An experimental investigation of the biaxial strength of IM6/3501-6 carbon/epoxy cross-ply laminates using cruciform specimens

Several variations of a thickness-tapered cruciform specimen have previously been used to experimentally determine the biaxial strength of an AS4/3501-6 carbon/epoxy cross-ply laminate. The present work represents a follow-up study of the original specimen design, and incorporates numerous specimen improvements made in an attempt to generate more accurate biaxial results. A total of 52 tests were performed at numerous biaxial stress ratios, utilizing six different specimen configurations. The experimental data generated in the present study for all specimen geometries, as well as a complete biaxial failure envelope in σ₁–σ₂ stress space for this laminate configuration, are presented. A desirable failure mode in the gage section of the specimen was achieved for all specimens tested in the present study, indicating that accurate biaxial stress states were being generated at ultimate specimen failure. The ability of the thickness-tapered cruciform specimen to determine the biaxial strength of composite materials at any stress ratio has been demonstrated.     

Study on the yield behavior of Al2O3–SiO2(sf)/Al–Si metal matrix composites

As the yield behavior of Al₂O₃–SiO₂(sf)/Al–Si MMCS is concerned, effects of heat treatment and parameters of short fiber, including volume fraction, size, distribution mode, were investigated. Dislocation configurations adjacent to interface between matrix and fiber were observed by TEM. Macro-yield stress (σ_0.2) and micro-yield stress (σ_MYS) vary with parameters of short fiber, and effects of these parameters on σ_0.2 appear to be opposite to those on σ_MYS. This phenomenon was interpreted by thermal residual stress in matrix and dislocation configuration. Suitable quenching followed aging treatment is an effective method to enhance the σ_MYS and the σ_0.2 simultaneously. For the specimen with heat treatment of 550 °C/1 h WQ + 170 °C/6 h (T6) AC, σ_0.2 and σ_MYS reach 200 and 58 MPa, respectively, and they are almost as twice as those as-cast.     

Matrix cracking behavior of K3B/IM7 composite laminates subject to static and fatigue loading

The matrix cracking behavior of a new high-performance thermoplastic composite material, K3B/IM7, was systematically investigated. Laminates in various grouped thickness and ply stacking sequences, [0₂/90₂/0₂], [0₂/90₄/0₂], and a quasi-isotropic laminate [+45/0/−45/90]_s were tested under static and tension–tension fatigue loading. Depending on the stacking sequence of the laminates and the type of loading, various matrix cracking behavior were found. Under static loading, the matrix cracks were mainly close to the specimen edges. A few cracks were found to penetrate the specimen width, even when the load was large enough to break the specimen. However, under fatigue cyclic load, the edge initiated cracks propagated fully across the specimen width. Combined with the fatigue Paris Rule and considering the ply thickness and stacking sequence, the energy release rate method was applied to predict the relations between the loading strain amplitude and fatigue cycles for matrix cracking failure.     

On the use of constraint parameter A2 determined from displacement in predicting fracture event

The constraint based fracture mechanics methodology, J–A₂ method, has been used to interpret cleavage fracture recently. In all previous studies, the constraint parameter A₂ was determined by stresses analytically calculated from finite element analyses (FEA). In the current paper, it is first demonstrated that A₂ can be measured during a fracture test using the crack tip opening displacement (CTOD). A single-edge-notched specimen under bending (SENB) is used to compare the A₂ values determined from δ₅ displacement and the stress components. Finally, cleavage fracture toughness values for A533-B reactor pressure vessel (RPV) steel at −40°C obtained from test programs at Oak Ridge National Laboratory (ORNL) and the University of Kansas (KU) are interpreted using the J–A₂ analytical model. Particular emphasis is placed on using the A₂ determined from CTOD to characterize the fracture event. It is demonstrated that the effects of crack depth (shallow vs deep) and specimen size (small vs large) on the fracture toughness from the test programs can be interpreted and predicted using J and the constraint level A₂ measured from the displacement.     

Elastic-plastic and failure properties of a unidirectional carbon/PMR-15 composite at room and elevated temperatures

A series of off-axis tensile tests at room and elevated temperatures have been conducted up to 316°C (600°F) to determine the elastic and plastic properties of a unidirectional carbon/PMR15 composite as a function of temperature. The transverse tensile and shear strengths of the composite as a function of temperature have also been determined. The effect of the specimen preparation process (type of machining) on the strength properties of the composite has also been evaluated. It has been shown that elastic (with the exception of Poisson ratios ν₁₂ and ν₂₁), plastic, and strength properties of the composite are significantly affected by elevated temperatures. It has also been demonstrated that the quality of machining can noticeably influence the normal and shear strength data at room and elevated temperatures. Even if the quality of machining is very high, failure of the specimens can occur either in the gage or grip sections. At room temperature, all specimens failed in the grip areas influencing the transverse tensile and shear strength measurements. However, the type of specimen failure does not noticeably affect the strength data at elevated temperatures. The transverse tensile and shear strength properties of the composite at room temperature could only be estimated by extrapolating the normal and shear strength vs temperature curves to room temperature.     

Residual stress fields in surface-treated silicon carbide for space industry—comparison of biaxial and triaxial analysis using different X-ray methods

Any mechanical surface treatment and machining leaves ‘footprints’ in the form of residual stress fields in the surface region of technical parts or components, which are detectable by X-ray diffraction. In the present paper, we applied different X-ray methods to investigate the residual stress state in the near-surface zone of sintered silicon carbide after mechanical surface processing. Using the sin² ψ-based ‘universal plot’ method, we found steep gradients for the in-plane components σ₁₁ and σ₂₂ in the form of high compressive stresses at the surface, which change into tensile stresses within a few microns. To gain information on the triaxial residual stress state, we applied the scattering vector method, which is based on strain depth profiling by sample rotation around the diffraction vector. For the in-plane stresses, we observed gradients similar to those obtained by the ‘universal plot’ method, but they were shifted on the absolute scale towards tensile stress. We explain this difference by ‘pseudo-macroscopic’ tensile residual stress fields σ₃₃, which act normal to the surface and therefore pretend higher in-plane compressive stresses σ_ii (i = 1, 2), if they are not regarded in the evaluation procedure.     

Interaction between plasticity and damage in the behaviour of [+φ, −φ]n fibre reinforced composite pipes in biaxial loading (internal pressure and tension)

In this paper, we propose a new model which describes the behaviour of [+φ, −φ]_n composite laminates. Tests were performed on glass-epoxy pipes subjected to biaxial tensile and internal pressure loading. Experiments showed that [+55, −55]_n pipes exhibit varying types of damaged elastoplastic behaviour depending on the stress ratio σ_zz/σ_θθ (axial stress/hoop stress). A plastic model is based on the definition of a yield criterion and an associated flow rule. Damaging occurs when transverse microcracks appear in the layer. A micromechanical model defines the anisotropy of the damage. Interaction between plasticity and damage was of major importance in the definition of damage kinetics. This effect was observed on proportional loadings as well as on sequential tests: a preliminary loading in pure internal pressure (σ_zz=0) induced large plastic phenomena which blocked crack propagation in additional internal pressure with closed ends effect (IPCEF) tests (R=σ_zz/σ_θθ=1/2), even though IPCEF caused considerable damage on an unloaded specimen.     

The effect of second principal stress on the fatigue propagation of mode I surface crack in Al2O3/Al alloy composites

Using a plate made of A2017-T6 metal matrix composites reinforced with 10 volume % and 20 volume % Al₂O₃ particles and Al alloy possesses the same composition as matrix alloy, the crack propagation rate da/dN of a mode I surface crack by the simultaneous action of plane bending and cyclic torsion are studied. And the effects of crack tip opening stress σ_top, crack opening displacement COD, biaxial stress ratio C (=second principal stress/first principal stress) and the surface roughness of crack section are examined. When stress intensity factor range ΔK is lower than the specific level, da/dN decreases with the increase of volume fraction of Al₂O₃ in C=0 and C=−0.55. But, da/dN of Al alloy becomes minimum in C=−1 and the effect of Al₂O₃ particles disappears. σ_top rises with the increase of volume fraction of Al₂O₃ particles and the decline of C. On the other hand, COD doesn’t always rise with the decline of C. These phenomena can be explained by the residual compressive stress formed at the surface layer of the specimen by the fatigue test and the surface roughness of crack section.     

Growth and spectroscopy of Dy doped in ZnWO4 crystal

Single-crystal ZnWO₄:Dy³⁺ was grown by Czochralski technique. The XRD, absorption spectra as well as fluorescence spectrum are investigated and the Judd–Ofelt intensity parameters Ω₂, Ω₄, Ω₆ are obtained to be 7.76 × 10⁻²⁰ cm², 0.57 × 10⁻²⁰ cm², 0.31 × 10⁻²⁰ cm², respectively. Calculated radiative transition rate, branching ratios and radiative lifetime for different transition levels of ZnWO₄:Dy³⁺ crystals are presented. Fluorescence lifetime of ⁴F_9/2 level is 158 μs and quantum efficiency is 66%.The most intense fluorescence line at 575 nm correlative with transition ⁴F_9/2 → ⁶H_13/2 is potentially for application of yellow lasers.     

Rate-Dependent Elasto-Viscoplastic Constitutive Model for Industrial Powders. Part 2: Model Evaluation

The PSU-EVP model's constitutive parameters for alumina powder are presented. The PSU-EVP model was also used to back-predict the triaxial test data obtained for MZF and alumina powders using constitutive parameters such as the initial voids ratio (e₀), compression index (λ), and spring-back index (κ). In the case of MZF powder, 8 out of 12 back-prediction cases had average relative difference (ARD) values below 20%. In the case of alumina powder, 7 out of 11 back-prediction cases had ARD values below 20%. Based on the back-prediction results, it was concluded that the PSU-EVP model gave fairly good results for most triaxial test data collected at 0.62 MPa/minute and 6.21 MPa/minute. However, the back-prediction results obtained at 20.7 MPa/minute had high ARD values. A sensitivity analysis was done to study the effect of changes in parameter values on the hydrostatic triaxial compression (HTC) and conventional triaxial compression (CTC) back-prediction results. From the sensitivity analysis,±10% (standard deviation variation from ±0.8σ to ±2.3σ) changes in λ and e₀ mean values had marked effect on the HTC results. However, changes in the λ, κ, and e₀ mean values do not produce any noticeable effect on the CTC prediction results. Overall, the PSU-EVP model can be considered to be the first step towards the development of a more robust and accurate model for prediction of stresses and strains in a dry powder compression process.     

Effect of CeO2 addition on structure and electrical properties of (Na0.5Bi0.5)0.93Ba0.07TiO3 ceramics prepared by citric method

(Na_0.5Bi_0.5)_0.93Ba_0.07TiO₃ ceramics added with 0–0.8 wt.% CeO₂ were prepared by a citrate method, and the influence of the CeO₂ addition on the structure and electrical properties was investigated. The specimens containing various amounts of CeO₂ show the coexistence of rhombohedral and tetragonal phases, with the relative content of the tetragonal phases gradually enhancing with increasing amount of CeO₂. Compared with (Na_0.5Bi_0.5)_0.93Ba_0.07TiO₃, the specimen added with a small amount of CeO₂ (≤0.2 wt.%) display a slightly improved electromechanical coupling factor (k_p) and piezoelectric constant (d₃₃) in conjunction with a reduced dielectric loss (tg δ) and an enhanced mechanical quality factor (Q_m), while higher CeO₂ amounts led to a rapid deterioration of the piezoelectric and ferroelectric properties. The variation of the electrical properties with the CeO₂ addition was tentatively interpreted with respect to doping effect, crystal-structural evolution and stability of ferroelectric domains.     

Optical absorption and emission properties of Er doped mixed alkali borosilicate glasses

This paper presents the optical absorption and luminescence properties of Er³⁺ doped mixed alkali borosilicate glasses: 59.5SiO₂ · 20B₂O₃ · xLi₂O · (20 − x)Na₂O · 0.5Er₂O₃ and 59.5SiO₂ · 20B₂O₃ · xLi₂O · (20 − x)K₂O · 0.5Er₂O₃, with x = 0, 4, 8, 12, 16 and 20 mol%. The variations of Judd–Ofelt intensity parameters (Ω₂, Ω₄, and Ω₆), hypersensitive transition intensities, total radiative transition probability (A_T), radiative lifetimes (τ_R), integrated absorption cross-sections (Σ) and stimulated emission cross-sections (σ_p) as a function of x are discussed in detail. The changes in Ω₂ and intensities of hypersensitive transitions are attributed to optical basicity changes in the host glass matrix, which leads to variations in the covalency of the Er–O bond. The luminescence properties are reported for certain transitions, and the emission cross-section is high at x = 8–12 in the case of lithium sodium glass, whereas in lithium potassium glass it is high at x = 8.     

Domain switching in ferroelectric single crystal/ceramics under electromechanical loading

Domain switching in PMN-PT single crystal and PZT-5 ceramics under electromechanical loading were studied in two different ways. For the single crystal, domain switching was in situ investigated with polarized light microscopy. A 90° domain-switching zone was observed near the crack tip and the size of the switching zone changed with the acuity of the crack tip. For PZT-5 ceramics, domain switching under orthogonal electromechanical loading (E₃ and compressive stress σ₁₁) was studied by measuring the hysteresis loops, butterfly curves and reversed butterfly curves (₁₁ versus E₃). Experimental results show that 90° domain switching is suppressed in the planes parallel to the compression direction. A domain-switching model dividing each 180° switching to two successive 90° switching was proposed to explain the experimental results.     

Homogenization kinetics of a cast Ti48A12W0.5Si alloy

The homogenization kinetics of a cast Ti48A12W0.5Si alloy with a duplex microstructure was studied in terms of γ-phase dissolution and -grain growth. It was found that the measured volume fraction of remnant γ grains can be well simulated by a model of interface-controlled dissolution in a dislocation mechanism, instead of a diffusion-controlled one. The activation energy for the /γ interface reaction was found to be Q_int = 476 kJ mol⁻¹, which is much higher than the interdiffusion activation energy in TiAl alloy. The grain growth of phase during homogenization can be categorized into three stages. During the first stage, where the volume fraction of remnant γ grains is higher than about 10%, the growth of grains follows the parabolic law D = k₁t^0.2, and the activation energy for grain growth was calculated to be Q₁ = 442 kJ mol⁻¹, very close to the Q_int for /γ interface reaction. In the second stage, where few fine γ grains (1–10 vol.%) remained, a dramatic grain growth occurs. During the final stage, as the single phase is obtained, the coarsening of grains again satisfies the grain growth law D = k₃t^0.4, with the grain growth activation energy Q₃ of 147 kJ mol⁻¹, lower than the reported interdiffusion energy of γ phase.     

Magneto-mechanical properties evolution of Fe–C alloy during precipitation process

Evolution of magneto-mechanical properties of 160 ppm Fe–C alloy due to carbides precipitation during isothermal annealing at 473 K (up to t=50×10³ s) was studied by means of classical Barkhausen noise (HBN) and mechanical Barkhausen noise (MBN) effects. The MBN was measured for the torsion mode of load with a torque motor. Also the B(H) hysteresis loop and the coercive field H_c were evaluated using a low-frequency magnetisation set. Magnetic hysteresis losses ΔW₁ were compared with the integral ΔW₂ of HBN intensity over one period of magnetisation and the integral ΔW₃ of MBN intensity over one period of the mechanical load. The internal stress distribution function and the resulting mean level of internal stress parameter σ_i were evaluated from the MBN ‘first load’ data. It was revealed that a correlated increase of ΔW₁ and ΔW₂ parameters exists. However, the relative increase of ΔW₃ is much lower than the relative increase of ΔW₁. The relationship between H_c and σ_i was found to be parabolic. This dependence explained by Néel’s model of the impact of the residual stress level on H_c. The presence of precipitates of type was confirmed by scanning electron microscopy.     

Domain size dependence of d33 piezoelectric properties for barium titanate single crystals with engineered domain configurations

Engineered domain configuration was induced into barium titanate (BaTiO₃) single crystals, and the d₃₃ piezoelectricity was investigated as a function of domain size. First, for the BaTiO₃ single-domain crystals, piezoelectric constant d₃₃ along [1 1 1]_c direction was calculated as 224 pC/N. Prior to the domain engineering, the dependence of domain configuration on the temperature and the electric-field was investigated, and above Curie temperature (T_c), when the electric-field over 6 kV/cm was applied along [1 1 1]_c direction, the fine engineered domain configuration appeared. On the basis of the above information, the 33 resonators with different domain sizes were successfully prepared. Their piezoelectric measurement revealed that the d₃₃ of the 33 resonators with fine engineered domain configurations was higher than that of BaTiO₃ single-domain crystals. Moreover, d₃₃ increased with decreasing domain sizes. The highest d₃₃ of 289 pC/N was obtained in the BaTiO₃ crystal with a domain size of 13 μm.     

Electro-optic properties of c-axis oriented LiNbO3 films grown on Si(1 0 0) substrate

We developed a spectroscopic–ellipsometric approach to evaluate the electro-optic coefficient of highly c-axis oriented LiNbO₃ films on an Si(1 0 0) substrate grown by electron cyclotron resonance plasma sputtering. Applying an electric field between the TiN transparent top electrode and Si substrate, the interference fringe appearing in the tan Ψ spectrum was slightly modulated by phase retardation in the wavelength domain. The change in effective wavelength was converted to refractive index change, yielding dispersion in the Pockels coefficient (r₃₃) between 0.3 and 0.8 μm. At 633 nm, we obtained an r₃₃ that was 57% of the bulk LN crystal value.     

Rotation numbers for quasi-periodically forced monotone circle maps

Rotation numbers have played a central role in the study of (unforced) monotone circle maps. In such a case it is possible to obtain a priori bounds of the form „ - 1/n ≤(1/n)(y_n - y₀) ≤„ + 1/n, where (1/n)(y_n - y₀) is an estimate of the rotation number obtained from an orbit of length n with initial condition y₀, and „ is the true rotation number. This allows rotation numbers to be computed reliably and efficiently. Although Herman has proved that quasi-periodically forced circle maps also possess a well-defined rotation number, independent of initial condition, the analogous bound does not appear to hold. In particular, two of the authors have recently given numerical evidence that there exist quasi-periodically forced circle maps for which y_n - y₀ - „n is not bounded. This renders the estimation of rotation numbers for quasi-periodically forced circle maps much more problematical. In this paper, a new characterization of the rotation number is derived for quasiperiodically forced circle maps based upon integrating iterates of an arbitrary smooth curve. This satisfies analogous bounds to above and permits us to develop improved numerical techniques for computing the rotation number. Additionally, the boundedness of y_n - y₀ - „n is considered. It is shown that if this quantity is bounded (both above and below) for one orbit, then it is bounded for all orbits. Conversely, if for any orbit y_n - y₀ - „n is unbounded either above or below, then there is a residual set of orbits for which y_n - y₀ - „n is unbounded both above and below. In proving these results a min-max characterization of the rotation number is also presented. The performance of an algorithm based on this is evaluated, and on the whole it is found to be inferior to the integral based method.     

Fracture mechanical characterisation of mixed-mode toughness of thermoplast/glass interfaces

According to studies conducted by, e.g. Liechti and Chai [J. Appl. Mech. 58 (1991) 680], Yuuki et al. [Eng. Fract. Mech. 47 (3) (1994) 367] and Ikeda and Miyazaki [Eng. Fract. Mech. 59 (6) (1998) 725], a significant increase of interfacial toughness is observed, whenever the magnitude of the bond tangential shear load of the asymptotic elastic mixed-mode state is increased in either direction. Between these extremes the interfacial toughness curve exhibits a pronounced minimum, which, according to Hutchinson and Suo [Mater. Sci. Eng. A 107 (1989) 135] is believed to represent the so-called intrinsic adhesion, i.e. the failure toughness under pure local mode I loading. Within linear elasticity, the biaxial, singular near-tip solution for an open interface crack may be employed for characterising the local stress state as long as non-linearities such as, e.g. crack-wall contact and plastic flow are contained within a zone small enough compared to the extension of the singular opening-dominated fields. Then, the critical stress state is given in terms of bimaterial stress intensity factors K_1,c, K_2,c and the fracture toughness under mixed-mode loading may be expressed in terms of the critical energy release rate as a function of the mode-mixity ψ=tan⁻¹K_2,c/K_1,c. The stress intensities have to be extracted from a stress analysis of the specimen under the critical load, which in the present work is performed by means of an FE-model of the loaded sample.     

Deposition and photoluminescence of sol–gel derived Tb:Zn2SiO4 films on SiO2/Si

Tb³⁺ doped Zn₂SiO₄ films have been deposited on SiO₂ buffered Si wafers by sol–gel method. The structures of these films have been investigated with X-ray diffraction (XRD), atomic force microscopy (AFM), and scanning electron microscopy (SEM). The results revealed that these films were composed of nanometer-size grains with a Willemite structure and had smooth surfaces. Photoluminescence measurements of the films showed a strong emission from ⁵D₄ to ⁷F₅ at 544 nm. The blue emission from ⁵D₃–⁷F_j was depressed because of cross-relaxation effect. The decay kinetics of the ⁵D₄–⁷F₅ green emission was studied and a best fitting was obtained by a double exponential function. The lifetime of the excited ⁵D₄ state is estimated to be 5.2 ms.