failure function
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Safety of the hazardous chemicals road transportation system (HCRTS) is an important, complex, social, and environmental sensitive problem. The complexity, dynamics, and multi-link features of HCRTS have made it necessary to think beyond traditional risk analysis methods. Based on the relevant literature, Functional Resonance Analysis Method (FRAM) is a relatively new systemic method for modeling and analyzing complex socio-technical systems. In this study, a methodology that integrates FRAM, fuzzy sets, and risk matrix is presented to quantitatively assess the risks factors representing failure function links in HCRTS. As the strength of function links can be illustrated by the RI (risk index) of risk factors identified in failure function links, 32 risk factors representing 12 failure function links were first identified by accident causes analysis and the framework of FRAM. Fuzzy sets were then utilized to calculate the weight of the likelihood and consequence of the risk factors. Finally, according to the assessment results of the identified risk factors by a two-dimensional risk matrix, the weaker function links in the whole HCRTS chain were identified. HCs road companies, regulatory authorities, relevant practitioners, and other stakeholders should pay more attention to these links.

The objects of the study were diagnostic features that allow determining the quality of controlling temperature modes of induction crucible melting. For this, in the normalized space of feature factors, which are the content of SiO2 and FeO+Fe2O3 in slag, a discriminant function is constructed and a decision rule is obtained in the form of a linear classifier, which allows determining in which mode the process was carried out. It is shown that this rule is the basis for identifying an event qualified as a parametric failure, and it can be included in the general structure of the parametric failure function. The parametric failure function constructed for the temperature control system of induction crucible melting makes it possible to ascertain that the control system does not meet the specified requirements for a specific temperature mode of melting. The mechanism of inferencing regarding the occurrence of a parametric failure based on this function is as follows. If the decision rule showed that the object belongs to the “low-temperature mode” class, although the process under these conditions should have been carried out in the high-temperature mode, a parametric failure is recorded. In this case, the numerical value of this function takes the value of “1”, otherwise – “0”. The inferencing mechanism works similarly if, on the basis of the decision rule, it is revealed that the process was carried out in the high-temperature mode, although under these conditions it should have been carried out in the low-temperature mode. Based on the constructed parametric failure function, practical problems related to planning maintenance of the temperature control system integrated into the melting complex or organizational and technical measures aimed at minimizing violations of the melting regulations can be solved

Failure criterion predictions often have substantial errors due to the complexity of failure mechanism or different material behaviors, especially composite failure. In this study, an example of delamination is employed to demonstrate the general failure criterion revision of composites. In the present research, the failure function can be raised to a higher order, and also be reduced to a lower one, by fitting the exponents of failure criterion. This method can be easily used to describe the observed, experimented, or computed data, particularly with no law or no rules. Further, the importance of this exponent revision is amplified when the failure surface becomes more complicated. The proposed approach is also to define and calculate the failure criteria of multiplying laminates.

Although the linear Mohr–Coulomb criterion is frequently applied to predict the failure of brittle materials such as cast iron, it can be used for ductile metals too. However, the criterion has some significant deficiencies which limit its predictive ability. In the present study, the underlying failure hypotheses of the linear Mohr–Coulomb criterion were thoroughly discussed. Based on Mohr’s physically meaningful concept of fracture plane, a macroscopic strength criterion was developed to explain the failure mechanism of isotropic metals. The failure function was expressed as a polynomial expansion in terms of the stresses acting on the fracture plane, and the quadratic approximation was employed to describe the non-linear behavior of the failure envelope. With an in-depth understanding of Mohr’s fracture plane concept, the failure angle was regarded as a generalized strength parameter in addition to the failure stress (i.e., the conventional basic strength). The undetermined coefficients of the non-linear failure function were calibrated by the strength parameters obtained from the common uniaxial tension and compression tests. Theoretical and experimental assessment for different types of isotropic metals validated the effectiveness of the proposed criterion in predicting material failure.