One plausible explanation would be the stress concentrations as generated around the nanoparticles which are acting as the stress risers during the plastic deformation that is experienced by the composites, the intensity of which depends on the number of dispersed particles per unit volume or equally well weight percentage if one compares keeping the particle size invariant. Otherwise particle size plays very important role in the flexural strength.

The presence of the voids is the main reason for the reduction of the flexural strength of the composites containing nanoparticles, these voids wok as stress concentration centers. The formation of these voids is due to many reasons including:

1- The agglomeration of the particles.

2- The lack in wetting of the particles by the matrix that causes air trapping.

3- lack in drying the particles.

4- Air trapping due to the mixing process.

Hi

this could be attributed to high weight percentage of nano particles. This leads to increase the space between polymer chains due to particles agglomeration resulting in decreasing in the bonds between chains and reduction in the stiffness of matrix and nano composites.

The measurements of the flexural strength by Three points testing procedure strongly relies on the surface condition of the test piece on the convex side, which is exposed to uniaxial tensile stresses during the failure by micro size crack initiation, which is closely related to the surface roughness. That means one should worry to understand first to figure out how the nanosize particles situated at the surface layer or in its immediate vicinities can affect the surface roughness through their short range strain fields induced by the applied stress field during loading by the test machine. The sharp edges and corners of those particles situated at the surface and its vicinities are the primary source for the micro crack initiation which may have the high probability to tiger the propagation stage of the micro cracks observed at the surface when the load reaches to the threshold value above which spontaneous failure takes place. This probability roughly depends on the surface concentration of particles situated around and behind the surface layer of the test piece (convex -surface side) That means smaller the size of nano particles higher would be the reduction in the flexural strength of the test piece assuming that particles have greater elastic rigidity modulus comparing to the matrix.

The simplest an explanation - particles I gather in concentrators and form defects. But if it is serious, then it is necessary to know: what materials, what concentration of particles. how did mix up as were tested? But by and large, a bending - a bad method for a research of thin influences. The field of deformations in a sample very difficult

Simple. Starting nano particles today are the same in size as the first "micro" particles in "microfills" of the 80's. Microfills had the problem of weak tensile strengths and were prone clinically to early fracture of the margins and bulk fractures and exessive wear under force. Average "nano" particle size is 40 nanometers which is in essence .04 microns, same size as used in the first microfills. The normal max fill in microfills started out as about 50% because of wetting problems incurred because of greater surface area per particle needed to be wet buy the available monomers in the system and the inherent viscosities of the monomers. So today manufactures will usually artificially aglomerated with silanization or other means to make "hybrid" larger particles to allow for more weight volume with lower overall surface area per praticle and this agglomeration of particles actually decreases the available surface per particle to allow more weight and less available total surface area to wet. Heliomolar increased particle sizes by first loading microfills and then polymerizing the matrix, grinding the prepolymerized polymer and then using those bigger particles to easily wet and get good fracture resistance with less brittle monomers like the urethanes.. Greater surface area of the particles will allow for larger surface to suitably wet the particles taking in viscosities of the monomers. The best size of particles to withstand clinical fracture and mechanical breakdown and the best resistance to chemical degradation is an average particle size of 1 micron. But these are in gradations from about 1-5 microns to .04 microns and the "micro" or "nano" particles are kept to about 8-10% of filler volumes. This is all explained in papers from Karl Leinfelder and R Mazer, and Steve Bane, etal. back in the late 80's and 92. All of this has been forgotten for the sake of marketing. BTW great work has been shown that particles as small as .4 microns will actually agglomerate and actually cause centers of partially wet particles that will act as artificial "voids" and thus promote fractures.

If there were more explanations concerning the used materials and the treatements undergone by them, the discussion would be more concise.

The mechanical properties of polymer nanocomposites depend on several parameters : nature of polymer and particles, shape, size, amount and distribution of particles etc. The interaction of polymer and particles is also a very important parameter.

You can also add some other extrinsic parameters like the process of blending and shaping of the samples which will influence the mechanical properties of composites.

Before going further, I ask myself the questions below :

1) Is there any surface traitement of filler particles? Can we suppose that they are spherical? If not what is the shape of particles (shape factor?)?

2)Why not to use volume %? What is the range of w% of filler particles?

If the density of particles is very high compared to that of polmer, the high w% will correspond to a small v%. In the literature, several empirical equations can be found with volume% rather then the w%, one concerns the estimation of the mechanical properties of polymer composites.

3)How much the decrease of flexural strength compared to the neat polymer? Are the results are repeatable for a same filler amount?

4)Is the elastic modulus of nanocoposites increasis with increasing amount of filler?

5) Did you try to do additional tensile test experiments? If yes, did you get the same trend as 3 point flexural test?

6)Is the decrease of flexural strength mainly due to the increase of the filler amount or some other parameters are present?

The nature of the polymer and filler particles is not disclosed. If it is assumed that the Young modulus of nanofiller is greater than that of the polymer (this is the usual case) and the particles are homogenously distributed into the polymer matrix without any voids in the composites, Two extreme cases would be observed :

a) A strong adhesion between particles and the polymer would induce an increase of mechanical strength in the presence of particles (and with increasing amount of filler particles)

b) In the opposite case i.e. poor adhesion, the mechanical strength would expected to decrease in the presence of particles

In your case, no explanation is done. We don't know if the main reason to decrese the flexural strength is the increase of the filler particle amount.

If the particles have no surface treatement and the adhesion is poor between nanoparticles and polymer, as mentioned by Prof. Ogurtani, the particles would play a role of stress contcentration zones.

Another reason of the flexural strength decrease would be the agglomeration of nanoparticles. Again the properties of filler particles (nature, size, shape,...) were not informed. A study of the particle distribution is welcome. The agglomeration is frequently observed in the case of nanoparticle.

Micro mechanical behaviour of a micro/nanocomposite depends on a lot of aspects! You should explain better the specific case!

There is many reasons for this behavior I will list some of them:

• Non homogeneous distribution of Nano particles within the matrix
• extensive or non enough mixing which may be cause an agglomeration of Nano particles
• High volume % of Nano particles which maybe reduce bonding between polymer-polymer and Nano particles- polymer

One of the reason is that the addition of higher percentage of nano particles leads to formation of agglomeration tendency.

Yes. Good observation. Once the polymer matrix becomes filled and saturated, the base polymer finds it an up hill task to comprehensively wet the further inclusion of your nanoparticles. Relatively, most of the desired properties must have reached the optimum and hence the decrease in flexural strength beyond a certain level of weight increase.

Further related information with detailed query is added with following question.

The link is

https://www.researchgate.net/post/Why_does_adding_nanoclay_in_epoxy_resin_increase_tensile_strength_but_decrease_flexural_strength_at_5_wt_of_nanocaly

"The presence of the voids is the main reason for the reduction of the flexural strength of the composites containing nano particles,.." This was the answer presented by Dr. Imad Disher. As I have stated above the very existence of nano particles in the matrix as stress risers in quasi elastic materials are responsible for the failure of material for dynamic loading because they act as a source for the micro crack initiation and propagation. On the hand for the static loading they act as barriers for the dislocation motion which increases flow stress and thereby. Voids are noting to do with the flexural strength here.

The last comment given by the respected Mr Tarik Omar makes sense when we are talking about metal matrix composite, however, the question was about polymer matrix composite. In polymers, the particles may affect the dislocation motion within the crystalline regions of the polymers if there are any (that didn't specify in the question).

I do agree with the previous comment in which the effect of the surface defects were mentioned. However, these defects may produced due to many reasons, the reasons related to the addition of the nanoparticles are mentioned in my previous answer.