Experimental/analytical characterization of composite tubes under combined loading

The paper outlines the results of an investigation to characterize the response of P75/934 graphite/epoxy tubes with a stacking sequence of [15/0/±10/0/−15] _s under pure torsion and combined axial/torsion loading. The experimentally observed nonlinear response and path-dependent failure are discussed in terms of material nonlinearities at the ply level and first-ply failure loads with the help of an analytical model. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Experimental/analytical characterization of composite tubes under combined loading

The paper outlines the results of an investigation to characterize the response of P75/934 graphite/epoxy tubes with a stacking sequence of [15/0/±10/0/−15] _s under pure torsion and combined axial/torsion loading. The experimentally observed nonlinear response and path-dependent failure are discussed in terms of material nonlinearities at the ply level and first-ply failure loads with the help of an analytical model. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Experimental and theoretical predictions of first-ply failure strength of laminated composite plates

Experimental and theoretical methods are presented to study the first-ply failure strength of laminated composite plates under different loading conditions. An acoustic emission technique is used to measure the energy released in the plates during the failure process. The first-ply failure strength of the plates is then identified via the energy vs load diagrams which are constructed on the basis of the measured acoustic emissions. A finite element analysis, which is constructed on the basis of the layerwise linear displacement theory, and the Tsai–Wu failure criterion are used to predict the first-ply failure strength of the plates. The comparison between the experimental and theoretical results shows good agreement.     

The interfacial crack between two dissimilar elastic-plastic materials

This paper presents an exact asymptotic analysis on the interfacial crack between two dissimilar elastic-plastic materials. These two materials have identical hardening exponent (n ₁=n ₂) but different hardening coefficient (α₁ ≠ α₂). Two groups of the near-crack-tip fields have been obtained, which not only satisfy the continuity of both tractions (σ_θ, τ_rθ) and displacements (u _r ,u _θ) on the interface, but also meet the traction free conditions on the crack faces. The first group of fields have the mode mixityM ^P quite close toM ^P =1 (MODE I) within the whole range 0 ≤ α₁/α₂ < ∞. As for the second group of fields, which is only obtained within the narrow range 0.9 ≤ α₁/α₂ ≤ 1, it is found that the mode mixity changes sharply with the ratio value α₁/α₂. The project supported by National Natural Science Foundation of China     

Computer-aided photoelastic analysis of orthogonal 3D textile composites: Part 2. Combining least squares and finite-element methods for stress analysis

An approach combining least squares methods and finite element methods (FEM) is presented for subsequent photoelastic stress analysis of orthogonal 3D textile composites withR and α obtained in Part 1. Through this approach, these photoelastic stresses are obtained over a region of interest as if the composites were homogeneous materials. The least squares method is used for requiring the solution strain fields to best correlate with the distribution of the two photoelastic strain data of ɛ _x − ɛ _y and γ _xy calculated directly from the measuredR and α. The FEM uses the homogenized composite properties to construct the nodal force equilibrium equations as constraints in the least squares formulation. As a result of combining this least squares method and FEM with lagrange multipliers, a linear system of equations is formulated with the unknown nodal displacements. Once these nodal displacements are solved, the strains and stresses can be calculated through FEM formulations. This approach is tested with the two experimental results completed in Part 1 for the aluminum and composite plates. The stresses obtained for the aluminum plate show close agreement with those obtained with the plain FEM computation. In the case of the orthogonal 3D composite plate, the local variations as observed inR and α are already necessarily eliminated from these solved photoelastic stresses. Furthermore, these stresses also match well with those computed with the plain FEM from the homogenized composite properties.     

An experimental investigation on the tensile moduli and strengths of graphite/epoxy laminates

The results of a series of tensile tests on graphite/epoxy [0°]_8S and [0°/±30°/0°]_2S laminates at rates varying from 0.002 in/min to 2 in./min are reported. The loads are applied at various angles to the fiber directions in each case. The rate-dependent behavior of the stress-strain response is assessed. Evidence is presented to indicate that failure first occurs on inner plies. Also, evidence is presented to indicate that, in some cases, moduli increase with increased stress or strain level. Lamination theory is used to predict moduli and comparisons with experiment are given. This theory is also used in conjunction with three failure theories to predict ultimate strengths with varying degrees of success. Further, two approaches to ply unloading after first-ply failure are used and discussed. One is a standard method found in the literature while the other is a proposed ‘strength-of-materials’ type of technique which is computationally much simpler.     

Near-ground tornado-like vortex structure resolved by particle image velocimetry (PIV)

The near-ground flow structure of tornadoes is of utmost interest because it determines how and to what extent civil structures could get damaged in tornado events. We simulated tornado-like vortex flow at the swirl ratios of S = 0.03–0.3 (vane angle θ_v = 15°–60°), using a laboratory tornado simulator and investigated the near-ground-vortex structure by particle imaging velocimetry. Complicated near-ground flow was measured in two orthogonal views: horizontal planes at various elevations (z = 11, 26 and 53 mm above the ground) and the meridian plane. We observed two distinct vortex structures: a single-celled vortex at the lowest swirl ratio (S = 0.03, θ_v = 15°) and multiple suction vortices rotating around the primary vortex (two-celled vortex) at higher swirl ratios (S = 0.1–0.3, θ_v = 30°–60°). We quantified the effects of vortex wandering on the mean flow and found that vortex wandering was important and should be taken into account in the low swirl ratio case. The tangential velocity, as the dominant velocity component, has the peak value about three times that of the maximum radial velocity regardless of the swirl ratio. The maximum velocity variance is about twice at the high swirl ratio (θ_v = 45°) that at the low swirl ratio (θ_v = 15°), which is contributed significantly by the multiple small-scale secondary vortices. Here, the results show that not only the intensified mean flow but greatly enhanced turbulence occurs near the surface in the tornado-like vortex flow. The intensified mean flow and enhanced turbulence at the ground level, correlated with the ground-vortex interaction, may cause dramatic damage of the civil structures in tornadoes. This work provides detailed characterization of the tornado-like vortex structure, which has not been fully revealed in previous field studies and laboratory simulations. It would be helpful in improving the understanding of the interaction between the tornado-like vortex structure and the ground surface, ultimately leading to better predictions of tornado-induced wind loads on civil structures.     

Behavior of Pin-loaded Laminated Composites

In this study, an investigation was carried out to determine the effects of joint geometry and fiber orientation on the failure strength and failure mode in a pinned joint laminated composite plate. Behavior of pin-loaded laminated composites with different stacking sequence and different dimensions has been observed experimentally. E/glass–epoxy composites were manufactured to fabricate the specimens. Mechanical properties of the composites were characterized under tension, compression and in-plane shear in static loading conditions. Laminated composites were loaded through pins. Single-hole pin-loaded specimens were tested for their tensile response and width-to-hole diameter (W/D) and edge distance-to-hole diameter (E/D) ratios evaluated. A series of experiments was performed with six different material configurations ([0/±45]_s–[90/±45]_s, [0/90/0]_s–[90/0/90]_s and [90/0]_2s–[±45]_2s), in all, over 120 specimens. E/D ratios and W/D ratios of plates were changed from 1 to 5 and 2 to 5, respectively. Failure propagation and failure type were observed on the specimens. The influence of the joint geometry on the strength of the pin-loaded composites was assessed. When laminated composite plates were loaded to final failure, three basic failure modes consisting of net-tension, shear out and bearing failure were observed for the different geometric dimensions. All the connections tested showed that the fiber orientations have a definite influence on the position around hole circumference at which failure initiated. Net-tension failure occurred for specimens that had small width and large end distance. When the width was increased, the specimens which had small end distances failed in the shear-out modes. When the end distance was increased, bearing failure developed in addition to shear-out failure. The experimental results showed that the ultimate load capacities of E/glass–epoxy laminate plates with pin connection were increased by increasing W and E. However, increasing the E/D and W/D ratios beyond a critical value has an insignificant effect on the ultimate load capacity of the connection.     

Flexural fatigue behavior of threaded connections for large diameter pipes

Full-scale flexural fatigue tests were conducted to investigate the fatigue behavior of a patented threaded connection for large diameter (0.61 m (24 in) outside diameter, 25.4 mm (1 in) wall thickness) offshore pipes. Fifteen fatigue tests were performed by subjecting the threaded connection to constant amplitude stress ranges (between 69 MPa (10 ksi) and 151.8 MPa (22 ksi) on gross cross section) with zero mean stress. The corresponding measured fatigue lives varied from 45000 to 4852200 cycles. Fatigue failures were in the form of cracks through the thickness of the wall and located at the root of the first full contact thread. The failure surfaces were ‘typical’ with identifiable zones of crack initiation, propagation and fracture. Linear regression analysis of the experimental results, namely the applied stress range (S _r ) and the measured number of cycles to failure (N) data, in the log-log domain gave anR ² value of 0.88 and the least-squares best fit equation asS _r (MPa)=1573.2N ^−0.212. The 90% probable fatigue strength prediction equation was estimated asS _r =1393.8N ^−0.212. This equation is recommended for design purposes.     

An experimental study of dynamic tensile properties of glass fiber at low-temperatures

Tensile impact experiments of EC8.0−24×7 glass fiber bundles at different low temperaturesT(14°C, −40°C and −10°C) and strain rates ɛ were carried out, and complete stress-strain curves were obtained. Within the range of the experiment temperatures and strain rates, it is found that the initial modulusE, the ultimate strength σ_max and the unstable strain ɛ _b of the glass fiber bundles all increase with ɛ at an identicalT. At an identical ɛ, with the decrease ofT, E and σ_max increase; but ɛ _b increases when 10°C>T>−40°C and decreases when −40°C>T>−100°C. The strain-rate- and temperature-dependent bimodal Weibull statistical constitutive theory was adopted for the statistical analysis of the experimental results, and the Weibull parameters of single fiber were obtained. The results show that the bimodal Weibull distribution function is suitable to represent the strength distribution of the glass fiber at low temperature and different strain rates. The differences in the mechanical properties between EC8.0−24×7 and EC5.5−12 ×14 glass fiber bundles were also discussed. Project supported by the National Natural Science Foundation of China (No. 19772058).     

Centrifugal instability and the rib vortices in the cylinder wake

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v _θ)∂v _θ/∂r−1 is derived, wherev _θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China     

Bifurcations of Heteroclinic Orbits

The search for traveling wave solutions of a semilinear diffusion partial differential equation can be reduced to the search for heteroclinic solutions of the ordinary differential equation ü − cu̇ + f(u) = 0, where c is a positive constant and f is a nonlinear function. A heteroclinic orbit is a solution u(t) such that u(t) → γ ₁ as t → −∞ and u(t) → γ ₂ as t → ∞ where γ ₁, γ ₂ are zeros of f. We study the existence of heteroclinic orbits under various assumptions on the nonlinear function f and their bifurcations as c is varied. Our arguments are geometric in nature and so we make only minimal smoothness assumptions. We only assume that f is continuous and that the equation has a unique solution to the initial value problem. Under these weaker smoothness conditions we reprove the classical result that for large c there is a unique positive heteroclinic orbit from 0 to 1 when f(0) = f(1) = 0 and f(u) > 0 for 0 < u < 1. When there are more zeros of f, there is the possibility of bifurcations of the heteroclinic orbit as c varies. We give a detailed analysis of the bifurcation of the heteroclinic orbits when f is zero at the five points −1 < −θ < 0 < θ < 1 and f is odd. The heteroclinic orbit that tends to 1 as t → ∞ starts at one of the three zeros, −θ, 0, θ as t → −∞. It hops back and forth among these three zeros an infinite number of times in a predictable sequence as c is varied.     

Random Fiber Networks and Special Elastic Orthotropy of Paper

We consider a particular in-plane elastic orthotropy observed experimentally for various types of paper, namely: S ₁₁₁₁+S ₂₂₂₂−2S ₁₁₂₂=S ₁₂₁₂, where S _ijkm are components of the in-plane compliance tensor. This is a statement of the invariance of in-plane shear compliance S ₁₂₁₂, which has been observed in some studies but questioned in others. We present a possible explanation of this “special orthotropy” of paper, using an analysis in which paper is modeled as a quasi-planar random microstructure of interacting fiber-beams – a model especially well suited for low basis weight papers. First, it is shown analytically that without disorder a periodic fiber network fails the special orthotropy. Next, using a computational mechanics model, we demonstrate that two-scale geometric disorder in a fiber network is necessary to explain this orthotropy. Indeed, disordered networks with weak flocculation best satisfy this relationship. It is shown that no special angular distribution function of fibers is required, and that the uniform strain assumption should not be used. Finally, it follows from an analogy to the thermal conductivity problem that the kinematic boundary conditions, rather than the traction ones, lead quite rapidly to relatively scale-independent effective constitutive responses. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radiation-conduction interaction on mixed convection from a horizontal circular cylinder

A mixed convection flow of an optically dense viscous incompressible fluid along a horizontal circular cylinder has been studied with the effect of radiation when the surface temperature is uniform. Using appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity form. Solutions of the governing equations are obtained employing the implicit finite difference method. Effects of varying the pertinent parameters, such as, the Planck number, R _w the surface temperature parameter, θ_w and the buoyancy parameter, α on the local skin-friction and local heat transfer coefficients are shown graphically as well as in tabular form against the curvature parameter ξ, while taking Prandtl number Pr = 1.0. It is found that an increase of R _d,θ_w or α leads to increases in the values of the local skin-friction and the local rate of heat transfer coefficients. At the stagnation point asymptotic solutions for large value of α are also obtained and the effect of the other pertinent parameters on the formation of the flow separation are studied. Received on 28 July 1998     

The interaction between crack and electric dipole of piezoelectricity

Discrete dipoles located near the crack tip play an important role in nonlinear electric field induced fracture of piezoelectric ceramics. A physico-mathematical model of dipole is constructed of two generalized concentrated piezoelectric forces with equal density and opposite sign. The interaction between crack and electric dipole in piezoelectricity is analyzed. The closed form solutions, including those for stress and electric displacement, crack opening displacement and electric potential, are obtained. The function of piezoelectric anisotropic direction,p _a (θ)=cosθ+p _a sinθ, can be used to express the influence of a dipole's direction. In the case that a dipole locates near crack tip, the piezoelectric stress intensity factor is a power function with −3/2 index of the distance between dipole and crack tip. Supported by National Natural Science Foundation of China(No. 10072033)     

Heat transfer from a surface fitted with rectangular blocks at different orientation angle

 An experimental investigation was carried out to study the enhancement of the heat transfer from a heated flat plate fitted with rectangular blocks of 1 × 2 × 2 cm³ dimensions in a channel flow as a function of Reynolds number (Re_h), spacing (S _y ) of blocks in the flow direction, and the block orientation angle (α) with respect to the main flow direction. The experiments were performed in a channel of 18 cm width and 10 cm height, with air as the working fluid. For fixed S _x =3.81 cm, which is the space between the blocks in transverse to the flow direction, the experimental ranges of the parameters were S _y =3.33–4.33 cm, α=0–45°, Re_h=7625–31550 based on the hydraulic diameter and the average velocity at the beginning of the test section in the channel. Correlations for Nusselt number were developed, and the ratios of heat transfer with blocks to those with no blocks were given. The results indicated that the heat transfer could be enhanced or reduced depending on the spacing between blocks, and the block orientation angle. The maximum heat transfer rate was obtained at the orientation angle of 45°. Received on 13 December 2000 / Published online: 29 November 2001     

A unified approach to closed-form solutions of moving heat-source problems

A closed-form model for the computation of temperature distribution in an infinitely extended isotropic body with a time-dependent moving-heat sources is discussed. The temperature solutions are presented for the sources of the forms: (i) ₀₁(t)=₀ exp(−λt), (ii) ₀₂(t) =₀(t/t ^*)exp(−λt), and ₀₃(t)=₀[1+a cos(ωt)], where λ and ω are real parameters and t ^* characterizes the limiting time. The reduced (or dimensionless) temperature solutions are presented in terms of the generalized representation of an incomplete gamma function Γ(α,x;b) and its decomposition C _Γ and S _Γ. The solutions are presented for moving, -point, -line, and -plane heat sources. It is also demonstrated that the present analysis covers the classical temperature solutions of a constant strength source under quasi-steady state situations. Received on 13 June 1997     

Measurement of thermal expansion coefficients of composites using strain gages

The measurement of the coefficients of thermal expansion (CTEs) of composite materials using electrical resistance strain gages is addressed. Analytical expressions for the CTEs of an orthotropic lamina are derived, accounting for the effects of transverse sensitivity and possible misalignment of the gages. Experiments are performed for the characterization of the thermal expansion behavior of a fiber-glass-reinforced epoxy unidirectional lamina using an invar specimen as reference material. Preliminary training cycles are performed for the determination of an optimal heating rate for the measurements, which ensures thermal equilibrium conditions. Three measurement cycles yield the principal CTEs of the lamina α₁, α₂ and α₁₂ with repeatability within ±0.34×10⁻⁶, ±0.85×10⁻⁶ and ±2.8×10⁻⁶/°C, respectively. It is noted that inhomogeneity of the specimen and variation in thermomechanical properties of the gages can cause a noticeable spead in the measurements.     

Stability of Degenerate Stationary Waves for Viscous Gases

This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous gases in the half space. We discuss the following two cases: (1) viscous conservation laws and (2) damped wave equations with nonlinear convection. In each case, we prove that the solution converges to the corresponding degenerate stationary wave at the rate t ^−α/4 as t → ∞, provided that the initial perturbation is in the weighted space L²_a=L²(\mathbb R₊; (1+x)^a dx){L^2_\alpha=L^2({\mathbb R}_+;\,(1+x)^\alpha dx)} . This convergence rate t ^−α/4 is weaker than the one for the non-degenerate case and requires the restriction α < α_*(q), where α_*(q) is the critical value depending only on the degeneracy exponent q. Such a restriction is reasonable because the corresponding linearized operator for viscous conservation laws cannot be dissipative in L²_a{L^2_\alpha} for α > α^*(q) with another critical value α^*(q). Our stability analysis is based on the space–time weighted energy method in which the spatial weight is chosen as a function of the degenerate stationary wave.     

Precursor ionization ahead of strong shock waves in argon

The mechanism of precursor ionization ahead of strong shock waves has been studied in a low density shock tube. The experimental results are illustrated with Arrhenius plots with kink points dividing them into two parts with apparent activation energy ratio 1:2, namely with the values 7.7 eV and 15.3 eV, and varying with first and third power of the density respectively. A model is proposed to interpret the facts where the process taking place in the precursor region, is a two step photo ionization accompanied with the drift flow effect of the gas relative to the shock wave or the ionization recombination effect according to whether the shock speed and initial density are low enough. The product of the A-A collision excitation cross section coefficientS ^* multiplied by the radiation cross sectionQ ^* of ArgonS ^*×Q ^*=1×10⁻³⁶ (cm⁴eV⁻¹) and the three body recombination coefficient of Argon at room temperaturek _ra =1×10⁻²⁴ (cm⁻⁶s⁻¹). The project supported by the National Natural Science Foundation of China