Elastic-plastic fracture mechanics

In the previous sections, it was frequently stressed that linear-elastic fracture mechanics can only be used if the plastic zone near the crack tip is sufficiently small. If this is not the case, we enter the domain of elastic-plastic fracture mechanics (epfm) which can deal with a large plastic zone. The method, however, cannot be used for arbitrarily large plastic zones - plastic behaviour must stiU be restricted to the region around the crack tip and must be mainly determined by the surrounding elastic stress field. 

Two alternative methods are commonly used to describe the state near the crack tip The crack tip opening displacement and the J integral. Both methods can be shown to be mathematically equivalent. 

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The utility of K or any elastic plastic fracture mechanics (EPFM) parameter to describe the mechanical driving force for crack growth is based on the ability of that parameter to characterize the stress-strain conditions at the crack tip in a maimer which accounts for a variety of crack lengths, component geometries and loading conditions. Equal values of K should correspond to equal crack tip stress-strain conditions and, consequently, to equivalent crack growth behavior. In such a case we have mechanical similitude. Mechanical similitude implies equivalent crack tip inelastic zones and equivalent elastic stress fields. Fracture mechanics is... 

Elastic-plastic Fracture Mechanics Behavior of Graphite... 

Ernst, H. A., Elastic Plastic Fracture Mechanics Methodology for Surface Cracks, Georgia Inst, of Tech., 1994. 

In the case of thin sections the measure of toughness is given by plane-stress fracture toughness, Kc and elastic-plastic fracture mechanics (EPFM) are used. It is also necessary to bear in mind that plane-stress fracture toughness Kc is higher than plane-strain fracture toughness Xlc. 

It must be noted that the fracture mechanics framework described above only applies when plastic deformation of the material is limited. Substantial plastic deformation may accompany propagation of existing defects in structures fabricated from relatively low-strength materials, e.g., carbon steels. In these cases, the linear elastic stress intensity factor, K, does not accurately apply in structural design. Alternately, elastic-plastic fracture mechanics methods may apply. ... 

It is well known that the methods of elastic-plastic fracture mechanics provide more realistic models of cracked structures with high toughness compared with the methods of the linear elastic fracture mechanics. Ductile materials are used in structural elements not only in piping systems of power plants but in chemical industry, in aircraft propulsion systems and elsewhere [1-8], Evidently, cracked elements in chemical or power plants pose a serious threat to operation of these stmctures. Therefore, it is extremely important that the crack will not spread unstably through the pipe thickness. 

The deformation characteristic of more ductile polymer materials at ambient temperatures like most thermoplastics or all elastomers is highly non-linear, e.g., either mostly viscoelastic or entropy-elastic or a combination of both. Compared to concepts of LEFM relatively rarely used for polymer materials different concepts of non-linear elastic firacture mechanics such as elastic-plastic fracture mechanics (EPFM) or post-yield fracture mechanics (PYFM) are somewhat widely applied, therefore. One of the most important concepts of EPFM is the J integral concept. Notwithstanding the J integral is primarily defined to be valid... 

When yielding causes large departures from linearity in the force-displacement curve, such that valid Kiq data cannot be obtained, it is still possible to make geometry-independent measurements of the fracture resistance of the material, using the methods of elastic-plastic fracture mechanics. These usually require additional information to determine whether non-linearity is due to crack tip plasticity alone, or to a combination of plasticity and crack growth. Several different approaches have been developed, of which we will discuss onfy two the crack tip opening displacement (CTOD) and /-integral methods. 

VI.7. Methods 1 and 2 are based on the criteria of the first approach above, whilst Method 3 follows the basic fracture mechanics approach or the extensions to elastic plastic fracture mechanics described later. It should be noted that whilst linear elastic fracture mechanics can be used provided that small scale yielding limits prevail, if more extensive yielding occurs then elastic plastic fracture mechanics methods should be used. Other evaluation methods are possible. Any approach suggested by the package designer is subject to the approval of the competent authority. 

FIG. VI. 1. Failure assessment diagrams for elastic-plastic fracture mechanics treatments [VI.16]. (a) Level 2 assessment diagram, (b) Level 3 assessment diagram. 

In the 1980s and 1990s, further developments in elastic-plastic fracture mechanics allowed the use of WeibuU statistics (Landes and Shaffer, 1980), specimen size adjustments and a universal-shape Master Curve (Wallin, 1984) to determine bounding curves with small specimens, discussed in Section 10.3. The Master Curve development by Wallin (1984) is discussed in more detail in Section 10.3.4. 

Larsson L H (ed.) (1980), Advances in Elastic-Plastic Fracture Mechanics, Science Publishers, Ltd, London. 

The model Is based on elastic-plastic fracture mechanics principles, and Incorporates effects associated with thermal expansion mismatch and modulus mismatch of various constituents, as well as non-linear material behavior as a function of load and temperature. Key properties of the constituents, such as those of the interlayer, reaction zone, and base material are provided as a data base these data were measured in this program by using bulk samples, The model then uses the processing history, specimen geometry and loading conditions to evaluate the performance of the joint, The results of finite element analysis of cracked specimens have been consolidated In arriving at the engineering model, JADM,... 

This quick glance into elastic-plastic fracture mechanics completes the short primer of some terms and basic relationship of fracture mechanics. 

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