Stress Birefringence Measurements Research Articles

Additive manufacturing of variothermal injection moulding insert made of Al-40Si

Injection moulding has been a pivotal technology in the mass production of polymer optics for many years. The surface quality of the moulding inserts exerts a significant influence on the quality of the optics produced. In the production of micro-structured polymer optics, such as Fresnel lenses, conventional isothermal injection moulding is unable to achieve the requisite surface accuracy. Variothermal injection moulding allows for improved surface accuracy and reduced residual stresses, but increases technical effort and cycle times. To reduce the cycle time and residual stresses of variothermal injection moulding, the potential of additive manufacturing of Al-40Si for the fabrication of moulding inserts is investigated. In order to achieve these objectives, the offered design freedom of additive manufacturing is investigated with a view to developing optimised conformal cooling channels. Numerical methods will be used for thermal and structural analyses. The performance of the newly developed moulding insert is evaluated experimentally by thermographic measurements and the measurement of stress birefringence on replicated PMMA samples.

Stress Birefringence Measurement Based on Double Cascaded Photoelastic Modulation with Differential Frequencies

Stress Birefringence Measurement Based on Double Cascaded Photoelastic Modulation with Differential Frequencies

An experimental and simulation comparison of a 3-D abrupt contraction flow using the molecular stress function constitutive model

ABSTRACT The Molecular Stress Function (MSF) constitutive model with convective constraint release (CCR) mechanism has been shown to accurately fit a large range of viscometric data, and also shown to give strong vortex growth in flows of LDPE through planar and axisymmetric contractions. This work compares simulation and experimental results for 3-D flows of Lupolen 1840H LDPE through a contraction slit. Comparisons are made with vortex opening angles obtained from streak photography, and also with stress-birefringence measurements. The comparisons are made with two versions of the CCR mechanism. The simulated vortex angles for one version of the CCR mechanism are found to approach what is seen experimentally. The best-fit value for the stress optical coefficient was found to vary between CCRs and to decrease with flow rate. This is partially explained by different centreline elongational rates with the two CCRs, which in turn is related to different opening angles.

Mechanical stress birefringence of optical plates.

Modeling the mechanical stress birefringence and slow-axis distributions of optical plates is critical for optical lithography systems. In this paper, the distributions of mechanical stress birefringence and the slow axes of optical plates were modeled by the finite element (FE) model, stress optic relations, and the ray-traced Jones matrices method. To validate this model, the load incremental approach was utilized to reduce the disturbance of residual birefringence in mechanical stress birefringence measurement. The measured distributions of birefringence and the slow axis of the optical plate show a good agreement with our numerical simulation results. This model provides a better understanding of simulation of mechanical stress birefringence and provides a reference for optical design and polarization analysis of other optical elements.

Investigation of Photoelastic Property and Stress Analysis for Optical Polyimide Membrane through Stress Birefringence Method

Optical polyimide (PI) membranes have been increasingly attractive in optoelectronic substrate and optical element material applications. Controlled stress distribution is very important to optical PI membrane-based optics. However, nondestructive absolute stress measurement inside optical PI membranes remains challenging. In this letter, we adopted the stress birefringence method to experimentally investigate the correlation between stress and retardation in uniaxially, biaxially, and circularly stretched PI membranes. The calculated value of the photoelastic coefficient was found to be around 400 nm/Mpa·cm. A theoretical model was established where the retardation angle is the negative arctan of the principal stress ratio in the biaxially stretched membrane. We also found that the average retardation angle is an important parameter for evaluating the uniformity of stretching force in the circularly stretched membrane. This work provides a better understanding of the stress birefringence measurement of membrane materials.

Large range stress measurement system based on large frequency difference laser self-mixing interference

Stress-birefringence measurement is critical in optical glass materials. A laser self-mixing interference (SMI) stress measurement system with a measuring range of 1 deg to 179 deg is presented. The light source of the system is a He-Ne laser with a variable frequency difference. Birefringent external cavity SMI experiments are conducted with the laser with different frequency differences. Experimental results show that a large frequency difference decreases the cross-saturation effect between the two laser eigenstates, and alternate oscillations are more likely to occur, which directly improves the sensitivity and expands the measuring range of the system. A piece of neodymium glass is tested with the system and the results are given, proving that the large frequency difference laser SMI system provides a simple, low-cost, and high-sensitivity stress measurement method.

Sensitive measurement of stress birefringence of fused silica substrates with cavity ring-down technique.

A polarized cavity ring-down technique was employed to precisely measure the residual stress birefringence of fused silica substrates with greatly enhanced measurement sensitivity. Intracavity birefringence resulted in beating of two orthogonally resonant modes in a Fabry-Perot cavity. The beating frequency of the ring-down decay was directly related to phase retardation induced by stress birefringence of optical components inside the cavity. For fused silica substrates, measurement reproducibilities of phase retardation of 2.38×10-6 rad and of optical path difference of 2.4×10-4 nm were experimentally achieved. In addition, spatially resolved mapping of stress birefringence of a fused silica substrate was obtained, which was in good agreement with that measured with a commercial stress birefringence measurement instrument. The experimental results demonstrated that cavity ring-down is a sensitive technique for stress birefringence measurements of optical components.

Theoretical and experimental research on influence of cavity frequency difference in birefringent laser feedback system

The internal stress of glass material directly affects the processing quality of glass components and the service life of optical components. It is an important factor that relates to the overall system performance, safety, and reliability. Aerospace, precision optical systems, precision machining and other areas generally highly value the stress measurements of glass components. For example, the internal stress in the medium-glass material of precision imaging system will lead to the degradation of optical performance and reduce the image quality; the stress in the glass material used as the gain medium of high-power solid-state lasers not only directly affects the polarization state of the output light, but also shortens the service life of the laser; the stress concentration in the load-bearing glass of aircraft windshields, building glass curtain walls, etc., will cause serious accidents such as popping due to the reduction of glass mechanical properties. Therefore, the high sensitivity and large measurement range of stress detection technology has become a current research hotspot. Stress measurement techniques based on the birefringent external cavity laser feedback effect has received widespread attention due to its advanced and novel measurement principle. It is generally accepted in the traditional theory that the output phase of the laser in a feedback system is only determined by the phase retardation of birefringent element in an external cavity, and the measurement error is induced by the non-linear movement of external mirror. In this paper, the orthogonally polarized laser principle and the three-cavity equivalent model are combined to explain the influence of cavity frequency difference on the output of laser in feedback system. The frequency difference caused by the birefringence of the laser cavity is measured by comparing the intervals between adjacent longitudinal modes, and the frequency tuning feedback experiment is carried out. Theoretical analysis and experimental results show that the output phase of the laser is determined by the phase retardation of the external cavity, the frequency difference of the internal cavity, and the length of the external cavity. This conclusion is also confirmed by the measurement of the standard quarter wave plate. For a feedback system with an internal cavity frequency difference of 5 MHz and external cavity length of 150 mm, the phase difference induced by internal cavity frequency difference is about 0.573. The laser can output a single longitudinal mode below 40 MHz of the internal cavity frequency difference, and the length of the external cavity is generally larger than 150 mm when the actual system is designed, so the phase difference introduced by these two parameters cannot be ignored and must be calibrated. This study summarizes the phase characteristics of the orthogonally polarized laser under the joint of anisotropy feedback cavity, supplements the physical content of the laser feedback, and has great significance for accurate laser measurement of stress-birefringence, displacement, and distance.

Measuring Stress Birefringence in Small Si Samples

We report stress birefringence measurements for small (up to 150mm x 150mm) samples such as Si slabs, wafers and small ingot segments. Measured stress birefringence in an Si ingot segment exhibits an interesting four-fold symmetry that may be caused by the crystal growth process or subsequent squaring or grinding of the ingot. Stress birefringence map for an axially cut and mechanically polished cross section of the seed end of a CZ-grown Si ingot shows striations that could be a visualization of the solid-liquid interface of silicon crystals. Two instruments are used for measuring these small Si samples. The first instrument is a near infrared (NIR) Exicor birefringence measurement system that employs photoelastic modulator (PEM) technology. This is a point measurement instrument. The second instrument is a camera-based NIR imaging polariscope that uses a fixed circular polarizer and a rotating analyzer. Both instruments are designed primarily for Si material research at significantly lower cost than the previously reported system for measuring large, pseudo-square, PV Si ingots. The two instruments described in this paper complement each other for different applications.

Stress birefringence measurement in zirconia veneered crowns: A photoelastic study

Stress birefringence measurement in zirconia veneered crowns: A photoelastic study

Orientation Relaxation of Triblock Copolymer with Cylindrical Microdomain by in situ Stress-Birefringence Measurements

The orientation relaxation behavior of polystyrene-block-hydrogenated polyisoprene-block-polystyrene (SEPS) with cylindrical microdomains of polystyrene (PS) dispersed in the rubbery segments was investigated by simultaneous measurements of stress and birefringence, and small angel X-ray scattering (SAXS) measurements. At short relaxation time, the stress σ and the birefringence Δn decreased at almost constant rate with time and temperature. At long relaxation time, however, the σ and Δn decreased steeply with time, and the decrease became larger with increasing time and temperature. The decrease of the Δn stopped and large Δn remained at high temperature, while the σ was close to zero. Such characteristic relaxation behavior is ascribed to the form birefringence induced by the orientation of the parallel arranged cylindrical microdomains and the conformational change of the phenyl ring side group associating with the orientation relaxation of PS. The analysis of these results suggest that the orientation relaxation of the rubbery segments occurs at short relaxation time during the stress relaxation after the uniaxial stretching, and then the orientation relaxation of the PS segments in the cylindrical PS microdomains occurs associating with the conformational change of the phenyl side group at long relaxation time at high temperature while the orientation of the cylindrical domain is not changed.

Role of Architecture on the Conformation, Rheology, and Orientation Behavior of Linear, Star, and Hyperbranched Polymer Melts. 2. Linear Viscoelasticity and Flow Birefringence

In the preceding publication, we showed that the hyperbranched polystyrenes (HBPS) synthesized as part of this study may be viewed as starlike molecules with a high branch density, which are either unentangled or weakly entangled. In this paper, the role of architecture, especially the branch density, on the rheological and orientation behavior is investigated using simultaneous, quantitative stress and flow birefringence measurements in the melt state. Linear PS and eight-arm symmetric PS stars follow the stress−optical rule (SOR) over a wide dynamic range, with the stress−optical coefficient (C) governed by the arm molecular weight. When the branch density is “moderate” (greater than ∼20 arms), there is only a hint of nonterminal behavior in the viscoelastic moduli, while the C drops by 30% compared to a star with eight arms of comparable length. When the branch density is “high” (∼50 arms), and the arms are unentangled, the nonterminal behavior in G* is clearly apparent, and there is a dramatic breakdo...

Stress distribution and birefringence measurement in double-clad fiber

Modal birefringence and stress distribution measurements in a single-mode double-clad Nd +3-doped fiber are reported. The contribution of different mechanisms, such as stress-induced birefringence, bending and core ellipticity, to the total birefringence is determined for a fiber wound onto a drum. A stress distribution pattern in the cross-section of the fiber is presented. The stresses are shown to be applied to a fiber core along the cladding minor axis.

Stress and birefringence measurements during the uniaxial elongation of polystyrene melts

A rheometer for generating uniaxial elongations in molten polymers has been modified to allow for the simultaneous measurement of stress and flow-induced birefringence. Tensile stress σ and birefringence Δn′ data in flows at constant strain rates up to 1 s−1 were collected on a polydisperse polystyrene melt at temperatures of 160 and 170 °C. From these data, the stress-optic rule was followed for stresses below roughly 1 MPa. For stresses less than 1 MPa, the stress-optic coefficient |C|=|Δn′|/σ was found to have a value of 4.8×10−9 Pa−1, which was independent of strain, strain rate, and temperature. At stress levels higher than 1 MPa, |C| decreased indicating a failure of the stress-optic rule. A criteria for failure of the stress-optic rule was formulated using simple arguments from network models and characteristic times suggested by the tube model. This criteria, which is based on the hypothesis that failure of the stress-optic rule is the result of significant chain stretching, was found to be consistent with the data reported in this study and with data from previous studies on polystyrene melts.

Interferometric stress birefringence measurement

We describe a sensitive method for measuring the stress birefringence of an optical window that utilizes a phase-measuring Fizeau interferometer incorporating a variable retarder and a nonpolarizing beam splitter. When we test a material in an interferometer cavity, the wave front transmitted through the material is deviated by the surfaces, inhomogeneity, and birefringence of the material. Birefringence causes the transmitted wave front to have different optical path difference (OPD) profiles for the vertical and horizontal orientations of linear polarization. Subtracting these OPD profiles reveals the amount of phase difference between the fast and slow axes of the material. Hence, birefringence may be calculated. Phase-measurement techniques and a computer-controlled interferometer employing a variable liquid-crystal retarder provide a fully automated instrument for measuring stress birefringence. The theoretical derivation, discussion of the instrument, and experimental results are presented.

Interface Properties for Ceramic Composites from a Single-Fiber Pull-Out Test

AbstractAn experimental approach has been developed using a single-fiber pullout test to measure intrinsic interface properties for ceramic composites. The properties are determined from a pull-out, force-displacement curve, which is directly related to reinforcement toughening via fiber/matrix debonding and frictional pull-out. They were evaluated for a model composite system of continuous SiC fibers with various surface treatments in a borosilicate glass matrix. For the processing conditions used, the interface fracture toughness and the interface frictional shear resistance were found to be 1.0 ± 0.5 J/m2 and 3.3 ± 0.6 MPa, respectively, for as-received fibers. Experiments conducted with long embedded fiber lengths allowed the shear resistance to be deconvolved into an interface friction coefficient of 0.05 ± 0.01 and an initial fiber-clamping pressure of 65 ± 6 MPa. Nitric acidwashed fibers gave an increased interface toughness of 3.6 ± 0.1 J/m2 and friction coefficient of 0.08 ± 0.02, but nearly the same initial clamping pressure, 72 ± 12 MPa. Calculations of the clamping pressure from the fiber/matrix thermal expansion mismatch and from stress birefringence measurements in the glass were in general agreement with this value.

Stress optical behaviour of ammonium pentaborate under linear and hydrostatic stresses

Ammonium pentaborate (APB) is an orthorhombic crystal of mm2(C 2v ) class. In the present investigation the authors present the results on the stress birefringence of APB under linear and hydrostatic stresses. It is shown that from stress birefringence measurements under linear stresses alone, the effect of hydrostatic pressure on the birefringences of an orthorhombic crystal can be obtained. A comparison is drawn between the natural birefringence and stress birefringence under linear and hydrostatic stresses.

Stress-birefringence associated with facets of rare-earth garnets grown from the melt; A model and measurement of stress-birefringence observed in thin sections

A model where stress-birefringence associated with a facet is due to strain induced by lattice mismatch between the facet and the surrounding off-facet regions is proposed. In order to prove the validity of the model, the stress-birefringence associated with 〈211〉 facets of pure YAG grown by the Czochralski (CZ) method and pure NdGG grown by the floating zone (FZ) method was measured using two different methods: (1) using a “rectifier” polarizing microscope with a Brace-Köhler compensator and (2) Sénarmont's method using a He-Ne laser. The results of the quantitative measurements supported the validity of the mode. The experimental result, moreover, that the stress-birefringence associated with a facet of YAG was decreased by Cr 2O 3 doping also supported it.

Direct comparison of the loss of load transfer to ?E? and ?S? glass fibres manufactured by drawing into different environments

Accelerated water uptake tests have been used to compare the onsets of destruction of the ability to transfer shear stress at fibre/matrix interfaces in epoxy matrix glass reinforced plastic (GRP) manufactured with each of four different fibres. The ability to transfer shear stress has been monitored directly by measurement of stress birefringence through and adjacent to individual fibres. Full theoretical and practical details of the experimental method are given. “S” glass fibres, drawn into an atmosphere of ammonia in an attempt to promote the deposition of primary amines and/or secondary amines, rapidly lose their ability to receive shear stress from the matrix. This is attributed to neutralization of CO2 by NH3 within interfacial pockets of dissolved water, and the associated generation of osmotic pressure. Commercial samples of “S” and “E” glass fibres and “E” glass fibres drawn into an atmosphere of ammonia, all survive much larger water uptakes although, in the case of both kinds of “E” glass fibre, immersion in boiling water eventually gives rise to interfacial pressure pockets. These pressure pockets are also attributed to osmosis, with the role of dissolved solutes tentatively ascribed to the modifying agents present in “E” glass formulations.

Simultaneous measurement of transient stress and flow birefringence in one-sided compression (biaxial extension) of a polymer melt

Investigation of time dependent behaviour of a polystyrene melt is carried out with the aid of a new apparatus for biaxial extension. Use is made of the method of two impinging fluid streams guided by lubricated trumpet shaped metal walls. The flow birefringence is measured in the plane of symmetry and, at the same time, the force is measured which tends to separate the trumpets. The linear stress-optical relation turns out to be valid in this new flow geometry. An accurate value for the stress-optical coefficient can be determined from the relaxation experiments. The stress build-up as calculated from the optical measurements, is compared with the pertinent result of the theory of linear viscoelasticity. For the desired interconversion of dynamic moduli use is made of the approximation by Schwarzl and Struik. The steady state measurements are checked by the results of the non-linear model of Acierno et al.