Brittle System Analysis

BASED on vast experience watching the fruit of my hard work fall apart time and again, I feel highly qualified to discuss the manner in which systems break. In particular, the goal of this paper is to define and analyze systems which exhibit brittle behavior. This behavior is characterized by a sudden and steep decline in performance as system state changes as shown by point D along curve Ph in Figure 1. Ph is the performance curve for a high performance system with brittle characteristics, Pl is a lower performance system with less brittle characteristics. Clearly the slope from point D along curve Ph is much steeper than that of point E along curve Pl. The steep decline of performance along Ph can be due to input parameters which exceed a specified tolerance, or environmental conditions which exceed specified operating boundaries. This is equivalent to material fracture. Materials science provides a terminology which is apropos and flexible enough to describe the characteristics of this work. A table of materials science terms and their corresponding brittle system definitions is shown in Table I. Toughness [?] is the amount of energy absorbed by a material prior to failure. A brittle fracture occurs with very little energy absorption while a ductile fracture is accompanied by much energy absorption. Clearly toughness is the analog of the robustness of a system. To carry the analogy further, ductility is quantified as the amount of permanent strain prior to fracture. A system which does not exhibit brittle behavior will be called ductile [?]. Strain is unit-less and refers to the amount of deformation per unit length of a material and is caused by stress which is the force per unit area. Material deformation is analogous to degradation in a brittle system. In our work, stress is the distance by which a parameter exceeds its specified operating tolerance. There are two forms of strain, reversible and permanent. Reversible strain is called elastic strain and is characterized by Young’s modulus: the ratio of the stress over the strain. Permanent strain leaves the shape of a material permanently changed and is known as plastic strain. In a brittle system, plastic strain will be degradation from which the system cannot recover, while a brittle system can recover from reversible strain.