Initial Crack Shape Research Articles

Fatigue crack propagation characteristics of segmented egg-shaped pressure shells

This study focused on the fatigue crack propagation and fatigue life of an egg-shaped pressure shell fabricated by welding and hydroforming a six-segment frustum. First, the segmented egg-shaped pressure shell was designed, and the hydroforming was analysed by the finite element method (FEM). Moreover, the numerical simulation of the egg-shaped shell under uniform external pressure and welding residual stress was carried out, and the stress distribution at the weld was obtained. Second, the equivalent specimens were designed to have structures with maximum stress in the weld. Equivalent specimens with different initial crack shape ratios were tested, and the unified crack propagation rate model of 18Ni (250) was obtained by fitting the data. The fatigue life of the equivalent specimen was calculated by ABAQUS and FRANC3D software and compared with the test results. Finally, the crack propagation rate model was used to predict the fatigue life of the egg-shaped pressure shell. The results of this study provide a reference for prediction of fatigue damage and assessment of the safe operation of egg-shaped pressure shells.

A Creep Constitutive Model, Based on Deformation Mechanisms and Its Application to Creep Crack Growth

In this paper, a constitutive model, based on the creep deformation mechanism in P91 steel, under a wide range of stress levels, was established and embedded into finite element software. The accuracy and reliability of the model was verified by comparing the simulation of uniaxial creep tensile test results and the experimental data under different stress levels for P91 steel at 600 °C. The creep crack growth behavior of P91 steel, under a wide range of stress levels was simulated using a ductility-exhaustion-based damage model, combined with the stress-dependent creep ductility model, and the predicted creep crack growth (CCG) rates were compared with the experimental data. Finally, the established model was used to predict the CCG behavior for the pressurized pipes with axial surface cracks. The results show that the constitutive model, established on the basis of the creep deformation mechanism, agrees better with the experimental data than other constitutive models. The CCG rate varies at different direction angles θ for the axial surface cracks. The direction angle θ corresponding to the maximum creep crack length is about 33°, when the internal pressure exceeds 10 MPa. The initial crack shape (a0/c0) = 1, and it does not change with different initial crack depth ratios (a0/t). The established constitutive model can be well used in CCG life analyses and designs of high-temperature structures.

Mixed-mode fatigue crack growth analysis of I-shaped steel girders with trapezoidal corrugated-webs

In bridge industry, the composite box-girder with corrugated steel webs and concrete flanges is quite a common practice over recent years. However, this innovation encounters fatigue-sensitive details not fully investigated, especially in the research area of mixed-mode fatigue crack growth. This study addresses the mixed-mode fatigue crack growth analysis of an I-shaped corrugated web girder associated with the represented web-to-flange detail. A linear elastic fracture mechanics (LEFM) based numerical framework was established to simulate the mixed-mode crack propagation. For comparison, a semi-analytical weight function framework was also introduced to predict the pure Mode-I crack propagation life of the same detail. Experimental results of a full-scale inclined corrugated web girder were employed to evaluate these two proposed frameworks. A parametric study was presented based on the proposed frameworks to investigate the effect of initial crack depth and crack shape on fatigue crack propagation life. By comparing the simulation results with test results, the applicability of the proposed LEFM-based numerical framework to the simulation of mixed-mode fatigue crack propagation behaviour in corrugated web girders was discussed.

Fatigue fracture assessment of 10CrNi3MoV welded load‐carrying cruciform joints considering mismatch effect

AbstractFatigue experiments and numerical simulations based on the linear elastic fracture mechanics (LEFM) theory were conducted on the evenmatched (EM) and undermatched (UM) 10CrNi3MoV load‐carrying cruciform welded joints (LCWJs). The study firstly experimentally investigated the fatigue crack growth rate (FCGR) of base metal, EM, and UM weldments. The corresponding Paris parameters as essential input data are provided to assess the fatigue crack propagation behavior for weld toe and weld root failure caused by notch stress concentration variations. On the one hand, the stress intensity factors (SIFs) at weld toe and weld root were calculated considering the effects of LCWJ specimen geometries, initial crack types, and sizes. The comparisons between simulated results and standards analytical solutions were executed, which exhibit good accordance. It proved that the fatigue fracture simulation procedure based on LEFM is appropriate for the fatigue assessment of LCWJs. Eventually, it conducted the parametric analysis by predicted S–N curves, which included in the weld length, initial crack shape, initial crack size, penetration length, and materials fracture parameter, to explore some safety assessment reference lines for both failure modes of LCWJ.

Fracture mechanics-based mooring system fatigue analysis for a spar-based floating offshore wind turbine

This paper summarized a study that aims to investigate the applicability of a fracture mechanics (FM) based approach for calculating the fatigue lives of the mooring lines of a spar-based floating offshore wind turbine (FOWT) in time-domain. Tension ranges of mooring lines are calculated from a time-domain hydrodynamic analysis, taking into account the effects of wind, wave and current. Mooring tension cycles with corresponding ranges are counted by a rain-flow counting method. A comparison between fatigue lives of mooring system predicted by S–N curves, T-N curves, and the FM based approaches is made and the results show that the FM based approach generally provides reasonable estimate of fatigue lives of the mooring lines of the FOWT. Parametric studies were further performed to investigate the effects of loading sequence, stress concentration factor, initial crack shape, initial crack size and critical crack depth on fatigue life prediction of the FM based approach. It was observed that the predicted fatigue life is sensitive to stress concentration factor and initial crack size. A comparative study on three kinds of mooring design with different chain diameters is also made and the applicability of each design is discussed.

Internal Versus External Cracking—Their Impact on the Fatigue Life of Modern Smoothbore Autofrettaged Tank Gun Barrels

Abstract An extensive analysis of the fatigue life of a typical modern autofrettaged smoothbore tank barrel, cracked either internally or externally, in terms of the initial crack depth and shape, type and level of autofrettage, was conducted. Five overstraining cases were considered: no-autofrettage, 70% and 100% hydraulic autofrettage, and 70% and 100% swage autofrettage. KINmax, the maximum combined stress intensity factor (SIF) KINmax = (KIP + KIA) max, due to both internal pressure and autofrettage, as a function of crack depth for a large number of internal and external crack configurations was determined by the finite element method (FEM). A novel realistic experimentally based autofrettage model, incorporating the Bauschinger effect, was integrated into the finite element model, replicating both the hydraulic and swage autofrettage residual stress fields (RSFs) accurately. Fatigue lives were evaluated by integrating Paris' Law using the above values of KINmax. The following conclusions can be drawn from the results: hydraulic and swage autofrettage have a dramatic beneficial effect in extending the fatigue life of an overstrained barrel 4–11 times as compared to an identical nonautofrettaged tube. The fatigue life of overstrained barrels is controlled by internal cracking, for barrels overstrained by up to ε = 100% hydraulic autofrettage, by up to ε = 70% in the case of swage autofrettage, and by external cracking for ε = 100% swage autofrettaged. Eliminating or carefully designing stress concentrators on the tube's external face and keeping away from corrosive agents thus, extending the fatigue-crack initiation life of an external crack, enables the increase of the level of swage autofrettage to up to ε = 100%. Swage autofrettage is much more superior to hydraulic autofrettage. The fatigue life of a 70% swaged autofrettaged barrel is 1.5 times higher than that of a 100% hydraulically autofrettaged tube. If full swage autofrettage is permissible, the fatigue life of such a barrel is twofold that of a fully hydraulically autofrettaged tube. Unlike the commonly accepted concept, the level of hydraulic autofrettage should not be limited to 70%, and full hydraulic autofrettage should be used. Similarly, in the case of swage autofrettage, if the detrimental effect of external cracking is removed by proper design and maintenance of the tube's outer surface, the level of autofrettage can be increased to up to ε = 100%, thus, gaining an increase of 33% in the fatigue life as compared to overstraining the barrel to only ε = 70%. Initial crack depth and shape are major factors affecting the fatigue life of the barrel. The deeper the initial crack depth, a0, and the slenderer its shape, a/c→ 0, the shorter the fatigue life of the barrel.

Fatigue crack growth and interaction of bridge wire with multiple surface cracks

Multiple flaws are widely observed on the surface of corroded steel bridge wires, and the interaction between flaws can increase the stress intensity factor (SIF) to drive cracking. But the flaw combination criterion provided for plates in codes is not straight-ford to evaluate interacting surface cracks in steel wires. A model containing twin co-planar semi-elliptical surface cracks throughout a circular cross-section is thus established to investigate crack propagation of steel wires under axially tension in terms of initial crack shape, size and relative spacing. A new combination rule using a virtually effective crack is then proposed for interacting co-planar surface cracks based on the SIF amplification effect, which is quantified as a function of the initial crack aspect ratio, crack depth and relative spacing. The shape development of twin surface cracks is also simulated by numerical analysis based on the Paris law. The results show that the multiple-crack growth is sensitive to both the initial crack size and relative spacing, and the interaction should be considered for the neighbouring cracks when their relative spacing is within the crack depth range (s ≤ a). The comparison of the predicted fatigue lives between twin cracks and corresponding effective crack confirms the feasibility of the presented combination criteria.

Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel

Bridge weathering steel produced in China has been employed in bridges worldwide, among them Q345qNH is the most commonly used steel grade. Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel Q345qNH was explored in this paper. Fatigue tests were conducted on 13 specimens involving 9 stress ranges, S-N curve and its lower bound of 95% survival probability were established. It was observed that the design S-N curve for butt welded joint in Eurocode 3 is suitable for fatigue assessment of this batch of specimens and provides a considerable safety margin. Numerical simulation of mixed-mode fatigue crack propagation and analytical investigation of fatigue crack propagation were conducted, it was found that numerical simulation is preferred since it considers the variation in stress due to crack propagation. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were investigated, the expression between fatigue life and initial crack size was derived. Additionally, it is recommended that a semi-elliptical crack with initial crack depth of 0.2 mm and initial aspect ratio of 1/4 to be adopted when information on initial crack is unavailable. The fatigue test results provide reference for fatigue design of steel bridges made of coated weathering steel and serve as control for analysis of deterioration of fatigue behavior due to corrosion for corroded butt welded joints made of uncoated weathering steel.

Fatigue behavior of uncorroded non-load-carrying bridge weathering steel Q345qDNH fillet welded joints

Bridge weathering steel produced in China is being increasingly employed in bridges worldwide, Q345qNH is among the most commonly used steel grades. Fatigue behavior of uncorroded non-load-carrying fillet welded joints made of bridge weathering steel Q345qNH was explored in this paper. Fatigue tests were conducted on 10 specimens which were under 7 stress ranges, S–N curve and its lower bound of 95% survival probability were established. It was observed that the design S–N curve for non-load-carrying fillet welded joint in Eurocode 3 is suitable to evaluate fatigue behavior of this batch of specimens and offers a considerable safety margin. The influences of initial crack size, initial crack shape, initial crack location and misalignment of attachments on fatigue behavior of non-load-carrying fillet welded joints were explored, the relationship between fatigue life and initial crack size was derived. Furthermore, it is recommended to adopt a semi-elliptical crack with initial crack depth of 0.075 mm for numerical simulation when initial crack size is unknown. The fatigue test results provide reference for fatigue design of steel bridges made of coated weathering steel and serve as control to analyze deterioration of fatigue behavior caused by corrosion for corroded non-load-carrying fillet welded joints made of uncoated weathering steel.

Fatigue resistance of rib-to-deck welded joint in OSDs, analyzed by fracture mechanics

The orthotropic steel decks (OSDs) are widely used in bridge engineering to support traffic loads. A possible crack, initiating from the weld toe of rib-to-deck welded joint and growing into the deck plate, is studied using linear elastic fracture mechanics. A detailed FE model is created and the results are compared with the fatigue tests published. Good agreement is found between beach marks from experiments and calculated crack fronts in FE. An engineering approach with the crack shape simplified as a semi-ellipse is applied. Geometric correction factors for a hand calculation method is proposed based on the parametric analysis. Using the proposed correction factors, Monte Carlo simulation is carried out with failure criteria defined with respect of the crack depth reaching “50%” of the deck thickness, “75%” of the deck thickness, and the failure criterion “2A FAD” according to BS7910. Predicted results using the failure criterion “75%” show good agreement with experimental data, for 5%, 50%, and 95% survival probabilities. Effects of initial crack shapes and sizes are discussed using the improved hand calculation model. Lower fatigue resistance is found when the initial crack is shallow or large. In addition to the standard weld geometry in which the weld profile is represented by a straight line, concave and convex arc shape weld profiles are studied. Fatigue resistance is improved in the case with assumption of concave arc weld profile. The difference of fatigue resistance between the cases with a straight line and convex arc weld profiles is small.

Mooring system fatigue analysis for a semi-submersible

T-N curves, S-N curves, and fracture mechanics (FM) based mooring system fatigue analyses for a semi-submersible are presented. Stress ranges are calculated based on the tension ranges of mooring lines subjected to the combined loading process induced by the motions of wave frequency (WF) and low frequency (LF). A comparison between T-N curves, S-N curves, and FM based mooring fatigue analyses for the semi-submersible is made and the results show that the fatigue lives predicted by the three approaches are in general comparable if the safety factors suggested by API and DNVGL are considered in the T-N and S-N curves based approaches. In addition, the crown section of a mooring chain is prone to fatigue damage compared to bend and weld sections without considering the SCF. A parametric study to investigate the impact of initial crack shape, critical crack depth, and initial crack sizes on fatigue life of a mooring chain is also conducted and the results show that fatigue life of a mooring chain predicted by the FM approach is generally sensitive to initial crack shape and initial crack sizes, however, it is relatively insensitive to the critical crack depth.

SENT testing standard BS 8571 and its ongoing development

A standard for SENT (Single Edge Notched Tension) testing was published in 2014 as BS 8571:2014. Since then user feed-back was received, new research published, and editorial issues identified. The main proposed change is to the equations for calculating J to enable a single equation for specimens with W/B ratios from 0.5 to 2. The method for calculating CTOD remains the same. The range of the permitted a0/W ratio is reviewed, along with the limits for initial and final crack shape. Advice is also given on SENT testing at low temperatures. A new method to correct the value of J and CTOD where crack path deviation (i.e. out of plane ductile crack extension) occurs has been proposed which will increase the number of results that will be qualified. This paper summarises the status of the British Standard since its publication, and the changes planned for its ongoing development.

Damage evolution in plates subjected to fatigue loading

The aim of this paper is the numerical prediction of the cracking path followed by a surface crack front in plates constituted of different materials (determined by the exponent m of the Paris law), subjected to cyclic tension or cyclic bending loading. To this end, a numerical modelling was developed on the basis of the discretization of the crack front (characterized with elliptical shape) and the crack advance at each point perpendicular to such a front, according to a Paris law, using the stress intensity factor (SIF) calculated by Newman and Raju. Results show that the crack leads to a preferential propagation path that corresponds to a very shallow initial crack with a quasi-circular crack front. The increase of the Paris exponent produces a quicker convergence during fatigue crack propagation from the different initial crack shapes.

レーザかんな加工の最適初期き裂形状の検証

レーザかんな加工の最適初期き裂形状の検証

XFEM investigation on Knoop indentation cracking: Fracture toughness and aspect-ratio of radial-median cracks

In sharp indentation of brittle materials, cracks form below the impression or at its corners and propagate further during unloading. The dimensions of radial-median cracks can be exploited to derive the fracture toughness. Knoop indentation has the merit that only one large crack is produced. This and the shallow plastic zone make it the preferred method for crack growth experiments, but which require information on the initial crack shape. For investigation of the complex indentation stress field, which is moreover perturbed by cracking, the extended finite element method (XFEM) is an ideal tool. Results show that the point load assumption holds for sufficient loading, which means that Knoop indentation can be used for fracture toughness evaluation. During loading the plastic zone evolves linearly with depth h, while crack depth cz is found to evolve according to h ∝ cz3/4. For well-developed cracks, the crack aspect-ratio ρ ≡ cz/c (c is the length of the crack on the surface) is load-independent. The XFE model is validated through comparison with experimental results from the literature. Based on parameter studies, we establish functions that allow determination of fracture toughness and crack aspect-ratio. It is demonstrated that the mapping functions work well.

Fatigue Life Prediction Based on Crack Closure and Equivalent Initial Flaw Size.

Failure analysis and fatigue life prediction are necessary and critical for engineering structural materials. In this paper, a general methodology is proposed to predict fatigue life of smooth and circular-hole specimens, in which the crack closure model and equivalent initial flaw size (EIFS) concept are employed. Different effects of crack closure on small crack growth region and long crack growth region are considered in the proposed method. The EIFS is determined by the fatigue limit and fatigue threshold stress intensity factor △Kth. Fatigue limit is directly obtained from experimental data, and △Kth is calculated by using a back-extrapolation method. Experimental data for smooth and circular-hole specimens in three different alloys (Al2024-T3, Al7075-T6 and Ti-6Al-4V) under multiple stress ratios are used to validate the method. In the validation section, Semi-circular surface crack and quarter-circular corner crack are assumed to be the initial crack shapes for the smooth and circular-hole specimens, respectively. A good agreement is observed between model predictions and experimental data. The detailed analysis and discussion are performed on the proposed model. Some conclusions and future work are given.

Modelling 3D crack propagation in ageing graphite bricks of Advanced Gas-cooled Reactor power plant

In this paper, crack propagation in Advanced Gas-cooled Reactor (AGR) graphite bricks with ageing properties is studied using the eXtended Finite Element Method (X-FEM). A parametric study for crack propagation, including the influence of different initial crack shapes and propagation criteria, is conducted. The results obtained in the benchmark study show that the crack paths from X-FEM are similar to the experimental ones. The accuracy of the strain energy release rate computation in a heterogeneous material is also evaluated using a finite difference approach. Planar and non-planar 3D crack growth simulations are presented to demonstrate the robustness and the versatility of the method utilized. Finally, this work contributes to the better understanding of crack propagation behaviour in AGR graphite bricks and so contributes to the extension of the AGR plants’ lifetimes in the UK by reducing uncertainties.

Variation of stress intensity factor along a small interface crack front in singular stress fields

Stress singularities usually occur at vertexes in three-dimensional joints. Cracks frequently initiate at the vertex, and the joint fails under an external force or a thermal load. In the present study, the stress distribution near a small crack occurring at a vertex in a three-dimensional joint under a tensile load is examined, and the stress intensity factors at the crack tip are investigated along the crack tip front. The joint is made of Si and resin. In the analysis, three kinds of crack shapes (triangular, quarter circular, and concave) are supposed as the initial crack shape. The stress distribution around the crack is normalized using the singular stress near the vertex since the crack exists in the singular stress field. The stress intensity factor varies along the crack tip from the inner point to the free surface. The value of the stress intensity factor varies following the order of the stress singularity at the point of the free surface. In this analysis, the stress intensity factor is expressed as a function of the distance from the cross point of the free surface and the crack tip. Specifically, the function is composed of an exponential function of the difference between the order of the stress singularity at the cross point and the crack tip.

Prediction of shape change of semi-elliptical surface crack by fatigue crack growth circles parameter

As a fatigue crack grows, its shape changes. The shape of the growing crack can be affected by the initial crack shape, the load type and the fatigue crack growth rate of the material. Existing methods to predict the shape of the growing crack include finite element simulation techniques, which typically require the computation of several hundred increments to get accurate results. This paper describes a new technique that uses growth circles to model the growing crack. Since the circles are perpendicular to the current crack front as well as to the new crack front, it represents the real path of the fatigue crack well and yields more accurate results. The new technique is to be applied to the case of a surface crack in a thick plate under tension or bending. The effects of the Paris-Erdogan exponent are also investigated.

Investigation about crack propagation paths in thin rim gears

Crack propagation in gears is a problem related not only to the life of the components, but also to the concept of failsafe design. Fail safe design means to design a component in order that, if a failure occurs, this may cause a “safe failure”. This aspect is very important above all in aerospace industry. As a matter of fact, in aerospace application, the need of reducing weight brings to produce gears with very thick rim and web. Considering thin rim gears, when a crack is nucleated near the tooth root, it may propagate through the tooth (causing the loss of the entire tooth or a portion of it) or the propagation may follow a path across the wheel diameter (causing the projection of big parts of the gear that may break the gearbox and may cause serious damage to the aircraft). The first failure mode is define as “failsafe failure” and the second one as “catastrophic failure” and of course has to be avoided. Designers need to have robust design criteria in order to predict crack propagation paths and to avoid catastrophic failures. In literature, few works are present concerning this topic, in particular related to the effect of geometrical parameters that may affect the crack propagation. In this work a numerical analysis about crack propagation in gears with respect to the backup ratio (ratio between tooth height and rim thickness), initial crack position and shape has been done by means of the Extended FEM (XFEM) technique, realizing 3D models. XFEM 3D is a relatively new technique consisting in enriching traditional finite elements with more complex shape functions; in this way it is possible to propagate crack also between mesh nodes and to have mesh independent results. Aim of this paper is to highlight the crack propagation path in order to give to designers an high confident design criterion, related to the gear geometry. In particular, the effect of both rim thickness and orientation of the initial crack have been considered in order to enrich the literature knowledge. Numerical results obtained in this work have been compared with those found in the literature, showing a very good correlation.