Frictional Shear Stress Research Articles

Measurement and Calculation of Turbine Cascade Endwall Pressure and Shear Stress

The complex three-dimensional fluid flow on the endwall in an axial flow turbine blade or vane passage has been extensively investigated and reported on in turbomachinery literature. The aerodynamic loss producing mechanisms associated with the endwall flow are still not fully understood or quantitatively predictable. To better quantify wall friction contributions to endwall aerodynamic loss, low Mach number wind tunnel measurement of skin friction coefficients have been made on one endwall of a large scale cascade of high pressure turbine airfoils, at engine operating Reynolds numbers. Concurrently, predictive calculations of the endwall flow shear stress have been made using a computational fluid dynamics (CFD) code. Use of the oil film interferometry skin friction technique is described and applied to the endwall, to measure local skin friction coefficients and shear stress directions on the endwall. These are correlated with previously reported measured local endwall pressure gradients. The experimental results are discussed and compared to the CFD calculations, to answer questions concerning endwall aerodynamic loss predictive ability.

Photoelastic analysis of matrix stresses around a high modulus sapphire fibre by means of phase-stepping automated polariscope

Abstract The matrix stress field has been quantified and the micromechanics of fragmentation of sapphire fibres in an epoxy matrix have been investigated using phase-stepping photoelasticity and fluorescence spectroscopy. Contour maps of the isochromatic fringe order (related to the difference in principal stresses) have been used to describe in detail the changes in matrix stress field during stress transfer in the presence of a matrix crack and interfacial debonding. The profiles of interfacial shear stress at various levels of applied matrix stress indicate clearly the extent of interfacial debonding. The results show that the matrix crack significantly reduces the efficiency of stress transfer at the interface. The frictional shear stress at the debonded interface has been found experimentally to be 3–10 MPa for a sapphire fibre embedded in the LY5052/HY5052 epoxy system. The relationship between interfacial shear stress and axial fibre stress is discussed. The interfacial shear stress profiles obtained from photoelasticity has been compared to that calculated from the axial fibre stress measured by shifts in fluorescence spectral bands.

Shear/Compressive Strength of GFRP Under Mixed Load Condition at Low Temperature

Insulation of superconducting magnet systems requires excellent electrical insulating properties, compressive strength and flexibility so that it can bear the compressive stress of the electromagnetic force and the shear stress caused by the deformation of each conductor in these magnets. GFRP is suitable for these insulation systems and most superconducting magnet systems use it. Although the interlaminar shear strength of GFRP is about a tenth of its compressive strength, this strength increases under a combination of stresses. GFRP strengths under shear/compressive loading are specified for optimum designs. Therefore, we can apply GFRP against shear/compressive loading for which static and fatigue strengths are the dominant factors in magnet life assessment. The coefficient of friction of the surface affects the static and fatigue behavior at low temperature. Two types of tests were carried out to simulate the combined stresses, and shear/compressive static and fatigue tests were performed at 77 K on GFRP. Employing different angle test fixtures, GFRP specimens were loaded with various levels of shear and compressive stress. We evaluated the strength of insulators that sustain compressive and frictional shear stresses to take into account the stress redistributions for cases both with and without the occurrence of surface slips. A new criterion for the shear/compressive static and fatigue failure is proposed in this study.

Thermoforming-Stamping of Continuous Glass Fiber/Polypropylene Composites: Interlaminar and Tool–Laminate Shear Properties

The results of interlaminar and tool–laminate shear tests performed on a twill 2 2 PP/glass fabric are described in this paper. The influence of the laminate temperature, pullout velocity and normal pressure on the interlaminar shear stress and friction coefficient are evaluated, as well as the effect of cooling the specimen from the melt to simulate real forming conditions. Opposite trends were observed for the variation of the shear stress and friction coefficient whether the tests were performed above the melt temperature of the matrix or above the crystallization temperature (135, 140, and 155 after cooling from the melt temperature. For the interlaminar shear tests, this was caused by the shift from an interlaminar to an intralaminar shear deformation mode occurring. For the tool–laminate shear tests, this was caused by the shift from matrix shear at the interface tool–laminate to direct Coulomb friction of the fibers with the tool with an increase of the normal pressure and/or an increase of the matrix viscosity with decreasing temperatures. Above the melt temperature of the matrix, the friction coefficient and shear stress were higher at the tool–laminate interface than in the interlaminar region while at temperatures close to the crystallization temperature they became lower at the tool–laminate interface. A summary of these observations is made and a discussion of their possible impact on the forming of parts is enlightened.

A time dependent micro-mechanical fiber composite model for inelastic zone growth in viscoelastic matrices

In this work, a fiber composite model is developed to predict the time dependent stress transfer behavior due to fiber fractures, as driven by the viscoelastic behavior of the polymer matrix, and the initiation and propagation of inelastic zones. We validate this model using in situ, room temperature, micro-Raman spectroscopy fiber strain measurements. Multifiber composites were placed under constant load creep tests and the fiber strains were evaluated with time after one fiber break occurred. These composite specimens ranged in fiber volume fraction and strain level. Comparison between prediction and MRS measurements allows us to characterize key in situ material parameters, the critical matrix shear strain for inelastic zones and interfacial frictional slip shear stress. We find that the inelastic zone is predominately either shear yielding or interfacial slipping, and the type depends on the local fiber spacing.

Bottom friction and time-dependent shear stress for wave-current interaction

Bottom shear stresses in the wave-current interaction case are calculated using a numerical turbulent-closure model of the K-L type, where K is the turbulent kinetic energy and L is the length scale of the turbulence. Parameterized results of the friction coefficient are obtained in the case of a rough turbulent flow, as presented by Soulsby et al. [14], and these are here extended to the case of a smooth turbulent flow. Several comparisons with experiments and other results presented in the literature, particularly by Tanaka and Thu [19], show close agreement. A new parameterization of the time-series shear stress is proposed that includes a local friction coefficient and yields better results than the parameterization suggested by Soulsby et al. [14].

Slip-line modeling of machining with a rounded-edge tool—Part II: analysis of the size effect and the shear strain-rate

Part II of the present study quantitatively analyzes orthogonal metal cutting processes based on the new slip-line model proposed in Part I. The applicable range of the model is illustrated, followed by an explanation of the non-unique nature of the model. It is suggested that the tool edge roundness be comprehensively defined by four variables. Namely: tool edge radius, position of the stagnation point on the tool edge, tool–chip frictional shear stress above the stagnation point on the tool edge, and tool–chip frictional shear stress below the stagnation point on the tool edge. The effects of these four variables on eight groups of machining parameters are investigated. These include (1) cutting force, thrust force, resultant force, and the ratio of cutting force to thrust force; (2) ploughing force; (3) chip up-curl radius; (4) chip thickness; (5) tool–chip contact length; (6) thickness of the primary shear zone; (7) average shear strain in the primary shear zone; and (8) average shear strain-rate in the primary shear zone. The importance of tool edge roundness is further reinforced by a series of new research findings made in this paper. It is revealed that the size effect highly depends on the material constitutive behavior in machining. The dependence of the thickness of the primary shear zone and the dependence of the magnitude of shear strain-rate in the primary shear zone on the tool edge radius are well demonstrated. A surprisingly good agreement between theory and experiments is reached.

Machining with tool–chip contact on the tool secondary rake face—Part I: a new slip-line model

Given the growing number of applications of groove-type chip breaker tools in modern machining, it is becoming increasingly important to study the tool–chip contact on the tool secondary rake face. This type of tool–chip contact significantly changes not only the state of stresses in the plastic deformation region, but also changes the distribution of forces and temperatures over the tool rake face. A new slip-line model accounting for the tool–chip contact on the tool secondary rake face is proposed in this paper. The model also takes into account chip curl and incorporates seven slip-line models developed for machining during the last six decades as special cases. Dewhurst and Collins's matrix technique for numerically solving slip-line problems and Powell's algorithm of nonlinear optimization are employed in the mathematical formulation of the model. The inputs of the model include (a) the tool primary rake angle γ 1, (b) the tool secondary rake angle γ 2, (c) the tool land length h, (d) the undeformed chip thickness t 1, (e) the ratio of hydrostatic pressure P A to the material shear flow stress k, (f) the ratio of frictional shear stress τ 1 on the tool primary rake face to the material shear flow stress k, and (g) the ratio of frictional shear stress τ 2 on the tool secondary rake face to the material shear flow stress k. The outputs of the model include (a) the cutting force F c/ kt 1 w and the thrust force F t/ kt 1 w, (b) the chip up-curl radius R u, (c) the chip thickness t 2, and (d) the natural tool–chip contact length l n.

Evaporation heat transfer of steady thin film in micro capillary tubes of micron scale

AbstractThis paper reports that the heat transfer mechanism of phase change in a capillary tube belongs to liquid film conduction and surface evaporation. The surface evaporation is influenced by vapor temperature, vapor‐liquid interfacial temperature, and vapor‐liquid pressure difference. In the vapor‐liquid flow mechanism, flow is effected by both the gradient of disjoining pressure, and the gradient of capillary pressure. The mechanism of vapor‐liquid interaction consists of the shear stress caused by momentum transfer owing to evaporation, and frictional shear stress due to the velocity difference between vapor and liquid. In the model presented for a capillary tube, the heat transfer, vapor‐liquid flow, and their interaction are more comprehensively considered. The thin film profile and heat transfer characteristics have close relations with a capillary radius and heat transfer power. The results of calculation indicate that the length of the evaporating interfacial region decreases to some extent with decreasing capillary radius and increasing heat transfer power. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 513–523, 2002; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/htj.10050

Interfacial bond strength and fracture energy at room and elevated temperature in titanium matrix composites (SCS-6/Timetal 834)

Push-out experiments in the temperature range from room temperature to 530 °C have been performed. On the basis of the measured maximum load to break the fibre/matrix bond and the load to overcome frictional shear stresses finite element analyses are performed to derive an interfacial shear strength and interfacial fracture energy for the different test temperatures. The thus derived material properties decrease at increasing test temperature. In the analyses the in-homogeneity of the (shear) stress distribution plays an important role for the thermal as well as for the mechanical stress distribution. Although only the energy concept requires principally an initial debond length, it is shown that without an initial defect the shear strength concept leads to unrealistic results. The results presented are valid if it can be accepted that during specimen preparation an initial debonded zone of 12–18 μm at the surface is introduced.

Influence of Material Anisotropy and Friction on Ring Deformation

The influence of material anisotropy and friction on ring deformation has been examined in relation to the distribution of normal pressure and frictional shear stress, deformed ring shapes, and estimated errors in the coefficient of friction. Based on the flow rule associated with von Mises’ and Hill’s yield criteria, the analyses have been carried out with the finite element method (FEM) for three cases, namely, (1) an anisotropic ring oriented 90 deg to the axis of rotational symmetrical anisotropy under uniform coefficient of friction; (2) an isotropic ring under frictional anisotropy condition; and (3) an anisotropic ring oriented 0 deg to the axis of rotational symmetrical anisotropy under uniform coefficient of friction. In the first two cases, the results show that the influence of anisotropy on ring deformation is quite similar to that obtained by changing the frictional condition. Therefore, in the third case, if the anisotropic behavior is mistakenly attributed to friction, the possible estimated error for the coefficient of friction can be as high as 80 percent for a pronounced anisotropic material. Deformed ring shapes have been verified in experiments using the extruded annealed aluminum alloy AA6082 (Al-Si1Mg0.9Mn0.1).

Raman spectroscopy study of high-modulus carbon fibres: effect of plasma-treatment on the interfacial properties of single-fibre–epoxy composites: Part II: Characterisation of the fibre–matrix interface

High-modulus carbon fibres from different precursors were submitted to an oxygen plasma-treatment under similar conditions. Single-fibre epoxy composites were prepared from them, and fragmentation tests were performed in order to characterise fibre–matrix interfacial adhesion. Raman spectroscopy has been used in the present work to map the strain along the fibre during tensile loading of the matrix. The strain distributions obtained agreed well with the prediction of analytical models used conventionally to describe load transfer at interfaces. Interfacial shear stress distributions were then obtained from these distributions according to the conventional force–balance concept. The interfacial shear strength (IFSS) and frictional shear stress ( τ f) values were calculated to quantify the degree of fibre–matrix adhesion. It was found that both parameters increased dramatically after the surface treatment, confirming the ability of cold plasma oxidation to improve the adhesion of carbon fibre to epoxy matrices. A dependence of the IFSS on the degree of surface order, as given by the structural order parameter I D/( I D+ I G), calculated from the relative intensities of the D and G bands of Raman spectra, was found. This supports the role played by the graphitic structure in fibre–matrix adhesion.

An investigation into friction in dynamic plane upsetting

The evaluation of friction on the friction interface in plane-strain upsetting is developed. The distribution of friction shear stress is derived and found to be dependent on the ratio (called the F-coefficient) of the second derivative and the first derivative of the velocity in the x-direction. According to the value of the F-coefficient, friction conditions such as sticking, frictionless, and many kinds of function approximated to linear, exponential, and arc-tangent can be expressed easily. An optimal approach with velocity parameters is used to calculate the F-coefficient at various reductions in height in an experimental approach. It is shown that this method presents a good approach to evaluate friction in comparison with experimental data.

Role of Internal Friction in Indentation Damage in a Mica‐Containing Glass‐Ceramic

The indentation response of a mica‐containing glass‐ceramic that exhibits shear‐driven yield in an indentation test is interpreted in terms of events occurring on the microstructural scale. It is proposed that shear‐driven damage within the specimen occurs via internal sliding along cleavage planes within the mica platelets. The sliding surfaces in this case are considered to be atomically smooth so the real and apparent areas of contact coincide. The frictional shear stress is thus independent of the normal forces arising from thermal mismatch stresses and only depends on the work of adhesion of the interface and the scale of the contacts. The scale of contacts for these materials lies within an intermediate zone in which the frictional shear stress arises from the stress required to nucleate dislocation‐like discontinuities within the material. This leads to a size effect similar to that experienced by a crack in Mode II loading and is in accordance with previous work in which a connection between such a size effect and the macroscopic response of the material was identified. This work has particular relevance to the design and manufacturing of ceramics in machining, wear, bearings, and coatings applications.

A class of slipline field solutions for metal machining with Coulomb friction at the chip–tool interface

The present investigation is concerned with a class of slipline field solutions for metal machining involving chip-curl assuming Coulomb friction at the chip–tool interface. An elastic contact zone is assumed beyond the plastically stressed region to satisfy the statical requirements of the fields. The non-linearity arising due to Coulomb friction at the interfaces is analysed by the method proposed in the literature. At low coefficient of friction, the chip–tool contact is governed by slipping friction only and the frictional shear stress nowhere equals the yield stress in shear. As coefficient of friction increases, sticking of the chip begins at the tool tip and spreads to the plastic contact region. At high coefficient of friction, the plastic contact is therefore governed by sticking as well as slipping friction followed by slipping contact in the elastic contact zone. Results are presented for variation in natural contact length, sticking contact length, cutting forces and pressure distribution at the chip–tool interface with variation in rake angle and interface friction condition both for power law and exponential pressure distribution in the elastic contact zone.

A Study of the Pull-Out Performance of PPTA Fibres in Composites of Ethylene-Type Ionomer Matrices/PPTA Fibres

The mean frictional shear stresses of six ionomer resins and sized Kevlar fibre were determined from fibre pull-out tests. A study of the failure mechanisms occuring during pull-out revealed that fibre delamination and fibre resin adhesion were factors which increased the measured frictional shear stresses and that there was a definite grouping of high and low frictional shear stress values. The low frictional shear stress values were used to calculate the mean frictional shear stress values, τ B , because these were uncomplicated by fibre delamination and fibre resin adhesion, since these factors (delamination and adhesion) are certainly not unexpected in an ionomer/Kevlar composite. From these shear stress values, it was determined that critical fibre lengths should be between 35 and 72 mm for the high tensile strength Kevlar fibres within an ionomer matrix, for the composite to be used effectively. The ratio of the debonding force (F B ) to the frictional shear force (F F ), 0, did not vary significantly with the lengths of the embedded reinforcing fibres. Both debonding and frictional forces indicate increasing trends with the interfacial contact areas. The ratio of the interfacial bonding strength (τ B ) to the frictional shear stress (τ F ), o, for the resin PEA-6 compared to the surface modified poly(p-phenylene terephthalamide) (PPTA) fibre ranged from 2 to 24. These ratios were grouped into two, viz: those where o>11 and those with o 11 provided a mean frictional shear stress of 0.94 MPa and a standard deviation, s, of 0.23 MPa (the number of test samples, n, was 9). This value is little different from the frictional shear stresses measured for sized PPTA (0.84 MPa). The decrease in the value of o is attributed to the decrease in τ B , due to the surface modification reaction, without necessarily affecting the frictional shear stress, τ F .

A Study of the Pull-Out Performance of PPTA Fibres in Composites of Ethylene-Type Ionomer Matrices/PPTA Fibres

The mean frictional shear stresses of six ionomer resins and sized Kevlar fibre were determined from fibre pull-out tests. A study of the failure mechanisms occurring during pull-out revealed that fibre delamination and fibre resin adhesion were factors which increased the measured frictional shear stresses and that there was a definite grouping of high and low frictional shear stress values. The low frictional shear stress values were used to calculate the mean frictional shear stress values, τB, because these were uncomplicated by fibre delamination and fibre resin adhesion, since these factors (delamination and adhesion) are certainly not unexpected in an ionomer/Kevlar composite. From these shear stress values, it was determined that critical fibre lengths should be between 35 and 72 mm for the high tensile strength Kevlar fibres within an ionomer matrix, for the composite to be used effectively. The ratio of the debonding force (FB) to the frictional shear force (FF), θ, did not vary significantly with the lengths of the embedded reinforcing fibres. Both debonding and frictional forces indicate increasing trends with the interfacial contact areas. The ratio of the interfacial bonding strength (τB) to the frictional shear stress (τF), ϕ, for the resin PEA-6 compared to the surface modified poly(p-phenylene terephthalamide) (PPTA) fibre ranged from 2 to 24. These ratios were grouped into two, viz: those where ϕ > 11 and those with ϕ < 7. Using only the τF where ϕ > 11 provided a mean frictional shear stress of 0.94 MPa and a standard deviation, s, of 0.23 MPa (the number of test samples, n, was 9). This value is little different from the frictional shear stresses measured for sized PPTA (0.84 MPa). The decrease in the values of ϕ is attributed to the decrease in τB, due to the surface modification reaction, without necessarily affecting the frictional shear stress, τF.

A new methodology for determining the stress state of the plastic region in machining with restricted contact tools

In rigid-plastic slip-line theory, once the geometry of the slip-line field is established, the stress state of the plastic region (including the primary and secondary deformation zones) in restricted contact machining is governed by the hydrostatic pressure P A (at a point on the intersection line of the shear plane and the work surface to be machined) and the frictional shear stress τ on the tool rake face. Based on the recently established universal slip-line model and a detailed study of six representative machining cases, a new methodology for determining the stress state of the plastic region, i.e. maximum value principle, is presented in this paper. According to this principle, the stress state of the plastic region can be determined by giving both P A and τ their theoretical maximum permissible values. The theoretical maximum permissible values of P A and τ can be found by satisfying four mechanical and geometrical constraint conditions under which the universal slip-line model applies. A comprehensive assessment factor is introduced in this paper. It is shown that the three machining parameters investigated in this present study, i.e. cutting force ratio, chip thickness ratio, and chip back-flow angle can be simultaneously considered to form a comprehensive criterion to compare predicted and experimental results. The applicable range of the maximum value principle is also discussed.

A simulation of three-dimensional metal rolling processes by rigid–plastic finite element method

Using different frictional shear stress models, mesh division and number of elements in the deformation zone, this paper focuses on analysing the influence of friction variation on the convergence and results of simulation such as rolling pressure, forward slip and spread by 3D rigid–plastic FEM. The effects of mesh division and the number of elements on the precision, stability and convergence of the simulation are also discussed. This investigation shows that the frictional shear stress model with a variation in the deformation zone can provide satisfactory results that are in good agreement with experimental values, and are also more accurate than results from other methods. Suitable mesh division can improve the precision and effectiveness of the simulation. The results of the simulation are discussed for front and back tensions.

Phenomenological study of the bed–wall friction in axially compressed packed chromatographic columns

The properties of column beds prepared with slurries of Kromasil C 8 in 12 different solvents, using the same axial compression skid, were investigated. The extent of the consolidation of the column beds, their permeabilities, and the friction shear stress of these beds against the column wall were determined, as well as the column efficiencies (for an unretained tracer). The results of this study illustrate the influence of the wall effect on the consolidation. The permeability of columns consolidated under a constant compression stress was found to increase with increasing bed length. The bed–wall friction shear stress increases rapidly with increasing bed length and varies widely with the nature of the solvent used. No correlation was found between this shear stress and any physico–chemical property of the solvent. The best efficiency was observed for a column consolidated from a slurry in ethanol.