Linear elastic fracture mechanics stress intensity factor

Rates of CF crack propagation are uniquely defined by the linear elastic fracture mechanics stress intensity factor range that combines the effects of applied load, crack size, and geometry 17,40. The similitude principle states that fatigue and CF cracks grow at equal rates when subjected to equal values of AK [6-S]. The dal N versus AK relationship may be complex however, an effective approach is based on a power (or Paris) relationship of the form [4/]... 

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

The term fracture toughness or toughness with a symbol, R or Gc, used throughout this chapter refers to the work dissipated in creating new fracture surfaces of a unit nominal cross-sectional area, or the critical potential energy release rate, of a composite specimen with a unit kJ/m. Fracture toughness is also often measured in terms of the critical stress intensity factor, with a unit MPay/m, based on linear elastic fracture mechanics (LEFM) principle. The various micro-failure mechanisms that make up the total specific work of fracture or fracture toughness are discussed in this section. 

The fracture behaviour of polymers, usually under conditions of mode I opening, considered the severest test of a material s resistance to crack initiation and propagation, is widely characterised using linear elastic fracture mechanics (LEFM) parameters, such as the plane strain critical stress intensity factor, Kic, or the critical strain energy release rate, Gic, for crack initiation (determined using standard geometries such as those in Fig. 1). LEFM... 

Karger-Kocsis recorded the different fracture behaviors of non-nucleated and -modified PP (MFR 0.8 dg min 1) tested in a three-point bending configuration at 1 ms-1 at 23 °C, a-PP was semi-ductile and /3-PP ductile with a plastic hinge at - 40 °C a-PP was brittle, /i-PP ductile [72], The descriptors from the linear elastic fracture mechanics (LEFM), Kq, the stress intensity factor, and Gc, the energy release rate, used to quantify the toughness correlated well with the fracture picture. This conclusion is also valid for... 

Linear elastic fracture mechanics (LEFM) approach can be used to characterize the fracture behavior of random fiber composites. The methods of LEFM should be used with utmost care for obtaining meaningful fracture parameters. The analysis of load displacement records as recommended in method ASTM E 399-71 may be subject to some errors caused by the massive debonding that occurs prior to catastrophic failure of these composites. By using the R-curve concept, the fracture behavior of these materials can be more accurately characterized. The K-equa-tions developed for isotropic materials can be used to calculate stress intensity factor for these materials. 

Linear Elastic Fracture Mechanics (LEFM) describes the brittle behaviour of a material in term of the critical value of the stress intensity factor at the crack tip, Kq, at the onset of propagation at a critical load value Pc ... 

Linear elastic fracture mechanics (LEFM) has been used successfully for characterization of the toughness of brittle materials. The driving force of the crack advance is described by the parameters such as the stress intensity factor (K) and the strain energy release rate (G). Unstable crack propagates when the energy stored in the sample is larger than the work required for creation of two fracture surfaces. Thus, fracmre occurs when the strain energy release rate exceeds the critical value. Mathematically, it can be written as... 

When the stress intensity increases it will finally reach a critical value Kc above which the crack propagates. If the load and crack orientation is like that shown in Figure 7.57, the actual and the critical stress intensity factor are denoted by Ki and Kic, respectively. Kic is also called the fracture toughness of the material. A necessary condition for the applicability of linear elastic fracture mechanics is that the plastic zone ahead of the crack tip is small compared with the thickness of the component and with the crack length. To satisfy this condition we must have... 

When a material obeys linear elastic fracture mechanics, its tendency to undergo crack initiation or propagation as a result of mechanical stress can be assessed in terms of fracture toughness parameters, such as (critical stress intensity factor) or Gj, (strain energy release rate). Analogous parameters can be used with thermally induced cracking. 

Crack Fibre Fibril Fracture Fracture toughness Interfaces Linear elastic fracture mechanics (LEFM) Nanotube Polymer fibre Stress intensity factor Tensile stress Weibull model Whisker... 

The ideal linear elastic fracture mechanics gives rise to the Eq. (1.1) discussed in Chapter 1, which is expressed theoretically by critical stress intensity factors Kq or These parameters must be measured by experiment before they can be used for engineering design purposes. The ideal conditions in all theories discussed in fracture mechanics do not exist. Therefore, it is necessary to have a general theory/equation that can be used to measure fracture mechanics parameters in terms of critical stress intensity factors Kq or Kic for engineering applications (Zhang and Cresswell, 2015). 

A critical research gap in corrosion science is the absence of the corrosion equivalent for the stress intensity factor (K) that has been the mainstay of structural mechanics for the past several decades. The stress intensity factor was developed to predict the behavior of pre-existing flaws in structural materials and the eventual life of a component under conditions in which the flaw develops into stable cracks. The power of K is in the concept of similitude well-defined cracks and crack tips that are different in size or shape but possess the same K (as determined by geometry, loading, and the theories of linear-elastic fracture mechanics) will experience the same mechanical driving force for crack growth. Thus, similitude allows small, well-defined samples to be tested in the laboratory to determine the conditions of crack growth and fracture and the results to be quantitatively extended to more complicated real-world structures containing cracks. Virtually... 

ISO CD 13586, Plastic—Determination of energy per unit area of crack (Gc) and the critical stress intensity factor (Kc), linear elastic fracture mechanics approach, 2000. 

In metals, it is usually a few hundredth to tenth of a millimetre [113]. If a < a, linear-elastic fracture mechanics is not valid anymore, rendering the stress intensity factor useless. As shown in figure 10.32, the maximum allowed stress range does not depend on the crack length in this case. 

As we will see below, this is not true an5rmore as soon as linear elastic fracture mechanics can be applied. In this case, the increase of the stress intensity factor due to the growing crack is larger than the decrease of the stress in the notch root, see figure 10.38. 

The fundamental postulate of Linear Elastic Fracture Mechanics (LEFM) is that the behaviour of cracks is determined solely by the value of the Stress Intensity Factors (SIFs). The stress field in the vicinity of the crack tip is characterized by the SIFs Kj, K[i and Km. In the present paper the displacement extrapolation method for evaluating SIFs is employed [6]... 

From the path independence of a quantity known as the J integral [43], which is also the energy release rate when linear elastic fracture mechanics holds, we have that G = G. This, together with the fact that stresses are linearly related, allows the local stress intensity factors to be related to the global ones through... 

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