thin layers. Some causes of intergranular brittle fracture are given below, but the list is not exhaustive. It does, however indicate some of the possibilities that need to be considered, and either eliminated or confirmed, as contributing to the fracture The presence at a grain boundary of a large area of second-phase particles(such as carbides in Fe-Ni-Cr alloys or MnS particles in an overheated steel) Segregation of a specific element or compound to a grain boundary where a layer a few atoms thick is sufficient to cause embrittlement (embrittlement caused by the presence of oxygen in high-purity iron, oxygen in nickel, or antimony in copper and temper embrittlement of certain steels are examples of intergranular embrittlement where detection of a second phase at grain boundaries is difficult) The conditions under which a progressively growing crack may follow an intergranular path before final fracture occurs include SCC, embrittlement by liquid metals, hydrogen embrittlement, and creep and stress-rupture failures. These failure modes are discussed in more detail elsewhere in this Volume. In addition, the article"Intergranular Fracture"in this Volume discusses various causes Fracture Mechanics Applied to Failure Analysis The application of fracture mechanics is often pertinent to the investigation of failures, as well as to the formulation of preventive measures. In general, there are two types of conditions that may lead to structural failure Net-section instability where the overall structural cross section can no longer support the applied load The critical flaw size(ac) is exceeded by some preexisting discontinuity or when subcritical cracking mechanisms (for example, fatigue, SCC, creep)reach the critical crack size Failures due to net-section instability typically occur when a damage process such as corrosion or wear reduces the hickness of a structural section. This type of failure can be evaluated by traditional stress analysis or FEA, which are effective methods in evaluating the effects of loading and geometric conditions on the distribution of stress and strain in a body or structural system However, stress analyses by traditional methods or fea do not easily account for crack propagation from preexistin cracks or sharp discontinuities in the material. When a preexisting crack or discontinuity is present, the concentration of stresses at the crack tip becomes asymptotic (infinite) when using the conventional theory of elasticity. In this regard fracture mechanics is a useful tool, because it is a method that quantifies stresses at a crack tip in terms of a stress intensity parameter(K K=YG√ra where y is a geometric factor(typically on the order of about 1), o is the gross stress across the fracture plane, and a is the crack length. The stress-intensity parameter K quantifies the stresses at a crack tip, and a critical stress-intensity value(ke) thus can be defined as where or is the fracture stress occurring with a critical crack size, ae. The critical stress intensity, also known as fracture toughness(Kc), is the value of stress intensity(K)that results in rapid, unstable fracture. Fracture toughness(Kc) depend on both the thickness of the section and the ductility of the material. For a given material, the fracture toughness(or critical stress intensity, Kc) decreases as section thickness is increased. The value of Ke decreases with increasing section thickness until a minimum value is reached. The toughness at this minimum, which is an inherent material property, is the plane-strain fracture toughness (Kl). Plane-strain fracture is a mode of brittle fracture without any appreciable macroscopic plastic deformation and is thus referred to as linear-elastic fracture mechanics (LEFM). The gener conditions for LEFM analysis are expressed as thickness>2.5(KJo) where oy is the yield strength Linear-elastic fracture mechanics is a useful tool in failure analysis as many(and perhaps most) structural failures occur by the combined processes of crack initiation followed by subcritical crack growth mechanism(for example, fatigue, stress corrosion, creep) until a critical crack(ac) is reached. In this regard, fracture mechanics is an effective tool for evaluating critical flaw size(ac) that leads to rapid unstable fracture and can help answer questions during a failure analysis, such as Where should one look for the transition from subcritical crack growth to unstable rapid fracture?thin layers. Some causes of intergranular brittle fracture are given below, but the list is not exhaustive. It does, however, indicate some of the possibilities that need to be considered, and either eliminated or confirmed, as contributing to the fracture: · The presence at a grain boundary of a large area of second-phase particles (such as carbides in Fe-Ni-Cr alloys or MnS particles in an overheated steel) · Segregation of a specific element or compound to a grain boundary where a layer a few atoms thick is sufficient to cause embrittlement (embrittlement caused by the presence of oxygen in high-purity iron, oxygen in nickel, or antimony in copper and temper embrittlement of certain steels are examples of intergranular embrittlement where detection of a second phase at grain boundaries is difficult) The conditions under which a progressively growing crack may follow an intergranular path before final fracture occurs include SCC, embrittlement by liquid metals, hydrogen embrittlement, and creep and stress-rupture failures. These failure modes are discussed in more detail elsewhere in this Volume. In addition, the article “Intergranular Fracture” in this Volume discusses various causes. Fracture Mechanics Applied to Failure Analysis The application of fracture mechanics is often pertinent to the investigation of failures, as well as to the formulation of preventive measures. In general, there are two types of conditions that may lead to structural failure: · Net-section instability where the overall structural cross section can no longer support the applied load · The critical flaw size (ac) is exceeded by some preexisting discontinuity or when subcritical cracking mechanisms (for example, fatigue, SCC, creep) reach the critical crack size Failures due to net-section instability typically occur when a damage process such as corrosion or wear reduces the thickness of a structural section. This type of failure can be evaluated by traditional stress analysis or FEA, which are effective methods in evaluating the effects of loading and geometric conditions on the distribution of stress and strain in a body or structural system. However, stress analyses by traditional methods or FEA do not easily account for crack propagation from preexisting cracks or sharp discontinuities in the material. When a preexisting crack or discontinuity is present, the concentration of stresses at the crack tip becomes asymptotic (infinite) when using the conventional theory of elasticity. In this regard, fracture mechanics is a useful tool, because it is a method that quantifies stresses at a crack tip in terms of a stress￾intensity parameter (K): K =Y a s p where Y is a geometric factor (typically on the order of about 1), σ is the gross stress across the fracture plane, and a is the crack length. The stress-intensity parameter K quantifies the stresses at a crack tip, and a critical stress-intensity value (Kc) thus can be defined as: Kc =Y a s p f c where σf is the fracture stress occurring with a critical crack size, ac. The critical stress intensity, also known as fracture toughness (Kc), is the value of stress intensity (K) that results in rapid, unstable fracture. Fracture toughness (Kc) depends on both the thickness of the section and the ductility of the material. For a given material, the fracture toughness (or critical stress intensity, Kc) decreases as section thickness is increased. The value of Kc decreases with increasing section thickness until a minimum value is reached. The toughness at this minimum, which is an inherent material property, is the plane-strain fracture toughness (KIc). Plane-strain fracture is a mode of brittle fracture without any appreciable macroscopic plastic deformation and is thus referred to as linear-elastic fracture mechanics (LEFM). The general conditions for LEFM analysis are expressed as: thickness ≥ 2.5(KIc/σy) 2 where σy is the yield strength. Linear-elastic fracture mechanics is a useful tool in failure analysis as many (and perhaps most) structural failures occur by the combined processes of crack initiation followed by subcritical crack growth mechanism (for example, fatigue, stress corrosion, creep) until a critical crack (ac) is reached. In this regard, fracture mechanics is an effective tool for evaluating critical flaw size (ac) that leads to rapid unstable fracture and can help answer questions during a failure analysis, such as: · Where should one look for the transition from subcritical crack growth to unstable rapid fracture?