Research On Dynamic Crack Propagation In Brittle Materials

In this dissertation, systematic research was conducted on the problem of dynamic crackpropagations in brittle materials. Experimental studies, model analyses, and numericalsimulations were used to investigate the behaviors of a fast crack propagating at high speed in abrittle plate. The main research work and results are summarized below:1) To study the propagating behavior of a dynamic crack in brittle materials, anexperimental technique was developed that measures the velocity of a fast crack in a preloadedbrittle strip. The specimen is a rectangular PMMA plate clamped by two heavy steel fixturesthat are attached to a MTS test machine. After the specimen was tensile loaded to a prescribedload level, a sharp crack was initiated at the middle point on one side of the specimen. Due tothe brittleness of the material, the crack propagates fast across the specimen. The propagationvelocity of the crack was measured by using the equally spaced conductive lines that werepainted on the specimen surface before the experiment. The experimental results show that foreach preloaded strip, the crack arrives at a steady velocityv0after a short acceleration stage.The steady velocity of the crack,v0was found to be an increasing function of the energyGcstored in the preloaded strip. This represents a velocity-toughening effect of the PMMA material.2) With the increase of the applied loading and accordingly, the increase of the averagecrack velocityv0, the instantaneous crack speed oscillations was found to occur. For the case ofv0340m/s, the instantaneous crack speed is almost constant, for casesv0340~540m/s,the fluctuations of crack speed fall within the level of5010m/s, for the casesv0exceeds540m/s, the instantaneous crack fluctuations can be as large as200m/s To quantitativelyevaluate the crack speed oscillations, we define a parameter k, which is the root mean square(RMS) of crack speed deviations: k v v0vi2i i，where viis the crack speed ateach measurement point in the self-similar crack propagation stage. It was found that thisaverage relative crack speed fluctuations k stays at a constant level of around3.5%for the low crack speed cases, but increases significantly after the mean crack speed v0exceeds a thresholdspeed of about540m/s, and can be as high as7~8%. The observed sudden increase of crackspeed fluctuations cannot be attributed to simple experimental errors (since the experimentalerror is about3.5%), nor can it be attributed to the high level of crack propagation speed (sincethe relative deviation is measured). This confirmed that the observed crack speed oscillations isa genuine physical phenomenon.3) The phenomenon of crack speed oscillations in the very fast propagating stage isrelated to the microscopic cracking mechanisms, which occurs in the process zone at thepropagating crack tip. This complicated mechanism resulted in the fracture energy notexclusively dependent on the crack speed, but may also dependent on crack accelerations.Based on the energy conservation theory, a dynamic model describing the motion of the crackpropagations is established. The derived equation of the motion is used to explain the behaviorof the crack speed oscillations during propagations.4）The phenomena of crack curving, branching, and subsequently branching wereobserved. These crack path instabilities were related to the level of crack speed. The conditionsfor different types of crack path instablities were proposed.5）A rate-dependent cohesive fracture model is developed and implemented into theconmercial software ABAQUS explicit analysis modulus. The software is then used to simulatefast crack propagation problem. The numerical simulations provide results that fundamentallyagree with the experimental results.6）The experimental research on the crack propagations in preloaded tapzoidal plateswere conducted. Crack accelerations and decelerations were both found the the experiments,depending on the directions of crack propagation, and what site the crack propagates at. Theexperimental phenomena were re-established using the method of numerical simulations.7）The experimental research on the interactions of a dynamically propagating crack witha hole of different shapes were conducted. It is shown that the isolated hole can arrest thepropagation of the main crack. However, if the applied loading is very high, or the hole hassharp corners, subsequent cracks may be initiated at the opposite side of the hole and propagatefurther. The side curvature of the hole plays an important role controlling whether subsequentcracks will be initiated or not. Using the explicit FEM incorporating cohesive elements, thedynamic fractures of the plates were simulated. These numerical simulations provided resultsthat are in good agreement with the experimental observations.