Fatigue crack propagation assessment based on residual stresses obtained through cut-compliance technique

Crack growth rate versus crack length curves of heavily overloaded parent material specimens and fatigue crack propagation curves of friction‐stir‐welded aluminium samples are presented. It is shown that in both cases the residual stresses have a strong effect on the crack propagation behaviour under constant and variable amplitude loading. As a simplified engineering approach, it is assumed in this paper, that in both cases residual stresses are the main and only factor influencing crack growth. Therefore fatigue crack propagation predictions are performed by adding the residual stresses to the applied loading and by neglecting the possible effects of overloading and friction stir welding on the parent material properties. For a quantitative assessment of the residual stress effects, the stress intensity factor due to residual stresses K_res is determined directly with the so‐called cut‐compliance method (incremental slitting). These measurements are particularly suited as input parameters for the software packages AFGROW and NASGRO 3.0, which are widely used for fatigue crack growth predictions under constant and variable amplitude loading. The prediction made in terms of crack propagation rates versus crack length and crack length versus cycles generally shows a good agreement with the measured values.     

CRACK GROWTH ARRESTING PROPERTY OF A HOLE AND BRINELL-TYPE DIMPLE

Abstract— Fatigue tests of sheet specimens having a central crack were carried out to study the effects of holes and dimples on the arrest of fatigue crack propagation. Two holes were drilled at some distance from, and at either side of, a crack tip, and the dimple of a certain diameter was introduced by pressing steel balls in the specimen at a crack tip. Results showed that the two holes produced an increase in crack propagation life (about 3 times) when the holes were drilled at an appropriate distance. On the other hand, the effect of a dimple on the fatigue strength was remarkably large, i.e. in the greatest case a 2.2 times increase in the fatigue endurance limit of cracked specimens and about a 50 times increase in the crack propagation life, at stresses above the fatigue limit. The main reason for the remarkable recovery of fatigue strength was the residual compressive stresses produced by the dimple. To evaluate the effect of residual compressive stresses on the da/dN vs. δK relation, a simple model is proposed. By using this model, the effect of residual stresses on crack propagation can be estimated quantitatively. Furthermore, the fatigue life of dimpled specimens was estimated based on the model.     

Crack growth predictions using a strip‐yield model for variable‐amplitude and spectrum loading

Fatigue‐crack‐growth tests were conducted on compact, C(T), specimens made of D16Cz aluminum alloy. Constant‐amplitude tests were conducted over a range of stress ratios (R = P_min/P_max = 0.1 to 0.75). Comparisons were made between test data from middle‐crack tension, M(T), specimens from the literature and C(T) specimens. A crack‐closure analysis was used to collapse the rate data from both specimen types into a fairly narrow band over many orders of magnitude in rates using proper constraint factors. Constraint factors were established from single‐spike overload and constant‐amplitude tests. The life‐prediction code, FASTRAN, which is based on the strip‐yield‐model concept, was used to calculate the crack‐length‐against‐cycles under constant‐amplitude (CA) loading and the single‐spike overload (OL) tests; and to predict crack growth under variable‐amplitude (VA) loading on M(T) specimens and simulated aircraft loading spectrum tests on both specimen types. The calculated crack‐growth lives under CA and the OL tests were generally within ±20 % of the test results, the predicted crack‐growth lives for the VA and Mini‐Falstaff tests on the M(T) specimens were short by 30 to 45 %, while the Mini‐Falstaff+ results on the C(T) specimens were within 10 %. Issues on the crack‐starter notch effects under spectrum loading are discussed, and recommendations are suggested on avoiding these notch effects.     

Crack growth behavior and fatigue-life prediction based on worst-case near-threshold data of a large crack for 9310 steel

ABSTRACT Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks, near‐threshold growth behavior of large cracks at constant R‐ratio/decreasing ΔK and constant K_max/decreasing ΔK, respectively, for 9310 steel. The results showed that a pronounced small‐crack effect was not observed even at R = ?1, small cracks initiated by a slip mechanism at strong slip sites. Worst‐case near‐threshold testing results for large cracks under several K_max values showed that an effect of K_max on the near‐threshold behavior does not exist in the present investigation. A worst‐case near‐threshold test for a large crack, i.e. constant K_max/decreasing ΔK test, can give a conservative prediction of growth behavior of naturally initiated small cracks. Using the worst‐case near‐threshold data for a large crack and crack‐tip constraint factor equations defined in the paper, Newman's total fatigue‐life prediction method was improved. The fatigue lives predicted by the improved method were in reasonable agreement with the experiments. A three‐dimensional (3D) weight function method was used to calculate stress‐intensity factors for a surface crack at a notch of the present SENT specimen (with r/w = 1/8) by using a finite‐element reference solution. The results were verified by limited finite‐element solutions, and agreed well with those calculated by Newman's stress‐intensity factor equations when the stress concentration factor of the present specimen was used in the equations.     

Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

A new testing method to obtain mode II fatigue crack growth characteristics of hard materials

Flaking type failure in rolling‐contact processes is usually attributed to fatigue‐induced subsurface shearing stress caused by the contact loading. Assuming such crack growth is due to mode II loading and that mode I growth is suppressed due to the compressive stress field arising from the contact stress, we developed a new testing apparatus for mode II fatigue crack growth. Although the apparatus is, as a former apparatus was, based on the principle that the static K_I mode and the compressive stress parallel to the pre‐crack are superimposed on the mode II loading system, we employ direct loading in the new apparatus. Instead of the simple four‐point‐shear‐loading system used in the former apparatus, a new device for the application of a compressive stress parallel to the pre‐crack has been developed. Due to these alterations, mode II cyclic loading tests for hard steels have become possible for arbitrary stress ratios, including fully reversed loading (R=?1); which is the case of rolling‐contact fatigue. The test results obtained using the newly developed apparatus on specimens made from bearing steel SUJ2 and also a 0.75% carbon steel, are shown.     

Fatigue life prediction based on equivalent stresses for laser beam welded 6156 Al‐alloy joints under variable amplitude loading

In the present work, a simple fatigue life prediction approach is proposed using fracture mechanics for laser beam welded Al‐alloy joints under variable amplitude loading. In the proposed approach, variable amplitude loading sequence is transformed into an equivalent constant amplitude loading using the root mean square model. The crack growth driving force K^* is chosen to describe the fatigue crack growth rate. The influences of residual stress and its relaxation on fatigue life are taken into account in the proposed approach. The fatigue lives are also predicted using the traditional approach based on the S‐N curves and the rainflow counting method. The predicted results show that the proposed approach is better than the traditional approach.     

Non‐planar mixed‐mode growth of initially straight‐fronted surface cracks,in cylindrical bars under tension,torsion and bending,using the symmetric Galerkin boundary element method‐finite element method alternating method

In this paper, the stress intensity factor (SIF) variations along an arbitrarily developing crack front, the non‐planar fatigue‐crack growth patterns, and the fatigue life of a round bar with an initially straight‐fronted surface crack, are studied by employing the 3D symmetric Galerkin boundary element method‐finite element method (SGBEM‐FEM) alternating method. Different loading cases, involving tension, bending and torsion of the bar, with different initial crack depths and different stress ratios in fatigue, are considered. By using the SGBEM‐FEM alternating method, the SIF variations along the evolving crack front are computed; the fatigue growth rates and directions of the non‐planar growths of the crack surface are predicted; the evolving fatigue‐crack growth patterns are simulated, and thus, the fatigue life estimations of the cracked round bar are made. The accuracy and reliability of the SGBEM‐FEM alternating method are verified by comparing the presently computed results to the empirical solutions of SIFs, as well as experimental data of fatigue crack growth, available in the open literature. It is shown that the current approach gives very accurate solutions of SIFs and simulations of fatigue crack growth during the entire crack propagation, with very little computational burden and human–labour cost. The characteristics of fatigue growth patterns of initially simple‐shaped cracks in the cylindrical bar under different Modes I, III and mixed‐mode types of loads are also discussed in detail.     

Crack growth predictions in a complex helicopter component under spectrum loading

Fatigue crack growth predictions have been made on a helicopter round‐robin crack configuration. The crack configuration was a small corner defect at the edge of a large central hole in a flanged plate made of 7010 aluminium alloy and the component was subjected to a simulated helicopter spectrum loading. The crack growth rate data and the stress‐intensity factor (K) solution for the crack configuration were provided in the round‐robin. The FASTRAN life‐prediction code was used to predict fatigue crack growth under various load histories on the aluminium alloy, such as Rotorix and Asterix, on both compact tension C(T) specimens and the complex crack configuration. A BEASY three‐dimensional stress‐intensity factor solution for the round‐robin problem was also provided for this paper and is compared with the original K solution. Comparisons are made between measured and predicted fatigue crack growth lives for both crack configurations. The predicted lives for the C(T) specimens were 15–30% longer than the measured lives; and crack growth in the round‐robin configuration agreed very well in the early stages of crack growth, but the life was 30% short of the test results at the final crack length.     

A Continuum Mechanics Approach for Crack Initiation and Crack Growth Predictions

Very often, different approaches are used for crack initiation and crack growth predictions. The current article introduces a recently developed approach that can be used for the predictions of both crack initiation and crack propagation. A basic assumption is that both crack nucleation and crack growth are governed by the same fatigue damage mechanisms and a single fatigue damage criterion can model both stages. A rule is that any material point fails to form a fresh crack if the total accumulated fatigue damage reaches a limit. For crack initiation predictions, the stresses and strains are obtained either directly from experiments or though a numerical analysis. For the prediction of crack growth, the approach consists of two steps. Elastic‐plastic stress analysis is conducted to obtain the detailed stress‐strain responses. A general fatigue criterion is used to predict fatigue crack growth. Compact specimens made of 1070 steel were experimentally tested under constant amplitude loading with different R‐ratios and the overloading influence. The capability of the approach to predict both crack initiation and the crack growth under these loading conditions was demonstrated by comparing the predictions with the experimental observations.     

Three‐dimensional mixed‐mode (I and II) crack‐front fields in ductile thin plates — effects of T‐stress

It has been well‐established that the non‐singular T‐stress provides a first‐order estimate of geometry and loading mode (e.g. tension versus bending) effects on elastic–plastic crack‐front field under mode I loading conditions. The objective of this paper is to exam the T‐stress effect on three‐dimensional (3D) crack‐front fields under mixed‐mode (modes I and II) loading. To this end, detailed 3D small strain, elastic–plastic simulations are carried out using a 3D boundary layer (small‐scale yielding) formulation. Characteristics of near crack‐front fields are investigated for a wide range of T‐stresses (T/σ₀ = ?0.8, ?0.4, 0.0, 0.4, 0.8). The plastic zones and thickness and angular and radial variations of the stresses are studied, corresponding to two values of the remote elastic mixity parameters M_e = 0.3 and 0.7, under both low and high levels of applied loads. It is found that different T‐stresses have a significant effect on the plastic zones size and shapes, regardless of the mode mixity and load level. The thickness, angular and radial distributions of stresses are also affected markedly by T‐stress. It is important to include these effects when investigating the mixed‐mode ductile fracture failure process in thin‐walled structural components.     

Effects of an overload event on crack closure in 3-D small-scale yielding: finite element studies

This paper describes the effects of a single overload event, within otherwise constant amplitude cycles, on the plasticity‐induced closure process for mode I fatigue crack growth in the small‐scale yielding (SSY) regime. The 3‐D finite element (FE) analyses extend the initially straight, through‐thickness crack front by a fixed amount in each load cycle, using a node release procedure. Crack closure during reversed loading occurs when nodes behind the growing crack impinge on a frictionless, rigid plane. A bilinear, purely kinematic hardening model describes the constitutive response of the elastic–plastic material. Extensive crack growth in the analyses, both before and after the overload, allows the crack to grow out of the initial and the post‐overload transient phases, respectively. The work presented here shows that the large plastic deformation in the overload cycle reduces the crack driving force through enhanced closure. Further, the residual plastic deformations due to the overload cause a disconnected pattern of closure in the wake long after the crack front passes through the overload plastic zone. The computational studies demonstrate that the 3‐D scaling relationship for crack opening loads established in our earlier work for constant amplitude cycling (with and without a T‐stress) also holds before, during and after the overload event. For a specified ratio of overload‐to‐constant amplitude loading (R_OL=K^OL_max/K_max) , the normalized opening load (K_op/K_max) at each location along the crack front remains unchanged when the constant amplitude peak load (K_max) , thickness (B) and material flow stress (σ₀) all vary to maintain a fixed value of . The paper concludes with a comparison of the post‐overload response predicted by the 3‐D analyses and by the conventional Wheeler model.     

Fretting fatigue limit as a short crack problem at the edge of contact

This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S–N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ΔK change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ΔK change due to crack growth and the ΔK_th for a short crack. The formation of a non‐propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long‐life fretting fatigue test.     

Mixed mode crack tip parameters for different wheel positions relative to a vertical crack at the rail foot

Finite element method is used to analyze a rail with a vertical bottom up crack at its foot, under the axle load and surface traction of a wheel. The possibility of crack formation at the foot of the rail in the neighborhood of a welding connection is discussed. A brief review on the importance of T‐stress in brittle fracture is presented. Seven cases with different locations of the crack relative to rail's sleeper contact region are considered. Numerous positions of the wheel are considered, and in each case, 3 crack parameters K_I, K_II, and T‐stress are calculated. Then, the biaxiality ratio and the mixity parameter for each loading and crack condition are calculated. It is shown that the location of crack and wheel can create mixed mode loading in the cracked rail and that the magnitude of crack tip parameters are strongly dependent on these geometric variables. In particular, the magnitudes of T‐stress and biaxiality ratio are significant in some cases. The effect of friction between the crack faces in the presence of compressive mode I loading on the mode II stress intensity factor is studied. Under mixed mode loading, due to the axle load and surface traction, the most critical condition is the formation of vertical cracks near the sleeper contact region.     

Proposal of a new concept on creep fracture remnant life for a precracked specimen

Abstract

The creep life time of a smooth specimen can be predicted using existing laws for creep deformation and steady state creep rate. When crack growth behaviour is involved, it is necessary to construct a law of creep crack growth rate to predict creep fracture life. Creep fracture life can be measured by integrating the law of creep crack growth rate. One example is the creep crack growth rate, represented by the parameter Q*. In this study, we investigated the applicability of this prediction method to creep fracture remnant life for a cracked specimen. The Ω criterion is proposed to predict creep fracture remnant life for a smooth specimen for creep ductile materials. In this study, the correlation between Q*_L derived from the paremeters Q* and Ω is investigated. The correlation between Q_L* and Ω provided a unified theoretical prediction law of creep fracture remnant life for high-temperature creep-ductile materials in the range from smooth to precracked specimens.     

Bonded aircraft repairs under variable amplitude fatigue loading and at low temperatures

Bonded repairs can replace mechanically fastened repairs for aircraft structures. Compared to mechanical fastening, adhesive bonding provides a more uniform and efficient load transfer into the patch, and can reduce the risk of high stress concentrations caused by additional fastener holes necessary for riveted repairs. Previous fatigue tests on bonded Glare (glass‐reinforced aluminium laminate) repairs were performed at room temperature and under constant amplitude fatigue loading. However, the realistic operating temperature of ?40 °C may degrade the material and will cause unfavourable thermal stresses. Bonded repair specimens were tested at ?40 °C and other specimens were tested at room temperature after subjecting them to temperature cycles. Also, tests were performed with a realistic C‐5A Galaxy fuselage fatigue spectrum at room temperature. The behaviour of Glare repair patches was compared with boron/epoxy ones with equal extensional stiffness. The thermal cycles before fatigue cycling did not degrade the repair. A constant temperature of ?40 °C during the mechanical fatigue load had a favourable effect on the fatigue crack growth rate. Glare repair patches showed lower crack growth rates than boron/epoxy repairs. Finite element analyses revealed that the higher crack growth rates for boron/epoxy repairs are caused by the higher thermal stresses induced by the curing of the adhesive. The fatigue crack growth rate under spectrum loading could be accurately predicted with stress intensity factors calculated by finite element modelling and cycle‐by‐cycle integration that neglected interaction effects of the different stress amplitudes, which is possible because stress intensities at the crack tip under the repair patch remain small. For an accurate prediction it was necessary to use an effective stress intensity factor that is a function of the stress ratio at the crack tip R_{crack tip} including the thermal stress under the bonded patch.     

History effect in fatigue crack growth under mixed-mode loading conditions

Plastic deformation within the crack tip region introduces internal stresses that modify subsequent behaviour of the crack and are at the origin of history effects in fatigue crack growth. Consequently, fatigue crack growth models should include plasticity-induced history effects. A model was developed and validated for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this study was to extend this model to mixed-mode loading conditions. Finite element analyses are commonly employed to model crack tip plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modelled to predict the fatigue behaviour of an industrial component, the finite element method becomes computationally too expensive. By employing a multiscale approach, the local results of FE computations can be brought to the global scale. This approach consists of partitioning the velocity field at the crack tip into plastic and elastic parts. Each part is partitioned into mode I and mode II components, and finally each component is the product of a reference spatial field and an intensity factor. The intensity factor of the mode I and mode II plastic parts of the velocity fields, denoted by dρ_I/dt and dρ_II/dt, allow measuring mixed-mode plasticity in the crack tip region at the global scale. Evolutions of dρ_I/dt and dρ_II/dt, generated using the FE method for various loading histories, enable the identification of an empirical cyclic elastic–plastic constitutive model for the crack tip region at the global scale. Once identified, this empirical model can be employed, with no need of additional FE computations, resulting in faster computations. With the additional hypothesis that the fatigue crack growth rate and direction can be determined from mixed-mode crack tip plasticity (dρ_I/dt and dρ_II/dt), it becomes possible to predict fatigue crack growth under I/II mixed-mode and variable amplitude loading conditions. To compare the predictions of this model with experiments, an asymmetric four point bend test system was setup. It allows applying any mixed-mode loading case from a pure mode I condition to a pure mode II. Initial experimental results showed an increase of the mode I fatigue crack growth rate after the application of a set of mode II overload cycles.     

Avoiding knife-edge countersinks in GLARE through dimpling

Traditional machine countersinking practices create a knife‐edge condition in one or more of the outer aluminium layers in riveted GLARE joints. Press countersinking (dimpling) provides an alternative method of countersinking that prevents the formation of a knife‐edge; however, its application and potential benefits to fatigue performance in GLARE are not known. This paper investigates the dimple‐forming process and its application to GLARE, and the resulting benefits in fatigue crack‐initiation life in unfilled rivet holes. Initial results showed that the limited formability of GLARE complicates the dimpling process, but that dimpling shows promise as a method for increasing the crack‐initiation life of riveted GLARE joints.     

Mapping and load response of overload strain fields: Synchrotron X-ray measurements

High energy synchrotron X-ray diffraction measurements have been performed to provide quantitative microscopic guidance for modeling of fatigue crack growth. Specifically we report local strain mapping, along with in situ loading strain response, results on 4140 steel fatigue specimens exhibiting the crack growth retardation “overload effect”. Detailed, 2D, ε_yy-strain field mapping shows that a single overload (OL) cycle creates a compressive strain field extending millimeters above and below the crack plane. The OL strain field structures are shown to persist after the crack tip has grown well beyond the OL position. The specimen exhibiting the maximal crack growth rate retardation following overload exhibits a tensile residual strain region at the crack tip. Strain field results, on in situ tensile loaded specimens, show a striking critical threshold load, F_c, phenomenon in their strain response. At loads below F_c the strain response is dominated by a rapid suppression of the compressive OL feature with modest response at the crack tip. At loads above F_c the strain response at the OL position terminates and the response at the crack tip becomes large. This threshold load response behavior is shown to exhibit lower F_c values, and dramatically enhanced rates of strain change with load as the crack tip propagates farther beyond the OL position. The OL strain feature behind the crack tip also is shown to be suppressed by removing the opposing crack faces via an electron discharge cut passing through the crack tip. Finally unique 2D strain field mapping (imaging) results, through the depth of the specimen, of the fatigue crack front and the OL feature in the wake are also presented.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.