Long-range Residual Stresses Research Articles

Re-evaluation of fatigue design curves for offshore wind monopile foundations using thick as-welded test specimens

The dominant majority of existing offshore wind turbines are supported using monopile foundations which are fabricated by welding thick steel plates. In the current fatigue design recommendations for welded steel structures, which are commonly used in the design of monopile structures, the initial inverse slope of the S-N curve is fixed to −3. The historic rationales for this assumption are the ease of fatigue life calculations, the effect of long-range residual stresses that were not originally captured in the test data on thin welded specimens, and analogy with fatigue crack growth. While this introduces an unquantified level of conservatism to deterministic fatigue calculations, it was an acceptable (and wise) assumption when the S-N design curves were generated a few decades ago; however, current designs and assessments require more accurate calculations and the need to more confidently quantify the likelihoods attached to these evaluations. In the present study, it is argued that unlike large braced structures (e.g. jackets) in which long-range residual stresses may remain in place as fatigue cracks propagate, in circumferential welds of monopile structures the natural relaxation of residual stresses, in the absence of long-range residual stresses, must be accounted for by performing fatigue tests on thick welded samples. This paper presents a thorough analysis of the fatigue test results obtained from 50 mm thick as-welded samples with representative profiles of residual stresses that exist in monopiles. Basic and advanced statistical approaches were employed in the analysis and higher values of inverse slope were found using the large thickness test data. The results from this study are compared with the recommended fatigue design curves available in international standards. The outcomes from this research draw important observations concerning the need to employ an appropriate value of inverse slope in the design of monopile structures by excluding the conservative approach imposed by a fixed value of −3 which was originally implemented for braced structures with the assumption of large and long-range residual stresses.

Local residual stresses and microstructure within recrystallizing grains in iron

The intragranular strains and the microstructure within recrystallizing grains in single phase pure iron have been systematically studied in 3D using synchrotron micro-diffraction. In contradiction to common knowledge we observe that residual elastic strains of up to 1–2 × 10−3 are present in the recrystallizing grains. The local strain variations within individual grains can be similar in magnitude to those between different grains. The effects of processing parameters, including rolling reduction, recrystallized volume fraction, and cooling rate, as well as microstructural parameters, including grain size, orientation and internal misorientation, on the development of local residual elastic strains and microstructure have been quantified. It is suggested that the difference in local defect density between recrystallized grains and the surrounding deformed matrix, as well as the redistribution of medium to long-range residual stresses in the deformed grains, are the main reasons for the development of such strains in the recrystallized grains. The local residual stress levels are calculated and their possible impact on the mechanical properties and recrystallization processes are discussed.

Measuring residual stress in Ti-6Al-4V with HR-EBSD, using reference patterns from annealed material

Elastic strain and residual stress values in an engineering material were determined by high-resolution EBSD (HR-EBSD) using reference patterns from annealed, recrystallized material. Specifically, rolled Ti-6Al-4V sheet was analyzed using HR EBSD in both an as-annealed and a strained state, the latter established via a static two-point bend fixture. The commercial software CrossCourt4 (CC4) was used to evaluate the relative intragranular strain tensor components of the alpha grains mapped by HR-EBSD. The intragranular reference patterns identified in each grain by the software were then replaced with similarly-oriented patterns from scans of the as-annealed, recrystallized material. The CC4 analysis was then repeated to provide calibrated strain and residual stress values. Elastic strains on the order of 10−3 were detected, with corresponding residual stress values on the order of 1 GPa. Subsequent analyses using high energy synchrotron x-ray diffraction showed good correlation with the elastic strains measured by HR-EBSD using the annealed reference patterns. Additionally, the maximum macroscopic stress analytically predicted for two-point bending was in agreement with the residual stress observed. Good repeatability of the methodology and insight into the state of individual grains were also observed. The findings provide encouraging evidence that accurate intragranular and long-range residual stress measurements of engineering significance can be made with HR-EBSD using a physical reference pattern library.

A novel creep test rig to study the effects of long-range residual stress, elastic follow-up and applied load

One of the many challenges in the behaviour of structures is to understand if the presence of residual stress plays an important role in contributing to failure of a structure operating at high temperature. Assessments of the high-temperature integrity of practical structures are based on experiments carried out using standard laboratory-scale creep test specimens tested under either load- or displacement-controlled conditions. In practice, structures are subjected to combinations of residual and applied stresses which in turn lead to mixed boundary conditions. Conventional laboratory creep tests do not represent these circumstances. The purpose of this paper is to describe the design of a novel test rig to introduce long-range residual stresses at high temperature. The concept of rig is based on three-bar structure with an initial misfit introduced into the central bar to represent a long-range residual stress and could be characterised easily without using time-consuming residual stress measurement techniques. Initial results demonstrated that the magnitude and the interaction of the residual stress with the applied loading is a function of the initial misfit displacements and the relative stiffness of the components of the system. Additionally, the subsequent behaviour of the system, with and without the application of additional loading, is governed by (a) the degree to which the misfit is accommodated by plastic and creep strain and (b) the elastic follow-up provided by the system. The paper describes the design of a test rig and laboratory tests conducted to validate the concept.

Welding residual stresses as needed for the prediction of fatigue crack propagation and fatigue strength

Welding residual stresses have an impact on the performance of welded structures, on their fracture resistance, their resistance against fatigue crack propagation and, most important, their fatigue strength and fatigue lifetime. The present paper provides an overview on the issue mainly from the point of view of the application of fracture mechanics to the determination of the fatigue strength as the topic of this Special issue. Besides own experimental and theoretical data a comprehensive discussion is provided in that context which includes the definition and interaction of short- and long-range (or reaction) residual stresses, the effect of cyclic mechanical loading and its treatment in fracture and fatigue analyses.

The effects of long-range residual stress, elastic follow-up and applied load on creep crack incubation and material toughness

Creep crack incubation of Type 316H stainless steel at 550 °C is explored in this article. Fracture mechanics specimens, subjected to combinations of residual and applied loads and in the presence of elastic follow-up, are tested. The design of two new test rigs is described. The rigs introduce planned levels of elastic follow-up together with combined residual and applied loading conditions to the specimens. A series of high-temperature elastic–plastic and elastic–plastic–creep experiments are undertaken to compare the experimentally determined values of elastic follow-up with the theoretical values. A further series of fracture mechanics tests are performed to measure creep crack incubation and material toughness for samples subjected to constant load and for tests under combined loading with elastic follow-up. It is demonstrated that for tests subjected to the same initial reference stresses, longer incubation times are attained for elastic follow-up tests compared to constant load tests. Also, combined loading tests exhibit longer creep crack incubation times based on the same measured material toughness obtained from constant load tests. This suggests that not all the available strain energy provided by combined loading to a specimen at high temperature contributes to creep crack incubation.

The influence of long-range residual stress on plastic collapse of pressurised pipes with and without flaws

Structural integrity assessments of pressurised pipes include plastic collapse as a potential failure mode. This paper uses analytical and numerical models to explore the effect of the end conditions of the pipe on the collapse pressure. The pipe is open-ended and two bounding conditions are addressed: one where axial loading is applied to the ends of the pipe and the other where a fixed axial displacement is applied. The fixed axial displacement condition represents long-range or fit-up residual stress. It is common practice to treat long-range residual stress in the same way as axial loading, leading to the conclusion that such long-range residual stress reduces the collapse pressure. Pipes in a number of states are considered: pipes with no flaws, pipes with fully circumferential flaws and pipes with part circumferential flaws. The flaws consist of either a crack or a slot on the external surface of the pipe. For the axial load condition, the collapse pressure for a flawed pipe is reduced when higher magnitudes of tensile or compressive axial loads are applied. For the fixed displacement condition however, the magnitude of the displacement may have little or no effect on the collapse pressure. The results of the work indicate that substantially conservative assessments may be made of the collapse pressures of pipes containing flaws, when long-range residual stress is taken to be a form of axial loading.

Neutron diffraction measurements of time-dependent residual stresses generated by severe thermomechanical deformation

Residual stresses were generated by severe thermomechanical deformation in an aluminum alloy plate. The evolution of the residual stresses during natural aging was investigated by neutron diffraction up to 10,000 h. A data reduction method was developed to eliminate microstructure influences (solute variations) on the lattice spacing changes, thereby allowing the determination of the long-range macroscopic residual stresses. The residual stress decreased (∼25 MPa) with time due to the microstructural modification within the deformed region during natural aging.

Optimization of ceramic strength using elastic gradients

We present a new concept for strengthening ceramics by utilizing a graded structure with a low elastic modulus at both top and bottom surfaces sandwiching a high-modulus interior. Closed-form equations have been developed for stress analysis of simply supported graded sandwich beams subject to transverse center loads. Theory predicts that suitable modulus gradients at the ceramic surface can effectively reduce and spread the maximum bending stress from the surface into the interior. The magnitude of such stress dissipation is governed by the thickness ratio of the beam to the graded layers. We test our concept by infiltrating both top and bottom surfaces of a strong class of zirconia ceramic with an in-house prepared glass of similar coefficient of thermal expansion and Poisson’s ratio to zirconia, producing a controlled modulus gradient at the surface without significant long-range residual stresses. The resultant graded glass/zirconia/glass composite exhibits significantly higher load-bearing capacity than homogeneous zirconia.

Plate Residual Stress Effects on Dimensional Accuracy in Thermal Cutting

Dimensional inaccuracies induced by thermal cutting processes have not received sufficient attention in the open literature. A series of recent research initiatives, including this one, have demonstrated that thermal cutting can contribute significantly to dimensional inaccuracies in the form of two major mechanisms:thermally induced part distortions andplate movements as the residual stresses in the original plate are relieved to achieve new equilibrium conditions during cutting. For the former, laser cutting and managing heat sink conditions are effective in minimizing the cutting-induced distortions. For the latter, considerations must be given to the residual stress conditions in the plates to be cut so that a proper cutting sequence and layout plan can be developed to mitigate the plate residual stress effects on part/plate movements during cutting. In this paper, a major research program recently completed under the auspices of the Gulf Coast Regional Maritime Technology Center will be summarized. Some of the major findings are as follows:Although steel mill processes and parameters vary significantly from mill to mill, the important residual stress features that are relevant to cutting accuracy are dominated by only a few mill process parameters.Localized short-range residual stresses are not detrimental to cutting accuracy, even if the short-range residual stress magnitude can be high. Long-range residual stress distributions that achieve equilibrium conditions at a length scale of plate width are most important for cutting sequence planning purposes.As a result, a generalized residual stress distribution (long range) has been established for cutting planning purposes, although the detailed features may vary from mill to mill.Through a detailed series of parametric analyses using advanced modeling techniques, it was found that cutting sequencing is very important in mitigating the plate residual stress effects.It is important and practical to ensure the consistency in steel conditions so that a set of cutting procedures can be developed for mitigating plate residual stress effects on cutting accuracy, rather than trying to eliminate residual stresses in mill plates.

Residual stresses in punched laminations: Phenomenological analysis and influence on the magnetic behavior of electrical steels

The magnetic properties of laminated electrical steels are degraded by punching because of plasticity localized along the cutting edge, but also because of residual stresses, which may spread over the whole lamination. In this article, long-range residual stresses are analyzed via a simplified mechanical analysis. Then, their effect on the global magnetic behavior of the lamination is calculated by a magnetoelastic coupled model. It is found that the relative influence of residual stress is as important as the one of plasticity alone.

Engineering the resistance to sliding-contact damage through controlled gradients in elastic properties at contact surfaces

Experimental and computational results are presented to demonstrate that controlled gradients in elastic modulus alone can result in a pronounced enhancement in the resistance of a surface to frictional sliding contact. The model material chosen for the demonstration of this new concept is polycrystalline alumina infiltrated with aluminosilicate glass. In this system, the elastic modulus increased continuously by 50% from the contact surface to a depth of about 2 mm beneath the surface, with essentially no long-range residual stresses. The strength and local fracture toughness of the contact surface markedly deteriorates as a result of elastic modulus gradation. However, the gradation in elastic modulus alone reduces the principal tensile stresses introduced by frictional sliding contact to such an extent that the glass-infiltrated alumina is far more resistant to contact damage than either monolithic alumina or glass or alumina–glass composite of uniform composition which is equal to the composition of the contact surface. A wide variety of mechanics and materials issues pertaining to sliding contact resistance of homogeneous and graded materials are also addressed.

Hertzian‐Crack Suppression in Ceramics with Elastic‐Modulus‐Graded Surfaces

Hertzian (spherical) indentation experiments were carried out in a graded alumina‐glass composite whose Young's modulus increased with depth beneath the indented surface. An in situprocessing method involving impregnation of a dense, fine‐grained alumina by an aluminosilicate glass was employed to fabricate such a composite. With this technique, a monotonic, unidirectional variation in Young's modulus of as much as 50% was introduced over a distance of approximately 2 mm, while keeping the coefficient of thermal expansion and the Poisson ratio for the glass and the alumina nearly the same. The macroscopically graded, elastic composite so produced with nearly full density has essentially no macroscopic, long‐range residual stresses following processing. The unidirectional variation in Young's modulus under the indenter is shown to fully suppress the formation of Hertzian cone cracks. Without these elastic‐modulus gradients, cone‐crack formation was observed in bulk glass and alumina. Finite‐element analyses of spherical indentation on elastically graded substrates were also performed to develop a quantitative understanding of the experimental trends. It is reasoned that the present innovations, involving functionally graded surfaces and their in situprocessing, provide new possibilities for enhancing certain contact‐damage resistance characteristics in various ceramic materials for a broad range of engineering applications. Furthermore, this contact‐damage‐resistance phenomenon in functionally graded ceramics is elastic in nature, and is, therefore, likely to be immune to mechanical fatigue within the elastic limit.

Microstructural evolution upon thermomechanical processing of non-sag tungsten

The thermally activated detachment of dislocations from bubbles may explain the variable stress sensitivity of the stationary creep in a broad stress region. The models of this kind of creep predict that, on the one hand, there should be an optimum bubble size that depends markedly on the applied stress while, on the other hand, the length of the bubble rows should play a secondary role, as the creep rate is primarily governed by the size of the individual bubbles. Although the kinetics of the detachment of the grain boundaries from bubbles should govern the final microstructure of non-sag tungsten both in the stress relieved and in the recrystallized conditions, a recent model on the thermally activated detachment will be really effective, only if the size of the dispersoid is in the nanosized region. A simple method is also described for monitoring the relaxation of the long-range residual stresses in thin non-sag wires.

Separation of macroscopic, elastic mismatch and thermal expansion misfit stresses in metal matrix composite quenched plates from neutron diffraction measurements

Neutron diffraction measurements of the strain profile in a quenched plate of an aluminium-dash;silicon carbide particle-reinforced metal matrix composite are reported. The results have been used to evaluate the efficacy of an analysis technique which allows distinction of the stiffness mismatch and shape misfit stresses between the matrix and reinforcement, as well as between these and any macrostress present. The analysis is presented for measurements made on a metal matrix composite plate which, as a consequence of quenching from elevated temperature, shows large variations in residual stress as a function of position through the plate thickness. The measurements illustrate the additional insight which can be obtained through the separation of the elastic mismatch and thermal misfit stresses. The stress components thus obtained show good agreement with calculated long-range residual and mismatch stresses.

The Structure and Stress State of Lamellar Interfaces in Two-Phase Titanium Aluminides

ABSTRACTTitanium aluminide alloys with compositions slightly on the Ti-rich side of stoichiometry consist of the intermetallic phases α2 (Ti3Al) and γ(TiAl). The two phases form a lamellar microstructure with various types of coherent and semicoherent interfaces. The lattice mismatch occurring at the semicoherent interfaces is largely accommodated by networks of interfacial dislocations. Nevertheless, a significant homogeneous straining seems to remain at these interfaces, resulting in long-range residual stresses. The present paper reports an electron microscope study of the correlation between the misfit strain of adjacent lamellae and the atomic structure of the interfaces. The residual coherency stresses were determined by analyzing the curvature of dislocation loops which were emitted from the network of the interfacial dislocations. The estimated stresses are close to the shear stresses applied during macroscopic deformation experiments. The effects of these stresses on the deformation behaviour of the material are discussed.

Lattice imperfection studies in polycrystalline materials by x-ray diffraction line-profile analysis

This review concerns our recent investigations with a series of binary fcc Ag- and Cu-base alloys (viz Ag-Ga, Ag-Ge, Ag-Al and Cu-Ga, Cu-Ge) from detailed analyses of x-ray diffraction line profiles, the importance of which has been briefly summarized. The theoretical formulations of the Warren-Averbach’s method of Fourier analysis of peak-shapes along with the methods of peak-shift and peak-asymmetry have been outlined. A preview on the significant studies carried out earlier with Ag- and Cu-base (fcc) binary alloys has been made in short. A detailed analyses on the recorded profiles in the present considerations revealed, in general, quantitative estimates of several microstructural parameters characterising the deformed state of the materials namely, propensity of stacking faults (intrinsic, extrinsic and twin faults), rms microstrains, coherent domain sizes, long-range residual stresses, lattice parameter changes, dislocation density and stacking fault energy. The results indicate a general trend of increase in the concentrations of stacking faults, primarily, of intrinsic character, with increase in solute concentrations; which are solely responsible for the observed peak-shifts as well as domain size broadening. Small asymmetry in the profiles is due to the presence of extrinsic stacking faults, relatively less in magnitude compared to the intrinsic ones while the deformation twin faults are almost absent—an observation with significance. The dislocation density, quite appreciable in magnitude, has been evaluated from the anisotropic values of the coherent domain sizes and rms microstrains. The stacking fault energies of pure Ag and Cu, an important parameter have also been estimated and compared with those obtained from electron microscopy. Annealing experiments with a Ag-5·8% Al alloy, aluminium being a precipitating solute, do not reveal any detectable evidence of solute segregation at the stacking faults. The occurrence of stacking faults in the alloy systems has been correlated with a number of physical factors involving solvent-solute types.

An x-ray diffraction study of lattice imperfections in cold-worked face-centered-cubic alloys. V. Silver-aluminum (α phase)

X-ray peak-shift, peak-asymmetry, and peak-broadening analyses have been performed on cold-worked α-phase Ag-Al alloys containing 5.8, 9.2, 15.8, and 18.2 at. % Al based on the diffraction profiles recorded with copper radiation and a counter diffractometer equipped with (100) LiF crystal monochromator. Following the procedures adopted earlier in this series of work, a detailed analyses of the recorded profiles revealed quantitative estimates of the microstructural parameters, namely, propensity of stacking faults (intrinsic, extrinsic, and twin faults), rms microstrains, coherent domain sizes, long-range residual stresses, lattice parameter changes, dislocation density, and stacking fault energy. As in earlier alloy systems of this series, the results indicate an increase in the stacking fault density, primarily of intrinsic character with increasing solute concentration, and these are mainly responsible for the observed peak shifts and domain size broadening. Small asymmetry in the profiles has been found to be due to the presence of extrinsic stacking faults, relatively less in magnitude compared to intrinsic ones while the deformation twin faults are almost absent. The dislocation density ρ has been evaluated from the anisotropic values of the coherent domain sizes and rms microstrains. The stacking fault energy γ0 for pure silver has been estimated to be 6–9 mJ/m2, which is lower than the previously reported values. Finally, annealing experiments with Ag-5.8 at. % Al alloy do not show any detectable evidence of solute segregation at stacking faults.

An X-ray diffraction study on the lattice imperfections in vapour-deposited FCC (Ag-4.5 at.% Ge) alloy films

Fourier analyses of both multiple and single-order reflections in FCC (Ag-4.5 at.% Ge) alloy films (68 to 238 nm thick) indicated appreciable coherent domain size and lattice strain effects with slight lattice contraction and significant compressive long-range residual stress. The study further reveals large concentrations of growth twin stacking faults but none that were intrinsic or extrinsic. The films showed a high dislocation density and a strong preferential texture along (111).

An x-ray diffraction study on the microstructures of cold-worked fcc Cu-Ni-Zn alloys

The state of cold work in the ternary Cu-Ni-Zn alloy system (fcc) has been investigated by x-ray diffraction from a detailed analysis of the peak shift, peak asymmetry, and peak broadening. Cold working in the system produces an appreciable amount of intrinsic stacking faults which play the most important role in peak broadening as well as in shifting the positions of the diffraction profiles. For the observed peak shift, the other contributing factors (namely, lattice-parameter change and long-range residual stresses) are relatively small. Asymmetry in the profiles is due to the presence of a very small amount of extrinsic stacking fault, and deformation twins have been found to be totally absent. The estimations of domain size, rms strains, and the dislocation density in the alloys have been made from the peak-broadening analysis, and the stacking-fault energy for pure copper has also been evaluated and has been found to be comparable. The presence of the transitional solute Ni from 1 to 15 wt% has a very small influence in altering the microstructural parameters, which, however, vary gradually with the increase of zinc concentration from 24 to 34 wt% uninfluenced by the nickel content in a manner similar to that observed earlier for the binary Cu-Zn system.