Experimental studies on shear failure of freeze-bonds in saline ice: Part I. Set-up, failure mode and freeze-bond strength

The strength of freeze-bonds in thin saline ice has been investigated through two series (in 2008 and 2009) of experiments in the Hamburg Ship Model Basin (HSVA) as a function of the normal confinement (σ), the submersion time (Δt) and the initial ice temperature (T_i). The freeze-bonds were mostly formed in a submerged state, but some were also formed in air. The experimental set-up was improved in the 2009 experiments. In 2008 a ductile-like failure mode dominated (78%), whereas in 2009 the brittle-like dominated (93%). We suggest that this is a combined ice and test set-up effect. The 2009 experimental procedures allowed for careful sample handling giving higher strength and it was softer. Both these things should provoke a more brittle-like force-time response. The average freeze-bond strength in brittle-like samples was around 9 kPa while in ductile-like samples was around 2 kPa. The maximum freeze-bonds strength were measured for short submersion times, from 1 to 20 min, and reached a maximum value of 30 kPa.A Mohr-Coulomb like failure model was found appropriate to represent the freeze-bond shear strength as function of the normal confinement. Saline freeze-bonds in saline water had cohesion/friction angle around 4 and 1.4 kPa/25° for the brittle- and ductile-like samples respectively, which fitted well with previously published data.A bell-shape dependence for τ_c vs. Δt was found, which agreed with the predictions by Shafrova and Høyland (2007). We suggest that this is essentially a freeze-bond porosity effect and propose three phases in time with subsequent cooling, heating and equilibrium to account for this trend. Qualitative experiments showed that the submersion time and the initial ice temperature were strongly coupled.To account for the connection between contact time, block dimensions and ice properties and the freeze-bond strength, dimensionless number were used. Fourier scaling was more appropriate than Froude scaling to scale freeze-bonds.The freeze-bonding made in air developed fast (in less than 30 s) when the ice was cold and dry, but no freeze-bonding occurred for the same contact times when the ice was warm and wet.     

Mechanical properties of model ice ridge keels

Rubble ice presents pressure dependent yield strength and its behaviour can be described by mathematical models based on several mechanical parameters. They are investigated for HSVA model rubble ice through the analysis of three different tests: the oedometer test, the pile test and the punch test. This last test is analysed with the non-linear Eulerian finite element method. The tests were performed on 4 ice ridges with two different submersion times. A 0.5 to 1.2 kPa model scale Mohr-Coulomb cohesion (0.6 to 1.5 kPa Drucker-Prager cohesion), depending on the ridge history, was used in the simulations of the model scale punch tests. The friction angle is estimated between 30 and 45° (40 and 50° Drucker-Prager friction angle). The upper value was used in the punch test simulations. A 0.9 MPa Young modulus was derived and the hydrostatic compressive yield curve was determined. The numerical model is able to estimate the rubble action during the entire penetration of the punch test in the keel and it is shown that a cohesive softening occurs in the rubble. In order to reproduce the experimental load time series for the short submersion time ridges it was necessary to use a vertical distribution of the cohesion representing the vertical distribution of the freeze-bond strength. A sensitivity analysis of the punch test shows that the keel depth and the ice density are the main parameters governing the keel frictional resistance. A precise determination of these parameters is therefore crucial for a correct determination of the rubble mechanical properties from the numerical simulation of experimental punch tests. The punch test is not appropriate for the determination of the friction angle due to the low confinement pressure at the failure plane. The numerical analysis of the punch test allows the estimation of different assumptions used in analytical models for the rubble failure: the cohesion averaging is an under-conservative approximation, and the non-simultaneity of the cohesive and shear resistance maximum values can be considered in the peak load estimation by the computation of their quadratic mean. The comparison with full scale values shows a reasonably good scaling of the cohesion for the model ice ridges with a long submersion time.     

Sliding-induced adhesion of stiff polymer microfibre arrays. II. Microscale behaviour.

The adhesive pads of geckos provide control of normal adhesive force by controlling the applied shear force. This frictional adhesion effect is one of the key principles used for rapid detachment in animals running up vertical surfaces. We developed polypropylene microfibre arrays composed of vertical, 0.3 microm radius fibres with elastic modulus of 1 GPa which show this effect for the first time using a stiff polymer. In the absence of shear forces, these fibres show minimal normal adhesion. However, sliding parallel to the substrate with a spherical probe produces a frictional adhesion effect which is not seen in the flat control. A cantilever model for the fibres and the spherical probe indicates a strong dependence on the initial fibre angle. A novel feature of the microfibre arrays is that adhesion improves with use. Repeated shearing of fibres temporarily increases maximum shear and pull-off forces.     

Indentation of functionally graded beams and its application to low-velocity impact response

The problem of contact between a rigid cylindrical indenter and a functionally graded (FG) beam is studied. The elastic modulus of the material varies in an exponential fashion across the thickness of the beam. For the sake of comparison indentation of a homogeneous beam is also considered. In the case of FG beams indentation of both soft and hard sides of the beam are studied. Results are presented for contact force–contact length relations and contact stresses in the three types of beams. Maximum normal strains and stresses and maximum transverse shear stresses are plotted as a function of strain energy (work done by the indenter) in the beam. The results are extended to low-velocity impact problems. It is seen that for a given impact energy in low-velocity impacts, the maximum stresses and strains are significantly lower in FG beams when the impact occurs on the softer side of the beam.     

Mechanisms for acoustic emissions generation during granular shearing

Shear deformation of granular media leads to continual restructuring of particle contact network and mechanical interactions. These changes to the mechanical state include jamming of grains, collisions, and frictional slip of particles—all of which present abrupt perturbations of internal forces and release of strain energy. Such energy release events typically result in the generation of elastic waves in the kHz frequency range, termed acoustic emissions (AE). The close association between grain-scale mechanics and AE generation motivated the use of AE as surrogate observations to assess the mechanical state of complex materials and granular flows. The study characterizes AE generation mechanisms stemming from grain-scale mechanical interactions. Basic mechanisms are considered, including frictional slip between particles, and mechanical excitation of particle configurations during force network restructuring events. The intrinsic frequencies and energy content of generated AEs bear the signature of source mechanisms and of structural features of the grain network. Acoustic measurements in simple shear experiments of glass beads reveal distinct characteristics of AE associated with different source mechanisms. These findings offer new capabilities for non-invasive interrogation of micromechancial interactions and linkage to a stochastic model of shear zone mechanics. Certain statistical features of restructuring events and associated energy release during shearing were predicted with a conceptual fiber-bundle model (FBM). In the FBM the collective behavior of a large number of basic mechanical elements (representing e.g. grain contacts), termed fibers, reproduces the reaction of disordered materials to progressive loading. The failure of fibers at an individual threshold force corresponds to slipping of a particle contact or a single rearrangement event of the granular network. The energy release from model fiber breakage is the equivalent to elastic energy from abrupt grain rearrangement events and provides an estimate of the energy available for elastic wave generation. The coupled FBM–AE model was in reasonable agreement with direct shear experiments that were performed on large granular assemblies. The results underline the potential of using AE as a diagnostic tool to study micro-mechanical interactions, shear failure and mobilization in granular material.     

On a matrix cracking model using Coulomb’s friction law

A matrix cracking model is developed based upon Coulomb friction law instead of a constant frictional shear stress usually assumed in the matrix cracking analyses. A Lamé formulation incorporated with Coulomb friction law is adopted to solve the elastic states of fiber/matrix stress-transfer through a frictionally constrained interface in the slipping region and a modified shear lag model is applied to evaluate the elastic responses in the intact region. By using an energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber reinforced composite is formulated in terms of the frictional coefficient rather than the frictional shear stress usually equated in the matrix cracking stress formulations. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model will be compared with those predicted by the constant frictional shear stress models. The effect of Poisson contraction caused by stress redistribution between the fiber and matrix on the matrix cracking mechanics will be shown and discussed in the present analysis.     

STRESSES DUE TO CONCENTRATED LOADS IN RESTRAINED BENDING TESTS

The paper describes an analytical method using finite element techniques for evaluating the "pinching" stresses in a beam subjected to opposing concentrated forces acting on upper and lower faces. These conditions arise in restrained modulus of rupture tests on concrete beams when it is required to know the magnitude of these local stress concentrations in relation to the normal "straight line" flexural stress field.
The analytical values are compared with results taken from a photo-elastic model with suitably simulated loading conditions. There is excellent correlation between the patterns of principal shear contours as plotted from the finite element solution and the isochromatic lines observed in the loaded model.     

Evolution of ultrasonic velocity and dynamic elastic moduli with shear strain in granular layers

Ultrasonic wave transmission has been used to investigate processes that influence frictional strength, strain localization, fabric development, porosity evolution, and friction constitutive properties in granular materials under a wide range of conditions. We present results from a novel technique using ultrasonic wave propagation to observe the evolution of elastic properties during shear in laboratory experiments conducted at stresses applicable to tectonic faults in Earth’s crust. Elastic properties were measured continuously during loading, compaction, and subsequent shear using piezoelectric transducers fixed within shear forcing blocks in the double-direct-shear configuration. We report high-fidelity measurements of elastic wave properties for normal stresses up to 20 MPa and shear strains up to 500 % in layers of granular quartz, smectite clay, and a quartz-clay mixture. Layers were 0.1–1 cm thick and had nominal contact area of $5 \mathrm{cm} \!\times \! 5 \mathrm{cm}$ . We investigate relationships among frictional strength, granular layer thickness, and ultrasonic wave velocity and amplitude as a function of shear strain and normal stress. For layers of granular quartz, P-wave velocity and amplitude decrease by 20–70 % after a shear strain of 0.5. We find that P-wave velocity increases upon application of shear load for layers of pure clay and for the quartz-clay mixture. The P-wave amplitude of pure clay and quart-clay mixtures first decreases by $\sim $ 50 and 30 %, respectively, and then increases with additional shear strain. Changes in P-wave speed and wave amplitude result from changes in grain contact stiffness, crack density and disruption of granular force chains. Our data indicate that sample dilation and shear localization influence acoustic velocity and amplitude during granular shear.     

Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp

This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson’s ratio is taken as a constant. Coulomb’s dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity problem is formulated utilizing Fourier transforms, and the resulting Cauchy-type singular integral equation of the second type is solved by applying an expansion–collocation technique. The finite element method is used in the computational analysis of the contact problem. In the finite element model, continuous variation of the shear modulus is taken into account by specifying this property at the centroid of each finite element. The finite element-based solution procedure is verified by making comparisons to the results obtained through the analytical method. Numerical results generated for the laterally graded medium with an exponential variation in the shear modulus illustrate the influences of lateral gradation and coefficient of friction upon the contact stress distributions. The capability of the proposed finite element method is further demonstrated by providing numerical results for a laterally graded medium whose shear modulus is represented by a power function.     

Analysis of stitched laminated ENF specimens for interlaminar mode II fracture toughness

Two simple micromechanics based models are proposed to predict the effect of through-thickness reinforcement (stitching) on the improvement of delamination crack growth resistance in end-notched flexure (ENF) specimens. In the first model, it is assumed that stitches stretch elastically and then rupture when the load carried approaches the failure load. In the second model, it is assumed that stitches are discontinuous and that the stitch thread-matrix interface is completely frictional. Approximate closed form solutions for energy release rates are obtained, and the effects of stitch density, matrix-stitch thread interfacial shear stress, stitch thread diameter, volume fraction of stitches, critical energy release rate and Young's modulus are then examined. A simple design study for sizing the ENF specimen to minimise geometric nonlinear response is presented. The influences of interlaminar shear deformation and friction between the crack surfaces on the strain energy release rate are examined.     

THE EFFECT OF FINAL FRICTION COEFFICIENT ON FRETTING FATIGUE WAVEFORMS

Abstract— The waveforms of the frictional forces and the relationship between the frictional forces and the applied forces are derived for a fretting fatigue model in which the coefficient of friction is not constant. This study is a continuation of a previous one in which it was assumed that the coefficient of friction was a constant. In this new model it is assumed that the coefficient of friction between the rubbing surfaces is initially zero and slowly increases to a constant value during the early cycles of the fatigue life. The consequences of this change are examined and the results from the two models compared. It is observed that the two models give different frictional forces if the deformation of the surfaces is elastic, but are identical when non-linear macroslip occurs on both loading and unloading.     

Ice loads on offshore structures: The transition from creep to fracture

During landfast winter ice conditions an offshore structure experiences loads due to static wind-driven sea ice. The load is generally not applied suddenly, but gradually increases as winds build up during the course of minutes or hours. Typical stress-rates for a structure 100 m wide are 0.02 kPa s⁻¹ and extreme stress-rates may be 1–5 kPa s⁻¹. Laboratory investigations by Sinha (1983) enable us to predict the onset of crack formation in ice as stress increases, using a delayed elastic strain criterion (Sinha, 1982). If we apply this criterion to realistic offshore cases, we find that first cracks in ice should typically occur at 0.4–0.7 MPa and in extreme conditions may occur at 0.8–1.8 MPa. We speculate that complete failure of the ice should occur soon afterwards. This would explain why existing measurements of winter ice forces on offshore structures seldom exceed 1 MPa. We cannot, however, exclude the possibility that higher stress-rates and higher stresses could, under different conditions, be achieved.     

Aggregate breakage under dynamic loading

Numerical simulations with the Discrete Element Method are used to study agglomerate breakage under two different kinds of dynamic loading: normal impact and shear loading. Simple mechanical models based on energy balance are developed herein for each one and show good agreement with the results of the simulations. For impact, damage is found to depend on a dimensionless number N _i , which describes the ratio of the incoming kinetic energy to the internal bonding energy. For shear loading, damage is shown to depend on another dimensionless number N _f which describes the ratio of the frictional work to the internal bonding energy. The friction force is first modelled as a solid-like friction force, then the model is improved by using a granular frictional force. The two types of loading as damaging processes are then compared. These results appear to be consistent with the available experimental data on impact and abrasion wear tests.     

The effect of matrix stresses on fibre pull-out forces

A pull-out test was developed to measure the bond strengths and frictional forces between steel wires, and polycarbonate and epoxy matrices when the matrix was under tensile stress. Some debonding occurred due to the matrix stress. Despite this, the nominal bond strength, in the polycarbonate case, increased with increasing matrix applied stress. When the pull-out force had caused complete debonding, sliding under approximately constant friction coefficient,, occurred. The value of for steel sliding in polycarbonate was 0.6, and for epoxy it was 0.19. The values were reduced to 0.12 and 0.10 respectively when the steel was coated with a fluorocarbon release agent. The normal stresses at the interface, in the absence of any applied stresses, were found to be about 7 MN m^–2 in the polycarbonate, and 3.0 MN m^–2 in the epoxy case. It was observed that the frictional forces due to these residual stresses could be less than one third of those generated by the applied stresses on the matrix. Thus residual stresses are not as important for fibre reinforcement as are matrix Poisson's shrinkage stresses.     

Failure mechanisms and fracture energy of hybrid materials

A shear-lag model of hybrid materials is developed. The model represents an alternating arrangement of two types of aligned linear elastic fibres, embedded in a linear elastic matrix. Fibre and matrix elements are taken to fail deterministically when the axial and shear stresses in them reach their respective strengths. An efficient solution procedure for determining the stress state for arbitrary configurations of broken fibre and matrix elements is developed. Starting with a single fibre break, this procedure is used to simulate progressive fibre and matrix failure, up to composite fracture. The effect of (1) the ratio of fibre stiffnesses, and (2) the ratio of the fibre tensile strength to matrix shear strength, on the composite failure mechanism, fracture energy, and failure strain is characterised. Experimental observations, reported in the literature, of the fracture behaviour of two hybrid materials, viz., hybrid unidirectional composites, and double network hydrogels, are discussed in the framework of the present model.     

冻融条件下公路桥梁板式氯丁橡胶支座抗剪试验

公路桥梁橡胶支座比建筑橡胶支座更容易受到气候的影响,为了研究公路桥梁板式氯丁橡胶支座在受到气候影响时的各项抗剪性能指标变化情况,采用标准冻融试验箱模拟低温气候变化,对氯丁橡胶支座进行冻融循环处理25、50、75、100次,并对其进行抗剪试验,采用与标准试件进行对比分析的方法,研究冻融循环对氯丁橡胶支座的抗剪承载力、抗剪强度、水平等效刚度、抗剪弹性模量的影响。结果表明,氯丁橡胶支座在冻融循环处理条件下比标准试件更易发生破坏,且钢板外露、裂缝等破坏现象更严重。氯丁橡胶支座的抗剪承载力、抗剪强度、水平等效刚度、抗剪弹性模量都随冻融程度的加深而降低。采用最小二乘法对其抗剪强度和抗剪弹性模量变化进行分析并给出衰减曲线和衰减函数,抗剪强度和抗剪弹性模量的变化趋势基本符合幂函数规律。     

Friction and adhesion of silica fibres

Sliding friction between orthogonally crossed silica monofilaments was measured as a function of applied normal load using an electronic microbalance. In the adhesion model of friction, the friction is interpreted in terms of shearing the junction. With the assumption that the ploughing term of friction can be ignored, the shear strength can simply be represented by =F/A whereF is frictional force,A is the real area of contact, and is the interfacial shear strength. Assuming a single point contact between two fibres, the estimation of the real area of contact was made from Hertzian analysis by taking the normal load as a sum of the applied force and independently determined adhesional force. The results showed that the shear strength of freshly drawn silica fibre increases linearly with the contact pressure.     

Friction and adhesion of silica fibres in liquid media

Contact adhesion and sliding friction between orthgonally configured silica fibres were measured in water, hexadecane, and cyclohexane. In the adhesion model of friction, the friction is interpreted in terms of shearing the junction and the shear strength () can simply be represented by =F/A whereFis frictional force andA is the real area of contact. While this model works well for the frictional behaviour of silica fibre in air, this was not the case in liquid media. The influence of liquid on the force required to break the adhesive junction cannot simply be interpreted in terms of the reduction in adhesional forces between two fibres; but the interpretations have to also include the nature of the liquids.     

Silicon carbide (NicalonTM) fibre-reinforced borosilicate glass composites: mechanical properties

The objective of this study was to assess the applicability of an extrinsic carbon coating to tailor the interface in a unidirectional NicalonTM–borosilicate glass composite for maximum strength. Three unidirectional NicalonTM fibre-reinforced borosilicate glass composites were fabricated with different interfaces by using (1) uncoated (2) 25 nm thick carbon-coated and (3) 140 nm thick carbon coated Nicalon fibres. The tensile behaviours of the three systems differed significantly. Damage developments during tensile loading were recorded by a replica technique. Fibre–matrix interfacial frictional stresses were measured. A shear lag model was used to quantitatively relate the interfacial properties, damage and elastic modulus. Tensile specimen design was varied to obtain desirable failure mode. Tensile strengths of NicalonTM fibres in all three types of composites were measured by the fracture mirror method. Weibull analysis of the fibre strength data was performed. Fibre strength data obtained from the fracture mirror method were compared with strength data obtained by single fibre tensile testing of as-received fibres and fibres extracted from the composites. The fibre strength data were used in various composite strength models to predict strengths. Nicalon–borosilicate glass composites with ultimate tensile strength values as high as 585 MPa were produced using extrinsic carbon coatings on the fibres. Fibre strength measurements indicated fibre strength degradation during processing. Fracture mirror analysis gave higher fibre strengths than extracted single fibre tensile testing for all three types of composites. The fibre bundle model gave reasonable composite ultimate tensile strength predictions using fracture mirror based fibre strength data. Characterization and analysis suggest that the full reinforcing potential of the fibres was not realized and the composite strength can be further increased by optimizing the fibre coating thickness and processing parameters. The use of microcrack density measurements, indentation–frictional stress measurements and shear lag modelling have been demonstrated for assessing whether the full reinforcing and toughening potential of the fibres has been realized. This revised version was published online in November 2006 with corrections to the Cover Date.