On the possibly multifractal properties of dissipated energy in brittle materials

The paper reports an analytical study on the properties of fracture networks in brittle materials. Micro-deformation gradients are considered random fields and/or scaling fields. Under dynamic crack propagation conditions the possibly fractal properties of the (macro) crack pattern are governed by the interplay of fluctuations and spatial correlations. For "slow" crack propagation they are governed by the kinematic fields in the vicinity of crack or notch tips. The spatial distribution of dissipated energy, due to fracture, is evaluated. It is shown that there is a strong possibility that the dissipated energy is multifractal. Here, its properties are characterized in a fashion similar to the so-called p-model where p herein denotes normalized dissipated energy. For the three cases analyzed -uniaxial tension, pure shear, and dilatation -the dissipated energy under pure shear shows the strongest disorder, the one under dilatation the weakest, and the tension case is always between these two. INTRODUCTION Engineering materials are, in general, heterogeneous due to the presence of microstructure. If interest is in mechanical properties at scales much larger than the atomic, heterogeneity for materials like ceramics, rocks, concretes, composites means several things: size and properties of grains, aggregates, pores, microcracks, interfaces, composite structure, interactions with discontinuities and surfaces. These influence the analysis of such materials substantially, experimentally (in the choice of scales, methods of observation) and theoretically, for example in the limitations of homogenization methods. The fracture behavior of materials is important, so it continues to be the subject of intensive research. Microcracking, crack bridging, crack arrest are some of the many mechanisms that absorb energy during the fracture process. Physical reasoning suggests that these mechanisms are affected by the heterogeneity of the material before (macro) fracture activation. Thus heterogeneity contributes to the energy absorption mechanisms, which then contribute to the tendency of the (macro) crack network to follow a tortuous path. One problem examined herein is the following. Consider a brittle material loaded at a low loading rate, either by controlling the external load or the external displacement. At some point a macrocrack network will form. Does this network form dynamically or quasi-statically? Let us assume, for a moment, that crack propagation is dynamic. Then, there may not be enough time for the stress/strain fields to redistribute to an equilibrium state until the crack propagates further. Of course, this is a heuristic argument that is difficult to verify experimentally. In dynamic fracture mechanics literature, i.e., If the specimen/structure is loaded dynamically, the macrocrack network develops dynamically and several factors influence its characteristics -the waves propagating in the medium influence the crack pattern significantly. Especially near surfaces strong surface waves usually result in disintegration of the material from the surfaces inward. Such problems are difficult to treat analytically. Of course, near boundaries the behavior is expected to be different than in the bulk, i.e. In a recent study, Frantziskonis (1993a, b), it is shown that under certain conditions a statistical approach to material heterogeneity yields results analogous to the so-called gradient theories. These conditions call for small heterogeneity fluctuations allowing a spatial Taylor series expansio

Thermo-mechanical strain rate-dependent behavior of shape memory alloys as vibration dampers and comparison to conventional dampers

A study on shape memory alloy materials as vibration dampers is reported. An important component is the strain rate-dependent and temperature-dependent constitutive behavior of shape memory alloy, which can significantly change its energy dissipation capacity under cyclic loading. The constitutive model used accounts for the thermo-mechanical strain rate-dependent behavior and phase transformation. With increasing structural flexibility, the hysteretic loop size of shape memory alloy dampers increases due to increasing strain rates, thus further decreasing the response of the structure to cyclic excitation. The structure examined is a beam, and its behavior with shape memory alloy dampers is compared to the same beam with conventional dampers. Parametric studies reveal the superior performance of the shape memory alloy over the conventional dampers even at the resonance frequency of the beam-damper system. An important behavior of the shape memory alloy dampers is discovered, in that they absorb energy from the fundamental and higher vibration modes. In contrast, the conventional dampers transfer energy to higher modes. For the same beam control, the stiffness requirement for the shape memory alloy dampers is significantly less than that of the conventional dampers. Response quantities of interest show improved performance of the shape memory alloy over the conventional dampers under varying excitation intensity, frequency, temperature, and strain rate.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]