General laws of multiple fracture at static, cyclic and dynamic loading Luidmila R. Botvina Department of SSA, A.A.Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences, 119991 Moscow, Russia, botvina@imet.ac.ru Abstract Multiple fracture patterns of specimens from low - and medium carbon steel tested in conditions of static, dynamic and cyclic loading were studied. Cumulative distributions of microcracks by length under static and cyclic loading, distributions of the number of fragments by their mass under dynamic loading and amplitude distributions of acoustic emission signals were plotted. The parameters of these distributions at different stages of loading were estimated. It was studied the influence of specimen thickness, the distance to the fracture surface, the grain size and the failure mechanism on these parameters. The general laws characterizing multiple fractures at different loading conditions were found. They include, in particular, a change in function describing the distributions and a reduction of the exponents of these functions before fracture. The physical meaning of the estimated distribution parameters, the possibility of their use for the fracture prediction and material selection are discussed. Keywords Multiple fracture, Damage evolution, General fracture laws 1. Introduction The fundamental problem of materials science is associated with the need to relate macro characteristics of mechanical behavior of material with parameters of structure and its response to the loading conditions. This response is expressed in the formation of the localized plastic zone with a certain geometry and accumulation of internal damage, characterized by the size and density of microcracks. The evaluation of these parameters by the method of replicas removed from the surface of the polished specimens tested under different types of loading showed that there are some general regularities of the damage accumulation or the multiple fracture at the stage of macrocrack initiation, which will be discussed below. 2. Results of the study 2.1 Two stage of defect growth Multiple fracture under conditions of irradiation and thermal fatigue [1], was studied using the histograms of the number - size distribution of voids in the aluminum irradiated using different neutron doses [2] and histograms of the distribution of thermal fatigue microcracks in the 06Cr18Ni11steel tested at different number of cycles [3]. Analysis of the cumulative number - size distributions of radiation defects with size of several angstroms in the aluminum [1] showed that these curves corresponding to different neutron doses can be reduced to a single distribution curve by normalization. This demonstrates the self-similarity of the process of accumulation defects at this early stage of their growth [4]. The thermal fatigue microcracks are longer than the radiation voids by several orders of magnitude. Figure 1 shows that the first self-similar stage of defect accumulation is described by an exponential law (the curves 1 – 3, Fig.1, a, b) and the second stage, by a power law (the curves 4 - 5). The exponents in the exponential laws decrease with the number of cycles and are 0.38, 0.17, 0.09 (R2>0.92), respectively. The distribution curves 4 - 5 corresponding to stage of coalescence of voids are well described by a power law with the exponent 0.91 (R2=0.98) (Fig.1, b, solid lines). Thus, there are two stages of accumulation of defects: the first stage of growth of isolated voids
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