Mejora del comportamiento térmico de los morteros de cal aditivados y su empleo en la rehabilitación de inmuebles = Improvement of thermal behaviour of additived lime mortars and their use in rehabilitation of buildings

La envolvente de la edificación es la responsable de equilibrar el intercambio energético entre el interior y el exterior, por lo tanto cualquier actuación encaminada a la reducción del consumo energético ha de establecer, como uno de sus objetivos prioritarios, la mejora del comportamiento de la misma. Las edificaciones anteriores a 1940 constituyen la mayor parte de las existentes en áreas rurales y centros urbanos. En ellas, la repercusión de la fachada sobre las transmitancias globales pone de manifiesto la necesidad de intervención. Sin embargo, su elevada inercia térmica y los importantes saltos térmicos característicos de gran parte de España plantean la importancia de que aquélla se efectúe por el exterior. A tal respecto, la falta de disponibilidad de espesor suficiente para implantar sistemas tipo SATE deriva en que, frecuentemente, la única solución viable sea la de aislar por el interior perdiendo con ello la capacidad de acumulación térmica del muro y con el asociado riesgo de condensaciones. La amplia tradición en el empleo de revestimientos, especialmente en base de cal, permiten que éstos sean utilizados no sólo como elemento estético o de protección de la obra de fábrica antigua sino también para la mejora del comportamiento térmico del soporte, si se aprovecha el mecanismo de transmisión térmica por radiación. Éste es el objetivo de la presente Tesis Doctoral en la que se estudia la modificación de las propiedades radiantes de los morteros de revestimiento para la mejora de la eficiencia energética de las construcciones históricas, principalmente las constituidas por muros monolíticos, aunque podría ser de aplicación a otro tipo de construcciones compuestas por diversas capas. Como punto de partida, se estudió y revisó la documentación disponible sobre las investigaciones de las tres áreas científico-tecnológicas que convergen en la Tesis Doctoral: rehabilitación, material y comportamiento térmico, a partir de lo cual se comprobó la inexistencia de estudios similares al objeto de la presente Tesis Doctoral. Complementariamente, se analizaron los revestimientos en lo concerniente a los materiales que los constituyen, la composición de las mezclas y características de cada una de las capas así como al enfoque que, desde el punto de vista térmico, se estimaba más adecuado para la obtención de los objetivos propuestos. Basándonos en dichos análisis, se preseleccionaron ochenta materiales que fueron ensayados en términos de reflectancia y emisividad para elegir cuatro con los que se continuó la investigación. Éstos, junto con la cal elegida para la investigación y el árido marmóreo característico de la última capa de revestimiento, fueron caracterizados térmicamente, de forma pormenorizada, así como química y físicamente. Los fundamentos teóricos y los estudios preliminares desarrollados con distintos materiales, en estado fresco y endurecido, fueron empleados en la dosificación de componentes de las mezclas, en dos proporciones distintas, para el estudio del efecto del agregado. Éstas se ensayaron en estado fresco, para comprobar su adecuación de puesta en obra y prever su VI adherencia al soporte, así como en estado endurecido a 28 y 90 días de curado, para conocer las propiedades que permitieran prever su compatibilidad con aquél y estimar el alcance de la reducción de transferencias térmicas lograda. Además, se estudiaron las características generales de las mezclas que sirvieron para establecer correlaciones entre distintas propiedades y entender los resultados mecánicos, físicos (comportamiento frente al agua) y energéticos. Del estudio conjunto de las distintas propiedades analizadas se propusieron dos mezclas, una blanca y otra coloreada, cuyas características permiten garantizar la compatibilidad con la obra de fábrica antigua, desde el punto de vista físico y mecánico, y preservar la autenticidad de los revestimientos, en cuanto a la técnica de aplicación tradicional en sistemas multicapa. El comportamiento térmico de las mismas, sobre una obra de fábrica de 40 cm de espesor, se estimó, en estado estacionario y pseudo-transitorio, demostrándose reducciones del flujo térmico entre 16-48%, en condiciones de verano, y entre el 6-11%, en invierno, en función de la coloración y de la rugosidad de la superficie, en comparación con el empleo de la mezcla tradicional. Por lo que, se constata la viabilidad de los materiales compuestos propuestos y su adecuación al objetivo de la investigación. VII ABSTRACT The envelope is responsible for balancing the energy exchange between the inside and outside in buildings. For this reason, any action aimed at reducing energy consumption must establish, as one of its key priorities, its improvement. In rural areas and urban centers, most of the constructions were built before 1940. In them, the impact of the façade on the global transmittance highlights the need for intervention. However, its high thermal inertia and fluctuation of temperatures in the majority of Spain bring up that it should be placed outside the insulation. In this regard, the lack of availability of enough thickness to implement systems such as ETICS results in that often the only viable solution is to isolate the interior, losing thereby the wall’s heat storage capacity with the associated risk of condensation. The tradition in the use of renders, especially lime-based, allows us to use them not only as an aesthetic element or to protect the ancient masonry, but also for improved thermal performance of the support by taking advantage of the heat transfer mechanism by radiation. This is the aim of this Doctoral Thesis in which the modification of the radiative properties of lime mortars for renders to improve the energy efficiency of historic buildings, mainly composed of monolithic walls, is studied, although it could be applied to other structures composed of several layers. As a starting point, the available literature in the three scientific-technological areas that converge at the Doctoral Thesis: rehabilitation, material and thermal behaviour, was reviewed, and confirmed the absence of researches similar to this Doctoral Thesis. Additionally, the renders were studied with regard to the materials that constitute them, the composition of the mixtures and the characteristics of each layer, as well as to the approach which, from a thermal point of view, was deemed the most suitable for achieving the objectives sets. Based on thre aforementioned analysis, eighty materials tested in terms of reflectance and emissivity were pre-selected, to choose four with which the research was continued. Common marble sand, used in the last layer of the renders, together with the appointed materials and hydrated lime were characterized thermally, in detail, as well as chemically and physically. The theoretical bases and preliminary studies with different materials, in fresh and hardened state, were used in the dosage of the composition of the mixtures. In order to study their effect they were used in two different proportions, that is, ten mixtures in total. These were tested in their fresh state to evaluate their setting-up suitability and foresee their adhesion to the support, as well as in their hardened state, at 28 and 90 days of curing, to establish the properties which enabled us to anticipate their compatibility with the old masonry walls and estimate the scope of the reduction of heat transfers achieved. In addition, the general characteristics of the mixtures used to establish correlations and to understand the mechanical, physical and energy results were studied. Two mixtures, one white and one colored, were proposed as the result of the different properties analysed, whose characteristics allow the guarantee of mechanical and physical compatibility VIII with the old masonry and preserve the authenticity of the renders. The thermal behavior of both, applied on a masonry wall 40 cm thick, was estimated at a steady and pseudo-transient state, with heat flow reductions between 16-48% during summertime and 6-11% during wintertime, depending on the color and surface roughness, compared to the use of the traditional mixture. So, the viability of the proposed composite materials and their fitness to the aim of the research are established.

Thermal behaviour of Sunrise, a balloon-borne solar Telescope

Sunrise is a solar telescope, successfully flown in June 2009 with a long duration balloon from the Swedish Space Corporation Esrange launch site. The design of the thermal control of SUNRISE was quite critical because of the sensitivity to temperature of the optomechanical devices and the electronics. These problems got more complicated due the size and high power dissipation of the system. A detailed thermal mathematical model of SUNRISE was set up to predict temperatures. In this communication the thermal behaviour of SUNRISE during flight is presented. Flight temperatures of some devices are presented and analysed. The measured data have been compared with the predictions given by the thermal mathematical models. The main discrepancies between flight data and the temperatures predicted by the models have been identified. This allows thermal engineers to improve the knowledge of the thermal behaviour of the system for future missions.

Thermal behaviour of bitumen modified by sulphur addition

The most frequent use of bitumen is as binder for pavement applications. The effect of sulphur addition on the properties of the bitumen has been extensively studied several decades ago. Recently, there is a renewed interest in researching the behaviour of sulphur-bitumen combination, because off 1.The future availability of bitumen may be limited and 2. The beneficial consumption of great amounts of sulphur compounds from petroleum refining is advisable. The addition of sulphur to bitumen provokes the beginning of chemical reactions depending on the sulphur content and heating temperature. At heating temperatures T< 140 ºC liquid sulphur reacts with naphthenic-aromatic fraction forming polysulphides. At temperatures above 150 ºC dehydrogenization reactions with emission of hydrogen sulfide take place and naphthenic-aromatic molecules are transformed into asphaltenes. Therefore, the addition of sulphur to bitumen provokes changes in the chemical structure of the bitumen. The objective of this work is to analyze, the thermal behaviour of sulphur-bitumen mixtures of different composition (0-35 %wt sulphur content) prepared at 130 and 140 ºC, by means of differential scanning calorimetry (DSC). Besides, the volatile emissions of the mixtures at high temperature have been estimated from loss weight measurements as a function of stored time

Mechanical and thermal behaviour of isotactic polypropylene reinforced with inorganic fullerene-like WS2 nanoparticles: Effect of filler loading and temperature

The thermal and mechanical behaviour of isotactic polypropylene (iPP) nanocomposites reinforced with different loadings of inorganic fullerene-like tungsten disulfide (IF-WS2) nanoparticles was investigated. The IF-WS2 noticeably enhanced the polymer stiffness and strength, ascribed to their uniform dispersion, the formation of a large nanoparticle?matrix interface combined with a nucleating effect on iPP crystallization. Their reinforcement effect was more pronounced at high temperatures. However, a drop in ductility and toughness was found at higher IF-WS2 concentrations. The tensile behaviour of the nanocomposites was extremely sensitive to the strain rate and temperature, and their yield strength was properly described by the Eyring s equation. The activation energy increased while the activation volume decreased with increasing nanoparticle loading, indicating a reduction in polymer chain motion. The nanoparticles improved the thermomechanical properties of iPP: raised the glass transition and heat deflection temperatures while decreased the coefficient of thermal expansion. The nanocomposites also displayed superior flame retardancy with longer ignition time and reduced peak heat release rate. Further, a gradual rise in thermal conductivity was found with increasing IF-WS2 loading both in the glassy and rubbery states. The results presented herein highlight the benefits and high potential of using IF-nanoparticles for enhancing the thermomechanical properties of thermoplastic polymers compared to other nanoscale fillers.

Analytical study of the thermal behaviour and stability of a small satellite

In this work the thermal analysis of a small satellite orbiting around the Earth has been approached by direct integration of the heat balance equations of a two-node reduced model, obtaining a linearized second order ODE problem, similar in form to the classical case of the forced vibration of a damped system. As the thermal loads (solar radiation, albedo, etc.) are harmonic, the problem is solved by means of Fourier analysis methods. Research on that field can be directly applied to the analysis of thermal problems and the results obtained are satisfactory. Working on the frequency domain streamlines the analysis, simplifies the study and facilitates the experimental testing. The transfer functions are obtained for the two-node case but the study can be extended to an n-node model.

Transient thermal analysis during the ascent phase of a balloon-borne payload. Comparison with SUNRISE test flight measurements

The thermal design of stratospheric balloon payloads usually focuses on the cruise phase of the missions, that is, the floating altitude conditions. The ascent phase usually takes between 2 and 4 h, a very small period compared to the duration of the whole mission, which can last up to 4 weeks. However, during this phase payloads are subjected to very harsh conditions due mainly to the convective cooling that occurs as the balloon passes through the cold atmosphere, with minimum temperatures in the tropopause. The aim of this work is to study the thermal behaviour of a payload carried by a long duration balloon during the ascent phase. Its temperature has been calculated as a function of the altitude from sea level to floating conditions. To perform this analysis it has been assumed that the thermal interactions (convection and radiation) depend on the altitude, on the environmental conditions (which in turn depend also on the altitude) and on the temperature of the system itself. The results have been compared with the measurements taken during the SUNRISE test flight, launched in October 2007 by CSBF from Fort Sumner (New Mexico).

An experimental study on the effect of rolling shutters on the field measurements of airborne sound insulation of façades

The façade is the visible part of a building, and generally consists of various different constructive systems. The sound reduction index of the closing elements for the openings on a room’s façade is a determining factor in the sound insulation from airborne noise inside the space. Windows are the transparent part of the façade, and to improve their thermal behaviour and control solar radiation, they are often fitted with a series of external and internal protections such as shutters, slats and blinds. This work contains a summary of studies carried out using field measurements of airborne sound insulation on façades in rooms, in application of the standard UNE-EN ISO 140-5:1999. In all the rooms the windows were fitted with shutter boxes and rolling shutters, and the acoustic tests were made with the shutter in two positions (extended and fully retracted). The results were analysed considering the window opening system (openable or sliding) and the type of glass pane (monolithic or insulating glass unit, IGU). In the case of sliding windows, the airborne sound insulation of façades is greater when the shutter is extended than when it is retracted, and this should be taken into account when applying the aforementioned standard.

Interaction between a laser beam and semiconductor nanowires: application to the raman spectrum of Si nanowires

One presents in this work the study of the interaction between a focused laser beam and Si nanowires (NWs). The NWs heating induced by the laser beam is studied by solving the heat transfer equation by finite element methods (fem). This analysis permits to establish the temperature distribution inside the NW when it is excited by the laser beam. The overheating is dependent on the dimensions of the NW, both the diameter and the length. When performing optical characterization of the NWs using focused laser beams, one has to consider the temperature increase introduced by the laser beam. An important issue concerns the fact that the NWs diameter has subwavelength dimensions, and is also smaller than the focused laser beam. The analysis of the thermal behaviour of the NWs under the excitation with the laser beam permits the interpretation of the Raman spectra of Si NWs, where it is demonstrated that temperature induced by the laser beam play a major role in shaping the Raman spectrum of Si NWs

Esfuerzos inducidos en presas, arco-gravedad en operación por la acción térmica medioambiental : una aportación a su análisis y evaluación

Cyclic fluctuations of the atmospheric temperature on the dam site, of the water temperature in the reservoir and of the intensity of solar radiation on the faces of the dam cause significant stresses in the body of concrete dams. These stresses can be evaluated first by introducing in analysis models a linear temperature distribution statically equivalent to the real temperature distribution in the dam; the stress valúes obtained from this first step must be complemented (especially in the área of dam faces) with the stress valúes resuiting from the difference between the real temperature law and the linear law at each node. In the case of arch gravity dams, and because of their characteristics of arch dam featuring a thick section, both types of temperature-induced stresses are of similar importance. Thermal stress valúes are directly linked to a series of factors: atmospheric and water temperature and intensity of solar radiation at dam site, site latitude, azimuth of the dam, as well as geometrical characteristics of the dam and thermal properties of concrete. This thesis first presents a complete study of the physical phenomenon of heat exchange between the environment and the dam itself, and establishes the participation scheme of all parameters involved in the problem considered. A detailed documental review of available methods and techniques is then carried out both for the estimation of environmental thermal loads and for the evaluation of the stresses induced by these loads. Variation ranges are also established for the main parameters. The definition of the geometrical parameters of the dam is provided based on the description of a wide set of arch gravity dams built in Spain and abroad. As a practical reference of the parameters defining the thermal action of the environment, a set of zones, in which thermal parameters reach homogeneous valúes, was established for Spain. The mean valué and variation range of atmospheric temperature were then determined for each zone, based on a series of historical valúes. Summer and winter temperature increases caused by solar radiation were also defined for each zone. Since the hypothesis of thermal stratification in the reservoir has been considered, máximum and mínimum temperature valúes reached at the bottom of the reservoir were determined for each climatic zone, as well as the law of temperature variation in function of depth. Various dam-and-foundation configurations were analysed by means of finite element 3D models, in which the dam and foundation were each submitted to different load combinations. The seasonal thermal behaviour of sections of variable thickness was analysed through the application of numerical techniques to one-dimensional models. Contrasting the results of both analyses led to conclusions on the influence of environmental thermal action on the stress conditions of the structure. Las oscilaciones periódicas de la temperatura ambiente en el emplazamiento y de la temperatura del agua en el embalse, así como de la incidencia de la radiación solar sobre los paramentos de la presa, son causa de tensiones importantes en el cuerpo de las presas de hormigón. Estas tensiones pueden ser evaluadas en primer lugar introduciendo en los modelos tridimensionales de análisis, distribuciones lineales de temperatura estáticamente equivalentes a las correspondientes distribuciones reales en el cuerpo de la presa; las tensiones así obtenidas han de complementarse (sobre todo en las cercanías de los paramentos) con tensiones cuyo origen está en la temperatura diferencia entre la ley real y la lineal en cada punto. En el caso de las presas arco-gravedad y en razón de su doble característica de presas arco y de sección gruesa, ambas componentes de la tensión inducida por la temperatura son de magnitud similar. Los valores de estas tensiones de origen térmico están directamente relacionados con la temperatura del emplazamiento y del embalse, con la intensidad de la insolación, con la latitud y el azimut de la presa, con las características geométricas de la estructura y con las propiedades térmicas del hormigón. En esta tesis se realiza, en primer lugar, un estudio completo del fenómeno físico del intercambio de calor entre el medio ambiente y el cuerpo de la presa, estableciendo el mecanismo de participación de todos los parámetros que configuran el problema. En segundo lugar se realiza a cabo una revisión documental detallada de los métodos y técnicas utilizables tanto en la estimación de las cargas térmicas ambientales como en la evaluación de las tensiones inducidas por dichas cargas. En tercer lugar se establecen rangos de variación para los principales parámetros que configuran el problema. Los parámetros geométricos de la presa se definen a partir de la descripción de un amplio conjunto de presas arco-gravedad tanto españolas como del resto del mundo. Como referencia práctica de los parámetros que definen la acción térmica ambiental se establecen en España un conjunto de zonas caracterizadas por que, en cada una de ellas, los parámetros térmicos alcanzan valores homogéneos. Así, y en base a series de valores históricos, se establecen la media y la amplitud de la variación anual de la temperatura ambiental en cada una de las zonas. Igualmente, se han definido para cada zona los incrementos de temperatura que, en invierno y en verano, produce la insolación. En relación con el agua del embalse y en la hipótesis de estratificación térmica de este, se han definido los valores, aplicables en cada una de las zonas, de las temperaturas máxima y mínima en el fondo así como la ley de variación de la temperatura con la profundidad. Utilizando modelos tridimensionales de elementos finitos se analizan diferentes configuraciones de la presa y la cimentación sometidas, cada una de ellas, a diferentes combinaciones de carga. Aplicando técnicas numéricas a modelos unidimensionales se analiza el comportamiento térmico temporal de secciones de espesor variable. Considerando conjuntamente los resultados de los análisis anteriores se obtienen conclusiones parametrizadas de detalle sobre la influencia que tiene en el estado tensional de la estructura la consideración de la acción térmica ambiental.

Interaction between a laser beam and semiconductor nanowires: application to the raman spectrum of Si nanowires

One presents in this work the study of the interaction between a focused laser beam and Si nanowires (NWs). The NWs heating induced by the laser beam is studied by solving the heat transfer equation by finite element methods (FEM). This analysis permits to establish the temperature distribution inside the NW when it is excited by the laser beam. The overheating is dependent on the dimensions of the NW, both the diameter and the length. When performing optical characterisation of NWs using focused laser beams, one has to consider the temperature increase introduced by the laser beam. An important issue concerns the fact that the NW's diameter has subwavelength dimensions, and is also smaller than the focused laser beam. The analysis of the thermal behaviour of the NWs under the excitation with the laser beam permits the interpretation of the Raman spectrum of Si NWs. It is demonstrated that the temperature increase induced by the laser beam plays a major role in shaping the Raman spectrum of Si NWs.

Design, development and construction of an outdoor testing facility for semi-transparent photovoltaic modules

Building-integrated Photovoltaics (BIPV) is one of the most promising technologies enabling buildings to generate on-site part of their electricity needs while performing architectural functionalities. A clear example of BIPV products consists of semi-transparent photovoltaic modules (STPV), designed to replace the conventional glazing solutions in building façades. Accordingly, the active building envelope is required to perform multiple requirements such as provide solar shading to avoid overheating, supply solar gains and thermal insulation to reduce heat loads and improve daylight utilization. To date, various studies into STPV systems have focused on their energy performance based on existing simulation programs, or on the modelling, normally validated by limited experimental data, of the STPV modules thermal behaviour. Taking into account that very limited experimental research has been conducted on the energy performance of STPV elements and that the characterization in real operation conditions is necessary to promote an energetically efficient integration of this technology in the building envelope, an outdoor testing facility has been designed, developed and built at the Solar Energy Institute of the Technical University of Madrid. In this work, the methodology used in the definition of the testing facility, its capability and limitations are presented and discussed.

Influence of grain size and compaction of different solid fuels on the layer ignition temperature

The results obtained from these analyses provide some clarifications about the thermal behaviour of the products and also enough information to design some prevention measurements in these facilities to avoid or at least minimize the risk of ignition of a dust layer.

Tritium permeation experiment at IFMIF Medium Flux Test Module

Tritium release experiments using different breeding material candidates are planned for the medium flux region of the IFMIF Test Cell. Nowadays, only ceramic breeder materials have been suggested to be tested in the Tritium Release Module located in the Medium Flux Test Module of IFMIF. Liquid breeder blankets are very promising and for that reason, several concepts will be tested in ITER. One of the main problems concerning the liquid blankets is the permeation of the generated tritium in the breeder throughout the walls. Since tritium permeation is highly influenced by irradiation conditions, IFMIF is a suitable scenario to perform tritium permeation related experiments. In this paper, a preliminary design of a tritium permeation experiment for the Medium Flux Test Module of IFMIF is proposed, in order to contribute to the progress of the liquid breeder blanket concept validation. The conceptual design of the capsule in which the experiment will be performed is carried out, taking into consideration the experiment necessities and its implementation in the Tritium Release Module. In addition to this, some thermal hydraulic calculations have been performed to evaluate the thermal behaviour of the irradiation capsule

Thermal diffusion profile by NRA of Deuterium implanted in solid breeder blanket materials

This paper studies the relationship between aging, physical changes and the results of non-destructive testing of plywood. 176 pieces of plywood were tested to analyze their actual and estimated density using non-destructive methods (screw withdrawal force and ultrasound wave velocity) during a laboratory aging test. From the results of statistical analysis it can be concluded that there is a strong relationship between the non-destructive measurements carried out, and the decline in the physical properties of the panels due to aging. The authors propose several models to estimate board density. The best results are obtained with ultrasound. A reliable prediction of the degree of deterioration (aging) of board is presented. Breeder blanket materials have to produce tritium from lithium while fulfilling several strict conditions. In particular, when dealing with materials to be applied in fusion reactors, one of the key questions is the study of light ions retention, which can be produced by transmutation reactions and/or introduced by interaction with the plasma. In ceramic breeders the understanding of the hydrogen isotopes behaviour and specially the diffusion of tritium to the surface is crucial. Moreover the evolution of the microstructure during irradiation with energetic ions, neutrons and electrons is complex because of the interaction of a high number of processes.

Flow and fracture behaviour of high performance alloys

Based on our needs, that is to say, through precise simulation of the impact phenomena that may occur inside a jet engine turbine with an explicit non-linear finite element code, four new material models are postulated. Each one of is calibrated for four high-performance alloys that can be encountered in a modern jet engine. A new uncoupled material model for high strain and ballistic is proposed. Based on a Johnson-Cook type model, the proposed formulation introduces the effect of the third deviatoric invariant by means of three different Lode angle dependent functions. The Lode dependent functions are added to both plasticity and failure models. The postulated model is calibrated for a 6061-T651 aluminium alloy with data taken from the literature. The fracture pattern predictability of the JCX material model is shown performing numerical simulations of various quasi-static and dynamic tests. As an extension of the above-mentioned model, a modification in the thermal softening behaviour due to phase transformation temperatures is developed (JCXt). Additionally, a Lode angle dependent flow stress is defined. Analysing the phase diagram and high temperature tests performed, phase transformation temperatures of the FV535 stainless steel are determined. The postulated material model constants for the FV535 stainless steel are calibrated. A coupled elastoplastic-damage material model for high strain and ballistic applications is presented (JCXd). A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson-Cook failure criterion. The weakening in the elastic law and in the Johnson-Cook type constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. A transversely isotropic material model for directionally solidified alloys is presented. The proposed yield function is based a single linear transformation of the stress tensor. The linear operator weighs the degree of anisotropy of the yield function. The elastic behaviour, as well as the hardening, are considered isotropic. To model the hardening, a Johnson-Cook type relation is adopted. A material vector is included in the model implementation. The failure is modelled with the Cockroft-Latham failure criterion. The material vector allows orienting the reference orientation in any other that the user may need. The model is calibrated for the MAR-M 247 directionally solidified nickel-base superalloy.