Brittle Fracture Analysis Research Articles

Radiation and thermal embrittlement of RPV steels: the links of embrittlement mechanisms, fracture modes and microcrack nucleation and propagation properties. Part 3: Brittle fracture modelling and analysis of the link of microcrack nucleation and propagation properties and embrittlement mechanisms

Radiation and thermal embrittlement of RPV steels are studied from viewpoint of links of brittle fracture properties on micro- and macroscales. Brittle fracture properties on macroscale (such as fracture toughness and fracture stress) and the critical parameters controlling nucleation and propagation of microcracks are determined on the basis of the probabilistic brittle fracture model Prometey. The experimental and numerical investigations are performed for 2Cr–Ni–Mo-V steel and A533 steel used for RPVs of WWER and PWR types. RPV steels are studied in the following states: (1) the initial (as-produced) state; (2) the thermally-embrittled state modelling hardening mechanism of embrittlement; (3) the thermally-embrittled state modelling non-hardening mechanism of embrittlement; (4) the irradiated state. The test results of various specimens (smooth and notched round bars and cracked compact tension specimens) from the investigated steels in various states are represented over brittle fracture temperature range. Brittle fracture modelling is performed with the Prometey model for all the above specimens, and the experimental and numerical results are compared. On the basis of the obtained results the links between embrittlement mechanisms, fracture modes and microcrack nucleation and propagation properties are found.

Sparse polynomial chaos expansion and adaptive mesh refinement for enhanced fracture prediction using phase-field method

Phase-field models (PFMs) have proven to accurately predict complex crack patterns such as crack branching, merging, and crack fragmentation, but they are computationally costly. This study stems from the high computational costs associated with non-adaptive PFMs for brittle fracture analysis, which require dense meshes. This makes training data generation for surrogate models prohibitively expensive. To address these challenges, this paper proposes an adaptive mesh refinement (AMR) informed sparse polynomial chaos expansion (PCE) framework. The AMR algorithm is incorporated into the fracture analysis workflow to maximize the computational efficiency in data generation, eliminating the need for pre-refinement. The AMR informed sparse PCE is calibrated with Bayesian compressive sensing (BCS) to efficiently map domain input parameters to quantities of interest (QoIs), even with limited training data. We employ a multi-output QoI approach to predict load–displacement relationships with high resolution. The novelty of this work lies in the integration of AMR into the PFM workflow and the application of sparse PCE for brittle fracture analysis. Benchmark tests demonstrate the proposed method’s superior accuracy and computational efficiency compared to conventional AMR method, marking a notable improvement in fracture mechanics.

A new digital image correlation method for discontinuous measurement in fracture analysis

The Digital Image Correlation (DIC) method is commonly used in fracture analysis, but it has limitations in measuring discontinuities, which is crucial in fracture analysis. To address this issue, this paper proposes the Adaptive Discontinuous Digital Image Correlation (AD-DIC) method, which is explicitly designed to measure discontinuous displacement fields effectively and accurately in fracture analysis. The AD-DIC method both overcomes the limitations of previous methods by incorporating an adaptive subset tracking technique, which adaptively adjusts the binarization threshold, and improves the traditional Reliability Guided-Digital Image Correlation algorithm to reconstruct the displacement field near cracks. According to high-precision discontinuous displacement fields measured by AD-DIC method, we can accurately identify cracks, measure crack opening, and calculate inclination angles. To validate the effectiveness of the AD-DIC method, theoretical images of type I and mixed-mode I/II cracks are analyzed, as well as four actual experiments. The results show that the AD-DIC method achieves a high level of accuracy in calculating crack opening, with an error of less than 0.1 pixels. The actual experiments presented in this study demonstrate the wide-ranging applications of the AD-DIC method in fracture analysis, including identifying cracks that are difficult to detect with the naked eye, measuring crack opening and inclination angle, and tracking crack propagation processes over time. This study provides an effective tool for brittle fracture analysis, and the relevant algorithms can serve as a reference for discontinuous measurement.

Prediction of graphene's mechanical and fracture properties via peridynamics

Although graphene is believed to be the strongest material, many properties of this material are still worth exploring and discovering, especially the influence of inevitable defects in its preparation on the mechanical and fracture properties which are of high significance. This work provides a new feasible way to study the mechanical and fracture properties of graphene. The novelties of this study are threefold: (1) A novel peridynamic (PD) model is proposed for polycrystalline graphene in which grains of large size exist; (2) The coupling effect of the pre-crack length and the grain size on the inverse pseudo Hall-Petch relation is revealed; (3) The results confirm the applicability of classical Griffith theory in brittle fracture analysis of graphene. Based on the proposed PD model, dependence of the mechanical and fracture properties on the grain size which changes from a few to hundreds of nanometers is investigated in this study. The fracture forms of graphene are consistent with the experimental observations. Based on the Griffith theory, the obtained fracture toughness such as Kc (i.e. 3.8MPam - 6.3MPam) or Gc (i.e. 14.0 J/m2 – 40.9 J/m2) is comparable with previously reported theoretical and experimental values, which proves the validity of the proposed PD model. Besides, the fracture toughness can be greatly enhanced by the blunt pre-crack tip. This work presents insights into mechanical failure of graphene and guidance on fragmentation of graphene for its practical use.

A review of mixed mode I-II fracture criteria and their applications in brittle or quasi-brittle fracture analysis

Fracture criteria play a very important role in predicting crack propagation behavior and life evaluation of cracked bodies. In this paper, mixed mode I-II fracture criteria in the framework of linear elastic fracture mechanics and their applications in brittle or quasi-brittle fracture analysis are systematically reviewed. Meanwhile, the advantages and shortcomings of these criteria are briefly discussed. Furthermore, the effects of T-stresses on brittle fracture characteristics are also studied and some suggestions are given to select appropriate fracture criteria. The results show that different types of fracture criteria differ greatly in predicting the crack propagation behavior, and a suitable criterion can be chosen according to the crack types, loading modes and failure characteristics. Tension-based fracture criteria are applicable for the opening cracks under tensile-based failure, but not for the closed cracks under shear-based failure. T-stresses around the crack tip have significant effects on crack initiation angle, fracture resistance and crack tip plastic zone, which should be introduced into the classical fracture criteria only determined by singular terms for providing more accurate predictions. Moreover, the variable fracture process zone radius can be further considered in these modified criteria considering stress intensity factors and T-stresses, which are not only suitable for brittle materials, but also for plastic materials under small scale yielding. This review will contribute to the development of mixed mode fracture criteria.

A two-dimensional non-ordinary state-based peridynamic model based on three-body potential for elastic brittle fracture analysis

A two-dimensional non-ordinary state-based peridynamic model based on three-body potential for elastic brittle fracture analysis

A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

Failure trajectories, probable failure zones, and damage indices are some of the key quantities of relevance in brittle fracture mechanics. High-fidelity numerical solvers that reliably estimate these relevant quantities exist but they are computationally demanding requiring a high resolution of the crack. Moreover, independent simulations need to be carried out even for a small change in domain parameters and/or material properties. Therefore, fast and generalizable surrogate models are needed to alleviate the computational burden but the discontinuous and complex nature of fracture mechanics presents a major challenge to developing such models. We propose a physics-informed variational formulation of DeepONet (V-DeepONet) for brittle fracture analysis. V-DeepONet is trained to map the initial configuration of the defect to the relevant fields of interests (e.g., damage and displacements). Once the network is trained, the entire global solution can be rapidly obtained for any initial crack configuration and loading steps on that domain. While the original DeepONet is solely data-driven, we take a different path to train the V-DeepONet by imposing the governing equations in a variational form with some labeled data. We demonstrate the effectiveness of V-DeepOnet through two benchmarks of brittle fracture and verify its accuracy using results from high-fidelity solvers. Encoding the physical laws to the model with data enhancement in training renders the surrogate model capable of accurately performing both interpolation and extrapolation tasks. Considering that fracture modeling is very sensitive to fluctuations, the proposed V-DeepONet with a hybrid training strategy is able to predict the quantities of interests with good accuracy, which can be easily extended to a wide array of dynamical systems with complex responses.

Brittle fracture analysis and chronological evolution of medical applications apparatus

Relatively high drying of bones, the calcium present in the bones particles acquires the properties of brittle solid. This property of bones, open the field of experimentation on bones to visualize its hidden phenomena of brittleness. The purpose of this paper is to figure out systematic review of the techniques adopted for investigating the facture and indentation caused in bones due to its subjection in extreme physical and chemical environment. This paper will present the experimental aspects of two techniques namely, Macro- fracture analysis and Micro-CT. These two techniques are worthy in studying the fracture in bones caused due the impractical and dynamic loadings. Further in succeeding section of this paper a systematic chronological evolution of Macro-structural bio-implants has been discussed. The whole journey and cycle of this paper is concentrated toward providing substantial review on the study published in the field of Bio-Mechanics, especially bones. This paper tries to explore the fracture caused in the hunting bones when subjected to the sudden load factor. Macro-fracture techniques is quite adaptable due to its easy to work with property, further, this method is subjected to limitation due to its excessive cost factor. Micro-CT is basically a machine which provide different three-dimensional prospect of bone structure, which can be used to explore and study the change in the mechanical properties of bones. Finally, this paper is the outcome of rigorous and adaptive study which has been sought to provide a cumulative reviewed result for the researches engaged in this field.

Use of thick, heavy plates for bridge construction

AbstractModern steel or steel composite bridges need modern solutions in steel: often thick heavy plates play a crucial role in bridge building, possibly used as flange plate in heavy bridge beams or as thick deck plate in a trough bridge. Depending on the application thick heavy plates allow efficient fabrication or potentially increase the sustainability of a bridge construction. As today especially fabrication efficiency and durability gain importance, it leads to an increase in the application of thick heavy plates. However, when designing with thick heavy plates often the designer reaches technical or regulatory limits. This report will show some solutions to overcome these existing restraints, e.g. improved possibilities in the production of thick thermomechanically rolled steels or extension of the simplified brittle fracture analysis according to Table 2.1 of EN 1993‐1‐10. The consistent exploitation of these possibilities opens a variety of new advantageous options in constructing road or railway bridges.

Phase-field modeling of interactions between double cracks on brittle fracture of Zircaloy-4 cladding

The phase-field model was implemented in Abaqus via user-defined element (UEL) and user-defined material model (UMAT) subroutines for the brittle fracture analysis of a cladding tube. With this method, a scalar damage phase field was utilized to represent the diffuse crack topology, rather than numerical tracking of discontinuities in the cracking area. It was found that the burst hoop stress of the cladding was dependent on the competition of the interference effect and the damage field merging effect of double cracks. Moreover, there was a critical distance between the two cracks at which the burst hoop stress of the cladding reached a minimum. When the distance between two cracks was greater than the critical distance, the damage field merging effect was dominant, whereas when the distance was less than the critical distance, the interference effect was dominant. Furthermore, it was also observed that the burst hoop stress of the cladding was reduced due to the simultaneous initiation of two cracks.

Modeling of brittle fracture in thick plates subjected to transient dynamic loads using a hybrid phase field model

In this work, we propose a hybrid phase field model for the brittle fracture analysis of thick plates subjected to transient dynamic loads. Shear deformation effects which play important role on the behavior of thick plates are captured by using Reddy’s third-order shear deformation theory. The proposed model preserves the linearity of the elastic equilibrium equation within the staggered solution approach and ensures the evolution of damage due to the tensile part of the strain energy. The governing equations of motion of the proposed model are derived by seeking the minimization of the free energy functional. These governing equations are solved in a finite element framework using a staggered solution algorithm. The proposed model is compared with the model with no tension–compression split. Both these models show different mechanical response of thick plates. Using numerical examples, the efficiency of the proposed model in predicting the nucleation and propagation of damage in thick plates subjected to transient dynamic loads is presented.

An efficient and robust staggered algorithm applied to the quasi-static description of brittle fracture by a phase-field approach

The phase field method has been widely adopted in brittle fracture analysis for its ability to handle complex crack topology. This paper presents a novel efficient and robust phase field algorithm for quasi-static brittle fracture analysis. This algorithm overcomes two major issues that affect significantly the numerical cost of the method: the treatment of discontinuous crack propagation and the inequality constraint associated with the irreversibility of the damage evolution. To handle discontinuous crack propagation, a semi-implicit scheme, which combines the usual explicit and implicit schemes, is proposed. Different from explicit schemes that require small time steps and purely implicit schemes that lose immediately efficiency when encountering discontinuous propagation, the proposed method can alleviate the steps constraint while keeping a good robustness with discontinuous cracking. Concerning the irreversibility constraint, this work proposes a practical and easy-to-implement method. It is shown that this method is extremely efficient and robust without any supplementary numerical coefficient. The efficiency of the method is demonstrated by means of representative numerical examples.

In-situ brittle fracture analysis of sharp V-notched components using digital image correlation

In this manuscript, an in-situ framework is presented for fracture load assessment of sharp notched components. First, some fracture experiments are conducted on the V-notched semi-circular bending (V-SCB) samples having various notch opening angles. Then, two different approaches are employed for evaluating the stress field in the vicinity of the notch, and the corresponding results are linked to the maximum tangential stress (MTS) criterion for estimating the fracture loads obtained from the tests. The first approach is to use the in-situ method of digital image correlation (DIC) and the second one is to simulate the specimen by utilizing the finite element (FE) technique. It is demonstrated that the framework presented in this paper for in-situ fracture prediction using the DIC method can provide very good estimations mainly because it takes account of real loading and boundary conditions in the notched specimen, while the predictions based on the FE simulations show rather large errors. Finally, a discussion on the reasons for the disagreement between the predictions of these two approaches is provided.

Hybrid model of peridynamics and finite element method for static elastic deformation and brittle fracture analysis

A new hybrid model of peridynamics (PD) and finite element method (FEM) based on the implicit schemes is proposed to take advantage of PD in solving discontinuities and the computational efficiency of FEM. The region without failure is simulated by FEM. The improved prototype micro-elastic brittle (PMB) model of peridynamics is utilized for the regions where material failure is expected. The truss elements are introduced to bridge finite element (FE) subregions and perdynamic subregions. The present approach is demonstrated through some numerical examples. The displacements of a two-dimensional bar and a cantilever beam using the hybrid model are compared with solutions of theory and FEM. The crack intersection in a slab is simulated and compared with other methods. Numerical predictions of the mode I fracture in a three-point bending beam agree well with the experimental results.

Thermodynamically Consistent Variational Approach for Modeling Brittle Fracture in Thick Plates by a Hybrid Phase Field Model

AbstractIn this work, we propose a thermodynamically consistent phase-field model for the brittle fracture analysis of thick plates. A hybrid model, which is fast and accurate, is proposed for the phase-field modeling of fracture in thick plates. Reddy’s third-order shear deformation theory (TSDT) has been employed to capture the transverse shear deformation effects in thick plates. Governing equations are derived by seeking the minimization of the free-energy functional. A staggered solution algorithm with arc length control is used to solve the governing equations within the finite element framework. The nucleation and propagation of cracks in the thick plates subjected to uniformly distributed load is presented. The mechanical response corresponding to phase-field models based on both the classical plate theory and TSDT has been compared for the case of thick plates and a significant difference between these two models is observed. Parametric studies have been carried out to illustrate the effects of boundary conditions, shear deformation, and the mesh size.

Accident risk analysis of oil and gas facilities in Arctic climatic conditions

The probability of occurring emergency situations increases in conditions of severe climate of the Arctic. Therefore, addressing the problems related to the risk assessment of accidents at oil and gas facilities in the Arctic zones based on acceptable risk criteria is of particular importance. Uncontrollable development of emergency situations is followed by emission of a significant amount of oil products and constitutes serious ecological danger, and also can lead to considerable destructions and death of people resulted from fire and explosion. Therefore, the goal of the study is development of the methods for analysis and assessment of the risk of accidents in reservoirs and gas pipelines at low temperatures to increase the industrial safety of hazardous production facilities operating in conditions of the Arctic North. The results of brittle fracture analysis and accident risk assessment for reservoir and gas pipeline under arctic climatic conditions are presented. Statistical data processing of accidents allowed us to determine the rupture sources, develop a “fault tree” of brittle fracture of reservoirs, “event trees” of reservoir explosion and gas outflow from a gas pipeline, with allowance for the frequency of scenarios for quantitative risk assessment. Currently the probabilistic approach is considered one of the most promising. Accident statistics and experience of previous risk analyses can provide a useful contribution to the process of hazard identification. We focus on the scenario approach to the problems of hazard identification and assess the probability (frequency) of emergencies proceeding from the analysis and systematization of the statistical data on the accidents on reservoirs and gas pipelines at low ambient temperatures using the “event trees” and “fault trees” which provide determination of the most critical scenario and expected risk from accidents. Thus, risk assessment of accidents at hazardous production facilities in the Arctic zone using criteria of acceptable risk will allow estimation of hazards with unacceptable level of risk and development of recommendations and measures to reduce them.

Quasi-brittle fracture model in peridynamics

The safety of structure has been remarked because several natural disasters, such as earthquakes and flood, are increased. The concrete structures sometimes are destroyed these disasters. Numerical simulation is useful to evaluate the safety of structure and it helps understanding the phenomena. Peridynamics, one of numerical method, has been recently attracted. It has advantage for solving the discontinuity without the special treatment, such as FEM. Some brittle fracture analysis is studied by many researchers. However, so far, fracture model regarding quasi-brittle fracture such as the concrete material, has been little developed. In this study, a new quasi-brittle fracture model is developed introducing the Cohesive zone model. Several numerical examples are examined for size effect.

Brittle fracture analysis of Dissimilar Metal Welds between low-alloy steel and stainless steel at low temperatures

Dissimilar Metal Welds (DMW) between low-alloy steel (A533 steel) and austenitic 316L stainless steel are widely used within the French nuclear power plants where they connect the main components to the primary circuit pipes. In these DMW, the welding process and the post-weld heat-treatment generate a hard thin layer of carburized martensite and austenite in the vicinity of the fusion line (FL), resulting in a heterogeneous microstructure with high mechanical properties gradient, hence potentially, a higher sensitivity to brittle fracture in the hard layer. The present study aims to evaluate the brittle behavior of the DMW at low temperatures and more particularly of the interface between the carburized martensite and austenite (MA interface). Fracture toughness tests were carried out at temperatures between - 120°C and -50°C, with a precrack tip located on the ferritic side near the FL (i.e., between the ferritic steel and the stainless steel buttering). The analysis of the fracture behavior of the DMW was based on a SEM examination of CT (Compact Tension) specimens fracture surfaces. Coupled with a 2D plane strain numerical simulation of the tests, the results show that the presence of austenite in the fatigue precrack front and subsequent ductile tearing towards FL produced higher solicitations on the hard layer and caused intergranular fracture on the MA interface, resulting in lower toughness values for the specimen. To model the brittle behavior of the MA interface, a stress based criterion was used. Tensile tests on axisymmetric specimen, which were machined to initiate intergranular fracture in the MA interface and tested at -170°C, were used to define a threshold stress (σth), below which brittle fracture cannot occur. Then, a criterion to evaluate the brittle fracture risk of the DMW was proposed and applied to the CT specimen.

Frontiers of fracture and fatigue: Some recent applications of the local strain energy density

The phenomenon of brittle fracture occurs too often in various branches of engineering being the reason of unexpected termination of anticipated service lives of an engineering objects. This leads to unfortunate catastrophic structural failures resulting in loss of lives and in excessive costs. The theory of fracture mechanics enables the analysis of brittle and fatigue fracture and helps to prevent the occurrence of brittle failure. This field has engaged researchers from various fields of engineering from the early days until today. As its own scientific discipline, it is now less than fifty years old and encourages scientists and engineers to speak the same language when dealing with the design and manufacturing of the classical machinery as well as various intricate devices of nanometer scale, or even smaller, reasoning significant scale effects that arise. Attempting to strike a common ground will connect various physical events/phenomena as a natural result of curiosity arising in course of joint research activities. The interpretation provided by the strain energy density to face different problems and applications is presented in this paper considering some recent outcomes at different scale levels.

13.07: Extension of EN 1993‐1‐10 and EN 1993‐1‐12: To higher strengths and thinner sections

ABSTRACTThe Eurocode 3 sections EN 1993‐1‐10 and EN 1993‐1‐12 contain tables for the maximum permissible values of element thickness as a function of steel grade, quality and reference temperature. The tables cover steel strengths from S235 to S700 and section thicknesses above 10 mm. The tables have been constructed based on a fracture mechanical brittle fracture analysis using a Charpy‐V impact energy criterion as reference.Ultra high strength steels above 700 MPa are not covered by the tables. Such steels are generally used in thinner sections than 10 mm, when the tables in EN 1993‐1‐10 and EN 1993‐1‐12 are limited to section thicknesses above 10 mm. Here, the same basic procedure as used for the tables in EN 1993‐1‐10 and EN 1993‐1‐12 is used to extend them to higher strength steels and thinner sections. The procedure is modified slightly to account for special characteristics of ultra high strength steels and thin sections. These modifications do not affect the present tables, but they provide a smooth transition to higher strength steels and thinner sections. The strong inherent conservatism in the EN 1993‐1‐10 procedure is not affected either.