Dynamic Photoelasticity Research Articles

Dynamic path selection along branched faults: Experiments involving sub‐Rayleigh and supershear ruptures

Building upon previous laboratory earthquake experiments of dynamic shear rupture growth taking place along faults with simple kinks, new and complex fault geometries involving cohesively held fault branches are studied. Asymmetric impact at the specimen boundaries controls the incoming shear ruptures, which are manipulated to propagate at either sub‐Rayleigh or supershear velocities. High‐speed photography and dynamic photoelasticity are used with a model material, Homalite‐100, to monitor incoming and outgoing rupture propagation, acceleration, deceleration, or arrest at the vicinity of the branch location. Differences and similarities of rupture velocity history between cases involving faults with either simple kinks or branches, on the one hand, and sub‐Rayleigh and supershear incoming ruptures, on the other, are highlighted and explained. Results of the experiments show a clear general bias toward large branch inclination, smaller branch angles appearing to be overshadowed and suppressed by the stress field associated with the main fault. Of great interest, also, is the sustenance of rupture propagation along a branch by the Mach cone, when the initial rupture is supershear driven. Generally, higher rupture speeds favors larger arrays of branching angles to be triggered. A companion analysis by Templeton et al. (2009) featuring detailed numerical simulations of these experiments provides further insight into the observed phenomena.

Experimental validation of large-scale simulations of dynamic fracture along weak planes

A well-controlled and minimal experimental scheme for dynamic fracture along weak planes is specifically designed for the validation of large-scale simulations using cohesive finite elements. The role of the experiments in the integrated approach is two-fold. On the one hand, careful measurements provide accurate boundary conditions and material parameters for a complete setup of the simulations without free parameters. On the other hand, quantitative performance metrics are provided by the experiments, which are compared a posteriori with the results of the simulations. A modified Hopkinson bar setup in association with notch-face loading is used to obtain controlled loading of the fracture specimens. An inverse problem of cohesive zone modeling is performed to obtain accurate mode-I cohesive zone laws from experimentally measured deformation fields. The speckle interferometry technique is employed to obtain the experimentally measured deformation field. Dynamic photoelasticity in conjunction with high-speed photography is used to capture experimental records of crack propagation. The comparison shows that both the experiments and the numerical simulations result in very similar crack initiation times and produce crack tip velocities which differ by less than 6%. The results also confirm that the detailed shape of the non-linear cohesive zone law has no significant influence on the numerical results.

A simple ballistic material model for soda-lime glass

Various open-literature experimental findings pertaining to the ballistic behavior of glass are used to construct a simple, physically based, high strain-rate, high-pressure, large-strain constitutive model for this material. The basic components of the model are constructed in such a way that the model is suitable for direct incorporation into standard commercial transient non-linear dynamics finite-element based software packages like ANSYS/Autodyn [ANSYS/Autodyn version 11.0, User documentation, Century Dynamics Inc. a subsidiary of ANSYS Inc.; 2007.] or ABAQUS/Explicit [ABAQUS version 6.7, User documentation, Dessault systems, 2007.]. To validate the material model, a set of finite element analyses of the Edge-on-Impact (EOI) tests is carried out and the results compared with their experimental counterparts obtained in the recent work of Strassburger et al. [Strassburger E, Patel P, McCauley JW, Kovalchick C, Ramesh KT, Templeton DW. High-speed transmission shadowgraphic and dynamic photoelasticity study of stress wave and impact damage propagation in transparent materials and laminates using the edge-on impact method. In: Proceedings of the twenty-third international symposium on ballistics. Spain: April 2007, and Strassburger E, Patel P, McCauley W, Templeton DW. Visualization of wave propagation and impact damage in a polycrystalline transparent ceramic-AlON. In: Proceedings of the twenty-second international symposium on ballistics. Vancouver, Canada: November 2005.]. Overall, a good agreement is found between the computational and the experimental results pertaining to: (a) the front-shapes and propagation velocities of the longitudinal and transverse waves generated in the target during impact; (b) the front-shapes and propagation velocities of the “ coherent-damage” zone (a zone surrounding the projectile/target contact surface which consists of numerous micron- and sub-micron-size cracks); and (c) the formation of “ crack centers”, i.e. isolated cracks nucleated ahead of the advancing coherent-damage zone front. Relatively minor discrepancies between the computational and the experimental results are attributed to the effects of damage-promoting target-fixturing induced stresses and cutting/grinding-induced flaws located along the narrow faces of the target and the surrounding regions.

Analysis of Geometric Effects on Stress Wave Propagation in Epoxy Resins of Plate-Like Structure by Dynamic Photoelasticity Combined with Strain Gauge

Experimental studies have been conducted using the dynamic photoelastic technique combined with a strain gauge to investigate geometric effects on stress wave propagation in axially impacted epoxy resins of plate-like structure. Dynamic photoelasticity provides a means of visualizing the stress wave field inside a solid. A device that triggers the generation of stress waves by direct projectile impact is used to conduct high-speed photoelasticity and strain gauge measurements. This triggering is achieved by an electrical connection between projectile and sample. The geometric effects of the width-to-wavelength ratio on the propagation speed and attenuation coefficient of stress waves were analyzed for isotropic rectangular rods of different width-to-thickness ratios, the thickness being the same in each case. The experimental results for stress wave speed as a function of width-to-wavelength ratio are in reasonable agreement with theoretical predictions based on a modified Love's equation involving the geometric effects due to lateral inertia.

Interaction of dynamic mode-I cracks with inclined interfaces

In this paper, we report on an experimental study of the deflection/penetration behavior of dynamic mode-I cracks propagating at two different crack velocities (slower and faster) toward inclined weak interfaces of three dissimilar angles ( α): 30°, 45° and 60°. A simple wedge-loading specimen configuration as proposed by Xu et al. [Xu LR, Huang YY, Rosakis AJ. Dynamic crack deflection and penetration at interface in homogenous materials: experimental studies and model predictions. J Mech Phys Solids 2003;51:461–86], made of brittle Homalite-100, is used. A modified Hopkinson bar setup is used to achieve well-controlled impact loading conditions. Dynamic photoelasticity in conjunction with high-speed photography is used to capture real-time isochromatics associated with deflected/penetrated cracks.

Self-Healing Pulse-Like Shear Ruptures in the Laboratory

Models predict that dynamic shear ruptures during earthquake faulting occur as either sliding cracks, where a large section of the interface slides behind a fast-moving rupture front, or self-healing slip pulses, where the fault relocks shortly behind the rupture front. We report experimental visualizations of crack-like, pulse-like, and mixed rupture modes propagating along frictionally held, "incoherent" interfaces separating identical solids, and we describe the conditions under which those modes develop. A combination of simultaneously performed measurements via dynamic photoelasticity and laser interferometry reveals the rupture mode type, the exact point of rupture initiation, the sliding velocity history, and the rupture propagation speed.

Observing ideal “self-similar” crack growth in experiments

We here report on a detailed experimental study whose goal is to investigate spontaneous crack propagation in bonded and intact materials subjected to quasi-static far-field tensile loading. The cracks nucleate from a tiny circular hole and are triggered by an exploding wire. They subsequently propagate under the action of a constant far-field load. Dynamic photoelasticity in conjunction with high speed photography is used to capture the real-time photoelastic fringe patterns (isochromatics) associated with crack propagation. Dynamic stress intensity factors of propagating cracks are determined and the results are successfully compared with Broberg’s classical model of self-similar mode-I crack growth.

Sliding along frictionally held incoherent interfaces in homogeneous systems subjected to dynamic shear loading: a photoelastic study

An experimental investigation was conducted to study dynamic sliding at high strain rates along incoherent (frictional) interfaces between two identical plates. The plates were held together by a uniform compressive stress, while dynamic sliding was initiated by an impact-induced shear loading. The case of freely-standing plates with no external pressure was also investigated. The dynamic stress fields that developed during the events were recorded in a microsecond time scale by high-speed photography in conjunction with classical dynamic photoelasticity. Depending on the choice of experimental parameters (impact speed and superimposed static pressure), pulse-like and crack-like sliding modes were observed. Visual evidence of sub-Rayleigh, intersonic and even supersonically propagating pulses were discovered and recorded. Unlike classical shear cracks in coherent interfaces of finite strength, sliding areas in frictional interfaces seem to grow at various discrete speeds without noticeable acceleration phases. A relatively broad loading wave caused by the interference between the impact wave and the preexisting static stress field was observed emanating from the interface. There was a cusp in the stress contours at the interface, indicating that the propagation speed was slightly faster along the interface than in the bulk. The observed propagation speeds of the sliding tips were dependent on the projectile speed. They spanned almost the whole interval from sub-Rayleigh speeds to nearly the sonic speed of the material, with the exception of a forbidden gap between the Rayleigh wave speed and the shear wave speed. Supersonic trailing pulses generating Mach lines of different inclination angles, emanating from the sliding zone tips, were discovered. In addition, behind the sliding tip, wrinkle-like opening pulses were observed for a wide range of impact speeds and confining stresses. They always traveled at speeds between the Rayleigh wave speed and the shear wave speed of the material.

Dynamic sliding of frictionally held bimaterial interfaces subjected to impact shear loading

The fast frictional sliding along an incoherent interface of a bimaterial system composed of a Homalite and a steel plate is studied experimentally in a microsecond time-scale. The plates are held together by a static uniform compressive pre-stress while dynamic sliding is initiated by asymmetric impact. The full-field technique of dynamic photoelasticity is simultaneously used with a local technique of velocimetry based on laser interferometry. In the case where the impact loading is applied to the Homalite plate, a shear Mach line originates from a disturbance propagating along the interface supersonically with respect to the dilatational wave speed of Homalite and it crosses the P-wave front. The sliding starts well behind the P-wave front in Homalite and it propagates with a supershear speed with respect to Homalite. A fast interface wave and a wrinkle-like opening pulse (detachment wave) travelling along the interface are observed. When the impact loading is applied to the steel plate, the local sliding velocity measurement reveals that sliding initiates with the arrival of the P-wave front in the steel plate.

Spontaneous Mixed-Mode Fracture in Bonded Similar and Dissimilar Materials

In this paper, we report on an experimental study of spontaneous, mixed-mode, crack propagation in weakly bonded similar and dissimilar materials. A unique experimental configuration is proposed to induce spontaneous crack growth events along the interfaces. The cracks nucleate from tiny circular holes and are triggered by an exploding wire. They subsequently propagate under the action of a constant, far-field load. Dynamic photoelasticity in conjunction with high speed photography is used to capture the real-time isochromatics associated with crack propagation. In the case of identical materials, crack propagation is anti-symmetric with respect to the crack nucleation point while strong asymmetry is observed for the case of dissimilar materials. In both cases, cracks propagate at constant velocity from the initiation point. The time histories of dynamic stress intensity factors and of energy release rates of the propagating cracks along the bonded similar materials are also reported.

Particle Velocimetry and Photoelasticity Applied to the Study of Dynamic Sliding Along Frictionally-Held Bimaterial Interfaces: Techniques and Feasibility

A laser interferometry-based technique was developed to locally measure the in-plane components of particle velocity in dynamic experiments. This technique was applied in the experimental investigation of dynamic sliding along the incoherent (frictional) interface of a Homalite–steel bimaterial structure. The bimaterial specimen was subjected to uniform compressive stress and impact-induced shear loading. The evolution of the dynamic stress field was recorded by high-speed photography in conjunction with dynamic photoelasticity. The combination of the full-field technique of photoelasticity with the local technique of velocimetry was proven to be a very powerful tool in the investigation of dynamic sliding. A relatively broad loading wave with an eye-like structure emanated from the interface. The particle velocity measurements established that sliding started behind the eye-like fringe pattern. It propagated with supershear speed with respect to Homalite. A shear Mach line originating from the sliding tip is visible in the photoelastic images. A vertical particle velocity measurement revealed the existence of a wrinkle-like pulse traveling along the bimaterial interface. The wrinkle-like pulse followed the initial shear rupture tip and propagated at a specific subshear speed.

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K ID ) and crack-tip velocity ( $${\mathop a\limits^ \cdot }$$ ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar $${\mathop a\limits^ \cdot }$$ -K ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.

Dynamic photoelastic study of wave fields in elastic plates with stress concentrators

The method of dynamic photoelasticity is used to study the dynamic failure of structural members in the form of plates with a curvilinear (circular or elliptic) hole and an isolated crack under impulsive loading. The time-dependences of the stress intensity factors and the crack tip velocity are investigated for two types of models

Impact Damage Visualization of Heterogeneous Two-layer Materials Subjected to Low-speed Impact

A systematic experimental investigation of the generation and subsequent evolution of impact damage in heterogeneous two-layer materials is presented. Model layered specimens involving a compliant polymer layer bonded with a metal layer were designed and subjected to impact loading to simulate failure mechanisms in real time. High-speed photography and dynamic photoelasticity were utilized to visualize the nature and sequence of dynamic failure modes. A series of complex failure modes was documented. Interlayer crack growth (interfacial delamination) is the dominant dynamic failure mode. These cracks appear to be shear dominated and might proceed with intersonic speeds. Intralayer cracking always occurs in a local Mode I crack inside the weak layer. Both impact speed and interfacial bonding strength have significant influence on the impact failure. High-impact loading leads to high interlayer crack speeds. Specimens featuring ductile and weak bonds subjected to high-impact speeds are shown to feature intersonic cracks with clearly visible shear shock wave (Mach lines) emitted from the crack tips.

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

The dynamic fracture behavior of polyester/TiO2 nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,KI and the crack tip velocity,a, has been established. Dynamic photoelasticity coupled with high-speed photography has been used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.

Dynamic damage growth in particle reinforced graded materials

A scheme for preparing materials with continuous-graded properties using polyester resin and cenospheres is presented. The elastic and fracture property profiles of these materials are characterized and the results are discussed. Crack-tip stress, strain and displacement fields for a transient crack propagating along the direction of property gradation in functionally graded materials are obtained through an asymptotic analysis coupled with a displacement potential approach. The influence of the transient nature of crack-tip on contours of constant maximum shear stress, constant first stress invariant and constant in-plane displacements is discussed. Results of initial experimental investigations carried out using dynamic photoelasticity in conjunction with high-speed photography to characterize the behavior of a propagating crack in functionally graded materials are presented.

Dynamic damage growth in particle reinforced graded materials

A scheme for preparing materials with continuous-graded properties using polyester resin and cenospheres is presented. The elastic and fracture property profiles of these materials are characterized and the results are discussed. Crack-tip stress, strain and displacement fields for a transient crack propagating along the direction of property gradation in functionally graded materials are obtained through an asymptotic analysis coupled with a displacement potential approach. The influence of the transient nature of crack-tip on contours of constant maximum shear stress, constant first stress invariant and constant in-plane displacements is discussed. Results of initial experimental investigations carried out using dynamic photoelasticity in conjunction with high-speed photography to characterize the behavior of a propagating crack in functionally graded materials are presented.

A novel instrument for transient photoelasticity

A new instrument has been developed for the photoelastic analysis of transient events. The instrument is based on the Phase-Stepped Images Obtained Simultaneously (PSIOS) system developed by Patterson and Wang, which enables four phase-stepped photoelastic images to be collected simultaneously. Where the new instrument differs is that the original instrument requires four cameras to collect the four images, whereas the new instrument requires only one camera. This makes the use of phase-stepping viable for events, in which the fringe order varies with time. Three examples are given of the use of the instrument in static and dynamic photoelasticity to generate full field maps of isochromatic fringes. The instrument has been found to work well and significantly increases the potential for the use of photoelasticity to study transient and possibly dynamic events.

Dynamic crack deflection and penetration at interfaces in homogeneous materials: experimental studies and model predictions

We examine the deflection/penetration behavior of dynamic mode-I cracks propagating at various speeds towards inclined weak planes/interfaces of various strengths in otherwise homogeneous isotropic plates. A dynamic wedge-loading mechanism is used to control the incoming crack speeds, and high-speed photography and dynamic photoelasticity are used to observe, in real-time, the failure mode transition mechanism at the interfaces. Simple dynamic fracture mechanics concepts used in conjunction with a postulated energy criterion are applied to examine the crack deflection/penetration behavior and, for the case of interfacial deflection, to predict the crack tip speed of the deflected crack. It is found that if the interfacial angle and strength are such as to trap an incident dynamic mode-I crack within the interface, a failure mode transition occurs. This transition is characterized by a distinct, observable and predicted speed jump as well as a dramatic crack speed increase as the crack transitions from a purely mode-I crack to an unstable mixed-mode interfacial crack.

Dynamic crack growth along a polymer composite–Homalite interface

Dynamic crack growth along the interface of a fiber-reinforced polymer composite–Homalite bimaterial subjected to impact shear loading is investigated experimentally and numerically. In the experiments, the polymer composite–Homalite specimens are impacted with a projectile causing shear dominated interfacial cracks to initiate and subsequently grow along the interface at speeds faster than the shear wave speed of Homalite. Crack growth is observed using dynamic photoelasticity in conjunction with high-speed photography. The calculations are carried out for a plane stress model of the experimental configuration and are based on a cohesive surface formulation that allows crack growth, when it occurs, to emerge as a natural outcome of the deformation history. The effect of impact velocity and loading rate is explored numerically. The experiments and calculations are consistent in identifying discrete crack speed regimes within which crack growth at sustained crack speeds is possible. We present the first conclusive experimental evidence of interfacial crack speeds faster than any characteristic elastic wave speed of the more compliant material. The occurrence of this crack speed was predicted numerically and the calculations were used to design the experiments. In addition, the first experimental observation of a mother–daughter crack mechanism allowing a subsonic crack to evolve into an intersonic crack is documented. The calculations exhibit all the crack growth regimes seen in the experiments and, in addition, predict a regime with a pulse-like traction distribution along the bond line.