Numerical solution of cracked thin plates subjected to bending, twisting and shear loads

A semi-analytical method namely fractal finite element method is presented for the determination of mode I and mode II moment intensity factors for thin plate with crack using Kirchhoff's theory. Using the concept of fractal geometry, infinite many of finite elements is generated virtually around the crack border. Based on the analytical global displacement function, numerous degrees of freedom (DOF) are transformed to a small set of generalised coordinates in an expeditious way. The stress intensity factors can be obtained directly from the generalized coordinates. No post-processing and special finite elements are required to develop for extracting the stress intensity factors. Examples of cracked plate subjected to bending, twisting and shear loads are given to illustrate the accuracy and efficiency of the present method. The influence of finite boundaries on the calculation of the moment intensity factors is studied in details. Very accuracy results when compare with the theoretical and numerical counterparts are found.     

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

In this paper, the non‐isothermal elasto‐plastic behaviour of multiphase geomaterials in dynamics is investigated with a thermo‐hydro‐mechanical model of porous media. The supporting mathematical model is based on averaging procedures within the hybrid mixture theory. A computationally efficient reduced formulation of the macroscopic balance equations that neglects the relative acceleration of the fluids, and the convective terms is adopted. The modified effective stress state is limited by the Drucker–Prager yield surface. Small strains and dynamic loading conditions are assumed. The standard Galerkin procedure of the finite element method is applied to discretize the governing equations in space, while the generalized Newmark scheme is used for the time discretization. The final non‐linear set of equations is solved by the Newton method with a monolithic approach. Coupled dynamic analyses of strain localization in globally undrained samples of dense and medium dense sands are presented as examples. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A numerical study of the regularization properties of the finite element model is shown and discussed. A non‐isothermal case of incipient strain localization induced by temperature increase where evaporation takes place is also analysed. Copyright © 2016 John Wiley & Sons, Ltd.     

Support-induced restraint effect of thin-walled tube in a steam generator subjected to combined pressure and bending load

The restraint effects of support plates on limit load (LL) are evaluated for thin-walled tubes subjected to combined internal pressure and bending loads. To achieve this goal, three-dimensional (3D) finite element (FE) analyses assuming elastic-perfectly plastic material behaviour are carried out for tubes with various sizes of circumferential cracks. Two crack locations, both the top of the tube sheet (TTS) and transition regions, where circumferential cracks have been found in many steam generators during operation, are considered. FE analysis results show that LLs for the circumferential cracks are significantly affected by the boundary conditions of the tube and that the resulting LL solutions can be simply applied to the practical integrity assessment of steam generator tubes, because the comparison between experimental data and FE analysis results shows a good agreement.     

Strain rate concentration and dynamic stress concentration for double‐edge‐notched specimens subjected to high‐speed tensile loads

Engineering plastics provide superior performance to ordinary plastics for wide range of the use. For polymer materials, dynamic stress and strain rate may be major factors to be considered when the strength is evaluated. Recently, high‐speed tensile test is being recognized as a standard testing method to confirm the strength under dynamic loads. In this study, therefore, high‐speed tensile test is analysed by the finite element method; then, the maximum dynamic stress and strain rate are discussed with varying the tensile speed and maximum forced displacement. The maximum strain rate increases with increasing the tensile speed u/t, but the strain rate concentration factor is found to be constant independent of tensile speed, which is defined as the maximum strain rate appearing at the notch root over the average nominal strain rate at the minimum section . It is found that the strain rate at the notch root depends on the dynamic stress rate at the notch root and independent of the notch root radius ρ. It is found that the difference between the static and dynamic maximum stress concentration (σ_yA,max ? σ_yA,st) at the notch root is proportional to the tensile speed when u/t = 5000 mm/s. Strain rate concentration factors are also discussed with varying the notch depth and specimen length. Based on the elastic strain rate concentration factor, the master curve is obtained useful for understanding the impact fracture of polycarbonate for the wide range of temperature and impact speed.     

New plastic collapse moment equations of defect-free and throughwall circumferentially cracked elbows subjected to combined internal pressure and in-plane bending moment

Closed-form plastic collapse moments (PCM) equations were earlier proposed for throughwall circumferentially cracked (TCC) elbow subjected to pure in-plane bending moment. However, an elbow is often subjected to combined internal pressure and bending moment in actual service condition. Therefore, the present study investigates the effect of internal pressure on the in-plane PCM of a TCC elbow. The PCM of a cracked elbow is usually expressed as a product of two parameters: PCM of a defect-free elbow multiplied by a weakening factor due to the crack. Therefore, the present study also includes analysis of defect-free elbows. Elastic-plastic finite element analysis is employed for the present analysis. A total of 396 cases of elbows with various sizes of circumferential cracks (2θ = 0-150°), different wall thickness (R/t = 5-20), different levels of normalized internal pressure (p = PR/(tσ_y) = 0-1), different elbow bend radii (R_b/R = 2,3) and two different bending modes, namely closing and opening are considered in the analysis. Elastic-perfectly plastic stress-strain response of material is assumed. The load in the elbows is split in two components: a constant internal pressure applied initially followed by in-plane bending moment monotonically increasing in definite steps. PCM are evaluated from moment—end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate PCM of TCC and defect-free elbows subjected to combined internal pressure and in-plane closing/opening bending moment. Attempt has been made to compare the predictions of the proposed equations with the available experimental/numerical results and to rationally explain the behaviour where no experimental/numerical data is available for comparison.     

CDM prediction of creep failure modes in thin and thick section Cr‐Mo‐V Butt‐welded pipes under combined internal pressure and end loads at temperatures in the range 540–620 °C

The paper examines the dependence of creep failure modes of butt‐welded pipes upon: temperatures in the range 540–620 °C; the ratio of axial to pressure loadings (loading condition); and, load levels which result in failure times in the region 2000–250 000 h. Continuum damage mechanics (CDM) analyses have been used to analyse two extreme geometries: thin section pipes (4.52 mm) and thick section steam pipes (46 mm) of the type found in power generation plant. The thick pipes have been selected to allow through‐thickness constraint to be developed. Two predominant modes of failure have been predicted: Fusion Boundary failure and Type IV failure. For the thin section pipes the modes of failure are not strongly dependent on applied loading levels, and loading condition, but are dependent on temperature: at 540 °C failure is in the Fusion Boundary and at 620 °C it is in the Type IV region. Failure mode in the thick pipes is dependent on temperature, and applied loading levels, but is essentially independent of loading condition. At 540 and 565 °C failure is in the Fusion Boundary; whereas at 575 °C, failure is in the Type IV region at higher applied stress levels, and in the Fusion Boundary at lower applied stress levels.     

An efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage

This paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to quasistatic or dynamic loading conditions in a large deformation context. The main features of this algorithmic treatment are as follows:

• A unified treatment for the analysis and implicit time integration of thermo‐elasto‐viscoplastic constitutive equations including damage that depends on the strain rate for dynamic loading conditions. This formalism enables us to use dynamic thermomechanically coupled damage laws in an implicit framework.
• An implicit framework developed for time integration of the equations of motion. An efficient staggered solution procedure has been elaborated and implemented so that the inertia and heat conduction effects can be properly treated.
• An operator split‐based implementation, accompanied by a unified method to analytically evaluate the consistent tangent operator for the (implicit) coupled damage–thermo‐elasto‐viscoplastic problem.
• The possibility to couple any hardening law, including rate‐dependent models, with any damage model that fits into the present framework.

All the developments have been considered in the framework of an implicit finite element code adapted to large strain problems. The numerical model will be illustrated by several applications issued from the impact and metal‐forming domains. All these physical phenomena have been included into an oriented object finite element code (implemented at LTAS‐MN ²L, University of Liège, Belgium) named Metafor.Copyright © 2013 John Wiley & Sons, Ltd.