On the detachment of step-tapered doublers: Part 2—evolution of pressure loaded structures

One-dimensional edge debonding of layerwise step-tapered patches from both flat and cylindrical structures subjected to applied pressure is studied in the context of the general formulation presented in Part 1. Numerical simulations based on analytical solutions of the problems of interest are performed and intricate results presented in the form of threshold curves/delamination paths for various taper angles and support conditions. Configurations corresponding to full contact of the debonded segments, edge contact of the debonded segments and no contact of the debonded segments of the evolving composite structure are included in the model and found to significantly affect the predicted behavior of the debonding structure as does the manner of support. The degree of taper is generally found to influence the onset and characteristics of debonding in a nontrivial manner. It is seen that in many instances, the introduction of edge taper within a wide range of angles often enhances the structures propensity for debonding, rather than diminishing it, both with regard to the critical load level and with regard to the stability and extent of debond propagation.     

On the detachment of step-tapered doublers : Part 1—foundations

One-dimensional edge debonding of layerwise step-tapered patches from both flat and cylindrical structures is examined. The problems are approach from a unified point of view, as propagating boundary problems in the calculus of variations, with the models for both flat and curved structures being formulated simultaneously. The effects of a contact zone adjacent to the bonded region are incorporated as is the phenomenon of edge-point contact. The formulation results in a selfconsistent representation of the various intact and debonded segments of the composite structure comprised of a multilayer patch and a base structure. It concurrently yields the conditions which establish the locations of the propagating boundary of the bonded (intact) region, and the propagating boundary of the contact zone. The former condition yields the selfconsistent and physically interpretable expressions for the corresponding energy release rates for debonding. The conditions governing edge-point contact are likewise established. Three types of loading conditions are considered : (i) in-plane/circumferential tension, (ii) three-point transverse loading, and (iii) applied transverse (internal ) pressure. It is shown analytically, within the context of the mathematical models employed for both flat and curved structures, that of the loading types considered the third admits a contact zone for certain common conditions of the supports. Results of numerical simulations, based on analytical solutions, pertaining to the test configurations of flat structures subjected to applied in-plane tension and three-point transverse loading are presented for various taper angles and compared.     

On the inelastic behavior of solids — Part 1: Twinning

Recently, Wineman and Rajagopal [1990] “On a Constitutive Theory for Materials Undergoing Microstructural Changes,” Arch. Mech., 42, 53 and Rajagopal and Wineman [1992] “A Constitutive Equation for Nonlinear Solids which Undergo Deformation Induced Microstructural Changes,” Int. J. Plasticity, 8, 385, developed a theory that was particularly well suited to describing the inelastic behavior of polymeric materials. Here, we draw upon their ideas and generalize them to include a much larger class of materials. The versatility and efficacy of the theory are illustrated by studying the problem of twinning within the context of the theory. We find that the predictions of the theory are remarkably close — both qualitatively and quantitatively — with the experimental results of Madhava et al. [1972] “Discontinuous Twinning during Essentially Elastic Compression of Steel at 4.2K,” Phil. Mag., 25(2), 519 and Madhava and Armstrong [1974] “A Constitutive Relation for Deformation Twinning at High Strain Rates,” in Rohde, R.W., Butcher, B.M., Holland, J.R., and Karnes, C.H., eds., Metallurgical Effects at High Strain Rates. Plenum, New York, 1974.     

Mathematical and numerical modeling of the non-associated plasticity of soils—Part 2: Finite element analysis

The method of the implicit standard material has allowed the formulation of a consistent mathematical model of the boundary value problem for the non-associated plasticity of soil. The mean accomplished steps are the achievement of the bipotential function, the recovering of the stress–strain relationship under a normality rule, introduction of the bifunctional and the proof of the solution existence. Here the mathematical model is discretized by the finite element method. First, the stress update scheme was formulated, the tangent matrix is explicitly derived and then the non-linear system is solved by the Newton–Raphson method where a new algorithm using a symmetrical tangent matrix is improved. This is in opposition to conventional non-associated plasticity, which uses a non-symmetric tangent matrix. Through the numerical examples we show the feasibility and the efficiency of the algorithm. It is also seen that we perform some studies of the numerical solutions, particularly the comparison between associated and non-associated limit load.     

Study on steerability of articulated tracked vehicles — Part 1. Theoretical and experimental analysis

This paper presents theoretical and experimental analysis of steering performance of articulated tracked vehicles on level ground. A mathematical model for predicting the steerability of articulated units has been developed and computerized for numerical application. The accuracy of the analog has been verified by scale model tests.From the results of the simulation and scale model tests it was found that steerability was significantly improved and required sprocket torques for steering and track slippage were considerably decreased in articulated tracked vehicles when compared with a single and coupled tracked vehicles.     

Mathematical and numerical modeling of the non-associated plasticity of soils—Part 1: The boundary value problem

The soil is characterized by the influence of the hydrostatic stress, which leads to a yield surface with a shape of a pyramid for Mohr–Coulomb criteria and a shape of a cone for Drucker–Prager one. These materials are also characterized by a non-associated plasticity where the plastic yielding rule does not follow the normality rule. The usual mechanical models use two independent functions to describe this particular collapse. Unfortunately, this manner broke the model formulation. The purpose of this work is to present a consistent formulation of the non-associated plasticity of soil. The frame of the mathematical analysis is the concept of the implicit standard material. The cornerstone of this new idea is the construction of a single function called the bipotential playing in the same time the roles of the yield surface and the plastic potential. The bipotential concept is then intended to involve the constitutive law, cover the normality rule even for the non-associated soil and the proof of the solution existence. The formulation was initially performed for the case of a regular point out of the cone apex and in present, it is extended to the irregular point located at the apex. The paper presents firstly the implicit standard material method. Then, the methodology to build a full model for the boundary value problem is detailed. Particular expressions and relations are sufficiently explained and discussed. Attention is made to the evolution problem and the variational principles related to the elastic–plastic behavior.     

Biaxial crushing of honeycombs: —Part 1: Experiments

The in-plane compression and crushing of honeycombs is known to be closely related to the crushing behavior of the broader class of space filling cellular solids. Previously, the authors conducted an extensive study of uniaxial crushing of a polycarbonate honeycomb with circular cells. In this paper the same honeycomb is crushed biaxially. The crushing was performed in a custom testing facility between rigid platens which can be moved independently in two orthogonal directions. The facility allows testing at various biaxiality ratios and volume reductions as high as 95%. The facility was used to conduct several series of biaxial crushing experiments on nearly square honeycomb specimens (18×21 cells) . In each experiment we recorded the true stress–displacement responses in the x- and y-directions as well as full field views of the deformation using a video camera. Biaxial crushing is quite complex and the prevalent mechanisms of collapse depend on the biaxiality ratio (γ) . As is the case in uniaxial crushing, the onset of collapse involves localized instabilities, however, the extent of localized deformation varies with γ. The energy absorption capacity of the material depends on γ. The highest energy is required when the specimen is crushed at the same rates in the two directions.     

On the effect of Lüders bands on the bending of steel tubes. Part II: Analysis

Part II of this study presents a modeling framework that is shown to successfully simulate all aspects of the inhomogeneous bending of tubes associated with Lüders banding reported in Part I. The structure is discretized with solid finite elements using a mesh that is fine enough for Lüders bands to develop and evolve. The material is modeled as a finitely deforming, J₂ type, elastic–plastic solid with an “up–down–up” response over the extent of the Lüders strain, followed by hardening. Regularization of the solution was accomplished by introducing a mild rate dependence of the material. Simulation of the rotation controlled bending experiments confirmed most of the experimental observations and revealed additional details of the localization. Thus, the initial uniform-curvature elastic regime terminates with the nucleation of localized banded deformation on the tensioned and compressed sides of the tube. The bands appear in pockets that propagate into the hitherto intact part of the structure while the moment remains essentially unchanged. The tube develops two curvature regimes; a relatively high curvature in the Lüders deformed section and a low curvature in the unaffected one. Simultaneously, the plasticized zone develops higher ovalization and wrinkles with a wavelength that corresponds to the periodicity of the banded pockets. For tubes with lower D/t and/or shorter Lüders strain the higher curvature eventually spreads to the whole structure at which point homogenous bending resumes. For tubes with higher D/t and/or longer Lüders strain the localized curvature, ovalization, and wrinkle amplitude are larger and cannot be sustained; the tube collapses prematurely leaving behind part of its length essentially undeformed. For every tube D/t there exists a threshold of Lüders strain separating the two types of behavior. This bounding value of Lüders strain was studied parametrically.     

A comparative study on design standards of screw conveyors in China,Germany and the USA — Part I: Theoretical calculation and quantitative analysis

Screw conveyors, widely used devices for transporting bulk materials, play an irreplaceable role in the modern industrial system. Despite of their traditional advantages, designers of screw conveyors still heavily rely on their own country’s experiments and standards, which are closely related to empirical data. Therefore, the same conveying task often results in different designs. This work aims to compare the design standards of screw conveyors in China, Germany and the USA. Based on related standards acquired from renowned associations in the three countries, the similarities and particularities of these design guidances are compared. With preforming the geometrical and operational designs for horizontal, slightly inclined and vertical conveyance of three representative bulk solids (barley, lignite, sand), the advantages and disadvantages of these semi-empirical designs are comprehensively presented. Furthermore, the potential influence of empirical coefficients, which are not explicitly documented, are extensively discussed. By analysing all outcomes, the compatibility and applicability of each standard are qualitatively assessed.     

Variational principle of hybrid energy and the fundamentals of 3-D laminate theory—A new approach for the analysis of interlaminar stresses in composite laminates

This paper discusses the discontinuity of stresses and strains at interlaminar surfaces of the composue laminate and presents a 3-D laminate theory for composite materials. This paper also presents a new type of elastic energy based on the globally continuous variables in laminates, different from the traditional potential energy and complementary energy. Then, a variational principle corresponding to the 3-D laminate theory is developed. The theory and the principle could be a basis of verifying the 2-D laminate theory and determining the interlaminar stresses near the free edges.     

On the effect of Lüders bands on the bending of steel tubes. Part I: Experiments

In several practical applications hot-finished steel pipe that exhibits Lüders bands is bent to strains of 2–3%. Lüders banding is a material instability that leads to inhomogeneous plastic deformation in the range of 1–4%. This work investigates the influence of Lüders banding on the inelastic response and stability of tubes under rotation controlled pure bending. Part I presents the results of an experimental study involving tubes of several diameter-to-thickness ratios in the range of 33.2–14.7 and Lüders strains of 1.8–2.7%. In all cases the initial elastic regime terminates at a local moment maximum and the local nucleation of narrow angled Lüders bands of higher strain on the tension and compression sides of the tube. As the rotation continues the bands multiply and spread axially causing the affected zone to bend to a higher curvature while the rest of the tube is still at the curvature corresponding to the initial moment maximum. With further rotation of the ends the higher curvature zone(s) gradually spreads while the moment remains essentially unchanged. For relatively low D/t tubes and/or short Lüders strains, the whole tube eventually is deformed to the higher curvature entering the usual hardening regime. Subsequently it continues to deform uniformly until the usual limit moment instability is reached. For high D/t tubes and/or materials with longer Lüders strains, the propagation of the larger curvature is interrupted by collapse when a critical length is Lüders deformed leaving behind part of the structure essentially undeformed. The higher the D/t and/or the longer the Lüders strain is, the shorter the critical length. Part II presents a numerical modeling framework for simulating this behavior.     

Fracture mechanics analysis on Smart-Cut~ technology.Part 1:Effects of stiffening wafer and defect interaction

In the present paper,continuum fracture mecha-nics is used to analyze the Smart-Cut process,a recentlyestablished ion cut technology which enables highly efficientfabrication of various silicon-on-insulator(SOI)wafers ofhigh uniformity in thickness.Using integral transform andCauchy singular integral equation methods,the mode-I andmode-Ⅱ stress intensity factors,energy release rate,and crackopening displacements are derived in order to examine seve-ral important fracture mechanisms involved in the Smart...     

Limit analysis and homogenization of porous materials with Mohr–Coulomb matrix. Part II: Numerical bounds and assessment of the theoretical model

This second part of the two-part study is devoted to the numerical Limit Analysis of a hollow sphere model with a Mohr–Coulomb matrix and its use for the assessment of theoretical results. Brief background and fundamental of the static and kinematic approaches in the context of numerical limit analysis are first recalled. We then present the hollow sphere model, together with its axisymmetric FEM discretization and its mechanical position. A conic programming adaptation of a previous iterative static approach, based on a piecewise linearization (PWL) of the plasticity criterion, was first realized. Unfortunately, the resulting code, no more than the PWL one, did not allow sufficiently refined meshes for loss of convergence of the conic optimizer. This problem was solved by using the projection algorithm of Ben Tal and Nemriovski (BTN) and the (interior point) linear programming code XA. For the kinematic approach, a first conic adaptation appeared also inefficient. Then, an original mixed (but fully kinematic) approach dedicated to the general Mohr–Coulomb axisymmetric problem was elaborated. The final conic mixed code appears much more robust than the classic one when using the conic code MOSEK, allowing us to take into account refined numerical meshes. After a fine validation in the case of spherical cavities and isotropic loadings (for which the exact solution is known) and comparison to previous (partial) results, numerical lower and upper bounds (a posteriori verified) of the macroscopic strength are provided. These bounds are used to assess and validate the theoretical results of the companion (part I) paper. Effects of the friction angle as well as that of the porosity are illustrated.     

Travelling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchange — Part 1

We develop a model for solute transport in porous media, which takes into account equilibrium and nonequilibrium multiple-site adsorption. Binary ion exchange is included. Adsorption rate formulations and their isotherms are reviewed and their mathematical properties investigated. This forms the basis of the study of travelling-wave solutions in the second part of the paper.This work was supported by the EC project Filtration and Nonlinear Diffusion Processes (Contract No. SC1-OO19-C(TT)).     

Hidden components of 3D-DIC: Triangulation and post-processing—Part 3

Experimental Techniques -     

Dynamics of trains and train-like articulated systems travelling in confined fluid—Part 1: Modelling and basic dynamics

The dynamics and stability of a train of flexibly interconnected rigid cylinders travelling in a confined cylindrical “tunnel” subjected to fluid dynamic forces is studied theoretically. Each cylinder, which is coupled to other cylinders and supported by springs and dampers, has degrees of freedom in the lateral translational and rotational directions. The kinetic, dissipation, and potential energies of the system and the generalized forces associated with the fluid dynamic forces acting on the system, such as inviscid fluid dynamic forces, viscous frictional forces, and form drag, are obtained first. Then the equations of motion are derived in a Lagrangian framework. The principal aim of this study is to investigate the effect of the aerodynamic forces on the dynamics of a high-speed train running in a tunnel, or more generally of a train-like system travelling in a coaxial cylindrical tube. The results of this study show that the system loses stability by flutter and that viscous frictional drag has a considerable effect on stability of the system. In addition, the mechanism of instability of the system is clarified with the aid of a study of the modal shapes and energy considerations.     

Ductile–brittle transitions in the fracture of plastically-deforming,adhesively-bonded structures. Part I: Experimental studies

Rate effects for adhesively-bonded joints in steel sheets failing by mode-I fracture and plastic deformation were examined. Three types of test geometries were used to provide a range of crack velocities between 0.1 and 5000 mm/s: a DCB geometry under displacement control, a wedge geometry under displacement control, and a wedge geometry loaded under impact conditions. Two fracture modes were observed: quasi-static crack growth and dynamic crack growth. The quasi-static crack growth was associated with a toughened mode of failure; the dynamic crack growth was associated with a more brittle mode of failure. The experiments indicated that the fracture parameters for the quasi-static crack growth were rate independent, and that quasi-static crack growth could occur even at the highest crack velocities. Effects of rate appeared to be limited to the ease with which a transition to dynamic fracture could be triggered. This transition appeared to be stochastic in nature, it did not appear to be associated with the attainment of any critical value for crack velocity or loading rate. While the mode-I quasi-static fracture behavior appeared to be rate independent, an increase in the tendency for dynamic fracture to be triggered as the crack velocity increased did have the effect of decreasing the average energy dissipated during fracture at higher loading rates.     

Fracture mechanics analysis on Smart-Cut technology. Part 1： Effects of stiffening wafer and defect interaction

In the present paper, continuum fracture mechanics is used to analyze the Smart-Cut process, a recently established ion cut technology which enables highly efficient fabrication of various silicon-on-insulator （SOI） wafers of high uniformity in thickness. Using integral transform and Cauchy singular integral equation methods, the mode-I and mode-II stress intensity factors, energy release rate, and crack opening displacements are derived in order to examine several important fracture mechanisms involved in the Smart-Cut process. The effects of defect interaction and stiffening wafer on defect growth are investigated. The numerical results indi- cate that a stiffener/handle wafer can effectively prevent the donor wafer from blistering and exfoliation, but it slows down the defect growth by decreasing the magnitudes of SIF＇s. Defect interaction also plays an important role in the splitting process of SOI wafers, but its contribution depends strongly on the size, interval and internal pressure of defects. Finally, an analytical formula is derived to estimate the implantation dose required for splitting a SOI wafer.     

Hydraulic Fracturing of Soft and Hard Rocks: Part 1—Rock Behavior Due to Fluid Penetration Rate

Transport in Porous Media - Hydraulic fracturing (HF) can initiate, propagate, and coalesce cracks, by injecting fluids into rocks. Two papers provide experimental results on the performance of...