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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
41

Modelling tools for quieter vehicles : Waves in poro-and visco-elastic continua

Ostberg, Martin 07 June 2012 (has links) (PDF)
New modelling tools intended to contribute to the development of components for quieter vehicles are developed. The tools are based on continuum models for wave propagation in poro- and visco-elastic media. By using geometric attributes of the studied components, the computational cost may be radically decreased compared to traditional methods. By assigning known analytical functions for one or two of the spatial directions, the spatial dimension of the remaining numerical problem is reduced. This reduction of spatial dimensions is performed in two di↵erent ways. The first one treats wave propagation in infinitely extended homogeneous and hollowed cylindrical rods, or wave guides, consisting of visco-elastic media. The wave solutions obtained are then used to model rubber vibration isolators of finite length by mode-matching the fields to the radial boundary conditions of interest. The second one is a method for modelling rotationally symmetric multilayered structures consisting of poro-elastic, elastic and fluid domains. By using a harmonic expansion for the azimuthal spatial dependence, the original three-dimensional problem is split up into several, much smaller, two- dimensional ones, radically decreasing the computational load.Moreover, using a mixed measurement/modelling approach, the audible frequency range characteristics of a viscous damper from a truck is studied, illustrating the influence of the rubber bushings by which it is attached to surrounding structures.The modelling approaches presented in this thesis are intended as tools aiding the design process of new vehicles, enabling new technology striving for more sustainable vehicle concepts. More specifically, the tools aim to improve the modelling of sound and vibration properties which are often penalised when seeking new, more sustainable vehicle designs.
42

Revêtements polymères sous contraintes environnementales couplées

Nguyen, Dang Dan 21 December 2012 (has links) (PDF)
L'objectif de notre étude est de mettre en évidence les synergies existantes entre les différents facteurs de vieillissement lors de la dégradation d'un revêtement polymère modèle, représentatif d'une peinture anticorrosion.Notre travail a consisté à suivre le vieillissement hygrothermique du système DGEBA/TETA sous forme de film libre et de revêtement déposé sur substrat acier dans différentes solutions (eau pure et NaCl 3%) pour différentes températures et contraintes mécaniques visco-élastique appliquées. Nos résultats ont montré que le programme de cuisson affectait les propriétés physico-chimiques et mécaniques du système initial et que l'absorption d'eau, non homogène, suivait une loi non-Fickienne, suite à un phénomène de gonflement.La prise en eau et la diffusion ont été caractérisées par gravimétrie et spectroscopie d'impédance électrochimique. Nos résultats montrent que les propriétés barrière du revêtement diminuent avec la quantité d'eau absorbée et avec la température de vieillissement. Cependant, la contrainte plane appliquée sur le système tend à contrarier cet effet. La formalisation de nos observations expérimentales dans le cadre d'une approche thermodynamique a montré l'effet prépondérant de la partie entropique par rapport à la partie enthalpique de l'énergie d'activation des processus de transport de l'eau, en raison de l'orientation des chaînes sous l'action de la contrainte. De plus, une diminution de la permittivité relative du revêtement sec a été observée en fonction de la température et de la contrainte appliquée, indépendamment de son signe (tension ou compression). Dans ce cas, la contribution enthalpique semble être prépondérante.
43

Nano-scale temperature dependent visco-elastic properties of polyethylene terephthalate (PET) using atomic force microscope (AFM).

Grant, Colin, A., Alfouzan, Abdulrahman, Twigg, Peter C., Coates, Philip D., Gough, Timothy D. 2012 June 1920 (has links)
Visco-elastic behaviour at the nano-level of a commonly used polymer (PET) is characterised using atomic force microscopy (AFM) at a range of temperatures. The modulus, indentation creep and relaxation time of the PET film (thickness = 100 m) is highly sensitive to temperature over an experimental temperature range of 22¿175 ¿C. The analysis showed a 40-fold increase in the amount of indentation creep on raising the temperature from 22 ¿C to 100 ¿C, with the most rapid rise occurring above the glass-to-rubber transition temperature (Tg = 77.1 ¿C). At higher temperatures, close to the crystallisation temperature (Tc = 134.7 ¿C), the indentation creep reduced to levels similar to those at temperatures below Tg. The calculated relaxation time showed a similar temperature dependence, rising from 0.6 s below Tg to 1.2 s between Tg and Tc and falling back to 0.6 s above Tc. Whereas, the recorded modulus of the thick polymer film decreases above Tg, subsequently increasing near Tc. These visco-elastic parameters are obtained via mechanical modelling of the creep curves and are correlated to the thermal phase changes that occur in PET, as revealed by differential scanning calorimetry (DSC).
44

Modélisation thermo-visco-hyperélastique du comportement du PET dans les conditions de vitesse et de température du procédé de soufflage

Luo, Yun Mei, Luo, Yun Mei 11 December 2012 (has links) (PDF)
Le soufflage des bouteilles en polyéthylène téréphtalate (PET) génère des modifications importantes des propriétés mécaniques du matériau comme le montre l'étude de caractérisation des propriétés hétérogènes et anisotropes réalisée sur le fond pétaloïde, une partie 3D de géométrie complexe de bouteille soufflée présentée en fin de mémoire. L'étude principale présentée dans ce rapport s'inscrit dans le cadre du procédé de soufflage par bi-orientation où le matériau, qui se trouve à des températures légèrement supérieures à la température de transition vitreuse (Tg), est fortement biétiré générant ainsi de grandes modifications de morphologie microstructurale. Pour permettre à terme une simulation numérique du procédé qui prenne en compte ces modifications de propriétés en cours de soufflage, l'objectif de la thèse est de décrire le comportement du PET par un modèle visco hyperélastique original en grandes déformations, d'identifier ce modèle couplé à la thermique à partir des données expérimentales très récentes de tension biaxiale à des conditions de vitesse et de température proches du procédé et enfin d'implanter ce modèle pour la simulation du procédé. En parallèle, les aspects thermiques, qui s'avèrent fondamentaux pour le procédé, sont explorés via une identification des propriétés thermiques réalisée sur la base d'essais de chauffage infrarouge et de mesure de champs par caméra thermique. La proximité de Tg rend les propriétés mécaniques très sensibles aux moindres variations de température aussi est-il particulièrement important de prédire correctement les conditions thermique initiales de la préforme avant soufflage. De plus, la très forte viscosité à ces températures génère une dissipation importante et qui contribue à l'auto échauffement du matériau modifiant les propriétés mécaniques au cours du temps. La formulation de ce problème thermo-mécanique couplé est implémenté et résolu par la méthode des éléments finis pour simuler le gonflage des préformes
45

Effet des contraintes et de la température sur l'intégrité des ciments des puits pétroliers

Vu, Manh Huyen 23 February 2012 (has links) (PDF)
Durant la phase de construction des puits pétrolier, le ciment est coulé dans l'espace annulaire entre le cuvelage et la roche environnante. La gaine de ciment a pour but de tenir le cuvelage, garantir l'étanchéité des puits pétroliers, ou des réservoirs de stockage de CO2, et de protéger le cuvelage de la corrosion. Au cours de la vie du puits, cette gaine de ciment est soumise tout le long du puits à des sollicitations thermiques et mécaniques qui varient au cours du temps et qui peuvent modifier ses propriétés et altérer son étanchéité. L'objet de cette thèse est d'étudier l'effet de la température et des contraintes sur les propriétés mécaniques de la pâte de ciment en cours de prise et de la pâte de ciment durcie. L'approche est basée sur une étude expérimentale qui combine des essais calorimétriques, des mesures de vitesse des ondes et des essais oedométriques avec le système des cellules STCA (Slurry To Cement Analyzer) sur le ciment en cours de prise ainsi que des essais de compression uniaxiale et triaxiale sur la pâte de ciment durcie. Les résultats expérimentaux ont montré que la température et la pression accélèrent la cinétique d'hydratation et que la température affecte significativement les propriétés élastiques du matériau tandis que la pression ne les influence pas pour une gamme de pression limitée à 20MPa. Une modélisation de la cinétique d'hydratation associée à une technique d'homogénéisation est proposée afin d'interpréter les essais. On a mis aussi en évidence que lorsque la prise se fait sous contraintes mécaniques, des déformations irréversibles peuvent se développer dans la pâte de ciment, ce qui peut conduire à la formation d'un micro-annulaire entre la gaine ciment, le cuvelage et la formation géologique. Le comportement différé de la pâte de ciment durcie a été étudié à partir d'essais de fluage uniaxiaux et d'essais de compression isotrope. Les essais ont mis en évidence que le fluage sous chargement uniaxial est plus important pour un ciment hydraté à une température plus élevée, ce qui est attribué à une microstructure plus hétérogène. Un modèle visco-endommageable permettant de reproduire les phases de fluage primaire et tertiaire a été développé. Les essais de compression isotrope drainés et non-drainé isothermes sous forte contrainte ont montré un comportement différé avec hystérésis lors de cycles décharge-recharge. Ces essais ont été analysés à partir d'un modèle de comportement poro-visco-plastique. Le comportement élastoplastique à court terme a été abordé à l'aide des essais triaxiaux sous chargement déviatorique drainé. Ces essais ont mis en évidence que la température d'essai affecte fortement la surface de charge initiale et les déformations tandis qu'elle ne modifie pas significativement la surface de rupture. Un modèle de plasticité avec une surface de charge fermée et un écrouissage dépendant des déformations plastiques accumulées a été développé pour décrire ces essais. Enfin, une étude préliminaire sur les effets des cycles mécaniques et thermiques a été menée. Des cycles thermiques ne dépassant pas la température d'hydratation ne semblent pas affecter les propriétés mécaniques du matériau. Cependant, une dégradation très rapide avec le nombre de cycles mécaniques a été mise en évidence lorsque la contrainte dépasse 60% de la résistance en compression simple
46

Evaluation of malted barley with different degrees of fermentability using the Rapid Visco Analyser (RVA)

Visser, Magdalena Johanna 03 1900 (has links)
Thesis (MSc Food Sc)--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The relationship between malt fermentability and rheological variables, measured by means of the Rapid Visco Analyser (RVA) and application of multivariate data analysis, was investigated. The RVA Kilned Malt method was optimised to achieve maximum rheological discrimination between malt samples, differing in fermentability. Five concentrations and two particle sizes were used to investigate each malt sample. Data were analysed by two different data analysis techniques, namely principal component analysis (PCA) and analysis of variance (ANOVA). Rheological variables for peak-height, -width, -area and time occurrence, were able to discriminate between high (Metcalfe, Flagship), intermediate (SSG 585, PUMA) and low malt fermentability (SSG 506, SSG 564). Variation in particle size showed insignificant (P>0.05) fermentability discrimination. The malt to water ratio of 1:1.5 provided the best discrimination in fermentability. PCA applied to the entire dataset was the superior data analysis technique. Partial least squares (PLS) regression and Soft Independent Modeling of Class Analogy (SIMCA) were applied to predict malt fermentability. Recorded RVA data was regressed with both apparent attenuation limit (AAL) and free amino nitrogen (FAN), independently. Developed PLS calibration models were validated by test set and segmented crossvalidation for AAL and FAN, respectively. The SIMCA classification model developed was based on different malt fermentability classes, each PCA validated independently by test set validation. A strong correlation between RVA analysis and AAL was obtained (r=0.92), while FAN delivered a weak correlation (r=0.59). Regarding the SIMCA model; the proportion of test set samples correctly classified in terms of malt fermentability was 83%. South African malt blends were predicted to have low malt fermentability. Simulated blends were predicted to have high fermentability when using a minimum of 80% Metcalfe blended with SSG 506. Blends containing higher percentages of the low malt fermentability cultivar (SSG 506) were predicted to have an overall intermediate fermentability. Different experimental conditions were investigated during RVA analysis (i.e. instrument model; time/temperature profile, enzyme activity and heating/cooling rate). Rheological measurement using different RVA models gave similar PCA results, indicating adequate sensitivity of the older instrument for discrimination purposes. Matching the time/temperature profile used in the commercial brewery mashing process was rejected due to increased analysis time and rheological noise while reducing fermentability discrimination. Inactivating malt enzymes prior to RVA analysis provided useful sample information, such as the large starch granule’s mean diameter, extract and starch content, by measuring peak height and iv time to peak. The amount of starch damage inflicted on a malt sample increased after repeated centrifugal milling, but was unaffected by the sieve size used. Multivariate data analysis is a suitable statistical technique applied to rheological data and provided more relevant information than traditional univariate techniques. The RVA can be considered an ideal instrument within a grain laboratory as it allowed the investigation of different operating conditions. It is beneficial to use an inexpensive, routine method of analysis to measure various interacting factors. RVA rheological measurement demonstrated to be a decisive monitor of malt fermentability and is highly recommended to be incorporated within the barley breeding, malting and brewing industries. / AFRIKAANSE OPSOMMING: Die verwantskap tussen mout fermenteerbaarheid en reologie-veranderlikes, gemeet met die “Rapid Visco Analyser” (RVA) en toepassing van meerveranderlike data analise is ondersoek. Die RVA “Kilned Malt” metode is geoptimeer om maksimum reologiese diskriminasie, tussen gars kultivars van verskillende fermenteerbaarheid, te lewer. Vyf konsentrasies en twee partikel groottes is gebruik in die ondersoek vir elke mout monster. Data is deur beide hoof komponent analise (HKA) en variansie-analise (ANOVA) ondersoek om die verskillende data analise metodes met mekaar te vergelyk. Reologiese veranderlikes vir piek-hoogte, - wydte, -area en -vormingstyd, kon diskrimineer tussen hoë (Metcalfe, Flagship), intermediêre (SSG 585, PUMA) en lae (SSG 506, SSG 564) mout fermenteerbaarheid. Variasie in partikel grootte kon nie beduidende diskriminasie in fermenteerbaarheid aantoon nie. Die mout-totwater konsentrasie van 1:1.5 het die beste diskriminasie in fermenteerbaarheid gelewer. Die toepassing van HKA op die hele datastel was die beter analitiese tegniek. Parsiële kleinste kwadrate (PKK) regressie en Sagte Onafhanklike Modellering van Klas Analogie (SIMCA) is toegepas om mout fermenteerbaarheid te voorspel. Regressie tussen RVA data en skynbare attenuasie limiet (AAL), sowel as vrye amino stikstof (FAN) inhoud, is afsonderlik uitgevoer. Die geldigheid van regressie modelle is deur middel van toets stel en gesegmenteerde kruis-validasie vir AAL en FAN onderskeidelik uitgevoer. SIMCA klassifikasie modelle is gebaseer op verskillende mout fermenteerbaarheids-klasse, waarvan elke HKA klas individueel geldig is. RVA analise het ‘n sterk korrelasie met AAL (r=0.92), maar ‘n swak korrelasie met FAN (r=0.59) getoon. Die SIMCA model het 83% van toets stel monsters as korrek geklassifiseer in terme van mout fermenteerbaarheid. Suid Afrikaanse mout mengsels is voorspel as swak fermenteerbaar. Nagebootste mengsels is voorspel as hoogs fermenteerbaar wanneer minimum 80% Metcalfe met SSG 506 vermeng word. Sodra ‘n hoër persentasie van die swakker fermenteerbaarheids-kultivar (SSG 506) bygevoeg is, word intermediêre fermenteerbaarheid voorspel. Tydens RVA analise is verskillende eksperimentele toestande ondersoek (byvoorbeeld instrument model; tyd/temperatuur profiel; ensiem aktiwiteit en verhittings/verkoelings tempo). Die gebruik van verskillende RVA modelle het soortgelyke HKA resultate gelewer. Dus bevat die ouer instrument aanvaarbare sensitiwiteit vir diskriminasie doeleindes. Nabootsing van die tyd/temperatuur profiel in die kommersiële brouproses is verwerp, aangesien analise tyd en reologiese geraas toegeneem het, terwyl fermenteerbaarheidsdiskriminasie verminder het. Inaktivering van mout ensieme voor RVA analise lewer nuttige monster inligting; deur veranderlikes soos piek-hoogte en piek-tyd te meet, kan die groot stysel korrel se gemiddelde deursnit, ekstrakwaarde en stysel inhoud verkry word. Herhaalde sentrifugale maling van ‘n mout monster lei tot beskadiging van stysel, maar dit word nie deur sif grootte beïnvloed nie. Die toepassing van meerveranderlike data analise op reologiese data is waardevol en lewer meer relevante inligting in vergelyking met tradisionele eenveranderlike data analise. Die RVA is ‘n ideale instrument vir gebruik in ‘n graan laboratorium aangesien dit verskillende operatiewe kondisies kan ondersoek. Die gebruik van ‘n enkele, goedkoop, roetine analitiese metode is voordelig en het die potensiaal om ‘n magdom interaktiewe faktore te meet. RVA reologiese meting demonstreer die vermoë as ‘n deurslaggewende tegniek vir die bepaling van mout fermenteerbaarheid, gevolglik word toepassing sterk aanbeveel binne die gars teëlings-, vermoutings- en brouers-industrieë.
47

Modelos viscosos em mecânica dos solos: análise de uma equação visco-hipoplástica. / Visco models in soil mechanics: a visco-hypoplastic equation analysis.

Belén Cogliati 03 October 2011 (has links)
Cogliati, Belén. (2011). Modelos viscosos em mecânica dos solos: análise de uma equação visco-hipoplástica. Dissertação de Mestrado, Escola Politécnica da Universidade de São Paulo, São Paulo. Esta dissertação estuda o comportamento de um modelo visco-hipoplástico proposto por Niemunis (2002), com as funções constitutivas da equação hipoplástica de Nader (2003). Para entender o papel da viscosidade no comportamento do solo são discutidos o adensamento secundário, a influência da velocidade de deformação na resistência não-drenada e a variação do coeficiente de empuxo com o tempo. Como etapa preliminar, são apresentados os modelos reológicos simples em uma dimensão, formados por um só elemento (modelos de Hooke, Newton e Saint-Venant) e modelos compostos pela combinação desses elementos (modelos de Maxwell, Bingham, Kelvin- Voigt, sólido linear padrão e visco-plástico com endurecimento). São deduzidas as equações de fluência e relaxação para todos esses modelos. Em três dimensões, são apresentadas as formulações do modelo visco-hipoplástico de Niemunis (2002) com as funções constitutivas de Nader (2003). São deduzidas as expressões simplificadas desse modelo para ensaios triaxiais. Em seguida, as equações são aplicadas à simulação de ensaios de compressão isotrópica e compressão não-drenada, com o objetivo de investigar a relaxação e a fluência bem como para analisar a influência dos parâmetros na resposta do modelo. / This thesis studies the behavior of the visco-hypoplastic model proposed by Niemunis, using Nader\'s hypoplastic constitutive equations. To understand the importance of viscosity in soil behavior the following topics are first examined: secondary consolidation, strain rate effects on undrained strength and the time variation of the coefficient of lateral pressure at rest. As a preliminary step, the present work discusses one-dimensional rheological models formed by a single element (Hooke\'s, Newton\'s and Saint-Venant\'s models) or by the combination of these elements (Maxwell\'s, Bingham\'s, Kelvin-Voigt\'s models; the standard linear solid model and the visco-plastic hardening model). For all the rheological models creep and relaxation are investigated. Niemunis\' visco-hypoplastic model with Nader\'s constitutive equations is presented next. First, simplified expressions of this model for triaxial test are deduced. Then the equations are applied to the simulation of isotropic compression and undrainded compression tests, with the aim of investigating relaxation and creep as well as of analyzing the influence of each parameter on the model response.
48

Estudo da influência dos perfis de solo na resposta dinâmica de sistemas rotor-fundação / Study of the influence of soil profiles on dynamic response of rotor-foundation systems

Ramalho, Denise Alves 27 July 2006 (has links)
Orientador: Katia Lucchesi Cavalca Dedini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-09T21:40:12Z (GMT). No. of bitstreams: 1 Ramalho_DeniseAlves_M.pdf: 10823264 bytes, checksum: 8b25eba0e7c26b9c543a70020d208299 (MD5) Previous issue date: 2006 / Resumo: O objetivo deste trabalho é estender e melhorar a análise dinâmica de um sistema rotorfundação-solo através da inclusão de modelos distintos de perfis de solo. Obtém-se a resposta desbalanceada de um rotor Laval (Jeffcott) simples bidimensional com mancais rígidos. O rotor é colocado sobre uma fundação de bloco rígido. Os perfis de solo incluem o modelo clássico de semi-espaço e o modelo de solo sobre base rígida. Em particular, uma camada sobre base rígida com diferentes valores de profundidade será considerada. A resposta dinâmica do solo é obtida no domínio da freqüência. O mecanismo de amortecimento interno do solo é considerado. Vários estudos paramétricos são realizados para avaliar o papel da espessura da camada do solo, do coeficiente de amortecimento do solo, da inércia da fundação e da altura dos mancais na resposta ao desbalancemento do rotor. Acredita-se que a análise deste modelo simples de rotor-fundação-solo ajudará a esclarecer o papel dos parâmetros mencionados na resposta dinâmica do rotor / Abstract: The aim of the present work is to extend and improve the dynamic analysis of a rotorfoundation-soil system by including the modelling of distinct soil profiles. The unbalance response of a simple two-dimensional Laval (Jeffcott) rotor with rigid bearings is performed. The rotor is attached to a rigid strip foundation (block foundation). The soil profiles, on the other hand, include the classical half-space but also stratified soils. In particular, a layer with various depths over a bedrock will be considered. The soil¿s dynamic response is furnished in terms of frequency dependent complex impedances. The soil internal damping mechanism is also addressed by making the soil a viscoelastic continuum. A series of parametric studies are perfomed to assess the role of soil layer thickness, soil internal damping coefficient, foundation inertia and bearing height on the rotor unbalance response. It is believed that the analysis of this simple otor-foundation-soil model will help to clarify the role of the mentioned parameters on the rotor dynamic response / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica
49

Bonding and debonding mechanism of pressure sensitive adhesives

Akogyeram, Samuel January 2010 (has links)
Pressure-sensitive adhesives (PSAs) are complex macromolecular-based blend formulations that, in dry form will adhere permanently to diverse surfaces with the application of mere finger pressure. This thesis addresses the bonding and debonding mechanisms of coated films of different commercially available PSAs by systemically investigating the film characteristics on multiple levels. The methods implemented involve a novel procedure in investigating viscoelastic properties with Dynamic Mechanical Analysis, film surface chemistry with Time-of-flight Secondary Ion Mass Spectrometry and film morphology, modulus and bonding characteristics with Atomic Force Microscope. The theoretical aspect invoked rubber elasticity, viscoelasticity and thermodynamic concepts in representation of film morphology with corresponding adhesion nature. The results indicate that the bonding and debonding behaviour of PSA films are of a viscoelastic nature, dictated mainly by two fundamental morphological elements. These elements are; (1) the formation of phase-separated self-assembly of polystyrene-richcopolymer nano-domains within the adhesive matrix and (2) the inter-linking of the nanodomains by elastically active elastomer segments into a physical crosslinked network system that is highly efficient in dissipating large strain energy. These morphological factors are manifested through a profound contribution to the peel strength of the adhesive films when either coated at high temperatures or annealed. Increasing the content of the polystyrene endblock-tackifier in the adhesive blend formulation increased the PSA’s performance sensitivity to the film coating temperature. Meanwhile increasing the cis-C=C bond concentration in the formulation reduced the film’s performance sensitivity to coating temperature, as polydienes are premised to promote the entropy-elasticity of the film matrix by contributing to the nano-domain interconnections. This thesis generates many qualitative similarities, despite the significantly different adhesive blends investigated and hopefully the results reported here are more universal than one might expect.
50

Determination of Wear in Polymers Using Multiple Scratch Test.

Damarla, Gowrisankar 08 1900 (has links)
Wear is an important phenomenon that occurs in all the polymer applications in one form or the other. However, important links between materials properties and wear remain illusive. Thus optimization of material properties requires proper understanding of polymer properties. Studies to date have typically lacked systematic approach to all polymers and wear test developed are specific to some polymer classes. In this thesis, different classes of polymers are selected and an attempt is made to use multiple scratch test to define wear and to create a universal test procedure that can be employed to most of the polymers. In each of the materials studied, the scratch penetration depth s reaches a constant value after certain number of scratches depending upon the polymer and its properties. Variations in test parameters like load and speed are also studied in detail to understand the behavior of polymers and under different conditions. Apart from polystyrene, all the other polymers studied under multiple scratch test reached asymptotes at different scratch numbers.

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