Two-dimensional Creep Research Articles

Study on two-dimensional creep effects of RC slab structures

Reinforced concrete (RC) slab structures are common in civil engineering, yet they are susceptible to creep under sustained loading. The creep effects significantly impact the biaxial stress distribution of reinforced concrete slabs. Existing creep analysis and computation methods for these structures have some limitations. Therefore, exploring an appropriate two-dimensional creep analysis approach is essential. The two-dimensional stress creep properties of concrete and Poisson's ratio of creep are used to create a two-dimensional creep transformation matrix. A two-dimensional creep calculation formula using the age-adjusted effective modulus method is established to improve reinforced concrete slab creep analysis. Based on the stress states and geometrical characteristics of RC slabs, two-dimensional creep calculation methods are suitable for plain concrete slabs, reinforced concrete slabs with longitudinal reinforcement, and reinforced concrete slabs with both longitudinal and transverse reinforcement. Deflection rises due to the creep effect in the plain concrete slab, although the longitudinal and transverse stresses increase relatively slightly. The effect of the longitudinal reinforcement on deflection in RC slabs is negligible; as the longitudinal stress in concrete decreases, reinforcement stress rises with obvious stress redistribution; the lateral stress decreases compared with plain concrete but rises. The transverse reinforcement of RC slab affects concrete deflection and transverse stress twice as much as longitudinal reinforcement. Prolonged loading considerably redistributes longitudinal and transverse stresses in the reinforced concrete slab's concrete and steel reinforcing.

Analysis of finite creep strains in aluminum plates at static and cyclic loading

The formulation of the problem and the basis of the method for solving two-dimensional creep problems for the case of finite strains are presented. The method is based on the Arbitrary Lagrange-Euler (ALE) approach in numerical modeling using FEM. The method is implemented in the form of additional units to the creep calculation software. The plane stress state is considered. The results of an experimental study of the creep of AlMg6 alloy specimens under static and cyclic loading are described. The obtained creep curves were used to verify the calculation method. It is shown that for a material with viscous creep properties, calculations using finite strains quite satisfactorily describe the tertiary, accelerated section of the creep curve. The creep of square plates in tension by static and cyclically varying traction was considered, data on their shape change and stress redistribution were obtained. A significant intensification of creep due to the addition of a cyclic component to the static loading was established.

Method and software for finite element solution of two-dimensional creep problems at large deformations

The paper presents the formulation of a two-dimensional problem of the creep theory for the case of finite strains. A description of the foundations of the calculation method presents. The method is based on the use of the generalized Lagrange-Euler (ALE) approach, in which the boundary value problem in the current solid configuration is solved by using FEM. A triangular element is involved in the numerical modeling. At each stage of creep calculations in the current configuration, the initial problem is solved numerically using the finite difference method. The preprocessing data preparation is carried out in the homemade RD program, in which two-dimensional model is surrounded by a mesh of special elements. This feature implements the ALE algorithm for the motion of material elements along the model. The examples of preprocessing as well as of the mesh rebuilding in the case of finite elements transition are given. Creep calculations are performed in the developed program, which is based on the use of the FEM Creep software package in the case of finite strains. The regular mesh is used for calculations, which allow us to use the efficient algorithm for transition between current configurations. The numerical results of the creep of specimens made from aluminum alloys are compared with the experimental and calculated ones obtained by integrating the constitutive equations. It was concluded that for material with ductile type of fracture the presented method and software allow to obtain results very close to experimental only by use of creep rate equation. Creep simulations of material with mixed brittle-ductile fracture type demand use the additional equation for damage variable.

Numerical Analysis of Soil Settlement Prediction and Its Application In Large-Scale Marine Reclamation Artificial Island Project

Abstract In an artificial island construction project based on the large-scale marine reclamation land, the soil settlement is a key to affect the late safe operation of the whole field. To analyze the factors of the soil settlement in a marine reclamation project, the SEM method in the soil micro-structural analysis method is used to test and study six soil samples such as the representative silt, mucky silty clay, silty clay and clay in the area. The structural characteristics that affect the soil settlement are obtained by observing the SEM charts at different depths. By combining numerical calculation method of Terzaghi’s one-dimensional and Biot’s two-dimensional consolidation theory, the one-dimensional and two-dimensional creep models are established and the numerical calculation results of two consolidation theories are compared in order to predict the maximum settlement of the soils 100 years after completion. The analysis results indicate that the micro-structural characteristics are the essential factor to affect the settlement in this area. Based on numerical analysis of one-dimensional and two-dimensional settlement, the settlement law and trend obtained by two numerical analysis method is similar. The analysis of this paper can provide reference and guidance to the project related to the marine reclamation land.

Basic approach on creep deformation and damage of high temperature structural materials under temperature gradient condition

Deformation and failure behavior of a Ni-base superalloy specimen with thermal barrier coating were investigated when it was subjected to external load under a graded temperature condition. The experimental results demonstrated that the crack density in the ceramic top coat was higher at lower temperature side than that at higher temperature side. It was also observed that the inelastic strain rate of the specimen was higher, compared with that of the laboratory creep test without temperature gradient. In order to get basic understanding on the above specific behaviors, a simple two-dimensional creep deformation model was proposed, taking account of the effect of temperature gradient. In the model the stress state was analyzed when the material is uniformly deformed associating with diffusion creep. The numerical calculation result predicted the following noteworthy phenomena: higher stress state would be build up at the lower temperature side than at the higher temperature side, and this state is promoted with time. Cumulative creep strain develops more quickly at the lower temperature side than at the high temperature side. These predictions provided some reasonable explanations to the experimental results.

Linear and Non-linear Creep models for a multi-layered concrete composite

One- and two-dimensional linear and nonlinear creep models for predicting the time-dependent behavior of a concrete composite under compression are proposed. These models use the analytical and iterative solutions of the Volterra integral equation. The analytical approach is based on the age-adjusted effective modulus method, and the nonlinear technique applies an iterative approach to the system of non-linear equations, implying a generalization of the principle of superposition. Both models are validated in this study.It has been recently found that negative values of the aging coefficient can emerge in early age multi-layered composites when the stress redistribution between the layers is governed by the combination of considerably different creep strains and aging of the layers.In the plane-strain state, the two-dimensional creep analysis of multi-layered composites yields the same vertical stress-time history as that in a one-dimensional case if the Poisson ratios of the layers are equal. This is valid even though the average value of the vertical stress used to calculate the Volterra integral term is dependent on the Poisson ratio of the layers. In particular, the evolution of vertical stress with time is dependent only on the vertical strain and compatibility conditions in a direction parallel to the lamination.A fracture mechanics approach is also introduced to predict the gradual degradation of long-term strength for a multi-layered composite under a sustained compressive load. The results show that the stress redistribution near the crack-tip under the final period of a high level of sustained loading may lead to an additional required compressive stress for complete failure of the composite. Long-term failure primarily begins with the less deformable (stiffer) layers because the more-deformable layers can relieve the initial stresses. Thus, the long-term strength of the composite can exceed its instantaneous strength for early age composites or for composites composed of layers that possess considerably different creep and aging properties.

Time-dependent creep fracture using singular boundary elements

This paper presents a procedure for modelling singular crack tip regions of creeping, cracked structural components using singular boundary elements. These special boundary elements correctly simulate the time-dependent singular behaviour of stress and strain fields at the crack tip of creeping materials. The investigated structural components are considered to undergo time-dependent, two-dimensional creep deformation and to be subjected to remote loading conditions. The deformation of the components is assumed to be described by the elastic power law creep model. Examples of various crack problems are investigated to illustrate the efficiency of the proposed singular boundary elements for analysing creep stress and strain distribution problems and for determining some important creep fracture parameters. The effectiveness of the proposed approach is demonstrated and its accuracy is compared with the results obtained by finite element solutions for different creep conditions.

An Efficient Numerical Method for Studying Interfacial Motion in Two-Dimensional Creeping Flows

We present new methods for computing the motion of two-dimensional closed interfaces in a slow viscous flow. The interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex-variable theory for the biharmonic equation. The numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole-based iterative solution procedure, which requires only O(N) operations where N is the number of nodes in the discretization of the interface. The interface is described spectrally, and we use evolution equations that preserve equal spacing in arclength of the marker points. A small-scale decomposition is performed to extract the dominant term in the evolution of the interface, and we show that this dominant term leads to a CFL-type stability constraint. When in an equal arclength frame, this term is linear and we show that implicit time-integration schemes that are explicit in Fourier space can be formulated. We verify this analysis through several numerical examples.

Steady-state creep of a composite analysed by an energy balance method

The purpose of this paper is to analyse steady-state creep of a composite with spheroidal inclusions aligned along a tensile direction. It is an extension of a previous study of two-dimensional creep by Mori et al . (1997, Phil. Mag. Lett ., 75, 359). As in the previous study, interfacial diffusion and sliding play essential roles in inducing steady-state creep. A new method of analysis is introduced. Basically, it calculates energy dissipation rates from the rates of diffusional flow and sliding. Both rates are geometrically connected to a creep rate, in a manner depending on the shape of inclusions. By specifying the matrix creep law, a simple relation between the steady-state creep rate and an external tensile stress is obtained. Coble creep is also analysed as a simple and extreme case to which the present method can apply: grains in a polycrystal are treated as inclusions and deformation of plastic character is achieved by boundary diffusion and sliding.

Two-dimensional creep analysis of structural adhesive joints

A two-dimensional finite element program was developed to study the creep behaviour of bonded joints for two structural adhesives. The program used multiaxial viscoplasticity theory, and modelled creep by reducing the yield stress to zero. The necessary parameters for the finite element model were obtained from creep tests on beam specimens of the bulk adhesives. The results showed that creep led to a more even distribution of the stresses with the peak normal and shear stresses being reduced. However, the shear strain showed a large increase. The former effect could be beneficial in terms of joint strength, but the latter effect would be detrimental.

A Computational Model for Predicting the Life of Tubes Used in Petrochemical Heater Service

This paper describes a model developed for computer simulation of stresses in heater tubes used in petrochemical service. The model predicts the damage to the tube material and thus provides an assessment of both tube design life and residual-life of tubes that have been subjected to service exposure. The analysis procedure has been incorporated into a computer code (TUBE), which has been applied to a number of applications for heat-resistant alloys. The focus of these applications has been to address the effect of sustained and cyclic loadings on the predicted service lives of tubes used in elevated temperature service. The model was originally developed at Battelle-Columbus in the 1970s, as part of an industrial group research program on “Materials for Steam Reformer Furnaces.” The computer model uses conventional numerical approaches [1–4] to solve finite element models of two-dimensional creep problems. This paper addresses the practical difficulties of applying such models to real service conditions and real commercial alloys.

Application of Bipolar Coordinates to the Two-Dimensional Creeping Motion of a Liquid. III. Separation in Stokes Flows

When there is a linear shear flow along a plane wall with a cylindrical depression, flow penetrating into the cavity separates from the wall, if the ratio of the depth of the cavity to the width of its mouth exceeds a critical value which is about 0.32. The pressure becomes infinite at the sharp edges of the cavity, while for the flow over a projection the pressure is a continuous function which on the boundary has two extremum values symmetrically about the cylindrical portion. As another example of separation in Stokes flows, the flow generated by the rotation of a circular cylinder which is eccentrically encircled with a larger cylinder or placed near a plane is considered.

Application of Bipolar Coordinates to the Two-Dimensional Creeping Motion of a Liquid. II. Some Problems for Two Circular Cylinders in Viscous Fluid

The bipolar coordinate solution of the two-dimensional Stokes equations is applied to flows around two circular cylinders. It is proved that there are three cases which this kind of solutions can describe. Solutions are presented for a cylinder revolving eccentrically in a cylindrical frame, a cylinder in the neighborhood of a plane wall and two cylinders in rotary motion as a pair.

Application of Bipolar Coordinates to the Two-Dimensional Creeping Motion of a Liquid. I. Flow over a Projection or a Depression on a Wall

The bipolar coordinate solution of the two-dimensional Stokes equations is applied to the flow along a plane wall with a projection or a depression. The resultant integral is evaluated by the calculus of residues to give an eigenvalue expansion and the eigenvalues are calculated for various values of the parameter. Special consideration is made for a cylinder inlaid in the wall.

Progress Report on Tubular Creep Tests

Abstract This paper is a progress report describing the results which have been obtained on the creep of tubular specimens. The first part of this work was described in a previous paper. In this investigation similar apparatus and similar specimens are employed, but an attempt is made to correlate the stress between the tensile specimens and the tubular specimens more accurately. Also, tubes with thinner walls have been used. The results obtained to date indicate that the longitudinal creep of the tubes is substantially zero, and that the circumferential creep is approximately the same as the creep in the tensile specimen with a stress equivalent to the circumferential stress in the tube. In a companion paper, Professor Soderberg derives the relations in two-dimensional creep, and applies them to the experimental values.