Brittle Fracture Propagation Research Articles

Microscopic characterisation of brittle fracture initiation in irradiated and thermally aged low-alloy steel welds of a decommissioned reactor pressure vessel

Microstructure has a significant effect on material's integrity and in a heterogeneous weld microstructure the discontinuities affect the brittle fracture initiation and propagation and determine the fracture toughness. The knowledge of brittle fracture initiation mechanisms in high-Mn/high-Ni welds is limited. The brittle fracture initiation behaviour of the decommissioned Barsebäck Unit 2 reactor pressure vessel (RPV) welds of high-Mn/high-Ni weld metal from three different locations, the RPV head and the beltline regions, were investigated and compared with specimens from the surveillance program with high fluence. Systematic fractography has been performed on impact and fracture toughness specimens and the main features of the brittle fracture initiation in the component weld are presented and discussed. Two main types of initiators are identified as the weakest links to initiate the cleavage fracture and the initiation mechanism is found independent from the operation condition. The high-fluence surveillance specimens have a larger amount of intergranular cracking. The cleavage fracture initiation appears to be independent of the operation conditions but dependent on the welding process and metallurgical features. The findings aid in the development of improved material-property correlations which will result in better computational tools for predicting aging of welds based on microstructure.

Misorientation Angle Study on Cleavage Fracture Propagation Surfaces of a Grade a Ship Steel, through Charpy and Four-Point Double-Notch Bend Tests

Misorientation Angle Study on Cleavage Fracture Propagation Surfaces of a Grade a Ship Steel, through Charpy and Four-Point Double-Notch Bend Tests

The Low‐Temperature Toughness Improvement of High‐Strength Low‐Alloy Steel Due to the Microstructural Changes Caused by the Reheating/Rolling Temperature

Herein, the microstructure, low‐temperature toughness, and fracture characteristics of high‐strength low‐alloy (HSLA) steel prepared by various thermomechanical control processes are systematically studied. Three different reheating/rolling temperatures are designed to obtain microstructures with different prior austenite grain sizes: 20.12 μm (S810), 27.58 μm (S910), and 35.19 μm (S1010). After hot rolling, S810 steel with smaller prior austenite grain size can provide high‐density deformed grain boundaries that promote ferrite phase transformation. The S910 and S1010 steels predominantly undergo bainite transformation as the prior austenite grain size and rolling temperature increase. Also, excellent low‐temperature toughness is obtained by reducing the reheating/rolling temperature (i.e., S810 steel), reflecting that Charpy impact energy of the core of the steel plate is 118.53 J at −120 °C. High performances is mainly attributed to the higher ferrite content, grain refinement, lower dislocation density, and higher proportion of high‐angle grain boundaries. Furthermore, fracture morphology analysis demonstrates that the S810 steel exhibits ductile fracture and noticeable plastic deformation at −120 °C, while S910 and S1010 steels exhibit brittle fracture and rapid crack propagation. These findings manifest the applicability of the suggested technique in preparing HSLA steel with excellent low‐temperature toughness.

Dynamic strain gradient brittle fracture propagation: comparison with experimental evidence

<p>This paper presented a physico-mathematical model for dynamic fracture propagation in brittle materials with a purely continuum mechanics hemi-variational-based strain gradient theory. As for the quasi-static case, the simulation results, obtained by means of finite elements, revealed that strain gradient effects significantly affected the fracture propagation, leading to finite fracture thickness that was independent of the mesh size. It was also observed that nonsymmetric loading rate lead to a deviation from standard mode-Ⅰ crack propagation that cannot be revealed in the quasi-static case. The model results were compared against experimental data from fracture tests on notched specimens taken from the literature. The comparison showed good agreement between the model predictions and the experimental measurements. The presented model and simulation results can be useful in the design and optimization of structural components subjected to dynamic loading conditions.</p>

A local surface roughness mapping method for post-failure interpretation of brittle fracture propagation

Tensile fractures in brittle materials may exhibit striation features running along the surface that indicate the trajectory of fracture propagation. Because of the directional persistence of these features, directional roughness characterization methods can be used on subsampled fracture surface data to map localized roughness features that follow these striations. These maps can aid in the interpretation of fracture initiation sites and crack front positions with the use of post-processing visualization techniques such as vector maps and streamlines. Tensile fractures in rock and synthetic rock analogues are used to demonstrate the various fracture propagation patterns that emerge following this analysis. This mapping method and streamline analysis can be further used to analyze elevation profiles that follow fracture propagation along non-linear paths which may inform about the mechanisms that can associate surface features with the fracture process.

Peridynamic modeling of nonlinear surface acoustic waves propagating in orthotropic materials

Due to the elastic nonlinearity of the material, high-amplitude surface acoustic waves undergo nonlinear evolution during propagation and may lead to material failure. To enable the acoustical quantification of material nonlinearity and strength, a comprehensive understanding of this nonlinear evolution is necessary. This paper presents a novel ordinary state-based nonlinear peridynamic model for the analysis of the nonlinear propagation of surface acoustic waves and brittle fracture in anisotropic elastic media. The relationship between seven peridynamic constants and second- and third-order elastic constants is established. The capability of the developed peridynamic model has been demonstrated by predicting surface strain profiles of surface acoustic waves after propagating in the silicon (111) plane and the 〈112¯〉 direction. On this basis, the nonlinear wave-induced spatially localized dynamic fracture is also studied. The numerical results reproduce the main features of nonlinear surface acoustic waves and fracture observed in experiments.

Controlling the fracture response of structures via topology optimization: From delaying fracture nucleation to maximizing toughness

It is now a well-established fact that even simple topology variations can drastically change the fracture response of structures. With the objective of gaining quantitative insight into this phenomenon, this paper puts forth a density-based topology optimization framework for the fracture response of structures subjected to quasistatic mechanical loads. One of the two key features of the proposed framework is that it makes use of a complete phase-field fracture theory that has been recently shown capable of accurately describing the nucleation and propagation of brittle fracture in a wide range of nominally elastic materials under a wide range of loading conditions. The other key feature is that the framework is based on a multi-objective function that allows optimizing in a weighted manner: (i) the initial stiffness of the structure, (ii) the first instance at which fracture nucleates, and (iii) the energy dissipated by fracture propagation once fracture nucleation has occurred. The focus is on the basic case of structures made of a single homogeneous material featuring an isotropic linear elastic behavior alongside an isotropic strength surface and toughness. Novel interpolation rules are proposed for each of these three types of material properties. As a first effort to gain quantitative insight, the framework is deployed to optimize the fracture response of 2D structures wherein the fracture is bound to nucleate in three different types of regions: within the bulk, from geometric singularities (pre-existing cracks and sharp corners), and from smooth parts of the boundary. The obtained optimized structures are shown to exhibit significantly enhanced fracture behaviors compared to those of structures that are optimized according to conventional stiffness maximization. Furthermore, the results serve to reveal a variety of strengthening and toughening mechanisms. These include the promotion of highly porous structures, the formation of tension-compression asymmetric regions, and the removal of cracks and sharp corners. The particular mechanism that is preferred by a given structure, not surprisingly, correlates directly to the elastic, strength, and toughness properties of the material that is made of.

Prediction of brittle fracture propagation behaviour of hydroxyapatite (HAp) coating in artificial femoral stem component

Purpose: This study addresses the brittle fracture propagation behaviour modelling of hydroxyapatite (HAp) coating in artificial femoral stem component. Design/methodology/approach: A simple two dimensional flat-on-flat contact configuration finite element model consisting contact pad (bone), Ti-6Al-4V substrate and HAp coating is employed in static simulation. The HAp coating is modelled as elastic layer with pre-microcrack which assumed to be initiated due to stress singularity. Findings: The study revealed that reducing coating thickness, pre-microcrack length and artificial femoral stem elastic modulus along with increasing bone elastic modulus will result in significant stress intensity factor (SIF) to promote brittle fracture propagation behaviour. Research limitations/implications: The influence of coating thickness, pre-microcrack length, bone and artificial femoral stem elastic modulus on fracture behaviour is examined under different stress ratio using J-integral analysis approach. Practical implications: The proposed finite element model can be easily accommodating different Hap coating thickness, pre-microcrack length, bone and artificial femoral stem elastic modulus to perform detailed parametric studies with minimal costly experimental works. Originality/value: Limited research focussing on brittle fracture propagation behaviour of HAp coating in artificial femoral stem component. Thus, present study analysed the influence of coating thickness, pre-microcrack length, bone and artificial femoral stem elastic modulus on stress intensity factor (SIF) of HAp coating.

A laboratory study of hydraulic fracturing at the brittle-ductile transition

Developing high-enthalpy geothermal systems requires a sufficiently permeable formation to extract energy through fluid circulation. Injection experiments above water’s critical point have shown that fluid flow can generate a network of highly conductive tensile cracks. However, what remains unclear is the role played by fluid and solid rheology on the formation of a dense crack network. The decrease of fluid viscosity with temperature and the thermally activated visco-plasticity in rock are expected to change the deformation mechanisms and could prevent the formation of fractures. To isolate the solid rheological effects from the fluid ones and the associated poromechanics, we devise a hydro-fracture experimental program in a non-porous material, polymethyl methacrylate (PMMA). In the brittle regime, we observe rotating cracks and complex fracture patterns if a non-uniform stress distribution is introduced in the samples. We observe an increase of ductility with temperature, hampering the propagation of hydraulic fractures close to the glass transition temperature of PMMA, which acts as a limit for brittle fracture propagation. Above the glass transition temperature, acoustic emission energy drops of several orders of magnitude. Our findings provide a helpful guidance for future studies of hydro-fracturing of supercritical geothermal systems.

Weak imposition of Dirichlet boundary conditions for analyses using Powell–Sabin B‐splines

AbstractPowell–Sabin B‐splines are enjoying an increased use in the analysis of solids and fluids, including fracture propagation. However, the Powell–Sabin B‐spline interpolation does not hold the Kronecker delta property and, therefore, the imposition of Dirichlet boundary conditions is not as straightforward as for the standard finite elements. Herein, we discuss the applicability of various approaches developed to date for the weak imposition of Dirichlet boundary conditions in analyses which employ Powell–Sabin B‐splines. We take elasticity and fracture propagation using phase‐field modeling as a benchmark problem. We first succinctly recapitulate the phase‐field model for propagation of brittle fracture, which encapsulates linear elasticity, and its discretization using Powell–Sabin B‐splines. As baseline solution we impose Dirichlet boundary conditions in a strong sense, and use this to benchmark the Lagrange multiplier, penalty, and Nitsche's methods, as well as methods based on the Hellinger‐Reissner principle, and the linked Lagrange multiplier method and its modified version.

Phase-Field Modeling Fracture in Anisotropic Materials

The phase-field method is a widely used technique to simulate crack initiation, propagation, and coalescence without the need to trace the fracture surface. In the phase-field theory, the energy to create a fracture surface per unit area is equal to the critical energy release rate. Therefore, the precise definition of the crack-driving part is the key to simulate crack propagation. In this work, we propose a modified phase-field model to capture the complex crack propagation, in which the elastic strain energy is decomposed into volumetric-deviatoric energy parts. Because of the volumetric-deviatoric energy split, we introduce a novel form of the crack-driving energy to simulate mixed-mode fracture. Furthermore, a new degradation function is proposed to simulate crack processes in brittle materials with different degradation rates. The proposed model is implemented by a staggered algorithm and to validate the performance of the phase-field modelling, and several numerical examples are constructed under plane strain condition. All the presented examples demonstrate the capability of the proposed approach in solving problems of brittle fracture propagation.

Laponite gels - visco-elasto-plastic analogues for geological laboratory modelling

Laponite® is a synthetic clay that, depending on concentration, temperature and curing time, forms a clear, transparent thixotropic fluid or brittle visco-elasto-plastic gel when mixed with water. Here we present the results of rheological and mechanical testing of gel-forming Laponite RD (LRD) to evaluate its suitability as a rock analogue in laboratory analogue experiments. Rheological tests of 2–4 wt% concentrations of LRD in deionised water were carried out at temperatures between 20 and 50 °C, and after curing times of 3 to 14 days. Our results show that LRD gels change from a brittle, elastic-dominant, linear viscoelastic material to a plastic material as shear strain increases. The linear viscoelastic region occurs at shear strains, γ < 10% after which the material yields and then undergoes strain hardening before a peak stress occurs at γ = 15–20%. LRD then strain softens up to γ < 26.2%, beyond which it behaves as a plastic material. Empirical equations are provided that predict increases in the Young's and complex shear moduli of LRD with increasing concentration and ageing time. LRD can be used to model elastic deformation when γ < 10% at a shear strain rate of 0.1 s−1 and plastic deformation when γ > 26.2%. LRD is an ideal material for modelling the behaviour of rocks during the emplacement of magma and the propagation of brittle fractures in the upper crust. Its ease of preparation, low surface tension, full transparency, chemical and biological stability and photoelastic properties provide further advantages for analogue laboratory modelling compared to other frequently used visco-elastic gels, such as pig skin gelatine.

Effect of dispersed particles on TiAl alloys fracture behavior

γTiAl based alloys are very attractive for structural applications at high temperatures. The addition to the selected alloy of dispersed alumina particles increases the yield strength and the elastic modulus of γTiAl alloys but affects their fracture behavior by favoring the propagation of brittle fracture. The analysis of the fracture surface revealed that the addition to oxide particle, during component production by means of investment casting, favors brittle fracture propagation by intensifying stresses and by increasing the quantity of shrinkage cavities inside the casting.

Computation of brittle fracture propagation in strain gradient materials by the FEniCS library

Strain gradient continuum damage modelling has been applied to quasistatic brittle fracture within an approach based on a maximum energy-release rate principle. The model was implemented numerically, making use of the FEniCS open-source library. The considered model introduces non-locality by taking into account the strain gradient in the deformation energy. This allows for stable computations of crack propagation in differently notched samples. The model can take wedges into account, so that fracture onset can occur at wedges. Owing to the absence of a damage gradient term in the dissipated energy, the normal part of the damage gradient is not constrained on boundaries. Thus, non-orthogonal and non-parallel intersections between cracks and boundaries can be observed.

Validation of a 3-D adaptive stable generalized/eXtended finite element method for mixed-mode brittle fracture propagation

In this paper, a Stable Generalized/eXtended Finite Element Method (SGFEM) is combined with mesh adaptivity for the robust and computationally efficient simulation of mixed-mode brittle fracture propagation. Both h-refinement around the fracture front and p-enrichment of the analysis domain are used to control discretization errors. A Linear Elastic Fracture Mechanics (LEFM) model based on Griffith’s criterion is adopted. LEFM scaling relations are used at each fracture propagation step to back calculate SIFs that meet Griffith’s criterion. As a result, no iterations are necessary to find loading scaling parameters or fracture size that meets Griffith’s criterion. The method is validated against several experimental data sets for mode I and mode I+II fracture propagation problems. Very good agreement between SGFEM and experimental results is observed. These include fracture path, Crack Opening Displacement (COD), and load and fracture length versus COD curves. The computational efficiency of the method is also assessed.

On crack opening computation in variational phase-field models for fracture

Phase-field models for fracture have gained exceptional popularity in the last couple of decades and have been extended into areas well beyond brittle quasi-static fracture propagation to ductile, dynamic, or hydraulic fracturing. Despite the significant theoretical advancements in these more complex physical settings, little attention has been paid to the quantification of crack opening displacement to date as most applications do not explicitly require the crack opening displacement for the morphological evolution of cracks. However, one of the exemptions would be hydraulic fracturing where the crack propagation is driven by the fluid pressure which strongly depends on the crack opening displacement.In this study, we look into two known approaches, a line integral and a level-set method, for crack opening computation mainly from an implementation point of view. Firstly, we derive an approximation of a discontinuous function field in the variational phase-field setting which is then applied to obtain the crack opening (displacement jump) and verify the approximation against a closed solution. We then propose a “certain distance from the crack” required for the level-set function using a one-dimensional analysis. Finally, we compare these approaches under several different conditions such as crack alignment to the mesh or under loading (asymmetric displacement field) and investigate the convergence with respect to the mesh size.

An investigation of the ballistic performance of independent ceramic target

The ballistic experiments have been carried out on alumina 99.5% bare ceramic plates for studying the initiation and propagation of brittle fracture and the resistance offered by the target. The ceramic tiles of size, 100 mm × 100 mm, and thickness, 5 mm, were impacted by the ogival nosed hardened steel 4340 projectiles of diameter 10.9 mm and mass 30 grams at velocities in the range 52–275 m/s. The ceramic fragments were carefully collected to examine the cracking patterns at the front and the back surfaces. The cracks developed in the target were studied extensively to develop more insight into the fracture mechanism. The energy absorbed by the target has been studied and correlated with respect to the fracture mechanism of the target. Numerical simulations have been performed on a commercial finite element code and the experimental findings have been reproduced in order to further understand the fracture and fragmentation behaviour and its influence thereon the ballistic characteristics of the target. The Johnson-Holmquist-2 (JH-2) constitutive model has been used for simulating the material behaviour of ceramic and the Johnson-Cook (JC) elasto-viscoplastic material model for simulating the behaviour of the steel projectile. The behaviour of ceramic target under oblique impact was explored numerically. The damage in the projectile was found to be higher in case of oblique impact. Both the experimental and numerical findings have described an increase in the crack density with the increase in the incidence velocity of the projectile. The average size of the fragments has also been found to be reduced with the increase in the projectile incidence velocity.

Using Deep Learning to Predict Fracture Patterns in Crystalline Solids

Summary Fracture is a catastrophic process whose understanding is critical for evaluating the integrity and sustainability of engineering materials. Here, we present a machine-learning approach to predict fracture processes connecting molecular simulation into a physics-based data-driven multiscale model. Based on atomistic modeling and a novel image-processing approach, we compile a comprehensive training dataset featuring fracture patterns and toughness values for different crystal orientations. Assessments of the predictive power of the machine-learning model shows excellent agreement not only regarding the computed fracture patterns but also the fracture toughness values and is examined for both mode I and mode II loading conditions. We further examine the ability of predicting fracture patterns in bicrystalline materials and material with gradients of microstructural crystal orientation. These results further underscore the excellent predictive power of our model. Potential applications of this model could be widely applied in material design.

An auto-adaptive sub-stepping algorithm for phase-field modeling of brittle fracture

In this work, we propose an auto-adaptive displacement stepping algorithm to auto-adaptively adjust the displacement step size while solving the quasi-static brittle fracture propagation problem with the phase-field method. We employ a step size controller based on an ‘a posteriori’ error estimator to achieve adaptivity in the displacement step size. To capture correct crack propagation behavior near peak load, we propose an energy-based conditional. The conditional is evaluated in a sub-step of the primary displacement step, and it decides whether to accept or reject the step. Based on the step size controller algorithm and the sub-stepping algorithm, we formulate the auto-adaptive sub-stepping algorithm. We investigate the accuracy and computational cost of the proposed algorithm on several benchmark problems from the literature and compare it to the standard alternate minimization (AM) approach. The algorithm auto-adaptively adjusts the size of the displacement step and allows us to use step sizes that may vary by even three orders of magnitude. As compared to the standard AM algorithm, this results in a reduction of 78–90% in the CPU time required to reach peak reaction force, and 56–78% reduction in the CPU time needed to complete analysis, and always maintains the accuracy in crack path prediction.

Brittle anisotropic fracture propagation in quartz sandstone: insights from phase-field simulations

We developed a generalized multiphase-field modeling framework for addressing the problem of brittle fracture propagation in quartz sandstones at microscopic length scale. Within this numerical approach, the grain boundaries and crack surfaces are modeled as diffuse interfaces. The two novel aspects of the model are the formulations of (I) anisotropic crack resistance in order to account for preferential cleavage planes within each randomly oriented quartz grain and (II) reduced interfacial crack resistance for incorporating lower fracture toughness along the grain boundaries that might result in intergranular crack propagation. The presented model is capable of simulating the competition between inter- and transgranular modes of fracturing based on the nature of grain boundaries, while exhibiting preferred fracturing directions within each grain. In the full parameter space, the model can serve as a powerful tool to investigate the complicated fracturing processes in heterogeneous polycrystalline rocks comprising of grains of distinct elastic properties, cleavage planes, and grain boundary attributes. We demonstrate the performance of the model through the representative numerical examples.