Predicting corner crack fatigue propagation from cold worked holes

We predict the fatigue propagation of corner cracks from cold worked holes using three dimensional finite element models. The models account for the through thickness variation in residual stress left after cold working. The predictions are compared to experimental results in aluminum 2024-T351 and 7075-T651. The models show the evolution of P-shaped crack fronts similar to those observed in experiments. Predictions based on the initial residual stress field left after cold working were nonconservative, predicting either slower than experimental crack growth or crack growth that arrests. Predictions based on an estimate of the stable relaxed residual stress field near the hole were conservative, and predicted 5-10 times greater life than the current Department of Defense reduced initial flaw size approach.     

Numerical predictions and experimental measurements of residual stresses in fatigue crack growth specimens

Controlling macro residual stress fields in a material while preserving a desired microstructure is often a challenging proposition. Processing techniques which induce or reduce residual stresses often also alter microstructural characteristics of the material through thermo-mechanical processes. A novel mechanical technique able to generate controlled residual stresses was developed. The method is based on a pin compression approach, and was used to produce well-controlled magnitudes and distributions of residual stresses in rectangular coupons and compact tension specimens typically used in fatigue crack growth testing. Residual stresses created through this method were first computationally modeled with finite element analysis, and then experimentally reproduced with various levels of pin compression. The magnitudes and distributions of residual stresses in experimental specimens were independently assessed with fracture mechanics methods and good correspondence was found between residual stresses produced using the pin compression and processing techniques. Fatigue crack growth data generated from specimens with low residual stresses, high residual stresses resulting from processing, and high residual stresses introduced through the new pin compression technique were compared and validated. The developed method is proposed to facilitate the acquisition and analysis of fatigue crack growth data generated in residual stresses, validate residual stress corrective models, and verify fatigue crack growth simulations and life predictions in the presence of residual stresses.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

Evolution of residual stresses with fatigue loading and subsequent crack growth in a welded aluminium alloy middle tension specimen

Neutron diffraction has been used to measure the evolution of the residual stresses in a VPPA welded Al-2024 alloy middle tension (M(T)) specimen with fatigue loading and subsequent crack growth. The measurements were carried out on the diffractometer ENGIN-X, a time-of-flight instrument, at the ISIS Pulsed Neutron Source. Fatigue crack growth was performed in situ and strain measurements averaged through the thickness of the specimen were made along two orthogonal directions as the crack grew, allowing the stresses in the specimen to be calculated assuming plane stress. 2D finite element simulation of the evolution of the initial residual stress field with crack growth, using an elastic model produced predictions that were in reasonable agreement with the experimental results. The results further indicate that some re-distribution of the residual stress field occurred due to the crack tip plasticity associated with the fatigue loading.     

Effect of impact damage on fatigue performance of structures reinforced with GLARE bonded crack retarders

Fibre-Metal Laminates (FML) such as GLARE are of interest as bonded crack retarders (BCR) to improve the fatigue performance of aircraft structures. The degradation of the performance of the crack retarder in service if subjected to damage is a critical factor in designing with this concept. Bonded assemblies of an aluminium alloy substrate reinforced with a GLARE strap were prepared, and were subjected to low velocity impact damage onto the GLARE, with impact energies ranging from 10 to 60 J. The thermal residual stresses developed during the bonding process of the GLARE to the aluminium were determined using neutron diffraction, and the change in the thermal residual stresses owing to impact damage onto the GLARE was evaluated. Pre- and post-impact fatigue performance of the BCR assemblies has been investigated. The results show that the BCR provides an improvement in fatigue life, but the reduction is impaired following impact damage. The results show that monitoring of impact damage will be critical in the damage tolerance assurance for aerospace structures containing bonded crack retarders.     

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered.     

Fatigue analysis of post-weld fatigue improvement treatments using a strain-based fracture mechanics model

Untreated and post-weld treated (peened) fatigue details common to welded steel structures are analyzed herein using a strain-based fracture mechanics model. The model is first described and then evaluated by comparison with data from several test-based studies as well as analytical results obtained using two linear elastic fracture mechanics (LEFM) models. The strain-based model is then used to perform several parametric studies. Based on the results of these studies, loading conditions are identified for which ignoring the nonlinear material behaviour may lead to overestimation of the post-weld treatment benefit measured as in increase in the fatigue life of the weld.     

Predicting fracture and fatigue crack growth properties using tensile properties

The safe-life assessment of components requires information such as the plane stress (K_c), plane strain (K_Ic), part-through fracture toughness (K_Ie), and the fatigue crack growth rate properties. A proposed parametric/theoretical approach, based on an extended Griffith theory is used to derive fracture toughness properties and generate fatigue crack growth rate data for a range of alloys. The simplicity of the concept is based on the use of basic, and in most cases available, uniaxial stress-strain material properties data to derive material fracture toughness values. However since the methodology is in part based on an empirical relationship a wide ranging validation with actual data is required. This paper uses steel, aluminum and titanium based alloys from a pedigree database to quantify material properties sensitivity to the predictions for K_Ic and K_c and the subsequent estimation of ΔK_th threshold and the Paris constants, C and n values. A sensitivity analysis using experimental scatter bounds show the range of da/dN predictions can be achieved. It is found K_Ic/ΔK_th ratios designated as α has a range of 5-25 irrespective of tensile ductility, ε_f, and is insensitive to it. The value of ΔK_th for all the alloys considered was found to be proportional to the final elongation, ε_f, and an empirical relationship describing ΔK_th as a function of ε_f was established. Furthermore it is suggested that, with the knowledge of appropriate tensile properties and the estimated range of K_Ic/ΔK_th ratios for the different alloys applying this method could be an appropriate tool that can be used to conservatively predict fracture and fatigue in similar alloy categories. Thus helping to reduce costs and optimize the number of experimental tests needed for alloy characterizations.     

A two parameter driving force for fatigue crack growth analysis

A model for fatigue crack growth (FCG) analysis based on the elastic–plastic crack tip stress–strain history was proposed. The fatigue crack growth was predicted by simulating the stress–strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiation in the crack tip region. The model was developed to predict the effect of the mean stress including the influence of the applied compressive stress. A fatigue crack growth expression was derived using both the plane strain and plane stress state assumption. It was found that the FCG was controlled by a two parameter driving force in the form of: . The driving force was derived on the basis of the local stresses and strains at the crack tip using the Smith–Watson–Topper (SWT) fatigue damage parameter: D=σ_maxΔε/2.The effect of the internal (residual) stress induced by the reversed cyclic plasticity was accounted for the subsequent analysis. Experimental fatigue crack growth data sets for two aluminum alloys (7075-T6 and 2024-T351) and one steel alloy (4340) were used for the verification of the model.     

Analytical and numerical modelling of plasticity-induced crack closure in cold-expanded holes

The aim of this research was the development of an analytical model for plasticity-induced fatigue crack closure for cold expanded holes. This paper extends Nowell's plane stress model of plasticity-induced crack closure for a plate with a circular hole and two radial symmetric cracks. The possibility of existence of an initial residual stress field is also taken into account. This model has potential to be applied to other cracked geometries and arbitrary residual stress fields, although the paper is focused on the study of cold-expanded holes. Hole cold-expansion is widely used in aircraft industry, for improving the fatigue performance of rivet holes by delaying fatigue crack propagation. This paper shows that the residual stress field due to cold-expansion has a strong influence on the closure behaviour and therefore on fatigue crack propagation. The analytical model developed, was compared with finite element analyses of plasticity-induced crack closure with and without residual stresses. Finally, the model was used to predict fatigue lives for some experiments recently reported in the literature for fatigue crack propagation from cold-expanded holes. Predicted fatigue lives correlate well with experimental data.     

Proposed fatigue damage measurement parameter for shot-peened carbon steel based on fatigue crack growth behavior

A new technique for evaluating fatigue-damage accumulation in shot-peened (SP) carbon steel based on variations in residual stress is proposed. Using findings from previous studies, a fatigue damage parameter for a material treated with SP based on the change in induced compressive residual stress (CRS) is examined. A plastic replica method with the focused ion beam (FIB) technique is used to assess the relationship between the residual stress state and the fatigue crack growth (FCG) behavior of SP specimens over the fatigue lifespan. It is found that the residual stress relaxation phenomenon can be used as an effective parameter for determining the fatigue damage growth, provided the residual stress relaxation rate of each mechanical load and the critical threshold relaxation boundary of each material is known.     

On the hysteretic nature of variable-amplitude fatigue crack growth

Local Stress–Strain (LSS) approach as applied in notch fatigue analysis is extended to the fatigue crack in order to simulate the effect of variable-amplitude loading on near-tip stress and strain. Simulated near-tip stress–strain response appears to explain load sequence sensitivity of near-threshold fatigue crack growth. This observation is supported by fractographic evidence of near-threshold variable-amplitude fatigue crack in an Al–Cu alloy under closure-free conditions.     

The effect of residual stresses arising from laser shock peening on fatigue crack growth

Residual stresses have in the past been introduced to manipulate growth rates and shapes of cracks under cyclic loads. Previously, the effectiveness of shot peening in retarding the rate of fatigue crack growth was experimentally studied. It was shown that the compressive residual stresses arising from the shot peening process can affect the rate of crack growth. Laser shock peening can produce a deeper compressive stress field near the surface than shot peening. This advantage makes this technique desirable for the manipulation of crack growth rates. This paper describes an experimental program that was carried out to establish this effect in which steel specimens were partially laser peened and subsequently subjected to cyclic loading to grow fatigue cracks. The residual stress fields generated by the laser shock peening process were measured using the neutron diffraction technique. A state of compressive stress was found near the surface and tensile stresses were measured in the mid-thickness of the specimens. Growth rates of the cracks were observed to be more affected by the tensile core than by the compressive surface stresses.     

Analysis of cold expanded fastener holes subjected to short time creep: Finite element modelling and fatigue tests

The beneficial effects of cold expansion have been well documented in previous studies, yet the performance of cold expanded plates exposed to elevated temperatures is an area of technical interest. In this research, finite element (FE) simulations along with experimental fatigue tests have been carried out to investigate the effect of exposure to elevated temperature on residual stress distribution and subsequent fatigue life of cold expanded fastener holes. According to the obtained results, creep stress relaxation occurs due to exposure to 120 °C for 50 h. FE results demonstrate a non-uniform residual stress relaxation regime through the plate thickness around the cold expanded hole and the fatigue test results show that the subsequent fatigue lives have significantly decreased.     

A three-dimensional (3D) numerical study of fatigue crack growth using remeshing techniques

Numerical analyses based on the finite element (FE) method and remeshing techniques have been employed in order to develop a damage tolerance approach to be used for the design of aeroengines shaft components. Preliminary experimental tests have permitted the calculation of fatigue crack growth parameters for the high strength alloy steel adopted in this research. Then, a robust numerical study have been carried out to understand the influence of various factors (such as: crack shape, crack closure) on non-planar crack evolution in solid and hollow shafts under mixed-mode loading. The FE analyses have displayed a satisfactory agreement compared to experimental data on compact specimens (CT) and solid shafts.     

The effect of hold-time on fatigue crack growth behaviors of WASPALOY alloy at elevated temperature

The effect of hold-time on fatigue crack growth behaviors of WASPALOY alloy was investigated. It was found that the role of hold-time depends on the competition between the harmful environmental effect and the beneficial effect of creep. If temperature is not higher than 705 °C, fatigue crack growth rate of WASPALOY alloy increases with hold-time. On the contrary, hold-time plays a beneficial role on steady state fatigue crack growth of WASPALOY alloy at 760 °C and lower stress intensity factor. The beneficial effect of hold-time was attributed to the creep caused stress relaxation during the hold-time. However, accumulated creep damages cause to cavity nucleation and growth at the grain boundaries, and then accelerate fatigue crack growth. Hold-time plays a harmful role during the final stage of fatigue crack growth.     

Effect of residual stresses on ductile crack growth resistance

It is well known that residual stresses influence the ductile fracture behaviour. In this paper, a numerical study was performed to assess the effect of residual stresses on ductile crack growth resistance of a typical pipeline steel. A modified boundary layer model was employed for the analysis under plane strain, Mode I loading condition. The residual stress fields were introduced into the finite element model by the eigenstrain method. A sharp crack was embedded in the center of the weld region. The complete Gurson model has been applied to simulate the ductile fracture by microvoid nucleation, growth and coalescence. Results show that tensile residual stresses can significantly reduce the crack growth resistance when the crack growth is small compared with the length scale of the tensile residual stress field. With the crack growth, the effect of residual stresses on the crack growth resistance tends to diminish. The effect of residual stress on ductile crack growth resistance seems independent of the size of geometrically similar welds. When normalized by the weld zone size, the ductile crack growth resistance collapses into one curve, which can be used to assess the structural integrity and evaluate the effect of residual stresses. It has also been found that the effect of residual stresses on crack growth resistance depends on the initial void volume fraction f₀, hardening exponent n and T-stress.     

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.     

Prediction of shape change of corner crack by fatigue crack growth circles

As a fatigue crack grows, its shape changes. Conventional method for predicting the shape change typically requires the computation of several hundred increments to get accurate results. In this paper, a new finite element simulation technique that uses fatigue crack growth circles is developed. Since the circles are perpendicular to the new crack front as well as to the current crack front, they can represent the real path of the fatigue crack well and yield more accurate results. The new technique is validated by applying it to the case of a quarter-elliptical corner crack in a plate with an open hole subjected to tension loading. The effect of the Paris–Erdogan exponent is also investigated.     

Singular and non-singular approaches for predicting fatigue crack growth behavior

In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed: mechanisms acting before, at or after the crack tip. After reviewing the crack closure idea, which is based on what happens behind the crack tip, quantitative models are proposed to predict the effects at the crack tip due to crack bifurcation. To predict the behavior ahead of the crack tip, a damage accumulation model is proposed. In this model, fatigue cracking is assumed caused by the sequential failure of volume elements or tiny εN specimens in front of the crack tip, calculated by damage accumulation concepts. The crack is treated as a sharp notch with a small, but not zero radius, avoiding the physically unrealistic singularity at its tip. The crack stress concentration factor and a strain concentration rule are used to calculate the notch root strain and to shift the origin of a modified HRR field, resulting in a non-singular model of the strain distribution ahead of the crack tip. In this way, the damage caused by each load cycle, including the effects of residual stresses, can be calculated at each element ahead of the crack tip using the correct hysteresis loops caused by the loading. The proposed approach is experimentally validated and extended to predict fatigue crack growth under variable amplitude loading, assuming that the width of the volume element broken at each cycle is equal to the region ahead of the crack tip that suffers damage beyond its critical value. The reasonable predictions of the measured fatigue crack growth behavior in steel specimens under service loads corroborate this simple and clear way to correlate da/dN and εN properties.