Elastic-plastie Linear elastic fracture mechanics fracture mechanics behavior 、 regime 51/s Engineering design Strength-of-materials behavior 1/s Stress ratio(omaxoy) Fig.3A general plot of the ratios of the toughness and stress showing the relationship between linear elastic fracture mechanics and strength of materials as it relates to fracture and structural integrity(ref 18) Linear Elastic Fracture Mechanics. Brittle fractures. similar to those mentioned in Table 1. are avoided using a linear elastic fracture mechanics design approach. This approach considers that the structure, instead of being defect-free, contains a crack(Ref 18). The governing structural mechanics parameter when a crack is present, at least in the linear approach, is an entity called the stress-intensity factor. This parameter, which is conventionally given the symbol K,can be determined from a mathematical analysis similar to that used to obtain the stresses in an uncracked component. For a relatively small crack in a simple structure, an analysis of the flawed structure beam would give to a reasonable approximation K=1.12√ma (Eq1) where a is the depth of the bracket and omax is the stress that would occur at the crack location in the absence of the crack The basic relation in fracture mechanics is one that equates K to a critical value. This critical value is often taken as a property of the material called the plane-strain fracture toughness, conventionally denoted as Kle. When equality is achieved between K and Klc, the crack is presumed to grow in an uncontrollable manner. Hence, the structure can be designed to be safe from fracture by ensuring that K is less than Kle. The liberty warship fractures are a classic example of a structural failure caused by Klc exceeding K and uncontrolled crack growth The essential difference from the strength of materials approach is that the fracture mechanics approach explicitly introduces a new physical parameter: the size of a(real or postulated)cracklike flaw. In fracture mechanics the size of a crack is the dominant structural parameter. It is the specification of this parameter that distinguishes fracture mechanics from conventional failure analyses The generalization of the basis for engineering structural-integrity assessments that fracture mechanics provides is portrayed in terms of the failure boundary shown in Fig. 3. Clearly, fracture mechanics considerations do not eliminate the traditional approach. Structures using reasonably tough materials(high Klc)and having only small cracks (low K)will lie in the strength of materials regime. Conversely, if the material is brittle(low Klc)and strong(high oY), the presence of even a small crack is likely to trigger fracture. The fracture mechanics assessment is then the crucial one The special circumstances that would be called into play in the upper right-hand corner of Fig. 3 are worth noting. In this regime, a cracked structure would experience large-scale plastic deformation prior to crack extension. Additional information is provided in the article Failure Assessment Diagrams"in this Volume and in Ref 19 Damage Tolerance Approach Life assessment of aircraft and power-plant equipment stems largely from the development of the damage-tolerance philosophy based on fracture mechanics. Damage tolerance is the philosophy used for maintaining the structural safety of commercial transport, military aircraft, structures, and pressure vessels. The use of fracture mechanics and damage tolerance has evolved into the design program for structures that are damage tolerant, that is, designed to operate with manufacturing and in-service-induced defects(Ref 20) Thefileisdownloadedfromwww.bzfxw.comFig. 3 A general plot of the ratios of the toughness and stress showing the relationship between linear elastic fracture mechanics and strength of materials as it relates to fracture and structural integrity (Ref 18) Linear Elastic Fracture Mechanics. Brittle fractures, similar to those mentioned in Table 1, are avoided using a linear elastic fracture mechanics design approach. This approach considers that the structure, instead of being defect-free, contains a crack (Ref 18). The governing structural mechanics parameter when a crack is present, at least in the linear approach, is an entity called the stress-intensity factor. This parameter, which is conventionally given the symbol K, can be determined from a mathematical analysis similar to that used to obtain the stresses in an uncracked component. For a relatively small crack in a simple structure, an analysis of the flawed structure beam would give to a reasonable approximation: max K a = 1.12s p (Eq 1) where α is the depth of the bracket and σmax is the stress that would occur at the crack location in the absence of the crack. The basic relation in fracture mechanics is one that equates K to a critical value. This critical value is often taken as a property of the material called the plane-strain fracture toughness, conventionally denoted as KIc. When equality is achieved between K and KIc, the crack is presumed to grow in an uncontrollable manner. Hence, the structure can be designed to be safe from fracture by ensuring that K is less than KIc. The Liberty warship fractures are a classic example of a structural failure caused by KIc exceeding K and uncontrolled crack growth. The essential difference from the strength of materials approach is that the fracture mechanics approach explicitly introduces a new physical parameter: the size of a (real or postulated) cracklike flaw. In fracture mechanics the size of a crack is the dominant structural parameter. It is the specification of this parameter that distinguishes fracture mechanics from conventional failure analyses. The generalization of the basis for engineering structural-integrity assessments that fracture mechanics provides is portrayed in terms of the failure boundary shown in Fig. 3. Clearly, fracture mechanics considerations do not eliminate the traditional approach. Structures using reasonably tough materials (high KIc) and having only small cracks (low K) will lie in the strength of materials regime. Conversely, if the material is brittle (low KIc) and strong (high σY), the presence of even a small crack is likely to trigger fracture. The fracture mechanics assessment is then the crucial one. The special circumstances that would be called into play in the upper right-hand corner of Fig. 3 are worth noting. In this regime, a cracked structure would experience large-scale plastic deformation prior to crack extension. Additional information is provided in the article “Failure Assessment Diagrams” in this Volume and in Ref 19. Damage Tolerance Approach. Life assessment of aircraft and power-plant equipment stems largely from the development of the damage-tolerance philosophy based on fracture mechanics. Damage tolerance is the philosophy used for maintaining the structural safety of commercial transport, military aircraft, structures, and pressure vessels. The use of fracture mechanics and damage tolerance has evolved into the design program for structures that are damage tolerant, that is, designed to operate with manufacturing and in-service-induced defects (Ref 20). The file is downloaded from www.bzfxw.com