Dynamic Photoelasticity Research Articles

On the diversity of fracture behavior in a brittle solid with sets of preexisting small-scale cracks

Understanding the multiscale fracture behavior of brittle materials is of crucial importance not only in engineering applications but also in seismology where an earthquake source, usually assumed as one single, relatively large fracture region but in reality composed of relatively smaller multiple fractures, behaves mechanically in diverse ways, emit waves with different characters and may cause a single seismic event or even a cluster of earthquakes and earthquake swarms. For understanding the complex fracture processes, by employing the experimental technique of dynamic photoelasticity with high-speed video cameras, we have been simultaneously observing global, large-scale material behavior and local, smaller-scale evolution of waves and fractures in two-dimensional linear elastic brittle polycarbonate specimens. Each specimen has sets of preexisting small-scale parallel cracks prepared by a digital laser cutter and modeling large-scale geological fault planes, and it is subjected to external (quasi-)static and impact loads. Here we show some recent examples of the diverse fracture behavior observed in brittle birefringent solid specimens under tensile/compressive external loading. The fracture behavior is considerably dependent on the loading conditions, and developing fractures do not always break the specimen in an “unzipping” way, i.e. the specimen is not always divided along a perforation line consisting of small-scale cracks. Rather, the diverse fractures can easily jump to remote places, propagate back-and-forth or reversely move in the opposite direction compared with the initial one. Our findings may play a role in comprehending the generation mechanism of a cluster of fractures in brittle solids in general.

Study of the interaction mechanism of oppositely propagating cracks by dynamic photoelasticity and numerical simulation

The interaction mechanism of oppositely propagating cracks is an important basis for the study of rock fracture under dynamic loading. In this article, the stress field superposition and crack tip stress evolution are deeply investigated during the interaction of oppositely propagating cracks by using dynamic photoelastic experiment method and numerical simulation analysis. Obtained results indicate that the cracks interaction process is accompanied by the deflection of the crack, and the deflection of the cracks is mainly affected by the shear stress field at the crack tip. According to the difference of the crack deflection characteristics, the interaction process of the oppositely propagating cracks can be divided into two stages. The Stage I: the non-interlaced stage and Stage II: the interaction stage after the mutual staggered. It includes the period of Stage I that the oppositely propagating cracks are not interlaced with each other; the Stage II is the interaction period after the oppositely propagating cracks are interlaced with each other. The effects of stress intensity factor K I, stress intensity factor K II and far-field T stress on crack propagation process should be comprehensively considered when predicting the crack growth trajectory. The interaction of the stress field between cracks is the main factor determining the crack propagation trajectory. In addition, the vertical spacing between cracks also has a significant effect on the fracture behavior of oppositely propagating cracks. When the vertical distance between the two cracks is large, the local stress fields at the crack tip cannot overlap and interfere with each other, and the oppositely propagating cracks will expand independently of each other.

Investigation of constantly and transiently propagating cracks in functionally graded materials by dynamic photoelasticity

Investigation of constantly and transiently propagating cracks in functionally graded materials by dynamic photoelasticity

The effect of confinement and material heterogeneities on the dynamics of a granular medium subjected to impact loading

Compared with the mechanics of continua that has been established well, the mechanical characteristics of granular particles, in particular, the dynamic ones, have not been thoroughly clarified yet. Therefore, in our previous preliminary study, dynamic stress transfer as well as wave and fracture development in granular media has been recorded using the experimental technique of dynamic photoelasticity in conjunction with high-speed cinematography. Penny-shaped particles have been prepared by a digital laser cutter and piled on a rigid horizontal plane to form a model slope with some inclination angle. The two-dimensional slope has been subjected to dynamic impact on its top free surface. From the experimentally recorded particle motion and transient stress evolution, two dissimilar failure patterns have been identified. One is the complete collapse of the slope or mass flow due to unidirectional force-chain-like stress transfer, and the other one is the toppling-type separation of the slope face caused by broadly expanding two-dimensional waves. Whichever occurs seems to be governed by the temporal profile of the energy given by the impact. Here, in order to investigate the effect of confinement and possibly material heterogeneities on granular dynamics, first, experimentally, solid plates are additionally placed on some boundaries of the model slopes. It is found that stress transfer and dynamic motion in the confined granular medium is largely controlled by the additional solid boundaries. Then, in order to numerically confirm the above experimental observations, the open source code ESyS-Particle is employed. The numerical results compare well with the experimental ones if the parameters required for the numerics are carefully and properly selected.

Global and local fracture behavior in a brittle solid with a set of pre-existing small-scale cracks

For understanding the mechanics of complicated seismic activities, not only global observations of large-scale material behavior but also more local tracing of smaller-scale fractures is needed. In this study, therefore, by using the technique of dynamic photoelasticity, the evolution of fractures and waves is experimentally traced in a two-dimensional linear elastic brittle specimen that has a set of pre-existing small-scale parallel fracture regions. The small-scale fracture regions or cracks, modeling a large-scale geological normal fault plane, are prepared by a digital laser cutter. Our experimental observations with a high-speed video camera, together with finite difference numerical simulations, indicate that the global and local fracture behavior significantly depends on the initial inclination angle and distribution pattern of the set of parallel cracks. In the case of pre-existing cracks that are more vertically inclined with respect to the quasi-static external load applied by a tensile testing machine, the main fracture develops dynamically and then the secondary fractures appear at spatiotemporally remote distances from the main fracture. The secondary fractures extend also dynamically, into the direction opposite to the main fracture. On the other hand, in the case of smaller inclination angles, the main fracture tends to evolve quasi-statically. Nevertheless, in both cases, it is found that fracture can be arrested and jump without difficulties in a brittle solid having a number of small-scale cracks, which implies that such small-scale cracks may play an important part in the generation of a cluster of seismic events.

Dynamics of dip-slip fault rupture

This contribution summarizes our recent findings related to the dynamics of shallow dip-slip earthquakes, especially that of the asymmetric seismic motion in hanging walls and footwalls. First, by means of experimental dynamic photoelasticity and numerical finite difference simulations, dynamic rupture of a relatively large fault plane near a free surface is studied. It is found, for instance, that upon surfacing of the primary upward fault rupture, Rayleigh surface waves traveling outwards to the far-field and Rayleigh-type interface waves moving downwards back to the source can be induced. For an inclined fault plane, these Rayleigh and interface waves can interact with each other in the hanging wall to produce a “corner” shear wave with concentrated energy and thus the asymmetric seismic motion. Then, instead of considering only one single large-scale fault plane, more geometrically complex dip-slip faults that consist of damage zones with sets of smaller-scale parallel cracks are examined. The photoelastic study shows that depending on the dip angle, the rupture behavior may differ considerably. For a larger dip angle, secondary and further downward ruptures can be initiated, arrested and resume dynamic movement even without additional external load, seemingly due to the dynamic waves caused by the primary upward rupture.

Experimental study on the interaction between oblique incident blast stress wave and static crack by dynamic photoelasticity

In this paper, the interaction between the oblique incident blast stress wave and the prefabricated crack is studied using the dynamic photoelastic method and numerical simulation method. First, blast loading dynamic photoelastic experiment system is established. Second, blast stress wave and crack interaction experiments are carried out. Epoxy resin plate is used as specimen material, while lead azide explosive is used to apply blasting load. In the experiment, the evolution of stress field at crack wall and crack tip are observed by a high-speed camera. The experimental results show that incident angle of blast stress wave has a great influence on the way the stress wave interacts with the crack and the field at the crack tip. Finally, based on the experimental results, two numerical models are conducted using FEM software. The numerical results of stress field are in good agreement with photoelastic experiment, which verifies the experimental analysis.

Investigation of the effect of the blast waves on the opposite propagating crack

The stress waves have a significant effect on crack propagation during blasting. In this paper, a microsecond controlled blasting case involved with the interactions between blast waves and an opposite propagating crack is studied using dynamic photoelasticity method. The results show that the stress waves influence the local stress field of dynamic crack tip , and alter the crack propagation behavior. Moreover, during crack-wave interactions, both the singular stresses and the nonsingular stresses around the crack tip changed apparently. With the incidence of dilatational wave , the non-singular stresses σ ox and σ oy around the tip of opposite propagating crack increase remarkably, inducing an increase in the crack extension resistance, and decreasing both the crack velocity and the dynamic stress intensity factor K I d . Whereas, when the shear wave impinges onto the opposite propagating crack, the crack tends to increase the crack velocity. In addition, the fractal dimension of the crack velocity decreases during the incidence of dilatational wave, and increases when the shear wave impinges upon the opposite propagating crack.

Physical modeling of fluid-filled fractures using the dynamic photoelasticity technique

We have developed an optical apparatus based on the dynamic photoelasticity technique to visualize and analyze the propagation of the Krauklis wave within an analog fluid-filled fracture. Although dynamic photoelasticity has been used by others to study seismic wave propagation, this study adds a quantitative analysis addressing dispersion properties. We physically modeled a fluid-filled fracture using transparent photoelastic-sensitive polycarbonate and nonsensitive acrylic plates. Then we used a pixel-based framework to analyze the dispersion of a Krauklis wave excited in the fracture. Through this pixel-based framework, we thus demonstrate that the dynamic photoelasticity technique can quantitatively describe seismic wave propagation with a quality similar to experiments using conventional transducers (receivers) while additionally visualizing the seismic stress field. We observe that an increase in the fluid viscosity results in a decrease in the velocity of the Krauklis wave. We also determine the capability of the method to analyze seismic data in the case of complex geometry by modeling a sawtooth fracture. The fracture’s geometry can strongly affect the characteristics of the Krauklis wave as we note a higher Krauklis wave velocity for the sawtooth case, as well as greater perturbation of the stress field.

Quantification of photoelastic fringe orders using polarized light camera and continuous loading

Quantification of fringe orders is important in visualizing full-field stress in digital photoelasticity. Various methods have been developed to improve the calculated accuracy of fringe orders, such as the phase shifting, carrier, and RGB methods. However, in these methods, fringe orders are calculated using the photoelastic patterns under a certain load but not the patterns in the whole time series; this impedes quantification of the fringe orders in dynamic photoelasticity. In this study, a polarized light camera was employed to simultaneously capture the photoelastic patterns of the dark and bright fields under circular polariscope. Based on the light intensity difference of these patterns in the entire loading process, a method of quantifying fringe orders is proposed. Full-field fringe orders in a disk fabricated by 3D printer and subjected to three compressive loads were calculated using this method. Its good accuracy, improved by removing the background light and choosing a suitable capture frame rate, was verified by comparing the fringe orders calculated by the traditional and proposed methods. Furthermore, the determination of the full-field fringe orders in complex structures indicated that the complexity of tested models had no influence on the calculated accuracy.

LDV-based measurement of 2D dynamic stress fields in transparent solids

Laser Doppler Vibrometer (LDV) has been performed as a tool to observe stress fields of ultrasound longitudinal wave inside transparent solids due to its high sensitivity and intuitiveness. Besides, this method is only sensitive to dynamic stress and has no response to static stress, so it has the advantage of not being affected by residual stress in transparent solids. However, this method has limitations. LDV cannot directly detect shear wave, and for longitudinal wave, it can only obtain an approximate value of normal stress. In this paper, we analyze the limitations, and achieve observing shear wave by adding a rotatable linear polarizer to the optical system. Furthermore, the complete photo-elastic tensor can be obtained from the process of measuring longitudinal wave, and then the absolute 2D dynamic stress fields can be calculated. To check the applicability of our method, we compared LDV with the results of numerical analysis and dynamic photoelasticity, respectively.

Measurement method by inferring the thrust from the stress of the cantilever beam based on the photoelasticity theory.

A new, to the best of our knowledge, thrust measurement system based on the photoelasticity theory has been developed to infer the thrust from the stress of the cantilever beam. In this method, the cantilever beam is employed as the loading element to convert the low thrust into high stress, and the modified dynamic photoelasticity is used to infer the stress value of the cantilever beam from the Stokes parameters of the emergent light. The experimental results validated that the thrust stand could measure the thrust in the range of millinewton or millisecond, and the thickness of the beam was negatively correlated with the measurement accuracy. The average errors of the experimental measurements for ampere forces were higher than 25 mN and the pulse ampere forces whose widths were longer than 45 ms were less than ${\pm 5}\% .$±5%. As for the real plasma discharges, the errors of the measured thrust were less than ${\pm 10}\% $±10%.

Investigation of the Fracture of an Orthotropic Plate with Circular Hole and Two Edge Cracks Under Pulsed Loading by the Method of Dynamic Photoelasticity

By the method of dynamic photoelasticity, we study the dynamic fracture of structural elements in the form of plates made of transparent composites and weakened by a hole and two contour symmetric cracks under pulsed loading. The time dependences of the stress intensity factors and the rate of crack-tip propagation are analyzed.

One Micro-thrust Measurement Method Based on the Dynamic Photoelastic Theory

A new method is adopted to measure the micro-thrust of the plasma thruster. In this method, the dynamic photoelastic theory is used to record the stress loaded on the special structure. This technique is called dynamic photoelasticity method. The photoelastic element is the core of the whole system as it can transform the thrust changes into the variation of fringe images. The variation of thrust can be recorded by a CCD camera and then the thrust changes in real-time could be obtained, which is helpful for developing a higher precision propulsion system. This method built in this paper is not only non-contact and non-destructive but also easy to operate with simple structure and high precision.

Dynamic fracture and wave propagation in a granular medium: A photoelastic study

In our earlier work on the generation mechanisms of earthquakes and related failures, fracture phenomena were treated in the framework of continuum mechanics, and the existence of the universal critical condition for earthquake nucleation as well as the strong dependence of earthquake-induced structural failure patterns on the frequencies and types of incident seismic waves was pointed out. However, other significant seismic phenomena such as landslides and liquefaction may not be simply explained using the theories established for continuum media. For example, in order to clarify the physics of the formation of the geological flame structure, possibly due to liquefaction and ensuing gravitational instability in water-immersed sediments, the mechanical behavior of particles under dynamic load and the influence of waves, if any, on fracture should be understood for granular media beforehand. Here, as an initial investigation into wave and fracture propagation inside granular media, under dry conditions first of all, experimental technique of dynamic photoelasticity is employed. Penny-shaped particles made of birefringent polycarbonate are prepared and placed on a rigid horizontal plane to form two-dimensional model slopes with certain inclination angles. Dynamic impact is given to the top (approximately) horizontal free surface of the slope, and the transient evolution of stress and fracture is recorded by a high-speed digital video camera. It is shown that depending on the profile of energy imparted by the impact, (i) one-dimensional force-chain-like stress transfer or (ii) widely spread multi-dimensional wave propagation can be found. While the case (i) results in mass flow, i.e. total collapse of the slope, in (ii) waves can induce dynamic separation of only slope faces similar to toppling failure. The experimentally observed wave and fracture phenomena in granular media are compared to those in continuum media and the actual slope failure repeatedly caused in Japan, New Zealand and USA.

Dynamic Fracture of Layered Plates Subjected to In-Plane Bending

Layered structures typically used in applications such as windshields, thermal protection systems, heavy armor, etc., have property jumps at the layer interfaces. Present study focuses on understanding crack initiation and propagation in such systems under dynamic loading particularly when the property jumps are across the crack front. Layered plates were fabricated by joining polymethylmethacrylate (PMMA) and epoxy sheets using an epoxy-based adhesive (Araldite). Single-edge notched (SEN) specimens were subjected to dynamic loading using a modified Hopkinson bar setup. High-speed imaging coupled with dynamic photoelasticity was used to record the crack-tip isochromatic fringes from which the stress intensity factor (SIF) history was obtained. In selected experiments, a pair of strain gages installed on surfaces of specimen was used to record the strain history in the layers, from which the SIF in each layer was obtained. The results indicated that, prior to crack extension, the strain in both layers was identical. The crack tips in the layers start extending at different time instants with the one in the relatively brittle epoxy layer extending first followed by the one in the PMMA layer. At low impact velocity, the delay obtained was significantly higher than that at high impact velocity. The speed of epoxy crack was lower initially due to the bridging of the crack by the uncracked portion of the PMMA layer till initiation of the crack in the PMMA layer. This effect reduced at higher impact velocity for which the delay was much lower and the cracks propagated at a higher-speed.

Dynamic dip-slip fault rupture in a layered geological medium: Broken symmetry of seismic motion

As recorded recently on 22 November 2014 during the Nagano-ken Hokubu (Kamishiro Fault), Japan, earthquake, one important observation in dynamic rupture (fracture) related to a shallow dip-slip earthquake (usually assumed as mode-II shear crack propagation from depth towards a free surface) is the broken symmetry of seismic motion in the vicinity of the fracturing fault plane. Generally, the strong motion (particle motion) on the hanging wall is much larger than that on the footwall, but the physical mechanisms causing this asymmetry have not been fully clarified yet. Here, utilising the techniques of finite difference calculations and dynamic photoelasticity in conjunction with high speed cinematography, we investigate the fracture dynamics of a dip-slip fault plane situated near a free surface and try to explain the mechanics behind the asymmetry, numerically as well as experimentally. In our two-dimensional crack-like rupture models, we prepare a flat fault plane, which dips either vertically or at an angle, in a monolithic (scenario (1)) or layered (scenario (2)) linear elastic medium (representing rocks). In the basic scenario (1), when the primary fault rupture initiated at some depth approaches the free surface, four Rayleigh-type waves may be induced: two of them propagate along the free surface as Rayleigh surface waves into the opposite directions to the far field, and the other two travel back downwards along the fractured fault plane as interface waves into depth. If the fault plane is inclined, in the hanging wall, the interface and Rayleigh waves may interact with each other and a shear wave carrying concentrated energy (corner wave) can be produced to cause stronger disturbances. The corner waves, generated by primary fault rupture, may exist only when the fault plane is inclined, i.e. only when the geometry considered is asymmetric. In the scenario (2), however, we indicate that (anti-)symmetry of mode-II seismic motion can be easily broken even in geometrically symmetric models if the secondary fracture is allowed at an interface between layers. If primary vertical dip-slip fault rupture in an (anti-)symmetric model moves from depth and interacts with a horizontal interface that follows, for example, a tensile fracture criterion, basically only the interface segments where the primary rupture induces dynamic tension (in the relatively subsiding footwall) may be fractured and the segments in compression (in the rising hanging wall) may remain unbroken. In this case, in the hanging wall, the dynamic stresses in the upper layer above the interface become relatively large because the compressive parts of the primary rupture-induced wave (rupture front wave) can propagate from the lower layer across the still bonded interface into the upper layer, with less reflection back to the lower one. On the contrary, in the footwall, much of the energy carried by the rupture front wave in the lower layer is reflected at the broken interface and dynamic disturbances in the upper layer tend to become smaller. Thus, the strong motion on the hanging wall is expected to become larger than that on the footwall not only in geometrically asymmetric cases but also in symmetric ones.

Stress Wave Truncation Experimental Research Based on Dynamic Photoelasticity

How to truncate stress wave is an important problem that must be considered in design of engineering structure. As an effective detection method of stress distribution, the dynamic photoelasticity has been wide used in stress analysis, such as detection of mechanical structure, civil engineering and water conservancy etc. In this paper, the stress wave isochromatic fringe at different interface structure has been obtained through vertical shooting experiment. The structural stress wave propagation rule of three kinds of case is studied by comparison fringe pattern. The experimental research results show that the stress wave propagation can be effectively guided to a fixed direction through installed connecting parts in structural connection position and the method can avoid integrity damage of structure caused by local large stress changes. Finally, the dynamic photoelasticity is an intuitive and effective way to study stress wave truncation problem.

Investigation of Dynamic Photoelasticity Based on a Three-Dimensional Model

Dynamic photoelasticity has been widely utilized to investigate the phenomena generated by impact loading. The dynamic parameters of structures, such as propagation of stress wave and stress concentration, are obtained through this method, which provide guidelines for structure design and optimization. In the previous studies, two-dimensional models are wildly used by researchers. In these models, the inaccuracy of the boundary conditions leads to error amplification during the conversion of the tested results into real ones. In this study of dynamic photoelasticity, three-dimensional models are used. An improved digital dynamic photoelastic system is also adopted to calculate elastic wave propagation in the medium, where the diode-pumped solid-state green laser and high-speed CCD are used as light source luminaries and recording system respectively. Based on these models, where the boundary conditions approach to true value, the resulting data are higher in resolution than is possible with other experimental techniques. This method has been adopted and tested successfully by generating better results with less amplification of errors.

Solution of nonstationary problems in the mechanics of anisotropic bodies by the method of dynamic photoelasticity

The results obtained in developing and applying the method of dynamic photoelasticity to two-dimensional problems in the mechanics of anisotropic bodies are reviewed. The theory behind the method and its engineering implementation are described. The capabilities of the method are illustrated by solving specific nonstationary problems: dynamic stress concentration, diffraction of longitudinal and transverse waves by free and reinforced holes, dynamic fracture of orthotropic plates with holes and cracks under impulsive and explosive loads