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The commercial finite element software is usually used to analyze the failure modes of metal structures. In this work, we present a generalized ductile phase field model to solve the fracture problems of three-dimensional metal structures. This model can be easily implemented in Abaqus software. The isotropic hardening model and exponential hardening law were used to describe plastic behavior of metals. The different element types were introduced to mesh the structures conveniently. The ductile phase field governing equations were given and solved by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton monolithic algorithm. Moreover, an efficient and accurate adaptive analytic method of the third-order real symmetric matrix was proposed to implement the tension–compression decomposition. Some typical specimens commonly used in engineering were designed and manufactured. The corresponding static and fatigue tests were carried out, and the simulation results were compared with the experimental ones. The proposed model can predict the crack initiation and propagation of arbitrary three-dimensional metal structures under tensile, shear, torsional and fatigue loading.

Since aluminum alloys have the low melting point and high thermal conductivity, friction stir weld (FSW)has been successfully used in the aerospace industry as an alternative to traditional welding methods. In the service of FSWed structures, the residual stress and external load would result in a secondary deformation and residual stress redistribution. Therefore, it is necessary to investigate the effect of residual stress on the FSWed fatigue responses. This paper studied the fatigue crack growth behavior of 2024-T3 and 7075-T6 homogeneous and dissimilar FSWed joints. The finite element model was built to calculate the fatigue crack growth rate of FSWed specimen, and the results were compared with the experiment results. It was demonstrated that residual stress significantly affected on the fatigue crack growth rate. Tensile residual stress promoted the crack growth, and it offset the decrease of fatigue crack growth rate by grain refinement. The numerical results also indicated that the longitudinal residual stress showed the greatest effect on the crack deflection. Under the same welding speed, the fatigue crack growth rate of 2024 increased with the increasing rotational speed. For the same rotational speed, the fatigue crack propagation rate of 7075 decreased with the increasing welding speed.

Additive manufacturing (AM) has many advantages over traditional manufacturing technologies as it allows the fabrication of lattice structures with complex designs and inherent features within a single part without any separation. Currently, lattice structures have wide application prospects due to their excellent mechanical performance and design freedom. This paper provides both experimental and numerical investigations for the failure behaviors of selective laser melting (SLM) Ti6Al4V lattice structures under uniaxial compressive loading. Lattice structures with different cell topologies and strut radii were chosen to conduct quasi-static compression simulations to examine their mechanical properties and failure modes. It is found that adding [Formula: see text]-direction struts in the loading direction could significantly improve the load-carrying capacity and the most superior mechanical properties were presented by FCCZ. The slopes of the double logarithmic relationship between the equivalent stiffness and the relative density of lattice structures can be distinguished as close to 1.0 and 3.0, implying bending-dominated or stretch-dominated behavior of lattice structures, respectively. For stretch-dominated lattice structures under uniaxial compression, FCCZ, BCCZ and FBCCZ, the failure modes would experience a transformation from strut buckling to fracture with the increase of strut radii, which is different from FCC and BCC demonstrated as the bending-dominated lattice structures.

This paper focuses on the buckling instabilities of periodic porous elastomers under combined multiaxial loading. A numerical model based on the periodic boundary condition (PBC) for the 2D representative volume element (RVE) is proposed, in which two proportional loading parameters are employed to control the complex stressing state applied to the RVE model. A homogenization-based orthogonal transformation matrix is established by satisfying the equality of the total work rate to realize a proportional multiaxial loading on the RVE. First, the transition behavior of buckling patterns of periodic porous structures is revealed through instability analysis for the RVE consisting of [Formula: see text] primitive cells with circular holes subjected to different proportional loading conditions. Simulation results show that the first-order buckling mode of RVE may change suddenly from a uniaxial shearing buckling pattern to a biaxial rotating buckling pattern at a critical loading proportion. Then the influences of the number of primitive cells in the enlarged RVE on the buckling behavior are discussed. When the number of primitive cells in any enlarging direction is odd, the points of buckling pattern transition of the enlarged RVEs vary significantly with the number of cells in RVE. When the number of primitive cells is even in both enlarging directions, there is no apparent difference for the critical buckling stresses of the enlarged RVEs.

In this work, the effect of residual stress on mixed-mode crack propagation behavior in friction stir welded (FSW) 7075-T6 panel under biaxial loading was investigated. The cruciform sample was designed and manufactured by FSW. Residual stress profiles across the welded sample were measured by the X-ray diffraction technique. Crack propagation behaviors were simulated with five different biaxial loading ratios. Stress intensity factors (KΙ and KΙΙ) were evaluated by finite element method (FEM) and used to study the effects of residual stress on crack behaviors. It was observed that residual stress has a considerable effect on the mixed-mode crack growth. In most of the cases, the crack deflection is mainly affected by residual stress at the beginning of crack propagation. The variation of crack propagation path is strongly linked with the residual stress as well as the biaxial loading ratio. In addition, KΙ and KΙΙ are susceptible to residual stress under biaxial loading conditions. Residual stresses contribute to a higher proportion of KΙΙ compared to that of KΙ. KΙ and KΙΙ in the retreating side are more affected by the residual stress.

As known, friction stir welded (FSWed) joints are mature to be applied in aircraft structure. However, the weld creates local discontinuity in property and local tensile residual stress, which harm the damage tolerance of welded panels. So crack retarders were bonded in the weld zone to improve damage tolerance. Finite element method was used to calculate stress intensity factors by ABAQUS software. Finite element models were built to simulate the function of bonded retarder. Cohesive elements were used between the substrate panel and bonded retarder. A Fortran program was made to input residual stress to finite element models. Stress intensity factors from residual stress with and without bonded retarders were calculated and compared. Effects of residual stress on stress intensity factors and redistribution of residual stress were taken into considered. Effective R ratios were calculated with crack growing through the weld. Effects of bonded retarder on stress intensity factors were calculated. The results were compared with the experimental findings.

A total of 2195 T8 samples were designed, and the friction stir weld lines were kept in the sample center. Two kinds of crack retarders were designed and bonded onto the samples in three different positions. Fatigue tests were performed with and without crack retarders bonded on the samples. Crack growth rates and fatigue lives were measured and compared with each other. The effect of crack retarder’s width and position on damage tolerance was studied. Crack paths were observed and studied. It is shown that the wider size crack retarder can improve fatigue life even two times more than the narrower one, and it can make crack paths smooth. The damage tolerance of the panel achieves the best performance when the retarder covers the weld zone completely.

Series of welds were made by friction stir welding (FSW) with various backplates made out of materials ranging from low diffusivity granite to high diffusivity copper in order to reveal the effect of backplate diffusivity on the joint microstructure and properties. The temperature, microstructure, microhardness and tensile properties of joints were compared and discussed. Results show that the backplate with high diffusivity effectively decreases the heat input to the workpiece during FSW. With decreasing the backplate diffusivity the sizes of equiaxed recrystallized grains in the nugget zone increase obviously, while the hardness of the nugget zone also increases a little. The interface between the thermo-mechanically affected zone and nugget zone at the retreating side disappears under the granite backplate. Moreover, the ductility of the joint is more excellent under the copper backplate, but under the granite backplate the failure has mixed fracture characteristics of quasi-cleavage and dimples.

2198 Al–Li alloy welds were performed by friction stir welding (FSW) to investigate the influence of the ratio of rotation speed to welding speed (ω/ν) on joint microstructure, microhardness, and tensile properties. Transmission electron microscopy (TEM) was used to reveal the precipitate type across the weld cross-section. Results show that ω/ν has a little impact on both macroscopic morphology and microstructure of joints. Dissolution of precipitates has occurred in the weld nugget (WN). The density of T1 phase and its size in the WN decrease remarkably. Changes to the T1 phase are linked to a significant reduction in microhardness across the weld. With increasing ω/ν the microhardness of the joints decreases. The value of ω/ν also has impact on the fracture mode of the joints as well as the elongation.

A 2.0 mm thick Al–Li alloy 2198-T8 plate is welded by friction stir welding in this work. Four dog-bone type samples are designed to use and measure stress–strain curves and mechanical properties. M(T) samples with transverse weld in the center are designed. Fatigue tests under different R ratio loads are performed on the welded samples with crack growing in the welded nugget and parent material samples. Fatigue crack growth rates in these welded nuggets are obtained and compared. It is shown that there is no peculiar yielding process in the stress–strain curve of the welded nugget compared with the parent material. Yield strength and tensile strength have a “U” shape through the weld zone and a lower value in the weld zone while the elongation is in reverse. Unlike the parent material, fatigue crack growth rates in the welded nugget are not sensitive to R ratios. Based on K res , finite element models are built and the crack closure method is used to calculate the effect of residual stress. Redistributions of residual stress with crack growth are taken into account. Fracture surfaces are investigated to summarize the fracture feature of the welded nugget under fatigue load.

Crack paths in friction stir-welded 2198-T8 SE(T) plates with pad-up are investigated. Fatigue tests are performed with and without a friction stir weld in a range of samples, and crack paths and fatigue crack growth rates are compared. The effects of the weld on the damage tolerance of samples are studied. A hole is drilled through the specimen to study its effects on the crack trajectory. It is shown that the crack growth rate is slower with a weld than without a weld. The position of hole can change crack path and crack trajectories. A program is developed to input the residual stress distribution into an ABAQUS finite element model, and the crack paths are predicted to understand the effects of the weld. These predictions are compared with experimental data gathered on crack deviation behavior. The predictions agree well with the experimental findings.

Before friction stir welded integral panels are used in main aircraft structure, the corrosion behavior of welded joint need to be studied in detail. 2024 T3 samples were designed and welded by friction stir welding; the microstructure crossing the weld zone was observed by scanning electron microscopy (SEM), the feature of different zones (base material, thermo-mechanical affected zone, nugget) was seen; the corrosion testing in NaCl smoking box was carried out, and microstructure was observed after corrosion, localized corrosion predominantly occurs in the thermo-mechanical affected zone.

This paper was retracted by the authors and publisher since it contained material used without the permission of Cranfield University, the copyright owner.

GLARE (Aluminium with glass fibres) has become known since it was successfully and widely used in aircraft structure for its excellent fatigue and damage tolerance behavior. In this study, fatigue testing samples with 3/2 Glare were designed according to the standard. The finite element method was used to build the numerical model of the sample; the fibre bridging was modeled and the bridging stress was calculated. The delamination growth behavior can be predicted based on the energy release rate. This numerical method considered both damage modes (fatigue and delamination) at the same time.

Withdrawn at authors request.

Al-Li alloy 2198-T8 was used in the fuselage application. Integral fuselage panels were joined by double friction stir welds. Fatigue tests were conducted in the R=0.1. Notch was made between two welds. Residual stresses were measured and analyzed in the test samples with double welds. Cracks grew from the centre of two welds and across the two welds were observed, and crack growth rates were measured and compared with parent material. It is shown that crack growth rates are lower between double welds, and it is close to parent material after cross the two welds. The virtual crack closure technique (VCCT) method was used to calculate stress intensity factor from residual stress (Kres) in aim to explain the experimental findings.

In this work, Compact-Tension (C(T)) specimens with transverse welds in the sample centre were designed. The residual stress distributions were measured parallel and perpendicular to the weld nugget. Fatigue crack growth (FCG) rates were measured in the lab air. It is shown that compressive residual stresses around notch have significant effect on FCG rates and the effect deceases with crack growing. FCG rate is lower in the nugget than in parent material. Effects of residual stress were studied with crack growing. The lower crack growth rate in nugget is believed to be linked in part to compressive residual stress, but also in part to a microstructure effect present when crack grows in the recrystallized nugget.

Residual stress fields were measured in three different sizes of Compact-Tension (C(T)) and eccentrically loaded single edge notch (ESE(T)) specimens containing transverse or longitudinal welds. The effect of size on residual stress profiles was studied. Fatigue crack growth tests were carried out with cracks growing into or away from the weld line, as well as growing along the weld centre line. Effects of weld residual stresses on fatigue crack growth rates parallel and perpendicular to the friction stir welds were studied. It was found that compressive residual stresses around the sample notch had significant retarding effects on both crack initiation and crack growth rates for cracks growing towards the weld line. Effects of residual stress on crack growth rates declined with increasing crack length. When cracks grew parallel to the weld line in C(T) samples the crack growth rate was around 20% lower than in parent material.

Applications of friction stir welding in a fuselage structure were studied. Samples with two different friction-stirweld orientations in the fuselage panelwere tested: one is along the fuselage longitudinal direction and the other one is along the fuselage circumferential direction. Then fatigue cracks were investigated that were set in three different types: parallel and perpendicular to friction stir welds and between doublewelds. Sample geometries weremachined from identical welds in order to remove the effect of theweld process on fatigue behavior. Tests were conducted onM (T) specimens with either longitudinal or transverse welds. Cracks growing into or growing away from the weld center, as well as in the nugget zone, were investigated. It is shown that fatigue crack growth for cracks growing away from the center seems similar to that of the parentmaterial; for crack growing in the nugget, crack grows slower than in the parent material; and for cracks starting between double welds, the crack grows slower than in the other two types. The virtual crack-closure technique method was used to calculate stress intensity factor from residual stress (Kres) and effective R ratio in an attempt to explain the experimental findings.

To improve damage tolerance performance, GLARE was used as bonded crack retarders in this paper. Fatigue tests were run with unbonded and bonded samples; then test results between them was compared. Thermal residual stresses had been studied. It was found that bonded crack retarders can improve damage tolerance performance and capability. Thermal residual stresses have a detrimental effect on the fatigue crack growth rates by means of increasing the effective R-ratio applied on the aluminium substrate. Finite element analysis was carried out and the result was in good agreement with the experimental data.

Third generation Al-Li alloy 2195 and 2198 were studied. The material properties of these two Al-Li alloy were compared with traditional alloy 2024; damage tolerance properties was tested and compared with 2024 as well. Microstructure of parent material and welded sample was studied and compared. Crack growth rate was tested and compared. Some conclusions were drawn: Al-Li alloy had a great strength and damage tolerance; local inhomogeneities microstructure in welded samples, which created the difference of damage tolerance and the tendency of crack growth rate in welded samples.

Stem respiration is an important part of the annual carbon balance of forest ecosystems and consumes ca. 11%-33% of total net daytime carbon assimilation. Because of difficulties in measurement, little attention was paid to stem respiration studies in the past. However, with increasing atmospheric CO2 concentration, studies of stem respiration have become popular. Several methods were applied in earlier studies, including gas exchange measurements and closed method. An open flow system is employed in recent studies. Results from recent research show that the diurnal pattern of stem respiration is bimodal with a midday depression and that rates are the greatest in the growing season. Controlling factors include meteorological factors (e.g., stem temperature, CO2 concentration and humidity) and biological factors (tree species, tree age, diameter at breast height, sapwood size and nitrogen content in stem). Latitude, altitude and topographic factors indirectly influence respiration rates through meteorological or biological factors, in particular stem temperature. Stem respiration rate is positively correlated with stem temperature. The mechanism of stem respiration and its controlling factors will continue to be subjects of future research. Integration of meteorological and biological factors into models of stem respiration will provide insight into contribution of stem respiration to the carbon balance of forest ecosystems, role of forest ecosystems in reducing CO2 concentration elevation in the atmosphere, response of forest ecosystems to global changes, and development of carbon cycle models of forest ecosystems. These issues and measurement techniques remain challenging and fruitful areas for future research.

The use of residual K (Kres) approaches for prediction of fatigue crack growth rates in residual stress fields was studied. Finite element models of the samples were built and the measured residual stress data put into the model. The virtual crack closure technique (VCCT) was used to calculate (stress intensity factor from residual stress) together with its changes with crack length using data from the part I paper. Local Kres values were used to calculate effective R values. Kop and ΔKeff values throughout the crack path in the weld were calculated. The master curve approach was used to relate these to corresponding values for crack growth rates. Predicted crack growth rates were compared with experimental results. Changes in crack growth rate found as the crack grows through the weld can successfully be predicted via application of this closure based model. Agreement between predictions and experimental data was best for tensile residual stress fields and was not as exact in compression. Possible reasons for this discrepancy are discussed.