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Graphite components, used as moderators, reflectors, and core-support structures in a High-Temperature Gas-Cooled Reactor, play an important role in the safety of the reactor. Specifically, they provide channels for the fuel elements, control rods, and coolant flow. Fracture is the main failure mode for graphite, and breaching of the above channels by crack extension will seriously threaten the safety of a reactor. In this paper, a new method based on digital image correlation (DIC) is introduced for measuring crack extension in brittle materials. Cross-correlation of the displacements measured by DIC with a step function was employed to identify the advancing crack tip in a graphite beam specimen under three-point bending. The load-crack extension curve, which is required for analyzing the R-curve and tension softening behaviors, was obtained for this material. Furthermore, a sensitivity analysis of the threshold value employed for the cross-correlation parameter in the crack identification process was conducted. Finally, the results were verified using the finite element method. [ABSTRACT FROM AUTHOR]

• Grain size Effect: larger grain sizes in graphite lead to higher fracture toughness values under quasi-static loading, but the trend is opposite under dynamic loading. • Loading-Rate Effect: the dynamic fracture toughness exhibits a near-linear correlation with the impact velocity. • Fracture mode Transition: the fracture mode changes from intergranular to transgranular fracture as the impact velocity increases. Graphite materials play critical roles as moderators, reflectors, and core structural components in high-temperature gas-cooled nuclear reactors. During the reactor operation, graphite materials may experience a variety of loads, including thermal, radiation, fatigue, and dynamic loads, potentially leading to crack initiation and propagation. Therefore, it is imperative to investigate their fracture properties. Despite this, there remains a paucity of comprehensive studies on the fracture toughness of graphite materials with varying grain sizes, particularly concerning dynamic fracture toughness. This study addresses this gap by employing a digital-image-correlation-based virtual extensometer to analyze crack propagation in graphite materials of different grain sizes, enabling precise measurement of crack propagation length and fracture toughness. Findings reveal that static fracture toughness increases with larger grain sizes, while under dynamic loading, smaller grain sizes exhibit greater fracture toughness. Additionally, dynamic fracture toughness shows a near-linear increase with impact speed. Scanning electron microscopy analysis of fracture surface morphology highlights the impact of grain size and impact speed on fracture toughness. Nuclear graphite specimens with larger grain sizes have more irregular grain and pore distributions, enhancing crack deflection and propagation resistance, thereby increasing fracture toughness. The observed loading rate dependence of dynamic fracture toughness is attributed to a gradual transition from intergranular to transgranular fracture modes with increasing impact speed. [ABSTRACT FROM AUTHOR]

• Loading-rate dependency observed on fracture toughness of IG-11 graphite. • Dynamic fracture toughness of IG-11 graphite was influenced by inertial effect. • Crack propagation during the impact process was considered in dynamic fracture toughness measurement. • Graphite changes from intergranular to transgranular fracture with increasing impact velocity. Graphite materials are widely used as moderators, reflectors, and core structural materials in high-temperature gas-cooled reactors. During operation, graphite materials in nuclear reactors may be subjected to dynamic loads caused by earthquakes or other factors. Therefore, the dynamic fracture properties of graphite materials need to be investigated. In this study, dynamic three-point bending drop hammer impact experiments were conducted on IG-11 graphite specimens with precracks to measure their dynamic fracture toughness under medium- and low-speed impacts using a digital image correlation method. Traditional methods for measuring fracture toughness based on ASTM standards do not consider the influence of the inertial effect, leading to unreasonably large measurement results. To address this disadvantage, the dynamic fracture toughness of IG-11 graphite was evaluated using a spring–mass model that considers the inertial effects of materials. Results indicated that the measured fracture toughness was significantly lower than that obtained based on the ASTM standard and increased almost linearly with increasing impact velocity. The toughening mechanism was analysed by observing the fracture morphology of the samples using a scanning electron microscope. The results showed that as the impact velocity increased, the fracture mode of the graphite samples gradually changed from intergranular to transgranular fracture, and the samples absorbed sufficient energy, resulting in a noticeable toughening phenomenon. [Display omitted] [ABSTRACT FROM AUTHOR]

• A regularized polynomial smoothing (RPS) method based on Tikhonov regularization is proposed to improve previous local Hermite (LH) method and measure noisy high-gradient strain field (HSF). • RPS is nearly insensitive to window size and produces lower error than point-wise least-squares (PLS) method in resolving local HSF. • In match/overmatch case, Tikhonov regularization in RPS greatly decreases the degree of the morbidity caused by ill-posedness in PLS and ensure the smoothness and stability of solution. Digital image correlation (DIC) is an effective tool for studying the deformation of tested materials. However, high-gradient strain field (HSF) measurement remains a challenging issue in DIC, because multifold factors have a significant effect on the first correlation calculation step of the original displacement and the exact strain reconstruction in the second post-processing step. In this study, we focus on the second step. The formerly proposed local Hermite has been proven as an accurate and robust method, yet substantial programming work is involved in constructing a Hermite element. To solve this issue, a regularized polynomial smoothing (RPS) method is proposed, which replaces the Hermite function of the polynomial. The RPS applies the same kernel function as the point-wise least-squares (PLS) method for easy implementation. Tikhonov regularization and the generalized cross-validation (GCV) function are also used to decrease unavoidable noise and weaken the dependence on window size. The experiments demonstrate that, in the matched/overmatched case, Tikhonov regularization in RPS can greatly decrease the degree of morbidity caused by ill-posed problems in the PLS method, thereby ensuring smoothness and stability of the solution. Moreover, the influences of window size and polynomial order of both the RPS and PLS are also closely studied. In conclusion, the proposed RPS provides a practical, robust and accurate method for HSF measurement. [ABSTRACT FROM AUTHOR]

Highlights • Three novel strategies are proposed to minimize the thread competition for the existing path-dependent parallel DIC. • The proposed method could upgrade the 2D-DIC speed up to 145,000 points per second using 48 threads. • The proposed fast DIC method can be used to monitor the structural health with ROI containing less than 5000 points in real time. Abstract With the increasing demands on the real-time measurement using digital image correlation (DIC), the fast and ultra-fast computation are attracting much more attention from academic and engineering fields in last decades. Multi-thread parallelization is a recognized effective method to raise the correlation speed of traditional single-thread DIC up to higher order of magnitude. However, for the path-dependent parallel DIC based on specific initial guess propagation method, competition between different threads greatly cuts down the overall speed, because different threads visit the same queue or status matrix at the same time. Therefore, the desired linear speed-up ratio growth could hardly be achieved especially for large thread number. In this work, three novel strategies are proposed to minimize the thread competition for the existing path-dependent parallel DIC, including i) allocating private queues for private thread, ii) restarting idle thread if others are busy, and iii) collecting more uncorrelated neighboring points for subsequent correlation. In this way, the conflict between threads is obviously decreased and experiment results reveal that the proposed method could upgrade the 2D-DIC speed up to 145,000 points per second using 48 threads, which makes the real-time measurement feasible for region of interest (ROI) with less than 5000 points. [ABSTRACT FROM AUTHOR]

• Proposed damage measurement tests of nuclear graphite under unidirectional tensile and compressive stress states. • Unveiled the effects of stress states on the damage evolution law of nuclear graphite. • Nuclear graphite is more prone to damage by tensile stress. • The curves of damage factors and young modulus can guide the design of nuclear graphite components. Nuclear graphite, a quasi-brittle material containing microdefects, is essential for constructing the neutron moderators, reflectors, and cores in very-high-temperature gas-cooled reactors. Such reactors are prone to damage during loading, resulting in the failure of nuclear graphite materials or structures and possibly affecting the integrity of the entire core structure. Therefore, the damage evolution law of nuclear graphite should be studied while assessing the safety of the core. In addition, considering the different mechanical characteristics of quasi-brittle materials under tensile and compressive stresses as well as the complex stress states of quasi-brittle nuclear graphite structures in the core, the effects of stress states on the damage evolution law of nuclear graphite should be unveiled. These aspects are difficult to evaluate owing to the complexity of damage characterisation and measurement throughout the test loading of nuclear graphite under different stress states. Therefore, we propose damage measurement tests of nuclear graphite under unidirectional tensile and compressive stress states based on digital image correlation to obtain damage evolution laws under different stress states. By analysing the effects of different stress states on the damage evolution laws of nuclear graphite, we found that the damage properties under unidirectional tensile and compressive stresses show variations and that damage more likely occurs under tensile stress. [ABSTRACT FROM AUTHOR]

Nuclear graphite is a key material in high-temperature gas-cooled reactors (HTGR). The evaluation of its damage evolution is significant for the safety assessment of nuclear graphite structures. However, it is difficult to characterise the damage properties of nuclear graphite using conventional testing approaches such as uniaxial compression and tension tests, considering the inconvenience of conducting uniaxial tension tests. Therefore, an inverse method was developed in this study to identify the damage parameters of a graphite material IG11, which has almost the same mechanical properties as nuclear graphite IG110. The method is based on the non-contact digital image correlation (DIC) and finite element model updating (FEMU) techniques, and damage-induced nonlinear stress–strain curves for both tension and compression were simultaneously obtained by conducting only one four-point bending test. To improve the inverse efficiency, a double iterative technique was employed using the Nelder–Mead optimisation algorithm. The inverse method was verified by simulated tests and a rapid convergence with good accuracy was achieved. The results show that the IG11 graphite material exhibits distinct damage evolution behaviours under tensile and compressive loading, with the former inflicting more damage at the same strain level. [ABSTRACT FROM AUTHOR]

A new photogrammetry based measurement technique for contact areas in line contact structures is developed. From the data collected by this technique, a method for measuring the contact strength of contact structures in high temperature applications is proposed. The contact strength of a line contact structure of polyimide at different temperatures is measured; the results show that the increase in temperature decreases the contact strength of the structure. The effect of temperature on the contact strength is studied by investigating the occurrence and evolution of yielding core within the structure at different temperatures. The decrease in the yield strength and elastic modulus of the polyimide material at high temperature induces core yielding at lower loads and eases the propagation of core yielding to the surface. [ABSTRACT FROM AUTHOR]

• The estimations of random error and under-matched error caused by two strain calculation methods (point-wise least squares (PLS) and regularized polynomial smoothing method (RPS)) are proposed, based on two assumptions on the noise error of calculated displacement. • For the typical kernel function of 3rd order polynomial, a self-adaptive algorithm minimizing the total error is proposed to choose the optimal parameters. • The self-adaptive algorithm can give the optimal parameters in restoring the displacement and strain field, and obtain a more accurate result if the provided displacement field conforms strictly to assumptions. The strain error analysis is greatly concerned recently as digital image correlation (DIC) is used to measure the heterogeneous deformation. This paper focuses on the estimation of random error and under-matched error caused by two strain calculation methods, i.e. the point-wise least squares (PLS) and the regularized polynomial smoothing method (RPS). Two assumptions are put forward on the noise error of the calculated displacement that are: a) it is pure random error without bias and b) in each strain window, it is the independent Gaussian white noise with zero-mean. Based on the assumptions, the random error of displacement and strain is estimated, and the under-matched error of displacement and strain is theoretically analyzed by the aid of Laplacian operator. These two error solutions are verified by some stimulated experiments. Then for the typical kernel function of 3rd order polynomial, a self-adaptive algorithm minimizing the total error is proposed to choose the optimal parameters, i.e. window size and parameter λ. Experiments show that when the original displacement noise conforms to the assumptions strictly, 1) the estimated random error and under-matched error agrees very well with the experimental value, 2) the self-adaptive algorithm can give the optimal parameters in restoring the displacement and strain field, and 3) the estimation of random error and under-matched error is affected by DIC noise greatly, and it is better to use low-pass Gaussian filter before utilizing self-adaptive algorithm. [ABSTRACT FROM AUTHOR]

• Proposed approach to accurately measure dynamic crack propagation length of graphite. • Obtained fracture toughness via virtual extensometers and digital image correlation. • Dynamic fracture toughness increases with increase in impact velocities. • Proposed approach is simple to operate. Nuclear graphite is widely used as a moderator, reflector, and core structure material in very/high temperature gas-cooled reactors. However, because graphite may experience impacts with medium-low velocities during its transport and installation or under extreme conditions such as severe earthquakes, it is necessary to evaluate the dynamic fracture toughness of graphite to assess the safety of the reactors. The ASTM standard recommends a formula to calculate the fracture toughness; however, this formula includes the crack length parameter, which cannot be measured accurately in a dynamic process. To enable the accurate measurement of the dynamic crack propagation length of graphite and subsequently obtain the fracture toughness, a virtual extensometer method based on digital image correlation was established in this study. Three-point bending experiments were conducted using pre-cracked specimens to obtain the dynamic fracture toughness of graphite IG11 under medium-low impact velocities. The results indicated that the dynamic fracture toughness of graphite IG11 increased with the increase in the impact velocities, and its value was substantially higher than the static fracture toughness in certain cases. The proposed approach involves a simple operation, yields a high accuracy, and can enable automatic calculation. Moreover, this approach can be used to evaluate the dynamic fracture performance of other brittle or quasi-brittle materials. [ABSTRACT FROM AUTHOR]

• DIC and XFEM simulation results agree with each other very well. • Specimen misalignment will lead to the asymmetry of DIC horizontal displacement fields. • We propose a new method to determine when the crack will propagate to the position. In the steam generator (SG) of the high temperature reactor – pebble-bed module (HTR-PM), the outlet connection tubes are made of Incoloy 800H. The fatigue analysis of these tubes is necessary since there are periodic flow-induced forces by the high-speed helium gas. In this paper, we focus on the crack propagation of the outlet connection tubes at room temperature by means of digital image correlation (DIC) and extended finite element method (XFEM). First, a uniaxial tensile sample was fabricated from the 800H tube with a pre-crack in the middle edge. Then, the sample was painted with spackle pattern for DIC measurement. Afterwards, the displacement and strain fields of region around the crack were calculated by DIC as the sample was subjected to static tensile load. Two bi-telecentric lenses of distinct magnification levels were used to image the crack at two scales. Also, a method based on virtual strain gauge was proposed to locate the crack tip and to characterize the crack propagation process. Finally, the DIC results were compared with those by XFEM. It was found that the results by these two methods agreed with each other very well in general. The results are useful for investigating the fracture behavior of 800H at room temperature. [ABSTRACT FROM AUTHOR]

As a key material in high-temperature gas-cooled reactors (HTGR), nuclear graphite is a type of quasi-brittle material with complex damage mechanisms. However, it is difficult to characterise the damage properties of nuclear graphite under complex stress states using conventional testing approaches or inverse methods. In this study, a hybrid identification method based on 8-node quadrilateral element digital image correlation (Q8-DIC), a double iterative finite element model updating (FEMU) technique, and artificial neural networks (ANNs) is presented to characterise the damage properties of IG11 graphite material under complex stress states. First, this method is verified using simulated tests on a ring under diametrical compression, then applied to actual mechanical testing of graphite material to evaluate its damage properties. Finally, factors affecting the evolution of damage are discussed. The results indicate that the first principal strain has the most significant effect on the damage evolution of the graphite material. Unlabelled Image • Damage behaviour of graphite material under complex stress states was determined. • A novel hybrid damage variable identification method using Q8-DIC, FEMU and ANNs was proposed. • The damage evolution law of the material under complex stress states can be obtained by a single test. • The ANN model exhibits very successful damage prediction of the material. [ABSTRACT FROM AUTHOR]