Physical characterization of laser interaction and shock generation in laser shock processing: coupled theoretical-experimental analysis

Laser Shock Processing is developing as a key technology for the improvement of surface mechanical and corrosion resistance properties of metals due to its ability to introduce intense compressive residual stresses fields into high elastic limit materials by means of an intense laser driven shock wave generated by laser with intensities exceeding the 109 W/cm2 threshold, pulse energies in the range of 1 Joule and interaction times in the range of several ns. However, because of the relatively difficult-to-describe physics of shock wave formation in plasma following laser-matter interaction in solid state, only limited knowledge is available in the way of full comprehension and predictive assessment of the characteristic physical processes and material transformations with a specific consideration of real material properties. In the present paper, an account of the physical issues dominating the development of LSP processes from a moderately high intensity laser-matter interaction point of view is presented along with the theoretical and computational methods developed by the authors for their predictive assessment and new experimental contrast results obtained at laboratory scale.

Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Determining the elastic-plastic properties of metallic materials through instrumented indentation

En los últimos años, y asociado al desarrollo de la tecnología MEMS, la técnica de indentación instrumentada se ha convertido en un método de ensayo no destructivo ampliamente utilizado para hallar las características elástico-plásticas de recubrimientos y capas delgadas, desde la escala macroscópica a la microscópica. Sin embargo, debido al complejo mecanismo de contacto debajo de la indentación, es urgente proponer un método más simple y conveniente para obtener unos resultados comparables con otras mediciones tradicionales. En este estudio, el objetivo es mejorar el procedimiento analítico para extraer las propiedades elástico-plásticas del material mediante la técnica de indentación instrumentada. La primera parte se centra en la metodología llevada a cabo para medir las propiedades elásticas de los materiales elásticos, presentándose una nueva metodología de indentación, basada en la evolución de la rigidez de contacto y en la curva fuerza-desplazamiento del ensayo de indentación. El método propuesto permite discriminar los valores de indentación experimental que pudieran estar afectados por el redondeo de la punta del indentador. Además, esta técnica parece ser robusta y permite obtener valores fiables del modulo elástico. La segunda parte se centra en el proceso analítico para determinar la curva tensión-deformación a partir del ensayo de indentación, empleando un indentador esférico. Para poder asemejar la curva tension-deformación de indentación con la que se obtendría de un ensayo de tracción, Tabor determinó empíricamente un factor de constricción de la tensión () y un factor de constricción de la deformación (). Sin embargo, la elección del valor de y  necesitan una derivación analítica. Se describió analíticamente una nueva visión de la relación entre los factores de constricción de tensión y la deformación basado en la deducción de la ecuación de Tabor. Un modelo de elementos finitos y un diseño experimental se realizan para evaluar estos factores de constricción. A partir de los resultados obtenidos, las curvas tension-deformación extraidas de los ensayos de indentación esférica, afectadas por los correspondientes factores de constricción de tension y deformación, se ajustaron a la curva nominal tensión-deformación obtenida de ensayos de tracción convencionales. En la última parte, se estudian las propiedades del revestimiento de cermet Inconel 625-Cr3C2 que es depositado en el medio de una aleación de acero mediante un láser. Las propiedades mecánicas de la matriz de cermet son estudiadas mediante la técnica de indentación instrumentada, haciendo uso de las metodologías propuestas en el presente trabajo. In recent years, along with the development of MEMS technology, instrumented indentation, as one type of a non-destructive measurement technique, is widely used to characterize the elastic and plastic properties of metallic materials from the macro to the micro scale. However, due to the complex contact mechanisms under the indentation tip, it is necessary to propose a more convenient and simple method of instrumented indention to obtain comparable results from other conventional measurements. In this study, the aim is to improve the analytical procedure for extracting the elastic plastic properties of metallic materials by instrumented indentation. The first part focuses on the methodology for measuring the elastic properties of metallic materials. An alternative instrumented indentation methodology is presented. Based on the evolution of the contact stiffness and indentation load versus the depth of penetration, the possibility of obtaining the actual elastic modulus of an elastic-plastic bulk material through instrumented sharp indentation tests has been explored. The proposed methodology allows correcting the effect of the rounding of the indenter tip on the experimental indentation data. Additionally, this technique does not seem too sensitive to the pile-up phenomenon and allows obtaining convincing values of the elastic modulus. In the second part, an analytical procedure is proposed to determine the representative stress-strain curve from the spherical indentation. Tabor has determined the stress constraint factor (stress CF), and strain constraint factor (strain CF), empirically but the choice of a value for and is debatable and lacks analytical derivation. A new insight into the relationship between stress and strain constraint factors is analytically described based on the formulation of Tabor’s equation. Finite element model and experimental tests have been carried out to evaluate these constraint factors. From the results, representative stress-strain curves using the proposed strain constraint factor fit better with the nominal stress-strain curve than those using Tabor’s constraint factors. In the last part, the mechanical properties of an Inconel 625-Cr3C2 cermet coating which is deposited onto a medium alloy steel by laser cladding has been studied. The elastic and plastic mechanical properties of the cermet matrix are studied using depth-sensing indentation (DSI) on the micro scale.

Ethics and materials: Some Spanish Cases

The problem is general: modern architects and engineers are trying to understand historic structures using the wrong theoretical frame, the classic (elastic) thery of structures developed in the 19th Century for iron and stell, and in the 20th century for reinforced concrete, disguised with "modern" computer packages, mainly FEM, but also others. Masonry is an essentially different material, and the structural equations must be adapted accordingly. It is not a matter of "taste" or "opinion", and the consequences are before us. Since, say 1920s, historic monuments have suffered the aggression of generations of archietcts and engineers, trying to transform masonry in reinfored concrete or steel. The damage to the monuments and the expense has been, and is, enormous. However, as we have an adequate theory (modern limit analysis of masonry structures, Heyman 1966) which encompasses the "old theory" used successfully by the 18th and 19th Century practical engineers (from Perronet to Sejourné), it is a matter of "Ethics" not to use the wrong approach. It is also "contra natura" to modify the material masonry with indiscriminate injections, stitchings, etc. It is insane to consider, suddenly, that buildings which are Centuries or milennia old, are suddenly in danger of collapse. Maintenance is necessary but not the actual destruction of the constructive essence of the monument. A cocktail of "ignorance, fear and greed" is acting under the best of intentions.

Determination of the mechanical properties of amorphous materials through instrumented nanoindentation

A novel methodology based on instrumented indentation is developed to determine the mechanical properties of amorphous materials which present cohesive-frictional behaviour. The approach is based on the concept of a universal hardness equation, which results from the assumption of a characteristic indentation pressure proportional to the hardness. The actual universal hardness equation is obtained from a detailed finite element analysis of the process of sharp indentation for a very wide range of material properties, and the inverse problem (i.e. how to extract the elastic modulus, the compressive yield strength and the friction angle) from instrumented indentation is solved. The applicability and limitations of the novel approach are highlighted. Finally, the model is validated against experimental data in metallic and ceramic glasses as well as polymers, covering a wide range of amorphous materials in terms of elastic modulus, yield strength and friction angle.

A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials

A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

Microstructural and mechanical characterization of tungsten based materials for fusion reactors

El wolframio (W) y sus aleaciones se consideran los mejores candidatos para la construcción del divertor en la nueva generación de reactores de fusión nuclear. Este componente va a recibir las cargas térmicas más elevadas durante el funcionamiento del reactor ya que estará en contacto directo con el plasma. En los últimos años, después de un profundo análisis y siguiendo una estrategia de reducción de costes, la Organización de ITER tomó la decisión de construir el divertor integramente de wolframio desde el principio. Por ello, el wolframio no sólo actuará como material en contacto con el plasma (PFM), sino que también tendría aplicaciones estructurales. El wolframio, debido a sus excelentes propiedades termo-físicas, cumple todos los requerimientos para ser utilizado como PFM, sin embargo, su inherente fragilidad pone en peligro su uso estructural. Por tanto, uno de los principales objetivos de esta tesis es encontrar una aleación de wolframio con menor fragilidad. Durante éste trabajo, se realizó la caracterización microstructural y mecánica de diferentes materiales basados en wolframio. Sin embargo, ésta tarea es un reto debido a la pequeña cantidad de material suministrado, su reducido tamaño de grano y fragilidad. Por ello, para una correcta medida de todas las propiedades físicas y mecánicas se utilizaron diversas técnicas experimentales. Algunas de ellas se emplean habitualmente como la nanoindentación o los ensayos de flexión en tres puntos (TPB). Sin embargo, otras fueron especificamente desarrolladas e implementadas durante el desarrollo de esta tesis como es el caso de la medida real de la tenacidad de fractura en los materiales masivos, o de las medidas in situ de la tenacidad de fractura en las láminas delgadas de wolframio. Diversas composiciones de aleaciones de wolframio masivas (W-1% Y2O3, W-2% V-0.5% Y2O3, W-4% V-0.5% Y2O3, W-2% Ti-1% La2O3 y W-4% Ti-1% La2O3) se han estudiado y comparado con un wolframio puro producido en las mismas condiciones. Estas aleaciones, producidas por ruta pulvimetalúrgica de aleado mecánico (MA) y compactación isostática en caliente (HIP), fueron microstructural y mecánicamente caracterizadas desde 77 hasta 1473 K en aire y en alto vacío. Entre otras propiedades físicas y mecánicas se midieron la dureza, el módulo elástico, la resistencia a flexión y la tenacidad de fractura para todas las aleaciones. Finalmente se analizaron las superficies de fractura después de los ensayos de TPB para relacionar los micromecanismos de fallo con el comportamiento macroscópico a rotura. Los resultados obtenidos mostraron un comportamiento mecánico frágil en casi todo el intervalo de temperaturas y para casi todas las aleaciones sin mejoría de la temperatura de transición dúctil-frágil (DBTT). Con el fin de encontrar un material base wolframio con una DBTT más baja se realizó también un estudio, aún preliminar, de láminas delgadas de wolframio puro y wolframio dopado con 0.005wt.% potasio (K). Éstas láminas fueron fabricadas industrialmente mediante sinterizado y laminación en caliente y en frío y se sometieron posteriormente a un tratamiento térmico de recocido desde 1073 hasta 2673 K. Se ha analizado la evolución de su microestructura y las propiedades mecánicas al aumentar la temperatura de recocido. Los resultados mostraron la estabilización de los granos de wolframio con el incremento de la temperatura de recocido en las láminas delgadas de wolframio dopado con potasio. Sin embargo, es necesario realizar estudios adicionales para entender mejor la microstructura y algunas propiedades mecánicas de estos materiales, como la tenacidad de fractura. Tungsten (W) and tungsten-based alloys are considered to be the best candidate materials for fabricating the divertor in the next-generation nuclear fusion reactors. This component will experience the highest thermal loads during the operation of a reactor since it directly faces the plasma. In recent years, after thorough analysis that followed a strategy of cost reduction, the ITER Organization decided to built a full-tunsgten divertor before the first nuclear campaigns. Therefore, tungsten will be used not only as a plasma-facing material (PFM) but also in structural applications. Tungsten, due to its the excellent thermo-physical properties fulfils the requirements of a PFM, however, its use in structural applications is compromised due to its inherent brittleness. One of the objectives of this phD thesis is therefore, to find a material with improved brittleness behaviour. The microstructural and mechanical characterisation of different tunsgten-based materials was performed. However, this is a challenging task because of the reduced laboratory-scale size of the specimens provided, their _ne microstructure and their brittleness. Consequently, many techniques are required to ensure an accurate measurement of all the mechanical and physical properties. Some of the applied methods have been widely used such as nanoindentation or three-point bending (TPB) tests. However, other methods were specifically developed and implemented during this work such as the measurement of the real fracture toughness of bulk-tunsgten alloys or the in situ fracture toughness measurements of very thin tungsten foils. Bulk-tunsgten materials with different compositions (W-1% Y2O3, W-2% V- 0.5% Y2O3, W-4% V-0.5% Y2O3, W-2% Ti-1% La2O3 and W-4% Ti-1% La2O3) were studied and compared with pure tungsten processed under the same conditions. These alloys, produced by a powder metallurgical route of mechanical alloying (MA) and hot isostatic pressing (HIP), were microstructural and mechanically characterised from 77 to 1473 K in air and under high vacuum conditions. Hardness, elastic modulus, flexural strength and fracture toughness for all of the alloys were measured in addition to other physical and mechanical properties. Finally, the fracture surfaces after the TPB tests were analysed to correlate the micromechanisms of failure with the macroscopic behaviour. The results reveal brittle mechanical behaviour in almost the entire temperature range for the alloys and micromechanisms of failure with no improvement in the ductile-brittle transition temperature (DBTT). To continue the search of a tungsten material with lowered DBTT, a preliminary study of pure tunsgten and 0.005 wt.% potassium (K)-doped tungsten foils was also performed. These foils were industrially produced by sintering and hot and cold rolling. After that, they were annealed from 1073 to 2673 K to analyse the evolution of the microstructural and mechanical properties with increasing annealing temperature. The results revealed the stabilisation of the tungsten grains with increasing annealing temperature in the potassium-doped tungsten foil. However, additional studies need to be performed to gain a better understanding of the microstructure and mechanical properties of these materials such as fracture toughness.