Stress–strain and fracture behaviour of 0°/90° and plain weave ceramic matrix composites from tow multi-axial properties

A computationally economic finite-element-based multi-linear elastic orthotropic materials approach has been developed to predict the stress–strain and fracture behaviour of ceramic matrix composites with strain-induced damage. The finite element analysis utilises a solid element to represent a homogenised orthotropic medium of a heterogeneous uni-directional tow. The non-linear multi-axial stress–strain behaviour has been discretised to multi-linear elastic curves, which have been implemented by a user defined subroutine or UMAT in the commercial finite element package, ABAQUS. The model has been used to study the performance of two CMC composites: a SiC (Nicalon) fibre/calcium aluminosilicate (CAS) matrix 0°/90° cross-ply laminate Nicalon/CAS; and, a carbon fibre/carbon matrix–SiC matrix (C/C–SiC) plain weave laminate DLR-XT. The global stress–strain curves with catastrophic fracture behaviour and effects of fibre waviness have been predicted. Comparisons have been made between the predictions and experimental data for both materials. The predicted results when fibre waviness is taken into account compare well with the experimental data.     

Influence of applied in-plane strain on transverse thermal conductivity of 0°/90° and plain weave ceramic matrix composites

A computationally economic finite-element-based stress analysis model, developed previously by the authors, has been extended to predict the thermal behaviour of ceramic matrix composites with strain-induced damage. The finite element analysis utilises a solid element to represent a homogenised orthotropic medium of a heterogeneous uni-directional tow. The non-linear multi-axial strain dependent thermal behaviour has been discretised by multi-linear curves, which have been implemented by a user defined subroutine, USDFLD, in the commercial finite element package, ABAQUS. The model has been used to study the performance of two CMC composites: a SiC (Nicalon) fibre-calcium aluminosilicate (CAS) matrix, 0°/90° cross-ply laminate Nicalon-CAS; and, carbon fibre-dual carbon-SiC matrix (C/C-SiC), plain weave laminate DLR-XT. The global through-thickness thermal conductivity degradation with composite uni-axial strain has been predicted. Comparisons have been made between the predictions and experimental data for both materials, and good agreement has been achieved. For the Nicalon-CAS 0°/90° cross-ply the dominant mechanism of thermal conductivity degradation is combined fibre failure and associated wake debonding; and, for the DLR-XT plain weave the same mechanisms act in combination with out-of-plane shear failure.     

Stress–strain behaviour of aluminium alloys at a wide range of strain rates

The stress–strain behaviour of extruded AA6xxx and AA7xxx aluminium alloys in T6 temper was studied at a wide range of strain rates. Tensile tests at low to medium strain rates were performed in a standard tensile test machine, while a split-Hopkinson tension bar was used to carry out tests at high rates of strain. Extruded aluminium alloys have anisotropic mechanical properties, and tests were therefore done in three directions with respect to the extrusion direction. It is found that the AA6xxx alloys exhibit no significant rate sensitivity in the stress–strain behaviour, while moderate rate sensitivity was found for the AA7xxx alloys. There seems to be no significant difference between the rate sensitivity in the three tensile directions. The experimental data were used to identify the parameters of a thermo-viscoplastic constitutive relation for the extruded alloys, which includes the effects of strain hardening, strain-rate hardening, thermal softening and plastic anisotropy.     

Determination of the microscale stress–strain curve and strain gradient effect from the micro-bend of ultra-thin beams

A simple method is established to determine the microscale uniaxial stress–strain curve from the load and deflection data for a doubly clamped beam. The method is based on the fact that, for beam deflection much larger than the beam thickness, the axial stretching dominates the deformation in the doubly clamped beam and the doubly clamped beam behaves like a simple plastic hinge. The microscale uniaxial stress–strain curve, together with the cantilever beam experiments, is used to determine the strain gradient effect in Au thin beams. The effect of finite rotation is also discussed.     

Analyzing the stress–strain state of thick cylindrical shells

Two approaches to the analysis of the stress–strain state of thick cylindrical shells are elaborated. The shell is divided by concentric cross-sectional circles into several coaxial cylindrical shells. Each of these shells has its own curvature determined on its midline. The stress–strain state of the original shell is described by satisfying the interface conditions between the component shells. The distribution of unknown functions throughout the thickness is determined by finding the analytic solution of a system of differential equations in the first approach and is approximated by polynomial functions in the second approach. The stress–strain state of thick shells is analyzed. It is revealed that the effect of reduction becomes stronger with increasing curvature     

Identification of the parameters of the stress–strain problem for a multicomponent elastic body with an inclusion

Explicit expressions for residual functional gradients are derived. They are used to identify, using gradient methods, the parameters of elastic problems for multicomponent bodies. The method employs the solutions of conjugate problems in the theory (developed by the authors) of optimal control of distributed multicomponent systems     

Spline-approximation solution of stress–strain problems for beveled cylindrical shells

The problem of bending of beveled circular cylindrical shells is solved by parametrizing the shell and reducing the two-dimensional boundary-value problem to a one-dimensional one by the spline-collocation method. This problem is solved by the stable discrete-orthogonalization method. The effect of the variability of the geometrical parameters on the displacement fields of circular cylinders is analyzed     

Dynamic problems for and stress–strain state of inhomogeneous shell structures under stationary and nonstationary loads

This paper reviews studies and analyzes results on the effect of discrete ribs on the dynamic characteristics of rectangular plates and cylindrical shells. Use is made of the vibration equations derived from the classical theories of beams, plates, and shells. The effect of Pasternak’s elastic foundation on the critical velocities of a structurally orthotropic model of a ribbed cylindrical shell is determined. Nonstationary problems are solved for perforated and ribbed shells of revolution filled with a fluid or resting on an elastic foundation and subjected to moving or impulsive loads. Results from studies of the behavior of sandwich shell structures under impulsive loads of various types are presented     

Stress–strain state of a composite anisotropic plate with curvilinear cracks and thin rigid inclusions

A complexpotential solution of a mixed problem of the linear theory of elasticity is given for an infinite plate composed of two anisotropic halfplanes. The plate contains cuts and thin undeformable inclusions shaped like arbitrary open smooth curves that do not intersect each other and the interface between the halfplanes.     

DEM investigation of strain behaviour and force chain evolution of gravel–sand mixtures subjected to cyclic loading

The strain characteristic and load transmission of mixed granular matter are different from those of homogeneous granular matter. Cyclic loading renders the mechanical behaviours of mixed granular matter more complex. To investigate the dynamic responses of gravel–sand mixtures, the discrete element method (DEM) was used to simulate the cyclic loading of gravel–sand mixtures with low fines contents. Macroscopically, the evolution of the axial strain and volumetric strain was investigated. Mesoscopically, the coordination number and contact force anisotropy were studied, and the evolution of strong and weak contacts was explored from two dimensions of loading time and local space. The simulation results show that increasing fines content can accelerate the development of the axial strain and volumetric strain but has little effect on the evolution of contact forces. Strong contacts tend to develop along the loading boundary, presenting the spatial difference. Weak contacts are firstly controlled by confining pressure and then controlled by axial stress, while strong contacts are mainly controlled by axial stress throughout the whole cyclic loading. Once compression failure occurs, the release of axial stress causes the reduction of strong contact proportion in all local regions. These findings are helpful to understand the dynamic responses of gravel–sand mixtures, especially in deformation behaviours and the Spatio-temporal evolution of contact forces.     

The effect of the irregular interface geometry in deformation and fracture of a steel substrate–boride coating composite

Presented in this paper is a computational analysis of the mechanisms involved in plastic deformation and fracture of a composite with coating under compressive and tensile loading. Using a steel specimen surface-hardened by diffusion borating, a role of the irregular geometry of the interface between the base material and hardened surface layer is investigated. In order to describe the mechanical behavior of the steel substrate and brittle coating, use is made of a plastic flow model including isotropic strain hardening and a fracture model, respectively. Using the Huber fracture criterion, the model takes into account the difference in the critical strength values for different types of local compressive and tensile states. It is shown that the irregular, serrated shape of the substrate–coating interface retards propagation of a longitudinal crack into this coating and prevents it from spalling under external compression of this composite. It is found out that even in the case of a simple uniaxial compression of the mesovolumes of this composite the boride “teeth” are subjected to tensile stresses, whose values are comparable with those of the external compressive load, and the direction of crack propagation and the general fracture behavior largely depend on the external loading conditions.     

On the stress–strain states of cellular materials under high loading rates

A virtual Taylor impact of cellular materials is analyzed with a wave propagation technique, i.e. the Lagrangian analysis method, of which the main advantage is that no pre-assumed constitutive relationship is required. Time histories of particle velocity, local strain, and stress profiles are calculated to present the local stress–strain history curves, from which the dynamic stress–strain states are obtained.The present results reveal that the dynamic-rigid-plastic hardening(D-R-PH) material model introduced in a previous study of our group is in good agreement with the dynamic stress–strain states under high loading rates obtained by the Lagrangian analysis method. It directly reflects the effectiveness and feasibility of the D-R-PH material model for the cellular materials under high loading rates.     

Quasi-soft opto-mechanical behavior of photochromic liquid crystal elastomer: Linearized stress–strain relations and finite element simulations

Based on the neo-classical elastic energy of liquid crystal elastomers, the opto-mechanical behavior is modeled by considering the effect of photoisomerization on the nematic-isotropic transition of liquid crystal phase. Linearized stress–strain relation is derived for infinitesimal deformations with a very unusual shear stress that does not vanish identically as in the case of the soft behavior but is proportional to the rotation of directors. In other words, the shear stress depends on both the shear strain and the skew symmetric part of the displacement gradient with the shear modulus induced by the effect of photoisomerization. Finite element implementation for plane stress problems is obtained through a self-defined material subroutine in ABAQUS FEA tool. Numerical simulations show that the light induced deformations of two dimensional specimens consist of contractions, expansions and bending in different directions. The stress distributions indicate that the driving force for the light induced bending is produced by the bending moment of the normal stress along the director, while the other stress components are much smaller for two dimensional beam shaped specimens. However, the shear stress of the soft LCE is generally nonzero under light illumination due to the inhomogeneity of the opto-mechanical effect. It can be concluded from the strain distributions that the transversal plane cross section could remain plane after deformation if the light intensity or the decay distance is not too small and the sample is in the deep nematic phase. However, the shear strain and in plane rotation are of the same order as the other strain components, and thus should not be neglected. This indicates that the classical simple bending assumptions such as the Euler–Bernoulli beam theory should not be directly applied to model the light induced bending of neo-classical liquid crystal elastomers due to the soft behavior of the materials.     

Influence of the cavitation on the stress–strain fields of compressible Blatz–Ko materials at finite deformation

The aim of this article is the analysis of fracture growth in media characterized by random distribution of micro-failure mechanisms per unit volume. The deformation behavior of the material was investigated in terms of a spherical unit cell model, containing an initially spherical cell of porous. The effective elastic bulk modulus as a function of micro-failures concentration was computed and using the Griffith critirium and certain boundary conditions the rate at which the void area varies was determined too. Along the analysis a special form of the strain energy function for compressible Blatz–Ko material was used. The applied traction on the unit cell of the material was determined as a function of the porosity of the material, as well as the strain field within the solid. At low values of the porosity, as the applied external traction was increased instabilities were observed in the void growth.     

Extracting the stress–strain properties of non-linear viscoelastic materials using the bubble inflation test

In this study, an inverse method based on the Levenberg–Marquardt algorithm was evaluated in a numerical experiment to determine the large strain viscoelastic properties from the bubble inflation test. The properties were determined by iteratively matching the calculated bubble pressure–piston displacement data from finite element simulations to a single set of bubble pressure–piston displacement data. The strain-dependent behaviour was characterised by a two-parameter Mooney–Rivlin hyperelastic model, while the time-dependent behaviour was characterised by a three-parameter power law equation. Different initial guesses were used to evaluate the inverse method, and transformation functions were applied to constrain the intermediate guesses to be within bounds. It was found that estimates of the viscoelastic properties could be obtained reasonably using only one set of bubble pressure–piston displacement data. Estimates of the properties were likely affected by the limited time duration of the test, as the behaviour at shorter and particularly larger time scales was less accurately predicted.