Stability of crack propagation associated with fracture energy determined by wedge splitting specimen

The wedge splitting test is performed on notched shaped specimens that enables the determination of energies for large fracture surfaces and material exhibiting brittle behaviour. A stability condition is deduced and found to depend on the Young's modulus and the R-curve behaviour. The latter is defined by the fracture toughness K_R and fracture energy R_c both of which depend on the crack length. A stable crack propagation is enhanced by high ratios of K′_R/K_R and R_c/K_R². The wedge loading tends to behave like raising the rigidity of the testing machine. The results are applied on an example with a special geometry.     

Analytical and experimental determination of dynamic impact stress intensity factor for 40 Cr steel

A linear elastic three-dimensional finite element analysis is made to analyze the near field stress behavior of an edge cracked rectangular bar simply supported and subjected to central impact at the back side of the crack. The material is made of 40 Cr steel. Determined numerically are the local time histories of the stress wave, displacement near load point, crack tip strain, and dynamic stress intensity factor K_(d)¹. The above quantities were also measured experimentally by performing impact tests; they agreed well with the analytical results and determine the load at fracture initiation and hence the critical dynamic stress intensity factor K_(d)^1c. The interaction effect between the loading bar and specimen appears to be negligible.     

Modeling of colloid and colloid-facilitated contaminant transport in a two-dimensional fracture with spatially variable aperture

Mathematical models are developed for two-dimensional transient transport of colloids, and cotransport of contaminant/colloids in a fracture-rock matrix system with spatially variable fracture aperture. The aperture in the fracture plane is considered as a lognormally distributed random variable with spatial fluctuations described by an exponential autocovariance function. Colloids are envisioned to irreversibly deposit onto fracture surfaces without penetrating the rock matrix; whereas, the contaminant is assumed to decay, sorb onto fracture surfaces and onto colloidal particles, as well as to diffuse into the rock matrix. The governing stochastic transport equations are solved numerically for each realization of the aperture fluctuations by a fully implicit finite difference scheme. Emphasis is given on the effects of variable aperture on colloid and colloid-facilitated contaminant transport. Simulated breakthrough curves of ensemble averages of several realizations show enhanced colloid transport and more pronounced fingering when colloids are subject to size exclusion from regions of small aperture size. Moreover, it is shown that an increase in the fracture aperture fluctuations leads to faster transport and increases dispersion. For the case of contaminant/colloids cotransport it is shown, for the conditions considered in this work, that colloids enhance contaminant mobility and increase contaminant dispersion.Nomenclature b fracture aperture, L - c contaminant concentration in the fracture, M/L³ - c _m contaminant concentration in the rock matrix, M/L³ - c _o source contaminant concentration, M/L³ - c ^* contaminant concentration adsorbed onto fracture surfaces, M/L² - c _m ^* contaminant concentration adsorbed inside the rock matrix, M/M - d _p colloidal particle diameter, L - D hydrodynamic dispersion coefficient dyadic, L²/t - D Brownian diffusion coefficient for colloids and molecular diffusion coefficient for contaminants, L²/t - D _m effective diffusion coefficient in the rock matrix, L²/t - h total head potential in the fracture, L - K _f partition coefficient for contaminant sorption onto fracture surfaces, L - K _m contaminant partition coefficient in the rock matrix, L³/M - K _n partition coefficient for contaminant sorption onto suspended colloids, L - K _n* partition coefficient for contaminant sorption onto deposited colloids, L³/M - _x fracture length in thex-direction, L - _y fracture length in they-direction, L - n colloid concentration in the liquid phase, M/L³ - n _o source colloid concentration, M/L³ - n ^* colloid concentration adsorbed onto fracture surfaces, M/L² - n _max ^* maximum deposited colloid concentration on fracture surfaces, M/L² - N ^* number of deposited colloidal particles per unit surface area of the fracture, 1/L² - N _max ^* maximum number of deposited colloidal particles per unit surface area of the fracture, 1/L² - q ^* diffusive mass flux into the rock matrix, M/L²t - R retardation factor in the fracture - R _m retardation factor in the rock matrix - s contaminant concentration adsorbed on colloids in the liquid phase, M/M - s _o source solid-phase contaminant concentration onto suspended colloids, M/M - s ^* contaminant concentration adsorbed on deposited colloids, M/M - t time, t - U interstitial velocity vector, L/t - x coordinate along the fracture length, L - y coordinate along the fracture width, L - z coordinate perpendicular to the fracture plane, L - area blocked by a deposited colloidal particle, L² - _L longitudinal dispersivity, L - _T transversal dispersivity, L - fluid specific weight, M/L²t² - fraction of the fracture surface physically covered by colloids - gz dummy integration variable - porosity of the rock matrix - colloid deposition coefficient, L - first-order decay coefficient, 1/t - fluid dynamic viscosity, M/Lt - defined in (18) - _b bulk density of the rock matrix, M/L³ - _p colloidal particle density, M/L³ - standard deviation of the lognormally distributed fluctuations of the fracture aperture     

Influence of stress triaxiality and temperature on void growth and ductile/brittle transition behavior of 40 Cr steel

Examined experimentally are the influence of stress triaxiality and temperature on the growth of microvoids and the ductile/brittle transition (DBT) macrobehavior of 40 Cr steel subjected to two different heat treatments. This is accomplished by testing more than 300 smooth and notched specimens over a temperature range of 20°C to −196°C. Changes in the microstructure morphology are examined by scanning electron microscopy (SEM) and identified with fracture data on a surface constructed from the uniaxial strain ε_c at fracture, the stress triaxiality R_σ and the temperature T. While stress triaxiality has a significant influence on the DBT temperature T_c, it does not affect the ratio of the average radius of voids R_o to that of inclusions R_i. The ratio R_o/R_i is found to increase with temperature and remains constant in specimens with different notch radii regardless of the temperature. Empirical relations between T_c and R_σ⁻ and R_o/R_i and T are proposed to better understand how macrofracture parameters are influenced by microstructure entities.     

Strain energy density criteria for dynamic fracture and dynamic crack branching

Dynamic extension of Sih's fracture criterion based on strain energy density factor, r_c (dW/dV), is used to analyze dynamic crack propagation and branching. Influence of the nonsingular components, which are known as the higher order terms (HOT) in the crack tip stress field, on the strain energy density distribution at a critical distance surrounding the crack tip moving at constant crack velocity is examined. This r_c (dW/dV) fracture criterion is then used to analyze available dynamic photoelastic results of crack branching and of engineering materials.     

Collision dynamics of bubble pairs moving through a perfect liquid

Equations are derived describing the inertial motion of a bubble pair through a perfect liquid. The relative bubble motion is driven by an interactional force induced by the centre of mass motion. This force can be derived from a potential that is proportional tos ⁿ (n3) and that depends on the bubble pair orientation. The path of two bubbles passing each other is investigated. The angle of deflection of the relative velocity in a two-bubble encounter is calculated numerically as a function of the impact parameter, the relative velocityg and the ratio of the centre of mass velocity componentsc ₂/c ₁. The specific conditions necessary for two bubbles to collide are determined. Ifc ₂/c ₁>1 there is a region with irregular behaviour of the deflection angle. The collision cross-section is calculated and depends smoothly ong, approximately proportional tog ^–1, and has a weak dependence onc ₂/c ₁.     

Allowable crack sizes for railway wheels and rails

Determined are the critical crzes and crack growth characteristics for train car wheels and rails. Service and test limit size of cracks need to be distinguished in view of the difference between subcritical and the onset of rapid crack propagation. Probabilistic calculations have many advantages, but they cannot accurately predict neither the real critical minimum crack size (a_c)_min nor the real maximum crack growth increment Δa_max. As representative values of the minimum critical crack size a_c^* and maximum crack growth increment Δa^* are chosen for the calculations, therefore, that values which have a survival and crack growth probability, respectively, of 90%. Safety factors S(a) and are needed to account for the scatter of a_c and Δa for probabilities of more than 90%. Probabilistic fracture mechanics is applied to analyze the behavior of transverse cracks in the rim of tread-braked monobloc wheels, transverse head cracks in rails and aluminothermic rail welds. These informations are supplied by the German State Railways (DR) the Office of Research and Experiments (ORE) of the International Union of Railways (UIC).     

Constitutive relation of an orthorhombic polycrystal with the shape coefficients

An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function (CSF) and the orientation distribution function (ODF), respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D–functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s ^l _m0 and the texture coefficients c ^l _mn , respectively. Assuming that C ^eff in the constitutive relation depends on the shape coefficients s ^l _m0 and the texture coefficients c ^l _mn , by the principle of material frame-indifference we derive an analytical expression for C ^eff up to terms linear in s ^l _m0 and c ^l _mn , and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C ^eff contains six unspecified material constants (λ, μ, c, s ₁, s ₂, s ₃), five shape coefficients (s ² ₀₀ , s ² ₂₀,s ⁴ ₀₀ , s ⁴ ₂₀ , s ⁴ ₄₀ ), and three texture coefficients (c ⁴ ₀₀ , c ⁴ ₂₀ , c ⁴ ₄₀ ). The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients s ² _m0 and s ⁴ _m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results. The project supported by the National Natural Science Foundation of China (10562004), and the Oversea Returning Grant of China. The English text was polished by Keren Wang.     

Stochastic functional expansion in elasticity of heterogeneous solids

The Volterra-Wiener functional expansion is employed to the analysis of statistic properties for random heterogeneous solids. For simplicity, the technique is displayed on an elastic suspension of spheres. The basis function in the expansion is chosen as that corresponding to the so-called “perfect disorder” of spheres (PDS), recently introduced by the authors. An infinite hierarchy of equations for the kernels in the expansion is derived whose truncating after the nth equation is shown to yield results for the averaged statistical characteristics which are valid to order cⁿ_f, where c_f is the volume fraction of the spheres. The kernels for the first and the second approximations, n = 1, 2, are found and related to the displacement fields in an infinite elastic body containing, respectively, one and two spherical inhomogeneities. Within the frame of the so-called singular approximation the overall tensor of elastic moduli for a suspension of perfectly disordered spheres is shown to coincide to the order c²_f with a formula, earlier obtained by means of the method of the effective field.     

On the modeling of miscible flow in multi-component porous media

An analytical model of miscible flow in multi-component porous media is presented to demonstrate the influence of pore capacitance in extending diffusive tailing. Solute attenuation is represented naturally by accommodating diffusive and convective flux components in macropores amd micropores as elicited by the local solute concentration and velocity fields. A set of twin, coupled differential equations result from the Laplace transform and are solved simultaneously using a differential operator for one-dimensional flow geometry. The solutions in real space are achieved using numeric inversion. In addition, to represent more faithfully the dominant physical processes, this approach enables efficient and stable semi-analytical solution procedure of the coupled system that is significantly more complex than current capacitance type models. Parametric studies are completed to illustrate the ability of the model to represent sharp breakthrough and lengthy tailing, as well as investigating the form of the nested heterogeneity as a result of solute exchange between macropores and micropores. Data from a laboratory column experiment is examined using the present model and satisfactory agreement results.Roman Letters a rate coefficient of internal flow - b velocity ratio (v ₁/v ₂) - h dispersion ratio (D ₂/D ₁) - c ₁ macropore concentration - c ₂ micropore concentration - ¯c ₁ macropore concentration in Laplace space - ¯c ₂ micropore concentration in Laplace space - c ₁ ⁰ macropore concentration at source location - c ₂ ⁰ micropore concentration at source location - D ₁ macropore dispersion coefficient - D ₂ micropore dispersion coefficient - f fraction of pore space occupied by fluid in primary channel - L length of laboratory sample column - K mass exchange rate - t time from initial stage - v ₁ primary flow channel velocity - v ₂ micropore interstitial velocity - x distance from source - y dimensionless distance Greek Letters equivalent Péclet number - dimensionless time, or injected pore volume     

A new ductile fracture theory and its applications

This investigation discusses further the extent to which a new damage theory recently proposed by the author can serve as a unified theory to characterize various ductile failure problems. A general damage integral and corresponding criterion for ductile fracture are presented. A new parameter for ductile fracture is emphasized, which is experimentally verified as a material constant independent of stress state, has clear physical meaning, and can easily be determined. The applicability of this theory to evaluation of the ductility of welds and engineering materials under various conditions is examined. Also, it is used to predict the effect of residual stress on failure of welds, to predict sheetforming limits, and to correlate the variability of elasto-plastic fracture toughness valuesJ _1c and δ _c with different specimen geometries. A new constraint correction method is proposed, and constraint corrected new toughness parameterJ _dc and δ _dc are recommended. Experiments have shown that the toughness variation with different specimen geometries can effectively be removed by use of the method. The general applicability of the theory to characterization of various ductile failures provides a new design tool for engineering components or structures.     

Global Semigroup of Conservative Solutions of the Nonlinear Variational Wave Equation

We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation u _tt − c(u)(c(u)u _x ) _x  = 0. We allow for initial data u| _{t = 0} and u _t | _t=0 that contain measures. We assume that 0 < k^-1 \leqq c(u) \leqq k{0 < \kappa^{-1} \leqq c(u) \leqq \kappa}. Solutions of this equation may experience concentration of the energy density (u_t²+c(u)²u_x²)dx{(u_t^2+c(u)^2u_x^2){\rm d}x} into sets of measure zero. The solution is constructed by introducing new variables related to the characteristics, whereby singularities in the energy density become manageable. Furthermore, we prove that the energy may focus only on a set of times of zero measure or at points where c′(u) vanishes. A new numerical method for constructing conservative solutions is provided and illustrated with examples.     

Boundary Layers and KPP Fronts in a Cellular Flow

We study an eigenvalue problem associated with a reaction-diffusion-advection equation of the KPP type in a cellular flow. We obtain upper and lower bounds on the eigenvalues in the regime of a large flow amplitude A ≪ 1. It follows that the minimal pulsating traveling front speed c _*(A) satisfies the upper and lower bounds C ₁ A ^1/4≦ c _*(A)≦ C ₂ A ^1/4. Physically, the speed enhancement is related to the boundary layer structure of the associated eigenfunction – accordingly, we establish an “averaging along the streamlines” principle for the unique positive eigenfunction.     

Consecutive chemical reactions in an annular reactor with non-newtonian flow

The purpose of this paper is to analyze the homogeneous consecutive chemical reactions carried out in an annular reactor with non-Newtonian laminar flow. The fluids are assumed to be characterized by a Ostwald-de Waele (powerlaw) model and the reaction kinetics is considered of general order. Effects of flow pseudoplasticity, dimensionless reaction rate constants, order of reaction kinetics and ratio of inner to outer radii of reactor on the reactor performances are examined in detail.Nomenclature c _A concentration of reactant A, g.mole/cm³ - c _B concentration of reactant B, g.mole/cm³ - c _A0 inlet concentration of reactant A, g.mole/cm³ - C ₁ dimensionless concentration of A, c _A/c _A0 - C ₂ dimensionless concentration of B, c _B/c _A0 - C ₁ dimensionless bulk concentration of A - C ₂ dimensionless bulk concentration of B - D _A molecular diffusivity of A, cm²/sec - D _B molecular diffusivity of B, cm²/sec - k _A first reaction rate constant, (g.mole/cm³)^1–m /sec - k _B second reaction rate constant, (g.mole/cm³)^1–n /sec - K ₁ dimensionless first reaction rate constant, k _A r ₀ ² c _A0 ^m–1 /D _A - K ₂ dimensionless second reaction rate constant, k _B r ₀ ² c _A0 ^n–1 /D _B - K apparent viscosity, dyne(sec) ^m /cm² - m order of reaction kinetics - n order of reaction kinetics - P pressure, dyne/cm² - r radial coordinate, cm - r _i radius of inner tube, cm - r _max radius at maximum velocity, cm - r _o radius of outer tube, cm - R dimensionless radial coordinate, r/r _o - s reciprocal of rheological parameter for power-law model - u local velocity, cm/sec - u _max maximum velocity, cm/sec - u bulk velocity, cm/sec - U dimensionless velocity, u/u - z axial coordinate, cm - Z dimensionless axial coordinate, zD _A/r ₀ ² /u - ratio of molecular diffusivity, D _B/D _A - ratio of inner to outer radius of reactor, r _i/r _o - ratio of radius at maximum velocity to outer radius, r _max/r _o     

Structuration de la convection mixte en milieu poreux confiné latéralement et chauffé par le bas : effets d''inertiePattern formation of mixed convection in a porous medium confined laterally and heated from below: effect of inertia

We consider the onset of convection in a porous medium heated from below and subjected to a horizontal mean flow. The effect of porous inertia is studied, and the transverse aspect ratio a of the medium is taken into accout. We find that the dominant modes are longitudinal rolls (L.R) if a is an integer or transverse traveling rolls (T.R) if a is below a_c with a_c<1. When a is not an integer with a>a_c, the setting on patterns are oscillatory three-dimensional structures (3D) for a>1 or T.R for a_c<a<1 provided that the Reynolds number remains below a critical value Re_K^*. We show that these structures are replaced by L.R if Re_K>Re_K^*. To cite this article: A. Delache et al., C. R. Mecanique 330 (2002) 885–891.     

Calculation of tracer travel times in fractured geothermal reservoirs

A new method is presented for calculating the time taken for tracer to move between wells in a fractured geothermal reservoir. The reservoir model considered is a two-dimensional confined layer, but many wells and a background regional flow can be included. Also, either a straight or dog-leg, finite length, high permeability fracture can be included. The fracture can alternatively be considered as a barrier to lateral flow. The flow field is represented by complex potentials which are used to accurately calculate the streamline locations and tracer travel times are evaluated by numerical integration along the streamlines. The methods developed are used to model the dispersion of tracer produced by large-scale differences in the flow paths along which the tracer travels from the release well to the observation well(s).Notation C _d concentration, kg m^-3 - C dimensionless concentration - C _obs dimensionless concentration at the observation well - f dimensionless distance between the injection and production wells - h _d fracture half length, m - h dimensionless fracture half length - H reservoir thickness, m - Ln(·) complex algorithm - M mass of tracer released, kg - n porosity, dimensionless - N _b number of streamlines calculated for blob release - N _f number of subdivisions for the high permeability fracture - N _w number of streamlines calculated for injection well release - ¢P _d complex potential, m² s^-1 - P dimensionless complex potential - Q _c characteristic well volume flow rate, m³ s^-1 - q _p production well volume flow rate, m³ s^-1 - R _c characteristic length, m - t _d time, s - t _b dimensionless response start time - t dimensionless time - t _td tracer travel time (without dispersion), s - t _t dimensionless tracer travel time - u average fluid velocity, ms^-1 - v _d background fluid speed, m s^-1 - v dimensionless background fluid speed - x _d Cartesian coordinate, m - x dimensionless Cartesian coordinate - y _d Cartesian coordinate, m - y dimensionless Cartesian coordinate - (·) Dirac delta distribution - _d velocity potential, m² s^-1 - dimensionless velocity potential - angle from the positive x axis to the direction of the background flow - _d stream function, m² s^-1 - dimensionless stream function - complex number - circle mapped to the fracture by the Joukowski transformation - region occupied by the blob - complex number - p production/observation well - r release well     

Edge fracture in cone-plate and parallel plate flows

Edge fracture is an instability of cone-plate and parallel plate flows of viscoelastic liquids and suspensions, characterised by the formation of a `crack' or indentation at a critical shear rate on the free surface of the liquid. A study is undertaken of the theoretical, experimental and computational aspects of edge fracture. The Tanner-Keentok theory of edge fracture in second-order liquids is re-examined and is approximately extended to cover the Criminale-Ericksen-Filbey (CEF) model. The second-order theory shows that the stress distribution on the semi-circular crack is not constant, requiring an average to be taken of the stress; this affects the proportionality constant, K in the edge fracture equation −N _2c = KΓ/a, where N _2c is the critical second normal stress difference, Γ is the surface tension coefficient and a is the fracture diameter. When the minimum stress is used, K = 2/3 as found by Tanner and Keentok (1983). Consideration is given to the sources of experimental error, including secondary flow and slip (wall effect). The effect of inertia on edge fracture is derived. A video camera was used to record the inception and development of edge fracture in four viscoelastic liquids and two suspensions. The recorded image was then measured to obtain the fracture diameter. The edge fracture phenomenon was examined to find its dependence on the physical dimensions of the flow (i.e. parallel plate gap or cone angle), on the surface tension coefficient, on the critical shear rate and on the critical second normal stress difference. The critical second normal stress difference was found to depend on the surface tension coefficient and the fracture diameter, as shown by the theory of Tanner and Keentok (1983); however, the experimental data were best fitted by the equation −N _2c = 1.095Γ/a. It was found that edge fracture in viscoelastic liquids depends on the Reynolds number, which is in good agreement with the inertial theory of edge fracture. Edge fracture in lubricating grease and toothpaste is broadly consistent with the CEF model of edge fracture. A finite volume method program was used to simulate the flow of a viscoelastic liquid, obeying the modified Phan-Thien-Tanner model, to obtain the velocity and stress distribution in parallel plate flow in three dimensions. Stress concentrations of the second normal stress difference (N ₂) were found in the plane of the crack; the velocity distribution shows a secondary flow tending to aid crack formation if N ₂ is negative, and a secondary flow tending to suppress crack formation if N ₂ is positive. Received: 4 January 1999 Accepted: 19 May 1999     

Non-self-similar crack growth in elastic-plastic finite thickness plate

This work is concerned with non-self-similar crack growth in medium strength metal plates while the loading step, plate thickness and material properties are altered. The three-dimensional elastic-plastic finite element stress analysis is combined with the strain energy density criterion for modeling the material damage process from crack initiation to final global instability including the intervening stage of slow crack growth. Both inelastic deformation and crack growth are accounted for each increment of loading such that the redistribution of stresses and strains are made for each new crack profile. Numerical results are obtained for the center cracked plate configuration under uniform extension with twenty-seven (27) different combinations of specimen thickness, loading step and material type. The fracture toughness S_c being related to K_1c for three different materials are predicted analytically from the corresponding uniaxial tensile test data. Effective strain energy density factor and half crack length are defined so that the results can be compared with their two-dimensional counterparts. Crack growth resistance curves (R-curves) are constructed by plotting as a function of . The condition is found to prevail during slow crack growth. Translation and/or rotation of the lines can yield results other than those calculated and serve a useful purpose for scaling component size and test time. The minimum thickness requirement for the ASTM valid K_1c test is also discussed in connection with predictions based on the strain energy density criterion. The corresponding K_1c for smaller specimens that exhibit moderate ductility and nonlinearity can also be obtained analytically. In such cases, the influence of loading step can be significant and should not be neglected. Notwithstanding the shortcomings of the theory of plasticity, the qualitative features of non-self-similar crack growth are predicted by the strain energy density criterion. Any refinements on the analytical modeling of the material damage process would only affect the results qualitatively, a subject that is left for future investigation.     

Viscosity of concentrated protein solutions

The viscosity of solutions of four proteins (Bovine Serum Albumin, Ovalbumin, _s-1 Casein, Lysozyme), brought to the random coil conformation, has been measured over a large concentration range extending into the entanglement region. A master curve is obtained in the dilute and semi-dilute regions with the reduced variables and of Simha and Utracki.By using Graessley's expression for the polymer coil expansion at a given concentration in the semi-dilute region (c ^* c c ^**), a simple equation is established giving the relative viscosity _r as a function of concentrationc: forc ^* c c ^**, ln _r = 2a[]c ^*(c/c ^*)^1/2a – (2a - 1)[]c ^*; wherec ^* is the incipient overlap concentration, [] the intrinsic viscosity, anda the Mark-Houwink exponent for the polymer-solvent considered.This equation fits well the experimental results. The adjustment yields for the parametera values which are comprised between 0.6 and 0.7, as expected, for Bovine Serum Albumin and Ovalbumin, but very close to 0.5 for _s-1 Casein and Lysozyme. This can be explained by the fact that the molecular weights of the two latter proteins are lower than, or very close, the critical molecular weight; the critical molecular weight is estimated to be about 20000.     

The ultra-low Reynolds number airfoil wake

Lift force and the near wake of an NACA 0012 airfoil were measured over the angle (α) of attack of 0°–90° and the chord Reynolds number (Re _c ), 5.3 × 10³–5.1 × 10⁴, with a view to understand thoroughly the near wake of the airfoil at low- to ultra-low Re _c . While the lift force is measured using a load cell, the detailed flow structure is captured using laser-Doppler anemometry, particle image velocimetry, and laser-induced fluorescence flow visualization. It has been found that the stall of an airfoil, characterized by a drop in the lift force, occurs at Re _c  ≥ 1.05 × 10⁴ but is absent at Re _c  = 5.3 × 10³. The observation is connected to the presence of the separation bubble at high Re _c but absence of the bubble at ultra-low Re _c , as evidenced in our wake measurements. The near-wake characteristics are examined and discussed in detail, including the vortex formation length, wake width, spanwise vorticity, wake bubble size, wavelength of K–H vortices, Strouhal numbers, and their dependence on α and Re _c .