The residual stress intensity factors for cold‐worked cracked holes: a technical note

Cold‐working of riveted holes reduces the stress intensity factor associated with cracks that may develop at the hole boundary, by creating a compressive residual stress field. The residual stress field is determined using the finite‐element method and the reduction of the stress intensity factor for different values of the interference is evaluated with the weight function method, in the case of an infinite plate made from an elastic–perfectly plastic material, and having a hole with two symmetrical cracks. Once the weight function of the structure is known, further calculation of the stress intensity factors for different loadings such as a remote uniform stress, or a point load that simulates the action of the rivet can be performed without difficulty.     

Dual boundary element method modelling of aircraft structural joints with multiple site damage

The computation of crack growth from a bolt or rivet hole in a structural joint practically requires that the geometry be approximated to some degree. In this paper a simplified quasi-2D stress analysis method, using the boundary element method is presented, where the load transfer rate and the contact stresses at the hole edge for the full 3D geometry are fairly well approximated. Coupled with a dual boundary element formulation for the crack propagation problem, this model is used to evaluate stress intensity factors for through cracks emanating from holes in several double shear lap joint configurations. As the calculated stress intensity factors compare well with experimental data, this procedure is considered to approximate satisfactorily the load transfer rate and the contact stresses at the hole edge of the full 3D geometry, when secondary bending is not a factor.     

A weight function method for mixed modes hole‐edge cracks

A weight function approach is proposed to calculate the stress intensity factor and crack opening displacement for cracks emanating from a circular hole in an infinite sheet subjected to mixed modes load. The weight function for a pure mode II hole‐edge crack is given in this paper. The stress intensity factors for a mixed modes hole‐edge crack are obtained by using the present mode II weight function and existing mode I Green (weight) function for a hole‐edge crack. Without complex derivation, the weight functions for a single hole‐edge crack and a centre crack in infinite sheets are used to study 2 unequal‐length hole‐edge cracks. The stress intensity factor and crack opening displacement obtained from the present weight function method are compared well with available results from literature and finite element analysis. Compared with the alternative methods, the present weight function approach is simple, accurate, efficient, and versatile in calculating the stress intensity factor and crack opening displacement.     

Weight function,stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks

Periodic collinear edge hole cracks and arbitrary small cracks emanating from collinear holes, which are two typical multiple site damages occurred in the aircraft structures, are studied by using the weigh function method. An explicit closed form weight function for periodic edge hole cracks in an infinite sheet is obtained and further used to calculate the stress intensity factor and crack opening displacement for various loading cases. Compared to finite element method, the present weight function is accurate and highly efficient. The interactions of the holes and cracks on the stress intensity factor and crack opening displacement are quantitatively determined by using the present weight function. An approximate weight function method is also proposed for arbitrary small cracks emanating from multiple collinear holes. This method is very useful for calculating the stress intensity factor for arbitrary small cracks.     

Finite element method and experimental investigation on the residual stress fields and fatigue performance of cold expansion hole

Cold expansion is an efficient way to improve the fatigue life of an open hole. The residual stress fields of cold expansion holes are vital for key components designing, manufacturing and fatigue properties assessment. In this paper, three finite element models have been established to study the residual stress fields of cold expansion hole, experiments were carried out to measure the residual stress of cold expansion hole and verify simulation results. Three groups of specimens with different cold expansion levels are examined by fatigue test. The fracture surfaces of specimens are observed by scanning electron microscope. The finite element method (FEM) results show, with interference values develop, the maximum values of circumferential residual compressive/tensile stresses increase in “infinite” and “finite” domain, and a higher positive stress values are obtained at the boundary of “finite” domain. The effects of the friction between the mandrel and the hole’s surface and two cold expansion techniques on the distribution of residual stress is local, which only affects the radial residual stress around the maximum value and the circumferential residual stress near the hole’s edge. Crack always initiates near entrance face and the crack propagation speed along transverse direction is faster than that along axial direction.     

Influence of foreign object damage on fatigue crack growth of gas turbine aerofoils under complex loading conditions

Foreign object damage (FOD) has been identified as one of the main life limiting factors for aeroengine blades, with the leading edge of aerofoils particularly susceptible. In this work, a generic edge ‘aerofoil’ geometry was utilized in a study of early fatigue crack growth behaviour due to FOD under low cycle fatigue (LCF), high cycle fatigue (HCF) and combined LCF and HCF loading conditions. Residual stresses due to FOD were analyzed using the finite element method. The longitudinal residual stress component along the crack path was introduced as a nodal temperature distribution, and used in the correction of the stress intensity factor range. The crack growth was monitored using a nanodirect current potential drop (DCPD) system and crack growth rates were correlated with the corrected stress intensity factor considering the residual stresses. The results were discussed with regard to the role of residual stresses in the characterization of fatigue crack growth. Small crack growth behaviour in FODed specimens was revealed only after the residual stresses were taken into account in the calculation of the stress intensity factor, a feature common to LCF, HCF and combined LCF + HCF loading conditions.     

Residual stress/strain evolution due to low‐cycle fatigue by removing local material volume and optical interferometric data

Three experimental methods, based on optical interferometric measurements of deformation response to local material removing, have been implemented for residual stresses determination. Two first techniques are employed to characterize initial residual stress values and their evolution near welded joints of aluminium plates under low‐cycle fatigue. The hole‐drilling method gives high‐accurate dependencies between residual stress components and number of cycles. The second approach comprises cracks modelling by narrow notches to describe residual stress distributions in more wide spatial range near the weld. The results demonstrate residual stress evolution is of complex character and cannot be uniquely qualified as a gradual relaxation. Besides, the secondary hole drilling method is developed and used as a fast and reliable tool to quantify the redistribution of residual strains near cold‐expanded holes due to low‐cycle fatigue. Dependencies of circumferential residual strains along the secondary hole edge versus number of cycles are constructed.     

MACROSCOPIC RESIDUAL STRESS DISTRIBUTION AT A FATIGUE CRACK TIP

Abstract— Residual stress distribution in the vicinity of fatigue cracks was determined experimentally by means of the X-ray method and theoretically calculated by finite element analysis. Both the intensity and the extent of residual stress increase with the increasing stress intensity factor amplitude. There is good agreement between experimental and theoretical results.     

Effect of local cold working on the fatigue life of 7475-T7351 aluminium alloy hole specimens

Different degrees of cold working (ranging from 0% to 5.58%) were applied to the hole of plate specimens of 7475-T7351 aluminium alloy. These specimens were then subjected to cyclic loading. In each test, the crack initiation was detected and subsequently the crack length was monitored, using a video camera system. The experimental results were analysed in order to determine the cold working effect on the fatigue initiation period, on the propagation life and finally on the overall fatigue life. It was found, for example, that the propagation life improvement factor for a degree of cold working of 5.58% is about 43.0 and 4.9 for applied nominal stresses of 191 and 300 MPa, respectively. For the same conditions, the fatigue life improvement factor is about 3.2 and 1.5. A numerical analysis was also performed, using three-dimensional finite element method to establish the stress and strain distributions resulting from the superposition of the cold working process and the fatigue loading. Then, the results were used in connection with the non-cold worked hole data for calculating the cold worked plate initiation period according to the strain-life concept; for determining the propagation life, the weight function technique was applied. The predictions are very close to the experimental results.     

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.     

The effect of residual stress due to interference fit on the fatigue behavior of a fastener hole with edge cracks

The fatigue property of riveted lap joint is greatly related to the riveting-induced residual stress. However, an accurate study of the fatigue property considering the influence of residual stress quantitatively can be very difficult. A 3D interface element based on the virtual crack closure technology (VCCT) was developed to calculate the stress intensity factor (SIF) for through cracks at the hole edge. The riveting process was analyzed prior to the tensile test in the finite element code, so that the residual stress can be taken into account to get the eventual value of SIF. The result shows that, with the presence of fatigue cracks, the initial stress-strain state in the structure would change, especially near the crack tip, where great compressive stress can be found. The eventual residual stress cannot be derived by simply superimposing the riveting-induced residual stress with the crack-induced residual stress. The 3D-VCCT interface element shows strong ability to solve the SIFs. The FE analysis results agree well with the reported models both in the fatigue crack growth rate (FCGR) and in the shape of the crack front. However, when the crack is extremely short, not only the reported models, but also the present numerical model would fail. Besides, unlike Elber's model and Schijve's model, this study shows that the crack opening stress should not be a function of the stress ratio solely, but also with the crack length included.     

Numerical simulation of residual stress relaxation around a cold‐expanded fastener hole under longitudinal cyclic loading using different kinematic hardening models

Cold expansion of fastener holes creates compressive residual stresses around the hole. This well‐known technique improves fatigue life by reducing tensile stress around the holes. However, cyclic loading causes these compressive residual stresses to relax, thus reducing their beneficial effect. Estimation of the fatigue life without considering the residual stress relaxation might lead to inaccurate results. In this research, numerical studies were carried out using 2D finite element (FE) models to determine the initial tangential and radial residual stress distributions generated by cold expansion and their relaxation under cyclic loading. To predict the stress relaxation, four nonlinear kinematic hardening models were applied in simulation of stress/strain path. The results obtained from the FE analysis were compared with available experimental results. A good agreement between the numerical and experimental results was observed.     

Investigation of the stress intensity factor changing on the hole crack subject to laser shock processing

Laser shock processing (LSP) is a new surface modification technology. The effect of the compressive residual stresses generated due to laser shock processing (LSP) on the stress intensity factor (SIF) of a through-the-thickness radial crack at the edge of the circular hole was investigated. The residual stresses around the hole induced by LSP were measured by using X-ray method. The relationship between the SIF and the residual stress was determined on the basis of the weight function theory in fracture mechanics. Crack propagation characteristics for such cracks subjected to the combination of the applied stress and residual stress were discussed. And the results showed that the compressive residual stress could lead to the decrement of the SIF. Moreover, the number of the laser shocks had an important influence on the SIF.     

Fatigue life of cold‐expanded fastener holes with interference‐fit fasteners at short edge margins

The fatigue life of 7075‐T6 aluminium specimens with countersunk fastener holes with cold expansion and interference‐fit fasteners with short edge margins was studied. The study was performed experimentally and through finite element analysis. The experiments measured the total fatigue life and crack growth. The results from the finite element analysis consisted of tangential residual stress profiles, which were combined with applied cyclic stresses for fatigue analysis. The experiments showed that the fatigue life improved with interference‐fit fasteners and cold expansion at all edge margins. The fatigue life also increased with increasing edge margin. The finite element results were used to make fatigue life predictions that corresponded reasonably well with the experimental results.     

An inverse method for evaluating weld residual stresses via fatigue crack growth test data

This paper presents an inverse method for calculating the thermal residual stresses in welded specimens via measured fatigue crack growth rates. Firstly, fracture-mechanics superposition law has been used to extract the stress intensity factor due to residual stress contribution from measured crack growth rate. Secondly, a so-called B matrix has been established by performing finite element analysis. Residual stress distribution is then determined by solving linear algebraic equations relating the B matrix and residual stress intensity factors obtained from crack growth test data. The inverse method has been validated by a well-established residual stress distribution and corresponding stress intensity factor, and then applied to an M(T) sample in 2024-T3 alloy with a longitudinal weld. Agreement with the measured residual stresses is reasonably good and reasons for certain differences between the calculated and measured are discussed.     

Foreign object damage and fatigue crack threshold: Cracking outside shallow indents

Foreign Object Damage (FOD) usually happens when objects are ingested into jet engines powering military or civil aircraft. Under extreme conditions, FOD can lead to severe structural damage. More commonly it produces local impacted sites of the fan and compressor airfoils, lowering fatigue life of these components. FOD is a prime cause for maintenance and repair in aircraft engines. In this paper, a framework for analyzing FOD and its effect on fatigue cracking is established. A finite element analysis is used to identify three relevant regimes of FOD related to the depth of penetration into the substrate, and to determine the residual stresses. Most of the emphasis in this paper focuses on fatigue cracks emerging from shallow indentations, which are generally expected to be of most practical concern. Full three-dimensional finite element solutions are obtained for semi-circular surface cracks emerging from specific locations at the indentation revealing the influence of the residual stress on the stress intensity factor distribution. For shallow indents, a relatively simple dimensionless formula for the relation between the residual stress intensity factor, the crack size, and the indentation width are developed. These results, together with results for the intensity factor variations due to cyclic loading, have been used to address the question: To what extent do the residual stresses caused by the FOD reduce the critical crack size associated with threshold fatigue crack growth? Formulas for the critical crack size are obtained. Specific results are presented for the blade alloy, Ti-6Al-4V, revealing that FOD can reduce the critical crack size by as much as 60%.     

Investigation of residual stress relaxation under cyclic load

Compressive residual stresses induced by mechanical surface treatment such as shot peening, autofretage, hole expansion, laser shock peening, and low-plasticity burnishing can be highly beneficial to fatigue resistance. Cyclic relaxation of compressive residual stress, however, reduces the benefit. An analytical model is proposed for estimation of residual stress relaxation. Parameters considered by the model include the magnitude and distribution of the residual stress, the degree of cold working required, the applied alternating and mean stresses, and the number of applied loading cycles. An elasto–plastic finite element model was used to demonstrate the model.     

自增强厚壁圆筒轴向内表面裂纹的应力强度因子

本文研究用有限元通用程序计算具有残余应力的自增强厚壁圆筒内半椭圆形表面裂纹的应力强度因子的方法。所考虑的应力强度因子被分为相应于工作内压及残余应力两部分，分别用三维有限元通用程序算得的裂纹前沿单元节点的垂直位移直接计算，对后者又运用了＂叠加原理＂。结果表明，残余应力的存在能有效地降低内裂纹的应力强度因子值，自增强度高者这一作用亦显著，残余应力引起的应力强度因子对裂织数目不敏感。     

Stress intensity factors for cracks emanating from two-dimensional semicircular notches using the composition of SIF weight functions

This paper presents stress intensity factor (SIF) solutions for edge cracks emanating from semicircular notches using the composition of SIF weight functions. The method isolates and combines the geometrical influences defined by constitutive SIF weight functions to yield SIFs for semicircular notches in finite thickness bodies. Finite element analysis was employed to obtain the required stress distributions and to generate reference constitutive SIFs. Problems encountered with curve fitting high gradient stress distributions were addressed and a robust mathematical solution for these was formulated. The new SIF solutions were verified by comparison with published solutions showing a high degree of accuracy and reliability. The composition model was demonstrated to allow rapid generation of SIFs for mode I cracks in complex geometries where the relevant simple constitutive solutions are available. These new solutions expressed as SIF weight functions allow interpolation between the geometrical parameters for which they are valid and also to include the effect of complex stress distributions such as those due to residual stresses.