A fast algorithm for the elastic fields due to interacting fibre breaks in a periodic fibre composite

Monte Carlo simulations of the failure of unidirectional fibre composites typically require numerous evaluations of the stress-state in partially damaged composite patches. In a simulated composite patch comprised of N fibres, of which \(N_b\) fibres are broken in a common cross-sectional plane transverse to the fibre direction, the stress overloads in the intact fibres are given by the weighted superposition of the unit break solutions associated with each of the breaks. Determining the weights involves solving \(N_b\) linear equations, and determining overloads in the intact fibres requires matrix-vector multiplication. These operations require \(O(N_b^3)\), and \(O(N N_b)\) floating point operations, respectively. These costs become prohibitive for large N, and \(N_b\); they limit Monte Carlo failure simulations to composite patches of only a few thousand fibres. In the present work, a fast algorithm to determine the overloads in a partially damaged composite, requiring \(O( N_b^{1/3} N \log N)\) floating point operations, is proposed. This algorithm is based on the discrete Fourier transform. The efficiency of the proposed method derives from the computational simplicity of weighted superposition in Fourier space. Computations of the stress state ahead of large circular clusters of breaks in composite patches comprised of about one million fibres are used to demonstrate the efficiency of the proposed algorithm.     

Damage in carbon fibre composites due to repetitive low-velocity impact loads

The effect of repetitive impacting with increasing impact energy on unsupported thermoset matrix and thermoplastic matrix carbon fibre laminates was studied. In the case of the thermoset laminates, there were two abrupt losses in stiffness, the first corresponding to through-the-thickness damage and the second to the damage extending to the specimen edges. The thermoplastic matrix laminates exhibited a continuous decline in stiffness but again the damage sequence was through-the-thickness followed by extension to the specimen edges. Static bend testing of these composites resulted in the same type and extent of damage as was observed for impact loading. The effect of increasing the unsupported area and laminate thickness were investigated. Impacting with increasing impact energy was compared to repetitive impacting at a constant impact energy.     

Number of phase levels of a talbot array illuminator

The number of phase levels of a Talbot array illuminator is an important factor in the estimation of practical fabrication complexity and cost. We show that the number (L) of phase levels of a Talbot array illuminator has a simple relationship to the prime number. When there is an alternative pi-phase modulation in the output array, the relations are similar.     

Passively Q-switched fibre laser utilizing erbium-doped fibre saturable absorber for operation in C-band region

In this paper, a stable and robust all-fibre passively Q-switched erbium-doped fibre laser (EDFL) emitting at 1558?nm is described. The proposed laser utilizes an 11?cm long erbium-doped fibre as saturable absorber (SA). The fibre SA features a linear optical absorption of about 13?dB in the Q-switched EDFL operating regime. By elevating the input pump power from the threshold of 60?mW to the maximum available power of 142?mW, a pulse train with a maximum repetition rate of 86?kHz, minimum pulse width of 3.39?µs, maximum average output power of 10.5?mW, maximum pulse energy of 122?nJ and maximum peak power of 36?mW are obtained. The signal to noise ratio (SNR) of the spectrum is measured to be around 70?dB. This fibre SA is simple, reliable, compact and alignment free. Thus it is suitable for making a portable pulse laser source.     

Limitations of interferometry due to the flicker noise of laser diodes

Interferometry with laser diodes is a cost-effective way to perform displacement measurement. The tunability of laser diodes is also of great interest in multiple-wavelength interferometry. However, the additional flicker noise in the frequency-noise spectrum of semiconductor lasers may become a limiting factor. Investigations on the limitations due to the 1/f noise of laser diodes are presented for both classical and multiple-wavelength interferometry. Measurements at the limit of the coherence length of laser diodes with the corresponding phase fluctuations are reported. The theoretical results are verified experimentally.     

In-phase supermode selection in a multicore fiber laser array by means of a self-Fourier external cavity

A procedure is developed to determine the transverse-mode structure of a cavity consisting of a dense, evanescently coupled, waveguide laser array, which, in addition, is externally coupled by feedback from an external cavity. The formalism is used to determine the loss and phasing properties of a multicore fiber array coupled to an external self-Fourier cavity. Best performance is predicted for linear arrays of up to five cores, or two-dimensional arrays of up to 25 cores. A low-loss, in-phase, fundamental array mode is predicted, which achieves better than 30 dB discrimination against higher-order modes at periodically spaced values of the array length. However, we show that a shift in operating wavelength of typically a few nanometers can bring about near-perfect phasing and loss operation over a continuum of fiber lengths. With increased fill factor, significantly more of the output power can be concentrated in the central lobe of the far field but at the penalty of increased loss in the fundamental eigenmode.     

Fractal laser mode structure due to iterated diffractive multiple imaging

A variation on iterated multiple imaging in optical resonators, a mechanism that creates fractal structure in the resonator's eigenmodes, is presented. During each round trip, side-by-side images of the intensity distribution in a plane are placed into the same plane by a grating in the resonator. It is shown that this leads to fractal structure in the eigenmodes. Interestingly, a very similar mechanism can be said to be at work in almost every canonical resonator; however, it creates fractal eigenmode structure only over a negligible range of length scales.     

Stress disturbance due to broken fibres in metal matrix composites with non-uniform fibre spacing

Premature fracture of weaker fibres causes stress disturbances in composites. These disturbances are affected by non-uniformity of fibre spacing. In order to evaluate quantitatively how the disturbances in metal matrix composites are affected by the extent of non-uniformity of fibre spacing, a method of calculation is presented on the basis of two-dimensional shear lag analysis. Static tensile stress concentrations in the intact fibres to broken fibres, tensile stress distribution along the fibre axis in the broken and intact fibres and shear stresses between broken and intact fibres were calculated by the method presented, using some examples. It is shown quantitatively that the spacing between broken and intact fibres and that between intact and next fibres has a significant influence on tensile stress concentrations in intact fibres and also on the shear stresses between broken and intact fibres: the narrower the former spacing and the wider the latter spacing, the higher become both tensile and shear stress concentrations. This tendency is enhanced when the number of broken fibres is large and when the strain hardening of the matrix is high.     

Carbon fibre composites with improved fatigue resistance due to the addition of tin-lead alloy particles

The addition of tin-lead (60 wt% Sn) alloy particles (about 21–25 μm in diameter, in an amount up to 37 wt% or 7.2 vol%) between continuous unidirectional carbon fibre layers in an epoxy-matrix composite was found to improve the fatigue life by over 100 times. The alloy addition had little effect on the tensile strength, tensile modulus, compressive strength, compressive modulus (with the compressive force parallel and perpendicular to the fibres), but increased the electrical resistivity. The composites were fabricated by compression moulding at 185–200°C and 1 MPa for 30 min. The heating allowed the alloy to melt while the epoxy cured. The fatigue life enhancement is probably due to the hindering of the fatigue crack growth by the alloy particles.     

Narrow-linewidth passively Q-switched fibre laser based on microsphere resonator

We experimentally demonstrate a stable narrow-linewidth passively Q-switched fibre laser based on a microsphere resonator (MSR) and graphene saturable absorber (SA). The MSR made by the arc discharge method has the characteristics of easy fabrication, broad free spectral range (FSR) and flexibility. And it acts as a narrow band-pass filter to ensure narrow-linewidth operation. A stable passively Q-switched pulse with 0.016?nm narrow spectral linewidth is successfully achieved. The output pulse has the pulse width of 5.2 µs, repetition frequency of 28 kHz and high signal to noise ratio (SNR) of ～60?dB. The results demonstrate that our works may provide an effective way to achieve narrow-linewidth pulsed fibre lasers.     

Study on fibre laser spot welding of TRIP980 steel

A 980 MPa transformation induced plasticity (TRIP) steel was fibre laser spot welded by different Argon (Ar) shielding conditions, laser power (1000 up to 2500 W) and defocusing distances (?8 up to +8 mm). The surface appearance, cross-section macrostructure, microstructure, hardness, tensile shear properties and fatigue properties of laser spot welds were evaluated. The results showed that the welds with Ar shielding had larger weld appearance and bonding sizes, better tensile shear properties compared with the welds without Ar shielding. With the increase in laser power, the laser welding mode changed from conduction to keyhole, which improved the bonding size and mechanical properties. The bonding size and mechanical properties increased in the order of defocusing distances of +8, ?8, +4, ?4 and 0 mm. During the fatigue tests of laser spot weld, the fusion zone pullout and sheet transverse fracture failure modes were observed.     

Mutual alignment errors due to wave-front aberrations in intersatellite laser communications

We analyze mutual alignment errors due to wave-front aberrations. To solve the central obscured problem, we introduce modified Zernike polynomials, which are a set of complete orthogonal polynomials. It is found that different aberrations have different effects on mutual alignment errors. Some aberrations influence only the line of sight, while some aberrations influence both the line of sight and the intensity distributions.     

Hyperbolic heat conduction due to a mode locked laser pulse train

In situations which involve repetitive pulsing of a material with a mode locked Nd:YAG laser, the pulse duration can be sufficiently small (i.e. in the picosecond range) that the classical parabolic heat conduction equation fails to adequately predict the resulting temperature distribution in the material. In such cases, the hyperbolic heat conduction equation, which accounts for the finite time to the commencement of heat flow, is appropriate. In the present work, the hyperbolic heat conduction equation is used to predict the temperature distributions in both semi-infinite and finite isotropic media due to a train of temporally rectangular pulses which approximate the Gaussian temporal profile of mode locked laser pulses. The energy carried in the pulses is assumed to be absorbed in the surface plane of the material. The spatial profile of the pulses can be either Gaussian, doughnut or a combination of the two. The parabolic and hyperbolic models are examined for selected pulse frequencies.     

Transportable optical frequency comb based on a mode-locked fibre laser

A new transportable frequency comb has been developed at the National Physical Laboratory. The transportable frequency comb is based around a MenloSystems FC1500 optical frequency synthesizer, which is capable of measuring any frequency between 500 and 2100 nm. Measurements made by the comb while off-sites are referenced to the SI second via a global positioning system (GPS)-disciplined Rapco 2804AR rubidium oscillator. All components of the system (except for the GPS antenna) have been integrated into a single mobile unit. Measurements of high-stability narrow-band optical sources using this system, with either the GPS-disciplined oscillator or a hydrogen maser as a reference, are described. Some of these measurements were made simultaneously with a hydrogen-maser-referenced Ti:sapphire-based comb. It was found that the GPS-referenced transportable comb has a fractional inaccuracy of better than 4 10^-12 (averaged over several hours) when compared with the maser-referenced Ti:sapphire comb, and a fractional frequency instability of 1times10^-12 for an averaging time of 10 s. It was also demonstrated that continuous frequency measurements are possible with this system over a period of 60 h or more.     

Study on UV laser machining quality of carbon fibre reinforced composites

The large differences in material properties of the carbon fibre and the epoxy resin in carbon fibre reinforced plastic (CFRP) composite make laser processing very challenging. The heat affected zone (HAZ) has been the major obstacle for wide industry applications of laser machining of CFRP composites. This paper investigates the quality of CFRP machined by a diode pumped solid state (DPSS) UV laser. The results show that minimum HAZ (about 50 μm) is achievable in machining of CFRP composite by using short pulsed UV laser. The study found that heat is easily accumulated in the material during laser processing, especially when the carbon fibres are sliced into small pieces. The paper discusses how to make use of the heat accumulation and how to avoid potential damage by the heat accumulation. Bearing strengths test and fracturing mechanisms study were conducted. Method of characterization of thermal damage in polymer matrix is developed.     

Room-temperature dual-wavelength erbium-doped fibre laser based on a sampled fibre Bragg grating and a photonic Robin Hood

With the assistance of a kind of photonic Robin Hood that is originated from four-wave mixing in a dispersion-flattened high-nonlinearity photonic-crystal fibre, a novel dual-wavelength erbium-doped fibre (EDF) laser is proposed and demonstrated by using a sampled fibre Bragg grating. The experiments show that, due to the contribution of the photonic Robin Hood, the proposed fibre laser has the advantage of excellent uniformity, high stability and stable operation at room temperature. Our dual-wavelength EDF laser has the unique merit that the wavelength spacing remains unchanged when tuning the two wavelengths of laser, and this laser is simpler and more stable than the laser reported by Liu et al. [Opt. Express, 13 142 (2005)].     

Thermoelastic stresses in a bonded layer due to repetitively pulsed laser radiation

Summary A method is presented for the calculation of thermoelastic stress and displacement fields in a bonded layer that absorbs thermal energy from a repetitively pulsed laser in its surface plane. A function with three adjustable parameters is used to simulate the temporal variation of each pulse while the radial intensity distribution (or mode structure) of each pulse follows a Gaussian profile. The pulse duration is of the order of the characteristic time for heat to diffuse across the layer thickness, and hence axial heat conduction cannot be neglected. Stress and displacement components due to heat absorption from three successive pulses are calculated and examined specifically at the free surface, at selected points within the layer, and at the bonded interface. The stress components at the bonded interface are also examined over a range of layer thicknesses to illustrate key differences between the thermoelastic responses of thin and thick layers.List of symbols a, b, c temporal shape parameters - g(r, z, t/r, 0, 0) function defined by Eq. (6) - g₁(z, p/) function defined by Eq. (27) - g₂(z, p/) function defined by Eq. (29) - j summation index - k _c parameter related to characteristic beam radius - m parameter defined by Eq. (22) - n summation index - p Laplace transform variable - r radial spatial variable - t time - t _r pulse rise time - t _w pulse width - t ^p(j) time at which pulsej achieves peak power - u _r radial displacement - u _z normal displacement - z normal position variable - A, B, C, D functions defined by Eq. (43) - F ₁ function defined by Eq. (39) - F ₂ function defined by Eq. (40) - F ₃ function defined by Eq. (48) - F ₄ function defined by Eq. (53) - G(t–/) function defined by Eq. (33) - (z, t–/) function defined by Eq. (32) - H _i() functions defined by Eqs. (74)-(81) - H(t) unit step function - K thermal conductivity - L layer thickness - N number of pulses in pulse train - P _a average power - P _p peak power - Q _o maximum incident flux for Gaussian source - Q(r) radial intensity distribution - T(r, z, t) auxiliary temperature field - (t) temporal profile of a single pulse - Y(t) temporal profile of pulse train Greek symbols thermal diffusivity - integration variable - o(t) Dirac delta function - duty cycle or ratio of temporal pulse width to pulse train period - ₁ parameter defined by Eq. (39) - ₂ parameter defined by Eq. (40) - coefficient of thermal expansion - shear modulus - v Poisson's ratio - _ij (r, z, t) thermoelastic stress field - temporal integration variable - (r, z, t) thermoelastic displacement potential - pulse train period - (r, z, t) temperature field due to repetitive pulsing - (r, z, t) Love function - (t) function defined by Eq. (15) - ₁ functions defined by Eqs. (64)-(69) Dimensionless quantities are indicated with an asterisk (r ^*, ^*, etc.). An overbar indicates a Laplace transform.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday