Why is It Easy to See Stress Optics Effects in a Polymer
Experimental Stress Analysis
E.J. Hearn PhD; BSc(Eng) Hons; CEng; FIMechE; FIProdE; FIDiagE , in Mechanics of Materials 2 (Third Edition), 1997
6.12 Photoelasticity
In recent years, photoelastic stress analysis has become a technique of outstanding importance to engineers. When polarised light is passed through a stressed transparent model, interference patterns or fringes are formed. These patterns provide immediate qualitative information about the general distribution of stress, positions of stress concentrations and of areas of low stress. On the basis of these results, designs may be modified to reduce or disperse concentrations of stress or to remove excess material from areas of low stress, thereby achieving reductions in weight and material costs. As photoelastic analysis may be carried out at the design stage, stress conditions are taken into account before production has commenced; component failures during production, necessitating expensive design modifications and retooling, may thus be avoided. Even when service failures do occur, photoelastic analysis provides an effective method of failure investigation and often produces valuable information leading to successful re-design, typical photoelastic fringe patterns are shown in Fig. 6.18.
Fig. 6.18. Typical photoelastic fringe patterns, (a) Hollow disc subjected to compression on a diameter (dark field background). (b) As (a) but with a light field background. (c) Stress concentrations as the roots of a gear tooth.
Conventional or transmission photoelasticity has for many years been a powerful tool in the hands of trained stress analysts. However, untrained personnel interested in the technique have often been dissuaded from attempting it by the large volume of advanced mathematical and optical theory contained in reference texts on the subject. Whilst this theory is, no doubt, essential for a complete understanding of the phenomena involved and of some of the more advanced techniques, it is important to accept that a wealth of valuable information can be obtained by those who are not fully conversant with all the complex detail. A major feature of the technique is that it allows one to effectively "look into" the component and pin-point flaws or weaknesses in design which are otherwise difficult or impossible to detect. Stress concentrations are immediately visible, stress values around the edge or boundary of the model are easily obtained and, with a little more effort, the separate principal stresses within the model can also be determined.
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Polymer Characterization
Derek Hemsley , in Comprehensive Polymer Science and Supplements, 1989
33.4.6.1 Stress birefringence
Unfortunately the birefringence shown by specimens does not arise only from molecular orientation. Stress can also produce effects which may be difficult to separate from those due to orientation and which may be of comparable magnitude. Photoelastic stress analysis has long been used to assess the magnitude, direction and distribution of stresses in loaded transparent or translucent components or models. 41 Assumptions made in that work are that the strains are small and that the stress optical coefficient relating stress to birefringence is independent of strain. The effect of large strains has been considered by Treloar. 43
Stresses in microscopic specimens may have developed during product manufacture, or have been introduced by specimen preparation, particularly thin sectioning. In the later case high strains may be involved but fortunately in the case of oriented films and fibres the problem does not usually arise, since these are often examined without sectioning. Discrimination between strain- and orientation-induced birefringence can be attempted by measuring birefringence as a function of temperature in the region of the material's T g and relating measurements to other properties such as deformation. This can be difficult to do on the microscopic scale, even with the aid of a microhotstage. It is therefore fortunate that if polymers are subjected to processes designed to introduce molecular orientation then orientation birefringence usually dominates and stress effects can be ignored.
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Examination and analysis of failed components
Peter Rhys Lewis , Colin Gagg , in Forensic Polymer Engineering, 2010
2.3.4 Photoelastic strain analysis
Indirect stress or strain analysis is a versatile method for investigating possible or actual failure of a product or part. Failure can be from externally applied stress or from residual (moulded-in) stresses. Both external stress and moulded-in strain (or a combination of both) can cause a part to fail prematurely. It is more straightforward to detect failure due to poor design, or excessive service forces. However, residual stresses and strains are altogether different. Here, poor moulding practice can generate residual strain just about anywhere, anytime. Photoelastic inspection will allow detection of frozen-in strains, allowing identification of failure, with the method revealing the actual levels of orientation in the part.
Some transparent plastics such as polycarbonate are highly birefringent and lend themselves to photoelastic stress analysis. The part is placed between two polarizing media and viewed, in the crossed polar position, from the opposite side of the light source. Fringe patterns are observed -without applying external stress, thus allowing observation of moulded-in or residual strains in the part. Figure 2.10 shows a set square containing residual moulding stresses that are clearly visible under the photoelastic viewing method. A high fringe order indicates areas of high chain orientation whereas low fringe order represents an unstressed area. Close spacing of fringes represents a high strain gradient, whereas uniform colour will be an indicator of uniform strain in the part. The injection point of polymer at P shows high residual strain, and the corners to the central hole an exceptional level. A weld line formed beyond the hole is also clearly visible (WW).
2.10. Birefringence in polycarbonate set square showing gate at P and weld line at WW.
Plastic models can be used to simulate 'in-service' conditions. Both applied and residual stress fields can be exposed using models of structures in photosensitive material placed between polarizing filters in the crossed polar position. Figure 2.11 shows the stress fields present in a section of a bridge beam used in the first rail crossing of the Dee at Chester. It failed in May 1847 by brittle fracture. One possible initiation point lay in the corners present in the cavetto moulding shown in section on either side of the lower part of the cast iron structure. Straining the lower flange showed that the upper corner was the most seriously strained and thus the likely cause of the failure. The method is used widely for examining how structures respond to various load conditions (7).
2.11. Birefringence in girder section showing stress raiser at upper corner.
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Developments in Imaging and Analysis Techniques for Micro- and Nanosize Particles and Surface Features
Rajiv Kohli , in Developments in Surface Contamination and Cleaning: Detection, Characterization, and Analysis of Contaminants, 2012
5.8.1 Stress Patterns and Defects in Bonded Silicon Wafers
The size of silicon wafers used in fabricating integrated circuits has steadily increased, yielding more parts per processing step. As wafers grow to 300 and 400 mm in diameter, they become increasingly fragile and are prone to stress buildup during crystal growth, sawing, lapping/grinding, etching, and polishing operations. Cracks may be generated throughout processing and, if undetected, the wafers that survive can be rendered unusable in subsequent manufacturing stages. Because stress distribution field is often at least an order of magnitude larger than the defects themselves, the stress caused by flaws of submicrometer dimensions can be imaged at much lower magnification than that necessary to find the flaw itself.
A newly developed inspection system, called the IR gray-field polariscope (IR-GFP), can locate, classify, and quantify defects in bonded semiconductor wafers [402,406–408] . This system combines an IR transmission (IRT) system with a photoelastic stress analysis system to achieve 1-μm spatial resolution and 0.05 MPa shear stress resolution for a bonded pair of wafers. A crack that is only a few millimeters long is difficult to see when the wafer surface is illuminated with a flashlight at an oblique angle, even under high magnification. By measuring the transmitted infrared light intensity field, the crack is more apparent because of reflective losses at the crack faces (Fig. 5.32a). However, the stress patterns generated by the crack are even more visible in the polarized near-IR view with the imaging camera (Fig. 5.32b). Further inspection of similar wafers indicates that large residual stress buildup at the edge of the batch of wafers may be responsible for the damage [402,407,408]. For other defects such as debonds due to trapped gas bubbles, trapped particles, or a combination of both, commonly employed inspection techniques including scanning acoustic microscopy or IRT will result in similar surface images. However, the IR-GFP can differentiate between these two types of defects and also accurately measure the residual stresses due to these defects [408].
FIGURE 5.32. Near-infrared stress imaging of fracture in silicon wafers. (a) Traditional IR transmission image visible from one side only. (b) Near-IR stress image reveals the stress patterns in the vicinity of the crack [402].
By employing broad-field illumination and the near-IR camera, specimens with very rough surfaces can be inspected quickly and conveniently throughout the production process. A higher wafer throughput also can be achieved, making 100% online inspection at rates of up to 10 meters per second, a distinct possibility for many applications.
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Applications of Characterization Techniques
In Developments in Surface Contamination and Cleaning, Volume 12, 2019
3 Chemical-Specific Infrared Imaging Camera
Thermal infrared (IR) imaging is an important tool in the optoelectronics industry, and it is used routinely in industrial sensing, security, and firefighting. Major developments in detector technology have made IR imagers and focal plane arrays available for developing chemical-specific imaging cameras that can capture the chemical composition and distribution of a sample in seconds. Chemical information derived from the fundamental vibrations of molecules is available in the 2- to 20-μm IR wavelength region of the spectrum. Coupling a Fourier transform IR (FTIR) instrument to a focal-plane-array detector provides the basic components of a chemical-specific IR imaging camera [1259]. Near-IR microscopic imaging can be used to determine composition uniformity, particle sizes, and distributions of all the sample components, polymorphic phase distributions, moisture content and location, contaminants, coating and layer thickness, residual stress and cracking, and other structural details without damaging the product [1259–1265].
To illustrate the power of the spectrochemical imaging technique, an IR camera system was used to measure the decontamination efficiency of a chemically contaminated system [1259]. Methyl salicylate was applied to a metal surface, which was then cleaned with a swab. This compound has several IR absorptions in the mid-IR region. Figure 5.4 shows the metal surface after contamination with methyl salicylate and cleaning with a swab. The image, generated at 1675 cm−1, shows hot spots (red) where the contaminant was not removed. This data set was collected in approximately 80 seconds. At 1090 cm−1, a similar image confirmed the contamination in the lower right corner (Figure 5.4b). The full area of a typical 1-cm diameter sample can be interrogated with a spatial resolution of about 40 μm × 40 μm in only a few minutes, providing both enhanced sensitivity, and location information.
Figure 5.4. Infrared images at characteristic frequencies of a metal surface contaminated with methyl salicylate (a) and subsequently cleaned (b) show areas (red) where contamination was not removed [1259].
Reproduced with the permission from the American Institute of Physics3.1 Stress Patterns and Defects in Bonded Silicon Wafers
The size of silicon wafers used in fabricating integrated circuits has steadily increased, yielding more parts per processing step. As wafers grow to 300 and 400 mm in diameter, they become increasingly fragile and are prone to stress buildup during crystal growth, sawing, lapping/grinding, etching and polishing operations. Cracks may be generated throughout the processing, and if undetected, the wafers that survive can be rendered unusable in subsequent manufacturing stages. Because stress distribution field is often at least an order of magnitude larger than the defects themselves, the stress caused by flaws of sub-μm dimensions can be imaged at much lower magnification than that necessary to find the flaw itself.
A newly developed inspection system, called the IR grey-field polariscope (IR-GFP), can locate, classify, and quantify defects in bonded semiconductor wafers [1260, 1266–1268] . This system combines an IR transmission (IRT) system with a photoelastic stress analysis system to achieve 1 μm spatial resolution and 0.05 MPa shear stress resolution for a bonded pair of wafers. A crack that is only a few millimeters long is difficult to see when the wafer surface is illuminated with a flashlight at an oblique angle, even under high magnification. By measuring the transmitted infrared light intensity field, the crack is more apparent because of reflective losses at the crack faces (Figure 5.5a ). However, the stress patterns generated by the crack are even more visible in the polarized near-IR view with the imaging camera (Figure 5.5b). Further inspection of similar wafers indicates a large residual stress buildup at the edge of the batch of wafers and may be responsible for the damage [1260, 1267, 1268]. For other defects such as debonds due to trapped gas bubbles, trapped particles, or a combination of both, commonly employed inspection techniques including scanning acoustic microscopy or IRT will result in similar surface images. However, the IR-GFP can differentiate between these two types of defects and also accurately measure the residual stresses due to these defects [1268].
Figure 5.5. Near-infrared stress imaging of fracture in silicon wafers. (a) Traditional IR transmission image visible from one side only. (b) Near-IR stress image reveals the stress patterns in the vicinity of the crack [1260]. Reprinted with permission from the August 2004 edition of Photonics Spectra, online at www.PhotonicsSpectra.com.
Copyright 2019, Photonics Media, Pittsfield MA, https://www.photonics.com/Articles/NIR_Imaging_Detects_Cracks_in_Silicon_Wafers/a19673By employing broad-field illumination and the near-IR camera, specimens with very rough surfaces can be inspected quickly and conveniently throughout the production process. A higher wafer throughput can also be achieved, making 100 percent online inspection at rates of up to 10 meters per second a distinct possibility for many applications.
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Biomaterials and Clinical Use
B. Al-Nawas , W. Wagner , in Comprehensive Biomaterials II, 2017
7.19.3.2.1 Mechanical testing and modeling
Mechanical testing of dental implants has two central objectives. One is to study the influence of the implant macrostructure on primary stability in various bone densities, and the other is the stability of the implant abutment connection. The latter one classically is studied by mechanical testing [285]. The accepted method of fatigue testing is described in ISO/FDIS. 14801:2007 (Fig. 9).
Fig. 9. Schematic drawing of the fatigue testing setup due to ISO 14801 (4=loading device, F=Force applied in 30degree).
One method to determine the influence of the thread design on primary stability is photoelastic analysis. It helps to visualize critical stress points using a photoelastic, homogeneous, isotropic material. By studying the fringe pattern of polarized light, one can determine (visualize) the state of stress at various points in the material [286,287] . Photoelastic stress analysis was introduced into dentistry to evaluate different types orthodontic movements [288]. Since then, the application of this method has started to be used in different areas of dental research, focusing on stress distribution [289]. It is an important tool for visualizing stress points. The main and inherent limitation of the method is its capacity to model the non-homogeneous and anisotropic characteristics of bone and its limitation to qualitative data [286].
The application of strain-gage method on dental implants is based on the use of electrical resistance strain gauges. A strain gage utilizes the property of electrical conductance's dependence on not only the electrical conductivity of a conductor, but also the conductor's geometry [290,291]. It mainly provides in vitro measurement strains under static and dynamic loads. In vivo studies were also developed to quantify the degree of stress that occurs in the bone around implants associated with fixed partial denture [292], to measure strains involved in connecting implants to a natural tooth [293], and to measure the force transmission onto implants supporting overdentures [294]. The limits of the in vivo use of the strain-gage method are obvious, as it provides only the data regarding strain at the gage.
The finite element analysis is based on the idea that a complex situation is divided into small elements which allow an estimation of the solution. Thus, it is a method whereby instead of seeking a direct solution function for the entire domain, one formulates the solution functions for its finite elements and combines them properly to obtain the solution to the entire structure [295]. By using computer aided design software and engineering experience, the power of the finite element method is its versatility. The anistropic structure of bone and the wish for a 3D model, which are the limit of the method, are frequently solved by improved PC possibilities. The model is used for a variety of questions in dental implantology [286].
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FAILURES OF MATERIALS
W.G. KNAUSS , in Handbook of Materials Behavior Models, 2001
7.13.2 STRESS ANALYSIS
One of the perennial questions surrounding discrepancies between analytical (for linearly elastic materials) and experimental results concerned the accuracy with which analyses could explain the physical situation. Although numerous examples had been established for quasi-static situations over the last few decades, no comparative certainty existed with respect to the dynamic case. A sizable body of dynamic photoelastic stress analysis emerged during the 1970s and early 1980s. Qualitatively, the stress distribution around crack tips that were suddenly loaded or moving at high rates agreed with the asymptotic expansions, but their matching with initial and temporal boundary conditions was rather uncertain, since early solutions were prevalent only for the infinite domain.
Besides the mainstay of photoelasticity for experimentally determining the stress and deformation state around dynamically affected crack tips, the late 1970s experienced a growing use of the caustic method, which depends on the out-of-plane surface deformations in the crack tip vicinity [17, 20, 21, 37]. Critical experiments have shown that this method does rather well when applied to brittle materials but is questionable in its accuracy where plastically deforming solids are involved. An example of the former case, as applied in dynamic situations [27, 32], is shown in Figure 7.13.1. Here a comparison is effected between the computational result of a time-dependent stress-intensity factor in a plate of Homalite 100 (a "brittle solid" by all engineering standards) and the computation of the stress-intensity factor following Freund's formulation [12] and using a well-calibrated load history applied to the crack surfaces. The experimentally determined stress-intensity factor corroborates the computed one very well, including the transient effects as the crack starts to move.
FIGURE 7.13.1. Comparison of analytically determined stress-intensity histories (solid lines) with experimentally determined values (solid dots) for two loading conditions on the crack faces. a. "Point force" applied to crack faces. b. Uniform pressure, including the effects of initial crack propagation. It is essential in the experimental determination of the stress-intensity factor that the domain from which the optical (caustic) information is gathered is of the proper size to all the transient information that has radiated out from the crack tip to the "initial curve."
(Reproduced with kind permission by Kluwer Academic Publishers from Ravi-Chandar, K., and Knauss, W. G., Dynamic crack-tip stresses under stress wave loading: A comparison of theory and experiment, International Journal of Fracture, 20, pp. 209−222, 1982.) Copyright © 1982For the case of plastically deforming solids, the situation is not so clear-cut. Although no analytical (closed form) solution for a crack moving dynamically through an infinite (or finite) domain exists in this case, results developed for static cracks shed light on this question without the complication of dynamic effects. In a study of crack tip deformations utilizing the highly precise methods of Twyman-Green interferometry (out-of-plane) and moiré-interferometry (in-plane) [34–36], displacement profiles were compared to finite element computations involving a thorough elastoplastic characterization of the material behavior (incremental J2-theory) and the maximal discretization allowed by a Cray Y2 computer. It was found that as long as plastic deformations do not play a significant role, linear elastostatics describes the physical displacement exceedingly well with a precision at the micron level. However, when the stresses exceed levels of those corresponding to about half the failure load, measurable deviations arose, which increased at the fracture point to differences on the order of 25%, as illustrated in Figure 7.13.2. Thus a sizable error can exist when out-of-plane deformations are used to deduce the in-plane crack tip stress field. The most troubling feature of this discrepancy is that the deformation field, as represented by optical fringes or by the shape of a caustic, looks just like it is supposed to, except that the numbers are incorrect, so that one has no a priori or practical criterion as to whether the caustic analysis is appropriate in the presence of plastic material behavior or not. One must deduce then that all methods for determining the in-plane stress-intensity field from out-of-plane deformations in non-linearly deforming solids are suspect, even if the best numerical methods available today are being utilized. This caution must thus also be applied to caustics as well as to gradient sensing methods [38] when significant plastic deformations arise at the crack tip.
FIGURE 7.13.2. Comparison of computationally and experimentally determined displacements at the tip of a crack in 4340 steel, a. Displacement normal to the specimen surface along crack extension line. b. In-plane surface displacement parallel to the crack along line at 60° with respect to crack extension.
(Reproduced with kind permission by Kluwer Academic Publishers from Schultheisz, C., Pfaff, R. D., and Knauss, W. G., An experimental/analytical comparison of three-dimensional deformations at the tip of a crack in a plastically deforming plate, III. Comparison of numerical and experimental results, International Journal of Fracture, 90, pp. 47−81, 1998.) Copyright © 1998Read full chapter
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