Mirror Constants Research Articles

Validation of the Orr theory in dental resin-based composites: A fractographic approach

ObjectivesThe present study aimed to assess the applicability of Orr's equation on light-cured resin-based composites (RBCs) tested in 3- and 4-point bending tests, as well as assess the operator reliability of this method. MethodsFracture mirrors of 320 specimens (n = 320) made of four RBCs that had failed in the two tests were analyzed microscopically and consequently two radii of each specimen were measured by two operators, each measuring twice. The mirror constant A was calculated using Orr's equation. The results of the two operators were compared using a t-Test and further assessment of the data was performed using a MANOVA, Tukey's post hoc test and regression analysis. ResultsWith the exception of 11 specimens, the measurement of the fracture mirror radii was carried out successfully. The calculation of the mirror constant proved successful with a high coefficient of determination (R2 > 0.98). The calculated mirror constants were operator-independent if the results of more than one measurement was taken into consideration. The ratio of the mirror constant A to the fracture toughness KIc lay between 2.1 and 2.4 for three of the four RBC. The fourth RBC had a ratio of 1.6 and was the only one where different mirror constants were observed as a function of the testing method. SignificanceThe present study proves the applicability of brittle fracture mechanics on RBCs despite them often being regarded as not brittle due to their also plastic behavior.

Fractography of silicon nitride based ceramics to guide process improvements

Fractography is an important tool to understand and identify the cause of the failure in materials. This understanding can be used to make changes in raw materials selection and processing to increase the strength of brittle materials. This study reports the fracture behavior of hot-pressed silicon nitride based ceramics, with focus on dominant flaw identification with respect to material and process parameters. Silicon nitride is an important material for structural applications which require high strength and wear resistance, such as bearings, nozzles, and cutting tools. Silicon nitride with a target base composition of Si6-zAlzOzN8-z (z = 0.5), along with varying boron dopant levels, was explored in this work. Detailed fractographic analyses revealed that the majority of fracture origins were internal flaws due to the foreign impurities introduced at various stages of processing. All materials were found to have reasonably high strength (800−1100 MPa). Strength was inversely proportional to the square root of the flaw size, however no correlation was found between measured flexural strength and fracture origin types. Mirror constants calculated from fracture mirror measurements ranged between 5.8 and 9.8 MPa.m1/2.

Design of Very High-Resolution Satellite Telescopes Part I: Optical System Design

The telescope design of a very high-resolution earth observation satellite is a challenging task, due to several constraints, including the size, mass, performance, tolerance, assembly, integrating, and environmental aspects. However, the demand for very high-resolution satellite imageries has increased day by day due to the numerous commercial and military applications. In this paper, two different optical configurations with ground sampling distance of 25 cm are investigated according to a definite mission statement. The first configuration represents an on-axis Korsch scheme, whereas the second design is based on the arrangement of the off-axis three-mirror anastigmatic configuration. Both designs have the advantage of small conic mirror constants without higher order parameters. Tolerance analysis of both designs utilizing a Monte Carlo algorithm is performed. The suggested baffling arrangements are simulated and tested according to a series of point sources with different off-axis angles. Finally, a comparison between the performance of the proposed designs and a recent study given by the French space agency is presented. The results show that the proposed designs can be implemented by the existing technologies and launched into space by the available launch vehicles.

Optical Design, Tolerance Analysis, and Baffling of Very High-Resolution Satellite Telescopes

The telescope design of a very high-resolution earth observation satellite is a challenging task due to several constraints, including the size, mass, performance, tolerance and environmental aspects. However, the demand for very high-resolution satellite imagery has increased day by day due to the numerous commercial and military applications. In this paper, an optical configuration for a ground sampling distance (GSD) of 25 cm is investigated according to a definite mission statement. The configuration represents on-axis Korsch scheme with the advantage of small conic mirror constants without higher-order parameters. In addition, a tolerance analysis utilizing a Monte Carlo algorithm is performed. The suggested baffling arrangement based on a series of point sources with different off-axis angles isderived. The size of the telescope is applicable to be launched into space by the current launch vehicles.

Effect of physical aging on fracture behavior of Te2As3Se5 glass fibers

Fracture surface characteristics of Te2As3Se5 (TAS) glass fibers aged in light and in dark have been investigated respectively for understanding physical aging effect on their fracture behavior. The properties including tensile strength (σ), surface flaw depth (α), and mirror radii (rm) were measured by DY30 Adamel Lomarghy and SEM, respectively. Shape factor extracted by fitting of σ vs α confirms that fractures of fibers aged in dark for 4 months originate from their surface flaw, but it does not work for fibers aged in light for 4 months. However, mirror constants (=σrm1/2) of fracture surface for the TAS glass fibers aged in dark are in a good agreement with those aged in light. One possible reason is that the photoinduced effect changes the structure of glass surface during the physical aging.

Fracture mirror of optical fibers

Optical fiber specimens with and without polymer surface coating (stripped) were tested under tensile and two-point bending. Their fracture surfaces were evaluated. A distinctive fracture mirror region can be seen at the fracture origin of every stripped fiber failed under stress. Using the known relationship equation between the fracture stress and mirror radius, the fracture mirror constants for the stripped optical fibers subjected to tension and bending were determined to be 1.3 and 9.4 MN m 3/2, respectively. However, the fracture mirror region of as-received optical fiber (with polymer coating) cannot be found from the fracture surface. The fracture hackle marks directing to a fracture initiation flaw are observed. The mirror region formation in bare glass fiber may shed a light for the mechanism of environmental assisted crack growth.

Crack branching in float glass subjected to biaxial loading

Failure of float glass plates in biaxial loading, occurs by well defined crack branching. As part of a study of the effect of handling damage on the strength of annealed glass, extensive observations have been made of crack branching in 4 mm thickness plates with strengths between 40 and 270 MPa, and more limited observations in plates of other thicknesses. Testing was carried out on discs loaded by hydraulic pressure against a circular anvil. For the 4 mm thick 280 mm diameter glass samples a 254 mm diameter anvil was used. Crack length at branching 2c b is related to the applied fracture stress σ b: σ b − σ 0 = A b/✓c b, where the branching constant, A b, is close to published mirror constants for uniaxial loading. The intercept σ 0 is larger than the residual surface stress in the sample, of which it is often considered to be a measure. The results have been analysed using the stress intensity factors for circular and elliptical cracks in a finite thickness plate and found to give good agreement with experiment for the variation of branch length with failure stress.

Fracture Mirror‐Failure Stress Relations in Weathered and Unweathered Window Glass Panels

Published results for window glass panel failures were analyzed by using finite‐difference methods to determine the stress states at the fracture origins. Although the state of stress was often complex, it was found that the maximum principal tensile stress at the fracture origin correlated with the fracture mirror. size. Fracture mirror constants were calculated and found to agree closely with published values.

Fractographic Analysis of Delayed Failure in Soda‐Lime Glass

Fractographic analysis of soda‐lime bars which failed under dead weight loading shows that the fracture mirror to initial flaw size ratio is a function of time under load, but that the mirror to critical flaw size ratio is a constant. The mirror constants are the same in delayed and rapid failure. The experimental results correlate with fracture mechanics predictions of time‐to‐failure based on subcritical crack growth. Scatter of the data about the prediction is discussed in terms of variations in flaw geometry.

ChemInform Abstract: Effect of Grinding on Flaw Geometry and Fracture of Glass.

Fracture mechanics is combined with fracture surface analysis to analyze brittle failure of glass bars which were tested relative to the direction of grinding. Grinding essentially produces two sets of flaws from which failure occurs. In the most severe set, formed basically parallel to the grinding direction, the ratio of the average depth (a) to the half-width (b) is 0.5. In the less severe set, formed perpendicular to the grinding direction, the average a/b ratio is 1.6. In both sets the most severe flaws are generally associated with a particularly deep grinding groove or gouge. The strength reduction resulting from testing perpendicular to the grinding direction results from the larger flaw size and slightly higher stress-intensity factor resulting from the greater ellipticity of the flaws formed parallel to the grinding grooves and perpendicular to the tensile axis. Detailed analysis of these 2 sets of flaws causing failure of appropriately oriented specimens shows that (1) the fracture mirror radius, r, occurs at a constant stress-intensity level independent of flaw geometry; (2) unsymmetric fracture mirrors result from unsymmetric, irregular flaws leading to unsymmetric stress-intensity distributions; (3) is constant for semielliptical flaws; and (4) fracture energy calculated from an expression including mirror constants, the flaw-to-mirror size ratio, and the flaw geometry agrees with measured values over a wide range of a/b values.

Effect of Grinding on Flaw Geometry and Fracture of Glass

Fracture mechanics is combined with fracture surface analysis to analyze brittle failure of glass bars which were tested relative to the direction of grinding. Grinding essentially produces two sets of flaws from which failure occurs. In the most severe set, formed basically parallel to the grinding direction, the ratio of the average depth (a) to the half‐width (b) is 0.5. In the less severe set, formed perpendicular to the grinding direction, the average a/b ratio is 1.6. In both sets the most severe flaws are generally associated with a particularly deep grinding groove or gouge. The strength reduction resulting from testing perpendicular to the grinding direction results from the larger flaw size and slightly higher stress‐intensity factor resulting from the greater ellipticity of the flaws formed parallel to the grinding grooves and perpendicular to the tensile axis. Detailed analysis of these 2 sets of flaws causing failure of appropriately oriented specimens shows that (1) the fracture mirror radius, r, occurs at a constant stress‐intensity level independent of flaw geometry; (2) unsymmetric fracture mirrors result from unsymmetric, irregular flaws leading to unsymmetric stress‐intensity distributions; (3) is constant for semielliptical flaws; and (4) fracture energy calculated from an expression including mirror constants, the flaw‐to‐mirror size ratio, and the flaw geometry agrees with measured values over a wide range of a/b values.

Fracture surface analysis of ceramics

Flaw size, c, fracture mirror boundaries, r, fracture stress, σ, and critical fracture energy were measured for glasses, glass ceramics, and single and polycrystalline ceramics. The relationship σr1/2 = constant was verified for all these materials. The mirror constants, A, in these materials were shown to be directly proportional to the average critical stress intensity factor for crack propagation, KIC. Based on the A — KIC relationship, the outer mirror to flaw size ratio is shown to scatter about a value of 13∶1. Thus, the mirror constants were used to predict critical flaw sizes in these materials. The observed flaw sizes in most cases correlated well with those calculated. The cases in which poorer correlation was obtained are those in which flaw sizes were smaller than the grain size, flaws were pores or surrounded by porous regions, or where severe microcracking existed. It is shown that the elastic modulus is proportional to the mirror constant and probably to the critical fracture energy, but that the latter is highly dependent on local microstructure. The smaller inner to outer mirror ratios for polycrystalline ceramics over glasses is attributed to the difference in available paths for crack propagation.

Corrector Systems for Cassegrain Telescopes

Most modern reflecting telescopes have relative apertures of about f/3 and f/8 for the primary and first secondary foci in accordance with the suggestions of Bowen. The angular field which can be used at the first secondary focus is limited by the size of available plates for large instruments but can approach ±1° for smaller systems. The factors influencing the choice of the field corrector system in the first secondary focus are discussed. It is an important point whether the Ritchey-Chretien form of the mirrors is strictly maintained—giving an optimum field without the corrector—or whether the aspheric constants are allowed to vary as free parameters. The differences are small but significant. The performance of a number of secondary focus correctors consisting of one, two, and three elements is discussed, spot diagrams being given in each case. Systems with fixed Ritchey-Chretien mirror constants are inferior to those with free mirror constants. Test methods for the manufacture of the mirrors of telescopes of this type are compared. A doublet type corrector is suitable for compensation testing of primary mirrors or for secondaries tested from the back, but the testing of the latter from the front is more difficult. Several possible techniques are discussed.

Corrector Systems for Cassegrain Telescopes

Most modern reflecting telescopes have relative apertures of about f/3 and f/8 for the primary and first secondary foci in accordance with the suggestions of Bowen. The angular field which can be used at the first secondary focus is limited by the size of available plates for large instruments but can approach +/-1 degrees for smaller systems. The factors influencing the choice of the field corrector system in the first secondary focus are discussed. It is an important point whether the Ritchey-Chrétien form of the mirrors is strictly maintained-giving an optimum field without the corrector-or whether the aspheric constants are allowed to vary as free parameters. The differences are small but significant. The performance of a number of secondary focus correctors consisting of one, two, and three elements is discussed, spot diagrams being given in each case. Systems with fixed Ritchey-Chrétien mirror constants are inferior to those with free mirror constants. Test methods for the manufacture of the mirrors of telescopes of this type are compared. A doublet type corrector is suitable for compensation testing of primary mirrors or for secondaries tested from the back, but the testing of the latter from the front is more difficult. Several possible techniques are discussed.