A cumulative model of fatigue crack growth and the crack closure effect

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated using the local stress/strain at the crack tip by assuming that a small highly strained area $\text{x}{}^1$, existing at the crack tip, is responsible for the fatigue crack growth, and that the fatigue crack growth may be regarded as the cumulation of successive crack re-initiations over a distance $\text{x}{}^1$. It is shown that crack closure can be modelled using the effective contact zone g behind the crack tip. The model allows the fatigue crack growth rate over the near threshold and linear ranges of the general da/dN versus ΔK curve to be calculated. The fatigue crack growth retardation due to overload and fatigue crack arrest can also be analysed in terms of g and $\text{x}{}^1$.Calculated fatigue crack growth rates are compared with experimental ones for low and high strength steel.     

Nonlinear fatigue crack propagation in a baffle module of Wendelstein 7‐X under cyclic bending loads

Simulation of the fatigue crack propagation in a Wendelstein 7‐X baffle module is performed in this study using both a finite element method‐based software and the UniGrow nonlinear model for small‐scale yielding (SSY) conditions. Some experimental fatigue tests of several cracked baffle modules have been performed through a servo‐hydraulic machine. One of these experimental tests has been considered to simulate fatigue crack propagation in the baffle module. Before starting the experimental test, a first crack partly contained in the welding seam and partly in the steel pipe is found. Subsequently, owing to the applied load, the crack propagated both into the welding seam and into the steel pipe until the plastic zone in the near field attains SSY conditions. Finally, owing to the increase in the extension of the plastic zone, SSY conditions are not more valid, and the breakage of the steel pipe is produced by plastic collapse.     

Empirical model for plasticity‐induced crack closure based on Kmax and ΔK

The mean stress has a significant effect on crack propagation life and must be included in prediction models. However, there is no consensus in the fatigue community regarding the dominant mechanism explaining the mean stress effect. The concept of crack closure has been widely used and several empirical models can be found in literature. The stress ratio, R, is usually the main parameter of these models, but present numerical results showed a significant influence of K_max. A new empirical model is therefore proposed here, dependent on K_max and ΔK, with four empirical constants. The model also includes the effect of material's yield stress, and two additional parameters were defined to account for stress state and crack closure parameter. A comparison was made with Kujawski's and Glinka's parameters, for a wide range of loading conditions. ΔK_eff lies between Kujawski's and Glinka's parameters, and some agreement is evident, although the concepts are quite different. The crack opening model was applied to literature results and was able to collapse da/dN–ΔK curves for different stress ratios to a single master curve.     

A threshold fatigue crack closure model: Part I – model development

A fatigue crack closure model is developed that includes the effects of, and interactions between, the three closure mechanisms most likely to occur at threshold; plasticity, roughness, and oxide. This model, herein referred to as the CROP model (for Closure, Roughness, Oxide, and Plasticity), also includes the effects of out‐of‐plane cracking and multi‐axial loading. These features make the CROP closure model uniquely suited for, but not limited to, threshold applications. Rough cracks are idealized here as two‐dimensional sawtooths, whose geometry induces mixed‐mode crack‐tip stresses. Continuum mechanics and crack‐tip dislocation concepts are combined to relate crack face displacements to crack‐tip loads. Geometric criteria are used to determine closure loads from crack‐face displacements. Finite element results, used to verify model predictions, provide critical information about the locations where crack closure occurs. The CROP model is verified with experimental data in part II of this paper.     

Assessment of fatigue crack closure under in-phase and out-of-phase thermomechanical fatigue loading using a temperature dependent strip yield model

In this paper fatigue crack closure under in-phase and out-of-phase thermomechanical fatigue (TMF) loading is studied using a temperature dependent strip yield model. It is shown that fatigue crack closure is strongly influenced by the phase relation between mechanical loading and temperature, if the temperature difference goes along with a temperature dependence of the yield stress. In order to demonstrate the effect of the temperature dependent yield stress, the influence of in-phase and out-of-phase TMF loading is studied for a polycrystalline nickel-base superalloy. By using a mechanism based lifetime model, implications for fatigue lives are demonstrated.     

Utilization of partial crack closure for fatigue crack growth modeling

Load ratio effects are of prime concern when modeling of fatigue crack growth (FCG) rate is required as a prerequisite for a reliable life prediction. The majority of research efforts regarding the load ratio effects are based on Elber's ΔK_eff approach. However, there are intrinsic difficulties encountered with its consistent application to FCG prediction. In this paper two popular crack-growth-life prediction codes FASTRAN and AFGROW are modified utilizing the enhanced partial crack closure model. The proposed utilization aggregates apparent closure mechanisms involved and demonstrates a better correlation and a significant scatter reduction of FCG data taken from literature, especially in the near-threshold region.     

Improved test method and analytical modelling for fatigue crack growth in coarse‐grain titanium alloy with rough fatigue surfaces

Fatigue crack growth rate properties are typically determined by experimental methods in accordance with ASTM Standard E647. These traditional methods use standard notched specimens that are precracked under cyclic tensile loads before the main test. The data that are produced using this approach have been demonstrated elsewhere to be potentially adversely affected by the test method, particularly in the threshold region where load reduction (LR) methods are also required. Coarse‐grained materials that exhibit rough and tortuous fatigue surfaces have been observed to be strongly affected by the tensile precracking and LR, in part because the anomalies caused by crack closure and roughness‐induced closure become more important. The focus of the work reported in this paper was to further develop methods to determine more accurate fatigue crack growth rate properties from threshold through to fracture for coarse‐grained, β‐annealed, titanium alloy Ti‐6Al‐4V extra low interstitial thick plate material. A particular emphasis was put upon the threshold and near threshold region, which is of strong importance in the overall fatigue life of components. New approaches that differ from the ASTM Standard included compression precracking, LR starting from a lower load level and continuing the test beyond rates where crack growth would otherwise be considered below threshold. For the threshold regime, two LR methods were also investigated: the ASTM method and a method where the load is reduced with crack growth such that the crack mouth opening displacement is held constant, in an attempt to avoid remote closure. Constant amplitude fatigue crack growth rate data were produced from threshold to fracture for the titanium alloy at a variety of stress ratios. Spike overload tests were also conducted These data were then used to develop an improved analytical model to predict crack growth under spectrum loading and the predictions were found to correlate well with test results.     

Microstructural effects on crack closure and propagation thresholds of small fatigue cracks

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack-tip slip band model with the plasticity-induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack-tip opening displacement range (Δ CTOD ), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, Δ CTOD began to decrease. The arrest condition of cracks was given by the threshold value of Δ CTOD . At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation.     

A threshold fatigue crack closure model: Part II – experimental verification

Predictions from an analytical model that considers contributions and interactions between plasticity, roughness, and oxide induced crack closure are presented and compared with experimental data. The analytical model is shown to correctly predict the combined influences of crack roughness, oxide debris, and plasticity in the near‐threshold regime. Furthermore, analytical results indicate closure mechanisms interact in a non‐linear manner such that the total amount of closure is not the sum of closure contributions for each mechanism.     

Residual stress effects on fatigue crack growth in a Ti‐6Al‐4V friction stir weld

Recent studies have illustrated a predominant role of the residual stress on the fatigue crack growth in friction stir welded joints. In this study, the role of the residual stress on the propagation of fatigue cracks orthogonal to the weld direction in a friction stir welded Ti‐6Al‐4V joint was investigated. A numerical prediction of the fatigue crack growth rate in the presence of the residual stresses was carried out using AFGROW software; reasonable correspondence between the predictions and the experimental results were observed when the effects of residual stress were included in the simulation.     

A model for evaluating the effect of fatigue crack repair by the infiltration method

Infiltration of foreign materials into a fatigue crack has previously been shown to be able to retard the crack and extend fatigue life. Most of the related studies were empirical and phenomenological in nature. To aid engineering decisions, it would be advantageous if the possible outcome of a repair can be evaluated beforehand. To this end, a crack closure model taking into account the additional closure effect of the infiltrant has been developed and verified against experimental results. With this model, the sensitivity of the repair effect to various parameters such as mechanical properties of the infiltrant, depth of penetration and infiltration load level can be assessed.     

On the Frost–Dugdale plot for non‐propagating cracks

The Frost–Dugdale plot is re‐examined and the subject of the non‐propagation of fatigue cracks is updated to emphasize that fatigue crack closure is the principal factor responsible for the non‐propagation of fatigue cracks which originate at notches. The limitations of the original Frost–Dugdale plot with respect to notch depth are also discussed.     

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.     

Experiments and model predictions for fatigue crack propagation in riveted lap‐joints with multiple site damage

In this paper, the growth of long fatigue cracks up to failure in aircraft components is studied. A deterministic model is presented, able to simulate the growth of fatigue through cracks located at rivet holes in lap‐joint panels. It also includes criteria to assess the link‐up of collinear adjacent cracks in a MSD scenario. To validate the model, a fatigue test campaign was carried out on riveted lap‐joint specimens in order to produce experimental crack growth and link‐up data. Accurate measurements of naturally occurred surface cracks were automatically performed by the Image Analysis technique, thus allowing the tests to run 24 h a day. The comparison between experimental tests and numerical simulations is good, thus confirming the model as a useful tool for the assessment of fatigue life of aircraft riveted joints.     

Fatigue crack closure: a review of the physical phenomena

Plasticity‐induced, roughness‐induced and oxide‐induced crack closures are reviewed. Special attention is devoted to the physical origin, the consequences for the experimental determination and the prediction of the effective crack driving force for fatigue crack propagation. Plasticity‐induced crack closure under plane stress and plane strain conditions require, in principle, a different explanation; however, both types are predictable. This is even the case in the transition region from the plane strain to the plane stress state and all types of loading conditions including constant and variable amplitude loading, the short crack case or the transition from small‐scale to large‐scale yielding. In contrast, the prediction of roughness‐induced and oxide‐induced closures is not as straightforward.     

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.     

Using fatigue crack propagation mechanism maps to predict changes in propagation mechanisms

The conditions determining the fatigue fracture mechanism in quenched and tempered steel are discussed with reference to fatigue crack propagation mechanism (FCPM) maps. Criteria for the change from one fatigue mechanism to another are presented.     

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.     

The effect of stress ratio on fatigue crack growth rate in the absence of closure

A fractographic study¹ was performed on Al-alloy fatigue fracture surfaces produced by programmed load sequences. The load sequences included steps of constant amplitude cycles at three different stress ratios, each step is preceded by a small number of high amplitude cycles designed to avoid the influence of crack closure and to serve as fractographic markers. The experiments were conducted on different specimen geometries to produce conditions associated with a long crack under fully elastic conditions and a short crack in a notched coupon seeing high local post yield stress conditions. Crack sizes covered in the study ranged from 0.02 to 12 mm, and growth rates ranged from 2×10⁻⁷ to 4×10⁻⁵ mm cycle⁻¹. Fractographic evidence from the study suggests that the crack growth rate can vary by up to a factor of five with applied stress ratio change from 0.64 to 0.73. In the case of the long crack, the effect is less noticeable or totally absent. In the case of naturally initiating notch root cracks, the effect is more pronounced at higher stress level and lower crack growth rate.