Devido a suas vantagens comparadas aos métodos tradicionais de união mecânica, a utilização de juntas coladas estruturais só tende a crescer, entretanto, devido suas propriedades e modos de falha dependerem de diversos parâmetros (tratamento superficial, geometria, material, condições de tralho, etc.) uma utilização mais ampla desta técnica ainda é restrita pela ausência de modelos de falhas confiáveis. O presente trabalho consiste na apresentação de métodos para fabricação de juntas coladas em material compósito e verificação da influência da espessura da camada adesiva na resistência de juntas simples coladas (single lap joints) submetidas à tração. São também apresentados métodos para fabricação dos aderentes, corpos de prova de adesivo puro para ensaios de caracterização e realização de ensaios mecânicos para obtenção das propriedades mecânicas tanto dos aderentes quanto do adesivo. As propriedades mecânicas dos aderentes e do adesivo foram obtidas através de ensaios realizados em uma máquina de tração universal com o auxílio da técnica de correlação digital de imagem, e a obtenção das energias críticas de resistência à fratura (GIc,GIIc) da camada adesiva foram calculadas através de ensaios Double Cantilever Beam (DCB) e End Notched Flexure (ENF). Foram estudados métodos para gerar falha coesiva nas juntas adesivas, sendo que o melhor método encontrado foi o de tratamento superficial dos aderentes com jateamento abrasivo seguido pela limpeza superficial com acetona. O controle preciso da espessura da camada adesiva foi alcançado através do desenvolvimento de um dispositivo de fácil construção, compostos por suportes de madeira, hastes e linhas de nylon. Nos ensaios em juntas coladas foi constatado uma relação inversamente proporcional entre a espessura da camada adesiva e a resistência máxima suportada pela junta, ou seja, quanto maior a espessura do adesivo menor sua resistência. Os métodos aqui apresentados foram os resultados de vários meses de estudo e compreensão das normas e técnicas disponíveis na literatura, o aprimoramento das técnicas foram frutos de um ciclo compostos por fabricação, testes e análise de resultados. / Amongst the joining techniques, adhesively bonding joints are one of the most commonly applied nowadays. However, a lack of reliable failure criteria still exists, limiting in this way a more widespread application of adhesively bonded joints in principal load-bearing structural applications. An accurate strength prediction of the adhesively bonded joints is essential to decrease the amount of expensive testing at the design stage. This work consists to show methods for manufacturing single lap joints and to verify the adhesive thickness influence on the joint resistance. The manufacturing process of the composite adherends and adhesives for bulk tests was also covered. The mechanical properties of the adherends and bulk adhesive were performed on a universal testing machine with assistance of a digital image correlation (DIC) technique. The fracture toughness energy release rates (GIc,GIIc) of the adhesive layer were obtained respectively through Double Cantilever Beam (DCB) and End Notched Flexure (ENF) tests. Cohesive failure was achieved by grit blasting the adherents followed by cleaning with acetone. A constant adhesive thickness was guaranteed by placing nylon fishing lines between the adherents. Single lap joints tests showed that the joint resistance decrease with increasing adhesive thickness.

La finalité de cette thèse est d’étudier la pertinence et les limites des méthodes de vision 3D couplées à une caméra ultra-rapide pour la mesure de champs vibratoires, sans contact et de manière synchrone, dans le domaine des fréquences associées à la vibro-acoustique. Un premier montage pseudo stéréoscopique, issu de la robotique, mobilisant un jeu de quatre miroirs afin de générer deux vues virtuelles à partir d’une seule caméra réelle, a été testé sur une plaque et un haut-parleur. Les résultats, validés par comparaison avec ceux obtenus avec un vibromètre laser, attestent de la pertinence de l’approche en dépit des contraintes liées aux éléments optiques. Dans une logique de simplification, trois autres montages ont alors été proposés et testés, permettant de concevoir deux techniques de mesure de vibration plein champ et une méthode itérative de rectification d’images (IRIs), adaptées au contexte. La méthode sans miroir utilise une ligne mathématique pour la triangulation et est fondamentalement adaptée à la mesure de vibrations mono-axiales d'objets globalement plans, affichant des déplacements non-répétables selon la normale de la surface ou selon un axe connu. La méthode à caméras asynchrones, quant à elle, utilise une caméra ultra-rapide et une caméra rapide, et permet la mesure de vibrations multi-axiales de phénomènes vibratoires 3D. Les résultats obtenus sur le capot d’une voiture et sur un haut-parleur attestent de son potentiel pour la caractérisation de panneaux ou le test qualité de fin de chaine d’assemblage de haut-parleurs par exemple. En conclusion, les trois protocoles de mesure et les résultats associés sont comparés afin de cibler leurs potentialités et limites respectives dans le contexte de la mesure de vibrations. / The objective of this Ph.D is to study the relevance and limits of 3D vision methods coupled to high-speed cameras and applied to non-contact synchronous vibration measurement, in the vibro-acoustic range of frequencies. A first pseudo stereoscopic set-up, taken from robotics, using a four-mirror adapter in order to generate two virtual viewpoints from a single real camera, has been tested on a plate and a loudspeaker. The results, validated by comparison with those obtained with a laser vibrometre, prove the relevance of the approach, despite some constraints related to the optical elements. In a logic of simplification, three other set-ups have then been proposed and tested, allowing designing two full-field vibration measurement techniques and a method for the Iterative Rectification of Images (IRIs), adapted to the context. The no-mirror method uses a mathematical line to triangulate positions and is basically suited to measure the single-axis vibrations of globally plane objects, displaying non-repeatable displacements along the normal of the surface or along a known axis. The asynchronous cameras technique requires a high-speed and an industrial camera used simultaneously to measure the multi-axis displacements of 3D vibratory phenomena. The results obtained on a car bonnet and a loudspeaker prove its potential to characterise large panels or to carry out end-of-line testing of loud-speakers for example. In conclusion, the three measurement protocols and the associated results are compared in order to assess their respective potentialities and limits in the context of vibration measurement.

La formulation de nouveaux adhésifs durant les dernières décennies a permis de développer des procédés de collage innovants pour l’industrie du bois. Dans cette optique, le collage du bois à l’état vert permet de créer une chaîne d’élaboration de matériaux techniques, sans ruptures de charges dans le processus industriel grâce à un séchage en fin de cycle. Or le collage implique un retrait empêché des assemblages au cours du séchage, induisant un développement de contraintes. À ce jour, de nombreuses études numériques portant sur le comportement du bois collé soumis à des variations hydriques ont été effectuées, sans pour autant avoir été mises en relation avec des études expérimentales. L’extension récente des techniques de corrélation d'images permet d'effectuer des mesures de champs sans contact, particulièrement adaptées à un matériau hygroscopique tel que le bois. L’objectif de la thèse est d’appréhender par des approches expérimentale et numérique les contraintes hydromécaniques qui peuvent survenir dans des assemblages contrecollés. Une expérimentation, permettant de mesurer les champs durant le séchage a été mise en place. Le modèle numérique retenu est un modèle élastique orthotrope, permettant de prendre en compte la morphologie du matériau bois. Nous pouvons identifier les paramètres gouvernant les mécanismes d'endommagement du joint de colle et proposer des conditions de mise en œuvre optimisant la tenue de l'assemblage au séchage. / The development of new adhesives during the last decades has implied radically changes in the sawmill industry. The gluing of unseasonned wood, called green gluing, allows a new order in the process of engineered wood products, thanks to the final position of the drying step. Nevertheless, the jointing prevents the free shrinkage of wood during the mass transfer, involving a stress development. Nowadays, numerous drying models have been developed to predict the deformations and stresses of wood, but few have been confirmed by experimental tests. For an organic material such as wood, the measurement of hygromechanical properties will be more efficient if there is no interaction between the material and the measurement system. One of the most promising experimental techniques for this kind of issue is noncontact optical measurement based on Digital Image Correlation principles. The objective of this study is to evaluate by experimental and numerical solutions the stress development in green-glued wood laminated timber subjected to drying conditions. An experimental method has been set up and the results allow to validate a numerical finite elements model. The model which has been chosen is an orthotropic elastic model, able to describe the morphology of the wood material. This study allows to identify the parameters governing the damage of the interface. This approach leads to suggest some preconizationsin order to optimize the behavior of product during the drying procedure.

Artificial Neural Networks (ANNs) can be viewed as a mathematical model to simulate natural and biological systems on the basis of mimicking the information processing methods in the human brain. The capability of current ANNs only focuses on approximating arbitrary deterministic input-output mappings. However, these ANNs do not adequately represent the variability which is observed in the systems’ natural settings as well as capture the complexity of the whole system behaviour. This thesis addresses the development of a new class of neural networks called Stochastic Neural Networks (SNNs) in order to simulate internal stochastic properties of systems. Developing a suitable mathematical model for SNNs is based on canonical representation of stochastic processes or systems by means of Karhunen-Loève Theorem. Some successful real examples, such as analysis of full displacement field of wood in compression, confirm the validity of the proposed neural networks. Furthermore, analysis of internal workings of SNNs provides an in-depth view on the operation of SNNs that help to gain a better understanding of the simulation of stochastic processes by SNNs.

For years, the modelling of the brain tissue has been widely investigated. Indeed, a biomechanical model of the brain would find applications in fields like image-guided neurosurgery or safety system design (helmets, car manufacturing, security fences design,...). In the present thesis, we propose an original, fractional calculus-based, constitutive equation of the brain tissue. Different types of experiments (unconfined compression, relaxation and cyclic tests) were carried out in order to characterize the mechanical behaviour of the brain tissue. The use of the digital image correlation enabled us, for the first time to our best knowledge, to prove the incompressibility of the brain tissue, a widespread assumption. The constitutive model was calibrated and validated using these experiments. The agreement between the model and the experimental results is very satisfactory. The model reproduces with only a few percent error the stress-strain curves for the compression tests at three different loading rates covering two orders of magnitude as well as the behaviour in the relaxation and cyclic tests. La modélisation du tissu cérébral fait l'objet de nombreuses recherches depuis quelques années. En effet, un modèle biomécanique du cerveau trouverait des applications dans le domaine de la neurochirurgie guidée par l'image et chez les fabricants de système de sécurité (casques, automobiles, barrières de sécurité,...). Dans cette thèse, nous proposons un modèle d'équation constitutive original pour le tissu cérébral basé sur l'utilisation des dérivées d'ordre réel arbitraire (aussi connues sous le terme de dérivées fractionnaires). Divers types d'essais (compression, relaxation et essais cycliques) ont également été réalisés afin de caractériser le comportement mécanique du tissu cérébral. L'utilisation de la corrélation d'images numériques a permis, pour la première fois à notre connaissance, de démontrer expérimentalement son incompressibilité, justifiant ainsi une hypothèse couramment rencontrée. La loi constitutive développée a été calibrée et validée à partir de ces essais. L'accord entre le modèle et les résultats expérimentaux est très satisfaisant en ce qui concerne le comportement en compression à trois vitesse de déformation différentes s'étalant sur deux ordres de grandeur. Il en va de même pour les comportements en relaxation et lors des essais cycliques.

Currently, the maintenance and repair of civil engineering infrastructures (especially bridges and highways) have become increasingly important, as these structures age and deteriorate. Interface between two different mixes or strengths of concrete also appear in large concrete structures involving mass concreting such as dams, nuclear containment vessels, cooling towers etc., since joints between successive lifts are inevitable. These joints and interfaces are potential sites for crack formation, leading to weakening of mechanical strength and subsequent failure. In case of a bi-material interface, the stress singularities are oscillatory in nature and the fracture behavior of a concrete-concrete bi-material interface is much more complicated. A comprehensive experimental work has been undertaken for characterization of the behavior of different concrete-concrete interfaces under static and fatigue loading. The effect of specimen size on the concrete-concrete interfaces is studied and the non-linear fracture parameters such as fracture energy, mode I fracture toughness, critical crack tip opening displacement, critical crack length, length of process zone, brittleness number, size of process zone, crack growth resistance curve and tension softening diagram. These parameters are required for modeling the concrete-concrete interfaces in non-linear finite element analysis. Presently, the advanced non-destructive techniques namely acoustic emission, digital image correlation and micro-indentation have great capabilities to characterize the fracture behavior. The damage in plain concrete and concrete interface specimens is characterized both qualitatively and quantitatively using acoustic emission technique by measuring the width of fracture process zone and width of damage zones. The DIC technique is used to obtain the fracture parameters such as mode I and mode II fracture toughness and critical energy release rate. The micro-mechanical properties are obtained by performing depth-sensing micro-indentation tests on the concrete-concrete interfaces. Civil engineering structures such as long-span bridges, offshore structures, airport pavements and gravity dams are frequently subjected to variable-amplitude cyclic loadings in actual conditions. Hence, in order to understand the fracture behaviour under fatigue loading, the fatigue crack growth in plain concrete and concrete-concrete interface is also studied using the acoustic emission technique. An attempt is made to apply the Paris’ law, which is applicable to mechanical behaviour of metals, for acoustic emission count data. All these studies show that, as the difference in the compressive strength of concrete on either side of the interface increases, the load carrying capacity decreases and the fracture parameters indicate the increase in the brittleness of the specimens. It is concluded that the repair concrete should be selected in such a way that its elastic properties are as those of the parent concrete.

Accurate three-dimensional stress-strain constitutive properties are essential to understanding complex deformation and failure mechanisms for materials with highly anisotropic mechanical properties. The large number of different methods and specimen types currently required to generate three-dimensional allowables for structural design slow down the material characterization. Also, some of the material constitutive properties are never measured due to prohibitive cost of the specimens needed. A method for measurement of three-dimensional constitutive properties using short-beam specimens subject to three-point bend load has been recently developed. This method is based on the Digital Image Correlation (DIC) full-field deformation measurement and closed-form stress approximation. The purpose of this work is to improve the accuracy of the constitutive properties through accurate stress solution. A method is developed based on a combination of full-field strain measurement and nonlinear finite element stress analysis in the material characterization. The nonlinear shear stress-strain relations are the major concern in this work. An iterative procedure is applied to update the nonlinear shear properties using iterative finite element simulations. The accuracy of the numerical procedure is verified by comparing the finite element strain results with full-field measurements. The procedure is further verified using the V-notched beam test results. Excellent agreement has been achieved in the verification. Simplicity of the short-beam specimens and accuracy of the constitutive property approximations make the present method attractive for measurement of three-dimensional stress-strain relations for anisotropic materials at various load rates.

Une des méthodes les plus populaires et largement utilisée pour l’amélioration des sols compressibles est la technique d'inclusions rigides verticales qui constitue une alternative intéressante aux techniques plus traditionnelles telles que le pré-chargement, la mise en place de drains verticaux, le remplacement du sol en place, etc.Le Projet National ASIRI (Amélioration du Sol par Inclusions Rigides) a permis d’apporter des réponses sur le comportement de cette technique de renforcement et d’établir des recommandations de dimensionnement et de réalisation. Celui-ci comprend un volet expérimental (expérimentations en vraie grandeur, modèles physiques réduits à 1g, études en chambre d’étalonnage) et un volet numérique. Cependant, les recommandations publiées par ASIRI sont limitées aux cas de chargement monotone. Pourtant, différents cas de structures sous chargement cyclique sont couramment rencontrés dans la pratique: chargement des vagues sur les structures offshore, force du vent, charge sismique, la charge de trafic, remplissage et vidange de réservoirs, chargement et déchargement des zones de stockage… Cela nécessite alors de comprendre le comportement sous chargement cyclique et/ou dynamique de ces ouvrages.Ce travail de thèse constitue une contribution à la compréhension du comportement de ce type d’ouvrage, et s’intéresse plus particulièrement à la modélisation des mécanismes qui se développent dans le matelas de transfert de charge lors d’un chargement cyclique vertical quasi-statique. Il se fait suivant deux approches complémentaires : Expérimentale : par des essais sur un nouveau modèle physique réduit tridimensionnel à 1g et à l’échelle 1/10ème, Numérique : par la modélisation numérique tridimensionnelle en milieu continu utilisant le logiciel FLAC3D.Dans un premier temps, le travail expérimental réalisé nous a permis d’étudier le comportement de cette technique de renforcement sous chargement monotone et cyclique mettant en œuvre la méthode de corrélations d’images. La modélisation physique réalisée nous a permis d’étudier l’influence de l’épaisseur de la plateforme de transfert de charge granulaire et des conditions aux limites (cas remblai/cas dallage).Dans un deuxième temps, les résultats expérimentaux nous ont servi comme une base de données pour la validation d’un modèle numérique en milieu continu. La première étape de la modélisation numérique consiste à valider un modèle numérique à la même échelle réduite du modèle physique. La validation de l’approche de modélisation numérique à échelle réduite nous a permis, dans une deuxième étape, de réaliser une étude paramétrique afin de déterminer l’influence des différents paramètres sur le comportement du système. / One of the most popular and widely used methods for soft soil improvement is the reinforcement using vertical rigid inclusions. It constitutes an interesting alternative to the other traditional techniques such as preloading, vertical drains, replacing soil etc...The national French project ASIRI (Amélioration du Sol par Inclusions Rigides) allowed to provide answers about the behavior of this technique and to establish recommendations for design and construction. It included an experimental part (full-scale, 1g physical model experiments and calibration chamber studies) and a numerical part. However, the recommendations established by ASIRI are limited to the case of monotonic loading. Yet, various cases of structures under cyclic loading are commonly encountered in practice: waves loading on offshore structures, wind strength, seismic load, traffic load, filling and emptying of tanks, loading and unloading of storage areas... This then requires the understanding of the behavior of this technique under cyclic and/or dynamic loading.The work done in this thesis constitutes a contribution to understanding the behavior of this type of structures, and is particularly interested in modeling the mechanisms that develop in the load transfer mattress under a quasi-static vertical cyclic loading . Two complementary approaches have been followed: Experimental: by performing experimental tests using a new 1g tridimensional physical model with a scale factor of 1/10, Numerical: by performing numerical tridimensional simulations in a continuous media using the software FLAC3D.At first, the experimental work has allowed us to study the behavior of this reinforcement technique under monotonic and cyclic loading implementing the digital image correlation method. A parametric study performed with the physical modeling allowed us to study the influence of the granular load transfer platform (LTP) and the boundary conditions (presence of a rigid slab at the surface of the LTP).Secondly, the experimental results have served as a database for the validation of a numerical model in continuous medium. The first step of the numerical modeling is to validate a numerical model at the same reduced scale of the physical model. The validation of the numerical modeling approach at the reduced scale allowed us in a second step to perform a parametric study in order to determine the influence of different parameters on the behavior of the system.

Cette thèse présente une étude expérimentale des mécanismes contrôlant la réponse macroscopique d’une interface sable-pieu sous sollicitations axiales monotones et cycliques. Une approche innovante associant la tomographie rayons X à des outils avancés d’analyses d’images en trois dimensions (3D) est utilisée dans le but d’extraire des informations à différentes échelles, notamment à l’échelle micro. L’analyse quantitative du comportement individuel des grains situés au voisinage du pieu fournit une collection de données 3D qui pourraient être utilisées pour la validation de modèles numériques ou théoriques.Une série de tests est réalisée sur un pieu instrumenté à pointe conique installé par vérinage monotone dans un échantillon dense de sable calcaire. Après l’installation, le pieu est soumis à un grand nombre de cycles axiaux contrôlés en déplacements (jusqu’à 2000 cycles), à contraintes constantes. Ces essais ont été conduits dans une mini chambre de calibration qui permet d’acquérir des tomographies rayons X à haute résolution après différentes étapes de chargement. Il est admis que le dispositif expérimental n’est pas représentatif des conditions d’essais sur pieux in-situ pour les raisons principales suivantes : le ratio entre le diamètre de la chambre le diamètre du pieu et le ratio entre le diamètre du pieu et la taille moyenne des grains sont bien inférieurs aux ratios recommandés dans la littérature afin de limiter les effets d’échelle. Par conséquent, les résultats obtenus dans ce travail ne peuvent et ne doivent pas être directement extrapolés pour le design de pieux réels. Cependant, un tel dispositif permet de reproduire qualitativement des tendances similaires à celles observées à l’échelle macro sur des essais à grande échelle et d’observer des mécanismes se déroulant à l’échelle micro.Les images 3D obtenues par reconstruction des tomographies rayons X sont utilisées afin d’identifier et de suivre l’évolution des grains individuels. Le champ cinématique complet en 3D est mesuré grâce à un code de corrélation d’images numériques 3D (DIC), « TomoWarp2 ». Des outils de traitement d’image sont également employés pour suivre les changements de porosité et la production de fines par broyage des grains à l’interface.Pendant la mise en place du pieu, plusieurs zones où les déplacements se concentrent sont identifiées. Une recirculation des grains le long du fût du pieu est mise en évidence. Globalement, le sable a un comportement dilatant à l’exception d’une fine couche (épaisseur d’environ 3 à 4·D50) autour du pieu où les fines sont produites. Pendant les cycles, la réponse macroscopique de l’interface montre une évolution en deux phases, avec une augmentation non négligeable de la résistance du fût dans la seconde phase. Pour ces deux phases, la mesure de la cinématique granulaire révèle un comportement du sol différent associé à une densification importante à l’interface. Dans la première phase, le sol se contracte radialement dans une zone de 4·D50 d’épaisseur. Ce phénomène est certainement dû au réarrangement granulaire mesuré par DIC. Dans la seconde phase, les grains de sables se déplacent difficilement et la densité à l’interface atteint un seuil pour lequel le frottement sur le pieu augmente de manière significative. / This doctoral work presents an experimental investigation into the mechanisms governing the macroscopic response of sand-pile interface during monotonic installation and subsequent axial cyclic loading. An innovative approach combining x-ray tomography and advanced image analysis tools is employed to extract information at different scales, including the micro-scale. A quantitative analysis of the behavior of individual sand grains in the vicinity of the pile offers valuable three-dimensional (3D) data set against which theoretical or numerical approaches could be tested.A series of tests is run on an instrumented close-ended conical model pile installed by monotonic jacking in a dense calcareous sand sample. Following the installation, the model pile is submitted to a large number of axial displacement-controlled loading cycles (a few thousands cycles) under constant normal stress. The tests are performed in a mini-calibration chamber that allows the acquisition of high resolution x-ray images at different stages of the loading. The chamber is admittedly not representative of field pile testing conditions for the main following reasons: the calibration chamber-to-pile diameter ratio and the sand particle-to-pile diameter ratio are far below the ratios recommended in the literature to limit scale effects on the interface response. Consequently, the results presented in this work can not, and should not, be directly extrapolated to field pile design. Yet, such a setup is able to reproduce qualitatively trends that are similar to those obtained at the macro-scale on large-scale experiments and allows the observation of full-field mechanisms taking place at the micro-scale.3D images resulting from the reconstruction of the x-ray scans are used to identify and follow the evolution of individual sand grains. Full-kinematics are measured thanks to a 3D Digital image Correlation (DIC) code, “TomoWarp2”. Image processing tools are also employed to measure local porosity changes and the production of fines by grain crushing at the interface.During pile installation, different zones where grains displacements concentrate are identified. A recirculation of the grains alongside the pile is also observed. Globally, the sand mass exhibits a dilative behavior except within a relatively thin layer (about 3 to 4·D50 thickness) around the model pile where grain crushing occurs. During subsequent loading cycles, the macroscopic response of sand-pile interface shows a two-phases evolution, with a non negligible increase of shaft resistance in the latter phase. For these two phases, the measurement of grain kinematics reveals a different behavior of the sand mass associated with a significant densification at the interface. In the first phase, the sand mass contracts radially within a region of thickness 4·D50. This mechanism is likely due to inter-granular rearrangement as measure by DIC. In the second phase, sand grains hardly move and the sand mass reaches a threshold density for which the friction on the shaft starts to increase substantially.

This thesis is concerned with the evaluation, in-situ, of the elastic strain energy release rate of cracks. This can define the criteria for crack propagation, and it is usually necessary to obtain this via calculation from the geometry and applied load. A new method is proposed, based on the conjoint use of digital image correlation to measure full-field displacements and finite element to extract the strain energy release rate of surface cracks. It has been extended to 3-D datasets with the use of digital volume correlation and tomographic imaging. A finite element model with imported full-field displacements measured by DIC/DVC acting as boundary conditions is solved and the J-integral is calculated. For linear elastic materials, modal contributions can be separated via the interaction integral. The method has been benchmarked using synthetic datasets to assess its sensitivity to noise and experimental uncertainties. It is very robust to experimental noise and can be used without knowledge of the specimen geometry and applied loads. The application of the method in 2-D is demonstrated in an analysis of experimental data for a mode I fatigue crack, introduced to an aluminium alloy compact tension specimen. Analysis of mixed-mode cracks in 2-D is shown on a PMMA sample with the Arcan geometry. In 3-D, static loading of a fatigue crack in nodular graphite cast iron is studied and the results from the method are compared with those obtained via a field-fitting approach. Diffraction analysis of polycrystalline materials can determine the full tensor of the elastic strains within them. Maps of elastic strains can thus be obtained typically using synchrotron X-rays or neutrons. A method is presented to calculate the elastic strain energy release rate of a crack from 2-D diffraction strain maps. The diffraction data is processed via a finite element approach to obtain the parameters required to calculate the $J$-integral. A validation is presented using a synthetic dataset from a finite element model. Its experimental application is demonstrated in an analysis of synchrotron X-ray diffraction strain maps of a propagating fatigue crack in a bainitic steel, before and after an overload. Finally, a complex case study of stable fracture propagation in polygranular isotropic nuclear graphite is presented. Synchrotron X-ray tomography and strain mapping by diffraction were combined with DVC and image analysis to extract the full-field displacements and elastic crystal strains. The displacement fields have been analysed using the developed methods to extract the critical strain energy release rate for crack propagation. Non-linear properties described the effect of microcracking on the elastic modulus in the fracture process zone. The analysis was verified by comparison of the predicted and measured elastic strain fields.