Made available in DSpace on 2016-12-08T15:56:18Z (GMT). No. of bitstreams: 1 Rinaldo Puff.pdf: 11901534 bytes, checksum: 902429cd8bc8c70d6eae9029243c8969 (MD5) Previous issue date: 2015-07-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This thesis was motivated by the study of voids and non-metallic inclusions influence on the high cycle fatigue of ferrous materials like steel, powder metal and gray cast iron. A second objective was to obtain simpler parameters, like the ones measured in hardness, static bending or axial tests, to evaluate materials in early phases of projects, in a way to avoid long fatigue tests. Initially the average fatigue strength was obtained for a high carbon steel. The effect of a silicon oxide inclusion near the surface on the performance of heavy-duty Cr-Si spring wire was also analyzed. The evaluation was done in terms of stress concentrating on the inclusion contours, due to the shot peening application on the surface and normal fluctuating loads. Mechanical properties of powder metal and cast iron were revised. Static tests without and with the presence of notches were performed, with the objective of obtaining a static notch sensitivity factor, to correlate with torsion fatigue results. The relation between hardness and torsion fatigue strength was evaluated for the cast iron, and simulations using linear elastic and nonlinear materials were performed to obtain geometric stress concentrating factors. A mesoscale simulation was done in plane stress, making it possible to evaluate local stress concentration in the cast iron matrix. / Esta tese foi motivada pelo estudo da influência de vazios e inclusões não metálicas na fadiga de alto ciclo de materiais ferrosos como aços, materiais obtidos por metalurgia do pó e ferros fundidos cinzentos. Foi objetivo também, avaliar parâmetros de medição mais simples, como os obtidos de ensaios de dureza e de flexão ou tração estáticos, como forma de avaliar materiais em fases iniciais de projeto, evitando-se longos ensaios de fadiga. Inicialmente obteve-se a resistência à fadiga de alto ciclo de um aço de alto teor de carbono. Analisou-se também o efeito da presença de uma inclusão de óxido de silício próximo à superfície de um arame de aço Cr-Si utilizado em molas submetidas a cargas reversas. A análise foi feita em termos de concentração de tensão nos contornos da inclusão, devido à aplicação de shot peening na superfície e também devido às cargas de operação. Uma revisão de propriedades mecânicas de aços obtidos por metalurgia do pó e do ferro fundido foi realizada, assim como ensaios estáticos sem e com entalhe, no intuito de obter um fator de sensibilidade ao entalhe estático, como forma de correlacionar com a sensibilidade ao entalhe na fadiga em torção. Foi avaliada a relação entre a dureza do ferro fundido e a sua resistência à fadiga na torção e realizadas simulações com material linear elástico e não linear para obter um fator de concentração de tensão geométrico. Uma simulação em mesoescala em estado plano de tensão foi realizada, podendo-se determinar a concentração de tensões locais na matriz do ferro fundido.

The presence of notches or cracks causes stresses to amplify in nearby regions. This phenomenon is studied by estimating the Stress Concentration Factor (SCF) for notches, and the Stress Intensity Factor (SIF) for cracks. In the present work, a semi-analytical method under the framework of linear elasticity is developed to give an estimate of these factors, particularly for cracks and notches in finite domains. The solution technique consists of analytically deriving a characteristic equation based on the general solution and homogeneous boundary conditions, and then using the series form of the reduced solution involving the (possibly complex-valued) roots of this characteristic equation to satisfy the remaining non-homogeneous boundary conditions. This last step has to be carried out numerically using, say, a weighted residual method. In contrast to infinite domain problems where a fully analytical solution is often possible, the presence of more boundaries, and a variety in configurations, makes the solution of finite do-main problems much more challenging compared to infinite domain ones, and these challenges are addressed in this work. The method is demonstrated on several classical and new problems including the problems of a semi-circular edge notch in a semi-infinite and finite plate, an elliptical hole in a plate, an edge-crack in a finite plate etc.

A armadura de tração de dutos flexíveis é a camada responsável por suportar as cargas axiais destes equipamentos em campo. Com a tendência de aumento das profundidades de exploração e produção de petróleo offshore, principalmente dos campos do pré-sal brasileiro, faz-se necessário o uso de materiais com desempenho superior. Este trabalho buscou avaliar e comparar dois aços de alta resistência mecânica para tal aplicação, um predominantemente perlítico e outro martensítico. Durante a vida em serviço destes componentes, eles sofrem tensões axiais cíclicas associadas ao processo de corrosão, que gera pites como concentradores de tensões. Considerando estes aspectos, os materiais foram avaliados segundo seu comportamento à fadiga sem e com a presença de um pequeno defeito conhecido, que atua como um entalhe e busca simular um pite de corrosão. Além disso, esses materiais foram caracterizados metalúrgica e mecanicamente e sua tenacidade à fratura foi estimada via o método do CTOD. A partir dos dados experimentais, foi quantificada a sensibilidade ao entalhe, guiada essencialmente pelo processo de iniciação de trinca, ao passo que a tenacidade à fratura não foi decisiva. O material martensítico apresentou desempenho superior em fadiga e menor sensibilidade ao entalhe e mostrou-se promissor para a aplicação como arame da armadura de tração. / The tensile armor of flexible pipes is the layer responsible for support axial loads of this equipment in field. With the trend of deep increase in offshore oil exploration and production, mainly in pre-salt fields, the use of materials with high performance becomes necessary. The aim of this dissertation is evaluate and compare two high strength steels for such application, one with perlite and other with martensitic matrix. During service life of these components, they are damaged by cyclic loading associated with corrosion process which promote corrosion pits like stress concentrators. Considering these aspects, the materials were evaluated according their fatigue behavior with and without a small defect that act as a notch and simulates a corrosion pit. In addition, they were characterized metallurgical and mechanically and their fracture toughness was estimated through CTOD test. From experimental data, notch sensitivity was quantified. This was driven by initiation process, and fracture toughness was not decisive. The martensitic material showed higher fatigue performance and lower notch sensitivity and presented itself promising for tensile armor wire application.

A armadura de tração de dutos flexíveis é a camada responsável por suportar as cargas axiais destes equipamentos em campo. Com a tendência de aumento das profundidades de exploração e produção de petróleo offshore, principalmente dos campos do pré-sal brasileiro, faz-se necessário o uso de materiais com desempenho superior. Este trabalho buscou avaliar e comparar dois aços de alta resistência mecânica para tal aplicação, um predominantemente perlítico e outro martensítico. Durante a vida em serviço destes componentes, eles sofrem tensões axiais cíclicas associadas ao processo de corrosão, que gera pites como concentradores de tensões. Considerando estes aspectos, os materiais foram avaliados segundo seu comportamento à fadiga sem e com a presença de um pequeno defeito conhecido, que atua como um entalhe e busca simular um pite de corrosão. Além disso, esses materiais foram caracterizados metalúrgica e mecanicamente e sua tenacidade à fratura foi estimada via o método do CTOD. A partir dos dados experimentais, foi quantificada a sensibilidade ao entalhe, guiada essencialmente pelo processo de iniciação de trinca, ao passo que a tenacidade à fratura não foi decisiva. O material martensítico apresentou desempenho superior em fadiga e menor sensibilidade ao entalhe e mostrou-se promissor para a aplicação como arame da armadura de tração. / The tensile armor of flexible pipes is the layer responsible for support axial loads of this equipment in field. With the trend of deep increase in offshore oil exploration and production, mainly in pre-salt fields, the use of materials with high performance becomes necessary. The aim of this dissertation is evaluate and compare two high strength steels for such application, one with perlite and other with martensitic matrix. During service life of these components, they are damaged by cyclic loading associated with corrosion process which promote corrosion pits like stress concentrators. Considering these aspects, the materials were evaluated according their fatigue behavior with and without a small defect that act as a notch and simulates a corrosion pit. In addition, they were characterized metallurgical and mechanically and their fracture toughness was estimated through CTOD test. From experimental data, notch sensitivity was quantified. This was driven by initiation process, and fracture toughness was not decisive. The martensitic material showed higher fatigue performance and lower notch sensitivity and presented itself promising for tensile armor wire application.

Ao longo deste trabalho foi proposta uma nova rota de tratamento térmico para o aço AISI 52100, principal material utilizado na fabricação de rolamentos. Esta nova rota visa refinar a microestrutura de carbonetos presentes no material, com o objetivo de otimizar as propriedades mecânicas. Os tratamentos térmicos realizados conduziram a uma diminuição no tamanho dos carbonetos quando comparados com a amostra tradicional. Para medir a tenacidade à fratura evitando a dificuldade experimental de se nuclear pré-trincas em materiais frágeis, foi utilizada a metodologia Chevron, como formalizada na ASTM E-1304(97). Algumas das amostras submetidas a nova rota apresentaram maior tenacidade à fratura quando comparadas a amostra tratada na rota convencional. O material tratado na nova rota de tratamento térmico foi avaliado também em ensaio de impacto, usando-se corpos de prova Charpy de secção reduzida, sem entalhe. Os resultados obtidos mostraram que o material com carbonetos mais finos apresentavam menor energia absorvida no impacto quando comparados com a amostra tratada na rota convencional. Este comportamento a princípio contraditório foi explicado pela maior presença de sítios de nucleação na amostra com carbonetos mais finos. A maior densidade de sítios nas condições do ensaio de impacto conduziu a uma intensificação da nucleação de trincas, levando a uma menor energia absorvida durante o ensaio de impacto; este efeito ocorre mesmo quando o mecanismo de nucleação de trincas envolve a nucleação e coalescimento de microcavidades. Procurou-se fazer uma correlação entre a morfologia das superfícies de fratura obtidas no ensaio Chevron, o tamanho do carboneto das amostras e o micromecanismo atuante. Para amostras com superfície de fratura com aspecto fibroso foi associado o micromecanismo de fratura controlado por deformação. Para amostras com superfície de fratura com aspecto intergranular foi associado o micromecanismo de fratura controlado por tensão. / This work proposes a new heat treatment route for AISI 52100 steel, the most used material for bearings. The new route is designed so as to refine the carbides distribution in material, with the aim of increasing the fracture toughness. In order to measure the fracture toughness a Chevron notch methodology was used, as described in ASTM E-1304(97). Obtaining a static pre-crack on brittle materials is difficult and expensive; the Chevron notch methodology allows avoiding this difficulty. The heat treatments reduced the carbide sizes as compared with conventionally heat-treated steels. Some samples treated by this new route presented an increase in Chevron notch fracture toughness. The materials treated by the new heat treatment route were also tested in impact using a subsize Charpy specimen, without notch. Materials with fine carbides presented less dissipated energy in impact test then the material conventionally treated. This behavior is associated with the increase in number of carbide particles, as second phase particles are known to behave as sites for microvoid initiation and growth. The higher density of such sites presented in the material with fine carbides enhance this mechanism, lowering the dissipated energy measured in impact test. A correlation between fracture morphology, carbide size and fracture mechanisms was attempted. Samples with fine carbides presents fibrous transgranular fracture morphologies with strain controlled fracture micromechanism while samples with coarse carbides presented intergranular type morphologies with stress controlled micro-mechanism.

As ligas Ti-??constituem um grupo promissor de ligas de titânio em termos de processamento, propriedades e aplicações potenciais. Além do projeto da liga em termos de composição, a obtenção de microestruturas adequadas por meio de tratamentos térmicos é necessária para otimizar o balanço entre resistência mecânica e tenacidade. O presente trabalho teve por objetivo estudar o comportamento em fadiga de alto ciclo da liga Ti-13V-11Cr-3Al, uma liga de alta resistência mecânica destinada ao emprego na indústria aeroespacial, sob duas condições de tratamento. O material foi recebido na forma de barras com 7,6 mm de diâmetro, apresentando microestrutura composta por grãos alongados e propriedades em tração combinando alto limite de resistência (1.479 MPa) e razoável ductilidade (deformação verdadeira de fratura igual a 0,217). O material foi tratado termicamente em duas condições: recozimento a vácuo a 750?C por 1 h com resfriamento lento, e tratamento flash em banho de sal a 650?C por 6 min, com posterior têmpera em água. O tratamento flash resultou em melhor combinação de resistência mecânica e ductilidade, avaliadas pelo ensaio de tração. O estudo da resistência à fadiga baseou-se na obtenção de curvas ?/N por meio de ensaios de flexão rotativa (R = -1) empregando-se corpos de prova do tipo viga em balanço. Para cada condição microestrutural, foram obtidas duas curvas ?/N, uma com amostras polidas e outra empregando-se corpos de prova com concentradores de tensão geométricos (entalhes), visando avaliar a sensibilidade ao entalhe desta liga nas duas condições microestruturais. O material submetido ao tratamento flash apresentou maior dispersão e menor resistência à fadiga, comparado ao material recozido; no entanto apresentou também menor sensibilidade ao entalhe em vidas longas (106 ciclos). O trabalho foi complementado por exames fractográficos para a identificação dos pontos de iniciação da fratura. / The Ti-??alloys are a promising group of titanium alloys in terms of processing, properties and potential applications. In order to achieve the optimum balance between strength and toughness it is necessary, besides determining a proper composition in the alloy design, to obtain suitable microstructures by means of thermo-mechanical process and heat treatment. This study aimed to assess the high cycle fatigue behavior of Ti-13V-11Cr- 3Al alloy, a high-strength alloy intended for use in the aerospace industry. The material was received in the form of bars with 7.6 mm in diameter, whose microstructure comprises elongated grains and whose mechanical properties combines high tensile strength (1,479 MPa), and reasonable ductility (true strain fracture equal to 0.217). The material was heat treated in two conditions: vacuum annealing at 750?C for 1 h with slow cooling, and flash 650?C salt bath for 6 min with subsequent water quenching. The study was based on obtaining ??/ N curves through by rotary bending (R = -1) fatigue tests employing cantilever beam specimens. For each microstructural condition, two ??/ N curves were obtained, the former with smooth samples and the latter employing specimens with geometric stress concentrators (notches), to evaluate the notch sensitivity of this alloy in both microstructural conditions. The material subjected to flash treatment showed greater dispersion and lower fatigue strength compared to annealed; however also showed lower notch sensitivity at long life (106 cycles). The study was complemented by fractographics analysis to identify the fracture initiation points.

Les propriétés centrales des cellules souches sont la pluripotence et la capacité d'auto-renouvellement. Les cellules souches hématopoïétiques (CSHs) sont dotées de ces caractéristiques qui leur permettent de générer toutes les cellules du compartiment hématopoïétique, tout en maintenant en parallèle leur compartiment. Nous menons des approches visant à amplifier ex vivo les CSHs en les activant par HOXB4 exogène (CSHs humaines) ou via la signalisation Notch/DLL-4 (CSHs murines). Or deux analyses transcriptomiques indépendantes de ces deux modes d'activation ont de manière étonnante convergé sur une augmentation de l'expression de deux gènes jamais identifiés auparavant comme étant impliqués dans le maintien des CSHs : Pumilio1 (Pum1) et Pumilio2 (Pum2). Pum1 et Pum2 sont des régulateurs post-transcriptionnels appartenant à la famille Pumilio-FBF (PUF) des protéines liant l'ARN. Bien qu'il ait été établi que le rôle princeps de ces protéines PUF est de soutenir la prolifération des cellules souches chez les Invertébrés, jusqu'à présent on ne sait rien du rôle de Pum1 et Pum2 dans les CSH humaines et murines.Pour toutes ces raisons, nous avons étudié le rôle et les mécanismes d'action de Pum1 et Pum2 dans les CSH murines et humaines en utilisant l'interférence ARN (ARNi). L'invalidation de Pum1 ou de Pum2 dans les CSHs murines conduit à une réduction de l'expansion et du potentiel clonogénique ex vivo, associée à une apoptose accrue et l'arrêt du cycle cellulaire en phase G0/G1. L'invalidation concomitante de Pum1 et Pum2 majore ces effets ce qui suggère un effet coopératif entre les deux protéines. L'expansion et le potentiel clonogénique des CSH invalidées pour Pum1 sont restaurés suite à l'expression forcée de Pum1 (insensible au shRNA utilisé), validant ainsi la spécificité de nos shRNAs. Par contre la surexpression de Pum1 dans les CSHs invalidées pour Pum2 ne restaure pas leurs fonctions, soulignant le rôle non redondant de chaque protéine. En outre, lorsque les CSHs invalidées pour Pum1 ou Pum2 sont inoculées à des souris irradiées létalement de suivre le potentiel hématopoïétique à long terme, seules quelques rares cellules de la moelle osseuse issues des CSH KD pour Pum1 ou Pum2 sont mises en évidence après 4 mois de reconstitution, contrairement aux CSH contrôles. Des résultats identiques ont été obtenus en invalidant Pum1 ou Pum2 dans les CSH humaines.En conclusion, nos résultats démontrent l'implication des facteurs Pumilio dans le maintien du potentiel souche, l'expansion et la survie des CSHs murines et humaines. L'identification des facteurs Pumilio et de leurs cibles comme nouveaux régulateurs des CSHs permettra d'envisager de nouveaux outils en vue de perspectives thérapeutiques. / The central properties of stem cells are the pluripotency and the capacity of self-renewal. Hematopoietic stem cells (HSCs) posses such common features that allows them to generate all the cells of the hematopoietic compartments, maintaining in the same time the HSC pool. We develop approaches focused on ex vivo HSC expansion through activation by exogenous HOXB4 (human HSCs) or Notch/Dll-4 ligand (murine HSCs). Two independent transcriptomic analyses surprisingly converged toward an increased expression of two genes never identified sofar as crucial for HSC functions: Pumilio1 (Pum1) and Pumilio2 (Pum2). Pum1 and Pum2 are posttranscriptional regulators belonging to the Pumilio-FBF (PUF) family of RNA-binding proteins. Although it was established that the primordial role of PUF proteins is to sustain mitotic proliferation of stem cells in Invertebrates, so far nothing is known about the role of Pum1 and Pum2 in human and murine HSCs.For these reasons, we have investigated the roles and mechanisms of action of Pum1 and Pum2 in murine and human HSCs through shRNA strategy. Pum1 and Pum2 knockdown (KD) in murine HSCs led to a decreased HSC expansion and clonogenic potential ex vivo, associated with an increased apoptosis and a cell cycle arrest in G0/G1 phase. KD of both Pum1 and Pum2 enhanced these effects, suggesting a cooperative effect. Expansion and clonogenic potential of KD Pum1 HSCs were rescued by enforced expression of Pum1 (insensitive to our shRNA), thus validating the specificity of our shRNA. Enforced expression of Pum1 could not rescue the functions of Pum2 KD HSCs, highlighting the non-redundant role of these proteins. Furthermore, when Pum1 or Pum2 KD HSCs were inoculated into lethally irradiated mice to follow the long-term hematopoietic potential, only rare bone marrow cells derived from Pum1 and Pum2 KD HSCs were evidenced after 4 months, contrary to control HSCs. Identical results were obtained with human Pum1 or Pum2 KD HSCs.In conclusion, our results demonstrate the involvement of Pumilio factors in stemness maintenance, expansion and survival of murine and human HSCs. Identification of Pumilio factors and their targets as new regulators of HSCs expansion will allow consider them as new tools for therapeutic perspectives.

L'engagement des cellules vers un destin donné, ou détermination cellulaire, est un processus clé du développement. Quels sont les mécanismes qui sous-tendent la détermination cellulaire ? Pour aborder cette question, nous utilisons le lignage des soies mécanosensorielles de la drosophile. Dans ce lignage, la diversité des cellules résulte de l'activation différentielle de la voie Notch ainsi que la ségrégation asymétrique de déterminants cellulaire à chaque division. Cependant, comment la répétition d’un même mécanisme peut-elle être à l’origine des destins cellulaires différents ? D'autres facteurs doivent être impliqués dans ce processus. Afin des les identifier, mon intérêt s’est porté sur les facteurs de transcription de la superfamille Snail, connus pour être impliqués dans la détermination cellulaire au cours du développement de la drosophile.Deux membres de cette superfamille, Escargot (Esg) et Scratch (Scrt) sont exprimés dans le lignage des soies, en particulier dans les cellules neurales et leurs précurseurs. Des analyses de perte et de gain de fonction indiquent qu’Esg et Scrt, agissant de manière redondante, sont nécessaires pour le maintien de l'identité du précurseur secondaire neural. Des tests d’interaction génétique ont montré que ces facteurs agissent en interaction avec la voie Notch, probablement via la répression de l’expression des gènes cibles de la voie. De plus, Esg, mais pas Scrt, a un rôle supplémentaire lors de la formation du lignage des soies. La perte de fonction de ce facteur provoque un défaut de l’arborisation et de la croissance axonales. En outre, l'expression des gènes impliqués dans la différenciation neuronale, tels que Elav et Prospero, est altérée dans ce contexte, suggérant qu’Esg contrôle la différenciation neuronale en régulant l'expression de gènes clés de l’identité neuronale.Ensemble, mes résultats ont montré qu’Esg et Scrt participent à la mise en place de la diversité cellulaire dans le lignage des soies de la drosophile. / The commitment of cells to a given fate, or cell fate determination, is a key process in development. Cell type diversity arises from variations in this process. What are the mechanisms underlying cell determination and how is cell diversity achieved? In order to approach these questions, we use the Drosophila mechanosensory bristle lineage. In this lineage, cell diversity arises from the differential activation of the Notch pathway as well as the asymmetric segregation of cell fate determinants at each division. However, how does the repetition of the same mechanism trigger different cell fates? Other factors might be involved in cell fate commitment. In order to identify such factors, I focused my interest on the transcription factor of the Snail superfamily, known to be involved in cell determination during Drosophila development.Two members of this superfamily, escargot (esg) and scratch (scrt) are expressed in the bristle lineage, specifically in the inner neural cells and their precursor cells. Loss and gain of function analysis indicate that Esg and Scrt, acting redundantly, are necessary for the maintenance of the neural secondary precursor cell identity. A genetics interaction test showed that this role is achieved in interaction with the Notch pathway, probably through the repression of Notch target genes expression. Moreover, Esg, but not Scrt, has an additional role during the inner bristle cell formation. Loss of function of this factor induces a defect in neuronal differentiation, specifically axon growth and patterning. Moreover, the expression of genes involved in neuronal differentiation, such as elav and prospero, is impaired in this context. Altogether, these data suggests that Esg is involved in neuronal differentiation by regulating the expression of key neuronal genes.Together, my results showed that Esg and Scrt participate to the establishment of cell diversity in Drosophila bristle cell lineage.

The fractal-like finite element method (FFEM) is developed to compute stress intensity factors (SIFs) for isotropic homogeneous and bi-material V-notched plates. The method is semi-analytical, because analytical expressions of the displacement fields are used as global interpolation functions (GIFs) to carry out a transformation of the nodal displacements within a singular region to a small set of generalised coordinates. The concept of the GIFs in reducing the number of unknowns is similar to the concept of the local interpolation functions of a finite element. Therefore, the singularity at a notch-tip is modelled accurately in the FFEM using a few unknowns, leading to reduction of the computational cost.The analytical expressions of displacements and stresses around a notch tip are derived for different cases of notch problems: in-plane (modes I and II) conditions and out-of-plane (mode III) conditions for isotropic and bi-material notches. These expressions, which are eigenfunction series expansions, are then incorporated into the FFEM to carry out the transformation of the displacements of the singular nodes and to compute the notch SIFs directly without the need for post-processing. Different numerical examples of notch problems are presented and results are compared to available published results and solutions obtained by using other numerical methods.A strain energy approach (SEA) is also developed to extract the notch SIFs from finite element (FE) solutions. The approach is based on the strain energy of a control volume around the notch-tip. The strain energy may be computed using commercial FE packages, which are only capable of computing SIFs for crack problems and not for notch problems. Therefore, this approach is a strong tool for enabling analysts to compute notch SIFs using current commercial FE packages. This approach is developed for comparison of the FFEM results for notch problems where available published results are scarce especially for the bi-material notch cases.A very good agreement between the SEA results and the FFEM results is illustrated. In addition, the accuracy of the results of both procedures is shown to be very good compared to the available results in the literature. Therefore, the FFEM as a stand-alone procedure and the SEA as a post-processing technique, developed in this research, are proved to be very accurate and reliable numerical tools for computing the SIFs of a general notch in isotropic homogeneous and bi-material plates.

The aim of this thesis is the construction of a diagram of fracture strain for high strength steel OCHN3MFA and its application for the estimation of fracture toughness of this material. The first part of the thesis contains the necessary theoretical framework for numerical modelling of tensile tests of various specimens - smooth specimen, specimen with a notch and specimen with a circumferential crack, it describes the influence of triaxiality on the fracture of bodies and the possibilities of construction of the diagram of fracture strain. Subsequently, a numerical model of these specimens is created using the finite element method (FEM). A non-linear, elastoplastic calculation is performed. Fracture is identified by means of comparing the true stress versus the strain obtained from tests with the finite element analysis results. Stress–strain states of specimens at the moment of fracture are obtained from a numerical model. A diagram of fracture strain is constructed, and it is used to estimate the fracture toughness of a cracked body. Finally, a local approach, which uses the diagram of fracture strain, and a classical approach of fracture mechanics, especially the stress intensity factor, are compared.