Residual Stresses and Stress Intensity Factor Calculations in T-Welded Joints

In welded joint, the residual stresses effect can be considered using the residual stress intensity factor (K _res). In this study, K _res is calculated using the analytic weight function method (WFM) and the polynomial distribution of residual stresses (σ _res). The different residual stress distributions have been used analytically. It is to be emphasized that the current approach is little investigated. This is because the weight function has already been developed to calculate K for a crack that had already existed, and hence to calculate the stress distribution and stress intensity factor over the crack face. Therefore, the current approach calculates K _res with σ _res consideration for the crack which initiates and propagates until failure. The validity to use the proposed weight function has been shown. The results of K _res have been compared with those obtained from FEM.     

Multiscale fatigue crack growth modelling for welded stiffened panels

The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, K_I, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, K_tot, is derived by a part due to the applied load, K_appl, and by a part due to welding residual stresses, K_res. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.     

Limited weld residual stress measurements in fatigue crack propagation: Part II. FEM-based fatigue crack propagation with complete residual stress fields

Using a limited set of residual stress measurements acquired by neutron diffraction and an equilibrium‐based, weighted least square algorithm to reconstruct the complete residual stress tensor field from the measured residual stress data, the effect of weld residual stress on fatigue crack propagation is investigated for 2024‐T351 aluminium alloy plate joined by friction stir welding. Through incorporation of the least squares, complete equilibrated residual stress field into a finite element model of the Friction Stir Weld (FSW) region, progressive crack growth along a direction perpendicular to the welding line is simulated as part of the analysis. Both the residual stress redistribution and the stress intensity factor due to the residual stress field, K_res, are calculated during the crack extension process. Results show that (a) incorporation of the complete, self‐equilibrated residual stress field into a finite element (FE) model of the specimen provides a robust, hybrid approach for assessing the importance of residual stress on fatigue crack propagation, (b) the calculated stress‐intensity factor due to the residual stress field, K_res, has the same trend as measured experimentally by the ‘cut‐compliance method’ and (c) the da/dN results are readily explained with reference to the effect of the residual stress field on the applied stress intensity factor.     

Stress-intensity factors for circular hollow section V-joints with a rack-plate chord

This study investigates the fatigue crack‐driving force, measured by the linear‐elastic stress‐intensity factors (SIFs), for a surface crack at the root of the welds in a thick‐walled, circular hollow section (CHS) V‐shape joint, typically installed in modern offshore jack‐up platforms. The primary (chord) member of the V‐joint consists of two half CHSs welded to both sides of a thick rack plate, while the secondary (brace) member adopts thick‐walled CHSs. The surface‐breaking crack considered in this study locates at the interface between the rack plate and the weld metal joining the half CHS, and represents an initial flaw introduced by lack of penetration in the welding procedure. The finite‐element model incorporates a very detailed, local crack‐front mesh in a global continuous mesh through a mesh‐tying procedure, which ensures displacement continuity between the independent master surface and the dependent slave surface. A simple plate model verifies the mesh‐tying procedure in computing the linear‐elastic stress‐intensity factors for two remote loading conditions. The computation of the stress‐intensity factors employs a linear‐elastic interaction integral approach. The comparison of the computed SIF values with a previous experimental measurement for a CHS T‐joint verifies the accuracy and feasibility of the interaction integral approach in computing SIF values for surface cracks in welded tubular connections. Subsequent numerical analysis on the gapped V‐joints examines the mixed‐mode SIF values for different loading conditions and includes an array of practical joint geometric parameters and crack sizes. The nondimensional mode I stress‐intensity factors generally increases with the following variations in the joint geometric parameters: an increase in the chord radius to the wall thickness ratio (γ=d₀/2t₀) , an increase in the brace diameter to the chord diameter ratio (β=d₁/d₀) , a decrease in the crack depth ratio (a/t) or an increase in the crack length c. The current study identifies a practical group of V‐joints that requires detailed treatment in the fatigue assessment procedure. These V‐joints adopt a large β ratio and demonstrate high mode‐mixity angles [ψ= tan^?1(K_II/K_I)] with correspondingly high mode I and mode II stress‐intensity factors.     

Residual stress induced crack tip constraint

This paper studies the effect of welding residual stresses on the near tip stress field in single edge notched bending and tensile specimens. A combined effect of mechanical stresses by the applied load and residual stress on the crack tip constraint is analyzed. Three initial residual stress distributions were considered. It has been shown that the crack tip stress field is strongly influenced by the residual stresses and a new parameter, R, is proposed to characterize the residual stress induced crack tip constraint. The results therefore suggest a three-parameter approach (CTOD, Q and R) to characterize the crack tip stress field in the presence of residual stress where CTOD sets the size scale over which large stresses and large strains develop, and the geometry constraint parameter Q and the new residual stress induced constraint parameter R control the actual crack tip constraint level. For the cases analyzed, R is in general positive, which indicates that residual stress can enhance the crack tip constraint. However, the results also indicate that the R decreases towards zero and the effect of residual stress on crack tip constraint can be neglected when a full plastic condition is approached in the specimen.     

The Bauschinger effect’s influence on the SIFs of multiple longitudinal coplanar cracks in autofrettaged pressurized cylinders

The influence of the Bauschinger effect (BE) on the three-dimensional, Mode I, stress intensity factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The SIFs for both “realistic” - Bauschinger effect dependent autofrettage (BEDA) and “ideal” - Bauschinger effect independent autofrettage (BEIA) are obtained and compared. The 3D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. The Bauschinger effect (BE) is found to significantly lower the beneficial stress intensity factor due to autofrettage, K_IA, by up to 52%, as compared to the “ideal” autofrettage case. The reduction in K_IA varies along the crack front with the maximum determined by the crack ellipticity, crack depth and crack separation distance. The detrimental influence of the BE increases as the crack density decreases and as crack depth decreases. For a partially autofrettaged cylinder, the influence of the BE is considerably reduced as the level of overstrain becomes smaller. Furthermore, the results indicate that in certain situations crack density and crack ellipticity have opposing effects on the autofrettage SIF.     

Analytical and Numerical Solution of the Stress Field and the Dynamic Stress Intensity Factors in a Cracked Plate under Sinusoidal Loading

A cracked plate subjected to a sinusoidal loading perpendicular to its plane is considered, and the analytical solution of the dynamic vibration behavior of a plate, which allowed the determination of the stress field near the crack tip, is developed. A mixed mode of loading near the crack tip has been established and described with dynamic stress intensity factors K _I (z,t) and K _II (z,t) associated with modes I and II crack openings, respectively. To validate the analytical results, a finite element analysis (FEA) of a 1 × 1 m square plate with a thickness of 1 cm, having a middle crack of 10 cm in length, is made. The results have shown significant agreement between analytical and FEA findings.     

Fatigue crack propagation simulation in an aircraft engine fan blade attachment

This paper discusses the computation of three-dimensional fatigue crack growth rates in a typical military aircraft engine fan blade attachment under centrifugal and aerodynamic loads. The three-dimensional crack growth simulations utilize FRANC3D, a state-of-the-art crack propagation software developed at Cornell University, which uses boundary elements and linear elastic fracture mechanics. With an existing three-dimensional finite element contact stress analysis with a prescribed coefficient of friction (COF) along the contact surface, the displacements and stress intensity factors are calculated on the crack leading edge to yield crack propagation trajectories and growth rates. Due to complex geometry of the fan blade attachment and loading conditions, all three-fracture modes are considered and the associated stress intensity factors (SIF) are calculated using the Crack Opening Displacement (COD) approach. Crack propagation trajectories under mixed-mode conditions are obtained using the planar and maximum tangential stress crack-extension criteria. The fatigue crack in the blade attachment is subjected to an over speed mission cycle that includes high cycle frequencies (i.e., spectrum load) and the crack growth rate is predicted utilizing the Forman–Newman–de Koning (FNK) model. Scanning Electron Microscope (SEM) images of a cracked component from an engine ASMET (Accelerated Simulated Mission Endurance Test) are used to evaluate and compare the simulation results. The calculated SIF's from the simulations indicate a strong Mode-I (K_I) and Mode-III (K_III) interaction at the edge of contact (EOC). However, on the free surface it is primarily a crack opening (K_I) condition only. The crack growth rates are determined using the planar extension criterion which correlates better with the test data than the maximum tangential stress extension criteria.     

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.     

Analysis of fatigue crack growth behavior of SS 316(N) welds using the unified approach

Fatigue crack growth (FCG) behavior of SS 316(N) weld has been evaluated at different R‐ratios at room temperature and compared with that of the base metal. The FCG resistance of weld is better than that of the base material and is due to the residual stresses developed during the welding. The data were analyzed using the unified approach that considers the two‐parametric (ΔK and K_max) nature of fatigue. The R‐ratio effects in both the base and weld metals are accounted for without invoking the extrinsic parameters, such as plasticity‐induced crack closure. Since the residual stresses are of the monotonic type, they affect the crack growth via the K_max‐parameter. The crack growth trajectory plots were developed, and they show how the two crack tip driving forces, ΔK and K_max, change to overcome the FCG resistance of the weld in relation to that of the base metal. The results also show that the effects from the compressive residual stresses are more dominant at low R‐values and occur via the K_max parameter.     

A Study of X-Ray analysis of fatigue fracture surface

An X-ray analysis was made of the fatigue fracture surface of SM50A steel. The residual stress and the half-value breadth of the diffraction intensity curve were examined on and under the fracture surface. An analytical study was also made of the residual stress and strain near the fatigue crack surface by using the finite element method. Emphasis was on finding the correlation between the residual stress or the half-value breadth and the applied stress intensity factor of K_max or 2K. It was found that both the residual stress and the halfvalue breadth distributions under the fracture surface were useful for the estimation of the monotonie plastic zone size or K_max.The correlation of the absolute value of the residual stress with K_max or 2K, however, was not clear in the present study. From the analytical study, it was found that the effect of the surface contact due to fatigue crack closure on the residual stress was less important and limited to the thin layer near the crack surface.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

FATIGUE CRACK GROWTH AND CLOSURE BEHAVIOUR THROUGH A COMPRESSIVE RESIDUAL STRESS FIELD

Behaviour of fatigue crack growth and closure through a compressive residual stress field is investigated by performing fatigue crack growth tests on welded SEN specimens of a structural steel (JIS SM50A). Depending on the type of the initial residual stress in the region of crack growth, the growth and closure of the crack show different behaviour. In particular, in the transition region from a compressive residual stress field to a tensile residual stress field, the fatigue crack growth rates cannot be described by the effective stress intensity factor range ΔK_eff, based on the measured crack opening stress intensity factor K_op. Also it is found that the R'-method using the data of da/dN vs ΔK for residual stress-free specimens, with the effective stress ratio R'[=(K_max+K_r)/(K_min+K_r)], gives non-conservative predictions of the growth rates in the transition region. Observations of crack closure behaviour in this study indicates that partial opening of the crack occurs and this plays an important role in crack growth through a compressive residual stress field. Based on the concept of a partial opening point (defined and measured in this work), fatigue crack growth behaviour can be better explained.     

3-D stress intensity factors for arrays of inner radial lunular or crescentic cracks in thin and thick spherical pressure vessels

Some spherical pressure vessels are manufactured from a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels, one needs to evaluate the stress intensity factors (SIF) distribution along the fronts of these cracks. In a recent paper by the authors, mode I SIF distributions for a wide range of lunular and crescentic internal, surface, radial cracks were evaluated for a typical spherical pressure vessel of an outer to inner radii ratio of η = R_o/R_i = 1.1. The present analysis is aimed to determine the influence of the spherical vessel geometry in terms of its outer to inner radii ratio η = R_o/R_i on the prevailing SIFs. Mode I SIF distributions for a wide range of lunular and crescentic crack array configurations are evaluated. The 3-D analysis is performed by means of the FE method, employing singular elements along the crack front, for five geometries representing thin, moderately thick, and thick spherical pressure vessels with outer to inner radius ratios of η = R_o/R_i = 1.01, 1.05, 1.1, 1.7, and 2.0. SIFs are evaluated for arrays containing n = 1–20 cracks; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.95; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are affected considerably by the geometry of the spherical pressure vessel-η, and by the following parameters: the number of cracks in the array-n, the depth of the cracks-a/t, and their ellipticity-a/c.     

Effect of sudden load decrease on the fatigue crack growth in cold drawn prestressing steel

This paper analyzes the overload retardation effect (ORE) on the fatigue crack growth (FCG) of cold drawn prestressing steel when different loading sequences are used. The ORE is more intense for elevated load decrease or for low initial stress intensity factor (SIF) range ΔK₀. A transient stage can be observed in the Paris curve (da/dN–ΔK) when the K_maxΔK value suddenly decreases, associated with the ORE and with the evolution of the plastic zone and compressive residual stresses near the crack tip. In tests with K_max decrease, a small zone appears related to FCG initiation, with a fatigue fractography resembling the tearing topography surface (TTS) mode, and associated with a decrease of crack tip opening displacement (CTOD).     

Weight function for a single edge cracked geometry with clamped ends

A single edge cracked geometry with clamped ends is well suited for fracture toughness and fatigue crack growth testing of composites and thin materials. Analysis of fiber bridging phenomenon in the composites and determination of stress intensity factors due to non-uniform stress distributions such as residual and thermal stresses generally require the use of a weight function. This paper describes the development and verification of a weight function for the single edge cracked geometry with clamped ends. Finite element analyses were conducted to determine the stress intensity factors (K) and crack opening displacements (COD) due to different types of stress distributions. The weight function was developed using the K and COD solution for a constant stress distribution. K and COD predicted using this weight function correlated well with the finite element results for non-uniform crack surface stress distributions.     

Application of a variable order singular element to dynamic fracture mechanics

The dynamic response characteristics of a variable order singular element proposed by Akin (1976) have been examined in application to several stationary crack/dynamic boundary condition problems in the work by Thesken and Gudmundson (1985). Presented here are the numerical solutions for the benchmark problem of that study, an infinite strip/semi-infinite crack problem having a closed analytical solution form given by Nilsson (1973). Time integration of the problem was conducted explicitly using the central difference scheme. The dynamic stress intensity factor K_I(t) was computed using two different approaches: a local approach using the COD relation to K _I and a global approach employing the dynamic J-integral. The effects of mesh refinement and time step duration were examined with a series of refined grids and proportionally decreasing time steps. Results are presented in the form of non-dimensional K _J(t) histories and are compared to the existing analytical solution.     

Examination of fatigue crack driving force parameter

Most of the previous parameters that utilized as a crack driving force were established in modifying the parameter K_op in Elber's effective SIF range ΔK_eff(=K_max?K_op). However, the parameters that replaced the traditional parameter K_op were based on different measurements or theoretical calculations, so it is difficult to distinguish their differences. This paper focuses on the physical meaning of compliance changes caused by plastic deformation at the crack tip; the tests were carried out under different amplitude loading for structural steel. Based on these test results, differences of several parameter ΔK_eff in literature are analysed and an improved two‐parameter driving force ΔK_drive(=(K_max)ⁿ(ΔK^∧)^1‐n) has been proposed. Experimental data for several different types of materials taken from literature were used in the analyses. Presented results indicate that the ΔK_drive parameter was equally effective or better than ΔK(=K_max?K_min), ΔK_eff(=K_max?K_op) and ΔK*(= (K_max)^α(ΔK⁺)^1?α) in correlating and predicting the R‐ratio effects on fatigue crack growth rate.     

Effects of CTE-induced residual stresses around hard alpha particles on fatigue crack growth in Ti–6Al–4V

The presence of hard alpha (HA) anomalies in titanium alloys represents a significant potential degradation to gas turbine component performance. Although HA defects in titanium alloys are rare, when they are present, they can crack and ultimately result in failure. In static fracture and fatigue test specimens, embedded HA defects had significantly higher fracture strengths than anticipated. The objective of this work was to determine if residual stresses caused by thermal expansion mismatch during material fabrication were the cause of the observed behaviour. The residual stress fields in and around surface and embedded HA particles in Ti–6Al–4V (Ti–6–4) were determined using an elasticity solution and measured coefficient of thermal expansion (CTE) data. The calculated stress distributions serve as the foundation for comparisons of the local stress and the fracture strength, the stress intensity factor K and the crack growth threshold ΔK_th, with the experimentally determined fatigue lives. The analytical results indicated that CTE‐induced residual stress around HA particles can contribute to the fatigue strength of Ti–6–4 by delaying microcracking of HA anomalies and reducing the driving force (effective ΔK) of the fatigue crack. Based on the analysis results, the differences between the surface and subsurface results as well as the difference between predicted and measured fatigue lives could be largely attributed to the residual stress effects caused by the mismatch of the particle and matrix properties.