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Universidade Estadual de Campinas
Faculdade de Odontologia de Piracicaba
Tales Candido Garcia da Silva
AVALIAÇÃO DA METODOLOGIA DO FIO QUENTE E ANÁLISE
TERMOMECÂNICA DE LAMINADOS OCLUSAIS ULTRAFINOS
POR ELEMENTOS FINITOS
EVALUATION OF HOT-WIRE TECHNIQUE AND
THERMOMECHANICAL FINITE ELEMENT ANALYSIS OF
ULTRATHIN OCCLUSAL VENEERS
Piracicaba
2016
Tales Candido Garcia da Silva
AVALIAÇÃO DA METODOLOGIA DO FIO QUENTE E ANÁLISE
TERMOMECÂNICA DE LAMINADOS OCLUSAIS ULTRAFINOS
POR ELEMENTOS FINITOS
EVALUATION OF HOT-WIRE TECHNIQUE AND
THERMOMECHANICAL FINITE ELEMENT ANALYSIS OF
ULTRATHIN OCCLUSAL VENEERS
Tese apresentada à Faculdade de Odontologia de
Piracicaba, da Universidade Estadual de Campinas como
parte dos requisitos exigidos para obtenção do Título de
Doutor em Materiais Dentários.
Thesis presented to the Piracicaba Dental School of the
University of Campinas in partial fulfillment of the
requirements for the degree of Doctor in Dental Materials.
Orientador: Prof. Dr. Rafael Leonardo Xediek Consani
Este exemplar corresponde à versão final da Tese de
doutorado defendida pelo aluno Tales Candido Garcia
da Silva, e orientada pelo Prof. Dr. Rafael Leonardo
Xediek Consani.
Piracicaba 2016
DEDICATÓRIA
Aos meus pais José Candido da Silva e Valdete Garcia de Souza e Silva
por toda atenção e ensinamentos ao longo dos anos, pelas inúmeras vezes que renunciaram
a seus momentos para que eu pudesse realizar os meus, buscando sempre mostrar o melhor
caminho, presentes mesmo quando a distância era necessária. Agradeço ao amor
incondicional, principalmente nos momentos difíceis, fazendo com que as dificuldades se
tornassem mais amenas. Tudo o que sou, devo a vocês!
Às minhas irmãs Taísa Garcia da Silva Del Pino e Tárcia Garcia da Silva
Soto, por sempre acreditarem em mim e entenderam todas as minhas renúncias em busca
de um objetivo. Pela presença em todos os momentos de minha vida, pelos abraços e
sorrisos, por todo amor, por sermos cada vez mais unidos.
À minha sobrinha Ana Clara Garcia Del Pino, que apesar de sua pouca idade
seu carinho e alegria são fundamentais. O abraço mais sincero, que me enche de ânimo a
cada vez que preciso estar distante.
Amo vocês! Obrigado por tudo...
AGRADECIMENTOS ESPECIAIS
Ao meu orientador, Prof. Dr. Rafael Leonardo Xediek Consani, inicialmente
por acreditar em meu potencial e oportunidade de fazer parte do seu grupo de trabalho. Sou
grato por todo conhecimento adquirido, atenção, confiança e auxílio nos momentos em que
precisei.
Ao Prof. Dr. Antheunis Versluis, por todo conhecimento compartilhado,
convívio fraterno e oportunidades ofertadas. Sua humildade e busca de conhecimento
contínuo é fonte de estímulo na caminhada diária. Obrigado por acreditar em minha
capacidade, comprometimento e por contribuir para o meu crescimento pessoal e
profissional.
Meu reconhecimento e gratidão pela orientação
Obrigado!
AGRADECIMENTOS
A Deus por todo amparo e proteção em todos os momentos de minha vida.
Ensinando-me a ser paciente e persistente com as dificuldades do caminho.
A Faculdade de Odontologia de Piracicaba – UNICAMP, na pessoa do seu Diretor
Prof. Dr. Guilherme Elias Pessanha Henriques pela oportunidade da realização do Curso de
Doutorado nesta instituição.
A Coordenadoria da Pós-Graduação em nome da Profa. Dra. Cínthia Pereira
Machado Tabchoury e ao Programa de Pós-Graduação em Materiais Dentários em nome da
coordenadora Profa. Dra. Regina Maria Puppin Ronatini.
A Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES pela
concessão da bolsa de doutorado e oportunidade de realizar parte do meu doutorado em
uma universidade estrangeira, com a concessão da bolsa de Doutorado Sanduíche na
University of Tennesse Health Science Center.
Ao Prof. Dr. Carlos José Soares por todo apoio e solicitude desde o primeiro
contato, por disponibilizar o CPBio e toda estrutura da UFU para que a realização deste
trabalho fosse possível. Por todo conhecimento compartilhado, convívio afetuoso e
preocupação. Exemplo de conduta pessoal e profissional.
A todos os alunos do CPBio que não mediram esforços quando precisei. Em
especial a Aline Aredes Bicalho, por toda paciência e auxílio com os testes laboratoriais
durante a realização deste trabalho.
A Profa. Dra. Daranee Tantbirojn Versluis, pela receptividade e preocupação.
Pelo conhecimento partilhado e oportunidade de trabalharmos juntos durante minha
estadia na Universidade do Tennessee
A José Estevam Vieira Ozório. Diante da solidão do inesperado, mais que amigo,
se tornou um irmão. Obrigado pelas palavras de incentivo, pelos momentos de descontração
e também de seriedade, pela disponibilidade em auxiliar e compartilhar não apenas
conhecimento científico, mas também de vida. Junto, também agradeço a Melissa Andréia
Marchesan, por toda a preocupação e fazer que a saudade de casa e da família fosse
amenizada com toda atenção e cuidado dispendidos.
Ao Prof. Dr. Paulo Francisco César, pela prontidão e auxílio com as amostras
deste experimento.
Aos docentes do Curso de Pós-Graduação em Materiais Dentários, pelos
ensinamentos e experiências cotidianas fundamentais para minha formação.
Aos técnicos do departamento de Materiais Dentários, engenheiro Marcos
Blanco Cangiani e Selma Segalla pela disponibilidade e auxílio quando solicitado.
Aos amigos de doutorado: Renata Fernandes, Eveline Soares, Camila Sobral,
Raquel Viana, Rafael Pacheco, Caio Vinícius, Daniel Sundfeld, Valéria Bisinoto, Pedro
Freitas, Tóride Cellegati, Ana Paula Ayrese Dayane Oliveira.
A todos os amigos da área de Materiais Dentários e também amigos de outras
áreas: enfrentarmos momentos de dificuldades e conquistas. A nossa amizade e troca de
experiências foi essencial para o crescimento pessoal e profissional de cada um.
Aos meus cunhados Thiago Fernandes Del Pino e Cristiano Soto Armindo por
todo apoio durante esta caminhada.
Aos companheiros de Pós-Graduação e residência Marco Aurélio de Carvalho e
Antônio Pedro Ricomini, que com a convivência diária se tornaram irmãos nestes últimos
tempos. Obrigado pela amizade fraterna.
A todos meus amigos, estivessem eles perto ou longe, presentes ou apenas em
pensamento, se fizeram sempre presentes me auxiliando a ser mais forte quando
necessário, principalmente nos momentos de distância e solidão. Vocês alegram meus dias e
me ajudaram a tornar possível a conclusão de mais esta etapa.
A Sirona Brasil que me possibilitou o uso de suas estruturas permitindo a
realização da fresagem das amostras deste trabalho.
A todos que direta ou indiretamente contribuíram para a realização deste
trabalho.
Obrigado!
EPÍGRAFE
“A persistência é o menor caminho do êxito.”
Charles Chaplin
RESUMO
O desgaste da estrutura dental resulta em alteração da distância interoclusal,
comprometimento da função e desfiguração estética. O protocolo restaurador depende do
grau de estrutura perdida. Entretanto, as técnicas tradicionais para restaurar a superfície
oclusal envolvem preparo de tecido dental sadio. Laminado oclusal ultrafino é uma nova
proposição de restauração indireta minimamente invasiva para reabilitação de superfícies
oclusais sem a necessidade de preparos extensos ou retentivos. O objetivo neste trabalho
foi: 1) avaliar o método do Fio Quente na mensuração da condutividade térmica de materiais
CAD/CAM Lava Ultimate e IPS e.max CAD; 2) calcular o módulo de elasticidade dos materiais
restauradores e contração pós-gel do RelyX Ultimate e 3) avaliar a termomecânica de
laminados oclusais ultrafinos de diferentes espessuras por elementos finitos. Para avaliar a
condutividade térmica pela metodologia do fio quente, amostras (n=5) constituídas por dois
blocos retangulares (18 × 14,5 × 4 mm) foram prensadas uma contra a outra. Em um deles,
um sulco ortogonal foi confeccionado para acomodar a cruz de medição composta por uma
resistência de Kanthal e um termopar. Corrente elétrica de 0,7 A para Lava Ultimate e 1,5 A
para emax CAD e 5V de tensão foi estabelecida para as amostras. Os dados foram coletados
pelo tempo de 500 s e frequência de 4 Hz. A análise de extensometria bidirecional mensurou
a contração pós-gel do RelyX Ultimate (n=10). O módulo de elasticidade dos materiais
restauradores (n=10) foi estabelecido por teste de flexão de três pontos. Os modelos de
elementos finitos 2D foram construídos no MENTAT baseados em corte de microtomografia
de um primeiro molar inferior humano por importação de pontos gerados no ImageJ. A
simulação da contração da camada de cimento, variação da temperatura (55/37/5°C) na
superfície do modelo e aplicação de carga axial oclusal de 228 N com uma esfera de 6 mm de
diâmetro foram realizadas pelo MARC. As tensões foram avaliadas pelo critério de von Mises
modificado. A condutividade térmica do Lava Ultimate foi determinado em 0,87 W/mK e IPS
e.max CAD em 2,52 W/mK. A contração volumétrica pós-gel do cimento 1,13%. O módulo de
elasticidade foi 93,85±6,6 GPa; 12,81±0,3 GPa e 9,08±0,21 GPa para e.max CAD, Lava
Ultimate e RelyX Ultimate, respectivamente. Conclui-se que o método do fio quente cruzado
foi eficaz na mensuração da condutividade térmica dos materiais CAD/CAM. A ciclagem em
baixa temperatura concentrou maior tensão. Os laminados oclusais de IPS e.max CAD
propagaram maior quantidade de calor nos modelos que Lava Ultimate. A camada de
cimento foi a estrutura com maior concentração de tensão. IPS e.max CAD apresentou os
maiores valores de tensões mecânicas concentrado nos laminados, enquanto Lava Ultimate
distribuiu melhor as tensões nas camadas subjacentes; entretanto, o padrão de distribuição
das tensões não diferiu do dente não preparado. Os laminados mais espessos concentraram
maior tensão térmica e menor tensão mecânica que os laminados mais finos.
Palavras-chave: Condutividade térmica. Facetas dentárias. Análise de elementos finitos.
Cerâmicas. Resinas compostas.
ABSTRACT
The pathologic tooth wear results in an increase of interocclusal distance,
impaired function, and esthetic disfigurement. The restorative protocol depends on degree
of tooth structure lost, however the traditional techniques to restore the occlusal surface
involve preparing sound dental tissue. The occlusal veneer is an option of indirect
restorations minimally invasive only to replace the loss structure without extensive tooth
reduction or retentive preparations. Thus, the aim of this study was: 1) evaluate the Hot-
wire technique to measure the thermal conductivity of CAD/CAM materials Lava Ultimate
and IPS e.max CAD, 2) measure the restorative materials elastic modulus and RelyX Ultimate
post-gel shrinkage and 3) evaluate the thermomecanics of ultrathin occlusal veneers made
with different thickness by Finite Element Analysis. To evaluated the thermal conductivity by
hot-wire technique, the samples (n=5) consisted of two rectangular blocks (18 × 14.5 × 4mm)
stacked and clamped together. Orthogonal grooves were made to accommodate the
crosspiece formed by kanthal resistance hot-wire and thermocouple. An electrical current of
0.7A was applied for Lava Ultimate and 1.5A for emax CAD at 5V. Temperature signals were
recorded for 500s at frequency of 4Hz. Post-gel shrinkage (n=10) was measured by strain
gauge technique and Elastic Modulus of restorative materials (n=10) was determined by
deflectometer at 3-point bending test. Two-dimensional FEA models were built in MENTAT
based on a cross-sectional micro-CT human inferior molar by coordinate points of ImageJ.
Thermal load (5º-55ºC) at outer surface, a 228N occlusal axial load was applied by a 6mm
diameter simulated sphere and post-gel shrinkage of cement was simulated by MARC.
Modified von Mises thermal and mechanical stresses were calculated. The thermal
conductivity of Lava Ultimate was determined at 0.87 W/mK and IPS e.max CAD at 2.52
W/mK. Cement shrinkage strain value (in volume %) was 1.13. Elastic Modulus was e.max
93.85±6.6 GPa, Lava 12.81±0.3 GPa and Relyx 9.08±0.21 GPa. In conclusion, the hot-wire
cross technique could be used for determination of the thermal conductivity of CAD/CAM
materials. Cold temperature created higher stress distribution. IPS e.max CAD conducted
more heat within models than Lava Ultimate. Cement layer concentrated the highest
thermal stress. Modified von Mises stress was higher in IPS e.max CAD veneer and
underlying of Lava Ultimate restoration but stress distribution pattern not different of a non-
prepared tooth. Thicker veneers accumulated more thermal and lower mechanical stress
compared with thin veneer.
Keywords: Thermal conductivity. Dental veneers. Finite element analysis. Ceramics.
Composite resins
SUMÁRIO
1 INTRODUÇÃO ..................................................................................................................................... 16
2 ARTIGOS ............................................................................................................................................. 19
2.1 Artigo 1: Hot-wire technique for measurement of thermal conductivity of dental ceramic and
composite ......................................................................................................................................... 19
2.2 Artigo 2: Thermal and biomechanical analysis of CAD/CAM ultrathin occlusal veneers by Finite
Element Analysis ............................................................................................................................... 36
3 DISCUSSÃO ......................................................................................................................................... 62
4 CONCLUSÃO ....................................................................................................................................... 65
REFERÊNCIAS ......................................................................................................................................... 66
APÊNDICES ............................................................................................................................................ 70
Apêndice 1: Geração do modelo numérico a partir do modelo experimental .......................................... 70
Apêndice 2: Média e desvio padrão dos valores de contração pós-gel do RelyX Ultimate (volume %) ....... 71
Apêndice 3: Média e desvio padrão dos valores do Módulo de Elasticidade (GPa) dos materiais
restauradores utilizados no estudo ........................................................................................................ 71
ANEXOS ................................................................................................................................................. 72
Anexo 1: Comprovante de submissão do artigo (Artigo 1) ..................................................................... 72
Anexo 2: Certificado do comitê de ética em pesquisa ............................................................................ 73
16
1 INTRODUÇÃO
O desgaste natural da estrutura dental com o passar dos anos é
considerado um processo fisiológico, multifatorial, não patológico e não influenciado
por bactérias (Nunn et al., 1996). Esse desgaste em níveis avançados passa a ser
patológico causando alteração da dimensão vertical, desarmonia musculoesquelética,
sensibilidade dentária, danos pulpares e desfiguração estética levando a insatisfação
do paciente (Turner et. al., 1984; Bencharit et al., 2014; Egbert et al., 2015).
A quantidade da estrutura desgastada considerada normal ainda é fator
questionável, com valores variando entre 20-38 micrometros por ano ou até 65
micrometros em seis meses (Margeas et al., 2010). A biocorrosão se caracteriza pela
dissolução química da estrutura gerando um aspecto côncavo; enquanto a abrasão é
oriunda do desgaste mecânico característico pela formação das facetas de desgaste,
com aspecto plano e liso. Historicamente, os tratamentos restauradores convencionais
para esses tipos de lesões se baseiam no conceito de Odontologia curativa com
necessidade de cobertura total do elemento dental e preparos retentivos, desgastando
assim grande quantidade de tecido dental sadio. Com o desenvolvimento de novos
materiais e técnicas restauradoras, a eficácia dos procedimentos adesivos e inserção
tecnológica como o CAD/CAM, possibilitaram abordagens menos intervencionistas e
com máxima preservação da estrutura dental juntamente com a Odontologia
minimamente invasiva (Magne et al., 1999; Tsitrou et al.,2008; Dejak et al., 2012).
Os laminados são uma opção de tratamento bem estabelecido e
clinicamente aceitável para dentes anteriores com abordagem minimamente invasiva
frente às facetas, que necessitam maior desgaste do esmalte dental. Granell-Ruiz et
al., 2010, mostraram 94% de sucesso dos laminados anteriores em um estudo clínico
longitudinal avaliando mais de 300 restaurações em função por até 11 anos. Esse tipo
de restauração alcança notoriedade não só pela correção de pequenos maus
posicionamentos dentários, coloração, manchamento e mau formações congênitas
como também pela aceitação da Odontologia estética (Fradeani et al., 2005;
D’Arcangelo et al., 2012). Baseando-se nesses conceitos e diferentemente dos
tradicionais protocolos restauradores para dentes posteriores que exigem cobertura
17
total e preparos de até 2,0 mm (Dietschi et al., 1997; Federlin et al., 2007), um novo
tipo de restauração para dentes posteriores tem sido estudado: os laminados oclusais
ultrafinos. São laminados com espessuras inferiores às recomendadas pelos
fabricantes, minimamente invasivos, restaurando a face oclusal degastada,
reestabelecendo a dimensão vertical perdida e preservando a estrutura de esmalte.
Contudo, os poucos estudos que existem na literatura sobre esta técnica limitam-se na
avaliação da resistência à fratura das restaurações (Magne et al., 2010; Schlichting et
al., 2011; Johnson et al., 2014; Egbert et al., 2015).
Devido à complexidade do sistema biomecânico e das diferentes
geometrias e propriedades dos materiais na cavidade bucal, o método dos elementos
finitos tem sido uma importante ferramenta para análise nos experimentos
odontológicos. Os testes in vitro são limitados no que diz respeito ao comportamento
interno das estruturas analisadas (Soares et al., 2012). Neste caso, análise numérica
com soluções simplificadas de problemas físicos complexos por meio da discretização
das estruturas em pequenos elementos (Versluis & Tantbirojn, 2009), torna-se
também necessária. A caracterização dos modelos numéricos com a correta inserção
das propriedades e condições de contorno é essencial para a obtenção dos resultados
e validação dos experimentos (Ana et al., 2008).
A variação da temperatura na cavidade bucal, causada pela ingestão de
alimentos com diferentes estados térmicos (Palmer et al., 1992), se estabelece como
desafio para a longevidade das restaurações; gerando tensões térmicas nas interfaces
que induzem falhas nas restaurações, fratura dental (Toparli et al., 2003; Mezzomo et
al., 2011) e danos pulpares (Oskui et al., 2013). Estudos de Magne et al., 1999;
Papanicolaou et al., 2015; Köycü et al., 2015, correlacionaram as tensões térmicas
apenas pela diferença do coeficiente de expansão térmica, mas sabe-se que a
condutividade térmica também exerce relevante efeito no resultado dessas tensões
(Kingery et al., 1955; Hasselman et al., 1978). Em razão da escassez literária de
informações referente às propriedades térmicas dos materiais restauradores atuais,
mais especificamente da condutividade térmica, é necessário realizar a mensuração
laboratorial do coeficiente de condutividade térmica dos materiais restauradores, para
que possam então ser utilizados na análise de elementos finitos.
18
Apesar da dificuldade de se calcular os coeficientes térmicos em materiais
odontológicos em virtude do reduzido tamanho das amostras (Lisanti & Zander et al.,
1949), algumas metodologias como o dispositivo de Cenco-Fitch (Brady et al., 1974),
protótipos de Lisanti & Zander (Lisanti & Zander et al., 1949) e suas variações (Philips,
1956; Craig e Peyton, 1961), foram utilizadas para medição da condutividade térmica.
O método do fio quente, um método bem mais simplificado e muito aplicado na
engenharia (De Carvalho et al., 1996; Franco et al. 2007; Dos Santos et al. 2008), foi
adaptado para possibilitar a mensuração dos coeficientes dos materiais para CAD/CAM
e dar continuidade às análises numéricas, objetivo deste estudo.
Nos estudos anteriores avaliando o comportamento mecânico dos
laminados oclusais ultrafinos, assim como nas análises por elementos finitos (Magne et
al., 2012; Magne 2016), apesar das restaurações serem consideradas minimamente
invasivas, a superfície oclusal das amostras apresentavam exposição dentinária,
simulando o desgaste oclusal severo (Magne et al., 2010; Schlichting et al., 2011;
Johnson et al., 2014; Egbert et al., 2015). A camada de cimento também não foi
considerada em nenhumas dessas análises; e é sabido que durante a cimentação das
restaurações a contração de polimerização gera tensões deletérias às estruturas e
interfaces (Sakaguchi et al., 1997), somatizando tensões das cargas oclusais e fadiga
térmica, quando em função. Contudo, não foi encontrado nenhum estudo utilizando o
método dos elementos finitos que avaliasse o comportamento combinado da
contração pós-gel do cimento dos laminados oclusais ultrafinos frente às variações
térmicas sofridas na cavidade bucal e carregamento oclusal.
19
2 ARTIGOS
2.1 Artigo 11
Title: Hot-wire technique for measurement of thermal conductivity of dental ceramic
and composite
Author names and affiliations:
Tales Candido Garcia-Silvaa,b*, José Estevam Vieira Ozorioa, Carlos José Soaresc, Rafael Leonardo Xediek Consanid, Antheunis Versluisa
aDepartment of Bioscience Research, College of Dentistry, University of Tennessee Health Science Center, Memphis, TN, USA.
E-mail address: [email protected], [email protected]
bDepartment of Restorative Dentistry, Piracicaba Dental School, State University of Campinas, Piracicaba, SP, Brazil.
Av. Limeira 901, 13414-903, Piracicaba, SP, Brazil
E-mail address: [email protected]
cDepartment of Operative Dentistry and Dental Materials, Dental School, Federal University of Uberlândia, Uberlândia, MG, Brazil.
Av. Pará 1720, Bloco 4L Anexo A, Campos Umuarama, 38400-902, Uberlândia, MG, Brazil. E-mail address: [email protected]
dDepartment of Prosthodontics and Periodontics, Piracicaba Dental School, State University of Campinas, Piracicaba, SP, Brazil.
Av. Limeira 901, 13414-903, Piracicaba, SP, Brazil.
1 Artigo submetido à Dental Materials
20
Abstract
Objective: Dental structures are subjected to thermal stresses. To assess such stresses
it is essential to determine thermal properties. A hot-wire method is a transient
dynamic technique for measuring temperature rise by the Joule effect. The aim of this
study was to use the cross-array hot-wire method for determination of the thermal
conductivity of CAD/CAM materials. Methods: Two materials were tested:
nanoceramic composite (Lava Ultimate, 3M ESPE) and disilicate ceramic (IPS e.max
CAD, Ivoclar). The samples (n=5) consisted of two rectangular blocks (18 × 14.5 × 4mm)
that were stacked and clamped together. Orthogonal grooves were made in the upper
face of the lower section to accommodate the crosspiece formed by kanthal resistance
hot-wire and thermocouple. Thermally conductive paste was used to ensure good
thermal contact between the wires and test materials. An electrical current of 0.7A
was applied for Lava Ultimate and 1.5A for emax CAD at 5V using a DC power supply.
Temperature signals were recorded for 500s at 4Hz. Measurements for each sample
were repeated 6 times in alternating directions by reversing the polarity of the DC
power supply. Temperature versus time curves were plotted on logarithmic scale to
identify the linear data range used for determination of the thermal conductivity.
Results: The thermal conductivity of Lava Ultimate was determined at 0.87 W/mK and
IPS e.max CAD at 2.52 W/mK. Significance: It was concluded that the hot-wire cross
technique could be used for determination of the thermal conductivity of two types
dental CAD/CAM materials.
Keywords: Thermal conductivity; temperature; composite resin; ceramic; CAD-CAM
21
1. Introduction
In restorative dentistry, the longevity of restorations is challenged by,
among others, physical stresses. Stresses are created by functional occlusal loading
during mastication as well as rapid temperature changes when subjected to hot and
cold foods or beverages. Oral temperature changes can range between 0°C and 67°C
[1], and cause expansion or contraction in the tooth and restorative materials. Thermal
stresses across interfaces are thought to induce failure of restorations and may also
cause fracture of dental structures [2,3].
The two main thermo-physical properties that describe the expansion and
distribution of thermal effects are the coefficient of thermal expansion and thermal
conductivity. The coefficient of thermal expansion is commonly tested for
development and marketing purposes of dental materials, and it is mainly considered
in reference with the values for tooth structures. Smaller mismatch between them
presumably reduces thermal stresses [4]. Thermal conductivity is less often considered
or reported for dental materials. Conductivity reflects how fast a temperature within a
material spreads, and therefore the temperature gradient in a material. Temperature
gradients also cause thermal stresses because they cause gradients in expansion and
contraction even where the coefficient of thermal expansion is not mismatched.
The significance of stress in dental structures is well accepted, but
determining stress distributions requires the use of engineering methods such as finite
element analysis. Finite element analysis (FEA) is widely used in dentistry to study the
stress conditions. However, relatively few studies investigated thermal stresses and
temperature distributions [2,5,6,7]. This may be due, in part, to the challenge of
22
obtaining the thermal properties for the materials studied. Thermal properties are
mostly adopted from manufacturer information, when available, or from textbooks
where properties are usually not brand specific [3,8,9].
The objective of this study was to investigate if the ‘hot-wire’ technique
could be adapted to measure thermal conductivity of dental materials. The hot-wire
method measures temperature rise in a sample that is heated by a constant linear heat
induced by the Joule effect in a resistance wire that is embedded in the test material
[10]. This technique has been used in engineering for a wide range of materials like
ceramics, fluids, and polymers [11,12,13]. Since its first practical application by Haupin
in 1960 [14], some adaptations were made to simultaneously determine different
thermal properties from the same experimental thermal transient [10,12]. The heat
propagation derived from electric current through the wire generates a transient
temperature that is dependent on time [15]. In this study the thermal conductivity was
determined for two CAD/CAM materials (nanoceramic composite and disilicate
ceramic) using the cross-array hot-wire method described in ISO 8894-1:1987 part 21.
2. Materials and Methods
Two dental CAD/CAM materials were tested: (1) Lava Ultimate (3M ESPE,
St Paul, MN, USA), which is a nanoceramic composite, and (2) IPS e.max CAD (Ivoclar
Vivadent, Schaan, Lichtenstein), which is a disilicate ceramic. Material details are listed
in Table 1. Each sample (n=5) consisted of two blocks (18 mm long × 14.5 mm wide × 4
mm high) obtained from slicing of CAD/CAM blocks in slabs of 4 mm thickness using an
Isomet low speed saw (Buehler, Lake Bluff, IL, USA). The blocks were stacked with the
23
hot-wire and thermocouple placed between them. Crossing grooves were made in the
lower block to accommodate the wires (Figure 1a) using a high-speed carbide bur #245
(Brasseler USA, Savannah, GA) under abundant water irrigation to avoid heating. The
size of the grooves corresponded with the approximate diameter of the hot-wire and
thermocouple. The hot-wire was a 26 Gauge, 0.4 mm diameter kanthal resistance wire
A1 (Kanthal Co, City of Industry, CA, USA) with a resistance of 10.531 Ω/m. A 0.5 mm J-
type thermocouple (Omega, Stamford, CT, USA) was placed perpendicular to the hot-
wire, and soldered to the hot-wire where they met in the center. To avoid interference
of air, which acts as a thermal insulator, and to improve thermal contact, a thermally
conductive and electrically insulating paste Omegatherm 201 (Omega) was used in the
groves (Figure 1b). The two blocks, containing the crossing wires, were pressed
together using clamps (Figure 1c), ensuring good thermal contact between the
samples.
Electrical current through the hot-wire was provided by a DC power supply
(model 3010D, Maihao Eletronics, Dongguan, Guangdong, China). Applied voltage was
5.0 V and the currents were 0.7 A for the Lava Ultimate and 1.5 A for the IPS e.max,
which were kept constant (±1%) during the experiment. The material specific values
for the electric currents were determined in a series of proof runs to ensure that the
induced temperature changes would not exceed 100 °C [13,16,17]. The thermocouple
was connected to a NI 9211 thermocouple input module in a NI cDAQ-9178 USB
chassis (National Instruments, Austin, TX). Temperatures were collected at 4 Hz for 500
seconds using a custom acquisition macro (LabVIEW, National Instruments). Figure 2
shows a schematic drawing of experimental setup for the measurement of thermal
conductivity. The measurements were repeated six times for each sample in
24
alternating directions by reversing the polarity of the DC power supply to account for
any asymmetry in thermocouple wires and/or hot-wire.
Theoretically, the method assumes an infinitely thin and long hot-wire
producing a thermal pulse for a finite time with constant heating power, and
generating cylindrical coaxial isotherms in an infinite, homogeneous isotropic medium.
If the wire produces a constant heat flux q per unit wire length (W/m), the
temperature rise ΔT (°K) at any distance r (m) from the wire as a function of time is
described by [15]:
ΔT = (q/(4 π k)) ln [(4 a t)/(r2 c)] (1)
where k is the thermal conductivity (W/mK), a the thermal diffusivity (m2/s), t is time
(s), and c = exp(γ), with γ the Euler’s constant. Eq. (1) is valid only when the condition
r2 / 4at << 1 is fulfilled. So, the equation can also be written as:
ΔT = (q/(4 π k)) ln [(4 a t)/r2] – γ (2)
The temperature rise is thus a linear function of the natural logarithm of
time (Figure 3). Although actual experiments cannot fulfill the theoretical assumptions,
time-temperature curves exhibit similar characteristics within an intermediate zone
(Figure 3). Within this zone the temperature change is given by:
ΔT = T(t2) – T(t1) = (q/(4 π k)) ln [t2/t1] (3)
The thermal conductivity k can be calculated from the temperature change
ΔT over the time period (T2 – T1), which is the slope of the linear portion without being
affected by the diffusivity:
k = q/(4 π) ln [t2/t1]/(T2 – T1) (4)
25
T1 and T2 are the increase in temperature of the hot-wire at times t1 and t2. The heat
flux q in this equation can be determined from:
q = V2/R = V (V/R) = V I (5)
where V is the voltage drop per unit length of hot-wire (V/m), R is the electrical
resistance per unit length of the hot-wire at the test temperature (Ω/m), and I is the
heating current (A).
3. Results
A representative experimental temperature versus ln(time) curve for IPS
e.max is shown in Figure 4. The linear section between 1 and 10 s was used to
determine the thermal conductivity values. Table 2 shows the mean and standard
deviation of the six measurements for each sample and the average thermal
conductivity (k) of Lava Ultimate (0.87 ± 0.14 W/mK) and IPS e.max CAD (2.52 ± 0.24
W/mK).
4. Discussion
In some thermal analyses, only the thermal expansion coefficient is used to
evaluate thermal stresses [4,6,18]. However thermal stresses are not only the result of
a mismatch between coefficients of thermal expansion but also involves the heat
transfer that creates temperature gradients and thus expansion/contraction
mismatches in a material. Since thermal stresses can have a significant effect on a
structure's strength and stability, potentially causing failures, it is important to include
26
thermal conductivity in thermal stress analyses [19,20]. Due to lack of such values,
thermal analyses have often used values that were not specific for the investigated
materials [6,9,21]. However, material composition, nature and amount of fillers,
porosity, and crystallinity are known to affect the thermal conductivity of materials
[16,17,22]. Therefore, it will enhance thermal analyses if material specific properties
can be obtained. This study outlines a relatively simple measurement technique for
determination of thermal conductivity.
Thermal conductivity is a material-specific property used for characterizing
steady heat transport. Different methods to measure the thermal properties of
materials, including the coefficient of thermal conductivity, have been used in
engineering studies [17,23,24]. Most engineering methods are developed for samples
with dimensions larger than are feasible in dentistry. In this study was adapted the
cross-array hot-wire technique to determine the thermal conductivity of dental
CAD/CAM materials. There were other hot-wire configuration options, particularly the
parallel technique, where the hot-wire and thermocouple are placed parallel instead of
perpendicular [13]. With the parallel technique it is possible to simultaneously
determine thermal diffusivity, thermal conductivity, and specific heat from the same
experimental thermal transient. However, it requires higher electric currents that
could damage or melt polymeric materials. Therefore the cross-array configuration
was selected for this study and only needed an electric current generator,
thermocouple, resistance wire, and temperature acquisition device. This method is
known to be good for studying poor conductors such as the two CAD/CAM materials
tested [24].
27
Our results showed a good reproducibility considering the coefficient of
variation 16,1%- Lava Ultimate and 9,5% - IPS e.max CAD (Table 2). No thermal
conductivity values are available in the literature or from the manufacturers for Lava
Ultimate or IPS e.max CAD. Therefore, the values of this current study could not be
compared. However, in a cross-array hot-wire pilot test for a flowable dental
composite (SureFil SDR, Dentsply, Milford, DE) were found values of 0.98 ± 0.02 W/mK,
which is approximate the range of 1.09 to 1.37 W/mK reported for resin composites
[7,8,25]. The dimensions of samples tested were determined by the size of CAD/CAM
blocks. This suggests that the hot-wire technique can measure thermal properties from
samples that are smaller than recommended by ISO.
Sample dimensions and testing conditions affect the technique and need to
be considered in the experimental design. This can be seen, for example, when
comparing the initial and final sections of experimental with the theoretical curves
where the differences between the curves can be explained by the experimental
conditions (Figure 3). To avoid those sections, tmin and tmax were defined to omit the
nonlinear sections of experimental curves during the calculation of the thermal
conductivity value [12,15]. The initial nonlinearity can be explained by heat capacity of
the wire and thermal contact resistance between hot-wire, sample, and thermocouple.
The temperature drop across the interface between the materials can be considerable.
To reduce this effect conductive paste was used to ensure good transient heat flux
through the sample, while the blocks were pressed together by clamps to increase
contact. The paste also acted as an electrical insulator to prevent passage of electric
current from the hot-wire to the blocks, which can cause interference with the thermal
properties of materials. The non-linearity of final curve was generated by boundary
28
effects of the finite sample dimensions and hot-wire. To minimize this effect the tests
were done at relatively low temperatures, close to room temperature. In addition,
heat loss can be minimized for the samples [24].
5. Conclusion
Within the limitations of this study, it can be concluded that the cross-array
hot-wire technique is a practical method for determining thermal conductivity in
dental CAD/CAM materials and can be extrapolated the indication for measure the
thermal conductivity of other dental materials.
Acknowledgements
We would like to thank CAPES by the PhD sandwich scholarship (Process
number: 008816/2014-00 – UTHSC – Memphis, USA). Dr James F Simon for his
assistance with ceramic samples, the engineer Luís Renato Bego Machado for his help
with electric circuit and we would also like to acknowledge Dr Antonio José da Silva
Neto for sharing his knowledgement in this study with the hot-wire technique.
Conflict of interest
All authors declare no financial and personal conflict of interest.
29
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16. Brady AY, Lee H, and Orlowski JA. Thermal Conductivity Studies of Composite Dental
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32
Table 1. Material information
Material Manufacturer Batch number Shade/Size Compositiona
Lava Ultimate 3M ESPE N560554 A3 HT – 14L
Bis-GMA, UDMA, Bis-EMA, TEGDMA, SiO2 (20 nm), ZrO2 (4–11 nm), aggregated ZrO2/SiO2 (0.6–10 μm)
IPS e.max CAD Ivoclar Vivadent
T18888 A3 HT – C14 97% SiO2, Al2O3, P2O5, K2O, Na2O, CaO, F, 3% TiO2, pigments, water, alcohol, chloride
abis-GMA: Bisphenol A glycol dimethacrylate; UDMA: Urethane dimethacrylate; TEGDMA: Triethylene glycol dimethacrylate; bis-EMA: Ethoxylated bisphenol A glycol dimethacrylate
Table 2. Thermal conductivity (mean and standard deviation, SD) determined using the hot-wire technique. Measurements were repeated six times for each sample.
Thermal conductivity (W/mK)
Lava Ultimate IPS e.max CAD
Sample 1 0.69 ± 0.06 Sample 1 2.60 ± 0.22
Sample 2 1.09 ± 0.24 Sample 2 2.62 ± 0.22
Sample 3 0.84 ± 0.13 Sample 3 2.83 ± 0.24
Sample 4 0.84 ± 0.10 Sample 4 2.28 ± 0.11
Sample 5 0.91 ± 0.09 Sample 5 2.27 ± 0.20
Mean (SD) 0.87 ± 0.14 Mean (SD) 2.52 ± 0.24
33
Figure Legends
Figure 1. (a) Specimen consisting of two blocks with grooves to embed the cross-wires;
(b) The cross-wires, hot-wire and thermocouple, embedded in lower block using
conducting paste; (c) Blocks stacked and clamped during the experiment.
Figure 2. Schematic diagram of experimental setup electrical circuit with data
acquisition system.
Figure 3. Temperature rise versus natural logarithm of time: theoretical and
experimental curves.
Figure 4. Temperature change in the hot-wire embedded in IPS e.max CAD during the
experiment plotted on a logarithmic time scale. The straight line indicates the linear
portion of the curve that was used to calculate the thermal conductivity.
34
Figure 1
Figure 2
35
Figure 3
Figure 4
36
2.2 Artigo 2
Title: Thermal and biomechanical analysis of CAD/CAM ultrathin occlusal veneers by
Finite Element Analysis
37
Abstract
Traditional restorative protocols to restore worn surface involve preparing sound
dental tissue. So, occlusal veneer is a new option of indirect restorations minimally
invasive to replace the occlusal loss structure without extensive tooth reduction or
retentive preparations. The aim of this investigation was calculate elastic modulus
(EM) of restorative materials, post-gel shrinkage of resin cement and evaluate the
influence of ultrathin occlusal veneers of 0.3 or 0.6 mm-thick on temperature
distribution, and thermomechanical stresses by Finite Element Analysis (FEA). Two-
dimensional FEA models were created based on a cross-sectional micro-CT of a human
inferior molar importing points coordinates of ImageJ. Relyx Ultimate shrinkage stress
was input based on results of post-gel shrinkage measured by strain gauge technique
and Elastic Modulus of restorative materials was determined by deflectometer at 3-
point bending test. Using MARC/MENTAT was applied a thermal load (55º-37º-5ºC) at
outer surface and a 228N occlusal axial load was applied by a 6mm diameter simulated
sphere. Modified von Mises thermal and mechanical stresses were calculated. Cement
shrinkage strain value (in volume %) was 1.13±0.07. EM was e.max 93.85±6.6 GPa,
Lava 12.81±0.3 GPa and Relyx (9.08±0.21 GPa). The analysis showed that cold
temperature created higher stress than hot temperature, mainly at beginning of each
cycle, when the temperature changes. Thermal stress was more concentrated at
cement layer, and within e.max veneers. The mechanical analysis showed that thicker
veneers accumulate less stress than thin. At the restored tooth with e.max, the stress
concentration is within veneer and in enamel when Lava restoration was analyzed. The
dentin was not affected neither material type nor thickness. In conclusion, ultrathin
occlusal veneers were most affected by cold temperature and cement concentrated
higher thermal stress. Mechanical loading accumulated stress within e.max
restoration and underlying structures of Lava restoration. Thicker veneers accumulated
more thermal and lower mechanical stress compared with thin veneer
Keywords: temperature; finite element analysis; oclusal veneer; lithium disilicate
ceramic; composite
38
1 Introduction
The wear and reduction of coronal tooth structure is a biological condition
from aging process (Magne et al., 2002) not involving bacteria (Nunn et al., 1996). The
pathologic dental tissue loss is related to dietary, oral habits or combined etiologic
factors like abrasion, attrition, acid erosion or even amorphous and weak structure
from dental anomalies. These conditions results in an accelerated and premature loss
of enamel with destructive consequences increasing maxillomandibular vertical
distance, occlusal and musculoskeletal disharmony, impaired function and esthetic
disfigurement (Baroon et al., 2003; Lussi et al., 2009). So, the tooth wear facets are an
evidence of tooth tissue loss and can be detected at beginning of problem (Cunha-Cruz
et al., 2010).
The traditional protocols to restore the occlusal worn surface involve
preparation with usual thickness of 1.5 to 2.0 mm for porcelain restoration of the
sound dental tissue (Dietschi et al., 1997; Federlin et al., 2007). But higher wear
preparations can affect the biomechanical behavior associated with higher thermal
shocks of restored teeth (Magne et al., 2002; Torbjörner et al., 2004, Papanicolaou et
al., 2015). Nowadays, minimal intervention at healthy tooth tissue (preferably “non-
preparation”) is a desired clinical procedure. It is possible due new advances at
restorative materials, improvement at results with bonding strategies and CAD/CAM
technology that allow producing ultrathin veneers up to 0.3 mm minimum thickness
(Egbert et al., 2010; Johnson 2014).
Laminate veneers indicated to anterior teeth already are well accepted
concept with good long-term results (Stappert et al., 2005; Granell-Ruiz et al., 2010;
Schmidt et al., 2011). The posterior occlusal veneer is a new option of indirect
restorations minimally invasive, used as an additive treatment to replace the lost
structure and reestablish the vertical dimension of occlusion (Magne et al., 2010). In a
restorative treatment without retentive preparations to reach long-term clinical
success, the bonding strategy becomes essential (Tsitrou et al., 2010; Schlichting et al.,
2011). The successful of ceramics as a choice material for indirect restoration or in the
attempt to replacement of enamel (Federlin et al., 2005; Magne P., 2006; Manhart et
al., 2004) is supported by strength and aesthetic conditions (Manhart et al., 2004;
Roulet et al., 1997), with positive results of bonding to the natural tooth (Magne et al.,
39
2002; Bindl et al., 2004). The improvements of currently composite resins are
noticeable, mainly due the appropriated stress distribution through the tooth-
adhesive-restoration interface. Additionally, superior bond interaction and the
similarity of the elastic moduli between composite resin and dentin allow more
absorption of functional stresses and adequately mimics the substitution of tooth
structure (Craig RG, 1979; Schlichting et al., 2011).
Finite element analysis has been used in investigations of complex
structures and it is a relevant method to measure internal stresses, because is difficult
to obtain these results during in vivo or in vitro tests (Oskui, 2013; Deger, 2015).
Therefore, to investigate and better understand the behavior of these ultrathin
veneers cemented at non-preparation tooth, 2D numerical models were developed to
evaluate the influence of material type and restoration thickness on temperature
distribution and mechanical behavior after thermal loading.
2 Objective
The purpose of this study was measured 1) the elastic modulus of
restorative materials, 2) the post-gel shrinkage of dual-curing resin cement, and 3)
evaluate the influence of ultra-thin occlusal veneers of 0.3 and 0.6 mm-thick made of
nanoceramic composite or ceramic on temperature distribution and
thermomechanical stresses by Finite Element Analysis.
3 Materials and Methods
3.1 Post-Gel Shrinkage
The linear post-gel shrinkage of RelyX Ultimate dual-cure resin cement
(n=10) was determined by strain gauge method (Sakaguchi et al., 1997). A small
amount of resin cement was positioned on the top of a biaxial strain-gauge (CEA-06-
032WT-120, Measurements Group, Raleigh, NC, USA) after material mixing. This strain
gauge was used to monitoring the strain in two perpendicular axes (x and Y). A strain
40
conditioner (2101A Series, Micro Measurements Group) converted electrical resistance
changes in the strain gauge to voltage changes through a quarter-bridge circuit with an
internal reference resistance. A light-sensitive photocell detected accurate start-stop
time of photoactivation. The cement samples were light-cured using the VALO LED
curing light (Ultradent Products, South Jordan, UT, USA) for 20 s at inrradiance of 1,560
mW/cm² (31 J/cm²) quantified by MARC® Resin Calibrator (BlueLight analytics Inc.,
Halifax, Canada). The light tip was placed 1 mm distant from the sample surface. Strain
gauge and photocell output signals were recorded for 10 min in a computer trough an
analog-to-digital data converter. Ten samples were tested and post-gel shrinkage
results of each sample were determined by a mean of strains of both perpendicular
directions. Post-gel shrinkage of RelyX Ultimate was used as a linear shrinkage input
for the Finite Element Analysis. Linear post-gel shrinkage was converted to volumetric
shrinkage by the equation:
( ) ( ) ( )
where V is the volumetric shrinkage and Sh is the linear shrinkage. After,
the results were converted to percentage.
3.2 Elastic Modulus
The elastic modulus of materials was determined using a three-point
bending method. Ten rectangular bar-shaped samples (25mm x 2mm x 2mm – ISO
4049) were prepared for RelyX Ultimate adhesive dual-cure resin cement, using a
customized silicone impression material mold (Impregum soft; 3M ESPE, Saint Paul,
MN, USA) to facilitate sample removal without damage. Freshly-mixed cement was
inserted into the mold with a transparent polyester strip on top lined by a glass slide.
The light activation was performed using VALO LED curing light (Ultradent Products,
South Jordan, UT, USA) with two irradiations of 20 s each one (top and bottom), at a
distance of 1 mm from the sample surface. After 15 min from the photoactivation, the
samples were removed from the mold and stored in distilled water at 37°C in dark.
41
After 24 h, before the testing, the samples were measured using a digital calipter
(Mitutoyo).
Rectangular bar-shaped samples, for CAD-CAM materials (Lava Ultimate
nanoceramic composite and IPS e.max CAD lithium disilicate ceramic), were obtained
from slicing of blocks with a low speed saw (Isomet). The samples dimensions (16.5mm
x 1.44mm x 1.44mm) were stated by correlation of ISO Standart-4049 and maximum
long dimensions possible of blocks. After, the ceramic samples were sintered in a
ceramic furnace following the manufacturer’s instructions.
The three-point bending test was performed using a universal testing
machine (Instron 5565). Centrally load was applied on the bar, with 20 mm distance
between supports for RelyX samples, and 14.5mm for CAD-CAM materials at a
crosshead speed of 0.5 mm/min-1. A deflectometer (Epsilon W-E401-E, Instron) was
positioned at bottom of samples recording the displacement at the central portion.
Elastic modulus was calculated using data obtained from load-deformation
profiles during the bending test, according to the following equation:
where E is the flexural modulus (GPa), F is the load (N) corresponding to the
displacement d (mm), L is the distance between the supports (mm), B is the specimen
width (mm) and H is its height (mm). The elastic modulus of materials also were input
for the Finite Element Analysis.
3.3 Finite Element Analysis
3.3.1 FEA modeling and mesh generation
A geometric two-dimensional (2D) finite element model was created from
a cross-sectional micro-CT scan of a sound tooth to calculate the biomechanical and
thermal stresses. The CAD assembly consisted of a restored tooth with a 0.3 and 0.6
mm-thick occlusal veneer restoration cemented on enamel substrate created in
42
MSC.Mentat (MSC Software, Santa Ana, CA). To reproduce the natural worn and a non-
preparation tooth, the occlusal surface was equally reduced 0.3 and 0.6 mm both
groove as cusps. The design and dimensions of model reproduced the measures of a
first lower molar used at laboratory tests. Coordinate points of digital files were
obtained using Image J software (The National Institutes of Health, Bethesda, MD,
USA) and imported to finite element analysis software package MSC.Mentat. In
addition to the restorations (cement layer and tooth structures), the PDL and
Polystyrene resin were modeled 2 mm below the cementoenamel junction to simulate
the insertion of tooth in the alveolus. The mesh generation was created manually with
quadratic elements. Plain stress elements were used to cement set and plain strain
elements to other stes. The pulp chamber and root canals were generated as an
empty space (no elastic modulus). The models were considered to be linear, elastic,
homogeneous and isotropic, but also have different tensile and compressive strengths.
Therefore, modified von Mises equivalent stress criterion was used to express the
stress distribution and values of finite element analysis, using tensile and compressive
strength ratio (Apêndice 1).
3.3.2 Shrinkage Stress Analysis
The shrinkage and elastic modulus were obtained from the experimental
analysis. Polymerization shrinkage was simulated by thermal analogy. Temperature
was reduced by 1oC, while the linear post-gel shrinkage value was entered as the
coefficient of thermal expansion. The specific boundary conditions, load protocol and
configuration simulated previous laboratory definitions.
3.3.1 Thermal analysis
A plane stress-strain condition was assumed for transient thermal stress
analysis. To be possible reproduce the laboratory experiment, post-gel shrinkage stress
condition was adopted at the first increment, simulating the adhesion process,
followed by temperature steps. Thermal load was applied at the outline nodes of
43
model, deactivating PDL and resin base at this analysis, to reproduce the effect of
laboratory thermal fatigue. So, thermal shock cycling procedure was applied with
temperature changes of 37o - 55 o - 37 o - 5 o - 37 oC. Those temperatures were kept
constant for periods of 30 s each. Simplified boundary condition was assumed fixing a
point of root in zero-displacement in the 3 spatial dimensions in all degrees of freedom
(x, y and z axes). Attribution of thermal properties of materials according to existing
data in the literature and results obtained in laboratory tests are given at Table 1.
3.3.2 Mechanical Analysis
A plane stress-strain condition also was assumed to shrinkage and
mechanical stress analysis. The post-gel shrinkage of resin cement was carried out
followed by a uniform ramp loading of 228 N axial load applied occlusally by a 6 mm
diameter simulated sphere. This load was obtained from a previous fracture strength
test of laboratory samples based on equation below, to determine the correspondent
load of a 3D model to 2D model:
where F2 is the load to be applied at 2D model (N), F1 is maximum load of
fracture strength of samples (N), r is the radius of sample (mm), B is the specimen
width (mm), and H is its height (mm). The nodes at the bottom and sides surface of the
resin base were assigned fixed zero-displacement in the 3 spatial dimensions.
Attribution of mechanical properties of materials according to existing data in the
literature and results obtained in laboratory tests are given in Table 1.
4 Results
4.1 Post-gel Shrinkage
The mean of bidirectional strains of RelyX Ultimate resin cement
determined the linear post-gel shrinkage (0.0037 ± 0.00025) used at finite element
analysis. The volumetric post-gel shrinkage was 1.13 ± 0.07 (%) (Apêndice 2).
44
4.2 Elastic Modulus
The IPS e.max CAD (disilicate ceramic) had numerically the highest elastic
modulus (93.85±6.6 GPa); Lava Ultimate (composite nanoceramic) showed
intermediate value (12.81±0.3 GPa), and RelyX Ultimate (adhesive resin cement) the
lowest EM (9.08±0.21 GPa) of materials (Apêndice 3).
4.3 Finite Element Analysis
4.3.1 Thermal analysis
The finite element thermal analysis demonstrates the thermal flux curves
through the tooth at 5 different points against time at Figure 1. Curves of outside point
shows the temperature of cycles applied at models. Type of restorative material
influenced the thermal flux. It is necessary a longer time to reach the expected
temperature peak in a nanoceramic composite than when a ceramic is used, in reason
of the lower thermal conductivity coefficient of the material. An inverse influence of
thickness was observed. How much thicker the veneers are, less heat is transferred
through the material. The thermal flux through the biological structures demonstrated
the same behavior, but when Lava Ultimate veneer was used, the heat that reaches
the pulp chamber was 0.8 degrees lower than a non-prepared tooth, comparing with
mean of 0.25 degrees of IPS e.max.
The values of modified von Mises stress concentration during thermal
cycling are shown at Figure 2. Analysis of thermal stress for IPS e.max ceramic veneer
showed the maximum stress concentration at the cold cycle (5º C). Lava Ultimate
veneers were more affected by the hot cycle (55º C), and the cold cycle generated the
lowest peak stresses. The restorations with 0.3mm thick accumulated less stress than
restorations of 0.6 mm thick. The cement layer obtained the highest stress values of all
structures analyzed, but the behavior occurred similarly at models evaluated. It is
important highlighted that the cement layer shows the effect of fatigue thermal
loadings added the post-gel shrinkage. The cold cycle was responsible for the
45
maximum stresses at this layer. At the enamel, the thermal stress is shown during the
changes of temperature cycles. Cold bath demonstrated the highest stress
concentration. Initial temperatures of shock cycling resulted in stress values at non-
prepared model in a range from 251% to 1541% higher than final of cycle. Similar
behavior was followed by the dentin at non-prepared model. For restored models, the
cold fatigue produced stresses results three times more than average of thermal
cycling. Stress fields are illustrated at a colour-coded models at Figure 3.
4.3.2 Mechanical Analysis
The values of maximum stress of ultrathin occlusal veneer according to the
modified von Mises failure criterion were presented at Figure 4. The biomechanical
analysis showed lower stress concentration at thicker veneers (0.6 mm thick) than at
0.3mm thick veneers, whatever the material used for restoration. At the restored
teeth with IPS e.max, the highest values of stress occurred in ceramic veneers. When
the teeth were restored with Lava Ultimate, the lower elastic modulus of nanoceramic
composite transferred the stresses concentration to enamel. At non-prepared tooth,
the maximum mvM stress focused on enamel. Within all the situations evaluated, the
dentin was not affected neither material type nor thickness. The Figure 5 illustrates the
mvM stress fields at restored tooth.
5 Discussion
Stresses are developed during functional mastication loading, thermal
shock caused by different temperatures of foods and beverages intake and by
restorative procedures. The stresses generated into oral cavity usually are results of
the combination of these factors (Papanicolaou et al., 2015). Due the complexity of
tooth tissues and restored models, the finite element analysis is displayed as an
advantageous method to approach the problem. This methodology subdivides the
complex model in small elements and demonstrates visual and numerical results
46
within whole model, which otherwise it is not possible to evaluate and standardize at
in vitro or in vivo tests (Değer et al., 2015).
To validate the numerical models it is essential the correct input of
material properties and restrains. For this reason, the first part of this study was
laboratory-determined elastic modulus of restorative materials (IPS e.max CAD, Lava
Ultimate and RelyX Ultimate) and the shrinkage of resin cement (RelyX Ultimate). The
elastic modulus and post-gel shrinkage are in accordance with literature and data
provided by the manufacturer. An important coefficient of materials required in
thermal analysis studied by FEA is the thermal conductivity. The thermal conductivity
coefficients inputted in this study were obtained in a previous laboratory investigation
of use of hot wire technique method for dentistry materials, once these values was not
found at literature or manufacturer data.
Many studies using the FEA aimed predict only fracture strength and stress
distribution of occlusal veneers (Dejak et al., 2012; Magne et al., 2012; Mange et al.,
2016). However, the purpose of this study was evaluating the effect of combined
analysis of stress in oral cavity. Therefore at the first increment of analysis, was
adopted the post-gel shrinkage of resin cement before loadings, both thermal and
mechanical, likewise occurs in clinical procedures.
The FEA results of thermal flux through the restored tooth had difference
when different restorative materials were used. The lower thermal conductivity of
Lava Ultimate compared with IPS e.max CAD or even enamel was accountable for a
smaller amount of heat distributed within the restoration and to other structures, thus
reaching the pulp chamber 0.8 degrees lower than a non-prepared tooth. The greater
amount of material at 0.6 mm veneers than at 0.3 mm-thick influenced directly the
effectiveness of restorations acting as insulating medium. So, the thickness of
restorative materials needs to be considered, not only the thermal properties of
materials, when a thermal analysis is been evaluating once thermal coefficients are
independent of thickness (Craig et al., 1961).
The feature of dental tissues is to act as an insulator medium against
thermal shock, avoiding that large temperature changes reaches the pulp tissue.
47
Because if the temperature rise in the pulp exceed more than 5.5 ºC induces
irreversible pulp damage (Oskui et al., 2013). Dental tissues composition differ the
thermal coefficient, exemplifying the difference at thermal conductivity of enamel and
dentin that the values are correlated with the amount of organic matrix existing (Craig
et al., 1961). Thus, the pattern of temperature distribution at intact enamel and worn
enamel was similar. It can be a reflection that the amount of enamel lost at restored
models (Oskui et al., 2013) is much smaller when it is necessary to do a conventional
preparation for posterior restorations. The amount of tissue lost it is not enough to
affect the temperature flux in this structure. Dentin results showed lower temperature
variation, not only caused by the lower thermal conductivity coefficient than enamel,
but it was also influenced by the highest value of specific heat of the dentin. The non-
prepared model had highest heat flux (4.5º C) reaching the pulp chamber, although the
temperature increase was below to cause pulp damage. One limitation of this study
was not simulating the effect of dentinal fluid and pulp blood perfusion. The constant
circulation of these fluids at dentinal tubules and pulp, carry heat away, decreasing
warming (Lisanti & Zander, 1950; Oskui et al., 2013).
When a restoration replaces the tooth structure, the differences at physical
and thermal properties like elastic modulus, specific heat, thermal conductivity and
thermal expansion coefficients may result in stress; although some studies correlate
that thermal stress are developed only by the mismatch at thermal expansion
coefficient (Papanicolaou et al., 2015; Magne et al., 1999; Köycü et al., 2015). In
general, the great difference of temperature at beginning of each cycle resulted at
higher thermal stress concentration at models structures in this study. The heat
transfer through materials by conduction during the 30 s decreased the stress at end
of cycle.
Previous study also showed that thicker restorations of 0.6mm, due the
great amount of material, showed more stress concentration than 0.3mm-thick
restorations (Güngör et al., 2004). IPS e.max accumulated at the occlusal central
groove more stress than Lava Ultimate in both thicknesses. It can be explained by the
low thermal expansion coefficient and high elastic modulus of ceramic. Thus,
composite materials with higher thermal expansion coefficient change the volume at
48
outer surface of material and transfer the additional stress to underlying structures
while the high elastic modulus of ceramic restoration allow slight changes of shape,
concentrating stress within material (Yang et al., 2001; Agnihotri et al., 2010).
The highest peak of thermal stress was concentrated at cement layer not
only due to the thermal changes but also to the additional stress by post-gel shrinkage
input at FEA before start the thermal analysis. Magne et al. in 1999 described that
shrinkage effect predominated over high thermal expansion even under best
conditions of a composite used as cement. Also, the specific heat coefficient of RelyX
Ultimate, 18-40% higher than those coefficients of restorative materials resulted in a
slow temperature change, taking a longer time to thermal equilibrium front a non-
uniform temperature stage, generating more stress (Cakan et al., 2015; Köycü et al.,
2015). This result showed that the highest stress concentration in the cement layer
and interfaces may lead firstly to bond failure when occlusal veneers are used, as
described by previous studies (Köycü et al., 2015; Magne et al., 1999; Agnihotri et al.,
2010 and Papanicolaou et al., 2015).
In intact natural tooth, the differences in properties of enamel and dentin
inherent of tissues, creates thermal stress at interfaces during cycling thermal changes;
this occurrence is exacerbated at restored teeth (Güngör et al., 2004), but minimum
stress was found for the non-prepared tooth, in accordance with Toparli et al., 2003.
Thermal stress accumulated at enamel was present at buccolingual surface or enamel-
cement and enamel-dentin interfaces, depending of cycle temperature. Models
restored with Lava Ultimate showed stress distribution more evenly under enamel-
cement interface, comparing with the high concentration of stress under cement layer
of IPS e.max restoration models. At dentin tissue, thermal stress showed very similar
behavior, with a slight stress concentration of nanoceramic composite veneer,
probably arising from the stress distribution more evenly trough the structures of
models restored with this restoration type.
Restorative materials and dental tissues expand when warmed and
contract at cold temperatures. The FEA thermal findings revealed that thermal stress
levels were closely related to the temperature gradient, although was highlighted
49
higher stress concentration mainly at outer enamel when submitting to 5 oC, in
accordance with previous studies (Oskui et al., 2013, Güngör et al., 2004, Köycü et al.,
2015, Magne et al., 1999) that showed more damaging effect on models in cold
temperatures. This result can explain enamel cracks generated during thermal shock
by substances intake with different temperatures, and the relevance to realize thermal
test also with cold temperatures.
The preparation or lost tooth tissues changes the mechanical behavior
comparing an intact tooth. Occlusal veneer has been studied (Egbert et al., 2014;
Johnson et al., 2015; Magne et al., 2010) as option for severely worn tooth with dentin
exposition, contrasting with this study that evaluated the mechanical stress
distribution of ultrathin occlusal veneer bonded at enamel substrate with additional
stress by post-gel shrinkage of resin cement. Thus, under biomechanical axial load,
thicker veneer (0.6 mm) showed lower stress concentration comparing to thin veneer
(0.3 mm), whatever the material used for restoration. This numerical analysis
corroborate with previous studies (Schlichting et al., 2011) that showed higher fracture
strength for ultrathin occlusal restorations when the thickness was increased, although
no statically significance at occlusal veneer restoration thickness on fracture strength
was found by Egbert et al., 2014. The modified von Mises indicated that Lava Ultimate
yield reduced stress than e.max CAD. This result can be explained by the elastic
modulus of the material; when stiffer material is used, the stress is accumulated within
the restoration. In the present study this fact occurred under the contact of load and
at central groove due the sharp design. The mechanical stress originated from
nanoceramic composite veneer was transferred underlying. For this reason, it was
noted the stress distribution at enamel under this type of restoration as already has
been described (Magne et al., 2012 and 2016). A relevant result was the stress
concentration at cervical portion of enamel in restored or non-restored teeth, since
studies of failure mode of ultrathin occlusal veneer by Egbert et al., 2014 and Johnson
et al., 2015 evidenced the failure at enamel as the second most frequent type of
failure. The behavior of dentin was similar and not altered by the use of occlusal
veneer restorations or intact tooth, in this sutdy.
50
Ultrathin occlusal veneers already demonstrated fracture strengths
exceeding the human masticatory forces (Egbert et al., 2014; Johnson et al., 2015;
Dejak et al., 2012), and the present FEA study suggests that ultrathin veneers up to
0.3mm-thick submitted to thermal or mechanical challenges as occur at oral cavity, is
prone to failure first at cement layer or cement interfaces followed by failures of the
restoration, preserving the tooth structure. Thus, marginal microleakage and
debonding tends to be more frequent at materials with low elastic modulus, as
nanoceramic composite - Lava Ultimate, due to stress distribution be located at
underlying structures (Dejak et al., 2012; Magne et al., 2010). Therefore, ultrathin
occlusal veneer appears a promising option for worn tooth to full-coverage crowns
without retentive preparation of tooth and reestablishing vertical dimensions.
6. Conclusion
Based on the findings of this finite element study it can be concluded that:
1. Lava Ultimate ultrathin veneer was more effective to block the heat; 2. Cement layer
concentrated the highest thermal stress, as also IPS e.max CAD veneer as Lava
Ultimate; 3. Cold temperature accumulated higher stress than hot temperature during
cycling thermal changes; 4. Modified von Mises stress was higher within thin IPS e.max
CAD veneer and underlying of Lava Ultimate restoration; and thicker veneers
accumulated more thermal and lower mechanical stress compared with thin veneer.
51
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Table 1 – Material properties used in the FEA
Poisson's rate
Elastic modulus
Thermal expansion
Density Thermal
conductivity Specific
heat Shrinkage
10³ MPa 10−6/°C g/cm³ W/mK J/g °C %
Enamel 0.30 a 84 a 11.40 b 2.80 b 9.37 b 0.71 b
Dentin 0.23 a 18 a 8.30 b 1.96 b 5.84 b 1.60 b
Lava Ultimate 0.30 c 12.52 d 32.60 e 2.10 e 0.87 d 0.82 e
E.max 0.30 f 93.85 d 10.20 e 2.50 e 2.52 d 0.98 e
RelyX Ultimate 0.30 g 9.08 d 40.00 e 1.90 e 2.61 d 1.15 e 1.13 d
Polyether 0.45 h 0.05 h
Polystyrene resin 0.30 i 1.37 i aVersluis, 2011; bLinsuwanont, 2008; cChen, 2014; dPrevious laboratory tests ; eData provided by the manufacture; fAboushelib, 2005; gAsmussen, 2005; hSoares, 2008; iSoares,2010
56
Figure Legends
Figure 1 - Thermal flux within models of restored tooth with ultrathin occlusal veneer.
Figure 2 - Thermal and shrinkage post-gel stress at models restored tooth with
ultrathin occlusal veneers (MPa)
Figure 3 - Colour-coded thermal and shrinkage post-gel stress distribution at models
restored with ultrathin occlusal veneer (MPa)
Figure 4 - Mechanical and shrinkage post-gel stress distribution at models restored
with ultrathin occlusal veneer (MPa)
Figure 5 - Colour-coded mechanical and shrinkage post-gel stress distribution at
models restored with ultrathin occlusal veneer (MPa)
57
Figure 1
time time
time
time time
58
Figure 2
59
Figure 3
60
Figure 4
0
50
100
150
200
250
300
emax 0.3 emax 0.6 lava 0.3 lava 0.6 non-prepered
Mo
dif
ied
vo
n M
ises
(M
Pa)
veneer
enamel
dentin
61
Figure 5
stress/strain_emax_0.3mm stress/strain_lava_0.3mm stress/strain_emax_0.6mm stress/strain_lava_0.6mm
stress/strain_emax_0.3mm stress/strain_lava_0.3mm stress/strain_emax_0.6mm stress/strain_lava_0.6mm stress/strain_non-restored
stress/strain_emax_0.3mm stress/strain_lava_0.3mm stress/strain_emax_0.6mm stress/strain_lava_0.6mm stress/strain_non-restoraded
veneer
enam
el
62
3 DISCUSSÃO
O avanço no desenvolvimento dos materiais dentários e a integração da
Odontologia minimamente invasiva (Dejak et al., 2012) com procedimentos laboratoriais
computadorizados, como é o caso do sistema de fabricação assistido CAD/CAM (Tsitrou et
al., 2008), possibilita a realização de novos protocolos restauradores frente aos
procedimentos tradicionais menos conservadores (Egbert et al., 2010). Os laminados
oclusais ultrafinos são uma nova opção de tratamento restaurador para dentes com perda
de estrutura dental na superfície oclusal; os quais não necessitam de preparos retentivos, se
baseando no princípio de adesão à estrutura dentária e na eminente longevidade dos
laminados anteriores (Fradeani et al., 2005). Informações sobre o comportamento deste
novo tipo de restauração posterior quando em função clinicamente, se torna um tópico
relevante e atual, para que este possa ser apontado como uma proposta de tratamento
segura e duradoura. Assim, o presente estudo inicialmente mensurou a condutividade
térmica de blocos CAD/CAM de resina nanocerâmica ou cerâmica de dissilicato de lítio com
o método do fio quente e avaliou a distribuição de temperatura, as tensões térmicas e
mecânicas de laminados oclusais ultrafinos de diferentes espessuras, cimentados com
cimento resinoso adesivo em um substrato puramente de esmalte, empregando a
metodologia dos elementos finitos.
A metodologia dos elementos finitos necessita de uma acertada caracterização
dos modelos quanto às condições de contorno e propriedades dos materiais para validação
dos modelos com os resultados in vitro. Em uma revisão literária, verificou-se a escassez de
estudos envolvendo análise térmica por elementos finitos. Grande parte dos mesmos
considera apenas a diferença de coeficiente térmico como gerador de tensões (Magne et al.,
1999; Papanicolaou et al., 2015; Köycü et al., 2015); e que as propriedades térmicas dos
materiais são fornecidas pelos fabricantes, quando disponíveis, ou obtidas em livros, onde os
valores não são específicos para os materiais testados (Anusavice et al., 2003; Toparli et al.,
2003).
A falta de informações dos materiais utilizados neste estudo, inclusive por parte
dos fabricantes, fez com que adaptássemos o método do fio quente cruzado, proposto
inicialmente por Haupin em 1960, para mensurar o coeficiente de condutividade térmica do
63
IPS e.max CAD (2,52 W/mK) e Lava Ultimate (0,87 W/mK). Apesar de não haver valores na
literatura para comparação com nosso estudo, nossos resultados apresentaram boa
reprodutibilidade considerando o baixo coeficiente de variação do teste; além dos valores
obtidos no teste piloto (0,98 W/mK) estarem muito próximos com o reportado para resinas
compostas (1,09 W/mK). Nota-se a relevância em considerar este coeficiente nas análises
(Kingery et al., 1955; Hasselman et al., 1978), pois, o baixo valor de condutividade térmica
dos laminados oclusais produzidos com Lava Ultimate foi o fomentador da menor
temperatura difundida no modelo restaurado com este material. Estudos prévios mostram
grande influência que a temperatura tem sobre compósitos, não só nos mecanismos de
união com a dentina, como também na interface carga/matriz (Lee et al., 2000; Lee et al.,
2001).
Ainda com o propósito da caracterização dos materiais, o módulo de elasticidade
foi obtido com teste de flexão por 3 pontos, para IPS e.max CAD (93,85 GPa), Lava Ultimate
(12,52 GPa) e RelyX Ultimate (9,08 GPa). O módulo de elasticidade tem grande influência nas
análises numéricas quando se avalia comportamento mecânico dos materiais e a produção
de tensões, como pôde ser ratificado na análise mecânica deste estudo. O critério de von
Mises modificado indicou maior tensão nas restaurações cerâmicas, que apresentam maior
módulo de elasticidade comparado às de compósito nanocerâmico. Experimentos prévios
corroboram com estes nossos achados (Magne et al., 2010; Egbert et al., 2014). O módulo
de elasticidade também teve correlação direta com as tensões térmicas, quanto maior o
módulo de elasticidade, maior o acúmulo de tensões.
Diferente dos trabalhos anteriores investigando laminados oclusais ultrafinos
que não consideraram a camada de adesão, alegando não haver influência nos resultados
em razão do similar módulo de elasticidade com a dentina e espessura reduzida da camada
(Magne et al., 2012; Magne et al., 2016), além da inserção do módulo elástico do RelyX
Ultimate obtido no teste de flexão, e o mesmo ter apresentado 50% do valor do módulo
elástico da dentina, também foi inserido o valor da contração pós-gel do mesmo. O valor da
contração pós-gel (1,13% em volume) do cimento resinoso foi obtido com a análise de
extensometria bidirecional. Com isso, pudemos verificar que a camada de cimento foi a mais
afetada, com a maior concentração de tensão, não só no interior, mas também nas
interfaces cimento/restauração e cimento/esmalte. Isso também pode ser resultado da
64
análise combinada. Não foi encontrado na literatura nenhum estudo avaliando ao mesmo
tempo o efeito térmico ou mecânico em conjunto com o efeito da contração de compósitos.
Essa combinação buscou a reprodução mais próxima possível dos procedimentos clínicos;
onde primeiro há a cimentação da peça e a geração de tensão por contração do material, e
posteriormente o desafio térmico-mecânico quando em função.
No estudo, em geral, os laminados oclusais ultrafinos confeccionados com
cerâmica IPS e.max CAD são responsáveis pela maior concentração de tensões nos modelos
analisados que as de compósito nanocerâmico Lava Ultimate. A análise de elementos finitos
demonstrou que as restaurações não alteram significativamente o aumento de temperatura
na câmara pulpar. O cimento tem papel de grande relevância nas análises numéricas,
principalmente quando se adiciona a contração pós-gel destes materiais, indicando a
camada com falha primordial nos modelos analisados, mesmo nas restaurações de 0,3 mm
de espessura. Os resultados deste estudo, em conjunto com os resultados já descritos na
literatura, sugerem assim, que os laminados oclusais ultrafinos são uma alternativa de
tratamento restaurador minimamente invasivo para reabilitar dentes posteriores com perda
de estrutura oclusal.
65
4 CONCLUSÃO
Baseado nos resultados obtidos e nas limitações das análises pode-se concluir que:
O método do fio quente cruzado é método prático e eficaz na mensuração da
condutividade térmica de materiais odontológicos;
Laminados oclusais confeccionados de Lava Ultimate apresentam melhores
resultados frente a menor quantidade de calor distribuída no elemento dental
comparado ao IPS e.max CAD;
A ciclagem em baixa temperatura causou maior tensão térmica que a ciclagem
quente;
A camada de cimento é a estrutura com maior concentração de tensão, sugerindo ser
a estrutura que primeiro falharia nos modelos;
IPS e.max CAD concentrou os maiores tensões mecânicas concentrado nos
laminados, enquanto Lava Ultimate distribuiu melhor as tensões nas camadas
subjacentes.
Os laminados mais espessos concentraram maior tensão térmica e menor tensão
mecânica que os laminados mais finos.
66
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APÊNDICES
Apêndice 1: Geração do modelo numérico a partir do modelo experimental
71
Apêndice 2: Média e desvio padrão dos valores de contração pós-gel do RelyX Ultimate
(volume %)
Volumetric shrinkage
sample 1 1.10 sample 2 1.07 sample 3 1.23 sample 4 1.17 sample 5 1.18
sample 6 1.05 sample 7 1.04 sample 8 1.26 sample 9 1.12
sample 10 1.10
Mean 1.13 ± 0.07
Apêndice 3: Média e desvio padrão dos valores do Módulo de Elasticidade (GPa) dos
materiais restauradores utilizados no estudo
E.max Lava Ultimate RelyX Ultimate
sample 1 87.14 12.86 9.00 sample 2 96.26 10.91 8.88 sample 3 106.68 12.63 8.98 sample 4 94.67 12.70 8.94 sample 5 98.53 12.84 9.05
sample 6 86.27 13.05 9.16 sample 7 94.38 12.74 9.25 sample 8 87.93 12.04 9.18 sample 9 87.82 12.45 9.56
sample 10 98.84 12.99 8.82
Mean (SD) 93.85 ± 6.60 12.52 ± 0.64 9.08 ± 0.21
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ANEXOS
Anexo 1
Comprovante de submissão do artigo (Artigo 1)
73
Anexo 2
Certificado do comitê de ética em pesquisa
