Numerical simulation of growth pattern of a fluid-filled subsurface crack under moving hertzian loading

Cracking of a fluid-filled subsurface crack is studied by means of the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The Griffith crack was initially opened by the application of hydrostatic pressure of an incompressible fluid within the crack. A moving Hertz line contact load distribution is applied at the surface of the half-plane in the presence of friction. The stress intensity factors at the tips of the fluid-filled crack are analyzed with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume. When the crack starts to propagate/kink, numerical results show that the internal fluid pressure will be relieved, and as the ratio of the branched crack length to main crack length increases, the elastic strain energy release rate decreases. The crack growth is assumed to be arrested when the energy release rate is below a certain value. Based on the energy criterion, predictions are attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed to simulate the growth pattern of the fluid-filled crack under moving Hertzian loading.     

Response of reinforced concrete beams to hydrostatic pressure acting within primary cracks

This paper investigates the response of reinforced concrete beams to hydrostatic pressure acting within primary cracks. Notched beams were initially pre-cracked before pressurised water was introduced into the primary crack. The deflection and strain increase at tensile reinforcement level (due to the pressurised water load) was measured. Tests were carried out using applied hydrostatic pressures of 0.2 and 0.325 MPa. Results show that both deflection and strain at tensile reinforcement level increases immediately after the introduction of hydrostatic pressure into open primary cracks. If the crack is held open and hydrostatic pressure is allowed to build up within the depth of the crack, additional deformation occurs. A finite element (FE) model was constructed to investigate the effects of greater hydrostatic pressures acting within the primary crack. The FE model was first validated against the test data, before being used to assess the structural response of the reinforced concrete section to applied hydrostatic pressures of up to 1 MPa. It was found that section deformations increased as hydrostatic pressure was increased. At applied hydrostatic pressures of 0.8 MPa and above, the increases in strain at tensile reinforcement level were shown to be significant. DNV-0S-C205, which is the Det Norske Veritas (DNV) standard for offshore concrete structures states that the ‘effects of water pressure within cracks may be neglected for structural elements exposed to less than 100 m (0.981 MPa) of water head.’ The current research suggests that the effects of water pressure within cracks for structural elements exposed to slightly less than 100 m water head may also be significant (based on a 10 % threshold criteria). However, it is accepted that a more comprehensive parametric study would be required to determine whether or not the DNV should be redressed.     

复合有限条法研究水压作用下加肋柱壳的后屈曲

为了研究水压作用下的加肋柱壳的后屈曲状况,并且能考虑到肋骨的实际截面形状和分布情况,本文将复合有限条方法应用于环加肋圆柱壳的后屈曲分析。在对后屈曲路径的跟踪过程中,使用了正交弧长法。算例表明,复合有限条方法同纯粹的有限元方法相比在速度上能提高10倍以上,并且方程阶数与壳体尺寸无关,是一种分析加肋板壳结构的理想方法;实际应用的加肋圆柱壳在水压下的后屈曲路径一般来说不存在分叉点,在后屈曲阶段,随着变形的增加常常要求压力有所增加。     

Creep behaviour in cellulose nitrate under superimposed tensile and hydrostatic loading

The creep behaviour under various combinations of superimposed tensile and hydrostatic loading are quantitatively investigated using nonlinear-viscoelastic cellulose nitrate heated at 65° C. The creep strain and the creep strain-rate are seriously affected by the effect of hydrostatic pressure. The trends of behaviour under superimposed tensile and hydrostatic loading cannot be predicted by the concepts which apply to uniaxial loading. The stress—strain relation of the creep behaviour under superimposed loading is deduced from the invariant theory using an hypothesis of creep potential. The creep data obtained on the cellulose nitrate at 65° C under superimposed loading, as well as uniaxial loading, are found to fit to the deduced relation well.     

Investigation of plastic zones near SCC tips in a pipeline after hydrostatic testing

Stress corrosion cracking (SCC) is an important failure mechanism for oil and gas pipelines. In the past, hydrostatic testing has been frequently used to assess and mitigate stress corrosion cracking. It is commonly agreed that an effective hydrostatic test not only eliminates critical crack-like flaws, but also blunts the sub-critical crack tip thereby suppressing further SCC propagation. However, little study has been done on the plastic deformation that results from the high stress intensity at the crack tip due to hydrostatic testing pressure and its possible role in subsequent SCC propagation. In this study, microstructural details were examined of an API 5L X52 SCC-containing pipe removed from field service. Plastic deformation generated by the hydrostatic testing pressure was revealed by using high-resolution imaging of a focused ion beam (FIB) microscope. The existence of the microscopic plastic zones around some crack tips suggests that caution should be taken when setting up pipeline hydrostatic tests.     

Effect of Hydrostatic Pressure on the Rate Dependence of the Fracture Toughness of High-Filled Polymeric Materials

The paper presents results of an experimental investigation of the effect of hydrostatic pressure on the fracture toughness of high-filled polymeric materials. It has been shown that the critical value of the stress intensity factor and hence the crack propagation rate increase with increasing hydrostatic pressure of the medium. To take into account the effect of pressure on the fracture toughness characteristics of the materials under investigation, it is proposed to employ the pressure-time analogy method. The method makes it possible to represent experimental plots of fracture toughness against crack propagation rate, obtained at various levels of hydrostatic pressure, as a generalized pressure-time plot that defines the influence of loading conditions on fracture characteristics of the material. Simple empirical relations are proposed for the approximation of the experimental data obtained.     

Creep behaviour in unloading process of cellulose nitrate under superimposed tensile and hydrostatic loading

The creep behaviour in unloading process under various combinations of superimposed tensile and hydrostatic loading are quantitatively investigated using non-linear-viscoelastic cellulose nitrate heated at 65° C. The creep strain and the creep strain-rate in the unloading process are quite influenced by the effect of hydrostatic pressure, but are not so influenced as those in the loading process mentioned in a previous paper. The deformation properties in the unloading process are also discussed with experiments for proportional loading (namely, uniform rate of stress increases or decreases with time). The stress-strain relation in the unloading process of the creep behaviour under superimposed loading is deduced by using the invariant theory. The deduced relation gives good agreement with the actual observations under the superimposed loading.     

Electronic states in double quantum well-wires with potential W-profile: combined effects of hydrostatic pressure and electric field

Within the framework of the effective mass and parabolic band approximations and using a variational procedure, a detailed theoretical study of the combined effects of hydrostatic pressure and in-growth direction applied electric field on the electronic states and binding energy of a donor impurity in a GaAs–(Ga,Al)As coupled double quantum well-wires is presented. The particular situation of W-shaped confining potential profile is analyzed. The results obtained show that the energy for the first confined electron states as well as the impurity binding energy bear strong dependences with the hydrostatic pressure, the strength of the applied electric field, and the shape of the confining potential barriers. In the case of the electron states, it is observed that their energies are increasing (decreasing) functions of the potential-shape-related \Uplambda\Uplambda-parameter (hydrostatic pressure). It is also found that, in the high hydrostatic pressure regime (25 kbar in this work), the binding energy of a donor impurity decreases with the pressure and the effects of hydrostatic pressure on the potential barriers are predominant over the effects of hydrostatic pressure on the GaAs static dielectric constant. It is shown that the binding energy can increase or decrease depending on the combined effects of the applied electric field and the dimensions of the transversal section of the coupled quantum well wires.     

Nonlinear constitutive equations for transient creep of viscoelastic polymers including the effect of hydrostatic pressure

The behaviour of polymers is known to be significantly influenced by the hydrostatic pressure in creep deformation or elastic-plastic deformation. The effect of the third stress invariant on the nonlinear viscoelastic deformation is much smaller than that of the hydrostatic pressure. In this paper, a constitutive equation for transient creep is proposed, which includes the effect of the hydrostatic pressure on the yield function. The creep and plastic strains or the creep strain rate converge to zero with increasing hydrostatic pressure. The proposed constitutive equation is in good agreement with the actual creep data of cellulose nitrate and cellulose acetate, under various combinations of superimposed tensile and hydrostatic loadings.     

Analysis of discontinuous bifurcations for elasto-plastic geomaterials with effect of damage

Summary The failure process of geomaterials can be regarded as the one in which the undamaged part of the material is transformed into the damaged part gradually. Thus by considering geomaterials as the mixture of the undamaged and damaged parts, a formulation of discontinuous bifurcation including the damage effect is presented, and the hardening modulus corresponding to the onset of discontinuous bifurcation is given in an explicit form. The damaged part is assumed not being able to support shear loading but having certain capacity to bear hydrostatic pressure as the hydrostatic pressure can make the microcracks closed to some extent. As a result, the properties of discontinuous bifurcation are much dependent on damage and the capacity of bearing hydrostatic pressure of the damaged part. Generally, damage may induce an earlier onset of discontinuous bifurcation and lead to instability of geomaterials.     

Application of fracture mechanics to plastics deformed at high strain-rates

Thin walled cylindrical specimens of poly(methylmethacrylate) containing artificial flaws of different length and machined along a generator of the cylinder, are subjected to internal pressure pulses (shock pulses) of increasing magnitude until fracture occurs. A shock tube is used to generate the shock pulse. The variation of the stress required to induce fracture with crack length is studied. It is found that an equation similar to the Griffith relationship applies over the range of crack lengths 38 mm>2c>16 mm, the surface energy value required to fit the Griffith type equation to the experimental data in this crack length range being similar to that derived from quasi-static testing of the same material. It is found that the range of applicability of the Griffith equation is determined by the magnitude of the fracture stress of the non-artificially flawed material at the particular strain-rate at which the test is conducted.     

Buckling of a compressible elastic ring

Summary We study stability of a circular ring subjected to uniform hydrostatic pressure. The constitutive equations of a ring are taken in a generalized form, allowing the compression of the ring axis. We show that the null space of the linearized differential equations has dimension three. On the basis of a single bifurcation equation the bifurcation diagram is obtained. It is shown that bifurcation could be both super- and subcritical, depending on the values of parameters.     

Influence of stress intensity and crack speed on fracture surface topography: mirror to mist to macroscopic bifurcation

The development of roughness on the fracture surfaces of a brittle, glassy, epoxy resin from the mirror-to-mist transition to macroscopic bifurcation has been investigated using optical microscopy, scanning electron microscopy (SEM) and contact and non-contact laser profilometry. Most of the observations were made on specimens fractured in edge-notched tension. In a series of tests the initial crack length was varied to obtain fracture surfaces formed by accelerating and decelerating cracks without macroscopic bifurcation (specimen A) and by cracks which accelerated continuously to macroscopic bifurcation (specimen B). Some observations were made on specimens tested in compact tension to study changes in fracture surface topography associated with crack arrest in stick-slip fracture. There was a close correlation between the topographical detail revealed by the different techniques. In specimen A the roughness increased progressively from the mirror-to-mist transition and reached a maximum before decreasing as the crack decelerated. The topographical features revealed by optical microscopy and SEM were the same for accelerating and decelerating cracks at the same roughness value. In specimen B the roughness increased continuously to macroscopic bifurcation. There was a close similarity between the topographical features at all levels of roughness. A simple model for the basic step involved in roughness formation is presented which involves an element of the crack tip tilting out of the plane of the main crack before stopping (micro-bifurcation). The scale of micro-bifurcation ranged from 3 m in the early stages of mist, when the crack velocity was close to 10% of the shear wave velocity, to the full width of the specimen (6 mm) at macroscopic bifurcation. The micro-bifurcation process develops from crack surface undulations and does not involve micro-crack nucleating ahead of the main crack. It is concluded that the relationships between crack velocity and dynamic stress intensity, and the value of the limiting crack velocity, must be interpreted in terms of micro-mechanical processes at the crack tip which are strongly dependent on specific material characteristics.Emeritus Goldsmiths' Professor Metallurgy, University of Cambridge, U.K.     

The yield behaviour of poly(phenylenebibenzimidazole)

The compressive yield behaviour of poly(2,2-m-phenylene-5,5-bibenzimidazole) (PBI) has been studied over a wide range of temperatures. The tensile behaviour was also studied under superimposed hydrostatic pressure. In both cases wet and dry samples were examined and the results revealed the considerable effects of moisture on the mechanical properties of PBI. The results of all these tests show that PBI has a remarkably high shear yield stress at room temperature. This results in a very high compressive yield stress and a very high tensile yield stress observed under superimposed hydrostatic pressure when brittle failure from surface flaws is prevented. It is concluded on the basis of quantitative analysis that the yield mechanism in PBI at room temperature is initiation controlled, as in a metal or ceramic, rather than a velocity controlled, thermally activated, viscoelastic process which is generally considered applicable in polymers.     

Numerical analysis on special cracking phenomena of residual compressive inter-layers in ceramic laminates

Finite element computations are performed to analyze the phenomena of edge cracking and crack bifurcation in two ceramic laminates composed by tensile thick layers and compressive thin layers. The difference between these two laminates is the thickness of the compressive thin layers. Experimental results performed by one of the authors in previous works show that edge cracks exist in only one laminate, while crack bifurcation occurs in both laminates under bending. To understand the cracking phenomena observed in experiments, the energy release rates are calculated. Numerical results show that the initiation of crack bifurcation can be explained by the near-tip J-integral, provided that micro-cracks exist near the crack tip.     

A theoretical investigation into the nucleation of stable crack precursors in polycrystalline ice

The possible formation of small stable cracks (crack precursors) at grain triple points in polycrystalline S2 ice subjected to stresses below that required to nucleate grain-size cracks is examined theoretically at –10° C. The investigation is based on the theory that stress concentrations can arise from the crystal elastic anisotropy and the pile-up of grain boundary dislocations at the triple point. Using an energy approach, numerical simulations of a model show that (i) small stable cracks can initiate from triple points under small stresses, (ii) unstable Griffith cracks can also nucleate, (iii) the smallest nucleation stresses are weakly dependent on hydrostatic compression and crystal orientation, and obey approximately the Hall-Petch relation with respect to the mean grain size, (iv) the crack to grain boundary length ratios are statistically distributed rather than constant, and (v) crack nucleation is strongly influenced by the orientations of the grain boundaries with respect to the applied stress and by the grain boundary dislocation configurations (positive or negative).     

Fracture of brittle multiphase materials by high energy water jets

High energy water jets are established in processing brittle, inhomogeneous materials like rocks and concrete. Despite their wide field of application, the failure mechanisms of these materials, especially the influence of inclusions, are not well known. This work examines the influence of grain inclusions on the fracture behaviour of a multiphase brittle material exposed to high energy water jet processing. The behaviour of the specimens is detected by mass removal measurements, microscopical observations and the mercury penetration technique. It is found that the failure is based on microcrack growth due to hydrostatic pressure. The fracture mechanical behaviour of the reference material changes considerably with the addition of aggregates. The addition of grains leads to a reduction of the threshold tool energy for the start of mass removal. On the other hand, the presence of inclusions permits a more reduced and controlled removal progress. The interfaces between matrix and grains are the preferred locations for crack growth and also for crack branching. The inclusions act as crack arresters and crack branchers. In the case of cracks growing through the grains, a higher amount of fracture energy is absorbed and the fracture performance is weakened.Feodor-Lynen Fellowship holder of the Alexander von Humboldt Foundation, Germany.     

Hydrostatic pressure effect on dislocation evolution in self-implanted Si investigated by electron microscopy methods

The influence of enhanced hydrostatic pressure on evolution of dislocations in self-implanted silicon during annealing at different temperatures was investigated by means of electron microscopy methods. It is found that the main cause of the pressure impact differs for various annealing temperatures. The annealing under enhanced pressure at lower temperature (1070 K) has a negligible effect on structure of dislocations located in a thin layer (end-of-range (EOR) defects). At this temperature, enhanced pressure mainly increases the density of microdefects with oxygen precipitation. It is found that after high-temperature annealing (1400 K), enhanced hydrostatic pressure (HP) reduces dislocation density near the surface; however, dislocations extend deeper into the substrate as compared to the samples annealed under atmospheric pressure. The effect is attributed mainly to the reduction of silicon interstitial-atoms migration towards the surface due to increase in energy necessary to make silicon interstitial atom occupy a lattice site at the surface.     

Strain energy release rates for a straight-fronted edge crack in a circular bar subject to bending

The strain energy release rate for a straight-fronted edge crack in a bar of circular cross section subjected to pure bending is determined. The cracked bar is modelled with two-dimensional plane-stress finite elements and strain energy release rates, determined from this model, are shown to be in close agreement with existing results for a bar subjected to three-point bending in which strain energy release rates were determined by measuring the compliance of the bar experimentally. The strain energy release rates for a crack in the circular cross section bar are found to be lower than those in a rectangular cross section bar having the same relative crack length and subjected to the same bending moment. Previously determined results for uniform tension are superimposed to obtain strain energy release rates for a circular cross section bar which is subjected simultaneously to a tensile load and a bending moment.     

Pressure sensitivity and strength-differential effect of fiber-reinforced polymer matrix composites

Based on an energy approach, a simple nonlinear theory for the fiber-reinforced polymer matrix composite is developed. The yield stress and elastic moduli of the polymer matrix are taken to be pressure-dependent, and the ensuring pressure sensitivity and the strength-differential effect of the overall nonlinear response are then investigated. The stress-strain curves of the transversely isotropic composite are calculated at several levels of superimposed hydrostatic pressure, and it is found that the flow stress, except for a pure tension or compression along the fiber direction, can increase markedly under a high pressure. The strength-differential effect, which characterizes the different responses of the material between tension and compression, also exhibits a strong dependence on the loading mode and the applied pressure. The simple theory is shown to be accurate enough to compare favorably with an exact solution; it also yields results which are in close agreement with the experimental data of a grap hite/epoxy system at several selected pressures.