Publication: Determinación numérica de propiedades mecánicas de espumas de aleación ß-TNTM para aplicaciones biómedicas
Date
2019
Authors
DAHER PÉREZ, JORGE JAIRO ALEJANDRO
Journal Title
Journal ISSN
Volume Title
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Abstract
Con el aumento en la expectativa de vida de la población se han vuelto más comunes las enfermedadesmusculoesqueléticas que implican un deterioro en las propiedades mecánicas de los tejidos óseos, condicionandola vida de las personas y convirtiéndose en un importante problema de salud pública.El desarrollo de los implantes biomédicos ha permitido el tratamiento de las enfermedades incapacitantes,recuperando las funciones físicas que se habían visto comprometidas. Diferentes políticas públicas de saludhan contribuido al aumento de la demanda por parte de la población de dichos implantes. Los materiales másempleados para la fabricación de estos dispositivos corresponden al titanio comercialmente puro (Ti c.p.)y aleaciones de este. La selección de estos materiales se debe a su equilibrio entre propiedades mecánicas,químicas y comportamiento in vivo. Sin embargo, aún existen limitaciones que se deben superar y comprometensu uso, entre las cuales se encuentran: (i) la rigidez del titanio es mucho mayor que la del hueso, lo cualproduce el apantallamiento de tensiones (stress shielding), promoviendo la reabsorción ósea y provocando eldebilitamiento del tejido óseo circundante, (ii) se debe mejorar la osteointegración, ya que se ha comprobadola aparición de tejido broso alrededor del implante, lo cual se relaciona con eventos de aojamiento de estos.El hueso humano, además de actuar como soporte mecánico, presenta ciertas funciones biológicas tales comohematopoyética, homeostasis de minerales y almacenamiento de triglicèridos. Se ha logrado establecer quelas funciones descritas anteriormente ocurren gracias a que los tejidos óseos son altamente porosos y queestos espacios sirven como reservorios. Considerando los antecedentes, los esfuerzos de los investigadores sehan centrado en lograr materiales con estructura y composición similar al hueso humano, siendo las espumasmetálicas una alternativa atractiva debido a la morfología y propiedades que poseen, las cuales se puedencontrolar mediante sus parámetros constructivos (propiedades del material en macizo, tamaño de poro, porosidad,etc.). El comportamiento mecánico de las espumas metálicas se caracteriza mediante desarrollosexperimentales los cuales emplean equipos costosos, demandan tiempo y necesitan de personal especializado,por lo cual es de interés contar con alternativas, tal como la simulación computacional para describir eldesempeñoo que tendrán.El objetivo de este trabajo es desarrollar una metodología numérica destinada a estimar las propiedadesmecánicas de las espumas de aleación -TiNbTa ( -TNT) obtenidas mediante pulvimetalurgia. Se trabajacon porosidades volumétricas entre 40% - 70% para replicar la alta porosidad presente en el hueso trabecular, valores entre 60% y 95 %. Conjuntamente, se emplean rangos de tamaños de poro de 100-200[um],350-450[um] y 660-900[um] debido a que se necesita un mínimo de 100[um] para la difusión de nutrientesesenciales para la supervivencia celular, además, se ha medido que el tamaño de las cavidades en el tejidotrabecular llega hasta 1500[um]. La metodología se separa en dos etapas: (i) uso de una distribución aleatoriade partículas a través del Método de Elemento Discretos (DEM), permitiendo conocer la ubicación de losporos. Se emplea el DEM simulando el comportamiento que tienen las partículas utilizadas como espaciador(space holder) en el proceso de mezclado de la técnica de pulvimetalurgia, (ii) empleo del Método de ElementosFinitos (MEF) para establecer los campos de deformaciones y esfuerzos al que se encuentra sometidoun Elemento de Volumen Representativo (RVE) al imponer desplazamientos como condiciones de contornopermitiendo extraer las propiedades mecánicas homogeneizadas de la geometría (módulo de Young y esfuerzode uencia). La simulación MEF se realiza utilizando un modelo elastoplástico bilineal de endurecimientoisotrópico siendo un modelo simpli cado del comportamiento en macizo de la aleación -TNT obtenidasmediante pruebas mecánicas experimentales.Cabe mencionar que la selección de la aleación -TNT se basa en el menor módulo de Young que presentanlas aleaciones b -Ti en comparación con las a-Ti, permitiendo que la porosidades necesarias paraalcanzar propiedades mecánicas similares a las del hueso sean menores, no comprometiendo la resistenciaa la uencia. Los elementos aleantes Nb y Ta se incorporan como elementos estabilizadores a aleacionesde base de Ti, lo cual asegura la ausencia de fase a, además, de garantizar un comportamiento biocompatible.De acuerdo a las curvas homogeneizadas obtenidas para el módulo de Young y para el esfuerzo de uencia, esposible obtener propiedades cercanas a las del hueso humano. Con el objetivo de igualar el módulo de Young sedebería emplear una porosidad cercana al 41% para el tejido cortical y del 47% para el hueso trabecular. Lasdos porosidades mencionadas anteriormente, entregan resistencia a la uencia mayores que la registrada porambos huesos, siendo aproximadamente 327[MPa] y 505[MPa] para el trabecular y cortical respectivamente.Para obtener los valores de los esfuerzos de uencia se utilizó la curva del rango 100-200[um] que entregalos valores mas bajos de resistencia y sería el caso más desfavorable para las porosidades mencionadas.Los resultados obtenidos proporcionan una herramienta y un criterio para identi car rutas de fabricaciónplausibles para la manufactura de implantes de espuma de aleación -TNT con un buen equilibrio entre unaprotección contra el apantallamiento de tensiones y un comportamiento mecánico adecuado.
With the increase in the life expectancy of the population, musculoskeletal diseases that involve a deteriorationin the mechanical properties of bone tissues have become more common, conditioning the lives of peopleand becoming a major public health problem.The development of biomedical implants has allowed the treatment of incapacitating diseases, recoveringthe physical functions that had been compromised. Diferent public health policies have contributed to theincrease in demand from the population of these implants. The most commonly used materials for the manufactureof these devices correspond to commercially pure titanium (c.p. Ti) and alloys of this. The selectionof these materials is due to their balance between mechanical and chemical properties and in vivo behavior.However, there are still limitations that must be overcome and compromise their use, among which are: (i)the sti ness of titanium is greater than bone, which produces the stress shielding promoting bone resorption,causing the weakening of the surrounding bone tissue, (ii) osseointegration must be improved, since the appearanceof brous tissue around the implant has been proven, which is related to loosening events of this.The human bone, in addition to acting as a mechanical support, has certain biological functions such ashematopoietic, mineral homeostasis and storage of triglycerides. It has been established that the functionsdescribed above take place because the bone tissues are highly porous and these spaces help as reservoirs.Considering the antecedents, the e orts of the researchers have focused on achieving materials with structureand composition similar to human bone, metallic foams being an attractive alternative due to the morphologyand properties they possess, which can be controlled by their constructive parameters (material propertiesin solid, pore size, porosity, etc.). The mechanical behavior of metal foams is characterized by experimentaldevelopments which use expensive equipment, demand time and require specialized personnel, so it is ofinterest to have alternatives, such as computer simulation to describe the performance they will have.The objective of this work is to develop a numerical methodology aimed at estimating the mechanical propertiesof the alloy foams -TiNbTa ( -TNT) obtained by powder metallurgy. It works with volumetricporosities between 40% - 70% to replicate the high porosity present in trabecular bone, values between60% and 95 %. Jointly, pore sizes ranges of 100-200[um], 350-450[um] and 660-900[um] are used becausea minimum of 100[um] is needed for the difusion of essential nutrients for cell survival, it has also beenmeasured that the size of the cavities in the trabecular tissue reaches up to 1500 [um]. The methodology is separated into two stages: (i) use of a random distribution of particles through the Discrete Element Method(DEM), allowing to know the location of the pores. The DEM is used simulating the behavior of the particlesused as a spacer (space holder) in the mixing process of the powder metallurgy technique, (ii) use of theFinite Element Method (FEM) to establish the elds of deformations and stresses to which a RepresentativeVolume Element (RVE) is subjected by imposing displacements as boundary conditions allowing to extractthe homogenized mechanical properties of the geometry (Young's modulus and yield stress). The FEM simulationis performed using an bilinear isotropic hardening model, being a simpli ed model of the bulkbehavior of the alloy -TNT obtained by experimental mechanical tests.It should be mentioned that the selection of the -TNT alloy is based on the lower Young's modulus whichpresents the b -Ti alloys in comparison with the a-Ti, allowing that the porosity necessary to achieve similarmechanical properties to the bone are smaller, not compromising the yield strength. The alloying elements,Nb and Ta, are incorporated as stabilizers elements to Ti base alloys, which ensures the absence of aphase, in addition, to guarantee a biocompatible behavior.According to the homogenized curves obtained for the Young's modulus and for the yield stress, it is possibleto obtain properties close to those of the human bone. In order to equal the Young's modulus, a porosityclose to 41% for cortical tissue and 47% for trabecular bone should be used. The two porosities mentionedabove, give yield strength greater than that recorded by both bones, being approximately 327[MPa] and505[MPa] for the trabecular and cortical respectively. To obtain the yield stress values, the 100-200[um]curve was used, which gives the lowest resistance values and would be the worst-case scenario. The resultsobtained provide a tool and a guideline to identify plausible manufacturing routes for the manufacture of -TNT alloy foam implants
With the increase in the life expectancy of the population, musculoskeletal diseases that involve a deteriorationin the mechanical properties of bone tissues have become more common, conditioning the lives of peopleand becoming a major public health problem.The development of biomedical implants has allowed the treatment of incapacitating diseases, recoveringthe physical functions that had been compromised. Diferent public health policies have contributed to theincrease in demand from the population of these implants. The most commonly used materials for the manufactureof these devices correspond to commercially pure titanium (c.p. Ti) and alloys of this. The selectionof these materials is due to their balance between mechanical and chemical properties and in vivo behavior.However, there are still limitations that must be overcome and compromise their use, among which are: (i)the sti ness of titanium is greater than bone, which produces the stress shielding promoting bone resorption,causing the weakening of the surrounding bone tissue, (ii) osseointegration must be improved, since the appearanceof brous tissue around the implant has been proven, which is related to loosening events of this.The human bone, in addition to acting as a mechanical support, has certain biological functions such ashematopoietic, mineral homeostasis and storage of triglycerides. It has been established that the functionsdescribed above take place because the bone tissues are highly porous and these spaces help as reservoirs.Considering the antecedents, the e orts of the researchers have focused on achieving materials with structureand composition similar to human bone, metallic foams being an attractive alternative due to the morphologyand properties they possess, which can be controlled by their constructive parameters (material propertiesin solid, pore size, porosity, etc.). The mechanical behavior of metal foams is characterized by experimentaldevelopments which use expensive equipment, demand time and require specialized personnel, so it is ofinterest to have alternatives, such as computer simulation to describe the performance they will have.The objective of this work is to develop a numerical methodology aimed at estimating the mechanical propertiesof the alloy foams -TiNbTa ( -TNT) obtained by powder metallurgy. It works with volumetricporosities between 40% - 70% to replicate the high porosity present in trabecular bone, values between60% and 95 %. Jointly, pore sizes ranges of 100-200[um], 350-450[um] and 660-900[um] are used becausea minimum of 100[um] is needed for the difusion of essential nutrients for cell survival, it has also beenmeasured that the size of the cavities in the trabecular tissue reaches up to 1500 [um]. The methodology is separated into two stages: (i) use of a random distribution of particles through the Discrete Element Method(DEM), allowing to know the location of the pores. The DEM is used simulating the behavior of the particlesused as a spacer (space holder) in the mixing process of the powder metallurgy technique, (ii) use of theFinite Element Method (FEM) to establish the elds of deformations and stresses to which a RepresentativeVolume Element (RVE) is subjected by imposing displacements as boundary conditions allowing to extractthe homogenized mechanical properties of the geometry (Young's modulus and yield stress). The FEM simulationis performed using an bilinear isotropic hardening model, being a simpli ed model of the bulkbehavior of the alloy -TNT obtained by experimental mechanical tests.It should be mentioned that the selection of the -TNT alloy is based on the lower Young's modulus whichpresents the b -Ti alloys in comparison with the a-Ti, allowing that the porosity necessary to achieve similarmechanical properties to the bone are smaller, not compromising the yield strength. The alloying elements,Nb and Ta, are incorporated as stabilizers elements to Ti base alloys, which ensures the absence of aphase, in addition, to guarantee a biocompatible behavior.According to the homogenized curves obtained for the Young's modulus and for the yield stress, it is possibleto obtain properties close to those of the human bone. In order to equal the Young's modulus, a porosityclose to 41% for cortical tissue and 47% for trabecular bone should be used. The two porosities mentionedabove, give yield strength greater than that recorded by both bones, being approximately 327[MPa] and505[MPa] for the trabecular and cortical respectively. To obtain the yield stress values, the 100-200[um]curve was used, which gives the lowest resistance values and would be the worst-case scenario. The resultsobtained provide a tool and a guideline to identify plausible manufacturing routes for the manufacture of -TNT alloy foam implants
Description
Catalogado desde la version PDF de la tesis.
Keywords
ALEACIONES DE TI , APANTALLAMIENTO DE TENSIONES , DEM , MEF , PROPIEDADES MEC ANICAS HOMOGENEIZADAS , PULVIMETALURGIA