Circumferential Residual Stress Research Articles

Residual stresses due to cladding, buttering and dissimilar welding of the main feed water nozzle in a power plant reactor

A 100 MW AP1000 Reactor was considered and welding processes were employed in joining of the main feed water nozzle, in primary circuit of nuclear reactors were simulated by means of finite element method. Distribution and magnitude of the residual stresses created by thermal processes including cladding inside the nozzle, buttering prior to dissimilar welding, heat treatment and dissimilar welding of the safe-end austenitic stainless steel to the nozzle ferritic steel were investigated. Norton-Bailey creep model was used for heat treatment simulations. Experimental results obtained in previous studies and residual stress measurements were applied for verification of the developed model. It was revealed that residual stresses after cladding were approximately equal to yield strength of the materials. Also, buttering led to reduction of residual stresses in the nozzle free end. Heat treatment decreased residual stresses in the base metal significantly; whereas, it had minor effects on those in the cladding layer. Besides, circumferential residual stresses were invariably tensile at inner and outer surfaces of the joint. Further discussions were provided to explain the obtained result.

Numerical study of springback using the split-ring test: influence of the clearance between the die and the punch

The split-ring test consists in cutting a ring from the wall of a drawn cylindrical cup, which is split to measure the springback. This springback measure can also be used to estimate the circumferential residual stresses in the ring. It is known that the distribution of the residual stresses in the cup depends on the specific combination of forming parameters selected to perform the deep drawing operation, which include the depth of the cup and the clearance between the die and the punch. Moreover, the forming parameters also seem to affect the distribution of the axial and circumferential through-thickness stress profiles along the cup height, since different ring opening trends have been observed, when rings are cut from the cup wall at different heights. The focus of this numerical study is the analysis of the impact of an ironing stage on the residual stress distributions in the cylindrical cup and, consequently, in the split-ring test. The analysis is performed considering a 6016-T4 aluminium alloy, for which experimental results are available. The results show that the ironing of the vertical wall changes the characteristic distribution of the axial and circumferential residual stresses in all locations of the cup wall, even for relatively small ironing strains. This affects the trend observed for the ring opening value, when rings are cut at different heights.

Analysis of Residual Stresses Induced by Riveting Process and Fatigue Life Prediction

Residual stress induced by riveting process is critical to the fatigue life of riveted structures. A residual stress model is proposed to predict the residual stress distribution after riveting process. In the residual stress model, the radial pressure at the hole boundary is obtained, and the strain hardening effect of the rivet material is taken into consideration. The other characteristic of the model is that the solution of radial and circumferential residual stresses is extended to include an unfree springback process by using a springback coefficient. The residual stresses on the faying surface with various parameters, such as the height of the rivet drive head, the hole diameter, and the material property, are predicted with the residual stress model. The residual stresses calculated by the model are employed in the fatigue life prediction using the multi-axial fatigue criterion. The predicted results of the fatigue life show a good agreement with the experimental data. The investigation in this paper can help the residual stress prediction of riveted joints and improve the awareness of the effect of the residual stress on the fatigue behavior of riveted structures.

Effects of the indentation process on fatigue life of drilled specimens: optimization of the distance between adjacent holes

The generation of permanent compressive stresses around the holes is recognized as a valuable mean to delay the onset and propagation of the defects and to extend the fatigue life of the mechanical components. In the work, a bilateral indentation process, performed on each side of the component, is widely used in order to create a residual circumferential stress field around the area to be drilled and that persists after the drilling operation. In order to evaluate the process parameters and to identify optimal geometric solutions, several static and fatigue tests are conducted on AW 6082-T6 aluminum alloy specimen where two holes are created. In particular, experimental tests on only drilled specimens (OD) and specimens subjected to Indentation process (IP) varying the indentation depth and the center-tocenter distance of the holes are performed. Several numerical analyses, conducted in ANSYS APDL environment with explicit solver, allow to determine the influence of the distance between two adjacent holes and the effect of the indentation depth on the residual stress distribution.

Экспериментальное исследование кинетики остаточных напряжений в упрочненных полых цилиндрических образцах из сплава Д16Т при осевом растяжении в условиях ползучести

Экспериментально исследовано влияние растягивающей осевой нагрузки на релаксацию остаточных напряжений в поверхностно упрочненных полых цилиндрических образцах из алюминиевого сплава Д16Т при температуре 125 $^\circ$C. Упрочнение выполнено пневмодробеструйной обработкой поверхности дробью. Описаны установки для испытаний и методика эксперимента. Получены экспериментальные кривые ползучести упрочненных образцов при осевых нагрузках $353$, $385$, $406.2$ и $420$ МПа при длительности испытаний 100-160 часов. Методом колец и полосок определены поля осевых и окружных остаточных напряжений после процесса упрочнения и после ползучести при заданных температурно-силовых условиях нагружения. Установлено, что по сравнению со случаем термоэкспозиции (температурная выдержка без нагрузки) под действием растягивающей нагрузки $\bar \sigma$ происходит существенное качественное и количественное изменение остаточных напряжений. Термоэкспозиция практически не влияет на процесс релаксации остаточных напряжений, а приложение нагрузки привело к существенной релаксации остаточных напряжений и изменению их характера распределения: окружное и осевое остаточные напряжения эволюционируют от сжимающих до растягивающих при росте осевой растягивающей нагрузки. Происходит изменение глубины залегания остаточных напряжений с увеличением растягивающей нагрузки с величины 600 мкм в исходном состоянии после пневмодробеструйной обработки до величины 250-300 мкм после ползучести при заданных нагрузках. Отмечено, что с точки зрения инженерных приложений выявленные закономерности изменения остаточных напряжений в упрочненных образцах из сплава Д16Т необходимо учитывать при прогнозировании характеристик сопротивления усталости поверхностно упрочненных деталей из этого сплава, работающих при повышенных температурах.

Helical buckling and postbuckling of pre-stressed cylindrical tubes under finite torsion

In this paper we analyze bifurcation and postbifurcation of a finite deformation boundary-value problem for a residually-stressed elastic body using the finite element method. In particular, the torsion of a circular cylindrical tube subject to radial and circumferential residual stresses is studied. The material model is given by a residual-stress dependent nonlinear elastic constitutive law in terms of invariants. Firstly, the numerical methodology able to capture the elastic stability of tubes under torsion is developed without including residual stress. The bifurcation point is initially estimated reducing the original problem to an algebraic eigenvalue problem. A nonlinear analysis is performed to capture the postcritical behavior. Secondly, prestress is introduced. The residual-stress dependent nonlinear elastic constitutive law is implemented in a finite element code. The dependence of bifurcation and postbifurcation behavior of tubes under torsion on residual stresses is illustrated and compared with results when there is no residual stress. Analytical solutions involve a complicated mathematical machinery that deals with specific material models and loads as well as, usually, a perfect geometry. Here, we provide a highly flexible approach that is implemented in a commercial finite element code, which allows this methodology to be easily used on other problems under different loading conditions and geometries. The numerical results obtained for the (thin) tubes are compared with the (analytical) solution for the torsion of an infinitely long circular cylindrical membrane to validate the methodology.

Residual stress in the cylindrical drawing cup of SUS304 stainless steel evaluated by split-ring test

The residual stresses in the wall of a SUS304 stainless steel cylindrical drawing cup were evaluated by split-ring tests, and the influences of stamping die parameters on the residual stress were investigated. A new theoretical model of a split-ring test was developed to evaluate the residual stress in a ring, which was verified to be reasonable and reliable by numerical simulations with ABAQUS code and by nanoindentation tests. Seven groups of split-ring tests were completed, and the residual stresses were calculated according to the theoretical model. The split-ring test results showed that the circumferential residual stress in the wall of the SUS304 stainless steel cylindrical drawing cup was very large and did not change with the different die corner radius. The circumferential residual stress first increased with the increase of drawing punch–die clearance, then was almost unchanged when the clearance increased greater than blank thickness 1 mm. Thus, a smaller clearance was suggested to be chosen to reduce the residual stress in the wall of the SUS304 stainless steel drawing cup. Seven groups, three samples in each group, and a total of 21 qualified cylindrical drawing cups in Fig. 2 were made from a circular SUS304 stainless steel sheet about 72 mm in diameter and 0.94 mm in thickness by deep drawing with different processing parameters. After the rings were cut from the cup walls, each ring was split along the radial direction. Two ends of each split ring opened a distance to release the circumferential residual stress in the closed ring. After measuring the opening distance, the residual stresses in the drawing cup walls were calculated by Eq. (18) in the newly developed split-ring test theoretical model of this paper. Then reasonable technology measures were found to reduce the residual stress by analyzing the influence of the mold parameters on residual stresses.

Исследование влияния анизотропии поверхностного пластического упрочнения на распределение остаточных напряжений в полых и сплошных цилиндрических образцах

surface plastic hardening, roller burnishing process, hydraulic shot blasting procedure, deformation anisotropy, solid and hollow cylindrical samples, residual stresses, mathematical model, experimental data For the calculation of residual stresses and plastic strains in hollow and solid surface-hardened cylindrical specimens we suggest the mathematical models, which take into account both the cases of hardening leading to the isotropy (hydraulic shot blasting procedure) and to the anisotropy (roller burnishing process) of plastic strains in the surface layer. The introduced mathematical model has a hardening anisotropy parameter which ties the axial and circumferential components of the residual plastic strains tensor. We use the determined axial and/or circumferential components of the residual stresses tensor as the input information. Also we use the following assumptions: smallness of the off-diagonal elements of the residual plastic strains tensor and residual stresses tensor, plastic incompressibility of material, absence of the secondary plastic strains of the material in the compression area of the surface layer. The boundary value problems of the hardened layer stress-strain state estimation after the hardening for the hollow and solid cylindrical specimens are solved and the solution is given in the paper. We give the method for the mathematical model parameter identification under the condition of selfequilibrated residual stresses and the method for the experimental determination of residual stresses by the circles and strips approach. Also, the cycle of the hardening experiments for the hollow and solid specimens from the 40Kh steel (having different proportions of internal and outer diameters) in the roller burnishing process and hydraulic shot blasting modes was performed with the determination of the residual stresses. The mathematical model adequacy is verified through the comparisons with experimental data; good agreement of the calculated and experimental data is demonstrated. The calculated numerical values of the hardening anisotropy parameter are given. The fact that the procedure of surface anisotropic hardening (roller burnishing process) leads to the strong layering of the epures of axial and circumferential residual stresses in depth of the hardened layer is established. Contrastingly, the case of the isotropic hardening (hydraulic shot blasting) leads to almost coinciding epures. Using the experimental and calculated data we have shown that the hardening of tool roller type leads to the larger absolute values of the compressing stresses, which by more than 30% exceeds the stresses after the hardening of hydraulic shot blasting type for the specimens of the same geometry. For the main results of the research we have given the necessary data in the table and also we have presented the epures for the residual stresses distribution. © PNRPU

Extension, inflation and torsion of a residually stressed circular cylindrical tube

In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress.

X線応力測定法による孔の円周方向残留応力の測定

The circumferential residual stress on the inner surface of a round pipe was measured by using the dual-axis inclining method. The dual-axis inclining method is an X-ray stress measurement technique using the iso-inclination method jointly with the side-inclination method. It is not possible to apply the conventional X-ray stress measurement method based upon the sin2ψ method to such measurement even if the irradiated area is at the neighborhood of the open-end of the hole. The dual-axis inclining method was described, and the analysis was made of the relation between the position of the irradiated area, the diameter of hole and the scannable angle range. On the assumption that the ψ angle should be scanned up to 30 deg for the stress measurement, the result of the analysis shows that the distance between the irradiated area and the open-end of the hole should be less than a quarter of the hole diameter. The experiment was conducted for a round pipe of carbon steel. It was found that even when the intensity of background decreased only on the lower side of diffraction peak due to the shielding by the side wall of the pipe, the circumferential stress can be evaluated by directly applying the parabola peak method or the 2/3-value breadth method to the collapsed diffraction profiles without processing the background.

Diagnostics of the Stress-Strain State of Multilayer Annular Welded Joints of Pipelines

Within the framework of the shell theory, we develop a mathematical model that describes the axisymmetric stress-strain states of multilayer annular welded joints of the pipes under the action of residual incompatible strains localized near the weld. The residual stresses are evaluated on the basis of the solutions of inverse problems of the shell theory with intrinsic stresses by using the experimental data obtained by the method of speckle interferometry. We created an experimental installation and special software that enable one to evaluate and reproduce residual stresses in the zone of multilayer welded joint. The plots of circumferential residual stresses as functions of the distance from the axis of the weld are presented.

Measurement of the Distribution of Residual Stresses in Layered Thick-Walled GFRP Pipes

The objective of this study is to measure the axial, circumferential, shear and radial residual stress distributions in three thick-walled glass fibre reinforced plastic (GFRP) filament-wound pipes, two of which are layered. The measurement of residual stresses was carried out using a recently published layer removal method which overcomes the limitations of previous techniques and can be applied to layered anisotropic pipes of any wall thickness. Layers of approximately 0.3 mm thickness were incrementally ground from the outer surface of the pipes. The resulting strains were measured on the inner surfaces. A least-squares polynomial was fitted to each measured data set, and used to calculate the corresponding stress distributions. All of the resulting axial, hoop and shear stress distributions adhere to the requirement of self-equilibrium and the radial stress distributions all vanish to zero at the inner and outer surfaces. The radial stresses of the layered pipes showed a tendency to have two peaks, one for each layer, a consequence of the two-stage manufacturing process of these pipes. The measured axial and hoop stresses of all three pipes were similar at the inner surfaces despite significant differences in the stiffnesses in the principal directions arising from different wind angles.

Residual Stress Assessment of Multiple Welding Repairs of Girth Welds in Pipeline Used in Oil Industry

This work presents the residual stress assessment of multiple welding repairs in the same area in seamless API X52 low carbon pipeline. Four conditions of shielded metal arc welding (SMAW) repairs and one as welded specimen of the girth weld were evaluated to determine changes in the microstructure (metal base, weld bead and heat affected zone) to evaluate their effect on the residuals stresses and mechanical properties of the welded joints. One of the mainly adverse effect of residuals stresses are in the susceptibility of stress corrosion cracking (SCC) of buried pipelines. The residual stresses were measured through X-ray diffraction (XRD). Samples were evaluated on the internal side of the pipe in longitudinal and circumferential direction. Circumferential residual stresses are greater than longitudinal stresses. Microstructural characterization of the welding joints through scanning electron microscopy (SEM) was performed. Relation between microstructure, mechanical properties and residual stresses was carried out. In general, the grain size increases with the number of repairs, and consequently there is an increase in residual stresses. Significant reduction in Charpy-V impact resistance with the number of weld repairs was observed overall in the weld fusion line. The hardness and strength increase in the first repair and in subsequent repairs decrease. As increasing the average grain size, the hardness and the absorbed energy decreases. Generally, the residual stresses showed a tendency to decrease in the first repair and after showed an increase with the number of repairs. It is clear that residual stresses depend more than the position of measurement than the welding repair number, which is directly relate with the microstructure and phases presented.

Research on measurement of residual stresses of hemispherical lithium hydride by blind-hole method

The released strains of sintered and machined lithium hydride of SR40 hyper-hemispherical and SR30 inner hemispherical sample could be shown in the measuring process by blind-hole method. The residual stresses of lithium hydride sample were calculated with the formulas of residual stress and released strains. The results show that the nearly 45 degrees direction residual stresses of SR40 hyper-hemisphere and SR30 inner hemisphere are the greatest stresses on spherical surface of lithium hydride samples. The radial residual stress σr of SR40 hyper-hemispherical and SR30 inner hemispherical sample is compressive stress and the circumferential residual stress σt is tensile stress.

Influence of welding speed and power on residual stress during gas tungsten arc welding (GTAW) of thin sections with constant heat input: A study using numerical simulation and experimental validation

The temperature distribution and residual stresses for a GTAW circumferential butt joint of AISI 304 stainless steel using numerical simulation have been evaluated. For evaluation of weld induced residual stresses, the analysis of heat source fitting was carried out with heat inputs ranging from 200 to 500J/mm to arrive at optimal heat input for obtaining proper weld penetration and heat affected zone (HAZ). For this chosen heat input, the influence of different weld speeds and powers on the temperature distribution and the residual stresses is studied. The heat source analysis revealed the best choice of heat input as 300J/mm. The residual stresses on the inner and outer surfaces, and along the radial direction were computed. Increase in temperature distribution as well as longitudinal and circumferential residual stresses was observed with the increase in weld speed and power. The validity of the results obtained from numerical simulation is demonstrated with full scale shop floor welding experiments.

Electro-thermo-mechanical Finite Element Analysis on DC Pulse Resistance Pressure Sintering Process of Zirconia Part

Some difficulties have arisen on appropriate design of the graphite dies, on applying the DC pulse resistance pressure sintering process, which is more efficient process than other conventional sintering processes such as hot pressing process, to a complex shaped part of non-conductive ceramics powder such as zirconia powder. In the present paper, the non-steady electro-thermo-mechanical finite element analysis of the sintering process of the zirconia cylindrical can was performed. As a result, it was found that the enough heating of the graphite dies that contacts with zirconia powder, and heat transmission from the die to zirconia powder was essential for the success of the sintering with adequate density. Moreover, the lower density region was found at the inside of the can during the process, which corresponded to the region where the convex shape formed in experiments. Furthermore, the high tensile residual circumferential stress was observed at the side wall from the simulation of the cooling process, which is caused by the different thermal expansion ratio of the graphite and zirconia materials. This stress was considered to be related with the fracture of the can longitudinally during cooling process in experiments.

Non-Euclidean Stress-Free Configuration of Arteries Accounting for Curl of Axial Strips Sectioned From Vessels

It is well known that arteries are subject to residual stress. In earlier studies, the residual stress in the arterial ring relieved by a radial cut was considered in stress analysis. However, it has been found that axial strips sectioned from arteries also curled into arcs, showing that the axial residual stresses were relieved from the arterial walls. The combined relief of circumferential and axial residual stresses must be considered to accurately analyze stress and strain distributions under physiological loading conditions. In the present study, a mathematical model of a stress-free configuration of artery was proposed using Riemannian geometry. Stress analysis for arterial walls under unloaded and physiologically loaded conditions was performed using exponential strain energy functions for porcine and human common carotid arteries. In the porcine artery, the circumferential stress distribution under physiological loading became uniform compared with that without axial residual strain, whereas a gradient of axial stress distribution increased through the wall thickness. This behavior showed almost the same pattern that was observed in a recent study in which approximate analysis accounting for circumferential and axial residual strains was performed, whereas the circumferential and axial stresses increased from the inner surface to the outer surface under a physiological condition in the human common carotid artery of a two-layer model based on data of other recent studies. In both analyses, Riemannian geometry was appropriate to define the stress-free configurations of the arterial walls with both circumferential and axial residual strains.

Analyzing the mechanisms of fatigue crack initiation and propagation in CRH EMU brake discs

A significant number of high-speed electric multiple units’ (EMU) brake discs, manufactured from forged steel, showed thermal cracks during work and NDT. There exist three kinds of cracks on the friction surface; namely, the crackle, radial crack and circumferential crack. Macro-morphologies of the friction surface indicate that the cracks appeared in the interior and edges of the hotspots. Crack growth methods include the single crack propagation and multiple crack connectivity. A finite element analysis (FEA) was performed to determine temperature and stress distribution in the brake disc as well as to estimate stress distribution during braking. Simulation results indicate more significant residual, circumferential tensile stress on the external friction surface after emergency braking. The maximum residual circumferential tensile stress is 200MPa after 300km/h emergency braking. In addition, there is only the circumferential compressive stress on a section which is a certain distance from the exterior of the friction surface, and the distance depends on braking conditions. Therefore, not taking into account thickness reduction of the friction surface due to wear, it can be concluded that when the cracks run along the thickness direction to the specified distance, they will cease to run along this direction and begin propagating mainly in the direction of the radius. In addition, based on the simulation results, a measure was presented to prevent and inhibit the crack propagation.

Stress Distribution in a Bilayer Elastic Model of a Coronary Artery

In earlier studies on stress distribution in arteries, a monolayer wall model was often used. An arterial wall consists of three layers, the intima, the media, and the adventitia. The intima is mechanically negligible as a stress supporting layer against the blood pressure in young healthy vessels, although it is important as an interface between blood and arterial wall. The media and adventitia layers are considered to support blood pressure. Recently, residual strain and a constitutive law for porcine coronary arteries have been investigated in separated media and adventitia. Using the data obtained through these investigations, a stress analysis considering residual stress (strain) in each layer was performed in this study, and residual strain and stress were computed for a bilayer model. The circumferential residual stress was compressive in the inner region, tensile in the outer region, and had discontinuity at the boundary between the media and adventitia. A peak circumferential stress occurred in the media at the boundary between the media and adventitia under a physiological condition, and an almost flat distribution was obtained in the adventitia. This pattern does not change under a hypertensive condition. These results suggest that a remodeling with hypertension occurs in the media.

Numerical Crack Growth Analysis in ICM Housing Using S-Version FEM

It has been reported that stress corrosion cracking damaged in-core monitor housing, which occurred in weld heat-affected zone because of the existence of residual stress. So it is important to evaluate crack growth behavior with high accuracy. In this study, crack growth behavior in ICM Housing is estimated using S-version FEM (S-FEM), which allows generation of core finite model and the detailed mesh representing the crack independently. At First, axial, slant and circumferential surface crack are assumed at two locations where residual stress fields are different from each other. One is isotropic residual stress field, and another is circumferential residual stress field. It is shown that crack growth behaviors are different under different residual stress fields. Next, effect of the slit, which exists between ICM Housing and Pressure Vessel is evaluated. It is shown that the existences of slit increases stress intensity factors of growing surface crack. Finally S-FEM results are compared with those of Influence Function Method (IFM), which assumes that an elliptical crack shape exists in a plate. It is shown that IFM result is conservative than that of S-FEM.