Fatigue crack growth

For decades, resistance spot welding (RSW) between aluminum and copper has encountered difficulties; however, it remains essential for modern applications. Additionally, crack propagation and the stress intensity factor (SIF) of dissimilar RSW have not been extensively investigated. The welding parameters used for Al-Al joints were as follows: welding current, time, and electrode force were set at 14,000 Amps, 0.8 seconds, and 7,000 N, respectively. Conversely, for Al-Cu joints, 14,000 Amps, 1 second, and 8,800 N were determined. The similar joints exhibited an average weld nugget size of 6 mm, whereas the dissimilar joints had a nugget size of 5.2 mm. The tensile shear force was 690 N and 780 N for dissimilar and similar joints, respectively. Accordingly, the fatigue load, as a percentage of the tensile force, was utilized at 414 N and 468 N for Al-Cu and Al-Al, respectively. Finite Element Analysis (FEA) was employed to determine the SIF. The initial crack length was determined to be 0.1 mm. The numerical solution was then compared with theoretical solutions for the opening SIF-KI, such as the equations proposed by Pook and Zhang. The FEA results showed higher values of SIF compared to those from theoretical solutions. Additionally, crack propagation was investigated for both dissimilar and similar joints at a determined failure load. Cracks tended to develop close to the heat-affected zone (HAZ) around the weld nugget diameter (d n). SIF and crack path have been verified.

Repair welding of cast iron components is widely employed to restore structural integrity in large-scale systems such as wind turbine hubs. However the brittleness and susceptibility of cast iron components to crack initiation and combined effect of weld bead geometry and Residual Stresses (RSs) on Fatigue Crack Growth (FCG) highlights the need for a thorough understanding and potential optimisation of the process. This study develops an integrated experimental–numerical framework to elucidate the FCG behaviour of repair-welded ductile cast iron, explicitly accounting for RS and geometric effects. FCG tests were conducted on welded specimens extracted from three different areas, namely Weld Metal (WM), Heat-Affected Zone (HAZ), and Base Metal (BM) to determine material-specific crack growth parameters. A coupled thermo-mechanical finite element model is used to predict the RS fields induced during single- and multi-pass repair welding, followed by three-dimensional FCG simulations incorporating semi-elliptical surface defects and elliptical embedded cracks under the influence of RS. Parametric analyses are performed to evaluate the effects of weld bead removal, number of passes, and inter-pass temperature on the RS evolution, Stress Intensity Factors (SIFs), and synthetic S–N curves. The experimental results show the WM exhibits the lowest threshold SIF range, while the BM shows the highest. The numerical results indicate that multi-pass welding with controlled inter-pass temperature reduces RS magnitudes by up to 25%, whereas weld bead removal improves the fatigue life by mitigating local stress concentration. The developed numerical framework is applied to a large-scale wind turbine hub to demonstrate its predictive capability, with the results showing that RS can entail a twofold reduction of the fatigue life. The proposed methodology provides a robust basis and highly cost efficient means for optimising repair welding parameters to enhance fatigue performance in service-critical cast iron structures.

One of the many advantages in the use of composite materials in engineering structures is their resistance to fatigue. Careful component design means that complex, weight-efficient components can be produced which are "intrinsically safe" in that they have an effectively infinite fatigue life. Excessive loading and manufacturing/design details may, however, invoke a process analogous to fatigue in metal components leading to ultimate failure of the component at a load below its design limit. A somewhat qualitative analysis has shown this mechanism to result primarily due to subcritical crack growth within the resin matrix material. Although the phenomena need further investigation, it was found that the crack growth could be suppressed by using a resin matrix with a much higher toughness. A short introduction to the use of composite materials in formula 1 is given along with a discussion to illustrate how the practical application of Materials Science and Fracture Mechanics principles were used to solve a potentially serious problem.

Sensor-based degradation signals measure the accumulation of damage of an engineering system using sensor technology. Degradation signals can be used to estimate, for example, the distribution of the remaining life of partially degraded systems and/or their components. In this paper we present a nonparametric degradation modeling framework for making inference on the evolution of degradation signals that are observed sparsely or over short intervals of times. Furthermore, an empirical Bayes approach is used to update the stochastic parameters of the degradation model in real-time using training degradation signals for online monitoring of components operating in the field. The primary application of this Bayesian framework is updating the residual lifetime up to a degradation threshold of partially degraded components. We validate our degradation modeling approach using a real-world crack growth data set as well as a case study of simulated degradation signals.

A new model is proposed in order to describe the three regimes (near-threshold, intermediate and high propagation rate) of fatigue crack growth for a range of load ratios with a generalized exponential equation. The FCG curves used in this work include experimental data comprising aluminium alloy AMS 7475 T7351 obtained by means of constant-load-amplitude tests with four load ratios and one K-decreasing test for R = 0.1, as well as crack growth data taken from literature for three aluminum alloys: 6013-T651, 2324 T39 and 7055 T7511. The performance of the proposed exponential equation is compared to the modified Forman model with respect to the goodness-of-fit and the ability to correlate the crack propagation rate for different Rratios with a reduced number of parameters.

This manuscript extends the TMFMT/NMFMT no-fit phasor-damage fatigue closure from metals to non-metallic polymer blends. The central claim is restricted: the polymer extension is not a universal proof of dominance over all fatigue models, but a reproducible no-fit benchmark showing that the model becomes predictive once the two-mode variables are computed from independently measured viscoelastic quantities. On six PMMA-PC/ABS blend states, the DMA-based TMFMT-PD3.0-P closure reduces the mean absolute percentage error from 3.316 % for the two-anchor Basquin baseline to 3.105 %. On the three states for which explicit Figure 8 hysteresis-energy values are available, the hysteresis-informed TMFMT-PD3.1-PH closure further reduces the mean error from 3.527 % to 2.576 %, winning on all three material states.

We introduce TMFMT-PD2.0, a no-fit cross-product phasor-damage closure for stress-life (S-N) fatigue prediction. The model is based on the longitudinal-transverse two-mode structure of the Two-Mode-Field Membrane Theory (TMFMT) and its N-mode generalisation (NMFMT). Its central invariant is the phasor cross-product factor C eff = 1 + ξ 2 + 2ξ cos ϕ, where ξ is the transverse/longitudinal amplitude ratio and ϕ is the internal phase lag. In the present benchmark no intermediate S-N data are fitted: the model uses only endpoint material anchors S ut , S e , N e , and predefined material-state closure rules for ξ and ϕ. Across 14 publicly tabulated S-N material states and 86 held-out intermediate validation points, TMFMT-PD2.0 reduced mean MAPE from 9.402% for the two-anchor Basquin no-fit baseline to 2.972%, and reduced mean RMSE from 24.865 MPa to 10.128 MPa. The model won against the Basquin no-fit baseline in 14/14 material states by MAPE and 14/14 by RMSE. The result is best described as a first mechanistic no-fit multi-material benchmark validation of a TMFMT/NMFMT phasor-damage closure, not as a final universal replacement for all existing fatigue models.

The problem of mixed-mode fatigue crack growth has been a persistent research challenge. The determination of fatigue crack propagation direction directly impacts the components and structures' safety and integrity, making it crucial in various industrial applications, including welded drilling pipes, aerospace, and automotive engineering. Unlike the uniaxial loading problem, mixed-mode cracks tend to change their direction frequently (kink), and having a cyclic loading adds to the complexity of the problem. This research aims to estimate the crack propagation direction of linear elastic materials subjected to mixed-mode (I+II) loading conditions, proportional or nonproportional cyclic loading. Numerical software was developed based on the approach of Maximum Energy Release Rate (MERR), which has many advantages over other crack propagation criteria. The crack propagation path in a thinwalled cylinder subjected to axial and torsion fatigue loading is investigated. The loading phase difference ranged from 0 degrees (proportional) to different nonproportional phase angles up to 90°. The model simulates the crack propagating a small increment at different angles ranging from 0° to 360°, and the energy released at each angle is calculated. The angle at which the crack releases the maximum energy is taken to be the direction of the crack. Results obtained from the numerical simulations were validated using experimental data from the literature and were also compared to results from other numerical LEFM approaches, demonstrating good agreement with both.

A study has been made of the role of aging treatment in influencing fatigue crack propagation and crack closure behavior in a high purity ingot metallurgy aluminum alloy 7150, with specific reference to crack growth at low and high load ratios in the near-threshold regime. A trend of increasing growth rates and decreasing threshold stress intensity AKth values with increased aging was seen to be consistent with lower measured levels of crack closure and a decreasing tortuosity in crack path. On the basis of crack growth measurements in moist room air, where closure due to corrosion product formation was found to be negligible in this alloy, the superior fatigue resistance of underaged microstructures (compared with overaged structures of similar strength and peak-aged structures of higher strength) was attributed to greater slip reversibility and to enhanced roughness-induced crack closure and deflection from the more tortuous crack paths. Such factors are promoted in alloy systems hardened by coherent shearable precipitates where the mode of deformation is one of non-homogeneous planar slip.

Boron-containing molybdenum silicides have been the focus of significant research of late due to their potentially superior lowtemperature ''pest'' resistance and high-temperature oxidation resistance comparable to that of MoSi 2 -based silicides; however, like many ordered intermetallics, they are plagued by poor ductility and toughness properties. Of the various multiphase Mo-Si-B intermetallic systems available, alloys with compositions of Mo-12Si-8.5B (at.%), which contain Mo, Mo 3 Si, and T2 phases, are anticipated to have higher toughnesses because of the presence of the relatively ductile Mo phase. In this study, we examine the ambient to high (1300 C) temperature fracture toughness (R-curve) and fatigue-crack growth characteristics of Mo-12Si-8.5B, with the objective of discerning the salient mechanisms governing crack growth. It is found that this alloy displays a relatively high intrinsic (crack-initiation) toughness at 800 up to 1200 C ($10 MPa p m), but only limited extrinsic R-curve (crack-growth) toughness. Although the lack of extrinsic toughening mechanisms is not necessarily beneficial to quasi-static properties, it does imply in a brittle material that it should show only minimal susceptibility to premature failure by fatigue, as is indeed observed at temperatures from ambient to 1300 C. Of particular significance is that both the fracture toughness and the threshold stress intensity for fatigue are increased with increasing temperature over this range. This remarkable property is related to a variety of toughening mechanisms that become active at elevated temperatures, specifically involving crack trapping by the a-Mo phase and extensive microcracking primarily in the Mo 5 SiB 2 phase. Published by Elsevier Science Ltd.

Mixed-mode, high-cycle fatigue-crack growth thresholds are reported for through-thickness cracks (large compared to microstructural dimensions) in a Ti-6Al-4V turbine blade alloy in both lamellar and bimodal microstructural conditions. Specifically, the effect of combined mode I and mode II loading, over a range of phase angles (␤ ϭ tan Ϫ1 (⌬K II /⌬K I )) from 0 to 62 deg (⌬K II /⌬K I ϳ 0 to 1.9), is examined at a load ratio (ratio of minimum to maximum loads) of R ϭ 0.1 and a cyclic loading frequency of 1000 Hz in ambient-temperature air. When the mixed-mode, crack-driving force is characterized in terms of the strain-energy release rate (⌬G), incorporating contributions from both the applied tensile and shear loading, the threshold for fatigue-crack growth is observed to increase significantly with the applied mode-mixity (⌬K II /⌬K I ) for both microstructures, an effect attributed to enhanced crack-tip shielding. The pure mode I threshold, in terms of ⌬G TH , is observed to be a lower bound (worst case) with respect to mixed-mode (I ϩ II) behavior. For large crack sizes, the threshold fatigue-crack growth resistance of the lamellar structure is observed to be superior to that of the bimodal material for all phase angles investigated. Consideration of mode I fatigue-crack growth thresholds for small cracks in these same microstructures suggests that this rank ordering of mixed-mode fatigue resistance may not hold for crack lengths that are comparable to microstructural size scales. Examination of the fatigue-crack wake indicates that, for the lamellar microstructure, the path of crack extension is significantly influenced by the local microstructure over length scales on the order of the relatively coarse lamellar colonies (ϳ500 m). Comparatively, the crack path in the bimodal material is more strongly influenced by the applied crack-driving force. This disparity in behavior is attributed primarily to the relatively heterogeneous crack-growth resistance of the coarse lamellar microstructure.

Nous nous intéressons à l'utilisation d'une méthode d'éléments finis étendue XFEM lorsque la singularité du problème n'est pas connue ou bien encore est très compliquée (par exemple, dans le cas d'une fissure interfaciale). Dans ce cas, l'idée d'utiliser la singularité pour enrichir la base éléments finis est inexploitable ou au moins très coûteuse. On considère une variante de XFEM qui consiste à enrichir les éléments finis sur un maillage donné par des solutions pré-calculées sur un maillage raffiné. Un résultat mathématique de convergence est donné et illustré par quelques simulations numériques. ABSTRACT. The extended finite element method XFEM is very efficient to solve problems where the nonsmooth behavior of the solution is known and numerically workable (e.g. a fracture in an isotopic material). In order to consider others situations (interfacial fractures, for instance), we study a variant of XFEM where the finite element basis is enriched with some pre-computed finite element solutions on a refined mesh. An optimal error estimate is given and corroborated by numerical tests.

Nous nous intéressons à l'utilisation d'une méthode d'éléments finis étendue XFEM lorsque la singularité du problème n'est pas connue ou bien encore est très compliquée (par exemple, dans le cas d'une fissure interfaciale). Dans ce cas, l'idée d'utiliser la singularité pour enrichir la base éléments finis est inexploitable ou au moins très coûteuse. On considère une variante de XFEM qui consiste à enrichir les éléments finis sur un maillage donné par des solutions pré-calculées sur un maillage raffiné. Un résultat mathématique de convergence est donné et illustré par quelques simulations numériques. ABSTRACT. The extended finite element method XFEM is very efficient to solve problems where the nonsmooth behavior of the solution is known and numerically workable (e.g. a fracture in an isotopic material). In order to consider others situations (interfacial fractures, for instance), we study a variant of XFEM where the finite element basis is enriched with some pre-computed finite element solutions on a refined mesh. An optimal error estimate is given and corroborated by numerical tests.

Introduction: Fatigue damage remains a major challenge in the design of composite structures, as cracks may initiate under low stress levels and evolve through multiple interacting failure mechanisms. To reduce reliance on extensive physical testing, finite element methods based on progressive damage analysis are increasingly used to predict fatigue-driven crack growth within structural substantiation workflows. However, most existing approaches require prior knowledge of the crack path, limiting their ability to represent complex, solution-dependent fracture trajectories. The eXtended Finite Element Method (XFEM) offers a promising alternative, as cracks can be modeled independently of the mesh, yet commercial implementations remain limited for fatigue loading. Materials and methods: This work introduces a fatigue-capable XFEM framework that combines the cohesive segments approach with a stress–life-based degradation law using only Abaqus built-in user subroutines and native elements. Crack initiation is governed by a fatigue endurance limit criterion, and damage evolution is driven by a user-defined internal variable that controls cohesive stiffness degradation along the crack interface. A dedicated bookkeeping strategy enables access and transfer of interfacial crack-opening quantities, ensuring consistent evaluation of the fatigue damage variable across the enriched interface. Results: The framework is verified against a classical Cohesive Zone Model (CZM) and applied to a two-dimensional single element model as well as Double Cantilever Beam (DCB) specimen under Mode I static and fatigue using the IM7/8552 carbon/epoxy material system. The results demonstrate excellent convergence between the proposed method and CZM approach for the single element model. Furthermore, the DCB results demonstrate accurate prediction of delamination growth and highlight the proposed formulation as a practical and more flexible alternative to the existing Virtual Crack Closure Technique (VCCT)-based XFEM fatigue capability in Abaqus, without requiring a pre-existing crack or inheriting the restrictions of linear elastic fracture mechanics. Conclusions: The proposed methodology effectively bridges cohesive zone modeling and XFEM, providing a tool for simulating progressive damage in composite structures without the limitations imposed by linear fracture mechanics. Future developments will extend the framework to mixed-mode loading and three-dimensional configurations, broadening its applicability to aerospace-grade laminates and structural components.

Boron-containing molybdenum silicides have been the focus of significant research of late due to their potentially superior lowtemperature ''pest'' resistance and high-temperature oxidation resistance comparable to that of MoSi 2 -based silicides; however, like many ordered intermetallics, they are plagued by poor ductility and toughness properties. Of the various multiphase Mo-Si-B intermetallic systems available, alloys with compositions of Mo-12Si-8.5B (at.%), which contain Mo, Mo 3 Si, and T2 phases, are anticipated to have higher toughnesses because of the presence of the relatively ductile Mo phase. In this study, we examine the ambient to high (1300 C) temperature fracture toughness (R-curve) and fatigue-crack growth characteristics of Mo-12Si-8.5B, with the objective of discerning the salient mechanisms governing crack growth. It is found that this alloy displays a relatively high intrinsic (crack-initiation) toughness at 800 up to 1200 C ($10 MPa p m), but only limited extrinsic R-curve (crack-growth) toughness. Although the lack of extrinsic toughening mechanisms is not necessarily beneficial to quasi-static properties, it does imply in a brittle material that it should show only minimal susceptibility to premature failure by fatigue, as is indeed observed at temperatures from ambient to 1300 C. Of particular significance is that both the fracture toughness and the threshold stress intensity for fatigue are increased with increasing temperature over this range. This remarkable property is related to a variety of toughening mechanisms that become active at elevated temperatures, specifically involving crack trapping by the a-Mo phase and extensive microcracking primarily in the Mo 5 SiB 2 phase. Published by Elsevier Science Ltd.

Strength mismatch effect across weld interfaces, generated by welding weak and strong steels, influences fatigue and fracture properties of a welded bimetallic composite. Advancing fatigue crack tip in weak parent steel is shielded from the remote load when it reaches near the interface of ultra strong weld steel. Entry of crack tip plasticity into weld steel induces load transfer towards weld which dips crack growth rates thereby enhancing the fatigue life of the composite. A computational model for fatigue life prediction of strength mismatched welded composite under K dominant conditions is validated by experimental work in this paper. Notched bimetallic compact tension specimens, prepared by electron beam welding of weak alloy and strong maraging steels, are subjected to fatigue testing in high cycle regime.

In this study, the main objective was the creation of a code, which gives the capability to a Finite Element Analysis Program with no builtin crack study tools, to study the propagation of a crack, in a cracked surface. For this purpose, the Finite Element Program FEMAP 11.3.2 with solver the NX NASTRAN has been used, and the proposed code was created, using the Application Program Interface (API) of the program. The Linear Elastic Fracture Mechanics (LEFM) theory has been applied to the code, and can predict, if the crack will propagate, the trajectory of the crack, as well as the number of cycle loads required for the propagation of the crack, for given boundary conditions and loads. Finally, the Stress Intensity Factors (SIF) produced by the program, were compared with results from an analytical method. Also, experimental results have been used, for the verification of the results of the trajectory of the propagation, and the cycle loads.

Cracking in teeth is often caused by defects, aging, or poorly designed fillings. Vertical opening fractures are particularly common. Therefore, Mode-I fracture mechanics were applied in the current simulation based on the simulated stress distribution at the dentin. Using finite element analysis, the crack path and fracture behavior were simulated. An oblique bite force of 453 N, applied at a 45° angle to the longitudinal axis of the tooth structure, was used. Minimum and maximum dentin properties were investigated to assess their influence on fracture initiation and propagation. Three different load levels were applied to examine and compare the degree of crack propagation and the effect of varying loads on crack growth. Results showed that teeth with maximum anisotropic dentin required approximately 100 N more force than those with minimum properties to transition into the crack development phase. The stress intensity factor (SIF), which determines stress concentration and crack tip propagation, was calculated for the applied loads. Higher loads resulted in higher SIF values, thereby reducing fatigue life.

The micromechanics-based damage model proposed by Golshani et al. (2005) is extended so that time-dependent behavior of brittle material can be taken into account, with special attention to the numerical analysis of an excavation damage zone (EDZ) around a tunnel, which is a major concern in assessing the safety of underground repositories. The present model is capable of reproducing the three characteristic stages of creep behavior (i.e., primary, secondary and tertiary creep) commonly observed in laboratory creep tests. Using the present model, sub-critical microcrack growth parameters (i.e. n and A) can be determined for Inada granite by fitting the numerical results of elapse time to failure versus the creep stress ratio curve with the experimental data under both dry and wet conditions. It is found that moisture has a significant influence on the parameter A rather than the parameter n. Use of the extended model makes it possible to analyze not only the extension of microcrack length, but also the development of the excavation damage zone (EDZ) around tunnels as a function of time. The disturbed zones mainly develop in the sidewalls of the tunnel in the case that the vertical stress is larger than the horizontal stress.

Ceramic materials are prone to slow crack growth (SCG) which is stress and environmentally assisted. We describe intergranular SCG in Zirconia within a cohesive zone methodology. Stress corrosion being thermally activated, a rate and temperature dependent cohesive formulation is proposed and shown able to capture SCG. Within a finite element analysis, the crack is allowed in places where the cohesive zones are inserted. The influence of microstructure in terms of anisotropic properties, the grain to grain disorientation, the initial thermal stress state that originate from the ceramic processing are shown to determine the kinetics of SCG and the level of the load threshold below which no SCG is observed. The influence of the water concentration (R.H.) on the magnitude of the minimum load threshold and on the kinetics of SCG is investigated.

This letter presents a focused, simulation-based investigation of the fatigue fracture behavior of human enamel and dentin, with an emphasis on stress intensity factors (SIFs) at crack tips under cyclic loading. The findings aim to contribute to a better understanding of crack propagation in biological materials using a simulator based on the Linear Elastic Fracture Mechanics (LEFM) approach.

Surface modification outcomes decompose into three first-order independent components: electronic asymmetry (Ψ), curvature geometry (κ), and residual stress (σ). We validate the decomposition against three canonical cases and derive quantitative predictions for the interactions between components. For the Ψ component, a four-variant apatite series (fluorapatite, hydroxyapatite, chlorapatite, strontium hydroxyapatite) validates the Ψ → U → Ksp chain against published solubility products spanning 12 orders of magnitude. Lattice energy U is the proximal predictor of dissolution stability (τ = +1.00 across all four variants). A factorial design separates Ψ from ionic radius: fluorapatite and chlorapatite share Ψ = 0 but differ by 4 log units in Ksp (pure radius effect); hydroxyapatite and strontium hydroxyapatite share Ψ = 0.35 but differ by 11 log units (pure cation radius effect). For the σ component, Rupert's drop demonstrates ΔK_Ic ≈ 1.2 MPa•m½ from compressive prestress alone. For the κ component, a companion paper establishes N_f/N_ref = exp(-α • m(m-2)/4 • erfinv(Gκ)²) at R² > 0.987. A hazard-rate model for the σ-κ interaction predicts an m-dependent optimal peening intensity: the peak shifts from I = 160 at m = 3 to I = 22 at m = 8, with improvement declining from 1.62× to 1.19×. At m = 8 with initiation-dominated baseline, polishing outperforms peening. The Ra-fatigue correlation depends on both m and baseline hazard partition, explaining contradictory peening results in the literature. A Lorenz-moment law is verified at R² > 0.97 across five moment orders, connecting this framework to protein backbone geometry and statistical fracture mechanics.

Surface roughness parameters such as Rₐ do not reliably predict fatigue life because they average over the curvature distribution rather than characterizing its inequality. We introduce the curvature Gini coefficient Gκ as a distributional descriptor and derive a closed-form scaling law: where m is the Paris crack-growth exponent and α is a distribution-family coefficient. Validation across 384 simulated surfaces (four distribution families, six m values) confirms within-family R² > 0.987 with α ranging from 0.41 (bounded beta) to 1.12 (lognormal). The scaling variable X = m(m-2)/4 • erfinv(Gκ)² is universal; α tracks tail weight. This yields a practical threshold table: at m = 6, surfaces exceeding Gκ ≈ 0.62 lose an order of magnitude of fatigue life. A cellpartition spatial Weibull model-mathematically equivalent to weakest-link fracture statistics-achieves Kendall τ = +0.90 versus +0.10 for marginal Gκ. Among eight candidate descriptors including ISO Rsk and Rku, Gκ ranks third in correlation (τ = +0.92) but provides 3-5 orders of magnitude better outlier robustness than ISO shape parameters, is stable under 20× downsampling (2% shift), and is independent of assumed crack depth.

Aluminum-lithium alloys are candidate materials for many aerospace applications because of their high specific strength and elastic modulus. These alloys have several unique characteristics such as excellent fatigue crack growth resistance when compared with that of the conventional 2000 and 7000 series alloys. In this study, fatigue crack propagation behavior has been examined in a commercial thin plate of Al-Li-Cu-Mg alloy (8090), with specific emphasis at the fatigue threshold. The results are compared with those of the traditional Al-Cu-Mg alloy (2024). Fatigue crack closure is used to explain the different behavior of the compared alloys.

Lately porous shape memory alloys (SMA) have attracted great interest as low weight materials characterized by high energy dissipation capability. In the present contribution a micromechanical study of porous SMA is proposed, introducing the simplifying hypothesis of periodic distribution of voids. The mechanical response of the heterogeneous porous medium is derived by performing nonlinear finite element micromechanical analyses considering a typical repetitive unit cell made of a circular hole in a dense SMA matrix and prescribing suitable periodicity and continuity conditions. The constitutive behavior and the dissipation energy capability of the porous Nitinol are examined for several porosity levels. Numerical applications are performed in order to test the ability of the proposed procedure to well capture the overall behavior and the key features of the special heterogeneous material.

There are different documents containing fatigue crack propagation curves and rules for the prediction of crack growth. The research work aimed to develop a new method for determination of fatigue crack propagation limit curves and determination of limit curves for different metallic materials (steels, austempered ductile iron, aluminium alloys) and their welded joints and non-metallic materials (ceramic, polymer, composite), under different loading conditions, based on statistical analysis of test results and the Paris-Erdogan law. With the help of the characteristic values of threshold stress intensity factor range (∆K th ), two constants of Paris-Erdogan law (C and n), fracture and fatigue fracture toughness (K Ic and ∆K fc ) a new method can be proposed. The limit curves represent a compromise of rational risk and striving for safety.

This paper studies the dimensionless compliance in cylindrical geometries with transverse surface cracks subjected to axial tensile loading. Compliance evolution is analyzed when round bars are subjected to fatigue with free and constrained sample ends, initial crack geometries of straight or circular fronts and several materials characterized through of the Paris parameter m. With this aim, a computer application that calculates the crack front's geometric evolution and the dimensionless compliance was made by discretizing the crack front and assuming that every point advance perpendicular to the crack front according to the Paris law. The results show that dimensionless compliance grows with the increase of the relative crack depth and the decrease of the aspect ratio, showing greater values for free sample ends than for constrained sample ends. Furthermore, during fatigue crack growth, materials with higher values of the Paris parameter m produce slightly greater dimensionless compliance and a better convergence between the results for straight or circular initial crack.

This paper discusses the implications of the aqueous hydrogen level stress corrosion cracking (SCC) functionality on modeling the temperature dependency (thermal activation energy) of nickel alloy SCC. Prior testing has identified a significant effect of hydrogen level on the SCC of nickel-based alloys in high temperature, high purity water. A maximum in susceptibility occurs near the Ni/NiO phase transition. This functionality has been fundamentality characterized by the extent that the alloy's electrochemical potential (EcP) deviates from the EcP of the Ni/NiO phase transition (∆EcP = EcP Ni/NiO -EcP). The implication of this understanding to the determination of SCC thermal activation energies is that thermal activation energy tests need to be conducted at a constant ∆EcP, not at a constant hydrogen level. Thermal activation energies are often biased high when determined from tests conducted at a constant hydrogen level. Recent testing and analyses show that the true (hydrogen level independent) thermal activation energy for Alloy 600 and X-750 is ~ 35 kcal/mol (146 kJ/mol). In order to better understand the dependence of the crack growth rate on the applied stress intensity factor, SCC growth rate tests were conducted on Alloy 600 as a function of the stress intensity factor and specimen size (0.6T to 2T compact tension specimens). Smaller specimens produced faster crack growth rates at high stress intensity factors (e.g., 66 MPa√m) relative to larger specimens tested at the same stress intensity factor. These results suggest that Alloy 600 stress intensity factor growth rate modeling could be biased by a data set largely populated with "small" specimens (1T CT and less) at high stress intensity factors.

In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evolution of a degradation mechanism that may arise in various structural components, namely, the fatigue crack growth. We first derive some probability results on the stochastic dynamics with the help of Markov renewal theory: a closed-form solution for the transition function of the PDMP is given. Then, we investigate some methods to estimate the parameters of the dynamical system, involving Bogolyubov's averaging principle and maximum likelihood estimation for the infinitesimal generator of the underlying jump Markov process. Numerical applications on a real crack data set are given.

Resistance spot welding (RSW) is widely used in the automotive industry, particularly for copper-aluminum alloys in electric cars. RSW joint conductivity is crucial for electric vehicles. Welded parts may fracture due to tension, altering conductivity. The study examines resistance spot post-weld joint metallurgy and deformation-induced conductivity changes. The electric resistance of similar and dissimilar RSW joints was examined during tensile tests. Metallurgical tests for RSW joints revealed an increase in grain size from the base metal (BM) to the heat-affected zone (HAZ) and finally the fusion zone (FZ). Satisfactory shear tension strength results were obtained for dissimilar joints (Al-Cu) at 690 N and similar joints (Al-Al) at 780 N, exceeding the minimum limit of 643 N. However, weld strength in similar joints (Cu-Cu) only achieved 933 N, less than the required strength of 1528 N. Furthermore, the relationship between deformation rate (i.e., applied stress) and electrical resistance has been shown. It was found that resistivity increases with increasing deformation stress, resulting in decreased electrical conductivity with a high percentage, which represents 99.8, 99.66, and 99.49% for Al-Cu, Al-Al, and Cu-Cu RSW joints, respectively. At the maximum force of 650 N and maximum stress of 33.1 MPa, the electrical resistance was measured, and the results show (15.7 Ώ, 5.9 Ώ, and 1.99 Ώ) and the electrical conductivities (0.063 IS, 0.169 IS, and 0.502 IS) for the joints (Al-Cu), (Al-Al), and (Cu-Cu), respectively.

Fatigue plays a significant role in the crack growth of the fuselage skin structures. In addition, the fuselage may suffer also from the corrosion damage, and the wear defects. The proper maintenance and scheduled test intervals can avoid the sudden skin failure. Therefore, the inspection interval has to be shortened. Nevertheless, the young machines may be also suffering from the unexpected skin rupture. The cracks are emanating from the rivets and the holes under cyclic loading. The stress concentration around the notch has an effective role under the effect of cyclic loading. The cracks propagate toward the high stressed area such as the notches or other crack locations. The propagation into a critical crack size is rather fast and causes a sudden aircraft fuselage cracking. Hence, the number of cycles to failure will be decreased dramatically. During the last decades, the fracture toughness, design, and the new alloying element have been enhanced. The previous fuselage failures show that the inspections against the cracking are recommended even after a few thousand of cycles. To prevent the crack extending, the crack arresting is recommended to use around the fuselage.

The fatigue failure is predominate in the aircraft fuselage. The fuselage skin consists of the shell and stingers. Fatigue plays a significant role in the crack growth of the skin structures. The proper maintenance and scheduled test intervals may avoid sudden skin failure and crack path (CP). With exiting the cracks, the propagation rate increases dramatically. Therefore, shortening the regular inspection intervals is recommended. Nevertheless, the young machines may have also unexpected skin rupture. The cracks are emanating from the notches such as rivets and the holes under the cyclic loading. The stresses concentrated around these notches. The stress concentration provides the unique conditions for crack initiation. Therefore, the cracks tend to connect with each other. Hence, the number of cycles to failure is decreased dramatically. Although the last decades, the fracture toughness, design, and new alloying element are enhanced. According to the traditional fuselage failure, the crack inspections are recommended even after a few thousand cycles.

To better understand the crack closure and propagation, an analytical model is established. The residual stress effect on fatigue crack growth equations has been considered using the residual stress intensity factor (SIF) (Kres). The joint geometries, residual stress distributions (σres) and residual stress ratio (Rres) were considered also. Kres are calculated using the analytical weight function (WF) method and different residual stress distributions. It is to be emphasized that the current approach is little investigated. This is because the WF has already been developed to calculate SIF for an existing crack. The current approach calculates Kres for the crack that initiates and propagates until failure. Different stress distributions have been used, and Rres is defined. The validity of using the WF has been shown. SIF due to applied load (Kapp) and applied stress ratio (Rapp) have been considered. Fatigue crack growth rate was investigated in accordance with the current approach...

In this work, the parameters stress intensity factor (SIF), initial and final crack lengths (ai and af), crack growth parameters (C and m), and fatigue strength (FAT) are investigated. The determination of initial crack length seems to be the most serious factor in fatigue life and strength calculations for welded joints. A fracture mechanics approach was used in these calculations based on SIF which was calculated with the finite element method (FEM). The weld toe crack was determined to be equal to 0.1 mm, whereas the weld root crack’s length was varied depending on the degree of the weld penetration. These initial crack length values are applicable for all types of joints which have the same crack phenomenon. As based on the above calculated parameters, the new limits of FAT for new geometries which are not listed yet in recommendations can be calculated according to the current approach.

The spot welds nugget cracking of austenitic stainless steel at temperatures between 700°C - 1010°C was investigated. Traditionally, the cracks have been observed around the spot nugget in welded temperature. Actually, these cracks are developed due to incomplete melting and inappropriate electrode pressure, which causes an expulsion of molten metal. These cracks start to grow and cause either the interface or plug fracture according to the loading type. In this work, the micro-cracks in the weld nugget were indicated for this type of steel at elevated temperature. Cracks appear in a certain range of temperature; about 700°C - 750°C. The cracks like defect and cavitations were presented. According to the fracture mechanics point of view, these cracks reduce the mechanical strength. Therefore, these cracks have to be taken into account with a certain precaution. Moreover, considering the working temperature and reducing the element may develop ferrite particles.

Materials’ cracking is a first step of the fracture. Enamel and dentin like other materials suffering from the cracks. During life or even through the denture treatments, the damage can be started. In this work, the crack path and fracture behavior of the teeth have been monitored. It was shown that the linear elastic fracture mechanics approach (LEFM) could evaluate the fracture toughness in teeth. The vertical crack is a traditional path of the fracture. The crack due to the cyclic loading like chewing will be propagated. The understanding of failure in teeth like another solid body, aims to decrease the failure risk. In addition, gives an insight for repairing treatments. Hence, early observations of the cracks will protect the teeth. Due to the brittleness of enamel and a little toughness of dentin, the dentin-enamel margins resist the crack propagation due to their fracture toughness and the cohesive properties. The crack path in teeth was simulated using the finite element sof...

The local stress concentrations around the discontinuities and the weld defects are fairly common. In this study, the investigation of thickness and stress concentration effects on fatigue strength (FAT) have been studied. The fracture mechanics tools and fracture analysis code (Franc2D) were used to consider these effects. The FE simulation of welded joints will provide a tool to determine the regions of stress concentration which in turn determine the crack initiating and FAT. Unfortunately, these tools are unable to calculate FAT at higher thicknesses. Therefore, the crack length was corrected with a suitable scale. The determination of fracture toughness values without the need to undertake experiments have been presented.

This project has elucidated approaches for managing damage evolution through control of matrix solute and multiphase structures. Radiation microstructures, microchemistries and properties affected by irradiation were evaluated with the goal of developing damage-resistant alloys for next generation nuclear power systems. Three complementary experimental approaches identified key factors for the development of alloys: Ni ++ irradiation, proton irradiation and manipulation of simulated irradiation characteristics in non-irradiated alloys. Specifically, alloys processed with oversized solute, i.e., Hf, and multiphase alloys show promise for retarding damage evolution. of voids. The concept of using ferritic/martensitic alloys with oxide-dispersion strengthening was reviewed and strategies for development of these alloys were assessed. Carbide precipitate distributions at grain boundaries were tailored in 304SS and 316SS along with the local segregation and depletion of alloying elements. The dependence of IASCC on irradiation and strength was evaluated using proton irradiation and in a separate experiment using cold/warm work on non-irradiated specimens. Cracking susceptibility was demonstrated in the proton-irradiated base 316SS and the 316SS+Pt alloys. Cracking was not observed in the 316SS+Hf optimized alloy. The dependence of crack growth rate on alloy strength in non-irradiated SSs was extensively evaluated. The strength effect was confirmed for contrasting conditions of electrochemical potential, martensite formation and hydrogen contribution. Grain boundary precipitates were found to reduce the crack growth rate by up to a factor of ten for an oxidizing environment.

Fatigue tests carried out in natural rubber containing carbon black fillers (NR-CB) show a drastic increase of lifetime when the mean fatigue stress is increased. This effect is often attributed to crystallisation which appears at high strain levels. The main objective of this work is to understand the combined effects of fatigue damage and crystallisation in the case of NR-CB. Crystallisation is characterized using in-situ X-rays diffraction analysis on both fatigue specimens and monotonic tensile specimens. The effect of the fatigue loading history and stress relaxation on crystallisation is studied. Effect of temperature is also investigated. It is shown that crystallisation increases with strain level and relaxation time. During fatigue, crystallisation tends to decrease but never completely disappears. The presence of crystallites improves the lifetime of the rubber.

The present paper aims at showing that coupling the eXtended Finite Element Method with X-ray microtomography and 3D digital image correlation provides a very promising tool to assess the 3D behaviour of arbitrary shaped cracks and to perform comparisons of "experimental" and simulated" crack shapes during propagation .

Selection of cable size in nonsinusoidal conditions is based only on ampacity considerations without any attention to the cost of the losses that will be suffered in the cable life. Since the cost of these losses (fundamental plus harmonics) can be high, the selection of a cross-section higher than required for ampacity considerations can result in large cost reductions. This article proposes a method that allows the optimal economic selection of medium voltage cables in nonsinusoidal operating conditions; it takes into account the initial investment costs and the cost in Joule losses, including the additional costs due to current harmonics. It employs simplified expressions similar to those adopted by IEC Standard in sinusoidal conditions, taking into account the harmonic presence by a proper definition of a harmonic loss factor and by the introduction of harmonic coefficients to be predicted. Numerical applications to medium voltage cables are developed and discussed, in order to ...

This paper presents the fundamental investigation on crack propagation rate (CPR) and Stress Intensity Factor (SIF) for a typical fatigue and welded specimens which are Compact Tension (CT) and Single Edge Notch Tension (SENT) as well as Butt and longitudinal T-joint. The material data of austenitic stainless steel SS316L was used to observe crack propagation rate with different initial crack length and different tensile load was used for the fracture mechanics investigation. The geometry of the specimens was modelled by using open source software CASCA while Franc 2D was used for post processing based on Paris Erdogan Law with different crack increment steps. The analysis of crack propagation using fracture mechanics technique requires an accurate calculation of the stress intensity factor SIF and comparison of the critical strength of the material (KIC) was used to determine the critical crack length of the specimens. it can be concluded that open source finite element method soft...

Fracture and fatigue behaviour of a laser additive manufactured Zr-based bulk metallic glass James P. Best (Conceptualization) (Methodology) (Investigation) (Visualization) (Writing -original draft) (Writing -review and editing), Halsey E. Ostergaard (Methodology) (Investigation) (Writingreview and editing), Bosong Li (Methodology) (Investigation), Moritz Stolpe (Conceptualization) (Investigation) (Resources) (Writingreview and editing), Fan Yang (Methodology) (Investigation) (Writing -review and editing), K. Nomoto (Methodology) (Investigation) (Writing -review and editing), M. Tarik Hasib (Methodology) (Investigation), Ondrej Mur ánsky (Methodology) (Investigation), Ralf Busch (Conceptualization) (Methodology) (Resources), Xiaopeng Li (Supervision) (Writing -review and editing), Jamie J. Kruzic (Conceptualization) (Methodology) (Project administration) (Supervision) (Writing -review and editing)

There is an ever increasing need for accurate understanding of the fatigue crack growth behaviour in major engineering materials and components. With the move towards more complex, probabilistic assessments, the traditional ‘safe’ or conservative approach for prediction of fatigue crack growth rate may no longer be attractive. Current codes and standards tend to be ambiguous about the treatment of compressive stress cycles: on the one hand code guidance on fatigue crack initiation may be non-conservative, while assessment of crack propagation may be inconsistently conservative. Where codes are non-conservative they could lead to dangerous assessments. The current paper provides a critical review of state-of-the-art in literature and a study of current code implications.

The majority of fatigue cracks in thick plate and tubular sections in structural components are two-dimensional surface cracks having significant propagation lives before becoming critical. The modelling of surface crack propagation life is important across a range of industries from power generation to offshore so that inspection, maintenance and repair strategies can be developed. Linear elastic fracture mechanics based predictions are commonplace, however, unlike thin sections with associated one-dimensional cracks frequently encountered in aerospace industries, crack shape or aspect ratio has a profound effect on crack front stress intensity factor and any resulting Paris Law based life prediction. The two most commonly used approaches are to calculate the crack growth rate at a number of points around the crack front and to consider only surface and deepest points, calculating the relative crack growth rates. Experience using these approaches has shown that the Paris Law coeffi...

The use of natural stone as facade cladding has been shown to have much lower life cycle costs and they are more environmentally friendly than comparable products of concrete, glass, and steel. Promoting the use of natural stone has therefore a great positive impact on the environment. However, the number of occurrences of bowing and expansion of marble and limestone panels has led to increased maintenance costs, significant safety risk, and negative publicity. The lack of knowledge of a solution to the problem of bowing marble has a large negative effect on the entire stone trade. In response, short-sighted and less durable construction solutions are used as an alternative, adding to the decreasing export figures and numbers of employees within the stone sector. The TEAM (TEAM=TEsting and Assessment of Marble and limestone) project addresses a problem with marble types, from several European countries, that display bowing on facades in both cold and warm climates. There is, therefo...

A novel piece of software is presented to connect Abaqus, a sophisticated finite element package, with Matlab, the most comprehensive program for mathematical analysis. This interface between these well-known codes not only benefits from the image processing and the integrated graph-plotting features of Matlab but also opens up new opportunities in results post-processing, statistical analysis and mathematical optimization, among many other possibilities. The software architecture and usage will be appropriately described and two problems of particular engineering significance addressed to demonstrate its capabilities. The source code, detailed documentation and a large number of tutorials can be freely downloaded from www.abaqus2matlab.com.