【正文】 he roll gap. In some cases the quantity of scrap has been quoted as 6% or more for certain aluminum magnesium alloys (45). Creating these cracks requires both inadequate ductility and secondary tensile stress on the edge (15). Obviously just like the need to predict the result of rolling, edge cracking has solicited research to better understand the concepts and causes associated with this defect.Because rolling is an industrial process, the concern of experiments is in making sure that results translate from the lab back to the factory floor. This is a plicated process, especially for hot rolling, because industrial mills are much larger than those typically used for laboratory experiments. While gross geometry is easily scalable, the metallurgical parameters including microstructural and thermal variables are not. For example, laboratory rolling mills are usually much smaller than the ones used in industry, therefore the work pieces are smaller, this causes issues because the thermal masses of the two differ. Therefore the heat distribution differs between the two cases which greatly effects flow stress. This problem has been addressed by Burman by reheating the specimens after a temperature drop of more than 40176。 for example, in order to accurately model forward slip conditions used in cold rolling an upsetting rolling test is used. This has been used to study the effect of changing the forward slip condition and contact conditions easily. In this test, the material is drawn through the device using a tensile test machine. This device only reproduces contact conditions on only one side of the strip (47). In different experiments, to estimate the creation of tensile stresses in rolling (which is related to crack propagation), often times a grid would be etched onto a material sample either on the side or between two pieces of material which then are riveted together. These test pieces are then rolled. After rolling, the stream line data is collected by measuring grid changes. Modeling is then employed to backtrack out the stresses (46). In studying material factors, oftentimes different methods are used to reveal the microstructure of the material including: optical microscopy, TEM, and xray diffraction (48). These not only attempt to look at locations and material inclusions that tend to cause cracking but attempt to track the evolution of the microstructure in these materials. To study edge cracking creating accurate finite element models have bee necessary as experiments are expensive and difficult to relate back to industrial conditions. The main debate in using this method is the damage model as discussed in Chapter 4. Perhaps the simplest method attempted to model cracking is using stress intensity factors (49). The stress intensity factor (SIF) helps characterizes the crack tip and is used monly in fracture studies. The determination of this factor is dependent on the size of the crack, geometry of the crack and part, the applied load, and boundary conditions. The factor is calculated then pared to fracture toughness information. While Xie et. al. study, as described here, provides some insights into edge cracking, care must be taken. The SIF is mainly valid for linear elastic materials and processes。 some are based on critical strain, critical stress, or plastic work (50). One example of this is the work of Oh and Kobayashi (51) where they use the principal tensile strains and principal pressive strain . The constants in these formulations are determined by experiment. An example is given below: （）This criteria validity is limited to material in question, AA7075T6 and only for rolling cases.The most plicated damage model, used in finite element analysis, utilizes the idea of void volume fraction. Since ductile cracking is based on the initiation, growth, and then linking of voids, this is a more physical based analysis. In this type of study the void volume fraction is allowed to increase and decrease until it reaches a critical value in which the material fractures. In a study by Riedel et al. (50) they attempted to model edge cracking this way using the Gologanu model, which is based on the more monly used Gurson model. The uses of either of these models are problematic due to model plexity and a difficult to determine set of material properties. But, since the model is believed to be closer to the physics of the situation it is more likely to be valid over different stress states. These types of models also show the evolution of damage throughout the model. There are two interesting things to note about this study: since they were trying to recreate the 45176。 as this ratio controls the likelihood of different slip systems being activated. In these materials, it was found that grain size had a weaker correlation to cracking than the lattice parameter ratio. This was caused by the interplay of these two lattice parameters and their ability to limit and or induce slipping and twinning. In addition, when these materials twinned the cracking resistance varied on the type of twin form, making this cracking case more plicated (53). The existence of inclusions is not enough to determine ductility, but the positions of the inclusions matters. For example, in machining steels that containing nonmetallic inclusions to improve machinability such as MnS or metallic inclusions such as Pb, Bi, and Sn, the need to balance the effects of inclusion interfaces, which both decreases the force required for machining and increases the likelihood of cracking by initiating voids, is difficult. This study was conducted by paring inclusions formed by Pd and Bi, in order to reduce PdS (lead) use, because of the human and environmental harm that it causes. It was found that BiS steels were more difficult to roll pared to the lead based ones. Apparently, the low melting temperature and the poor deformation of Bi with the matrix accelerates the formation of cra