':2200} )
fibers.append( {'name':'Kevlar29' , 'rho':1.45, 'E': 83, 'TS':3600} )
fibers.append( {'name':'Kevlar49' , 'rho':1.45, 'E': 130, 'TS':3600} )
fibers.append( {'name':'Kevlar149' , 'rho':1.45, 'E': 186, 'TS':3600} )
fibers.append( {'name':'Boron' , 'rho':2.60, 'E': 440, 'TS':3800} )
fibers.append( {'name':'Hemp' , 'rho':1.45, 'E': 90, 'TS': 900} )
fibers.append( {'name':'Steel' , 'rho':7.80, 'E': 210, 'TS':2000} )
fibers.append( {'name':'Aluminum' , 'rho':2.70, 'E': 70, 'TS':1000} )
Then, iterate through the list and compute the specific stiffness and strength for each:
print('Specific stiffness and strength:')
for fib in fibers:
specModulus, specStrength = round(fib['E']/fib['rho'],1) , round(fib['TS']/fib['rho'],1)
fib.update({'E/rho':specModulus, 'TS/rho':specStrength})
text='{0:10}: {1:10} {2:10}'.format(fib['name'], specModulus,specStrength)
print(text)
A graphical representation is useful for comparison and further discussion (Source code of plotMatIndex() in Plot gallery):
names,xdata,ydata=[],[],[]
for fib in fibers:
names.append(fib['name'])
xdata.append(fib['E/rho'])
ydata.append(fib['TS/rho'])
from plotlib import plotMatIndex
%matplotlib inline
plotMatIndex(names,xdata,ydata,'Specific Stiffness','Specific Strength')
Keep in mind that the data is for the fiber only, with tensile loading along the fiber direction. Properties are obviously reduced significantly for a composite consisting of fibers and matrix and in the form of a laminate where the loading may be inclined relatively to the fiber direction. Nevertheless, the results show the potential performance as well as the difference between the fibers.
Python tips & tricks¶
Use pandas to sort and present the fiber data (sort decending by specific tensile strength):
import pandas as pd
df = pd.DataFrame(fibers)
display(df.sort_values('TS/rho',ascending=False))
Fracture toughness and strength of brittle fibers¶
The strength of any sample of a glass or ceramic is actually determined by the size of the largest defect, or crack, which it happens to contain. Roughly, the strength is proportional to the inverse square root of the length. According to linear elastic fracture mechanics, the relation between fracture toughness $K_{Ic}$, stress or strength at fracture $\sigma_c$ and crack length $a$ is given by:
\begin{equation} K_{Ic} = Y \sigma_c \sqrt{\pi a} \tag{1} \end{equation}where $Y$ is a geometry parameter. The apparent strength for any crack length is therefore
\begin{equation} \sigma_c = \frac{K_{Ic}}{Y \sqrt{a\pi}} \tag{2} \end{equation}The fracture toughness for E-glass fiber is found to be approximately 1.1 $\text{MPa}\sqrt{\text{m}}$ while the geometry parameter $Y$ can be approximated by [10]
\begin{equation} Y=1.0 + 2\frac{a}{D} \tag{3} \end{equation}where $D$ is the fiber diameter.
The apparent strength for any given crack length can now be computed as:
def fiberStrengthEglass(D,a):
from math import pi
KIc=1.1
Y=1+2*(a/D)
sc=KIc/( Y*(a*1E-6*pi)**0.5) # a must be converted to m!
print('Strength when D=',D, 'um and', 'a=',a, 'um is', sc, 'MPa')
for ac in (1.0, 0.5, 0.1, 0.05):
fiberStrengthEglass(D=10.0, a=ac)
The results suggest that the larges flaw size of a typical E-glass fiber is less than 0.1 micrometer = 100 nanometer and therefore less than 1% of the fiber diameter.
References and further readings¶
- Campbell, F. C. Structural Composite Materials. Materials Park, Ohio: ASM International, 2010.
- Herakovich, Carl T. Mechanics of Fibrous Composites. New York: Wiley, 1998.
- Hull, Derek, and T.W. Clyne. An Introduction to Composite Materials. 2nd ed. Cambridge: Cambridge UP, 1996.
- Daniel, Isaac M., and Ori Ishai. Engineering Mechanics of Composite Materials. 2nd ed. New York: Oxford University Press, 2006.
- Muthu, Subramanian Senthilkannan, Rana, Sohel, and Fangueiro, Raul. Fibrous and Textile Materials for Composite Applications. 1st Ed. 2016 ed. Textile Science and Clothing Technology. Singapore: Springer Singapore, 2016.
- Lee, Stuart M. Handbook of Composite Reinforcements. John Wiley & Sons, 1993.
- http://www.torayca.com/en/download/pdf/torayca.pdf
- https://www.hexcel.com/user_area/content_media/raw/HexTowSelectorGuide.pdf
- David B. Dittenber, Hota V.S. GangaRao, Critical review of recent publications on use of natural composites in infrastructure, Composites Part A: Applied Science and Manufacturing, Volume 43, Issue 8, 2012, Pages 1419-1429,
- Herráez, M., A. Fernández, C. S. Lopes, and C. González. "Strength and toughness of structural fibres for composite material reinforcement." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2071 (2016): 20150274.
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