Strain dependence polymer composites

A8. The Helmholtz elastic free energy relation of the composite network contains a separate term for each of the two networks as in eq. 5. However, the precise mathematical form of the strain dependence is not critical at small deformations. Although all the assumptions seem to be reasonably fulfilled, a simpler method, which would require fewer assumptions, would obviously be desirable. A simpler method can be used if we just want to compare the equilibrium contribution from chain engangling in the cross-linked polymer to the stress-relaxation modulus of the uncross-linked polymer. The new method is described in Part 3. 

Fig. 29. Temperature dependence of complex piezoelectric strain constant of composite film of polyester resin and powdered PZT (50% of the volume) polarized at room temperature under a d.c. field of 100 kV/cm. Reproduced from Fukada and Date [Polymer Journal, 1,410 (1970)] by permission of the Society of Polymer...

By analyzing the compositional dependent relaxation time, the stress-strain relationships of polymer composites are determined as a function of the filler concentration and strain rate. As the volume fraction of filler increases, both the effective elastic modulus and yield stress increases. However, the system becomes more brittle at the same time. 

Non-linear viscoelastic properties were observed for fumed silica-poly(vinyl acetate) (PVAc) composites, with varying PVAc molar mass and including a PVAc copolymer with vinyl alcohol. Dynamic mechanical moduli were measured at low strains and found to decrease with strain depending on surface treatment of the silica. The loss modulus decreased significantly with filler surface treatment and more so with lower molar mass polymer. Copolymers with vinyl alcohol presumably increased interactions with silica and decreased non-linearity. Percolation network formation or agglomeration by silica were less important than silica-polymer interactions. Silica-polymer interactions were proposed to form trapped entanglements. The reinforcement and nonlinear viscoelastic characteristics of PVAc and its vinyl alcohol copolymer were similar to observations of the Payne effect in filled elastomers, characteristic of conformations and constraints of macromolecules. ... 

The traditional measuring devices such as strain gauge and extensometer are capable of providing a single point strain and average strain in a specific direction, respectively. It is well known that the damage processes are microstructure dependent and macromechanical behavior of particulate polymer composites mainly depend on their... 

Myounggu P, Flyonny K, Jeffrey PY (2008) Strain-dependent electrical resistance of multi-walled carbon nanotube/polymer composite films. Nanotechnology 19(5) 1-10 Myung JL, Cheol-Jin L, Singh VR, Kum-Pyo Y, Nam-Ki M (2010) Humidity sensing characteristics of plasma functionalized multiwall carbon nanombe-polyimide composite films. Proc IEEE Sens 430-433, art no 4716470... 

Zhang R, Baxendale M, Peijs T (2007) Universal resistivity-strain dependence of caibon nanotube/polymer composites. Phys Rev B 76 195433... 

There is considerable evidence that all the hysteresis effects observed in these materials and most of the viscoelastic behavior can be caused by the time dependent failure of the polymer on a molecular basis and are not due to internal viscosity [1,2]. At near equilibrium rates and small strains filled polymers exhibit the same type of hysteresis that many lowly filled, highly cross-linked rubbers demonstrate at large strains [1-8]. This phenomenon is called the "Mullins Effect" and has been attributed to micro-structural failure. Mullins postulated that a breakdown of particle-particle association and possibly also particle-polymer breakdown could account for the effect [3-5]. Later Bueche [7,8] proposed a molecular model for the Mullins Effect based on the assumption that the centers of the filler particles are displaced in an affine manner during deformation of the composite. Such deformations would cause a highly non-uniform strain and stress gradient in the polymer... 

---