Fracture Mechanics Approach Research Articles

A critical review on free edge delamination fracture criteria

Laminates experience three-dimensional singular stress near their free edges due to elastic mismatches between layers, which can cause delamination. This paper critically evaluates methods for predicting free edge delamination and highlights the limitations of conventional strength-of-materials and fracture mechanics approaches. The Theory of Critical Distances (TCD) uses a material-dependent critical distance parameter, while Finite Fracture Mechanics (FFM) employs a combined stress-energy criterion without needing a predefined length parameter. This review compares TCD and FFM, also discussing Cohesive Zone Models and Phase-Field Models, and aims to guide the selection of appropriate methods for analyzing free edge delamination.

Investigating the influence of bending stiffness and processing parameters on single-leg bending geometries of additively manufactured composites

In less than a decade, additive manufacturing technologies have been developed so successfully that they already produce small and medium-sized lot sizes of prototypes or customised components in the industry. With its new possibilities such as combining materials and technologies, the benefits of different technologies can be merged and broaden future application fields. One way is to print with one technology on a part produced by another. Thus, a thermally bonded part composed of, e.g., selectively sintered and material-extruded components can be created. This combination of technologies was considered in this study to investigate the bonding strength of extrusion-based layers on selectively sintered surfaces and the impact of nozzle temperature, orientation, and thickness of imprinted materials. The extrusion-based layers covered stiff (fibre-reinforced polyamide) and soft (thermoplastic polyurethane) material properties with pre-cracked single-leg bending (SLB) specimens to study their effect on delamination tendencies. This combination of materials and additive manufacturing technologies has not yet been studied for the SLB testing method. The scope of this study is to obtain more information on how relatively hard-hard and hard-soft combinations behave for this special testing method. The results of this testing method were evaluated using two different fracture mechanical approaches to determine the energy release rate. A clear trend towards an improved bonding, thus, higher values, was found for higher nozzle temperatures. Furthermore, a limitation regarding the required bending stiffness of the composites was found. Overall, the single-leg bending testing method enables a relative ranking for material combinations with a certain bending stiffness.

A proposal for the combined analysis of bone quantity and quality of human cortical bone by quasi-brittle fracture mechanics

Quasi-brittle fracture mechanics is used to evaluate fracture of human cortical bone in aging. The approach is demonstrated using cortical bone bars extracted from one 92-year-old human male cadaver. In-situ fracture mechanics experiments in a 3D X-ray microscope are conducted. The evolution of the fracture process zone is documented. Fully developed fracture process zone lengths at peak load are found to span about three osteon diameters. Crack deflection and arrest at cement lines is a key process to build extrinsic toughness. Strength and toughness are found as size-dependent, not only for laboratory-scale experimental specimens but also for the whole femur. A scaling law for the length fracture process zone is used. Then, size-independent, tissue fracture properties are calculated. Linear elastic fracture mechanics applied to laboratory beam specimens underestimates the tissue toughness by 60%. Tissue fracture properties are used to predict the load capacity of the femur in bending within the range of documented data. The quasi-brittle fracture mechanics approach allows for the assessment of the combined effect of bone quantity and bone quality on fracture risk. However, further work is needed considering a larger range of subjects and in the model validation at the organ length scale.

Theoretical Review of Weight Functions for Rigid Line Inclusions: Implications for Stress Singularities and Crack Propagation

A comprehensive theoretical analysis of weight functions for rigid line inclusions in elastic materials is presented. Classical fracture mechanics approaches were extended to accurately predict stress intensity factors (SIFs) at the tips of these inclusions, which are crucial for understanding material failure. The analysis covered both static and dynamic loading conditions, including transient Mode-III problems. Weight functions for various deformation modes were derived, and the impact of rigid line inclusions on stress singularities and crack propagation was explored. These insights are valuable for the design and analysis of composite structures and materials subjected to dynamic loading.

Non-Propagating Cracks at the Fatigue Limit of Notches: An Analysis of Notch Sensitivity and Size Effect.

The issues of the high-cycle fatigue resistance of notches and the role of non-propagating short cracks in defining the fatigue notch sensitivity and fatigue limit of the configuration are addressed. A fracture mechanics approach is employed to determine the threshold configuration that defines the associated fatigue limit. The influence of notch sharpness, notch size, intrinsic fatigue limit, microstructural dimensions, and the threshold for crack propagation is examined. A simple expression is proposed to estimate the maximum fatigue notch factor, kfMax, which incorporates the influence of these non-propagating cracks. The fatigue limits for both blunt and sharp elliptical notches are analyzed and predicted based on experimental results reported in the literature. Additionally, shallow notches or small defects are analyzed, where it is found that the same hypothesis may not be applicable.

Effects of thermal treatments on the fracture behaviour of a silica-filled NBR: A study on the recovery of the Mullins effect and on the stretch-induced cavity formation

This research work is focused on the study of the fracture behaviour of a silica-filled NBR. The Mullins effect and its thermally-induced recovery are initially studied performing tensile tests: comparing the material's response in uniaxial tension and pure shear deformation conditions, a lower recovery is observed in the pure shear configuration. A similar study is then performed considering the fracture behaviour of the material. Tests are performed in quasi-static loading conditions and by applying a fracture mechanics approach. The fracture toughness is evaluated as J-integral at the crack onset and at the unstable fracture initiation; further, the crack propagation is analysed and the resistance curve is obtained. The dependence of the overall fracture behaviour of the material on the applied thermal history is evaluated. Even though the crosslinking degree seems not to be affected by the thermal treatment, the fracture behaviour is modified. A correlation of these results with a change in the material's propensity to form cavities under stretching is proposed.

Fast fracture in toughened glass when impacted randomly by Ice

Modelling the triggering of fracture at a pre-existing flaw is an evolving method of predicting ultimate failure in glass. This fracture mechanics approach of modelling has been shown to give more reliable predictions than a calibrated probabilistic distribution model (as is commonly adopted) when dealing with hail impact which is highly transient in nature. The dynamic stress intensity factor controlling fast crack growth is sensitive to the complex stress state surrounding the critical flaw. Finite element simulations of localised stresses in 3D could incur high computation cost which is compounded by the need to repeat computations until convergence and to simulate multiple strikes in emulating a storm scenario. In this study, closed-form expressions were developed to waive away the need of any simulations. With hail impact, boundary conditions of the glass panel need not be factored into the modelling, as the highly transient stresses are wave controlled. Input parameters are the thickness and level of prestress in glass; offset of position of strike from the known crack and its depth; and the size, velocity, and temperature of the ice impactor. Results from 40 test scenarios involving 5 offset distances, 3 crack depths, 2 glass thicknesses, and 2 sizes of ice were used to validate the prediction, and to reveal the sensitivity of the outcome of the impact to changes in the impact position relative to the known crack.

Numerical Investigation of Fatigue Behavior in Ti-6Al-4V Orthopedic Hip Implants Subjected to Different Environments.

In this paper, hip implants made of Ti-6Al-4V titanium alloy are analyzed numerically using Extended Finite Element Method XFEM. The combined effect of corrosion and fatigue was considered here since this is a common cause of failure of hip implants. Experimental testing of Ti-6Al-4V alloy was performed to determine its mechanical properties under different working environments, including normal, salty, and humid conditions. The integrity and life of the hip implant were assessed using the Linear Elastic Fracture Mechanics (LEFM) approach. For this purpose, the conditional fracture toughness Kq using CT specimens from all three groups (normal, humid, salty conditions) were determined. This provided insight into how different aggressive environments affect the behavior of Ti-6Al-4V alloy; i.e., how much its resistance to crack growth would degrade depending on conditions corresponding to the real exploitation of hip implants. Next, analytical and XFEM analyses of fatigue behavior in terms of the number of cycles were performed for all three groups, and the obtained results showed good agreement, confirming the validity of the integrity assessment approach shown in this work, which also represented a novel approach since fatigue and corrosion effects were investigated simultaneously.

Finite element simulations on delamination-induced local stress shielding effects on aseptic loosening behavior by bone remodeling

Interfacial damages (wear, delamination) and bone damage (remodeling, micro-cracks) can significantly affect the local bone deterioration and loosening of the acetabular cup. However, limited research has been conducted on both delamination and bone remodeling. This study aims to analyze the loosening behavior of an acetabular cup caused by the interaction of both interfacial damages and bone remodeling under different boundary conditions. A three-dimensional model of the acetabular cup was developed, and mechanically-induced remodeling behavior was implemented for the surrounding bone while the interfacial delamination between the cup and bone was modeled using the fracture mechanics approach. The delamination in the low initial bone mineral density (BMDs) cases encompasses almost the entire cup surface, which significantly affects the local bone remodeling process. The bone density near the top edge could be reduced to 20% in the lowest BMDs case which exaggerates the local strain accumulation and causes it to approach the micro-breaking limit. The loosening risk of the 45∘ fixation was reported in the low BMDs case which is a major limitation in conventional operation procedures for elderly patients. The interactive effect of the low BDMs, inclination angle, and loading amplitude can reduce the aseptic loosening life by half. This can be attributed to the amplified embedding of the acetabular cup caused by the delamination-induced reduction of the bone density. In future works, we aim to further consider anisotropic bone remodeling, microstructure of the bone, and delamination initiation behavior of surface coating.

Consideration of special effects for the application of an optimized fracture mechanics approach for the RPV safety assessment (CAMERA)

A comprehensive fracture mechanics test program called CAMERA was carried out for seven RPV base and weld materials in unirradiated and irradiated conditions. The objective was to establish an application-oriented completion of the fracture mechanics approach for the RPV safety assessment over the entire relevant temperature range up to operating temperature. For this purpose, fracture toughness tests in the ductile-brittle transition region with and without warm pre-stress (WPS), and in the ductile region (upper shelf) were performed in order to complete the fracture toughness curves of the material concerned. The test program was completed by various analytical and numerical calculations and microstructural analyses. The benefit of the WPS effect was confirmed for both the material (higher apparent fracture toughness values) and the load path (no initiation after maximum loading). By fracture toughness tests in the ductile regime the fracture toughness curve could be completed up to the operating temperature and the T0 based criterion temperature TUS above which no brittle fracture occurs was determined and successfully verified. Based on the results obtained by the Master Curve, WPS and crack resistance tests it was demonstrated how to integrate the criterion temperature TUS in the fracture toughness-temperature diagram including the loading transient to an application window for the RPV safety assessment that is based on T0 only. For three out of nineteen data sets the homogeneity screening procedure described in ASTM E1921 did indicate a macroscopically inhomogeneous material for that a generally conservative reference temperature T0IN was calculated that is on average 11 K higher than the reference temperature T0. A higher susceptibility of weld materials for macroscopic material inhomogeneity compared to base materials was found. The suitability of the applied SE(B) and C(T) specimens for the specific fracture mechanics tests (WPS and/or crack resistance in ductile region) was proven. Micromechanical Local Approach damage models (Bordet and Gurson) were successfully applied for test design and prediction of fracture toughness. The overall results reveal even so some open gaps remaining for future work that are addressed as well.

Simulation of Stress Intensity Factor and J-Integral on UIC 54 Railway Failure Using A Fracture Mechanics Approach

Repeated loading on the railroad tracks will result in fatigue failure. Fatigue failure combined with a defect in the form of a crack in the railroad track will result in a decrease in strength. Defects in the form of cracks are formed due to improper manufacturing and treatment processes. One treatment that can cause the formation of defects in the form of cracks is thermite welding. Improper and non-standard thermite welding techniques can trigger the formation of defects in the form of cracks in the railroad joints. Based on these problems, this simulation aims to obtain information about the value of maximum stress, SIF, J-Intergal, number of cycles, and crack extension from variations in crack size to repeated loading. The method consists of preprocessing, processing and postprocessing. Preprocessing begins with the design of the UIC 54 railroad crack which consists of 3 variations of crack length, namely 10 mm, 15 mm, and 20 mm. The design was tested through static structural simulation using the ANSYS 2021 R2 application. Meshing is configured using an element size of 5 mm and uses curvature capture. The results of the simulation obtained maximum stress values, SIF, J-Integral, number of cycles, and crack extension. Based on the simulation of SIF 1 and J-Integral values on the specimen design with a crack length of 10 mm it shows 362.03 Mpa.mm1/2 of 0.5708 mJ/mm2, for an initial crack length of 15 mm that is equal to 482.81 Mpa.mm1/2 and 0.91738 mJ/mm2, and for an initial crack length of 20 mm, it is 600.54 Mpa.mm1/2 and 1.4465 mJ/mm2. The results show that the increase in SIF 1 and J-Integral will be proportional to the increase in the initial crack length value. .

Solutions of crack constraint parameter in 3D models − I: Through curve shape similarity

Two-parameter approaches of elastic plastic fracture mechanics, e.g., J-A(A2), J-Q, can be used to obtain more accurate fracture analysis results, especially under low crack constraint condition which commonly observed in practical engineering structures. While, theoretical solutions of the constraint parameters in the two-parameter approaches are not available, and substantial consumption of resources and time makes it inappropriate to numerically determine constraint parameters (e.g., A(A2), Q), especially in 3D solid models. In this work, based on the curve shape similarity, the estimation theory and formulae for constraint parameter A in 3D solid models are developed through theoretical and numerical analyses to obtain parameter A solutions quickly and efficiently, so as to enable the application of two-parameter approaches in practical engineering structures. The proposed estimation formulae here are used to predict the constraint parameter A in two actual engineering structures.

Dislocation penetration in basal-to-prismatic slip transfer in Mg: A fracture mechanics criterion

Understanding the transition mechanism from microscopic to macroscopic yielding is crucial for developing high-strength metallic materials. Basal-to-prismatic slip transfer at grain boundaries (GBs) of Mg alloys is known to trigger macroscopic yielding. Here, the penetration behavior of pileup dislocations at a simple basal–prismatic (BP) boundary was analyzed using molecular dynamics simulations. Edge dislocation penetration creates a step in the BP boundary at the intersection with the slip plane, widened via subsequent penetration of dislocations. Many GBs, including the BP boundary, have a regular GB dislocation network that corresponds to a coincidence site lattice. Dislocation penetrations must gradually destroy the initial GB dislocation network, requiring increasing driving force for subsequent dislocation penetrations; thus, slip transfer at the boundary occurs sporadically and stably via the penetration of individual lattice dislocations. As the width of the step created by dislocation penetration increases, a GB dislocation network can be formed in the step, which can stabilize the energy of the step with specific widths. When the energy of step decreases with increasing step width, a smaller driving force is required for the subsequent penetration of dislocations, and thus slip transfer occurs unstably via the penetration of several sequential lattice dislocations. Once the step has a low energy at a specific width, it strongly obstructs dislocation penetration. This formation and disruption of the GB dislocation network cause intermittent penetration of dislocations. Finally, dislocation penetration at the BP boundary is discussed based on a fracture mechanics approach, which well-reproduces the transition between penetration behaviors and the macroscopic yield stress.

Optimization of Fracture and Moisture Damage Resistance of Stone Matrix Asphalt Mixtures Containing Crumb Rubber-Modified Binder with the Fracture Mechanics Approach

Optimization of Fracture and Moisture Damage Resistance of Stone Matrix Asphalt Mixtures Containing Crumb Rubber-Modified Binder with the Fracture Mechanics Approach

Investigating the effects of steel strength and tensile overload level on fatigue crack growth performance

Individual overloads (OLs) might significantly relax tensile residual stresses (RS) besides generating compressive RS in welded components and, thus, influence the fatigue performance of these components. This study seeks to investigate the effects of steel strength and OL level on the fatigue life performance of welded components. Welding calculations were first performed for different steel grades to predict welding RS (WRS). A series of numerical fatigue calculations were conducted using the elastic–plastic fracture mechanics approach based on FEM to comprehend the fatigue performance under various OL levels. The fatigue calculations were performed in the absence and presence of the WRS effect. The results showed that the higher-level OLs improved the fatigue performance of components made of higher-strength steel when the WRS effect was considered. In contrast, in the absence of the WRS effect, an improvement in fatigue performance was achieved from the higher-level OLs by lower-strength steel. Also, a remarkable RS relaxation with varying degrees was induced from the higher-level OLs for the applied steel grades. This variation in the degree of RS relaxation could be attributed to the difference in WRS distributions over the crack surface. The crack driving force and retardation effect were also used to support the study.

Crack Catcher AI – Enabling smart fracture mechanics approaches for damage control of thin silicon cells or wafers

Silicon has been one among a few key technologically important materials especially in our modern world. Silicon, especially in its current most useful forms (thin layers), is a brittle material by nature. Thin silicon cells crack easily during manufacturing assembly. Every crack is a defect in any PV manufacturing lines, and if let to grow/propagate it will lead to reliability and quality issues with time. Nevertheless, the global silicon solar PV industry is aggressively reducing the cost of solar PV systems through cutting down the thickness of silicon solar cells. Cell cracks immediately lower PV module efficiency and can lead to premature aging of the entire module. The “Crack Catcher AI” was our research joint collaboration's entry in the Department of Energy (DOE)'s American-Made Solar Innovation competition in 2022 (Round 6) which later was selected as the national semifinalists and won an award announced by DOE in December 2022. It uses smart stress sensing and smart fracture prediction approaches utilizing fundamental fracture mechanics and big data analytics to reduce crack defects and enhance long-term durability/reliability of PV products/devices. Smart Stress Sensing uses a novel laser-based curvature methodology for fast in-line stress metrology in manufacturing lines. Smart Fracture Prediction uses Artificial Intelligence (AI) for defect control metrology and yield enhancement in PV production lines. It is based on monocrystalline silicon used in solar PV industries, but all scientific principles utilized and technological innovations developed in this article would be applicable as well for single crystal silicon semiconductor wafers.

Fracture mechanics approach to minimum reinforcement design of fibre-reinforced and hybrid-reinforced concrete beams

The problem of the minimum reinforcement condition in fibre-reinforced and hybrid-reinforced concrete flexural elements is addressed in the framework of fracture mechanics by means of the Updated Bridged Crack Model (UBCM). The model describes the crack propagation process occurring in the critical cross-section of the reinforced member, by assuming the composite as a multiphase material, whereby the toughening contribution of the cementitious matrix and of the reinforcements are independently evaluated. The key-point of the discussion is that, when the influence of the matrix nonlinearities on the response is neglected, the minimum reinforcement condition is defined by a linear relationship between the critical values of two dimensionless numbers: (i) the bar- reinforcement brittleness number, NP , proportional to the steel-bar area percentage, ρ; (ii) the fibre- reinforcement brittleness number, NP,f, proportional to the fibre volume fraction, Vf. The model is applied to several experimental campaigns of the literature, in order to assess its suitability in the minimum reinforcement design of reinforced members in a unified fracture mechanics-based framework.

Fracture mechanics modeling of aortic dissection

Aortic dissection, a critical cardiovascular condition with life-threatening implications, is distinguished by the development of a tear and its propagation within the aortic wall. A thorough understanding of the initiation and progression of these tears, or cracks, is essential for accurate diagnosis and effective treatment. This paper undertakes a fracture mechanics approach to delve into the mechanics of tear propagation in aortic dissection. Our objective is to elucidate the impact of geometric and material parameters, providing valuable insights into the determinants of this pivotal cardiovascular event. Through our investigation, we have gained an understanding of how various parameters influence the energy release rate for tear propagation in both longitudinal and circumferential directions, aligning our findings with clinical data.

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.

Fracture mechanics approach to TRISO fuel particle failure analysis

Weibull stress-based methods for failure probability assessment have been developed and analyzed to assess the integrity of tristructural isotropic (TRISO) fuel particles during fuel life cycles and accident operating conditions. While simple, these methods entail a number of drawbacks when stress concentrates near crack tips, including finite element mesh size dependency when the Weibull stress is averaged over the finite element domain. Fracture mechanics approaches involving the use of interaction integrals eliminate this lack of mesh convergence and produce consistent fracture predictions. In this work, we use an interaction integral approach to computing stress intensity factors for a crack in the inner pyrolytic carbon layer perpendicular to the silicon carbide layer, which is simplified representation of a failure mode in TRISO particles. The interface between these two TRISO layers has been shown to become porous, which we simulate by considering a transition of mechanical properties over such porous length, i.e. the layers are modeled as a functionally graded material. Aspects such as porosity and thermal and irradiation eigenstrains are considered in computing the stress intensity factor from a fracture mechanics approach and compared with the known Weibull stress failure approach. The methodology introduced in this paper enables a more general fracture probability assessment in TRISO particles and eliminates the need to identify best suited parameters when using local or averaged stress-based failure criterion. Finally, the numerical sensitivity studies show how parameters such as the porous transition zone length, the material stiffness, and creep affect the probability of TRISO fuel particle failure.