Rubber toughening

Rubber toughening is a process in which

The presence of a given failure mechanism is determined by many factors: those intrinsic to the continuous polymer phase,[6] and those that are extrinsic, pertaining to the stress, loading speed, and ambient conditions.^[8] The action of a given mechanism in a toughened polymer can be studied with microscopy. The addition of rubbery domains occurs via processes such as melt blending in a Rheomix mixer and atom-transfer radical-polymerization.^[4][8]

Current research focuses on how optimizing the secondary phase composition and dispersion affects mechanical properties of the blend. Questions of interest include those to do with

Different theories describe how a dispersed rubber phase toughens a polymeric substance; most employ methods of dissipating energy throughout the matrix. These theories include: microcrack theory, shear-yielding theory, multiple-crazing theory, shear band and crazing interaction theory, and more recently those including the effects of critical ligament thickness, critical plastic area, voiding and cavitation, damage competition and others.^[5]

Microcrack theory

In 1956, the microcrack theory became the first to explain the toughening effect of a dispersed rubber phase in a polymer.^[5] Two key observations that went into the initial theory and subsequent expansion were as follows: (1) microcracks form voids over which styrene-butadiene copolymer fibrils form to prevent propagation, and (2) energy stored during elongation of toughened epoxies is released upon breaking of rubber particles. The theory concluded that the combined energy to initiate microcracks and the energy to break rubber particles could account for the increased energy absorption of toughened polymers. This theory was limited, only accounting for a small fraction of the observed increase in fracture energy.^[6]

Matrix crazing

The matrix

Interaction between rubber particles and crazes puts elongation pressures onto the particles in the direction of stress. If this force overcomes the surface adhesion between the rubber and polymer, debonding will occur, thereby diminishing the toughening effect associated with crazing. If the particle is harder, it will be less able to deform, and thus debonding occurs under less stress. This is one reason why dispersed rubbers, below their own glass transition temperature, do not toughen plastics effectively.^[6]

Shear yielding

Shear yielding theory is one that, like matrix crazing, can account for a large fraction of the increase in energy absorption of a toughened polymer. Evidence of shear yielding in a toughened polymer can be seen where there is "necking, drawing or orientation hardening."^[6] Shear yielding will result if rubber particles act as stress concentrators and initiate volume-expansion through crazing, debonding and cavitation, to halt the formation of cracks. Overlapping stress fields from one particle to its neighbor will contribute to a growing shear-yielding region. The closer the particles are the more overlap and the larger shear-yielding region.^[5] Shear yielding is an energy absorbing process in itself, but furthermore initiation of shear bands also aids in craze arrest. The occurrence of cavitation is important to shear yielding theory because it acts to lower the yield stress. Cavitation precedes shear yielding, however shear yielding accounts for a much larger increase in toughness than does the cavitation itself.^[6]

Cavitation

Cavitation is common in epoxy resins and other craze resistant toughened polymers, and is prerequisite to shearing in Izod impact strength testing.^[10] During the deformation and fracture of a toughened polymer, cavitation of the strained rubber particles occurs in crazing-prone and non-crazing-prone plastics, including, ABS, PVC, nylon, high impact polystyrene, and CTBN toughened epoxies. Engineers use an energy-balance approach to model how particle size and rubber modulus factors influence material toughness. Both particle size and modulus show positive correlation with brittle-tough transition temperatures. They are both shown to affect the cavitation process occurring at the crack tip process zone early in deformation, preceding large-scale crazing and shear yielding.^[10][11]

In order to show increased toughness under strain, the volumetric strain must overcome the energy of void formation as modeled by the equation:

${\displaystyle U_{r}(r)={\frac {2}{3}}\pi R^{3}K_{r}{\Biggl (}\Delta V_{R}-{\frac {r^{3}}{R^{3}}}{\Biggl )}+4\pi r^{3}\Gamma +2\pi r^{3}G_{r}F(\lambda _{\gamma })}$^[10]

"where ${\displaystyle G_{r}}$ and ${\displaystyle K_{r}}$ are the shear modulus and bulk modulus of the rubber, ${\displaystyle \Delta V_{R}}$ is the volume strain in the rubber particle, ${\displaystyle \Gamma }$ is the surface energy of the rubber phase, and the function ${\displaystyle F(\lambda _{\gamma })}$ is dependent on the failure strain of the rubber under biaxial stretching conditions."^[11]

The energy-balancing model applies the physical properties of the whole material to describe the microscopic behavior during triaxial stress. The volume stress and particle radius conditions for cavitation can be calculated, giving the theoretical minimum particle radius for cavitation, useful for practical applications in rubber toughening. Typically cavitation will occur when the average stress on the rubber particles is between 10 and 20 megapascal. The volume strain on the particle is relieved and voiding occurs. The energy absorption due to this increase in volume is theoretically negligible. Instead, it is the consequent shear band formation that accounts for increased toughness. Before debonding, as the strain increases, the rubber phases is forced to stretch further strengthening the matrix. Debonding between the matrix and the rubber reduces the toughness, creating the need for strong adhesion between the polymer and rubber phases.^[10][11]

Damage competition theory

The damage competition theory models the relative contributions of shear yielding and craze failure, when both are present. there are two main assumptions: crazing, microcracks, and cavitation dominate in brittle systems, and shearing dominates in the ductile systems. Systems that are in between brittle and ductile will show a combination of these. The damage competition theory defines the brittle-ductile transition as the point at which the opposite mechanism (shear or yield damage) appears in a system dominated by the other mechanism.^[5]

Characterization of failure

The dominant failure mechanism can usually be observed directly using

Amorphous plastics are used below their glass transition temperature (${\displaystyle T_{g}}$). They are brittle and notch sensitive but creep resistant. Molecules are immobile and the plastic responds to rapidly applied stress by fracturing. Partly crystalline thermoplastics are used for application in temperature conditions between ${\displaystyle T_{g}}$ and ${\displaystyle T_{m}}$ (melting temperature). Partly crystalline thermoplastics are tough and creep-prone because the amorphous regions surrounding the rigid crystals are afforded some mobility. Often they are brittle at room temperature because they have high glass transition temperatures. Polyethylene is tough at room temperature because its ${\displaystyle T_{g}}$ is lower than room temperature. Polyamide 66 and polyvinylchloride have secondary transitions below their ${\displaystyle T_{g}}$ that allows for some energy absorbing molecule mobility.^[6]

Chemical structure

There are some general guidelines to follow when trying to determine a plastic's toughness from its chemical structure. Vinyl polymers like polystyrene and styrene-acrylonitrile tend to fail by crazing. They have low crack initiation and propagation energies. Polymers with aromatic backbones, such as polyethylene terephthalate and polycarbonate, tend to fail by shear yielding with high crack initiation energy but low propagation energy. Other polymers, including poly(methyl methacrylate) and polyacetal(polyoxymethylene), are not as brittle as "brittle polymers" and are also not as ductile as "ductile polymers".^[6]

Entanglement density and flexibility of unperturbed real chain

The following equations relate the entanglement density ${\displaystyle v_{e}}$ and a measure of the flexibility of the unperturbed real chain (${\displaystyle C_{\infty }}$) of a given plastic to its fracture mechanics:

${\displaystyle V_{e}={\frac {\rho _{a}}{3M_{v}C_{\infty }^{2}}}}$

Where ${\displaystyle \rho _{a}}$is the mass density of the amorphous polymer, and ${\displaystyle M_{v}}$ is the average molecular weight per statistical unit.^[6] Crazing stress ${\displaystyle (\sigma _{z})}$ is related to the entanglement density by:

${\displaystyle \sigma _{z}\varpropto v_{e}^{1/2}}$

The normalized stress yield is related to ${\displaystyle C_{\infty }}$ by

${\displaystyle log({\overline {\sigma }}_{y})\varpropto log(C_{\infty })+c}$

${\displaystyle c}$ is a constant. The ratio of the crazing stress to the normalized stress yield is used to determine whether a polymer fails due to crazing or yield:

${\displaystyle {\frac {\sigma _{z}}{{\overline {\sigma }}_{y}}}\propto {\biggl (}{\frac {\rho _{a}}{3M_{v}}}{\biggr )}^{1/2}C_{\infty }^{-2}}$

When the ratio is higher, the matrix is prone to yielding; when the ratio is lower, the matrix is prone to failure by crazing.^[6] These formulas form the base of crazing theory, shear-yielding theory, and damage competition theory.

Relationship between the secondary phase properties and toughening effect

Rubber selection and miscibility with continuous phase

In material selection it is important to look at the interaction between the matrix and the secondary phase. For example, crosslinking within the rubber phase promotes high strength fibril formation that toughens the rubber, preventing particle fracture.^[6]

Carboxyl-terminated butadiene-acrylonitrile (CTBN) is often used to toughen epoxies, but using CTBN alone increases the toughness at the cost of stiffness and heat resistance. Amine-terminated butadiene acrylonitrile (ATBN) is also used.^[12] Using ultra-fine full-vulcanized powdered rubber (UFPR) researchers have been able to improve all three, toughness, stiffness, and heat resistance simultaneously, resetting the stage for rubber toughening with particles smaller than previously thought to be effective.^[13]

In applications where high optical transparency is necessary, examples being poly(methyl methacrylate) and polycarbonate it is important to find a secondary phase that does not scatter light. To do so it is important to match refractive indices of both phases. Traditional rubber particles do not offer this quality. Modifying the surface of nanoparticles with polymers of comparable refractive indices is an interest of current research.^[8]

Secondary phase concentration