Dynamic caustics and its applications

For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K^d_I which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K^d_I evaluated. Also, crack propagation behaviour of notched composites in dynamic loading modes are reviewed and evaluated. A relatively large data base using metal-epoxy particulates, rubber-toughened poly(methyl methacrylate), and Sandwich plates are given. In all cases, a combination of high-speed photography and the optical method of dynamic caustics has been used. Results on the dynamic crack propagation mode, fracture toughness and crack propagation velocities of several rubber-modified composite models are presented. The composite models studied include specimens with one and/or two ‘complex’ two-stage inclusions, i.e. PMMA round inclusions surrounded by concentric rubber rings, one and/or press-fifting inclusions without rubber interface, all under dynamic loading. In all cases both qualitative and quantitative results were obtained. Also, results on crack propagation mode, crack propagation velocity, stress intensity factors and on the influence of the sandwich phases on crack propagation mode are presented.     

Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process

A simple holographic recording of a photo-elastic object under stress allows the isochromatics to be observed. The isopachics are obtained by double-exposure interferometry: a second traverse of the wavefront through the object after a 90° rotation of its polarization by a Faraday cell eliminates the unwanted isochromatics.     

Dynamic optical visualization on the interaction between propagating crack and stationary crack

Dynamic interactions between the propagating crack and the static crack in PMMA material are studied by combining high-speed Schardin camera with optical caustic method. A series of dynamic optical bifocal patterns (the specimen-focused image and the off-focused image) around the propagating crack tip and the static crack tip are recorded for PMMA thin strip which contains two collinear-edge-cracks subjected to tensile loading, the variations of the caustic diameter and the distortion of the caustic shape are revealed due to the influence of local stress singularity at the crack tip. Interactions between the moving crack and the static crack are analyzed by means of the evolution of dynamic fracture parameters. The influence of crack interaction on fracture parameters is discussed based on both a K-dominance assumption and a higher order transient crack-tip expansion. These results will be useful to the evaluation of dynamic properties and the design of structures in the cracked polymer material.     

Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis

Combining color imaging with phase shifting, a technique named five-step color phase shifting is presented to determine the whole-field isoclinic parameter. Relevant theory is derived and explicit conditions for directly determining the isoclinic parameter in the range of [0,π/2] are given. The unloaded light intensity of the model is systematically studied. A color camera recorded five isoclinic images coupled with isochromatics from a plane polariscope with five different settings, respectively. Experiments have been carried out with a circular disk under diametral compression and errors have been analyzed and estimated. This technique utilizes white light, which avoids undefined isoclinics near the locations where the isochromatics exist and will have active effect on experimental stress analysis and structural strength design.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

Crack propagation in amorphous polymers and their composites

The fracture energy of a polymer depends strongly on the viscoelastic responses of the material, and therefore is a function of temperature and crack velocity. The toughness of a composite is determined by the way in which the reinforcing filler modifies the energy dissipating mechanisms of the polymeric matrix.

The fracture toughness of a variety of polymeric glasses and their composites with glass beads, glass fibers, and rubber particles was measured. The velocity of rapidly moving cracks and the crack propagation rates under controlled loading conditions were also measured.

It was found that the crack propagation velocities in unfilled and glass bead filled materials were controlled by the longitudinal stress waves in the matrix and that the only effects of the glass beads were to blunt the crack tip and limit the viscous deformation. The effect on fracture toughness was relatively small and either positive or negative, depending on which of the above two factors dominated.

The presence of rubber particles as a second phase lowered terminal crack propagation velocities and greatly increased the fracture toughness, indicating a crack retarding effect of the rubber particles. This is related to the induction of crazes in the matrix by the rubber phase.

Glass fibers had a tendency to bridge the tip of a propagating crack, thereby greatly increasing the fracture toughness. In this case the work of fracture comes from a combination of the elastic strain energy stored in the fibers, the energy dissipated in debonding the fibers from the matrix, and the fracture energy of the matrix itself.     

On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate

Elastic–plastic stress analysis has been carried out for the plastic zone size and crack tip opening displacement of a sub-interface crack with small scale yielding. In our study, the shape of plastic zone is assumed as a long, slim strip at both crack tips. In the plastic zone, both normal stress and shear stress exist and are considered due to the bi-material interface. The values of the plastic zone size, normal stress and shear stress are determined by satisfying the conditions where both Modes I and II stress intensity factors vanish and Von Mises yield criterion is met. In the present paper, the sub-interface crack is simulated by continuously distributed dislocations which will result in singular integral equations. Those singular integral equations can be solved by reducing them to a set of linear equations. The values of the plastic zone size and crack tip opening displacement are obtained through an iterative procedure. Finally, the effect of normalized loading, normalized crack depth (distance to the interface) and Dundurs’ parameters on the normalized plastic zone size and the normalized crack tip opening displacement is discussed.     

Elliptically polarized white light photoviscoelastic technique and its application to viscoelastic fracture

The present paper demonstrates the successful application of the photoviscoelastic technique using elliptically polarized white light to the stress field evaluation of the crack growth in a viscoelastic strip. Using the proposed technique, which can determine both isochromatic and isoclinic parameters simultaneously from a single color image, the time-dependent stress state around a slowly propagating crack tip in a viscoelastic strip plate is successfully analyzed. Then, the time-dependent stress intensity factor extended for linearly viscoelastic materials is evaluated from the experimental results using a method based on the least squares. The results show that the proposed critical stress intensity factor for fast crack growth may be considered as a characteristic property of the material under monotonically increasing load.     

Faraday effect in glass fibers

Various types of glass fiber were studied to determine their suitability for transmitting linearly polarized light. Polarization and magnetooptical experiments were performed on index-gradient fibers. These fibers have birefringent properties as a result of mechanical stress created during fabrication. The interaction of double refraction and the Faraday effect in a longitudinal magnetic field is explained theoretically. The rule governing such fibers in industrial magnetic fields is that the Faraday rotation (φ < 5°/cm) per field length is always substantially smaller than the phase difference (δ_s = 57.2°/cm) per fiber length.     

Design of an optical fiber sensor for linear thermal expansion measurement

Design and operation of an optical fiber device for temperature sensing and thermal expansion measurement are reported. The modulated intensity has been measured by using a pair of 450 μm core fiber, one acting as the source and the other one as receiving fiber. In this design, the light intensity modulation is based on the relative motion of the optical fibers and a reflective coated lens. By using displacement calibration data for this sensor, the linear thermal expansion of the aluminum rod is determined. This sensor shows an average sensitivity of about 11.3 mV/°C for temperature detection and 7 μm/°C for thermal expansion detection. Device resolution for a linear expansion measurement is about 3 μm for a dynamic range of 600 μm corresponding to a temperature change of 100°C. The measured linear expansion results are checked against the expected theoretical ones and an agreement within ±2 μm is noticed. The operation of this sensor was also compared with other types and some advantages are observed, which verify the capability of this design for such precise measurements.     

The application of high speed photography and white light speckle to the study of dynamic fracture

A white light speckle technique is combined with high speed photography to study the dynamic fracture of a sample of PMMA. A series of single exposure speckle patterns are photographically recorded at the rate of 2 × 10⁵ frames s^-1 during fracture of the sample. The displacement field around the tip of the propagating crack may then be determined by superimposing pairs of individual frames to form a ‘double-exposure’ speckle pattern. It is shown that the method gives values for the stress intensity factor K which are consistent with those obtained from other techniques.     

Design and operation of a fiber optic sensor for liquid level detection

Design and construction of an optical fiber sensor for liquid level detection are reported. This sensor operates based on light intensity modulation, and such modulation results from alteration of total internal reflection into partial reflection at the interface. The modulated intensity has been measured by using a pair of fibers, one transmitting source light, another acting as receiving fiber, and a glass prism providing the total and partial reflections. During the level measurements, when a liquid in a vessel touches the 45° faces of the 45-90-45° prism, the total internal reflection is disturbed, and the reflected light is modulated. The performance of this sensor is tested with different source lights including a light emitting diode (LED), a diode laser, and a He–Ne laser. Extinction ratio has been measured for different liquids, and compared. This ratio for water using LED source is about 0.03, for diode laser is 0.006 and for He–Ne laser is 0.003. Although this device was tested as a liquid level sensor, but the distinct results obtained for samples with different index of refractions demonstrate that the reported sensor can also be used as a liquid refractometer.     

Adhesive fracture of heterogeneous interfaces

We have studied the effect of interface heterogeneity on fracture, at both local and global scales. The single cantilever beam adhesion test was used to investigate interfacial fracture between polycarbonate plates and an elastic/fragile epoxy adhesive. Two surface treatments were applied to a (given) polycarbonate plate giving zones of strong and weak adhesion parallel to the crack direction. Calculated fracture energies differed from those expected from a simple rule-of-mixtures. A perturbation method, proposed by Rice, was used and results compared with crack fronts observed in situ. The technique was applied successfully but the difference in values of stress intensity factor between the zones was found substantially different from the experimental value. In an attempt to explain discrepancies, specimens with discontinuous crack fronts (adhesive and/or plates severed along the strong/weak adhesion frontier) were tested. Good agreement was found with the rule-of-mixtures predictions raising questions about the role of crack front continuity in load transfer.     

Analysis of composite material interface crack face contact and friction effects using a new node-pairs contact algorithm

A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem(e.g., resistant coating and thermal barrier coatings) subjected to complicated load conditions.To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors(SIFs) and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors K?IIfor the friction coefficient decrease by 16% when f changes from 1 to 0.     

碳纤维布补强梁裂尖奇异性的光学焦散线实验研究

通过光学焦散线方法对碳纤维布加固含裂纹梁进行三点弯荷载下的静荷载和冲击实验,研究了其断裂特性。在静态实验研究中,记录了不同载荷状态下裂纹的焦散斑光学图像,计算了与之对应的裂纹尖端的应力强度因子,分析了试件在粘贴加固不同长度的碳纤维布情况下焦散斑和应力强度因子演化规律。在动态实验中,记录了裂纹扩展的过程和在此过程中不同时刻的焦散斑和裂纹扩展的路线。通过各瞬间的焦散斑图像,分析裂纹的扩展长度及速度,并得到各时刻的动态应力强度因子。     

Interphase characterization in polymer composites - monitoring of interphasial behavior in dependence on the mode of loading

Single fiber model composites consisting of epoxy resin matrix and differently sized glass fibers were investigated using pull-out tests, scanning electron microscopy (SEM), scanning force microscopy (SFM) and single fiber dynamic load test (SFDL). The inhomogeneous stress distribution along the embedded fiber length could be visualized by monitoring. SEM images showed either cohesive fracture or adhesive failure on pulled-out fibers with different sizings. The crack initiation and propagation were detected randomly and multiply distributed as the inhomogeneous interphase itself and depending strongly on the fiber-matrix model combination. The meniscus region acts as a material inhomogeneity and its appearence depends on the surface free energies of fiber and matrix and on the curing conditions of the resin. SFM in force modulation mode has visualized different interphase thicknesses and gradients of local stiffness. The SFDL test has been shown as a worthful tool for the comprehensive determination of fiber-matrix interaction.     

Determination of the interfacial properties between modified soy protein resin and kenaf fiber

The kenaf fiber/soy protein resin interface was characterized. The soy protein isolate (SPI) was modified using a polycarboxylic acid, Phytagel^® (PH), to make an interpenetrating network-like (IPN-like structure) structure of the resin. The effects of different PH contents on the interfacial properties were characterized using single fiber composite (SFC) tests and optical microscopy. Kenaf fiber strength was characterized using tensile tests. Kenaf fibers were extracted from nonwoven mats. The length of each kenaf fiber was extended by gluing it to long polyethylene filaments on both sides. After drying the glue, dog-bone shaped SFC specimens were prepared using pure and modified SPI resins. The dried SFC specimens were taken out from the mold and hot-pressed (cured) at 120°C. The interfacial shear strength (IFSS) was calculated using the shear-lag analysis. Single fiber tensile tests at different gauge lengths were performed. The average stresses were computed by fitting the data to Weibull distribution. These values were used in the calculation of the IFSS. After the SFC tests, the specimens were observed under the optical microscope to characterize the fiber fracture modes and the region around the fiber fracture. The SFC tests showed that the IFSS is a function of the PH content which controls the resin shrinkage. It was also seen that the interfacial failure mode is also a function of the PH content. These finding were confirmed by the microbead tests in which E-glass fibers were used with the modified SPI resins.