CO2 laser cutting of stained glass

This paper covers the CO₂ laser cutting of stained glass using a Ferranti MF400 CNC laser cutting machine. The report examines the various laser cutting parameters required to generate a cut surface in glass which will require minimal post-treatment to be carried out, and also investigates the degree of geometrical intricacy that can be attempted, together with the associated limitations, in cutting 2D glass components. The experimental procedure used to obtain the necessary information for a preliminary database on the laser cutting of stained glass is also detailed. Finally, the implications and applications of the investigative work are examined for commercial situations through construction of a simple 2D test artefact.Notation f pulse frequency (Hz) - k thermal conductivity (W/mK) - P laser beam power (W) - Pl pulse duration (10^–5 s) - Pr pulse ratio - Ps pulse separation (10^–5 s) - P shield gas pressure (bar) - R _a surface roughness (m) - t _s substrate thickness (mm) - V cutting speed (mm/min) - V _opt optimum cutting speed (mm/min) - w kcrf width (mm) - angle of deviation (deg.) - wavelength (m) - d perforation depth (mm)     

Three-parameter approach for elastic–plastic fracture of the semi-elliptical surface crack under tension

Systematic three-dimensional elastic–plastic finite element analyses are carried out for a semi-elliptical surface crack in plates under tension. Various aspect ratios (a/c) of three-dimensional fields are analyzed near the semi-elliptical surface crack front. It is shown that the developed J–Q annulus can effectively describe the influence of the in-plane stress parameters as the radial distances (r/(J/σ₀)) are relatively small, while the approach can hardly characterize it very well with the increase of r/(J/σ₀) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress σ_e, the hydrostatic stress σ_m and the stress triaxiality R_σ, the three-parameter J–Q_T–T_z approach is proposed based on the numerical analysis as well as a critical discussion on the previous studies. By introducing the out-of-plane stress constraint factor T_z and the Q_T term, which is determined by matching the finite element analysis results, the J–Q_T–T_z solution can predict the corresponding three-dimensional stress state parameters and the equivalent strain effectively in the whole plastic zone. Furthermore, it is exciting to find that the values of J-integral are independent of n under small-scale yielding condition when the stress-free boundary conditions at the side and back surfaces of the plate have negligible effect on the stress state along the crack front, and the normalized J tends to a same value when φ equals about 31.5° for different a/c and n. Finally, the empirical formula of T_z and the stress components are provided to predict the stress state parameters effectively.     

Measurement of springback

Springback, the elastically-driven change of shape of a part after forming, has been measured under carefully-controlled laboratory conditions corresponding to those found in press-forming operations. Constitutive equations emphasizing low-strain behavior were generated for three automotive body alloys: drawing-quality silicon-killed steel; high-strength low-alloy steel; and 6022-T4 aluminum. Strip draw-bend tests were then conducted using a range of die radii (3<R/t<17), friction coefficients (0<μ<0.20), and controlled tensile forces (0.5<F_b/F_y<1.5). Springback angles and curvatures were measured for bend and bend–unbend areas of the specimen, the latter corresponding to the “sidewall curl” region, which dominates the geometric change and the dependence on process variables. Friction coefficient and R/t (die-radius-to-sheet-thickness) greater than 5 have modest but measurable effects over the ranges tested. As expected, strip tension dominates the springback sensitivity, with higher forces reducing springback. For 6022-T4, springback is dramatically reduced as the tensile stress approaches the yield stress, corresponding to the appearance of a persistent anticlastic curvature. The presence of this curvature, orthogonal to the principal curvature, violates the simple two-dimensional models of springback reported in the literature. The measured springback angles and curvatures are reported both in graphical summary and tabular form for use in assessing analytical models of springback.     

Study of cutting quality for TFT-LCD glass substrate

The trend towards using a large area of thin-film transistor liquid crystal display (TFT-LCD) glass substrate introduces challenges for cutting quality and production yield. For the requirements of boosting manufacturing efficiency and reducing cost, the optimization of cutting parameters becomes very important. In this study, we use a cutting wheel to directly scribe the glass substrate so as to generate a cutting score depth of the glass. The glass is then cleaved utilizing the principles of mechanical stress. We investigate quality issues such as median crack, lateral crack, cutting score, and cleaved profile with respect to different cutting pressures and wheel depths, which are in the ranges of 0.16 to 0.24 MPa and 0.1 to 0.3 mm, respectively, with a cutting speed of 350 mm/s. The glass substrate for the experiment is Corning EAGLE 2000 with a thickness of 0.7 mm. It is found that the median and lateral crack length can reach 140 and 403 μm, respectively, when the cutting pressure increases to 0.24 MPa.     

A three-parameter model for fatigue behaviour of circumferential surface flaws in pipes

A three-parameter model, recently proposed by the authors for part-through-cracked round bars, is employed herein to examine the shape evolution of a circumferential external surface defect in a metallic round pipe under fatigue loading. The elliptical-arc flaw presents an aspect ratio α=a_el/b_el (a_el,b_el=ellipse semi-axes) and a relative crack depth ξ=a/t, where a and t are the depth of the deepest point on the crack front and the pipe wall thickness, respectively. The third parameter of the model is the ellipse shifting s=a_el/a, which defines the distance of the ellipse centre from the external boundary of the pipe cross-section. Thick- and thin-walled pipes are considered. Fatigue crack propagation paths in the diagram of α against s and ξ are numerically obtained for different initial flaw configurations under cyclic bending loading.     

Effects of substrate materials on fracture toughness measurement in adhesive joints

To understand the effects of substrate materials on the fracture behavior of adhesive joints, experimental studies and finite element analyses have both been conducted for double-cantilever-beams (DCB) with aluminum and steel substrates at different bond thickness (h). Numerical results show that the region dominated by the crack singularity is much smaller than by the bond thickness. Very small plastic deformation may hence violate the requirements for small-scale yielding where the crack-tip field can be characterized uniquely by the stress intensity factor. Both critical strain energy release rate and J-integral for the joints with steel substrate are lower than those for the joints with aluminum substrate. Compared to the critical strain energy release rate, the critical J-integral is less sensitive to the substrate material if small plastic deformation occurs before cohesive failure takes place through the adhesive layer. For the joints with aluminum substrate, the fracture toughness initially increases and then decreases with bond thickness. Elastic–plastic crack-tip analysis indicates that at the same level of loading, a higher opening stress is observed in the joint with a smaller bond thickness. A self-similar stress field can be obtained by the normalised loading parameter, J/hσ₀.     

A universal slip-line model with non-unique solutions for machining with curled chip formation and a restricted contact tool

A universal slip-line model and the corresponding hodograph for two-dimensional machining which can account for chip curl and chip back-flow when machining with a restricted contact tool are presented in this paper. Six major slip-line models previously developed for machining are briefly reviewed. It is shown that all the six models are special cases of the universal slip-line model presented in this paper. Dewhurst and Collins's matrix technique for numerically solving slip-line problems is employed in the mathematical modeling of the universal slip-line field. A key equation is given to determine the shape of the initial slip-line. A non-unique solution for machining processes when using restricted contact tools is obtained. The influence of four major input parameters, i.e. (a) hydrostatic pressure (P_A) at a point on the intersection line of the shear plane and the work surface to be machined; (b) ratio of the frictional shear stress on the tool rake face to the material shear yield stress (τ/k); (c) ratio of the undeformed chip thickness to the length of the tool land (t₁/h); and (d) tool primary rake angle (γ₁), upon five major output parameters, i.e. (a) four slip-line field angles (θ, η₁, η₂, ψ); (b) non-dimensionalized cutting forces (F_c/kt₁w and F_t/kt₁w); (c) chip thickness (t₂); (d) chip up-curl radius (R_u); and (e) chip back-flow angle (η_b), is theoretically established. The issue of the “built-up-edge” produced under certain conditions in machining processes is also studied. It is hoped that the research work of this paper will help in the understanding of the nature and the basic characteristics of machining processes.     

The influence of water vapour in air on the friction behaviour of pure metals during fretting

An investigation was conducted to determine the effect of water vapour content in air on the frictional behaviour during fretting of pure metals: iron, aluminium, copper, silver, chromium, titanium and nickel. The fretting experiments were carried out under various humidity levels, ranging from dry air to 50% relative humidity at 23°C. During the experiment the frictional force between fretting surfaces was measured. Pure metals, except iron, were found to have a maximum value of the coefficient of friction during the steady-fretting stage (μ_s) at a specific humidity (RH_max). Iron showed a rapid decrease in μ_s with increasing humidity at RH_max. Each pure metal also exhibited maximum fretting wear at RH_max. The value of μ_s at RH_max for each metal was strongly related to the heat of formation of the lower metal oxide, indicating that the adhesive contact area was larger at RH_max for the fretting of metals with less chemical activity. At high humidity levels water vapour generally reduced the coefficient of friction, μ_s.     

Critical load for wear particle generation in carbon nitride coatings by single sliding against a spherical diamond

The ‘critical load' for wear particle generation of carbon nitride coatings sliding against a spherical diamond under a linearly increasing load has been examined in situ in relation to different nitrogen incorporation conditions, i.e. assisted N ion acceleration energy and N ion beam current density, and different coating thickness. An environmental scanning electron microscope (E-SEM), in which a pin-on-disk tribotester was installed, has provided direct evidence in situ of when, how and where wear particle generation occurs during the sliding of carbon nitride coatings against a spherical diamond. The in-situ examination of non-conductive carbon nitride coatings are available in E-SEM free from surface charging with controllable relative humidity. The sliding tests under linearly increasing load up to 300 mN at a sliding speed of 10 μm/s have been carried out with the purpose of measuring the ‘critical load' for wear particle generation in a similar way to the traditional macro scratch testing. However, instead of the ‘critical load', the critical maximum Hertzian contact pressure P_max will also be used in the following for better understanding. Based on the systematic study of seven combinations of nitrogen incorporation parameters and five kinds of thickness (0, 10, 50, 100 and 200 nm), the applicable range of P_max for wear particle generation can be increased from 1.6Y to 1.831.92Y or to 1.801.89Y, where Y is defined as the yield strength of silicon of 7 GPa, by coating carbon nitride onto silicon with changing nitrogen incorporation conditions of ion acceleration energy and ion current density, or varing coating thickness from 10 to 200 nm. It also appears that the observed wear particle generation of carbon nitride coatings was associated with a failure initiated in the silicon substrate rather than within the carbon nitride coating or at the coating–substrate interface in the light of both the empirical identification and the theoretical discussion.     

Plastic flow localization in mechanism-based strain gradient plasticity

The theory of mechanism-based strain gradient (MSG) plasticity is used to study plastic flow localization in ductile materials. Unlike classical plasticity, the thickness of the shear band in MSG plasticity can be determined analytically from a bifurcation analysis, and the shear band thickness is directly proportional to the intrinsic material length, (μ/σ_Y)²b associated with strain gradients, where μ is the shear modulus, σ_Y is the yield stress, and b is the Burgers vector. The shear band thickness also depends on the softening behavior of the material. The analytical solution of the shear strain rate yields that the maximum shear strain rate inside the shear band is two orders of magnitude higher than that outside, which is a clear indication of plastic flow localization. The limitation of the present model is also discussed.     

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.     

2-D discontinuous chip cutting model by using strain energy density theory and elastic-plastic finite element method

The formation of discontinuous chip is investigated in this paper. The cutting simulation was conducted on 60–40 brass (60% Cu, 40% Zn) under an extremely low cutting speed. The region of the maximum strain energy density (SED) distribution value relative to the minimum value, i.e. (dw/dv)_min^max, was used as the criterion to predict the initial breakage location under the presumption that the curvature direction of the maximum SED was the direction of crack growth. The shape and cutting force of discontinuous chip crack, the stress and strain distribution of the workpiece and chip, and the variation of various nodal force on the chip–tool interface were derived.     

A new weighting function for solving nonlinear oscillation problems

A new approximation technique is presented for solving nonlinear oscillation problems. A solution of form x = x₀ sin ωt is assumed and put into the differential equation, which leads to an algebraic equation which can be solved for ω in terms of x₀. The new technique is to reduce the algebraic equation to an identity at ωt = π/3. This method is compared with other common approximation techniques and with the exact solution for several nonlinear problems. Overall, the new method works better than any other approximation technique. In addition, it has the very practical advantage of being purely algebraic; no integrals need be evaluated, as in several other methods.     

Upper-bound anisotropic yield locus calculations assuming 111-pencil glide

Deformation by 111-pencil glide has been analyzed by an upper-bound model which combines a least-shear analysis and Piehler's maximum virtual work analysis. The least-shear analysis gives exact solutions if three 111 slip systems are active, while the maximum work analysis provides solutions for the case of four active slip systems. Independent checks are used to determine which solution method is appropriate.Computer calculations using this model have been made to determine; (1) the orientation dependence of the Taylor factor for axisymmetric deformation; (2) the yield loci for textured materials having [100], [110] and [111] sheet metals and rotational symmetry; (3) the isotropic yield locus for randomly oriented materials; and (4) flow stresses along critical loading paths for various assumed textures with rotational symmetry. The latter calculations indicate that anisotropic yield loci of textured bcc metals with rotational symmetry are much better approximated by σ_x^a + σ_y^a + R¦σ_x − σ_y¦^a = (R + 1)Y^a where R is the strain ratio and Y is the tensile yield strength with an exponent a = 6 rather than with a = 2 as postulated by Hill. It is not known how well upper-bound calculations like these represent actual yielding behavior.     

Characterization of nanoscale recording mark on Ge2Sb2Te5 film

We have fabricated nanoscale recording marks on Ge₂Sb₂Te₅ (GST) films with conductive atomic force microscope (AFM). GST films were deposited on glass or polyimide film with thickness of 150–200 nm by the rf–sputtering method. Through current–voltage (I–V) spectroscopy, good cantilevers for fabrication and characterization of nanoscale marks on GST were selected. A fresh and highly conductive tip showed voltage-switching characteristic in the I–V curve, where the threshold voltage was 1.6 V. Nanoscale dot and wire arrays of crystalline phases were successfully obtained by varying sample bias voltage from −10 to 10 V. With highly conductive tips, nanowires having full-width at half-maximum of 20 nm could be fabricated, whereas nanowires could not be fabricated with bias voltage below −2 V. The width of the nanoscale mark was increased by repetition of AFM lithography even with same applied voltage and lithography speed. For a thicker nanowire, the width measured in current-image (C-image) was observed to be 2 times of that measured in topography-image (T-image). This result supports that current sensing provides an image of phase-changed GST area with higher resolution than topography sensing.     

Strengthening caused by power law creep deformation of dispersed particles in an elastic matrix

The interaction energy is approximated between an edge dislocation and a particle deformable by power law creep in an elastic matrix. The stress required to overcome the interaction energy barrier is found to be greater than the Orowan stress, and the dislocation bulges to escape the particle. If the ratio of the shear modulus of the matrix to the viscosity of the particle (μt^m/σ₀) is large, the stress required to climb over the particle is larger than the Orowan stress and the dilocation bulges before it climbs. It is concluded that even if the particle is soft enough to exhibit creep, the strengthening of alloys can be achieved by an Orowan mechanism. The critical resolved shear stress (CRSS) of Cu-B₂O₃, obtained experimentally by Onaka et al. [11], agrees closely with that obtained in our analysis. This supports our analysis that the strength of Cu-B₂O₃ alloy at high temperature may be accounted for by the Orowan mechanism and the attraction between a dislocation and viscous particles. The energy and the force to overcome the energy barrier increases significantly with decrease of m, the strain rate exponent associated with the power law creep particle. It is found through analysis that for m < 1.0 and for certain values of μt^m/σ₀ > 1, the particle repulses the dislocation, while for m = 1.0 and for all values of μt^m/σ₀ > 1, the particle attracts the dislocation, which is the expected interaction between an elastic particle and a dislocation in an elastic matrix.     

Vibrations of point-supported rectangular plates with variable thickness using a set of static tapered beam functions

This paper studies the free vibrations of point-supported rectangular plates with variable thickness using the Rayleigh–Ritz method. The domain of the plate is bounded by x=αa′, a′ (0α<1); y=βb′, b′ (0β<1) in the Cartesian coordinate system. The thickness of the plate varies continuously and is represented by a power function (x/a′)^s(y/b′)^t. Varieties of tapered rectangular plates can be described by giving s and t different values. A set of static tapered beam functions which are the solutions of a tapered beam (a unit width strip taken from the particular plate under consideration in one or the other direction parallel to its edges) under a Taylor series of static loads, are developed as the admissible functions for the vibration analysis of point-supported rectangular plates with variable thickness in one or two directions. The eigenfrequency equation is derived through the Rayleigh–Ritz approach, supplemented by the zero deflection conditions at the point-supports. A very simple program in common use has been compiled. The convergence study shows a small computational cost and the comparison with known solutions for point-supported rectangular plates with uniform thickness demonstrates the accuracy of the present method. Finally, some new numerical results are given, which may serve as the benchmarks for future research on the aforementioned problem.     

In-process estimation of fracture surface morphology during wheel scribing of a glass sheet by high-speed photoelastic observation

Defect-free glass separation techniques are in strong demand in glass processing industries. In this study, we intended to observe the internal stress field during/after wheel scribing of a glass sheet using the photoelastic method. First, we visualized the crack propagation behavior in a 0.7-mm-thick non-alkali glass sheet during mechanical scribing with a 2.0-mm-diameter serrated diamond wheel using high-speed imaging techniques. The observation results under various applied load conditions showed that the crack propagation behavior changed dramatically at a load of approximately 9–10 N; the generated crack hardly propagated in the thickness direction under lower load conditions, in contrast to the rapid propagation under higher load conditions. The fracture surface morphology that was observed after cleavage also changed, from damaged to defect-free surfaces with increments in the applied load around the transition point (9–10 N). This result indicated that the fracture surface morphology was determined by the crack propagation behavior. Second, the birefringence phase difference was measured from the upper side of the glass sheet to enable understanding of the stress fields induced by scribing wheel indentations. As a result, the phase differences that were distributed along the scribe line were shown to differ depending on the applied loads; the phase difference changed little under lower load conditions, but vanished immediately under higher load conditions. Therefore, these differences were dependent on whether or not rapid crack propagation occurred. The measured phase difference distribution thus included information about the crack propagation behavior, and this information could be used as a criterion for estimation of the fracture surface morphology. An in-process estimation method for the fracture surface morphology during mechanical wheel scribing was therefore developed based on high-speed polarization imaging techniques.     

Tribological and mechanical investigation of SiO2 and Si3N4 coatings on fused silica and borosilicate glass

Amorphous SiO₂ and Si₃N₄ plasma‐enhanced chemical vapour deposited (PECVD) coatings were deposited on two different substrate materials (fused silica and borosilicate glass), with three coating thicknesses (0.1, 0.5, and 1.0 μm). The mechanical properties (hardness and elastic modulus) were determined by depth‐sensing indentation, with loads from 700 mN down to 0.1 mN. Tribological behaviour was studied in instrumented oscillating sliding tests at room temperature with a ball‐on‐flat arrangement, in which the coated disc was tested against an alumina ball, at a load of 1 N. Interpretation of the measurement of hardness and modulus of the coatings has to take into consideration the influence of layer thickness and the effect of the substrate. Tensile film stress and crack generation were only observed for Si₃N₄ on fused silica above a threshold thickness. Friction and wear measurements show that the coating has an effect on friction, while wear is affected by the thin coatings only for a short running‐in phase. The morphology of the wear scars indicates that the coatings have good adhesion. Despite crack generation, delamination effects were not observed. Indentation patterns similarly showed excellent lateral homogeneity of the mechanical properties over the entire film surface, and indicated that load‐displacement curves may be used to characterise the system.     

Examination of internal stress by photoelasticity in laser cleaving of glass

Laser cleaving is a glass-cutting technique in which thermal stress induced by laser heating and cooling produces cracks in the glass. Stress measurement during the laser cleaving process is critical in elucidating the crack-propagation mechanism and solving the problems of the laser cleaving method. In this study, we measured the birefringence retardation using a high-speed polarization camera and evaluated the relevance and accuracy of the measured values by comparing them with the results of a numerical calculation. The birefringence retardation at the crack tip was also observed in the experimental process. For the experiment, a soda lime glass was cleaved using CO₂ laser irradiation. Then, the birefringence retardation and azimuthal angle obtained using the polarization camera were compared with the numerical calculation results. The birefringence retardation around the crack tip corresponded with that of the deformation caused by mode I. The crack propagation was arrested when the crack tip approached the edge of the glass. The birefringence retardation observed using the polarization camera confirmed that the mode I deformation decreased as the crack approached the edge.