In this talk, we will describe damage accumulation and failure of free-standing micro-cantilevers made of 7YSZ coatings during cyclic bending in a nanoindentation system in both, the as-sprayed condition as well as after low-temperature thermal cycling up to 700 oC while attached to the substrate. The technique has been established as a means of tracking elastic modulus, hysteresis/creep, and fracture behavior as a function of coating densification during isothermal treatment at high temperatures. In contrast, low-temperature thermal cycling is designed to simulate operating conditions during which crack healing and sintering, which are known to lead to stiffening, are minimal. The load-displacement curves typically display hysteretic behavior with an increasing permanent residual displacement (ratcheting) after each cycle which increases with an increase in load, accompanied by a reduction in stiffness that is characteristic of damage accumulation. Failure appears to result from the formation of macrocracks after a critical amount of ratcheting. The number of mechanical cycles to failure reduces with the number of prior thermal cycles and with increasing maximum load/stress. Thus, mechanical cycling can act as a proxy for thermal cycling in evaluating progressive damage accumulation in TBCs.
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This study proposes the new fracture model to assess the fracture toughness under complex loading mode subjected to cracked component on the brittle fracture toughness assuming combined stress state in plastic zone near crack-tip. This model newly considers non-linear energy release rate named Local-J as the elastic-plastic local fracture driving force for micro-crack nucleus in plastic zone. The effect of 3-dimentioinal combined stress state on local-J, which is different from the effect on the linear elastic energy release rate for Griffith crack, is formulated as the Local-J equivalent stress by conducting numerical analysis of unit-cell including a penny-shaped crack. Based on weakest link theory assuming this new model under combined stress field, Extended Weibull stress is derived as a new fracture parameter for cracked component. The characteristics of the proposal model is examined by predicting the critical load for pure mode II or III from fracture toughness assumed under pure mode I load. Fracture toughness assessed by this new model under mode II or III load is smaller than that assessed by conventional model. This result of numerical analysis implies the possibility of rational assessment of the effect of loading mode by applying the new model.
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Brittle failure by transgranular and intergranular mechanisms is commonly addressed by probabilistic methods based on the weakest-link concept. For homogeneous materials this approach is straightforward and well established. Different methods have been proposed in the past to incorporate the presence of heterogeneities, e.g. due to welding or segregated zones. A key issue in this context is the length that characterizes variations in the heterogeneous microstructure in relation to a representative size of the zone where brittle fracture typically has been observed to occure, i.e., fracture process zone (FPZ). Here, a new approach for weakest-link modelling of heterogeneous materials is proposed that accounts for the interplay between the different scales.
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Charpy impact tests are used in the nuclear industry to certify forging processes. However, the results of these tests may exhibit a strong variability in the context of large metal parts manufactured by Framatome. Preliminary studies have shown that the steel is highly heterogeneous at the millimeter scale in certain areas of forged parts. These heterogeneities are surmised to be the main cause of the variability observed in the results of impact tests. The aim of this study is to qualify and numerically quantify the effect of these heterogeneities on the distribution of fracture energies thanks to an innovative computational approach featuring deep learning to generate 3D realizations of the mechanical properties from sparse experimental results, and high-fidelity modeling of brittle fracture in heterogeneous Charpy specimens.
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A computational strategy to evaluate the Weibull stress for the Beremin model
is proposed to simultaneously solve problems caused by volumic locking and extreme element
distortion at the crack tip. It is based on the use of mixed elements and remeshing. It is shown that
a single simulation can be used to evaluate the Weibull stress for any range for the CTOD at failure.
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This paper provides an overview of recent progress in probabilistic modeling of cleavage fracture phrased in terms of a local approach to fracture (LAF) and the Weibull stress concept. Emphasis is placed on the incorporation of plastic strain effects into the probabilistic framework by approaching the strong influence of constraint variations on (macroscopic) cleavage fracture toughness in terms of the number of eligible Griffith-like microcracks which effectively control unstable crack propagation by cleavage. Some recent results based on a modified Weibull stress model to predict specimen geometry effects on Jc-values for pressure vessel grade steels are summarized in connection with an engineering procedure to calibrate the Weibull stress parameters. These results are compared against corresponding fracture toughness predictions derived from application of the standard Beremin model. Finally, the robustness of LAF methodologies, including specifically the Weibull stress approach, is critically examined along with a discussion of key issues and challenges related to engineering applications in fracture assessments of structural components.
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The presentation will briefly review the history of the development of fracture mechanics from 1921 to the present, including the evolution of its basic concept. Arguments will be made that Griffith’s basic concept, properly implemented in the context of modern non-equilibrium thermodynamics, remains valid.
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The scale- or the size-dependence of mechanical strength in many brittle materials appears to follow a ‘universal law,’ of the form: strength proportional as:L^-n or V^-n, where n is a number, L is the length and V is the volume of the specimen or structure. Broadly known as the “size-effect” in geology, civil engineering, mining and materials science, this behavior determines the strength of large structures such as ice sheets, rock formations, coal pillars in mines and concrete beams and columns in civil infrastructure. As of now, there is no reliable scientific basis or theory to explain the size effect or for determining a reliable value of ‘n’. This has been the missing link in strength of materials for nearly a century since the Griffith’s crack theory Here, we show that the change in net-section strain energy, due an initial crack in a structure, and its dissipation within a crack layer of finite thickness, leads to the necessary and sufficient physical basis to explain the size-dependence of strength as L^-0.5. Further, size-independence of strength is explained simultaneously when the crack layer volume approaches the specimen volume.
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