Finite element analyses of near-tip deformation in inhomogeneous elastic-plastic fracture specimens

Two types of path-independent expressions were derived for the nonlinear fracture parameter T^* integral in inhomogeneous multilayer materials. Finite element analyses were carried out for inhomogeneous elastic-plastic fracture specimens consisting of A533B steel and HT80 steel: these two materials have considerably different yield stresses, although their elastic properties are exactly the same. The T^*-integral for inhomogeneous materials demonstrated excellent path independence even in the stages of large deformations around the crack tip and material interfaces. Numerically generated moiré fringe patterns are in good agreement with experimentally recorded patterns. The shapes of plastic zones appearing in the specimens reveal large inhomogeneity effects. The applicability of a hybrid moiré-finite element method is demonstrated briefly.     

Transferability of fracture parameters from specimens to component level

The structural integrity of components is usually performed using the specimen fracture resistance curve. However, the specimen fracture resistance curve significantly differs from the component fracture resistance. This is the most serious limitation of classical fracture mechanics. To address this issue, several tests have been carried out on fractured specimens and piping components under an Indo-German bilateral project. Two approaches, namely, two-parameter fracture mechanics and micro-mechanical models are considered to investigate the feasibility of transferability. For the two-parameter fracture mechanics approach, the J-integral has been used as the crack driving force and q is used as a measure of stress triaxiality. The triaxiality quotient q is proportional to the ratio of the hydrostatic stress and the von Mises effective stress and is an additional parameter to make a decision about the initiation value of the J-integral for the failure behaviour of a component. It is shown that if the triaxial conditions match for any two arbitrary geometries, it is feasible to transfer the fracture parameters. The difficulty in transferability is largely overcome by damage mechanics, which models the drop in load carrying capacity of a material with increase in plastic strain. Such modeling is done considering nucleation, growth and coalescence of voids in a material following large-scale plasticity. The Gurson–Tvergaard–Needleman and Rousselier models are used. Some of the results obtained by these models and comparisons with experimental results are presented in this paper to demonstrate the usefulness of damage mechanics in analyzing components with flaws.     

Evaluation of fracture mechanics parameters for bimaterial compact tension specimens

Abstract

The elastic–plastic fracture mechanics parameter J and its analogous creep fracture parameter C* are widely used to measure the fracture resistance of a material. The non-linear component of the J and C* parameters can be evaluated experimentally using the η factor. For weldments, the η factor is dependent on the relative properties of the base (parent) and weld materials, particularly the mismatch in their yield strengths. In this work, the η factor has been evaluated using non-linear finite element analyses in a standard compact tension C(T) specimen for a power law material. A range of mismatches in base/weld material properties have been considered. A through thickness strip of weld material, of height 2h, has been modelled, which was positioned at the mid height of the specimen. The η factor has been evaluated for a range of crack lengths and power law hardening exponents under both plane stress and plane strain conditions and the results compared with literature where available. For a given crack length and weld width, the η solutions of the undermatched and overmatched conditions examined show a maximum variation of 12% from the mean value. A relationship has been proposed with respect to crack length for the C(T) specimen to describe the decrease in the η factor with an increase in mismatch ratio.     

Temperature-field measurements of a premixed butane/air circular impinging-flame using reference-beam interferometry

Reference-beam interferometry (RBI) was applied to study the axisymmetric temperature fields of a small-scale, low Reynolds-number, low-pressure and fuel-rich premixed butane/air circular-flame jet, when it was impinging vertically upwards onto a horizontal copper plate. By maintaining a Reynolds number, Re, of 500 and an equivalence ratio, , of 1.8, interferograms of the impinging-flame jet were obtained for various nozzle-to-plate-distances. Temperature fields of the flame were then determined using the inverse Abel transformation from the obtained interferograms. Temperatures at several locations were measured experimentally with a T-type thermocouple: they were used as a reference to help in the determination as well as the validation. In the present study, a non-contact method has been successfully developed to measure the temperature fields of a circular impinging gas-fired flame jet.     

Time-dependent deformation and fracture of multi-material systems at high temperature

The present work reports several recent research activities on the time-dependent deformation and fracture performance of multi-material system and structures at elevated temperature. A micro region deformation measuring technique is developed to achieve the full creep strain fields of multi-material systems at high temperature in light of the long-distance microscope and digital speckle correlation method. The mean field approach based on the self-consistent method and the generalized self-consistent method are introduced to predict the time-dependent deformation of the dual-components material system under the creep condition. For the pressure vessels with functionally graded materials under both internal and external pressures, an asymptotic solution for creep stress and strain is derived based on the Taylor expansion series. For the time-dependent fracture issue of multi-material structures, a modified creep crack fracture parameter prediction method for C^∗ integral in the mismatched weldments and the particle-reinforced composite is proposed based on the generalized equivalent homogenous model. Finally, time-dependent failure assessment diagram (TDFAD) for multi-material system is derived for defect assessment of structures with various combinations of materials.     

Three-dimensional modeling of a PEMFC with serpentine flow field incorporating the impacts of electrode inhomogeneous compression deformation

The effects of compression deformation of gas diffusion layer (GDL) on the performance of a proton exchange membrane fuel cell (PEMFC) with serpentine flow field were numerically investigated by coupling two-dimensional GDL mechanical deformation model based on Finite Element Analysis and three-dimensional two-phase PEMFC model with incorporating the deformation impacts. Emphasis is located on exploring the influences of assembly pressure on the non-uniform geometric deformation and distributions of transport properties in the GDL, flow behaviors and local distributions of oxygen and current density, cell polarization curves and net power densities of the PEMFC. It was indicated that the non-uniform deformation of GDL results in inhomogeneous distributions of porosity and permeability in the GDL due to the presence of rib-channel pattern, and the transport properties in the under-rib region are greatly reduced with increasing the assembly pressure, consequently weakening the gas flow and oxygen transport in the under-rib region and increasing the non-uniformity of local current density distribution. As for the overall cell performance, however, attributed to the tradeoff between the adverse impacts of GDL compression on mass transport loss and positive effects on reducing ohmic loss, the overall cell performance is firstly increased and then decreased with increasing assembly pressure from 0 MPa to 5.0 MPa, and the maximum cell performance can be achieved at the assembly pressure of about 1.0 MPa for all cases studied. As compared with the case for zero assembly pressure, the maximum net power density of the cell can be improved by about 7.7%, 9.9%, 10.5% and 10.7% for the cathode stoichiometry ratios of 2.0, 3.0, 4.0 and 5.0@i_ref = 1 A·cm⁻², respectively. Practically, it is suggested that the assembly pressure is controlled in an appropriate range of 0.5 MPa–1.5 MPa such that the cell net power can be boosted and pressure head requirement for the pump can be maintained in a appropriate level.     

In-situ measurements of concentration and temperature during transient solidification of aqueous solution of ammonium chloride using laser interferometry

The variation in temperature and concentration plays a crucial role in predicting the final microstructure during solidification of a binary alloy. Most of the experimental techniques used to measure concentration and temperature are intrusive in nature and affect the flow field. In this paper, the main focus is laid on in-situ, non-intrusive, transient measurement of concentration and temperature during the solidification of a binary mixture of aqueous ammonium chloride solution (a metal-analog system) in a top cooled cavity using laser based Mach–Zehnder Interferometric technique. It was found from the interferogram, that the angular deviation of fringe pattern and the total number of fringes exhibit significant sensitivity to refractive index and hence are functions of the local temperature and concentration of the NH₄Cl solution inside the cavity. Using the fringe characteristics, calibration curves were established for the range of temperature and concentration levels expected during the solidification process. In the actual solidification experiment, two hypoeutectic solutions (5% and 15% NH₄Cl) were chosen. The calibration curves were used to determine the temperature and concentration of the solution inside the cavity during solidification of 5% and 15% NH₄Cl solution at different instants of time. The measurement was carried out at a fixed point in the cavity, and the concentration variation with time was recorded as the solid–liquid interface approached the measurement point. The measurement exhibited distinct zones of concentration distribution caused by solute rejection and Rayleigh Benard convection. Further studies involving flow visualization with laser scattering confirmed the Rayleigh Benard convection. Computational modeling was also performed, which corroborated the experimental findings.     

Une méthode caractérisant l’influence réciproque entre parois: application aux échanges thermiques dans une cavité rotor–statorA method characterising the respective influence of the heated walls: application to the heat transfer in a rotor–stator cavity

This paper presents a heat transfer analysis for a turbulent flow in a rotor–stator system. A method based on the use of thermal influence coefficients is developed in order to determine wall heat transfer. This method is applied to an enclosed rotor–stator system as well as to an air-cooled rotor–stator system with centrifugal or centripetal injection. The comparison between numerical simulations and predicted heat fluxes shows small discrepancies. Then, the influence of the heated wall temperature on the other walls is discussed.     

Analysis of tracer particle migration in inhomogeneous turbulence

Previous studies [J.M. Maclnnes, F.V. Bracco, Stochastic particle dispersion modeling and the tracer particle limit, Physics of Fluids A 4 (1992) 2809–2824; X.Q. Chen, Heavy particle dispersion in inhomogeneous, anisotropic, turbulence flows, International Journal of Multiphase Flow 26 (2000) 635–661; T.L. Bocksell, E. Loth, Random walk models for particle diffusion in free-shear flows, AIAA Journal 29 (2001) 1086–1096] have shown that the commonly applied stochastic separated flow (SSF) model predicts unphysical results when dealing with the dispersion of tracer particles in inhomogeneous flows. This problem is explored, with regards to the discontinuous random walk model, by considering an idealized flow with constant mean velocity with two regions of constant turbulent kinetic energy. Using the probability density functions (PDFs) for the turbulent velocities it is shown that there is a higher probability of particles traveling into the low kinetic energy region than there are traveling to the region of high kinetic energy, thus resulting in a net migration of particles to the region of low kinetic energy. Corrections that apply a correction velocity and/or adjust the fluctuating velocity based on the local value of the turbulent kinetic energy are analyzed and tested.     

Global solar radiation measurements in Maceió, Brazil

This work focuses on the variability of the global solar radiation over the area of Maceió (9°40′S, 35°42′W, 127 m), located in Northeastern State of Alagoas, Brazil, during the1997–1999 period. Solar radiation variability was evaluated on 5 min, hourly, daily, monthly and seasonal scales. The results showed that the maximum values of the hourly global solar irradiation, , in the dry (September–February) and rainy (March–August) seasons were 3.18 and 2.50 MJ m⁻², respectively. The peaks of the hourly average, , for both periods were 2.79 MJ m⁻² and the daily average of the global solar irradiation, , was 19.89 MJ m⁻². The daily clearness index, , was found to be 0.53 (rainy period) and 0.59 (dry period). In clear, partially cloudy (the most frequent) and overcast days, the daily averages of global solar irradiation were 25.20, 19.00 and 8.00 MJ m⁻², respectively. On an annual scale the global solar irradiation changed from 15.00 MJ m⁻² by August to 24.04 MJ m⁻² by November.     

Low-temperature geothermal potential of the flooded Gaspé Mines, Québec, Canada

The low-temperature geothermal potential of the flooded Gaspé Mines, near Murdochville, Québec, Canada, has been estimated from a long-term pumping test and numerical groundwater flow modelling. A former mining shaft was used to pump water for 3 weeks at a rate averaging 0.062 m³/s (3720 L/min). A mean recovery temperature equal to 6.7 °C and a maximum drawdown of 3.63 m were observed during this test. The observed drawdown was reproduced with a three-dimensional finite element model that simulates groundwater flow through the mine workings and surrounding rock mass. The model was then used to simulate longer-term pumping performed for heat recovery. Modelling results combined with a simplified energy balance calculation suggest that a sustainable energy extraction rate is attained at a pumping rate of 0.049 m³/s (2940 L/min), with a corresponding geothermal energy production potential of 765 kW, assuming a return water temperature of 3 °C. This energy could be extracted with heat pumps and used for space heating at the town's industrial park.     

Advancement in the thermodiffusion theory of anisotropic inhomogeneous shells

This article represents the latter advancement in the modeling of diffusion processes in deformable solids. Special attention is given to the development of models for thin-walled shells with both thermal and atomic types of diffusion. Based upon these models, a number of general theorems and principles (i.e., the D'Alembert principle, Hamilton principle, mass forces analogy, Clapeyron theorem, fundamental energy theorem, and reciprocity theorem) are formulated and proved. These theorems allow for developing efficient methods for the solution of relevant boundary-value problems for the shells of this kind.     

Evaluation of a CCrMnNiSi pressure vessel steel using fracture mechanics and C-shaped specimens

The mechanical fracture toughness and subcritical crack growth properties of a CCrMnNiSi pressure vessel steel were evaluated using a compact specimen and a C-shaped specimen. It was determined that the material characteristics were highly directional. The transverse properties were generally below the longitudinal and differ by a factor of five in the reduction in area and a factor of at least two in fracture toughness. The crack growth characteristics were determined from the power relationship $\text{d}\text{a}\text{d}\text{n}\text{= A(ΔK)}{}^{\mathrm{n}}$ and were found to have different rates in the three directions of the material.     

Fracture of a steampipe—Analysis in terms of fracture mechanics

An investigation into metallurgical aspects of a large steampipe failure is described. It is explained how measurement of the local thinning of the fractured material allowed the toughness of the failed lap weld to be estimated. This information is then linked with the initial defect sizes by means of fracture mechanics relationships to predict stresses to cause local breaching and crack propagation along the pipe. A stress at least five times the nominal service stress must have been present to cause the failure. This was verified in controlled burst tests of identical pipes containing artificial defects similar to the one present at the site of the failure.A by-product of the investigation is a verification of some fracture mechanics relationships and the development of means for finding toughness at a location of fracture after the event.     

Transient heat transfer in Bénard convection

Experimental results are presented for a study of the effects of time-dependent heating on Bénard convection, where the fluids were 5cs (centistoke), 100cs and 500cs viscosity grades of silicone oil. Fluid layer depths were 0.00635 m, 0.01270 m and 0.01905 m. For each run the heat flux at the lower surface was approximately constant, and in the several runs a range of fluxes from 9.2 × 10²to 1.9 × 10⁷ (in dimensionless terms) was covered. The experiments were designed to examine the effects of different heating rates on the onset of convection, on the change of the Rayleigh number with time and on the development of motion. Observations were made from shadowgraph images, which were recorded photographically. As the heat flux at the lower surface is increased, the temperature difference required for the initiation of convection increases while the time to the onset of motion decreases. For the conditions of the present tests a “closed cell” pattern is the first to be observed, shortly after the onset of motion. This pattern does not appear in the steady-state system. Because of the “large” (greater than about 100) Prandtl number, specifying the time and the lower surface heat flux is sufficient to characterize the state of the fluid layer.     

Effects of crack depth and specimen size on ductile crack growth of SENT and SENB specimens for fracture mechanics evaluation of pipeline steels

A strong geometry dependence of ductile crack growth resistance emerges under large scale yielding. The geometry dependence is associated with different levels of crack tip constraint conditions. However, in a recent attempt to identify appropriate fracture mechanics specimens for pipeline steels, an “independent” relationship between the crack growth resistance curves and crack depths for SENT specimens has been observed experimentally. In this paper, we use the complete Gurson model to study the effects of crack depth and specimen size on ductile crack growth behavior. Crack growth resistance curves for plane strain, mode I crack growth under large scale yielding conditions have been computed. SENB and SENT specimens with three different specimen sizes, each specimen size with three different crack depths, have been selected. It has been found that crack tip constraint (Q-parameter) has a weak dependence on the crack depth for specimens in the low constraint regime.     

Deflagrations of localised homogeneous and inhomogeneous hydrogen-air mixtures in enclosures

Two original models for use as novel tools for the design of hydrogen-air deflagration mitigation systems for equipment and enclosures are presented. The first model describes deflagrations of localised hydrogen-air mixtures in a closed space such as a pressure vessel or a well-sealed building while the second model defines safety requirements for vented deflagrations of localised mixtures in an enclosure. Examples of localised mixtures include ‘pockets’ of gas within an enclosure as well as stratified gas distributions which are especially relevant to hydrogen releases. The thermodynamic model for closed spaces is validated against experiments available from the literature. This model is used to estimate the maximum hydrogen inventory in a closed space assuming the closed space can withstand a maximum overpressure of 10 kPa without damage (this is typical of many civil structures). The upper limit for hydrogen inventory in a confined space to prevent damage is found to be equivalent to 7.9% of the closed space being filled with 4% hydrogen. If the hydrogen inventory in a closed space is above this upper limit then the explosion has to be mitigated by the venting technique. For the first time an engineering correlation is presented that accounts for the phenomena affecting the overpressure from localised vented deflagrations, i.e. the turbulence generated by the flame front itself, the preferential diffusion in stretched flames, the fractal behaviour of the turbulent flame front surface, the initial flow turbulence in unburnt mixture, and the increase of the flame surface area due to the shape of an enclosure. Validation of the new vented deflagration model developed at Ulster has been carried out against 25 experiments with lean stratified hydrogen-air mixtures performed by the Health and Safety Executive (UK) and Karlsruhe Institute of Technology (Germany).     

Analysis of flamelet leading point dynamics in an inhomogeneous flow

Several studies have utilized “leading points” concepts to explain the augmentation of burning rates in turbulent flames by flow fluctuations. These ideas have been particularly utilized to explain the strong sensitivity of turbulent burning rates to fuel composition. Leading point concepts suggest that the burning velocity is controlled by the velocity of the points on the flame that propagate farthest out into the reactants – thus, they de-emphasize the classical idea that burning velocity enhancement is due to increases in flame surface area. Rather, within this interpretation, flame area creation is the effect, not the cause, of augmented turbulent burning velocities. However, the theory behind the implementation of leading point concepts in turbulent combustion modeling needs further development and the definition of “leading point” has not been fully clarified. For a certain class of steady shear flows, it is straightforward to demonstrate the leading point concept in an intuitive manner, but the problem becomes more complex when the leading points themselves evolve in time. In this paper, we use the G-equation to describe the flame dynamics and, utilizing results for Hamilton–Jacobi equations from the Aubry–Mather theory, demonstrate both the utility and limitations of leading points interpretations for front propagation, at least for deterministic problems. Specifically, we show how the large-time behavior of the solutions is controlled by discrete points on the flame under certain conditions and is, therefore, independent of the rest of the flow field details – a key hypothesis of leading points theories. However, it is possible to find other conditions where the large time behavior of the flame is not controlled by discrete points on the flame, but rather by the velocity field over its entire surface. Moreover, we also show that even in cases where the burning rate is controlled by discrete points, these points are not necessarily the most forward lying points in the flame front. Finally, we consider the case where the laminar flame speed is a function of flame front curvature and derive exact results for the sensitivity of the front speed to the Markstein length, ?, for ? > 0. These solutions explicitly illustrate how the reduction of front displacement speed for increasing ? can be interpreted in terms of leading points dynamics in some cases.