Elastic-plastic finite element analyses of short cracks

Stress and strain distributions and crack opening displacement characteristics of short cracks have been studied in single edge notch bend and centre cracked panel specimens using elastic–plastic finite element analyses incorporating both a non strain hardening and a power law hardening behaviour. J contour integral solutions to describe stress strain conditions at crack tips for short cracks differ from those for long cracks. The analyses show that (i) short cracks can propagate at stress levels lower than those required for long cracks and (ii) a two-parameter description of crack tip fields is necessary for crack propagation.

A mathematical study of finite-amplitude rock-folding

The problem of the finite-amplitude folding of an isolated, linearly viscous layer under compression and imbedded in a medium of lower viscosity is treated theoretically by using a variational method to derive finite difference equations which are solved on a digital computer. The problem depends on a single physical parameter, the ratio of the fold wavelength, L, to the "dominant wavelength" of the infinitesimal-amplitude treatment, L_d. Therefore, the natural range of physical parameters is covered by the computation of three folds, with L/L_d = 0, 1, and 4.6, up to a maximum dip of 90°.

Significant differences in fold shape are found among the three folds; folds with higher L/L_d have sharper crests. Folds with L/L_d = 0 and L/L_d = 1 become fan folds at high amplitude. A description of the shape in terms of a harmonic analysis of inclination as a function of arc length shows this systematic variation with L/L_d and is relatively insensitive to the initial shape of the layer. This method of shape description is proposed as a convenient way of measuring the shape of natural folds.

The infinitesimal-amplitude treatment does not predict fold-shape development satisfactorily beyond a limb-dip of 5°. A proposed extension of the treatment continues the wavelength-selection mechanism of the infinitesimal treatment up to a limb-dip of 15°; after this stage the wavelength-selection mechanism no longer operates and fold shape is mainly determined by L/L_d and limb-dip.

Strain-rates and finite strains in the medium are calculated f or all stages of the L/L_d = 1 and L/L_d = 4.6 folds. At limb-dips greater than 45° the planes of maximum flattening and maximum flattening rat e show the characteristic orientation and fanning of axial-plane cleavage.

High-strain composites and dual-matrix composite structures

Most space applications require deployable structures due to the limiting size of current launch vehicles. Specifically, payloads in nanosatellites such as CubeSats require very high compaction ratios due to the very limited space available in this typo of platform. Strain-energy-storing deployable structures can be suitable for these applications, but the curvature to which these structures can be folded is limited to the elastic range. Thanks to fiber microbuckling, high-strain composite materials can be folded into much higher curvatures without showing significant damage, which makes them suitable for very high compaction deployable structure applications. However, in applications that require carrying loads in compression, fiber microbuckling also dominates the strength of the material. A good understanding of the strength in compression of high-strain composites is then needed to determine how suitable they are for this type of application.

The goal of this thesis is to investigate, experimentally and numerically, the microbuckling in compression of high-strain composites. Particularly, the behavior in compression of unidirectional carbon fiber reinforced silicone rods (CFRS) is studied. Experimental testing of the compression failure of CFRS rods showed a higher strength in compression than the strength estimated by analytical models, which is unusual in standard polymer composites. This effect, first discovered in the present research, was attributed to the variation in random carbon fiber angles respect to the nominal direction. This is an important effect, as it implies that microbuckling strength might be increased by controlling the fiber angles. With a higher microbuckling strength, high-strain materials could carry loads in compression without reaching microbuckling and therefore be suitable for several space applications.

A finite element model was developed to predict the homogenized stiffness of the CFRS, and the homogenization results were used in another finite element model that simulated a homogenized rod under axial compression. A statistical representation of the fiber angles was implemented in the model. The presence of fiber angles increased the longitudinal shear stiffness of the material, resulting in a higher strength in compression. The simulations showed a large increase of the strength in compression for lower values of the standard deviation of the fiber angle, and a slight decrease of strength in compression for lower values of the mean fiber angle. The strength observed in the experiments was achieved with the minimum local angle standard deviation observed in the CFRS rods, whereas the shear stiffness measured in torsion tests was achieved with the overall fiber angle distribution observed in the CFRS rods.

High strain composites exhibit good bending capabilities, but they tend to be soft out-of-plane. To achieve a higher out-of-plane stiffness, the concept of dual-matrix composites is introduced. Dual-matrix composites are foldable composites which are soft in the crease regions and stiff elsewhere. Previous attempts to fabricate continuous dual-matrix fiber composite shells had limited performance due to excessive resin flow and matrix mixing. An alternative method, presented in this thesis uses UV-cure silicone and fiberglass to avoid these problems. Preliminary experiments on the effect of folding on the out-of-plane stiffness are presented. An application to a conical log-periodic antenna for CubeSats is proposed, using origami-inspired stowing schemes, that allow a conical dual-matrix composite shell to reach very high compaction ratios.

Linear multiscale analysis and finite element validation of stretching and bending dominated lattice materials

The paper presents a multiscale procedure for the linear analysis of components made of lattice materials. The method allows the analysis of both pin-jointed and rigid-jointed microtruss materials with arbitrary topology of the unit cell. At the macroscopic level, the procedure enables to determine the lattice stiffness, while at the microscopic level the internal forces in the lattice elements are expressed in terms of the macroscopic strain applied to the lattice component. A numeric validation of the method is described. The procedure is completely automated and can be easily used within an optimization framework to find the optimal geometric parameters of a given lattice material. © 2011 Elsevier Ltd. All rights reserved.

The impact of sand slugs against beams and plates: Coupled discrete particle/finite element simulations

The impact of a slug of dry sand particles against a metallic sandwich beam or circular sandwich plate is analysed in order to aid the design of sandwich panels for shock mitigation. The sand particles interact via a combined linear-spring-and-dashpot law whereas the face sheets and compressible core of the sandwich beam and plate are treated as rate-sensitive, elastic-plastic solids. The majority of the calculations are performed in two dimensions and entail the transverse impact of end-clamped monolithic and sandwich beams, with plane strain conditions imposed. The sand slug is of rectangular shape and comprises a random loose packing of identical, circular cylindrical particles. These calculations reveal that loading due to the sand is primarily inertial in nature with negligible fluid-structure interaction: the momentum transmitted to the beam is approximately equal to that of the incoming sand slug. For a slug of given incoming momentum, the dynamic deflection of the beam increases with decreasing duration of sand-loading until the impulsive limit is attained. Sandwich beams with thick, strong cores significantly outperform monolithic beams of equal areal mass. This performance enhancement is traced to the "sandwich effect" whereby the sandwich beams have a higher bending strength than that of the monolithic beams. Three-dimensional (3D) calculations are also performed such that the sand slug has the shape of a circular cylindrical column of finite height, and contains spherical sand particles. The 3D slug impacts a circular monolithic plate or sandwich plate and we show that sandwich plates with thick strong cores again outperform monolithic plates of equal areal mass. Finally, we demonstrate that impact by sand particles is equivalent to impact by a crushable foam projectile. The calculations on the equivalent projectile are significantly less intensive computationally, yet give predictions to within 5% of the full discrete particle calculations for the monolithic and sandwich beams and plates. These foam projectile calculations suggest that metallic foam projectiles can be used to simulate the loading by sand particles within a laboratory setting. © 2013 Elsevier Ltd.

Dependence of elastic strain field on the self-organized ordering of quantum dot superlattices

A systematic investigation of the strain distribution of self-organized, lens-shaped quantum dot in the case of growth direction on (001) substrate was presented. The three-dimensional finite element analysis for an array of dots was used for the strain calculation. The dependence of the strain energy density distribution on the thickness of the capping layer was investigated in detail when the elastic characteristics of the matrix material were anisotropic. It is shown that the elastic anisotropic greatly influences the stress, strain, and strain energy density in the quantum dot structures. The anisotropic ratio of the matrix material and the combination with different thicknesses of the capping layer, may lead to different strain energy density minimum locations on the capping layer surface, which can result in various vertical ordering phenomena for the next layer of quantum dots, i.e. partial alignment, random alignment, and complete alignment.

The strain distributions and carrier's confining potentials of self-organized InAs/GaAs quantum dot

On the basis of the finite element approach, we systematically investigated the strain field distribution of conical-shaped InAs/GaAs self-organized quantum dot using the two-dimensional axis-symmetric model. The normal strain, the hydrostatic strain and the biaxial strain components along the center axis path of the quantum dots are analyzed. The dependence of these strain components on volume, height-over-base ratio and cap layer (covered by cap layer or uncovered quantum dot) is investigated for the quantum grown on the (001) substrate. The dependence of the carriers' confining potentials on the three circumstances discussed above is also calculated in the framework of eight-band k (.) p theory. The numerical results are in good agreement with the experimental data of published literature.

Effect of the longitudinal and transverse stacking period of InAs/GaAs quantum dots on the distribution of strain field

A systematic investigation is made on the influence of the longitudinal and transverse period distributions of quantum dots on the elastic strain field. The results showed that the effects of the longitudinal period and transverse period on the strain field are just opposite along the direction of center-axis of the quantum dots, and under proper conditions, both effects can be eliminated. The results demonstrate that in calculating the effect of the strain field on the electronic structure, one must take into account the quantum dots period distribution, and it is inadequate to use the isolated quantum dot model in simulating the strain field.

Investigation on Elastic Strain Energy in Quantum Dots

In this paper, we calculated the elastic strain and elastic strain energy inside the semiconductor quantum dots by using the finite element programming package ANSYS 6.0. The values of elastic strain and strain energy in the three shapes of quantum dots were calculated, and led to the conclusion that the pyramid island structure of quantum dots is the most stable shape in the three shapes under thermal-equilibrium condition.

Fiber Bragg Grating Sensor for Strain Sensing in Low Temperature Superconducting Magnet

Fiber Bragg grating (FBG) sensor for monitoring the electromagnetic strain in a low temperature superconducting (LTS) magnet was studied. Before used to LTS magnet strain sensing, the strain response of the sensor with 1.54-mu m wavelength at liquid helium was experimentally studied. It was found that the wavelength shift showed good linearity with longitudinal applied loads and the strain sensitivity is constant at 4.2 K. And then, the hoop strain measurement of a LTS magnet was carried out on the basis of measured results. Furthermore, the finite element method (FEM) was used to simulate the magnet strain. The difference between the experimental and numerical analysis results is very small.

Fiber Bragg Grating Sensor for Strain Sensing in Low Temperature Superconducting Magnet

Fiber Bragg grating (FBG) sensor for monitoring the electromagnetic strain in a low temperature superconducting (LTS) magnet was studied. Before used to LTS magnet strain sensing, the strain response of the sensor with 1.54-mu m wavelength at liquid helium was experimentally studied. It was found that the wavelength shift showed good linearity with longitudinal applied loads and the strain sensitivity is constant at 4.2 K. And then, the hoop strain measurement of a LTS magnet was carried out on the basis of measured results. Furthermore, the finite element method (FEM) was used to simulate the magnet strain. The difference between the experimental and numerical analysis results is very small.

Finite element modelling of crack detection tests

Four non-destructive tests for determining the length of fatigue cracks within the solder joints of a 2512 surface mount resistor are investigated. The sensitivity of the tests is obtained using finite element analysis with some experimental validation. Three of the tests are mechanically based and one is thermally based. The mechanical tests all operate by applying different loads to the PCB and monitoring the strain response at the top of the resistor. The thermal test operates by applying a heat source underneath the PCB, and monitoring the temperature response at the top of the resistor. From the modelling work done, two of these tests have shown to be sensitive to cracks. Some experimental results are presented but further work is required to fully validate the simulation results.

A finite element solution scheme for an elastic–viscoplastic soil model

A Newton–Raphson solution scheme with a stress point algorithm is presented for the implementation of an elastic–viscoplastic soilmodel in a finite element program. Viscoplastic strain rates are calculated using the stress and volumetric states of the soil. Sub-incrementsof time are defined for each iterative calculation of elastic–viscoplastic stress changes so that their sum adds up to the time incrementfor the load step. This carefully defined ‘iterative time’ ensures that the correct amount of viscoplastic straining is accumulated overthe applied load step. The algorithms and assumptions required to implement the solution scheme are provided. Verification of the solutionscheme is achieved by using it to analyze typical boundary value problems.

Numerical study of the effects of reinforcement/matrix interphase on stress-strain behavior of YAl2 particle reinforced MgLiAl composites

For the potential influence produced by the reinforcement/matrix interphase in particle reinforced metal matrix composites (PMMCs), a unit cell model with transition interphase was proposed. Uniaxial tensile loading was simulated and the stress/strain behavior was predicted. The results show that a transition interphase with both appropriate strength and thickness could affect the failure mode, reduce the stress concentration, and enhance the maximum strain value of the composite.