Fiber-reinforced composite

FRC is high-performance fiber composite achieved and made possible by cross-linking cellulosic fiber molecules with resins in the FRC material matrix through a proprietary molecular re-engineering process, yielding a product of exceptional structural properties.

Through this feat of molecular re-engineering selected physical and structural properties of wood are successfully cloned and vested in the FRC product, in addition to other critical attributes to yield performance properties superior to contemporary wood.

This material, unlike other composites, can be recycled up to 20 times, allowing scrap FRC to be reused again and again.

The failure mechanisms in FRC materials include delamination, intralaminar matrix cracking, longitudinal matrix splitting, fiber/matrix debonding, fiber pull-out, and fiber fracture.[1]

Difference between wood plastic composite and fiber-reinforced composite:

The appropriate "average" of the individual phase properties to be used in describing composite tensile behavior can be elucidated with reference to Fig. 6.2. Although

this figure illustrates a plate-like composite, the results that follow are equally applicable to fiber composites having similar phase arrangements. The two phase

material of Fig. 6.2 consists of lamellae of ${\displaystyle \alpha }$ and ${\displaystyle \beta }$ phases of thickness ${\displaystyle l_{\alpha }}$ and ${\displaystyle l_{\beta }}$. and respectively. Thus, the volume fractions (${\displaystyle V_{\alpha }}$, ${\displaystyle V_{\beta }}$) of the phases are ${\displaystyle V_{\alpha }={\frac {l_{\alpha }}{l_{\alpha }+l_{\beta }}}}$ and ${\displaystyle V_{\beta }={\frac {l_{\beta }}{l_{\alpha }+l_{\beta }}}}$.

Case I: Same stress, different strain

A tensile force F is applied normal to the broad faces (dimensions Lx L) of the phases. In this arrangement the stress borne by each of the phases (= F/${\displaystyle L^{2}}$) is the same, but the strains (${\displaystyle \varepsilon _{\alpha }}$, ${\displaystyle \varepsilon _{\beta }}$) they experience are different. composite strain is a volumetric weighted average of the strains of the individual phases.

${\displaystyle \vartriangle l_{\alpha }=\varepsilon _{\alpha }l_{\alpha }}$, ${\displaystyle \vartriangle l_{\beta }=\varepsilon _{\beta }l_{\beta }}$

The total elongation of the composite, ${\displaystyle \vartriangle l_{c}}$ is obtained as ${\displaystyle \vartriangle l_{c}=N\vartriangle l_{\alpha }+N\vartriangle l_{\beta }}$

and the composite strain ${\displaystyle \varepsilon _{c}}$ is, ${\displaystyle \varepsilon _{c}}$=${\displaystyle {\frac {\vartriangle l_{c}}{N(l_{\alpha }+l_{\beta })}}}$=${\displaystyle V_{\alpha }\varepsilon _{\alpha }+V_{\beta }\varepsilon _{\beta }}$= ${\displaystyle \sigma {\biggl (}{\frac {V_{\alpha }}{E_{\alpha }}}+{\frac {V_{\beta }}{E_{\beta }}}{\biggr )}}$

Composite modulus ${\displaystyle E_{c}={\frac {E_{\alpha }E_{\beta }}{V_{\alpha }E_{\beta }+V_{\beta }E_{\alpha }}}}$

Case II: different stress, same strain

Fibers that are aligned parallel to the tensile axis, the strains in both phases are equal (and the same as the composite strain), but the external force is partitioned

unequally between the phases. ${\displaystyle F=F_{\alpha }+F_{\beta }=NL(\sigma _{\alpha }l_{\alpha }+\sigma _{\beta }l_{\beta })}$

${\displaystyle \sigma _{c}=\left({\frac {\sigma _{\alpha }l_{\alpha }}{l_{\alpha }+l_{\beta }}}+{\frac {\sigma _{\beta }l_{\beta }}{l_{\alpha }+l_{\beta }}}\right)=\sigma _{\alpha }V_{\alpha }+\sigma _{\beta }V_{\beta }}$

${\displaystyle E_{c}=V_{\alpha }E_{\alpha }+V_{\beta }E_{\beta }}$

When the fiber is aligned parallel to the direction of the matrix and applied the load as the same strain case. The fiber and matrix has the volume fraction ${\displaystyle V_{f}}$, ${\displaystyle V_{m}}$; stress ${\displaystyle \sigma _{f}}$ , ${\displaystyle \sigma _{m}}$; strain${\displaystyle \varepsilon _{f}}$,${\displaystyle \varepsilon _{m}}$; and modulus ${\displaystyle E_{f}}$, ${\displaystyle E_{m}}$. And here ${\displaystyle \varepsilon _{f}}$=${\displaystyle \varepsilon _{f}}$=${\displaystyle \varepsilon _{c}}$. The uniaxial stress-strain response of a fiber composite can be divided into several stages.

In stage 1, when the fiber and matrix both deform elastically, the stress and strain relation is ${\displaystyle \sigma _{c}=V_{f}E_{f}\varepsilon _{f}+V_{m}E_{m}\varepsilon _{m}=\varepsilon _{c}(V_{f}E_{f}+V_{m}E_{m})}$

${\displaystyle E_{c}=V_{f}E_{f}+V_{m}E_{m}}$

In stage 2, when the stress for the fiber is bigger than the yield stress, the matrix starts to deform plastically, and the fiber are still elastic, the stress and strain relation is

${\displaystyle \sigma _{c}=V_{f}E_{f}\varepsilon _{f}+V_{m}\sigma _{m}(\varepsilon _{m})=V_{f}E_{f}\varepsilon _{c}+V_{m}\sigma _{m}(\varepsilon _{c})}$

${\displaystyle E_{c}=V_{f}E_{f}+V_{m}\left({\frac {d\sigma _{m}}{d\varepsilon _{c}}}\right)}$

In stage 3, when the matrix the fiber both deform plastically, the stress and strain relation is

${\displaystyle \sigma _{c}=V_{f}\sigma _{f}(\varepsilon _{f})+V_{m}\sigma _{m}(\varepsilon _{m})=V_{f}\sigma _{f}(\varepsilon _{c})+V_{m}\sigma _{m}(\varepsilon _{c})}$

${\displaystyle E_{c}=V_{f}\left({\frac {d\sigma _{f}}{d\varepsilon _{c}}}\right)+V_{m}\left({\frac {d\sigma _{m}}{d\varepsilon _{c}}}\right)}$

Since some fibers do not deform permanently prior to fracture, stage 3 cannot be observed in some composite.

In stage 4, when the fiber has already become fracture and matrix still deforms plastically, the stress and strain relation is

${\displaystyle \sigma _{c}=V_{m}\sigma _{m}(\varepsilon _{m})}$

However, it is not completely true, since the failure fibers can still carry some load.

For discontinuous fibers (also known as whiskers, depending on the length), tensile force is transmitted from the matrix to the fiber by means of shear stresses that develop along the fiber-matrix interface.

Matrix has displacement equals zero at fiber midpoint and maximum at ends relative to the fiber along the interface. Displacement causes interfacial shear stress ${\displaystyle \tau _{m}}$ that is balanced with fiber tensile stress ${\displaystyle \sigma _{f}}$. ${\displaystyle d_{f}}$ is the fiber diameter, and ${\displaystyle x}$ is the distance from the fiber end.

${\displaystyle \tau _{m}(\pi d_{f})dx=\left({\frac {\pi d_{f}^{2}}{4}}\right)d\sigma _{f}}$

${\displaystyle {\frac {d\sigma _{f}}{dx}}={\frac {4\tau _{m}}{d_{f}}}}$

After only a very small strain, the magnitude of the shear stress at the fiber end becomes large. This leads to two situation: fiber-matrix delamination or matrix having plastic shear.

If matrix has plastic shear: interfacial shear stress ${\displaystyle \tau _{m}\leq \tau _{my}}$. Then there is a critical length ${\displaystyle l_{c}}$ that when ${\displaystyle l>l_{c}}$, after certain ${\displaystyle x}$, ${\displaystyle \sigma _{f}}$ remains constant and equals to stress in equal-strain condition.

${\displaystyle \sigma _{f}(\varepsilon _{c})=2{\frac {\tau _{my}l_{c}}{d_{f}}}}$

${\displaystyle {\frac {l_{c}}{d_{f}}}={\frac {\sigma _{f}(\varepsilon _{c})}{2\tau _{my}}}}$

The ratio, ${\displaystyle {\frac {l_{c}}{d_{f}}}}$ is called the "critical aspect ratio". It increases with composite strain ${\displaystyle \varepsilon _{c}}$. For the mid-point of a fiber to be stressed to the equal-strain condition at composite fracture, its length must be at least ${\displaystyle d_{f}\sigma _{f}^{tensile}/2\tau _{my}}$.

Then calculate average stress. The fraction of the fiber length carrying stress ${\displaystyle \sigma _{f}(\varepsilon _{c})}$ is ${\displaystyle {\frac {l-l_{c}}{l}}}$. The remaining fraction ${\displaystyle {\frac {l_{c}}{l}}}$ bears an average stress ${\displaystyle \sigma _{f}(\varepsilon _{c})/2}$.

${\displaystyle {\overline {\sigma }}_{f}=\sigma _{f}(\varepsilon _{c})\left[1-\left({\frac {l_{c}}{l}}\right)\right]+{\frac {1}{2}}\sigma _{f}(\varepsilon _{c})\left({\frac {l_{c}}{l}}\right)=\sigma _{f}(\varepsilon _{c})\left[1-\left({\frac {l_{c}}{2l}}\right)\right]\quad l\geq l_{c}}$

For ${\displaystyle l<l_{c}}$, average stress is ${\displaystyle \sigma _{m}ax/2}$ with ${\displaystyle \sigma _{m}ax=2\tau _{my}l/d_{f}}$.

${\displaystyle {\overline {\sigma }}_{f}={\frac {1}{2}}\sigma _{f}(\varepsilon _{c})\left({\frac {l}{l_{c}}}\right)\quad l\leq l_{c}}$

The composite stress is modified as following:

${\displaystyle \sigma _{c}=V_{f}\sigma _{f}(\varepsilon _{c})\left[1-\left({\frac {l_{c}}{2l}}\right)\right]+V_{m}\sigma _{m}(\varepsilon _{m})\quad l\geq l_{c}}$

${\displaystyle \sigma _{c}=V_{f}\sigma _{f}(\varepsilon _{c})\left({\frac {l}{2l_{c}}}\right)+V_{m}\sigma _{m}(\varepsilon _{m})\quad l\leq l_{c}}$

The above equations assumed the fibers were aligned with the direction of loading. A modified rule of mixtures can be used to predict composite strength, including an orientation efficiency factor, ${\displaystyle \eta _{0}}$, which accounts for the decrease in strength from misaligned fibers.[3]

${\displaystyle \sigma _{c}(\varepsilon )=V_{m}\sigma _{m}(\varepsilon )+\eta _{0}\eta _{f}V_{f}\sigma _{f}(\varepsilon )}$

where ${\displaystyle \eta _{f}}$ is the fiber efficiency factor equal to ${\displaystyle {\frac {l}{2l_{c}}}}$for ${\displaystyle l\leq l_{c}}$, and ${\displaystyle \left[1-\left({\frac {l_{c}}{2l}}\right)\right]}$for ${\displaystyle l>l_{c}}$. If the fibers are perfectly aligned with the direction of loading ${\displaystyle \eta _{0}}$ is 1. However, common values of ${\displaystyle \eta _{0}}$ for randomly oriented are roughly 0.375 for an in-plane two-dimensional array and 0.2 for a three-dimensional array.[3]

Appreciable reinforcement can be provided by discontinuous fibers provided their lengths are much greater than the (usually) small critical lengths. Such as MMCs.

If there is fiber-matrix delamination. ${\displaystyle \tau _{my}}$ is replaced by friction stress ${\displaystyle \mu P}$ where ${\displaystyle \mu }$ is the friction coefficient between the matrix and the fiber, and ${\displaystyle P}$ is an internal pressure.

${\displaystyle {\frac {l_{c}}{d_{f}}}={\frac {\sigma _{f}(\varepsilon _{c})}{2\mu P}}}$

This happens in most resin-based composites.

Composites with fibers length less than ${\displaystyle l_{c}}$ contribute little to strength. However, during composite fracture, the short fibers do not fracture. Instead they are pulled out of the matrix. The work associated with fiber pull-out provides an added component to the fracture work and has a great contribution to toughness.

There are also applications in the market, which utilize only waste materials. Its most widespread use is in outdoor deck floors, but it is also used for railings, fences, landscaping timbers, cladding and siding, park benches, molding and trim, window and door frames, and indoor furniture. See for example the work of Waste for Life, which collaborates with garbage scavenging cooperatives to create fiber-reinforced building materials and domestic problems from the waste their members collect: Homepage of Waste for Life

Adoption of natural fiber in reinforced polymer composites potentially to be used in automotive industry could significantly help developing a sustainable waste management.[4]

• Fiber volume ratio
• Fracture mechanics
• Plastic composite (disambiguation)
• Plastic lumber
• Wood plastic composite
• Fibre-reinforced plastic

3. Thomas H. Courtney. "Mechanical Behavior of Materials". 2nd Ed. Waveland Press, Inc. 2005. ISBN 1-57766-425-6