nanocomposites can be attributed to the inhomogeneous dispersion of the nano-reinforcement [ 6 – 9 ]. The possible states of dispersion are generally classiﬁed as either even, random or clustered [ 6 , 10 ]. However, an evenly and randomly dispersed state represents an optimal condition and usually correlates with enhanced properties. Achieving these optimal states is challenging, and has been reported as a signi ﬁcant limiting factor in nanocomposite fabrication [ 7 , 8 , 11 ]. The difﬁculty in achieving effective dispersion is attributed to the strong interparticle Van Der Waals forces which exceed the particle—matrix bond and consequently results in agglomeration [ 11 ]. Agglomerates resist intended property augmentation by compromising the mechanical integrity of the nanocomposite through void formations which are a source of crack initiation and possible failure during loading [ 7 ]. Therefore the need to improve dispersion and minimise agglomeration is vital to improving properties such as the mechanical (strength and stiffness) [ 12 – 16 ], thermal [ 17 , 18 ], electrical [ 14 ] barrier [ 19 , 20 ] and transparency [ 21 ]. Some of the techniques adopted for dispersion of nanoﬁllers within the polymermatrix include mechanical or high-speed stirring [ 8 ], sonication [ 9 , 22 ], high shear mixing or melting [ 23 , 24 ], incorporating surfactants or compatibilisers [ 25 ] and casting solvents [ 26 ].
ductivity is 10 ÿ2 S cm ÿ1 . We explored the DWNTs dispersion
using G band Raman imaging. Difference in the G band position of inner and outer tubes in DWNTs are used as a local sensor, to distinguish areas where the tubes are well dispersed in the matrix and where the DWNTs are agglomerated. By optimizing the excitation wavelength we were able to detect DWNTs concen- trations as low as 0.16 wt% using Raman spectroscopy. We find that DWNTs are difficult to detect in the polymermatrix at low concentrations due to their small diameter (1.8–3 nm) using elec- tron microscopy. We find that the dispersion of individual tubes is better at low concentration but the overall dispersion is not homogeneous. We find that at DWNTs concentrations, where electrical percolation is observed in PEEK matrix, a uniform distri- bution of nanotube agglomerates is observed. Our experimental results confirm that the percolation threshold can be reduced by improving the nanotube dispersion.
reducing the mechanical properties of the carbon fiber rein- forcement. The steam-thermolysis has been studied and confirmed efficient in treating epoxy based CFRP materials at bench scale. In order to optimize the process, an experi- mental design has been carried out by using Taguchi method at semi-industrial scale. Initially, an orthogonal array testing was applied to determine the potential influence of the operational parameters on the decomposition rate of the polymermatrix as wall as on the mechanical property of the reclaimed carbon fibers. Three operational parameters at two levels each (target temperature, isothermal dwell time and steam flow-rate) were identified and tested. During the test, some 100 g epoxy based CFRP scrap samples were loaded into a thermal reactor preheated till desired temper- ature. The steam is flushed with a flow of nitrogen throughout the test to avoid oxidative side reactions. Additional tests were also conducted to complete and validate the results. Keywords CFRP ! Epoxy resin ! Steam-thermolysis ! Experimental design ! Recycling
Laboratoire d’Ing´ enierie des Mat´ eriaux,
Arts et M´ etiers ParisTech, CNRS, 151 boulevard de l’Hˆ opital, 75013 Paris, France
The interaction between humid air and transversely isotropic fiber-reinforced com- posites with swelling polymeric matrix is considered. A model is proposed for the water saturation level in a polymer when stresses are applied, that uses directly obtainable material parameters only. In a composite, the reinforcements modify the water uptake of the polymermatrix because of the internal stresses that are induced by its restricted swelling, and this effect is evaluated. As a consequence of the cou- pling between stresses and absorption capacity, the sorption isotherm of a composite is ruled by the (nonlinear) Langmuir equation when the unreinforced matrix obeys the (linear) Henry’s law.
a b s t r a c t
Raman spectroscopy is used to access the dispersion state of DWNTs in a PEEK polymermatrix. The inter- action of the outer tube with the matrix can be determined from the line shape of the Raman G band. This allows us to distinguish regions where the nanotubes are well dispersed and regions where the nano- tubes are agglomerated. The percolation threshold of the electrical conductivity of the double wall carbon nanotubes (DWNTs)/PEEK nanocomposites is found to be at 0.2–0.3 wt.%. We find a maximum electrical conductivity of 3 10 ÿ2 S/cm at 2 wt.% loading. We detect nanotube weight concentrations as low as
The physical properties of nanostructured composites are the object of intense investigations for the fabrication of smart materials, nano-sensors and other electronic devices. [1-5] In this context, magnetic materials are especially interesting not only for their response to a magnetic field, but also for their sensibility to mechanical forces. In particular, the possibility of controlling the magnetization with piezoelectric means (especially through the so called inverse magnetostriction effect) is a promising technique for data storage and data processing applications [6-10]. On the other hand, the nanotechnology approach based ion-track shaping of polymer templates has proven to be very efficient for investigating the physical properties of magnetic nanostructures [11-17]. A systematic study of the physical properties of single- contacted magnetic nanowires embedded in an active thermoelastic and piezoelectric polymermatrix is reported. It is shown that a nanowire (NW) embedded in a matrix plays the role of a nanoscopic probe, which is sensitive to the amplitude and the direction of the mechanical stress.
In order to demonstrate that these conclusions can be gener- alised to other 3D architectures, a complementary experimental study has also been performed on another 3D highly unbalanced woven composite material provided by Safran group. The total thickness and the size of the RVE are rather similar to those of the previous material. Some additional impact tests have been per- formed at Onera, using the test configuration 1 (with circular jaws), at 3 different energy levels , inferior to 160 J. Firstly, the shape of the projected damaged area is more elliptical than previously because a highly unbalanced woven material is considered here. Moreover, the measured projected damage areas and the residual depths are different from those measured previously on the mod- erately unbalanced material, thereby confirming that the choice of the architecture plays a major role in the values of these quantities. Nevertheless, the damage patterns remain very similar (inter-yarn debondings and matrix cracking) and only diffuse damage mecha- nisms are observed (no large delamination crack). Using a contin- uum damage approach, as the ODM-PMC approach, is again relevant for this alternative material. The macroscopic ODM-PMC approach has been identified for this highly unbalanced 3D woven
This rigorous mathematical formulation turns out to have deep physi- cal significance, as it is discussed in the following. In particular, it enables us to clearly separate the material parameters which are influenced by the shear behavior of the matrix and, as such, which should display a viscoelastic long term behavior, from those which should remain elastic throughout the analysis. This approach is radically different from the one adopted in many viscoelastic models for transversely isotropic materials [4, 6, 5], which in- troduce different viscous relaxation functions for each of the classical elastic constants (E L , E T , µ L , µ T and ν LT ), with no clear link to the mechanical
5 Numerical Results
In order to assess the correctness of the modified Mori-Tanaka TFA damage framework in simulating progressive damage in heterogeneous materials, the present mean-field predictions are compared with the full-field finite-element homogenization simulations in Abaqus which is a gold standard. Further assessment and experimental validation of the proposed framework will be performed elsewhere in our future studies. To this end, the constitutive law implemented into the Abaqus code for the polymermatrix phase is exactly the same as that employed in the modified Mori-Tanaka TFA approach. The inelastic behavior is characterized by the viscoelastic- viscoplastic with ductile damage model; hence it is not repeated in this section. The reader can refer to the work by Praud et al. (2017a) for the numerical details of the implementation using a UserMATerial subroutine (UMAT). In the interphase layer, a viscoelastic-viscoplastic model with micromechanics-based damage described in the following is developed to characterize the nonlinear behavior and the damage in the interphase layer.
a temperature below the glass transition temperature
(T g ) of the polymer-gas system for a certain period to produce multilayered polymers. The weak entangle- ments are introduced into the polymer during the com- pression molding step by controlling inter-diffusion of the macromolecular chains with appropriate selection of processing temperature and time. These weak en- tanglements are periodically distributed throughout the polymer at the interfaces between the films or the beads. On exposure to compressed gas, the T g of the polymer is depressed [5, 6], the extent of depression depends on the polymer-gas system, and gas pressure and temper- ature used. When the gas-saturated polymer is heated to a temperature below the T g of the polymer-gas sys- tem, the gas is driven out from the polymermatrix to nucleate and expand in the regions where chain entan- glements are weak. Such entanglements cannot hold the gas pressure and, therefore, the chains in these re- gions are pushed apart by the expanding gas, resulting in the layered morphology. Layered morphologies with various geometries can be produced by using appro- priately designed compression molds or by deforming
One possible solution to bridge this gap is “assertion forcing”, i.e. adding as- sertions about intermediate identities until the sub-problems are small enough to be handled by ATPs. However, after trying to go this way, we found that even the identity above (the easiest one) requires an unreasonable number of explicit steps. Without support of automated provers, making use of an interactive one (typ- ically Coq) would be a standard choice. If the interactive prover has support for proving ring-like identities, then it would suffice to embed our matrix theory inside the prover’s ring framework. However, we were curious to see if we could embed some kind of similar ring support inside Why3 itself. That leads us to the tech- nique known as proof by reflection [ 2 ]. The methodology we follow is actually very similar to the one presented by Bertot and Cast´ eran [ 1 , chapter 16].
I. GENERAL DESCRIPTION OF THE SYSTEM
Consider a polymer chain that passes through a pore in a membrane (see figure 1). We assume that the motion of the polymer chain is equivalent to unbiased random walk, i.e., it is fully described by one parameter, the diffusion coefficient D. The pore is located at x = 0 and we focus on the polymer segment to the right of the membrane (the region located on the right-hand side of the pore is the target region of the translocation process). At a given moment, this polymer segment consists of a certain number L of monomer units, each of size a, labeled 1, . . . , L. Translocation is reversible and the polymer can move by one-monomer unit to the right or left with equal rates, resulting in a zero average translocation velocity and a non-vanishing diffusion coefficient D for the ‘bare’ polymer. We now suppose that the medium on the right side of the membrane contains a fixed density of special molecules — “chaperones” — that adsorb irreversibly, with a certain rate λ, onto unoccupied adjacent sites of the polymer. A chaperone is sufficiently large that it cannot pass through the pore (Fig. 1). As a result, the chaperones rectify the polymer diffusion so that it passes through the pore at a non-zero speed v and has a certain effective diffusion coefficient D. More precisely, L, the number of translocated monomers at time t, is a random variable. Let P (L, t) be the corresponding probability distribution. One anticipates that this distribution is asymptotically Gaussian,
+ SiC c }.
The preforms were infiltrated by a slurry impregnation under vacuum, using a suspension containing 30 vol.% of ceramic powders (Si 3 N 4 +Al 2 O 3 +Y 2 O 3 +TiB 2 ), as reported in a previous paper [ 2 ].
The impregnated preforms were then dried during 48h at 25°C. The dried carbon preforms charged with the silicon nitride + titanium diboride + sintering-aid powders were then put into a graphite die with an inner diameter of 50 mm for SPS. The SPS conditions are a compromise between minimizing fiber degradation and achieving full densification of the matrix. The choice of the sintering conditions resulted of the densification conditions of the monolithic matrix (Si 3 N 4 +TiB 2 + sintering-aid powders). The
59 184.108.40.206.1 Polyaniline
One of the most technologically promising electrically conductive polymers is polyaniline, due to its good environmental stability(Huang, D., & MacDiarmid, 1986), ease of synthesis, versatile processability and stable conductivity in relation with other conductive polymers. Investigations by Macdiarmid et al.(Macdiarmid et al., 1985) in the mid-1980’s resulted in the discovery of electrical conductivity for the emeraldine salt of polyaniline, which led to an explosion of interest in this fascinating polymer. Polyaniline is known to be crystalline, and a highly conducting state is accomplished by simple protonation of the imine nitrogen atoms in the emeraldine base backbone. Only one form of polyaniline, called the emeraldine salt, is electrically conducting. The main disadvantage of all intrinsically conductive polymers, including PANI, is its limited melt-processability. Addition of zinc compound to doped-PANI made some complex allowed a method to tailor the processability of sulfonic acid-doped PANI(Hartikainen et al., 2001; Ruokolainen et al., 2000). It has been observed that for polymer blends containing PANI, a range of conductivity between 10 -10 S cm -1 to 10 -1 S cm -1 (melt processing) and 10 -10 S cm -1 to 10 S cm -1 (solution processing) can be achieved(Panipol, 2000). There are several dopants belonging to the sulfonic acid group for PANI, such as dinonylnaphthalenedisulfonic acid (DNNDSA). Among the sulfonic acids, camphor-10-sulfonic acid (CSA) is much used for this purpose due to high solubility of PANI-CSA in m-cresol(Vikki et al., 1996). A soluble PANI-dodecylbenzenesulfonic acid (DBSA) dispersion was synthesized by Kababya et al.,(Kababya, Appel, Haba, Titelman, & Schmidt, 1999) showing that DBSA is molecularly miscible with PANI. PANI-DBSA dispersions have been recently used to prepare blends with other commodity plastics(Haba, et al., 2000).
One-bit matrix completion was further considered by [ 5 ] where a max-norm constrained maximum likelihood estimate is considered. This method allows more general non-uniform sampling schemes but still requires an upper bound on the max-norm of the unknown matrix. Here again, the rates of convergence obtained in [ 5 ] are slower than the rate of convergence of our estimator. Re- cently, [ 13 ] consider general exponential family distributions, which cover some distributions over finite sets. Their method, unlike our estimator, requires the knowledge of the “spikiness ratio” (usually unknown) and the uniform sampling scheme.