Application Of Fracture Mechanics Research Articles

Fracture of Epoxy Networks Using Atomistic Simulations.

Predicting fracture properties through all-atomistic simulations poses challenges due to classical force field limitations in breaking covalent bonds and the computational demands of reactive force fields like ReaxFF. In addressing this, we propose a scale-bridging method for forecasting the fracture behavior of highly cross-linked epoxy combining classical force fields, the LAMMPS package REACTER, and for bond breaking a parameter based on experimental distance criterion. In our analysis, we anticipate the macroscopic fracture energy GC of the epoxy network through the application of a continuum fracture mechanics model developed for fibrils. In addition, we extract the value of the stress intensity factor KI. This modeling approach is specifically implemented for a frequently used epoxy system that consists of bisphenol F and DETDA hardener. Notably, our results demonstrate a robust correlation with existing literature and experimental studies. Moreover, our approach boasts a substantial computational time advantage, facilitating calculations that are significantly faster compared to those performed using reactive force fields.

Lifetime study of uniform and non-uniform multi-crack fusion and extension in an approximate plane

The threat of cracks is very fatal for engineering structures. Usually, the main crack is fused by several secondary microcracks, so the investigation of the fusion mechanism and life of microcracks is crucial to improve the reliability of engineering structures. In this paper, firstly, the applicability and accuracy of linear elastic fracture mechanics are verified by comparing the test results and FEA results of small-scale yielding. Secondly, the fusion mechanism and life-solution of uniform and non-uniform multi-cracks are thoroughly investigated. It is also pointed out that the homogeneity of cracks is caused by the abrupt change of crack extension path by affecting the level of stress intensity factor (SIF). Finally, the effects of maximum load and stress ratio on crack fusion are explored. The results demonstrate that the maximum load has a positive effect on the ratio of the crack fusion life to the overall crack extension process life, but the effect of the stress ratio is essentially unchanged.

Determination of stress intensity coefficients using PC LIRA CAD

Today, the issue of involving fracture mechanics approaches to the calculation of structures with cracks is becoming more and more relevant. For the most part, the implementation of such approaches is carried out using software complexes in which the finite element method is implemented. Among them, such software complexes as Abaqus, Ansys, Nastran stand out, where the implementation of fracture mechanics approaches is constantly being improved. However, the cost of licenses for the use of such complexes, especially in the conditions of Ukraine, does not allow most researchers to fully use such programs. Therefore, it is relevant to study the possibility of applying fracture mechanics approaches in software complexes, the use of which is free. In construction, a significant number of structures are isotropic bodies. Operation of most of them is accompanied by elastic deformations. If there are cracks in them, the load-bearing capacity is assessed using stress intensity factors (SIF). This article examines the possibility of determining the TIN based on the results of the specified stress-strain state obtained with the help of the free software package "PC LIRA-SAPR 2016 R5 (non-commercial)". The calculation of SIF is performed by a direct method based on the determined distribution of displacements and stresses around the crack tip. The crack is modeled by setting appropriate boundary conditions. Implementation of the direct method is performed in 2 ways. According to the 1st method, the SIF calculation is performed in the apical area according to the values of stresses and displacements. According to the 2nd method, the SIF is calculated by moving the node closest to the top of the crack. Approbation of the approaches was carried out on the test problem of tension of a plate with a central crack. A study of the influence of the dimensionality of the discrete model and the types of finite elements both outside the apex region and in the apex region itself was conducted. The obtained results showed the possibility of obtaining reliable SIF values in this software complex in two ways, subject to compliance with certain rules for building a discrete model.

Experimental and Computational Study of Microhardness Evolution in the HAZ for Al–Cu–Li Alloys

The Laser Beam Welding (LBW) of aluminum alloys has attracted significant interest from industrial sectors, including the shipbuilding, automotive and aeronautics industries, as it expects to contribute to significant cost reduction associated with the production of high-quality welds. To comprehend the behavior of welded structures in regard to their damage tolerance, the application of fracture mechanics serves as the instrumental tool. However, the methods employed overlook the changes in the microstructure within the Heat-Affected Zone (HAZ), which leads to the degradation of the mechanical properties of the material. The purpose of this study is to simulate microhardness evolution in the HAZ of AA2198-T351 LBW. The material represents the latest generation of Al-Cu-Li alloys, which exhibit improved mechanical properties, enhanced damage tolerance behavior, lower density and better corrosion and fatigue crack growth resistance than conventional Al-Cu alloys. In this work, the microhardness profile of LBW AA2198 was measured, and subsequently, through isothermal heat treatments on samples, the microhardness values of the HAZ were replicated. The conditions of the heat treatments (T, t) were selected in line with the thermal cycles that each area of the HAZ experienced during welding. ThermoCalc and DICTRA were employed in order to identify the strengthening precipitates and their evolution (dissolution and coarsening) during the weld thermal cycle. The microstructure of the heat-treated samples was studied employing LOM and TEM, and the strengthening precipitates and their characteristics (volume fraction and size) were defined and correlated to the calculations and the experimental conditions employed during welding. The main conclusion of this study is that it is feasible to imitate the microstructure evolution within the HAZ through the implementation of isothermal heat treatments. This implies that it is possible to fabricate samples for fatigue crack growth tests, enabling the experimental examination of the damage tolerance behavior in welded structures.

Analytical Solution of Ice–Rock-Model Stress Field and Stress Intensity Factors in Inhomogeneous Media

The stress distribution and fracture parameter calibration of ice–rock models are important aspects of studying rock properties at high altitudes and latitudes. However, progress in ice–rock modeling has been slow and singular, and it is limited due to the discrete nature of rocks and the applicability of fracture mechanics. In this study, a circular inhomogeneous ice–rock model is proposed for the first time, and a method is provided for calculating the stress field of the model under biaxial loading. A method for calculating the single-crack stress intensity factor of the model subjected to biaxial compressive loading is also provided. The novelty of this work is that the inhomogeneous ice–rock model is treated as a superposition of two models, namely, a circular pore plate and circular ice, according to the superposition principle. The key is that the stress field distribution law of the ice–rock model is obtained based on the basis of the displacement continuity of the ice–rock interface. The analytical and approximate solutions of the stress intensity factor of a single crack were also obtained by considering the normal phase effect of the crack surface and combining the stress distribution law of the ice–rock model. Comparison with the CAE method was made to verify the correctness of the stress field and stress intensity factor calculation methods. The evolution laws of lateral pressure coefficients, the elastic modulus ratio of ice and rock on the stress field, and the stress intensity factor were analyzed. The effects of lateral pressure coefficients, elastic modulus ratios, and crack distributions on the failure modes were investigated using the extended finite element method (XFEM). This study can provide a theoretical basis for the evaluation of mechanical properties and prediction of the failure modes of frozen rock bodies.

Unusual Fatigue Crack Growth Behavior of Long Cracks at Low Stress Intensity Factor Ranges.

In this article, we characterize and review the unusual lack of threshold in fatigue crack growth (FCG) behavior for some alloys at low values of stress intensity factor ranges ΔK and its implications to damage-tolerant design approaches. This unusual behavior was first observed by Marci in 1996 in IMI 834 alloy. Conventional applications of linear elastic fracture mechanics to FCG analysis at constant R-ratio (or Kmax) assumes that (da/dN) decreases monotonically with decreasing ΔK and approaches the threshold value of ΔKth with (da/dN) ≤ 10-7 mm/cycle for a given R (or Kmax). However, instead of ΔK threshold behavior, some materials exhibit plateau or acceleration in da/dN rate with decreasing ΔK for long cracks tested in both constant R and Kmax conditions. This unusual (da/dN)-ΔK behavior is only observed experimentally but not understood and represents a challenge to scientists and engineers to model the safe fatigue life prediction of structures under low amplitude vibrating loads.

Review of Fracture Properties and Research Methods of Fiber Recycled Concrete

Aiming at the background of the application of fracture mechanics in fiber recycled concrete as well as the shortcomings of the current research, the relevant results and progress are summarized from three aspects, namely, the basic theory of fracture mechanics of fiber recycled concrete and the research progress of the fracture properties of fiber recycled concrete as well as the testing methods of the fracture of fiber recycled concrete, respectively. The development history of the application of fracture mechanics in concrete is described, three fracture forms, fracture process zones and three softening curve models of concrete are introduced, and it is proposed to combine the bilinear softening curve and the virtual crack zone model to construct the ontological relationship of the whole process of concrete cracking. The current research status of recycled brick aggregate concrete and polypropylene coarse fiber concrete is introduced. The incorporation of recycled brick aggregate adversely affects the workability, basic mechanical properties and fracture properties of concrete. The reinforcing effect of polypropylene fibers on concrete can effectively improve the adverse effects of brick aggregate on concrete, which opens up the research prospect of green concrete and has high research value. The applications of three-point bending test, four-point bending test and DIC technique in the study of concrete fracture characteristics are introduced.

Residual strength prediction of single lug and yoke joints based on the J-A2 method

To examine the effect of fatigue cracks on the residual ultimate strength of 30CrMnSiA steel single lug and yoke joints for pontoons, we developed a residual ultimate strength J-A2 model. This model was constructed by applying fracture mechanics principles, and the law of decay of the residual ultimate strength of aging single lug and yoke joints with crack propagation was obtained. Using this model, the empirical relationships of the remaining ultimate strength engineering applications of a certain equipment joint were determined, and the rationality and practicality of the method were verified by combining fatigue tests and finite-element simulations. The results provide a foundation for further analysis of the influence of crack propagation on the ultimate strength of single lug and yoke joint structures.

Autogenous self-healing induced by compressive fatigue in carbonated hydraulic lime mortars

This study investigates the autogenous self-healing mechanisms in carbonated natural hydraulic lime mortar exposed to cyclic compressive loads. We sought to explain the observed 40% surge in residual compressive strength compared to the quasi-static compressive strength following fatigue testing at frequencies of 5 Hz, 0.5 Hz, and 0.05 Hz [Theoretical and Applied Fracture Mechanics 118 (2022) 103201]. Central to our investigation is the hypothesis that cyclic loads mobilize the embedded water in the mortar, catalyzing chemical reactions that foster autogenous self-healing. To substantiate this, intact and post-compressive fatigue specimens were analyzed using differential thermal analysis (DTA), thermogravimetric assessments (TGA), mercury intrusion porosimetry (MIP), and scanning electron microscopy with energy dispersive X-ray analysis (SEM-EDX). The TGA-DTA highlighted the evolution of new hydration pathways, characterized by C–S–H gel and portlandite formation. The MIP results indicated a decline in pore volume, particularly in fine pores, affirming the synthesis of novel hydration compounds. The SEM-EDX analysis further authenticated the composition of these emergent microstructures. This work, therefore, presents a comprehensive understanding of the factors influencing autogenous self-healing in lime mortar systems.

Computational Fracture Evolution Analysis of Steel-Fiber-Reinforced Concrete Using Concrete Continuous Damage and Fiber Progressive Models.

The process of concrete cracking is a common problem because the first micro-cracks due to the loss of moisture may appear even before the concrete is loaded. The application of fracture mechanics allows for a better understanding of this problem. Steel-fiber-reinforced concrete (SFRC) samples with a notch were subjected to a three-point bending test, and the results for crack energy were used to analyze the concrete's material properties. In this paper, an experimental and numerical analysis of SFRC with rapid changes in the force (F) crack mouth opening displacement (CMOD) curve (F-CMOD) is presented. In order to obtain the relevant F-CMOD diagrams, three-point bending tests were carried out with non-standard samples with a thickness equal to one-third of the width of standard samples. For analysis purposes, crimped steel fibers were adopted. A probabilistic analysis of the most important parameters describing the material in question, such as peak strength, post-cracking strength, crack mouth opening displacement (CMOD), fracture energy, and the post-cracking deformation modulus, was conducted. The tests and the analysis of their results show that the quasi-static numerical method can be applied to obtain suitable results. However, significant dynamic effects during experiments that influence the F-CMOD curves are hard to reflect well in numerical calculations.

Influence of elevated temperature on the very high cycle fatigue properties of bearing steels

The influence of temperature on the very high cycle fatigue properties of three high carbon chromium bearing steels (52100, 52100-VIM/VAR and M50-VIM/VAR) is investigated. Ultrasonic fatigue tests up to more than 1010 cycles are performed at 22 °C, 200 °C and 300 °C. At all temperatures, the dominant failure mechanism is interior defect-initiated cracking. Nonmetallic inclusions are the origin of fracture for 52100 and carbides for 52100-VIM/VAR and M50-VIM/VAR. The fatigue strength (fracture probability of 50 % at 2 × 109 cycles) at 300 °C decreases by 56–57 % compared with 22 °C for both 52100 steels and by 41 % for M50. 52100 steels soften at elevated temperature due to low tempering temperature, but M50 is thermally stable. The hardness decrease at elevated temperature is more pronounced for 52100 steels than for M50.The results are evaluated applying fracture mechanics principles. Based on the area-parameter model, an equation to predict the fatigue strength in the VHCF regime at different temperatures is proposed.

Validation of the Orr theory in dental resin-based composites: A fractographic approach

ObjectivesThe present study aimed to assess the applicability of Orr's equation on light-cured resin-based composites (RBCs) tested in 3- and 4-point bending tests, as well as assess the operator reliability of this method. MethodsFracture mirrors of 320 specimens (n = 320) made of four RBCs that had failed in the two tests were analyzed microscopically and consequently two radii of each specimen were measured by two operators, each measuring twice. The mirror constant A was calculated using Orr's equation. The results of the two operators were compared using a t-Test and further assessment of the data was performed using a MANOVA, Tukey's post hoc test and regression analysis. ResultsWith the exception of 11 specimens, the measurement of the fracture mirror radii was carried out successfully. The calculation of the mirror constant proved successful with a high coefficient of determination (R2 > 0.98). The calculated mirror constants were operator-independent if the results of more than one measurement was taken into consideration. The ratio of the mirror constant A to the fracture toughness KIc lay between 2.1 and 2.4 for three of the four RBC. The fourth RBC had a ratio of 1.6 and was the only one where different mirror constants were observed as a function of the testing method. SignificanceThe present study proves the applicability of brittle fracture mechanics on RBCs despite them often being regarded as not brittle due to their also plastic behavior.

Fatigue Crack Growth Behavior of Different Zones in an Overmatched Welded Joint Made with D32 Marine Structural Steel

Applying fracture mechanics theory to heterogeneous welded joints might lead to an uncertain assessment of fatigue crack propagation behavior and, consequently, an inaccurate estimation of the cyclic loading capacity and fatigue life of welded structures. Combining experimental testing and analytical equations of the marine overmatched welded joints of D32 marine structural steel provided a view of the influence of strength heterogeneity on fatigue crack growth (FCG) behavior under constant cyclic loading. FCG testing was conducted using compact tension specimens under different stress ratios. The effect of residual stress on the FCG behaviors of the heat-affected zones (HAZs) and fusion zones (FZs) of the compact tension (CT) specimens was examined in the overmatched welded joints. Subsequently, the welding residual stresses were removed by post-welding heat treatment (PWHT) to focus the FCGR assessment on the microstructural effect. The results indicated that the FCG rates (FCGRs) of the FZ and HAZ materials obviously varied in as-welded and stress-relieved states. The existence of residual stress in the overmatched welded joints led to a decrease in FCG rates and prolonged the fatigue crack propagation life for the FZs and HAZs. Moreover, the FCGR increased in the base metal (BM), HAZ, and FZ with the increase in the stress ratio. The FCG curves of these materials were fitted to correct the stress ratios using the NASGRO equation. Finally, an analytical analysis of the FCGR based on the NASGRO equation revealed the relationship between different stress ratios for different materials.

Configurational Forces in a Phase Field Model for Fatigue

AbstractIn the last decades, the phase field method has drawn much attention for its application in fracture mechanics because it offers a simple unified framework for crack propagation. The core idea of phase field models for fracture is to introduce a continuous scalar field representing the discontinuous crack. Recently, a phase field model for fatigue has been proposed along this path. The fatigue failure differs from the other fracture scenarios since cracks only occur after a considerable number of load cycles. As fracturing happens, changes of the material microstructure are involved, which causes the evolution of the structural configuration. Thus, a new mathematical description not based on traditional spatial coordinates but the material manifold is desired, which will serve as an elegant analysis tool to understand the energetic forces for crack propagation. Configurational forces are a suitable choice for this purpose, as they describe the energetic driving forces associated with phenomena changing the material itself. In this work, we present a phase field model for fatigue. Furthermore, the phase field fatigue model is analyzed within the concept of configurational forces, which provides a straightforward way to understand the phase field simulations of fatigue fracture.

Fracture mechanics analysis of the stress corrosion cracking failure of stainless steel hexagonal head screws in a marine-industrial environment

This paper presents the fracture mechanics analysis of hexagonal head clamping screws of a diaphragm differential manometer located at the oil discharge head of an offshore facility. The failure mechanism was identified as chlorine stress corrosion cracking (CLSCC) in a marine-industrial environment containing chloride chemical species. The cause of failure was identified as overtightening up to 1.55 times above the nominal clamp-loads during the installation of the failed screws, while the partially failed screws were tightened closer to the nominal values. Data on the fracture toughness and CLSCC growth-rate of type 304 stainless-steel in the marine-industrial environment were obtained by applying fracture mechanics and fractographic examination. The kinetics data indicates that most of the crack growth time is spent in the Stage I of SCC, so the kinetics equation for this can be used to make conservative estimations of the remaining life if a reasonable Stage I crack-size is used.

A review on prediction of bone fracture using LEFM

Bone fractures are significant health concerns, particularly for the elderly population with osteoporosis. Prediction of the risk of fracture and its prevention can help in reducing the socioeconomic burden of osteoporotic fractures. The risk of bone fractures has been investigated at various length scales using analytical methods, computational models and physical experiments. Over the last few decades, significant developments have been reported on linear elastic fracture mechanics (LEFM) applications in predicting crack initiation and propagation. The objective of this study was to review the state-of-the-art of LEFM in the prediction of bone fractures. A brief overview of the LEFM was presented. Bone structural aspects associated with bone fractures were summarized along with the bone toughening mechanisms. Critical reviews of the literature on the use of LEFM-based modeling techniques for predicting bone fractures at various length scales were presented. The critical modeling parameters, challenges and limitations of using LEFM in simulating bone fractures were identified, showing future research directions.

Prediction of rolling contact fatigue crack propagation in bearing steels using experimental crack growth data and linear elastic fracture mechanics

Rolling contact fatigue (RCF) is a major life limiting factor for machine elements that employ non-conformal, rolling sliding, lubricated contacts such as rolling bearings and gears. This paper explores the application of linear elastic fracture mechanics (LEFM) principles, as commonly used in structural fatigue, for prediction of RCF crack propagation. A triple-disc contact fatigue machine is used to generate RCF cracks of varying lengths in AISI 52100 bearing steel roller specimens. Crack propagation rates across the surface are measured using optical inspection of test specimens and the final crack geometry is established through specimen sectioning. A numerical finite element model of surface breaking RCF cracks based on LEFM methods is devised to predict the evolution of stress intensity factors (SIFs) during over-rolling of the contact over the experimentally observed crack geometries. The model employs a suitable fracture mechanics mesh to resolve stresses at the crack tip and accounts for Hertzian contact stresses, contact friction and crack face friction. Potential effects of lubricant pressurisation within the crack are not modelled. The predicted SIFs are then related to the experimentally measured crack propagation rates to establish the applicability of the LEFM principles to RCF crack propagation. Results show that LEFM can be used to predict the growth of surface braking RCF cracks. For cracks longer than about 100 μm, a Paris law relationship with the stress intensity exponent of about 4 is derived. Mode II was seen to be the dominant mode of propagation for surface braking RCF cracks. Mode I SIFs are much smaller but can exhibit significant values when the contact is located just ahead of the crack mouth. Decreasing the crack face friction significantly increases mode II stress intensity suggesting that this is one important mechanism by which lubricant entry into the surface braking crack can accelerate its propagation. The findings can help in improving the reliability of mechanical systems by supporting the development of new tools for prediction of remaining useful life of machine components such as bearings and gears.

Study on fatigue behavior and crack propagation life of longitudinal fillet welded lap joint

Fifty longitudinal fillet welded lap joints with main plates (12 mm thick) and overlapping plates (8 mm thick) made of Q345B high-strength low-alloy structural steel, were tested. The joint specimens were fatigued at room and low temperatures (0 °C, −20 °C, and − 40 °C) under constant amplitude loading. The test life results were modelled by S–N curves and the crack growth was modelled in detail by applied fracture mechanics. The results show that the fatigue strength of the lap joint varies insignificantly when the temperature ranges from 20 °C to − 40 °C.

Experimental investigation of fracture process zone of rock in dynamic mode I fracturing and its effect on dynamic crack initiation toughness

Fracture process zone (FPZ) is critical to the applicability of linear fracture mechanics (LEFM) in rock fracturing, but little attention has been given to quantify the FPZ under dynamic loading condition in previous studies. This study presents the experimental results of notched semi-circular bending (NSCB) tests undertaken by split Hopkinson pressure bar (SHPB) to investigate the FPZ evolution for red sandstone under dynamic mode I fracturing and its effect on dynamic crack initiation toughness. A hybrid displacement–strain calibration method was proposed to characterize the FPZ with high-speed digital image correlation (DIC) technique. Results show that the FPZ initiation in dynamic fracturing is much earlier than that in quasi-static cases, and the FPZ length fully develops when crack initiation taking place at the pre-peak stage. The FPZ in dynamic fracturing is of a semi-elliptical shape with a width independent from the loading rate. The opening displacement exhibits a nonlinear decreasing trend along the FPZ boundary. LEFM theory underestimates the inherent dynamic crack initiation toughness, and the corrected dynamic crack initiation toughness was approximately 1.6 ∼ 2.1 times the uncorrected one within the loading rate ranging from 8.5 ∼ 78.2 GPa•m1/2/s in present study. The FPZ length in dynamic mode I fracturing lies in between the values predicted by Schmidt model and Irwin model, which indicates a non-linear cohesive stress with higher gradient near the FPZ tip is distributed along the FPZ.

A computational investigation of applicability of nonlinear fracture mechanics in nano-scale fracture of graphene

One of the main concerns for large-scale applications of graphene is unwanted fracture due to its low fracture toughness, close to that of an ideally brittle solid. However, graphene fracture properties and criteria have not been fully understood yet and the related understanding at the continuum-mechanics level is mostly limited to the linear elastic fracture mechanics (LEFM) investigations. In this paper, the applicability of nonlinear fracture mechanics (NLFM) to describe the fracture behavior of graphene is investigated through modeling the graphene sheets, including a center crack along the armchair and zigzag directions under mode I and mode II loading. A hyperelastic high-order continuum description is developed to be used in the nonlinear finite element simulations at the continuum level, by expanding the elastic strain energy in terms of the Lagrangian strains up to the seventh-order terms. The proposed continuum model is parameterized using the molecular dynamics (MD) simulation results to accurately reproduce the nonlinear mechanical behavior of graphene in uniaxial strain, equi-biaxial strain, and simple shear deformations. Finally, the applicability of NLFM, compared to LEFM, is investigated for graphene fracture through the continuum mechanics and MD fracture simulations. © 2001 Elsevier Science. All rights reserved