Linear Elastic Fracture Mechanics Approach Research Articles

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.

Development of corrosion-fatigue analysis method of cable hangers in tied-arch bridges considering train-bridge interaction

This study proposes an integrated corrosion-fatigue analysis method for bridge hangers by combining the dynamic bridge-train interaction analysis for random train arrivals with various speeds and the linear elastic fracture mechanics (LEFM)-based crack propagation analysis considering the corrosion-fatigue effects. Accordingly, a three-stage process, namely, zinc coating corrosion, pit-crack transition, and corrosion-fatigue crack propagation for wires in hangers, was proposed to simulate the total service life. A train-bridge-interaction analysis was conducted on a tied-arch bridge with multiple cable hangers using the vector form intrinsic finite element method, where the stresses in the hangers were generated under high-speed train loads. The pit-crack transition was analyzed based on the pit growth and fatigue growth; whose rates compete to dominate the transition phenomenon. The fatigue crack growth rate was estimated using a LEFM approach considering the equivalent stress ranges and number of stress cycles. The effects of reducing the cable cross-section and updating the internal stress of the multi-layered wires were investigated. The present method was compared with the continuum damage mechanics model for validation. A relatively short remaining corrosion-fatigue life was found in the cables under the train loads, after corrosion of the zinc coating and pit-crack transition in the steel wires were developed.

On Cyclic-Fatigue Crack Growth in Carbon-Fibre-Reinforced Epoxy-Polymer Composites.

The growth of cracks between plies, i.e., delamination, in continuous fibre polymer matrix composites under cyclic-fatigue loading in operational aircraft structures has always been a very important factor, which has the potential to significantly decrease the service life of such structures. Whilst current designs are based on a 'no growth' design philosophy, delamination growth can nevertheless arise in operational aircraft and compromise structural integrity. To this end, the present paper outlines experimental and data reduction procedures for continuous fibre polymer matrix composites, based on a linear elastic fracture mechanics approach, which are capable of (a) determining and computing the fatigue crack growth (FCG) rate, da/dN, curve; (b) providing two different methods for determining the mandated worst-case FCG rate curve; and (c) calculating the fatigue threshold limit, below which no significant FCG occurs. Two data reduction procedures are proposed, which are based upon the Hartman-Schijve approach and a novel simple-scaling approach. These two different methodologies provide similar worst-case curves, and both provide an upper bound for all the experimental data. The calculated FCG threshold values as determined from both methodologies are also in very good agreement.

Propagation of multiple hydraulic fractures in a transversely isotropic shale formation

Shale anisotropy can lead to deviated patterns of hydraulic fractures in multi-stage hydraulic fracturing (MSHF) operations, significantly hindering hydrocarbon production. Such deviation usually occurs in formations where the induced fractures interfere with natural bedding planes or where the stress shadow is created. In this work, the elastic behavior of a transversely isotropic shale rock during MSHF is investigated using the extended finite element method (XFEM) in conjunction with the cohesive zone model (CZM) in ABAQUS. In comparison to the linear elastic fracture mechanics approach, the CZM considers the plasticity and softening effects at the fracture tip, and therefore, leads to a more accurate prediction of fracture geometry. The XFEM model is capable of simulating fractures with an arbitrary path without requiring re-meshing. The 2D numerical model is first verified against the Kristianovich-Geertsma-de Klerk (KGD) analytical solutions. Five injection clusters in a single fracturing stage are simulated to analyze the effects of the material isotropy, the dip angle of shale bedding, and the fracture spacing on the geometry of multiple hydraulic fractures. The transversely isotropic poroelasticity model predicts narrower and longer hydraulic fractures than the isotropic poroelasticity model. The bedding dip angle plays a crucial role in the deviation and the shape of multiple hydraulic fractures. Increasing the dip angle from zero to 90° results in an increase in the average fracture width and an increase-peak-decrease trend in the fracture length. A strong correlation is observed between the fracture spacing and the fracture geometry, and a spacing of 75 m is considered optimal because it results in no discernible stress shadow at all dip angle cases.

Maximum aggregate size effects on the evolution of the FPZ and crack extensions in concrete – Experimental and numerical investigation

In this paper, an experimental/numerical investigation is proposed to study the effect of maximum aggregate size (Dmax) on the fracture process zone (FPZ) length variations and the crack extension. Experimentally, three-point bending tests have been realized on plain concrete with different maximum aggregate sizes under crack mouth opening displacement (CMOD) control. The crack growth is monitored using the acoustic emission (AE) technique. The numerical investigation is conducted at a mesoscale level. From the evolution of cohesive tangential stresses along the crack path, the variation of FPZ is explored. The crack extensions are investigated using the equivalent linear elastic fracture mechanics approach (LEFM) to investigate the R-curves. The results show a great influence of the maximum aggregate size both on the FPZ variation and on the global behavior.

Influence of crack configurations on fatigue crack growth behavior of Al 2024 alloy

The effect of inter crack distance on fatigue crack growth (FCG) on the multi-crack computational domain in Al 2024 was simulated using the extended finite element (XFEM) method. An in-house developed MATLAB code was used to simulate the experimentally reported FCG behavior of side edge crack and center cracked specimen. Numerical simulation was performed by using Nasgro constitutive model and this model was chosen over Paris equation due to the capability of predicting all regions (i.e., Region I, II, and III) of FCG regime. The empirical model constants of the Nasgro equation were calculated by using a genetic algorithm (GA). The genetic algorithm was implemented to optimize the model constants by minimizing the average error between simulated and experimental FCG regimes. This method was then extended to the multi-crack computational domain to investigate the effect of crack spacing on FCG rate. Al 2024 alloy is widely used in structural applications in the aerospace and automobile sector. Therefore, the prediction of fatigue crack growth behavior, especially in the high cycle fatigue region, becomes very important for predicting the damage tolerance of the material. In high cycle conditions, the stresses involved are lower than the yield stress, and hence the Linear elastic fracture mechanics (LEFM) approach was used. This LEFM approach was coupled with the XFEM method for comparing the fatigue crack growth behavior in the single crack and multi crack domains in the present work.

A Thermodynamically Consistent, Phase-Field Electro-Chemo-Mechanical Theory with Account for Damage in Solids: Application to Metal Filament Growth in Solid-State Batteries

Solid-state batteries (SSBs) present a promising technology and have attracted significant research attention owing to their superior properties including increased energy density (3860 mAh), wider electrochemical window (0-5V) and safer electrolyte design. From a safety standpoint, SSBs are particularly appealing in that replacement of flammable conventional organic electrolytes with highly conductive, mechanically stiff inorganic solid-state electrolytes (SSEs) can alleviate failure due to short circuit or ignition. However, operation of SSBs is hampered by numerous chemo-mechanical challenges [1 - 4], the most critical one associated with metal filament growth across the SSE.Filament protrusions can initiate at perturbations of the interface or microstructural heterogeneities and subsequently grow through the SSE, causing the battery to short-circuit. It is critical to understand from both an experimental and modeling perspective the interplay of various mechanisms including morphology of the SSE microstructure, elastic-viscoplastic behavior of Li-metal, critical current density and stack pressure on the morphology of filamentary protrusions across the SSE. While much has been done to understand the interplay of aforementioned mechanisms from an experimental standpoint [5,6], theoretical frameworks on modeling of filaments growth in SSBs are still at their infancy and typically simplify dendrites as pressurized cracks under a linear-elastic fracture mechanics (LEFM) approach [7-8]. In this work, we propose a thermodynamically consistent phase-field reaction-diffusion-damage theory to investigate the morphology of filament growth across the SSE under varying chemo-mechanical operational conditions. The theory is fully coupled with electrodeposition at the Li metal-SSE interface impacting mechanical deformation, stress generation and subsequent fracture of the SSE. Conversely, electrodeposition kinetics are affected by mechanical stresses through a thermodynamically consistent, physically motivated driving force that distinguishes the role of various chemical, electrical and mechanical contributions. Concurrently, the theory captures the interplay between crack propagation and electrodeposition phenomena by tracking the damage and reaction field using separate phase-field variables such that metal growth is preceded by and confined to damaged regions within the SSE accessible by Li-metal. This is a critical feature of the theory and confirms experimental observations that the crack front propagates ahead of Li. We specialize the theory and study the role of variations of chemo-mechanical properties (i.e. applied electric potential, SSE fracture energy) on the morphology of metal filament growth and map operational conditions to distinguish between domains of i) stable vs. unstable growth ii) intergranular vs. transgranular growth mode. In doing so, the proposed framework provides a quantitative understanding on mechanisms dictating metal filament growth in SSEs and identifies mitigation strategies to employ in future SSB designs for successful operation.

Distortion – Induced Fatigue Failure at Main Girders of a Railway Bridge – Strain Measurements in Service and Analyses Based on Fracture Mechanics

AbstractAt the main girders of a three span continuous plate girder railway bridge, built in the 1970s, through‐thickness cracks were detected in the web, at the location of the transverse stiffener to main girder connections. Based on former Austrian standards for steelwork, the transverse stiffeners are not welded to the main girder flanges in order to increase their fatigue resistance. Instead, fitting pieces between the stiffeners and the bottom flanges were used.Within the paper the geometry and the location of the cracks are presented. For the global stresses, due to moments and shear forces, numerical simulations of the train passages were done. Based on these global stresses only, the fatigue damage for the main girders was evaluated at each position of a transverse stiffener connection. Since there was no significant agreement between the distribution of the global fatigue damage along the main girder and the crack positions, the out‐of‐plane distortion in the web gap region was expected as the obvious cause for the cracks.To verify the complex local stress field in the web gap region (interaction of global and local stresses), comprehensive strain measurements were done during service. The relevant results, including passages of slow and fast individual locomotives, passenger and freight trains, are presented and compared.Finally, based on the measured stress range spectra the further crack growth behavior was analyzed and the residual fatigue life was predicted using a linear elastic fracture mechanics (LEFM) approach where also the mixed‐mode conditions at the crack tips were considered.

Elucidating the effect of cohesive zone length in fracture simulations of particulate composites

The influence of the cohesive zone length on the crack driving force is quantified and analyzed in a representative system of particles dispersed in a matrix of a composite material. For heterogeneous material systems, e.g. particulate composites, it is known that as a crack approaches the particles, the crack driving force may increase (shielding) or decrease (anti-shielding) depending on the relative stiffness of the particles. These results have been established in numerous studies using the classical linear elastic fracture mechanics approach (LEFM). The cohesive zone method (CZM) introduces a length scale parameter, referred to as the cohesive zone (or fracture process zone) length scale, into the formulation of fracture mechanics. It is generally established that fracture mechanics predictions using the CZM are similar to those obtained using LEFM in the limit case where the process zone is very small relative to a suitable characteristic dimension of the problem. However, the influence of the length scale parameter has not been clearly demonstrated for crack propagation in a heterogeneous material system, especially when the cohesive zone length is not negligible. By considering a simple crack-particle-matrix system, it is shown that, in addition to the elastic properties, the process zone length scale parameter exhibits a critical influence on the crack driving force. For this study, the concept of configurational forces is utilized and the eXtended Finite Element Method (XFEM) is employed as a tool to simulate crack propagation. Through numerical simulations, it is shown that (i) the magnitude of the driving force vector directly depends on the length scale parameter and (ii) the direction of the driving force is largely influenced by the presence of a cohesive zone. This, in turn, alters the crack trajectory in the particulate system if the criterion for the direction of crack propagation depends on the orientation of the driving force vector. Towards this end, two different criteria for direction of crack propagation, namely maximum principal stress and maximum energy dissipation, are compared in the presence of a cohesive zone and the results are reported. The study reveals the crucial influence of the inherent length scale associated with the cohesive zone method when applied to crack propagation in particulate composite systems and elucidates important differences when comparing predictions from distinct theories of fracture mechanics.

Early crack orientation prediction methods under fretting fatigue loading including wear effects

This paper investigates two different methods to predict crack initiation direction in fretting problems subjected to partial slip conditions. One of them is based on the Critical Direction Method (CDM) combined with the Smith Watson and Topper (SWT) fatigue damage parameter. The other consists in simulating early crack propagation using a Linear Elastic Fracture Mechanics (LEFM) approach associated with the SWT parameter. In addition, this paper also investigates the influence of considering wear in the crack initiation direction estimates. For validation of the methods, experimental data from fretting tests conducted on an AA7050- T7451 alloy were used. Results have shown that the CDM-based model provides very accurate estimates, whereas the LEFM-based approach failed to properly reproduce experimental observations. Besides, it was also verified that the inclusion of wear has little effect on the estimates despite the method considered.

Comparison between PSM and IBESS approaches for the fatigue life estimation of weldments

In the framework of the fatigue assessment of welded components, several methods are available in design standards such as the nominal stress, hot-spot stress, notch stress and linear elastic fracture mechanics approaches. The present paper aims at comparing two advanced local approaches for the fatigue strength assessment of different welded joints made of steel. The first one is IBESS which is based on short crack fracture mechanics. The second one is the PSM which instead involves the strain energy density approach. Both methods will be briefly presented, and the fatigue life prediction results discussed. The results obtained for the joint geometries considered in this work show advantages and drawbacks of the approaches, which are thoroughly analysed as well.

Early crack orientation prediction methods under fretting fatigue loading

This paper investigates two different methods to predict crack initiation direction in fretting problems subjected to partial slip conditions. One of them is based on the Critical Direction Method (CDM) combined with the Smith Watson and Topper (SWT) fatigue parameter. The other consists in simulating early crack propagation through a Linear Elastic Fracture Mechanics (LEFM) approach associated with the SWT parameter. For validation of the methods, experimental data from fretting tests conducted on an AA7050-T7451 alloy were used. Results have shown that the CDM-based model provides very accurate estimates, whereas the LEFM-based approach failed to properly reproduce experimental observations.

Experimental investigation of fracture toughness of fused deposition modeling 3D-printed PLA parts

The fracture toughness of Polylactic acid (PLA) parts printed using the Fused deposition modeling (FDM) additive manufacturing process is experimentally investigated in this study. The compact tension (CT) specimens were printed with 0°/90° and −45°/45° filament orientations at different printing speeds varying from 20 mm/s to 60 mm/s. Fracture toughness values for each process parameter were estimated using the linear elastic fracture mechanics (LEFM) approach. It is observed that the CT specimen printed at the highest speed showed the lowest value of fracture toughness; however, the energy absorbed before failure is the highest. The −45°/45° CT specimen showed higher value of fracture toughness compared to the 0°/90° specimen. Tensile tests were also conducted on PLA filament and part level coupons to estimate the mechanical behavior. The FDM printed tensile coupon showed a brittle failure. However, the PLA filament showed ductile behavior with a clear plastic zone.

Применение метода J-интеграла к оценке вязкости разрушения полимерных композиционных материалов

This paper discusses a relevant topic of improving the approaches to fracture toughness determination of layered composites. Current ASTM regulations imply the calculation of critical value for fracturing viscosity as per the test data following the classic approach of linear-elastic fracture mechanics (LEFM). For some materials, however, LEFM-based estimates are not realistic. As an alternative to LEFM in calculation of critical failure viscosity value, this paper suggests a method of J-integral. The data needed to apply this method were obtained through numerical experiments in ANSYS finite-element software package. The results of numerical experiments were used to construct load-displacement curves and compare them with the test data. The difference between critical viscosity fracturing values yielded as per LEFM and J-integral method might be as high as 33 %. This study revealed that J-integral method offers more accurate fracture toughness estimates for layered composites be- cause maximum design load results based on critical fracturing viscosity value obtained using J-integral deviated from average loads recorded during physical tests by not more than 2% whereas LEMF-based in certain cases had this deviation as high as 15 %. Still, J-integral method applied in this study required the inputs from numerical analysis, so it needs additional experimental verification.

Study of the micro-crack growth in the concrete material to predict its lifetime

The concrete always contains microstructures like micro-crack, voids, etc. These parameters affected the lifetime of materials. This article presents a computation algorithm to predict the lifetime of brittle materials like concrete which depends on the distribution of micro-crack in the materials. The proposed model is based on subcritical crack growth using the linear elastic fracture mechanics (LEFM) approach. The algorithm considers both tensile and shear fracturing. The proposed model was applied to a concrete sample under compressive loading for the prediction of a lifetime. The results showed a significant difference in failure zones and failure time under different magnitude compressive loadings and initial crack length.

Finite Element Simulation Technique for Evaluation of Opening Stresses Under High Plasticity

Abstract The crack closure phenomenon is important to study as it estimates the fatigue life of the components. It becomes even more complex under low-cycle fatigue (LCF) since under LCF high amount of plasticity is induced within the material near notches or defects. As a result, the assumptions used by the linear elastic fracture mechanics (LEFM) approach become invalid. However, several experimental techniques are reported on the topic, the utilization of numerical tools can provide substantial cost and time-saving. In this study, the authors present a finite element simulation technique to evaluate the opening stress levels for two structural steels (25CrMo4 and 30NiCrMoV12) under low-cycle fatigue conditions. The LCF experimental results were used to obtain kinematic hardening parameters through the Chaboche model. The finite element analysis (FEA) model was designed and validated, following the fatigue crack propagation simulation under high plasticity conditions using abaqus. Crack opening displacement versus stress data were exported from abaqus, and 1.5% offset method was employed to define opening stress levels. Numerical simulation results were compared with the experimental results obtained earlier through the digital image correlation (DIC) technique. To conclude, FEA could be a valuable tool to predict crack closure phenomena and, ultimately, the fatigue life of components. However, analysis of opening stresses using crystal plasticity models or extended finite element method (XFEM) tools should be explored for a better approximation in future studies.

Probability of instant rail break induced by wheel–rail impact loading using field test data

ABSTRACT The probability of an instant rail break, initiated at a single pre-existing rail foot crack due to a severe wheel impact loading, is predicted using statistical methods and a time-domain model for the simulation of dynamic vehicle–track interaction. A linear elastic fracture mechanics approach is employed to calculate the stress intensity at the crack in a continuously welded rail subjected to combined bending and temperature loading. Based on long-term field measurements in a wayside wheel load detector, a three-parameter probability distribution of the dynamic wheel load is determined. For a faster numerical assessment of the probability of failure, a thin plate spline regression is implemented to develop a meta-model of the performance function quantifying the stress intensity at the crack. The methodology is demonstrated by investigating the influence of initial crack length, fracture toughness and rail temperature difference on the risk for an instant rail break.

Microstructures and Fatigue Behavior of Additively Manufactured Maraging Steel Deposited on Conventionally Manufactured Base Plate

Maraging steel powder was additively deposited on the conventionally manufactured (CMed) maraging steel base plate by powder bed fusion type selective laser melting. Residual tensile stress was introduced into the additively manufactured (AMed) part due to the re-solidification of melted powder on the base plate. Tensile fatigue tests were conducted using the specimens having hybrid structure of AMed and CMed parts. The fatigue strengths of the specimens with hybrid structure were lower than those of the CMed specimens because fatigue cracks predominantly initiated at the defects in the AMed part. Two kinds of post-aging treatments could increase the hardness of the AMed and CMed parts, while had little effect on the fatigue strengths. The maximum size of the defects in the AMed part of the specimen was estimated based on the statistics of extremes. The fatigue limits of the as-built and post-aged samples were estimated by the linear elastic fracture mechanics approach. However, the predicted values were slightly higher than the experimental values.

Surface crack and fatigue analysis for cylindrical shaft

In the present work Surface Crack and fatigue analysis for combined cyclic twisting and tension loading using linear elastic fracture mechanics approach and Structure analysis with different orientations of cracks have been performed. The effective stress intensity factor was found to fluctuate during the crack growth when the loading conditions changed, Result shows that when the orientation change from 0 to 10 degree the minimum life of the cylindrical shaft has changed significantly, and its reduced life of the shaft but when the orientation change from 0 to 20 degree its minimum life has been an increase, for the rest 30 degrees and 40 degrees of the crack orientation the minimum life of the shaft get decrease again.

Fracture mechanics analysis of the effect of clamping stress on the fatigue life of riveted built-up railroad girders under variable amplitude loading

A linear-elastic Fracture Mechanics approach is used to estimate the fatigue life of riveted connections present in railroad bridge built-up steel girders under variable amplitude loading. Special care has been taken to analyze the effect of thermal clamping stresses on fatigue life. The analysis is developed using the variable amplitude stresses generated due to a traversing heavy axle train on a simply supported girder. Stress intensity factors for quarter elliptical corner crack emanating from a through-thickness (rivet) hole under remote tension were used. Thermal clamping stress, typically generated during the installation process, was quantified through a finite element simulation. Superposition principle was utilized to account for localized clamping stress present on the base material along with remote tension. Fatigue life estimations calculated using a linear-elastic Fracture Mechanics approach with and without considering clamping stress are compared. Finally, crack growth proved to be different under the effect of localized clamping stresses when compared to a crack growth emanating from a hole with no clamping stress.