Initial Stress Distributions Research Articles

Characterization of residual stresses for LTB simulations of modern welded girders

A number of factors affect the lateral–torsional buckling (LTB) behaviour of steel members. Residual stresses are known to influence LTB in the inelastic range, with differing patterns between rolled and welded sections causing differences in inelastic LTB capacity between the two section types, even if geometry is identical. Finite element simulations can facilitate detailed investigation of this phenomenon; however, it is important that assumed initial residual stress distributions used in such simulations are accurate. While residual stress data are available for welded sections, existing proposed predictive models for these stresses are based on limited data sets, making it unclear if the models are appropriate for a broader range of sections. Therefore, to address the need for accurate LTB simulations in research, a new predictive residual stress model for modern welded girders is proposed in this study, based on recent residual stress measurements on welded sections. The proposed model takes section geometry and welding parameters into account and is calibrated with multiple data sets from the literature. Finite element simulations of LTB are carried out using the proposed model and an additional model proposed by Chernenko and Kennedy.

Residual stress evolution in partial and full axisymmetric forming processes

Expedient residual stress distributions offer extensive opportunities for improved product properties. Metal forming process chains provide an excellent opportunity for the targeted manipulation of residual stresses. The required purposeful process design has to take into account the possible inheritance of residual stress states along the process chain. The paper at hand reveals new insights into the evolution of residual stresses by a distinction between partial and full forming and an analytical model derived for axisymmetric forming. Presented results show the relevance of initial residual stress distributions especially for partial forming processes.

Finite Difference Method for the One-Dimensional Non-linear Consolidation of Soft Ground Under Uniform Load

Initial stress and additional effective stress distributions in soil greatly influence the degree of ground consolidation when calculating one-dimensional soft clay ground consolidation in deep soil. The one-dimensional nonlinear consolidation governing equations of soft ground under uniform loads are derived and solved with the finite difference method. This method is based on the assumptions that the initial stress in soil varies with the ground depth and the additional effective stress caused by external loads changes with both the ground depth and consolidation time, and the hyperbolic model of the soil stress-strain relationship. Formulas for the degree of consolidation and the settlement of the ground are presented. A case study shows that the degree of consolidation of the ground calculated with the finite difference method agrees with the traditional analytical solution, and the computational efficiency of the finite difference method can be effectively improved when the segmental calculation method is used throughout the consolidation process. The results of another example show that the settlement of the ground calculated with the finite difference method agrees with the in situ data. The suggested method can greatly simplify the consolidation calculation and has a high application value in engineering.

Moment rate of the 2018 Gulf of Alaska earthquake

The 2018 Gulf of Alaska earthquake (Mw 7.9) occurred in a region of the Pacific plate southwest of the Alaskan subduction zone. The earthquake was a strike-slip event, with the hypocenter located at a depth of about 25 km and a seismic moment equal to 0.96 × 1021 Nm. Two observed moment rates have been obtained by the Geoscope Observatory, France, and by the United States Geological Survey (USGS). Both of them can be interpreted as due to the failure of two asperities on the fault surface. We consider a discrete fault model, with two asperities of different areas and strengths, and show that the observed moment rates can be reproduced by appropriate values of the model parameters, as inferred from the available data. A good fit to the observed moment rates is obtained by a sequence of three dynamic modes of the system, including a phase of simultaneous slip of the asperities. The two moment rates are however characterized by different initial conditions, in terms of different initial shear stress distributions on the fault. Shear stresses on the asperities are calculated as functions of time during the event and show a similar evolution in the two cases, but with different final values. The model results show that the presence of simultaneous asperity motion can significantly increase the seismic moment of a large earthquake.

Global buckling behaviour of welded Q460GJ steel box columns under axial compression

This paper describes an experimental and numerical study on the global buckling behaviour of welded Q460GJ steel box columns. In the experimental programme, seven steel columns with different cross sections and wall thicknesses were tested under axial compression. The load capacity of steel columns was quantified. Comparisons were made between experimental results and design values calculated in accordance with national standards. Furthermore, numerical models were established in which initial geometric imperfections and residual stress distributions were considered. The model was validated against test data with reasonably good accuracy. A parametric study was conducted on the effects of initial geometric imperfections and normalised slenderness on the load capacity of box columns. Experimental and numerical results indicated that Q460GJ steel box columns could develop higher global buckling resistances than the values calculated from GB50017-2003 and Eurocode 3, but ANSI/AISC360-10 might not be safe for welded box columns with small width-thickness ratios. Therefore, the design approaches for conventional steel columns were modified so that the buckling behaviour of box columns fabricated of Q460GJ steel could be accurately evaluated.

Effects of Partial Edge Loading and Fibre Configuration on Vibration and Buckling Characteristics of Stiffened Composite Plates

In this work, the influence of uniaxial and biaxial partial edge loads on buckling and vibration characteristics of stiffened laminated plates is examined by using finite element method. As the initial pre-buckling stress distributions within an element are highly non-uniform in nature for a given loading and edge conditions, the critical loads are evaluated by dynamic approach. Towards this, a nine-node heterosis plate element and a compatible three-node beam element are developed by employing the effect of shear deformation for both the plate and the stiffeners respectively. In the structural modeling, the plate and the stiffener elements are treated separately, and then the displacement compatibility is maintained between them by using a transformation matrix. Effect of different parameters such as loaded edge width, position of loads, boundary conditions, ply-orientations and stiffener factors are considered in this study. Buckling results show that the uniaxial loaded stiffened plate with around (+30º/-30º)2 layup can withstand higher load irrespective of boundary conditions and loading patterns, whereas the maximum load resisting layup for the bi-axially loaded stiffened plate is purely dependent on edge conditions and loading patterns.

Residual stress measurement in an extra thick multi-pass weld using initial stress integrated inherent strain method

Residual stresses existing in a multi-pass butt joint with a thickness of 70 mm, using a flux-cored arc welding process, were measured by an inherent strain method (ISM). Since such a thick plate before welding contains a large amount of initial residual stresses (−300 to +100 MPa), the initial stresses were integrated with conventional ISM in order to determine the total residual stresses in a welded joint. Two methods named as initial stress integrated ISM and initial inherent strain integrated ISM were suggested for the consideration of the initial stress distributions through the thickness of base plates. The results show that there is a significant difference between the integrated ISM with initial stresses or initial inherent strain and the conventional ISM without initial stresses. The residual stresses measured by any of the initial stress integrated ISM and initial inherent strain integrated ISM agreed well with the neutron diffraction measurement. Thus, the proposed initial stress integrated ISM is a proper destructive measurement method in the case of thick weld joints.

Simulations of a Centrifuge Test with Lateral Spreading and Void Redistribution Effects

Numerical simulations of a centrifuge test, in which dissipation patterns, lateral spreading, and shear strain localization were measured and recorded, are performed for validation of the numerical modeling approach and insight on the deformation mechanisms. The constitutive model calibration process is performed based on available laboratory data and is described in detail. The model container and construction sequence are simulated to provide good approximations of the boundary conditions and initial stress distributions. Two approaches for simulating successive shaking events are presented and compared. The key observations and mechanisms from the centrifuge test, namely (1) the dynamic response and onset of liquefaction, (2) the amount and pattern of surface deformation, (3) the patterns of pore pressure dissipation and void ratio redistribution, and (4) the difference in response between a sand profile treated and not treated with liquefaction drains, are all reasonably captured and bounded by the simulations.

Pseudodynamic Source Characterization for Strike-Slip Faulting Including Stress Heterogeneity and Super-Shear Ruptures

Abstract Reliable ground‐motion prediction for future earthquakes depends on the ability to simulate realistic earthquake source models. Though dynamic rupture calculations have recently become more popular, they are still computationally demanding. An alternative is to invoke the framework of pseudodynamic (PD) source characterizations that use simple relationships between kinematic and dynamic source parameters to build physically self‐consistent kinematic models. Based on the PD approach of Guatteri et al. (2004), we propose new relationships for PD models for moderate‐to‐large strike‐slip earthquakes that include local supershear rupture speed due to stress heterogeneities. We conduct dynamic rupture simulations using stochastic initial stress distributions to generate a suite of source models in the magnitude M w 6–8. This set of models shows that local supershear rupture speed prevails for all earthquake sizes, and that the local rise‐time distribution is not controlled by the overall fault geometry, but rather by local stress changes on the faults. Based on these findings, we derive a new set of relations for the proposed PD source characterization that accounts for earthquake size, buried and surface ruptures, and includes local rise‐time variations and supershear rupture speed. By applying the proposed PD source characterization to several well‐recorded past earthquakes, we verify that significant improvements in fitting synthetic ground motion to observed ones is achieved when comparing our new approach with the model of Guatteri et al. (2004). The proposed PD methodology can be implemented into ground‐motion simulation tools for more physically reliable prediction of shaking in future earthquakes.

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

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

Statistics of Earthquake Stress Drops on a Heterogeneous Fault in an Elastic Half-Space

We investigate properties of earthquake stress drops in simulations of evolving seismicity and stress field on a heterogeneous fault. The model consists of an inherently discrete strike-slip fault surrounded by a 3D elastic half-space. We consider various spatial distributions of frictional properties and analyze results generated by 150–300 model years. In all cases, the self-organized heterogeneous initial stress distributions at the times of earthquake failure lead to stress drops that are systematically lower than those predicted for a homogeneous process. In particular, the large system-sized events have stress drops that are consistently ∼25% of predictions based on the average fault strength. The type and amount of assumed spatial heterogeneity on the fault affect the stress-drop statistics of small earthquakes ( M L <5) more than those of the larger events. This produces a decrease in the range of stress drops as the earthquake magnitudes increase. The results can resolve the discrepancy between traditional estimates of stress drops and seismological observations. The general tendency for low stress drops of large events provides a rationale for reducing the statistical estimates of potential ground motion associated with large earthquakes.

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.

Dynamic Stability of Disks With Periodically Varying Spin Rates Subjected to Stationary In-Plane Edge Loads

This paper presents an analysis of dynamic stability of an annular plate with a periodically varying spin rate subjected to a stationary in-plane edge load. The spin rate of the plate is characterized as the sum of a constant speed and a small, periodic perturbation. Due to this periodically varying spin rate, the plate may bring about parametric instability. In this work, the initial stress distributions caused by the periodically varying spin rate and the in-plane edge load are analyzed first. The finite element method is applied then to yield the discretized equations of motion. Finally, the method of multiple scales is adopted to determine the stability boundaries of the system. Numerical results show that combination resonances take place only between modes of the same nodal diameter if the stationary in-plane edge load is absent. However, there are additional combination resonances between modes of different nodal diameters if the stationary in-plane edge load is present.

The possibilities of uncemented glenoid component––a finite element study

Objective. (1) Determine the initial stress distributions within an uncemented implanted glenoid during elevation of the arm and to investigate whether failure is caused by stresses generated within this implant–bone structure. (2) Compare stress patterns between the uncemented design and two basic models of cemented prostheses. Design. The uncemented component consists of a polyethylene cup with a metal-backing. All material interfaces were assumed to be fully bonded. Background. Cemented glenoid components have been frequently vulnerable to failure within itself and at the cement–bone interface. A 3-D finite element analysis of an uncemented design is required to investigate whether clinical observations on failure can be better explained with a stress analysis. Methods. A 3-D finite element submodel an uncemented prosthesis was generated using CT-scan data and realistic loading conditions (humeral abduction, 30–180°). The submodelling approach was based on an overall solution of a complete scapula acted upon by all muscles, ligaments and joint reaction forces. Results. High Von Mises stresses (20–70 MPa) were generated in the metal-backing during abduction. Stresses were reduced in the polyethylene cup by 17–20% as compared to the cemented designs. Stresses in the underlying bone were substantially lower than to the natural glenoid. Stress-shielding can be observed in the trabecular bone underlying the prosthesis. The implant–bone interface is secure against interface failure at moderate loads, although the implant–bone (metal–bone) interface around the superior edge of the prosthesis is subject to high stresses (normal: 11.85 MPa, shear: 6.67 MPa) as compared to the cemented prosthesis. Whereas, the cement–bone interface, appears more likely to fail either at locations adjacent to the keel or at locations around the superior edge of the cemented design. The uncemented design therefore appeared to be a reasonable alternative to fixation with cement. Relevance Results of this study strongly agree with clinical and radiographic findings. Although indications of stress-shielding and separation of modular parts of the prosthesis were apparent, the implant–bone interface seems less likely to fail as compared to cemented designs. Once initial fixation of the implant is achieved, the uncemented design appears to have better prospects than cemented ones.

소형펀치-크리프 시험에 대한 응력해석과 일축 크리프 시험과의 상관성에 관한 연구

A basic research was performed to ensure the usefulness of Small Punch-creep(SP-creep) test for residual life evaluation of heat resistant components effectively. This paper presents analytical results of initial stress and strain distributions in SP specimen caused by constant loading for SP-creep test and its experimental correlations with uniaxial creep(Ten-creep) test on 9Cr1MoVNb steel. It was shown that the initial maximum equivalent stress, from FE analysis was correlated with steady-state equivalent creep strain rate, rupture time, , activation energy, Q and Larson-Miller Parameter, LMP during SP-creep deformation. The simple correlation laws, , adopted to established a quantitative correlation between SP-creep and Ten-creep test data. Especially, the activation energy obtained from SP-creep test is linearly related to that from Ten-creep test at as follows : .

Some characteristics of the stress field of the 1995 Hyogo‐ken Nanbu (Kobe) earthquake

We investigate the characteristics of the stress field associated with the 1995 Hyogo‐ken Nanbu (Kobe) earthquake. We use for the study a tomographic model of the fault slip inferred from the numerous near‐field recordings, and we calculate the space and time evolution of shear stress on the fault during the earthquake. We show that the spatial distribution of stress drop is very heterogeneous. The apparent strength of the fault at the onset of the earthquake is low (of the order of 1 MPa or less), which indicates that the pre‐earthquake tectonic shear stress was close to the static friction over most of the fault. At many locations the stress drop rotates significantly during sliding. As was originally proposed by Spudich [1992], we use the requirement of colinearity between the directions of maximum shear stress and instantaneous slip to determine the initial stress on the fault at the onset of the earthquake. The pre‐earthquake tectonic stress varies greatly over the fault and ranges from about 1 to 10 MPa. Average values of the initial and final shear stresses over the fault are 3.3 and 1.6 MPa, respectively, indicating that about half of the pre‐earthquake tectonic stress was released during the earthquake. There is a relatively strong correlation between the initial and final stress distributions, which suggests that intrinsic fault properties, not modified by the earthquake, control the spatial distribution of tectonic stress over the fault. We show that on average over the fault the dynamic friction coefficient is equal to about 40% of the static friction coefficient. Diagrams depicting the evolution of shear stress as a function of slip are consistent with slip‐weakening behavior, but their interpretation is questionable because of the poor resolution of the data at high frequency and because of the constraints imposed on the model to perform the inversion.

An Orthotropic Viscoelastic Winding Model Including a Nonlinear Radial Stiffness

A realistic and adaptive viscoelastic model for prediction of transient wound roll stress distributions is presented. The web material is taken to be orthotropic with a nonlinear radial stiffness dependent upon interlayer pressure. Viscoelastic behavior is represented by a generalized Maxwell model for creep written as a convolution integral. Numerical solutions to the resulting integral boundary value problem give both initial and transient stress distributions within the wound roll. The model is successfully compared to the analytical solution for a simple case of isotropy as well as to published works on this topic. In contrasting the solutions, the advantages and adaptability of this formulation will be readily seen.

A Superposition-Rayleigh-Ritz Method For Free Vibration Analysis Of Non-uniformly Tensioned Membranes

An accurate analytical method is described for establishing initial stress distributions in corner-tensioned rectangular membranes. With the stress distributions available it is shown how the Rayleigh-Ritz method is employed to obtain membrane free vibration frequencies and mode shapes. The initial stress distributions are obtained by the superposition of three judiciously chosen Airy stress functions. Verification tests are performed to demonstrate that this general computational method gives results in agreement with known classical problems where uniform edge loading is employed. The method described has immediate application in the static and dynamic analysis of large membranes proposed for space antennae.

Inverse computation of initial residual stress distributions for prediction of fatigue crack propagation lives.

The present authors proposed two schemes for predicting the fatigue lives of cracks propagating in residual stress fields using initial residual stress distribution. To make applications of the schemes possible for cases where residual stresses redistributed due to crack initiation and propagation are given, this paper presents a method for determining initial residual stress fields form redistributed residual stresses measured at several points. Determination of the initial residual stress distribution was effectively achieved by introducing fundamental residual stress distribution functions which satisfied physical requirements for the residual stress. The least residual criterion was used in the determination. A sensitivity matrix was proposed to evaluate the effect of errors involved in the measurements and to select the best combination of measuring points. Numerical simulations of the determination on initial residual stress fields and the prediction of fatigue crack propagation lives showed the usefulness of the proposed method.

Inelastic response of deeply submerged stiffened shells subjected to transient loads from explosions

The large deflection elastoplastic response of stiffened cylindrical shells subjected to transient loadings from explosions is considered. Because the cylinders are located at deep submergence, the effects of initial stress distributions due to hydrostatic pressure are included in the analysis. A large deflection elastoplastic shell theory is utilized in the analysis. This shell theory defines a yield surface at each cross section of the shell in terms of the moment and direct force components at the section. An associated flow rule is utilized to define the plastic‐strain rate. The EPSA (elastoplastic shell analysis) code is utilized in the analysis of the shell response to the dynamic loadings. Results obtained from the analysis have compared well with the results of experiments.