Crack closure in friction stir weldment using non‐linear model for fatigue crack propagation

The fatigue crack propagation in a friction stir‐welded sample has been simulated herein by means of two 3‐dimensional finite element method (FEM)‐based analyses. Numerical simulations of the fatigue crack propagation have been carried out by assuming a residual stress field as a starting condition. Two initial cracks, observed in the real specimen, have been assessed experimentally by performing fatigue tests on the welded sample. Hence, the same cracks have been placed in the corresponding FE model, and then a remote load with boundary conditions has been applied on the welded specimen. The material behaviour of the welded joint has been modelled by means of the Ramberg‐Osgood equation, while the non‐linear Kujawski‐Ellyin (KE) model has been adopted for the fatigue crack propagation under small‐scale yielding (SSY) conditions. Owing to the compressive nature of the residual stress field that acts on a part of the cracked regions, the crack closure phenomenon has also been considered. Then, the original version of the KE law has been modified to fully include the closure effect in the analysis. Later, the crack closure effect has also been assessed in the simulation of fatigue propagation of three cracks. Finally, an investigation of the fracture process zone (FPZ) extension as well as the cyclic plastic zone (CPZ) and monotonic plastic zone (MPZ) extensions have been assessed.     

A modification of UniGrow 2‐parameter driving force model for short fatigue crack growth

In this paper, a modification of the UniGrow model is proposed to predict total fatigue life with the presence of a short fatigue crack by incorporating short crack propagation into the UniGrow crack growth model. The UniGrow model is modified by 2 different methods, namely the “short crack stress intensity correction method” and the “short crack data‐fitting method” to estimate the total fatigue life including both short and long fatigue crack propagations. Predicted fatigue lives obtained from these 2 methods were compared with experimental data sets of 2024‐T3, 7075‐T56 aluminium alloys, and Ti‐6Al‐4V titanium alloy. Two proposed methods have shown good fatigue life predictions at relatively high maximum stresses; however, they provide conservative fatigue life predictions at lower stresses corresponding high cycle fatigue lives where short crack behaviour dominates total fatigue life at lower stress levels.     

Experimental fatigue crack growth analysis and modelling in part‐through circumferentially pre‐cracked pipes under pure bending load

In the present work, an attempt has been made to study the fatigue crack growth in a part‐through circumferentially notched pipe specimen. It has been observed that under four‐point bend cyclic load, the crack propagates in a transverse plane in the radial direction initially followed by propagation in the circumferential direction. The crack extension in the circumferential direction resulted crack growth retardation in the radial direction. This behaviour of the fatigue crack growth has been modelled, and a fatigue life prediction methodology based on an exponential model has been applied for prediction of fatigue crack growth.     

Coupled FEM–DBEM approach on multiple crack growth in cryogenic magnet system of nuclear fusion experiment ‘Wendelstein 7‐X’

At the Max Planck Institute for plasma physics in Greifswald, Germany, the world's largest nuclear fusion experiment of modular stellarator type Wendelstein 7‐X has started plasma operation. The hot hydrogen plasma is confined in a plasma vessel by an electromagnetic field generated by 50 non‐planar and 20 planar superconducting coils. The superconducting coils are encased in cast stainless steel housings. The coils are bolted onto a central support ring and welded together by so called lateral support elements (LSEs). In this paper, a procedure, based on a global–local finite element method (FEM)–dual boundary element method (DBEM) approach, is developed to simulate the propagation of multiple cracks detected in LSEs and undergoing a fatigue load spectrum. The global stress analysis on the superconducting coils is performed by FEM whereas the sub‐modelling approach is adopted to solve the crack propagation in the DBEM environment. The boundary conditions applied on the DBEM submodel are the displacements calculated by the FEM global analysis, in correspondence of the cut surfaces (there are no body forces nor external loads applied on the submodel volume). Two cracks are simultaneously introduced, and a linear elastic fracture mechanics analysis is performed. Results in terms of cracks growth rates and evolving crack shapes are provided, and the residual life of the component is forecast.     

A local multigrid X‐FEM strategy for 3‐D crack propagation

A multiscale method for 3‐D crack propagation simulation in large structures is proposed. The method is based on the extended finite element method (X‐FEM). The asymptotic behavior of the crack front is accurately modeled using enriched elements and no remeshing is required during crack propagation. However, the different scales involved in fracture mechanics problems can differ by several orders of magnitude and industrial meshes are usually not designed to account for small cracks. Enrichments are therefore useless if the crack is too small compared with the element size. To overcome this drawback, a project combining different numerical techniques was started. The first step was the implementation of a global multigrid algorithm within the X‐FEM framework and was presented in a previous paper (Eur. J. Comput. Mech. 2007; 16 :161–182). This work emphasized the high efficiency in cpu time but highlighted that mesh refinement is required on localized areas only (cracks, inclusions, steep gradient zones). This paper aims at linking the different scales by using a local multigrid approach. The coupling of this technique with the X‐FEM is described and computational aspects dealing with intergrid operators, optimal multiscale enrichment strategy and level sets are pointed out. Examples illustrating the accuracy and efficiency of the method are given. Copyright © 2008 John Wiley & Sons, Ltd.     

Fatigue crack growth of a welded tube–flange connection under bending and torsional loading

In this contribution the results of an experimental investigation into the fatigue crack growth of welded tube-to-plate specimens of steel StE 460 under bending, torsion, and combined in-phase and out-of-phase bending/torsion loading are presented. The tests were performed at stress ratios of R = −1 and R = 0. The residual stresses were reduced by thermal stress relief. The fatigue crack development is compared with the prediction on the crack growth rates of Paris. Individual stress intensity factors for the semielliptical surface cracks in the tube-flange specimens are approximated on a weight function analogy using the published solutions of other workers.     

Evaluation of temperature‐sensitive fatigue crack propagation of a high‐speed railway wheel rim material

The fatigue crack growth rate (FCGR) of ER8C high‐speed railway wheel rim material was tested at various service temperatures. The temperature sensitivity of fatigue crack propagation was evaluated, and the effect of temperature on the crack propagation mechanism was analyzed. The obtained results indicate a fatigue ductile‐to‐brittle transition (FDBT) point at ?20°C for the ER8C wheel rim materials. A reverse relationship was found between FCGR and temperature for the near threshold and Paris regimes when the temperature was below the FDBT point. However, no evident changing rule was found when the temperature was above this transition point. An evident fatigue crack propagation mode transition was found from lamellar tearing to intergranular cracks, which was related to the FDBT for the near‐threshold regime.     

Fatigue crack propagation behavior of RC beams strengthened with CFRP under cyclic bending loads

A fatigue crack propagation equation of reinforced concrete (RC) beams strengthened with a new type carbon fiber reinforced polymer was proposed in this paper on the basis of experimental and numerical methods. Fatigue crack propagation tests were performed to obtain the crack propagation rate of the strengthened RC beams. Digital image correlation method was used to capture the fatigue crack pattern. Finite element model of RC beam strengthened with carbon fiber reinforced polymer was established to determinate J‐integral of a main crack considering material nonlinearities and degradation of material properties under cyclic loading. Paris law with a parameter of J‐integral was developed on the basis of the fatigue tests and finite element analysis. This law was preliminarily verified, which can be applied for prediction of fatigue lives of the strengthened RC beams.     

Sickle-shaped surface crack in a notched round bar under cyclic tension and bending

A sickle-shaped surface crack, also called crescent-moon (or crescent) crack, is assumed to exist at the root of a circular-arc circumferential notch in a round bar under tension and bending. For different notch sizes (i.e. different values of the stress concentration factor), the stress intensity factor along the crack front is computed through a three-dimensional finite-element analysis. The effect of the stress concentration factor on the stress intensity factor values is examined for several crack configurations. Finally, the surface crack growth under cyclic loading is analysed through a numerical procedure that employs the stress intensity factor values obtained. Some results of the present study are compared with those by other authors.     

Local strain accumulation in fatigue crack propagation process of Ti‐6Al‐4V alloy

Fatigue crack growth behaviours of the titanium alloy Ti‐6Al‐4V, with two different microstructures, at different maximum stresses were identified by digital image correlation technique. Full‐field strains were monitored around fatigue cracks after consecutive cycles in fatigue crack growth experiments. Results indicated that the Ti‐6Al‐4V alloy with a bi‐modal microstructure had a better fatigue resistance than that with a primary‐α microstructure. Typical behaviours of small cracks and the evolution of multi‐scale fatigue cracks were clarified. The strain accumulations around the micro‐notch and fatigue crack increased with increasing number of load cycles. On the basis of von Mises strain mapping, it was found that crack growth rate could be characterized by crack‐tip plastic zone size.     

Effect of steady torsion on fatigue crack initiation and propagation under rotating bending: Multiaxial fatigue and mixed-mode cracking

Axles and shafts are of prime importance concerning safety in transportation industry and railway in particular. Knowledge of fatigue crack growth under typical loading conditions of axles and shafts with rotating bending and steady torsion is therefore essential for design and maintenance purposes. The effect of a steady torsion on both small and long crack growth under rotating bending is focused in this paper. For small crack growth, a modified effective strain-based intensity factor range is proposed as the parameter that correlates small fatigue crack growth data under proportional or non-proportional multiaxial loading conditions. Results show that this parameter is appropriate for determining fatigue crack growth of small cracks on rotating bending with an imposed steady torsion.     

Experimental and analytical investigation of fatigue crack propagation of T‐welded joints considering the effect of boundary condition

T‐welded joints are commonly employed in ship and ocean structures. The fatigue failure of structure components subjected to cyclic loading always occurs in T‐welded joints because of the metallurgical differences, tensile residual stress fields and stress concentrations. The former researches about T‐welded joints fatigue have in common that the boundary condition needs to be taken into account as an influencing parameter to predict the crack propagation during cyclic loading. In this paper, the crack growth behaviour in T‐welded joint processed with Q345D steel (Pingxiang Iron & Steel Co., Ltd, Hukou, Jiangxi Province in China) under the fatigue loading was analysed via analytical model and verified via experiment. The results show that the influence of boundary condition should be considered in T‐welded joint structure during crack propagation in weld toe area. The correction factor concerning the effect of boundary condition and modified Paris' equation was proposed according to the experimental results and verified by the following repeated experiments.     

Fatigue crack growth law of API X80 pipeline steel under various stress ratios based on J‐integral

Load‐controlled three‐point bending fatigue tests were conducted on API X80 pipeline steel to investigate the effects of stress ratio and specimen orientation on the fatigue crack growth behaviour. Because of the high strength and toughness of X80 steel, crack growth rate was measured and plotted versus ΔJ with stress ratio. The fatigue crack length is longer in the transverse direction, whereas the fatigue crack growth rates are nearly the same in different orientations. Finally, a new fatigue crack growth model was proposed. The effective J‐integral range was modified by ΔJ_p in order to correlate crack closure effect due to large‐scale yield of crack tip. The model was proved to fit well for fatigue crack growth rate of API X80 at various stress ratios of R > 0.     

Effect of cyclic hardening on fatigue performance of slide burnished components made of low‐alloy medium carbon steel

The slide burnishing process causes cyclic loading of the surface being treated, which provokes cyclic hardening. Using a forced‐controlled indentation test, the sixth “loading‐unloading” cycle was stabilised. The effect of the number of passes and the cyclic loading coefficient (CLC) on the fatigue performance of slide burnished specimens was investigated. Rotating bending fatigue tests were conducted using nine groups of hourglass shaped specimens, which were slide burnished through a different number of passes and CLC values. A stabilised cycle of the surface layer achieved with six passes, lead to largest fatigue limit, whereas the CLC exerted negligible influence on the fatigue performance. The observed phenomenon was explained through different residual stress relaxation rates, due to the rotating bending load, as well as with the obtained surface layer microstructure. The residual stress relaxation was investigated through rotating bending fatigue tests, using cylindrical fatigue specimens, followed by X‐ray stress analysis.     

Effects of grain size on cyclic plasticity and fatigue crack initiation in nickel

Fatigue experiments were conducted on polycrystalline nickel of two grain sizes, 24 and 290 μm, to evaluate the effects of grain size on cyclic plasticity and fatigue crack initiation. Specimens were cycled at room temperature at plastic strain amplitudes ranging from 2.5×10⁻⁵ to 2.5×10⁻³. Analyses of the cyclic stress–strain response and evolution of hysteresis loop shape indicate that the back stress component of the cyclic stress is significantly affected by grain size and plastic strain amplitude, whereas these parameters have little effect on friction stress. A nonlinear kinematic hardening framework was used to study the evolution of back stress parameters with cumulative plastic strain. These are related to substructural evolution features. In particular, long range back stress components are related to persistent slip bands. The difference in cyclic plasticity behavior between the two grain sizes is related to the effect of grain size on persistent slip band (PSB) morphology, and the effect this has on long range back stress. Fine grain specimens had a much longer fatigue life, especially at low plastic strain amplitude, as a result of the influence of grain size on fatigue crack initiation characteristics. At low plastic strain amplitude (2.5×10⁻⁴), coarse grain specimens initiated cracks where PSBs impinged on grain boundaries. Fine grain specimens formed cracks along PSBs. At high plastic strain amplitude (2.5×10⁻³), both grain sizes initiated cracks at grain boundaries.     

Influence of non‐proportional bending with torsion on fatigue life of 10HNAP steel within the range of crack initiation and propagation

The paper presents a precise analysis of the influence of non‐proportional loading of specimens on fatigue life during initiation and propagation of fatigue cracks. Simulation of the fatigue life of specimens was based on relations describing propagation rate of the fatigue cracks. The Paris and Forman relations were applied; they were integrated after previous introduction of relationships for the equivalent range of the stress intensity factor ΔK_eq and including the phase shift angle ? between amplitudes of the bending moment and the torsional moment. Under bending with torsion, range of the equivalent stress intensity factor ΔK_eq includes ranges of stress intensity factors for loading modes I and III, i.e. ΔK_I and Δ K_III. The performed tests of 10HNAP constructional steel under cyclic bending with torsion allowed us to determine the influence of the phase shift angle ? on the fatigue life. It has been proved that increase of the phase shift angle from ?= 0° to ?= 60° and the ratio of amplitude of the bending moment M_ag to amplitude of the torsional moment M_as equal to 1.33, 2 and 4 cause increase of the fatigue life of the tested specimens. The maximum increase of the fatigue life of specimens made of 10HNAP steel was 73% (M_ag/M_as= 2, ?= 45°).     

Overload effect on the fatigue crack propagation in large‐scale tubular joints

This paper examines the overloading effect on the fatigue crack propagations monitored in a large‐scale tubular X‐joint specimen under two separate cyclic tests. The first cyclic test applies a constant‐amplitude brace in‐plane bending to the joint, with a single cycle of 150% overload before the crack depth reaches the mid‐thickness of the chord. The second fatigue test applies two batches of cyclic loads, with the amplitude of the second batch at 66% of the former. The X‐joint specimen experiences a 150% overload cycle during the first batch of loading, followed by the second batch after it has recovered from the overload effect. The experimental results reveal that deep surface cracks experience more significant overload retardation than does a shallow fatigue crack. The Paris law estimation indicates that the single overload cycle applied in the first specimen leads to a 7% increase in the fatigue life of the X‐joint.     

Effects of microstructural through‐thickness non‐uniformity and crack size on fatigue crack propagation and fracture of rolled Al‐7075 alloy

Some of the fatigue tests performed using the standard compact tension (CT) and a non‐standard specimen made of rolled 7075 aluminium alloy exhibit fatigue crack growth (FCG) lagging in a small region along the crack front. Through‐thickness microstructural evaluation shows that material grains in this region did not flatten as much as other regions. In the non‐standard specimen, surface cracks are either grown under fatigue loading or broken under monotonically increasing quasi‐static loads at different crack sizes. The aforementioned lagging also exists in a narrow region of 3‐D FCG for specimens with microstructural through‐thickness non‐uniformity. A more important feature for this type of specimen with surface crack is the deflection of fast fracture direction into the grain interfaces, namely from L‐T orientation to S‐L and S‐T directions. It is proved that this is due to significant levels of second principal stresses near the free surface for small cracks and lower fracture toughness of the material in S‐L and S‐T directions.     

Subsurface crack formation and propagation of fretting fatigue in Ni‐based single‐crystal superalloys

The fretting fatigue crack formation and propagation behaviors of Ni‐based single‐crystal (NBSX) superalloys are investigated in this paper. Subsurface crack formation process is revealed by in situ fretting fatigue experiment. The crack is observed to form on subsurface area, then propagates to the contact surface. Inclusions in materials are found to have obvious effects on crack propagation, and slip lines are closely related to the crack propagation direction. Crystal plastic finite element method (CPFEM) simulation is used to simulate crack formation position. The accumulative plastic strain peaks at the edge of contact zone and the subsurface area. The results show that the CPFEM simulation and in situ observation achieve good agreements.