31 research outputs found
New parameter for dynamic characterization of PET film surface topography
It is well-known that handling and winding flexible media involve aerodynamic phenomena which are crucial for the process. Among those parameters which govern the final thickness value of the air layers separating the film layers in a roll of film (for example PET), surface roughness plays an important role. In order to characterize the surface topography of such materials, in a dynamic way, an original experimental set-up was built. It has been described elsewhere, and only its basic features are recalled here. It consists in a polished glass disc with a circular slit connected to a vacuum pump. Having displayed a sample of PET film onto the glass plate, sub-ambient pressure is applied. The air layer which initially separates the film from the plate is partially reduced due to air aspiration: a circular front starts from the slit and propagates towards the center. For prescribed values of the film thickness, the total propagation time depends on sub-ambient pressure and slit diameter (i.e. squeezing surface) through relationships which involve a single parameter characteristic of film roughness.Here the same experimental set up is used to carry out further investigations dealing with the kinetics of both air layer thinning and front propagation. Using a monochromatic light to insulate the film from above, Newton rings are generated allowing the air gap thickness variation to be measured by means of a CCD camera associated with image processing. The main experimental result is that the air layer at the center decreases linearly versus time, the slope being characteristic of the film surface roughness. A simple theoretical model based on the concept of " equivalent smooth surfaces " is developed in order to predict the circular front propagation. Excellent agreement is observed with the experimental data, namely the front propagation kinetics. These results are extrapolated to the configuration of winding, leading to significant improvement of the existing model for lateral evacuation of the air layers confined between the film layers in a roll of film
Macroscopic effects of surface roughness in confined air-flow
One challenge when processing flexible media such as plastic films is to obtain rolls without any aspect defect : if one considers that a "defect" (i.e. wrinkling or buckling) is due to the fact that the stress generated within the roll is greater than some "plasticity yield", then it is crucial to predict the internal stress state.Several process parameters must be carefully mastered (winding tension, velocity, etc.) as well as the material pertinent properties. One key issue is to optimize the surface topography of the flexible medium so that to improve the quality of the wound roll.We propose here new parameters which describe the surface roughness of plastic films fairly well. The measurements were carried out by using a 3D roughness measurement device.A mathematical model based on homogenization techniques is proposed, where the heights of the roughness peaks, their diameter and their spatial distribution are the governing parameters.Sampling at different levels is carried out by expressing the percentage of peaks which exceed some given threshold value.For each tested film, the threshold value will be the only adjustable parameter.Introducing these parameters into the mathematical model which predicts the evolution of the squeezed air layer and comparing to the experimental data, the following results are obtained :- It is possible to adjust one single parameter so that to obtain a very good agreement between the experimental data and the theoretical results.- The smoother the film, the more important the highest peaks are in terms of air leakage
Winding plastic films: Experimental study of squeeze film flow between one smooth surface and one "rough" surface
The present paper is concerned with experiments which consist in squeezing an air layer between a rigid, smooth surface and a flexible, rough one.The experimental rig is composed of a smooth glass plate, with a circular slit allowing air aspiration to be done around it. A thin (few microns thick) plastic film is laid on the glass plate and air separating the glass and the film surfaces is removed by means of a vacuum pump. A circular front appears on the film surface, and moves towards the centre, as the film is pressed onto the glass plate.A monochromatic lamp is used to insulate the surfaces from above and Newton rings can be observed as the front moves. The duration of this operation is measured by a chronometer.Typically, the measured time depends on the plate diameter, the sub-ambient pressure exerted, the film flexural rigidity (or its thickness) and its surface roughness.A set of experiments have been carried out for several values of the sub-ambient pressure and of the slit diameter.The results are well reproducible: for a given sample, the characteristic time is proportional to the squared value of the diameter. The dependence on the sub-ambient pressure is more complicated. A simple model using a semi-empirical formulation is suggested on the basis of the experimental data
On-line control of tension in web winding systems based on wound roll internal stress computation
One of the key challenges in the processing of flexible media such as plastic films is to obtain rolls without any aspect defect: if one considers that a "defect" (i.e. wrinkling or buckling) is due to the fact that the stress generated within the roll is greater than some "plasticity threshold", then it is crucial to predict the internal stress. Several process parameters must be carefully mastered, among which the winding tension is very important. Offline optimization of the tension can a priori guarantee the production of perfect rolls, with respect to the internal stress. Nevertheless, the industrial control systems never generate perfect follow-up of the tension reference value, because the tension which is actually imposed (i.e. measured) exhibits oscillations due to the imperfections of the winding system, including geometrical irregularities of the rolls. The fluctuations about the tension nominal value induce variations in the stress within the roll as compared to the value which would result from an ideal control. As a consequence, it is judicious to change the tension reference value during the winding process, according to some criterion defined from the stress computed within the roll, and then to apply this new "up-dated" reference to the forthcoming web layers. This new way of online tension control requires new concepts such as "robust multivariable control", because distributed control may not work as well.The first step consists in computing the internal stress generated within a roll of a wound web (for instance plastic film). For that purpose, a modified non-linear model is developed in the spirit of Hakiel's. The web's winding process can be considered as a continuous accretion process, in the sense that the stress components at a given point are continuously modified by the upper superimposed layers. In addition, the residual air films which separate the web layers are taken into account in an indirect way through the radial Young's modulus of the roll which is a non-linear (polynomial) function of the compressive stress component. Several illustrative examples are presented and commented. Then, having prescribed an optimization criterion for the winding tension, an optimization algorithm based on the simplex principle is described. Finally, a new concept of online tension control, based on prediction-correction is proposed. Dividing the roll radius into several segments, the tension reference is computed and corrected for each range of roll radius values, by using the predictive model for the stress within the roll. The adjusted tension is reactualized step by step, following the optimization principle as described above and it will be considered as the new tension reference value for the coming layers. A comparison between offline and online tension controls clearly shows the improvement given by the new optimization technique (online)
Control and online tension reference optimization in winding systems: Application to an identified three-motors simulator
It is well known that the tension reference value, which a priori guarantees a good quality roll, is based on the stress generated within the roll. However, due to the imperfections of the winding systems and to the limited performances of the disturbances rejection controllers, a control with fixed reference never generates perfect follow-up of the tension. A solution would consist in adjusting the tension reference online, according to real measurements.In a previous paper, the criterion for tension adjustment was the tangential stress. A method for online control based on prediction-correction using the simplex algorithm was presented. This method was tested numerically.In the present paper, we propose to generalize the criterion of tension reference optimization by considering both the tangential and the radial stress within the roll during winding. The same optimization algorithm is used, taking into account the dynamic tension model. Moreover, a dynamic gauge is now introduced, so that it can vary during the winding process. It generally represents the limits of elastic deformations of the web.The new optimization algorithm for the on-line reference tension calculation has been validated on a dynamic non-linear winding model. This complete model used for simulations was validated on a three-motor setup using brushless motors. The setup is with PI controllers, where the web velocity is imposed by master traction motor and the tension is controlled by unwinding and winding motors.In this approach, a new tension-prediction algorithm using a linear parameter varying (LPV) model is used. The influence of the tension prediction algorithm is also analyzed.Several illustrative examples will be presented and the improvement as compared to an offline control will be commented
Gauge optimization of the reference tension in winding systems using wound internal stresses calculation
In winding process, the quality of the roll is directly connected to its stress state. The winding tension is the most significant parameter which plays an important role in the stresses generated within a roll, during winding. If the stresses exceed a critical value, defects can appear in the roll and make the web non usable.This work concerns the estimation and optimization of the maximal dispersion of the reference tension, so that the tangential and radial stresses values remain in a gauge. It aims to find automatically the maximum and minimum limits for the reference tension, so that all curves ranging between these two limits or thresholds, generate radial and tangential stresses, theirs selves included in a gauge fixed in advance. The results lead to a practical gauge optimization of the reference tension for industrial applications
A Computational Strategy for the Localization and Fracture of Laminated Composites. Part 2. Life Prediction by Mesoscale Modeling for Composite Structures
ΠΠΏΠΈΡΠ°Π½Π½ΡΠΉ Π² ΡΠΎΠΎΠ±ΡΠ΅Π½ΠΈΠΈ 1 ΠΎΠ΄Π½ΠΎΠΌΠ΅ΡΠ½ΡΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΡΠ°Π·Π²ΠΈΡ Π½Π° ΡΠ»ΡΡΠ°ΠΉ Π΄Π²ΡΡ
ΠΌΠ΅ΡΠ½ΠΎΠ³ΠΎ Π»Π°ΠΌΠΈΠ½Π°ΡΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ° Π’300/914, ΠΏΠΎΠ΄Π²Π΅ΡΠ³Π½ΡΡΠΎΠ³ΠΎ ΡΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΌΡ Π΄Π²ΡΡ
ΠΎΡΠ½ΠΎΠΌΡ ΡΠ°ΡΡΡΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠ΄Π²ΠΈΠ³Ρ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ Π΄Π°Π½Π½ΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΠ΅ΡΡΡ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΡΠ²ΠΎΠ»ΡΡΠΈΠΎΠ½Π½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Ρ ΡΡΡΠ΅ΠΊΡΠΎΠΌ Π·Π°Π΄Π΅ΡΠΆΠΊΠΈ
ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΠΉ ΠΏΡΠΈ ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½Π½ΠΎΠΉ ΡΠΊΠΎΡΠΎΡΡΠΈ ΠΈΡ
Π½Π°ΠΊΠΎΠΏΠ»Π΅Π½ΠΈΡ. Π Π°Π·ΠΌΠ΅Ρ Π·ΠΎΠ½Ρ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΡ Π² ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠΈ ΡΠ»ΠΎΠ΅Π² Π»Π°ΠΌΠΈΠ½Π°ΡΠ° Π·Π°Π²ΠΈΡΠΈΡ ΠΎΡ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈ, ΡΠ²ΡΠ·Π°Π½Π½ΠΎΠΉ Ρ Π·Π°Π΄Π΅ΡΠΆΠΊΠΎΠΉ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΡ ΠΈ ΡΠΊΠΎΡΠΎΡΡΡΡ Π½Π°Π³ΡΡΠΆΠ΅Π½ΠΈΡ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΠΎΠ²ΠΌΠ΅ΡΡΠ½ΠΎΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠ΅Π·ΠΎΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΈ ΡΠ²ΠΎΠ»ΡΡΠΈΠΎΠ½Π½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π·Π°Π΄Π΅ΡΠΆΠΊΠΈ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΠΉ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΎΡΠ΅Π½ΠΈΡΡ ΡΠ°Π·ΠΌΠ΅Ρ Π·ΠΎΠ½Ρ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΡ ΠΈ ΡΠΎΡΠ½ΠΎ ΠΎΡΠ΅Π½ΠΈΡΡ Π²ΡΠ΅ΠΌΡ ΡΠ°Π·ΡΡΡΠ΅Π½ΠΈΡ.ΠΠΏΠΈΡΠ°Π½ΠΈΠΉ Π² ΠΏΠΎΠ²ΡΠ΄ΠΎΠΌΠ»Π΅Π½Π½Ρ 1 ΠΎΠ΄Π½ΠΎΠ²ΠΈΠΌΡΡΠ½ΠΈΠΉ ΠΏΡΠ΄Ρ
ΡΠ΄ ΡΠΎΠ·Π²ΠΈΠ½ΡΡΠΎ Π½Π° Π²ΠΈΠΏΠ°Π΄ΠΎΠΊ Π΄Π²ΠΎΠ²ΠΈΠΌΡΡΠ½ΠΎΠ³ΠΎ Π»Π°ΠΌΡΠ½Π°ΡΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ° T300/914, ΡΠΎ Π·Π°Π·Π½Π°Ρ ΡΡΠ°ΡΠΈΡΠ½ΠΎΠ³ΠΎ Π΄Π²ΠΎΠ²ΡΡΠ½ΠΎΠ³ΠΎ ΡΠΎΠ·ΡΡΠ³Π°Π½Π½Ρ Ρ Π·ΡΡΠ²Ρ. Π ΠΎΠ·Π²βΡΠ·ΠΎΠΊ Π΄Π°Π½ΠΎΡ Π·Π°Π΄Π°ΡΡ Π²ΠΈΠΊΠΎΠ½ΡΡΡΡΡΡ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ Π΅Π²ΠΎΠ»ΡΡΡΠΉΠ½ΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π· Π΅ΡΠ΅ΠΊΡΠΎΠΌ Π·Π°ΡΡΠΈΠΌΠΊΠΈ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Ρ Π·Π° ΠΎΠ±ΠΌΠ΅ΠΆΠ΅Π½ΠΎΡ ΡΠ²ΠΈΠ΄ΠΊΠΎΡΡΡ ΡΡ
Π½Π°ΠΊΠΎΠΏΠΈΡΠ΅Π½Π½Ρ. Π ΠΎΠ·ΠΌΡΡ Π·ΠΎΠ½ΠΈ Π»ΠΎΠΊΠ°Π»ΡΠ·Π°ΡΡΡ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Π½Ρ Ρ ΠΏΠ»ΠΎΡΠΈΠ½Ρ ΡΠ°ΡΡΠ² Π»Π°ΠΌΡΠ½Π°ΡΠ° Π·Π°Π»Π΅ΠΆΠΈΡΡ Π²ΡΠ΄ ΡΠ°ΡΠΎΠ²ΠΎΡ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΌΠΎΠ΄Π΅Π»Ρ, ΡΠΊΠ° ΠΏΠΎΠ²βΡΠ·Π°Π½Π° ΡΠ· Π·Π°ΡΡΠΈΠΌΠΊΠΎΡ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Π½Ρ Ρ ΡΠ²ΠΈΠ΄ΠΊΡΡΡΡ Π½Π°Π²Π°Π½ΡΠ°ΠΆΠ΅Π½Π½Ρ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ ΡΠΏΡΠ»ΡΠ½Π΅ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΌΠ΅Π·ΠΎΠΌΠΎΠ΄Π΅Π»Ρ ΠΉ Π΅Π²ΠΎΠ»ΡΡΡΠΉΠ½ΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π·Π°ΡΡΠΈΠΌΠΊΠΈ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Ρ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ ΠΎΡΡΠ½ΠΈΡΠΈ ΡΠΎΠ·ΠΌΡΡ Π·ΠΎΠ½ΠΈ Π»ΠΎΠΊΠ°Π»ΡΠ·Π°ΡΡΡ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Ρ Ρ ΡΠΎΡΠ½ΠΎ ΠΎΡΡΠ½ΠΈΡΠΈ ΡΠ°Ρ ΡΡΠΉΠ½ΡΠ²Π°Π½Π½Ρ
A Computational Strategy for the Localization and Fracture of Laminated Composites. Part 1. Development of a Localization Criterion Adapted to Model Damage Evolution Time-Delay
ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ ΠΊΡΠΈΡΠ΅ΡΠΈΠΉ Π½Π΅ΡΡΠ°Π±ΠΈΠ»ΡΠ½ΠΎΡΡΠΈ ΠΈ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΠΉ Π² Π±Π°Π»ΠΊΠ΅ ΠΈΠ· ΠΎΠ΄Π½ΠΎΡΠΎΠ΄Π½ΠΎΠ³ΠΎ Π»Π°ΠΌΠΈΠ½Π°ΡΠ° T300/914 Π΄Π»Ρ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΠΉ Ρ ΡΡΠ΅ΡΠΎΠΌ ΡΡΡΠ΅ΠΊΡΠ° Π·Π°Π΄Π΅ΡΠΆΠΊΠΈ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ Π΄Π»Ρ ΠΎΠ΄Π½ΠΎΠΌΠ΅ΡΠ½ΠΎΠ³ΠΎ ΡΠ»ΡΡΠ°Ρ, ΡΠ²ΠΈΠ΄Π΅ΡΠ΅Π»ΡΡΡΠ²ΡΡΡ ΠΎΠ± ΠΎΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΌ ΠΏΠΎΡΠ²Π»Π΅Π½ΠΈΠΈ Π·ΠΎΠ½Ρ ΡΠ°Π·ΡΡΡΠ΅Π½ΠΈΡ ΠΏΠΎ Π²ΡΠ΅ΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅, ΠΊΠΎΡΠΎΡΠΎΠ΅ Π±Π°Π·ΠΈΡΡΠ΅ΡΡΡ Π½Π° ΠΌΠ΅Π·ΠΎΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ². ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° ΡΠ°ΡΡΠ΅ΡΠ½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ Π²ΡΠΏΠΎΠ»Π½ΠΈΡΡ ΡΠΎΡΠ½ΡΠΉ ΠΏΡΠΎΠ³Π½ΠΎΠ· ΠΏΠΎΡΠ΅ΡΠΈ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΠΎΠ±ΡΠ°Π·ΡΠ° ΠΏΡΠΈ ΡΡ
ΡΠ΄ΡΠ΅Π½ΠΈΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² Π΅Π³ΠΎ ΠΆΠ΅ΡΡΠΊΠΎΡΡΠΈ.ΠΠ°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΠΊΡΠΈΡΠ΅ΡΡΠΉ Π½Π΅ΡΡΠ°Π±ΡΠ»ΡΠ½ΠΎΡΡΡ Ρ Π»ΠΎΠΊΠ°Π»ΡΠ·Π°ΡΡΡ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Ρ Ρ Π±Π°Π»ΡΡ Π· ΠΎΠ΄Π½ΠΎΡΡΠ΄Π½ΠΎΠ³ΠΎ Π»Π°ΠΌΡΠ½Π°ΡΠ° Π’300/914 Π΄Π»Ρ ΠΌΠΎΠ΄Π΅Π»ΡΠ²Π°Π½Π½Ρ ΡΠΎΠ·Π²ΠΈΡΠΊΡ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Ρ Π· ΡΡΠ°Ρ
ΡΠ²Π°Π½Π½ΡΠΌ Π΅ΡΠ΅ΠΊΡΡ Π·Π°ΡΡΠΈΠΌΠΊΠΈ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ, ΡΠΎ ΠΎΡΡΠΈΠΌΠ°Π½Ρ Π΄Π»Ρ ΠΎΠ΄Π½ΠΎΠ²ΠΈΠΌΡΡΠ½ΠΎΠ³ΠΎ
Π²ΠΈΠΏΠ°Π΄ΠΊΡ, ΡΠ²ΡΠ΄ΡΠ°ΡΡ ΠΏΡΠΎ ΡΠ΅, ΡΠΎ Π·ΠΎΠ½Π° ΡΡΠΉΠ½ΡΠ²Π°Π½Π½Ρ ΠΏΠΎ Π²ΡΡΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π²ΠΈΠ½ΠΈΠΊΠ°Ρ ΠΎΠ΄Π½ΠΎΡΠ°ΡΠ½ΠΎ. ΠΠ°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΡΠΎΠ·Π²βΡΠ·ΠΎΠΊ, ΡΠΎ Π±Π°Π·ΡΡΡΡΡΡ Π½Π° ΠΌΠ΅Π·ΠΎΠΌΠΎΠ΄Π΅Π»ΡΠ²Π°Π½Π½Ρ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ². ΠΡΡΠΈΠΌΠ°Π½Ρ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ Π·Π°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎΠ³ΠΎ ΠΏΡΠ΄Ρ
ΠΎΠ΄Ρ ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΠΎΠ²Ρ Π΄Π°Π½Ρ
Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡΡΡ Π²ΠΈΠΊΠΎΠ½Π°ΡΠΈ ΡΠΎΡΠ½ΠΈΠΉ ΠΏΡΠΎΠ³Π½ΠΎΠ· Π²ΡΡΠ°ΡΠΈ ΡΡΡΠΉΠΊΠΎΡΡΡ Π·ΡΠ°Π·ΠΊΠ° ΠΏΡΠΈ ΠΏΠΎΠ³ΡΡΡΠ°Π½Π½Ρ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ² ΠΉΠΎΠ³ΠΎ ΠΆΠΎΡΡΡΠΊΠΎΡΡΡ
Prediction by a Genetic Algorithm of the Fiber-Matrix Interface Damage for Composite Material. Part 2. Study of Shear Damage in Graphite/Epoxv Nanocomposites
The objective in this paper is to apply the same genetic model as applied in Part 1 to optimizing the shear damage to the fiberβmatrix interface of nanocomposite material graphite epoxy. The results show good agreement between the numerical simulation and the actual behavior of the material chosen composite and nanocomposites, and these results are similar to results obtained by processing techniques expanded graphite reinforced polymer nanocomposites made by Asma Yasmine. These results were confirmed by calculating the rate of damage with a genetic simulation.ΠΠΏΠΈΡΠ°Π½Π½Π°Ρ Π² ΡΠΎΠΎΠ±ΡΠ΅Π½ΠΈΠΈ 1 Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΡΡΡ Π΄Π»Ρ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΡ Π² ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠΈ ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΡΡ
ΡΠ΄Π²ΠΈΠ³ΠΎΠ²ΡΡ
Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΠΉ Π½Π° ΡΡΡΠΊΠ΅ Π²ΠΎΠ»ΠΎΠΊΠΎΠ½ ΠΈ ΠΌΠ°ΡΡΠΈΡΡ Π² Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ½ΠΎΠΌ Π³ΡΠ°ΡΠΈΡΠΎ-ΡΠΏΠΎΠΊΡΠΈΠ΄Π½ΠΎΠΌ ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»Π΅. ΠΠΎΠ»ΡΡΠ΅Π½Π° Ρ
ΠΎΡΠΎΡΠ°Ρ ΠΊΠΎΡΡΠ΅Π»ΡΡΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ ΡΠΈΡΠ»Π΅Π½Π½ΡΠΌΠΈ ΡΠ°ΡΡΠ΅ΡΠ°ΠΌΠΈ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠΌΠΈ Π΄Π°Π½Π½ΡΠΌΠΈ Π΄Π»Ρ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ° ΠΈ Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ² Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π³ΡΠ°ΡΠΈΡΠ°, ΡΡΠΈΠ»Π΅Π½Π½ΠΎΠ³ΠΎ Π½Π°Π½ΠΎΠΏΠΎΠ»ΠΈΠΌΠ΅ΡΠ°ΠΌΠΈ. ΠΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠ΅ Π΄Π°Π½Π½ΡΠ΅ ΡΠ°ΠΊΠΆΠ΅ Ρ
ΠΎΡΠΎΡΠΎ ΡΠΎΠ³Π»Π°ΡΡΡΡΡΡ Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠΌΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ°ΡΡΠ΅ΡΠ½ΠΎΠΉ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ Π―ΡΠΌΠΈΠ½Π°. Π Π΄Π°Π»ΡΠ½Π΅ΠΉΡΠΈΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡΡ
ΠΏΠ»Π°Π½ΠΈΡΡΠ΅ΡΡΡ ΠΈΠ·ΡΡΠ΅Π½ΠΈΠ΅ Π²Π»ΠΈΡΠ½ΠΈΡ ΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΠΉ Π½Π° ΠΏΠΎΠ΄ΠΎΠ±Π½ΡΡ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΡ.ΠΠΏΠΈΡΠ°Π½Π° Π² ΠΏΠΎΠ²ΡΠ΄ΠΎΠΌΠ»Π΅Π½Π½Ρ 1 Π³Π΅Π½Π΅ΡΠΈΡΠ½Π° ΠΌΠΎΠ΄Π΅Π»Ρ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΡΡΡΡΡ Π΄Π»Ρ ΠΎΠΏΡΠΈΠΌΡΠ·Π°ΡΡΡ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Π½Ρ Π² ΠΏΠ»ΠΎΡΠΈΠ½Ρ ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΠΈΡ
Π·ΡΡΠ²Π½ΠΈΡ
Π½Π°ΠΏΡΡΠΆΠ΅Π½Ρ Π½Π° ΡΡΠΈΠΊΡ Π²ΠΎΠ»ΠΎΠΊΠΎΠ½ Ρ ΠΌΠ°ΡΡΠΈΡΡ Π² Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ½ΠΎΠΌΡ Π³ΡΠ°ΡΡΡΠΎ-Π΅ΠΏΠΎΠΊΡΠΈΠ΄Π½ΠΎΠΌΡ ΠΌΠ°ΡΠ΅ΡΡΠ°Π»Ρ. ΠΡΡΠΈΠΌΠ°Π½ΠΎ Ρ
ΠΎΡΠΎΡΡ ΠΊΠΎΡΠ΅Π»ΡΡΡΡ ΠΌΡΠΆ ΡΠΈΡΠ»ΠΎΠ²ΠΈΠΌΠΈ ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΠ°ΠΌΠΈ ΠΉ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΈΠΌΠΈ Π΄Π°Π½ΠΈΠΌΠΈ Π΄Π»Ρ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ° ΡΠ° Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡ ΡΠ² Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ Π³ΡΠ°ΡΡΡΡ, ΠΏΡΠ΄ΡΠΈΠ»Π΅Π½ΠΎΠ³ΠΎ Π½Π°Π½ΠΎΠΏΠΎΠ»ΡΠΌΠ΅ΡΠ°ΠΌΠΈ. ΠΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½Ρ Π΄Π°Π½Ρ ΡΠ°ΠΊΠΎΠΆ Π΄ΠΎΠ±ΡΠ΅ ΡΠ·Π³ΠΎΠ΄ΠΆΡΡΡΡΡΡ Π· ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ, ΡΠΎ ΠΎΡΡΠΈΠΌΠ°Π½Ρ Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΠΎΠ²ΠΎΡ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ Π―ΡΠΌΡΠ½Π°. Π£ ΠΏΠΎΠ΄Π°Π»ΡΡΠΈΡ
Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½ΡΡ
ΠΏΠ»Π°Π½ΡΡΡΡΡΡ Π²ΠΈΠ²ΡΠ΅Π½Π½Ρ Π²ΠΏΠ»ΠΈΠ²Ρ ΡΠ΅ΡΠΌΡΡΠ½ΠΈΡ
Π½Π°ΠΏΡΡΠΆΠ΅Π½Ρ Π½Π° ΠΏΠΎΠ΄ΡΠ±Π½Ρ ΠΎΠΏΡΠΈΠΌΡΠ·Π°ΡΡΡ
Study of the Effect of Water Intake by the Matrix on the Optimization of the Fiber Matrix Interface Damage for a Composite Material by Genetic Algorithms
The objective of this paper is study the influence
of the matrix swelling due to water on the
damage of the fiber matrix interface of a composite
material. The results obtained by a genetic
approach based on Weibull probabilistic
model, show good agreement between the simulation
and the actual behavior of the two
materials T300/914 and PEEK/APC2. Also the
absorption of water by the matrix increases significantly
the interface damage.ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΎ Π²Π»ΠΈΡΠ½ΠΈΠ΅ Π½Π°Π±ΡΡ
Π°Π½ΠΈΡ ΡΠΌΠΎΠ»Ρ (ΠΌΠ°ΡΡΠΈΡΡ) Π²ΡΠ»Π΅Π΄ΡΡΠ²ΠΈΠ΅ ΠΏΠΎΠ³Π»ΠΎΡΠ΅Π½ΠΈΡ Π²ΠΎΠ΄Ρ Π½Π° ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΠ΅ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ ΡΠ°Π·Π΄Π΅Π»Π° ΠΌΠ΅ΠΆΠ΄Ρ Π²ΠΎΠ»ΠΎΠΊΠ½ΠΎΠΌ ΠΈ ΠΌΠ°ΡΡΠΈΡΠ΅ΠΉ Π² ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ½ΠΎΠΌ ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»Π΅. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ Ρ ΠΏΠΎΠΌΠΎΡΡΡ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΠ½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ
ΠΠ΅ΠΉΠ±ΡΠ»Π»Π°, ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ Ρ
ΠΎΡΠΎΡΠ΅Π΅ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠ΅ ΠΌΠ΅ΠΆΠ΄Ρ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠΌ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠΌ
ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΠΈΠ΅ΠΌ Π΄Π²ΡΡ
ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»ΠΎΠ² (T300/914 ΠΈ PEEK/APC2). ΠΠΎΠ»Π΅Π΅ ΡΠΎΠ³ΠΎ, Π°Π±ΡΠΎΡΠ±ΡΠΈΡ Π²ΠΎΠ΄Ρ ΡΠΌΠΎΠ»ΠΎΠΉ
(ΠΌΠ°ΡΡΠΈΡΠ΅ΠΉ) Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΡΠ²Π΅Π»ΠΈΡΠΈΠ²Π°Π΅Ρ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΠ΅ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ ΡΠ°Π·Π΄Π΅Π»Π°.ΠΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½ΠΎ Π²ΠΏΠ»ΠΈΠ² Π½Π°Π±ΡΡ
Π°Π½Π½Ρ ΡΠΌΠΎΠ»ΠΈ (ΠΌΠ°ΡΡΠΈΡΡ) Π²Π½Π°ΡΠ»ΡΠ΄ΠΎΠΊ ΠΏΠΎΠ³Π»ΠΈΠ½Π°Π½Π½Ρ Π²ΠΎΠ΄ΠΈ Π½Π°
ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½Π½Ρ ΠΏΠΎΠ²Π΅ΡΡ
Π½Ρ ΠΏΠΎΠ΄ΡΠ»Ρ ΠΌΡΠΆ Π²ΠΎΠ»ΠΎΠΊΠ½ΠΎΠΌ Ρ ΠΌΠ°ΡΡΠΈΡΠ΅Ρ Π² ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ½ΠΎΠΌΡ
ΠΌΠ°ΡΠ΅ΡΡΠ°Π»Ρ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ, ΡΠΎ ΠΎΡΡΠΈΠΌΠ°Π½Ρ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ Π³Π΅Π½Π΅ΡΠΈΡΠ½ΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΡ Π½Π°
ΠΎΡΠ½ΠΎΠ²Ρ ΡΠΌΠΎΠ²ΡΡΠ½ΡΡΠ½ΠΎΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΠ΅ΠΉΠ±ΡΠ»Π»Π°, ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ Ρ
ΠΎΡΠΎΡΡ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΡΡΡΡ ΠΌΡΠΆ
ΠΏΡΠΎΡΠ΅ΡΠΎΠΌ ΠΌΠΎΠ΄Π΅Π»ΡΠ²Π°Π½Π½Ρ Ρ ΡΠ°ΠΊΡΠΈΡΠ½ΠΎΡ ΠΏΠΎΠ²Π΅Π΄ΡΠ½ΠΊΠΎΡ Π΄Π²ΠΎΡ
ΠΌΠ°ΡΠ΅ΡΡΠ°Π»ΡΠ² (Π’300/914 Ρ
PEEK/APC2). ΠΡΠ»ΡΡ ΡΠΎΠ³ΠΎ, Π°Π±ΡΠΎΡΠ±ΡΡΡ Π²ΠΎΠ΄ΠΈ ΡΠΌΠΎΠ»ΠΎΡ (ΠΌΠ°ΡΡΠΈΡΠ΅Ρ) Π·Π½Π°ΡΠ½ΠΎ Π·Π±ΡΠ»ΡΡΡΡ ΠΏΠΎΡΠΊΠΎΠ΄ΠΆΠ΅Π½ΡΡΡΡ ΠΏΠΎΠ²Π΅ΡΡ
Π½Ρ ΠΏΠΎΠ΄ΡΠ»Ρ