Linear elastic stress intensity factor

The average wall stress and the local stress near defects are related through the linear elastic stress intensity factor (K). The magnitude of the local stress is proportional to the stress intensity factor, K, according to the following relationship ... 

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. ... 

Plot of log vs. log AKis used to determine the value of from the slope, while C is estimated from the intercept of the Paris equation (extrapolating the value of AR to 10). AK is the range of the linear elastic stress intensity factor defined as and rep-... 

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. 

Secondly, Irwin 6) found that the stress field around a sharp crack in a linear elastic material could be uniquely defined by a parameter named the stress-intensity factor, K and stated that fracture occurs when the value of K, exceeds some critical value, K C. Thus, K, is a stress field parameter independent of the material whereas Klc, often referred to as the fracture toughness, is a measure of a material property. Again the subscript I is used to denote the tensile-opening mode. 

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 ... 

The second approach, due to lrwin is to characterise the stress field surrounding a crack in a stressed body by a stress-field parameter K (the stress intensity factor ). Fracture is then supposed to occur when K achieves a critical value K - Although, like Griffith s equation, this formulation of fracture mechanics is based on the assumptions of linear elasticity, it is found to work quite effectively provided that inelastic deformations are limited to a small zone around the crack tip. Like, however, the critical parameter remains an empirical quantity it cannot be predicted or related explicitly to the hysical properties of the solid. Like,, K. is time and temperature de ndent. 

In principle then, a fracture toughness parameter has been defined in terms of linear elastic analysis of a cracked body involving the strain energy release rate G, or the stress intensity factor K. For thick sections, the fracture toughness is defined as Gic, and for thinner sections, as Gc or R (referred only to mode 1 loading here). This value is to be measured in the laboratory and applied to design. The validity of... 

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... 

The configuration shown in Fig. 8.35 was used by the present author to determine the stress intensity factor for an annular crack located at the equator of a spherical void (Green, 1980). This geometry was meant to simulate the presence of pores in a linear elastic continuum. The solution is shown schematically in Fig. 8.37. As expected, the solution is similar to the edge crack solution for short cracks (a/R<0.1) and the internal circular crack solution (radius (R+a)) for long cracks (a/R>0.5). 

The stresses near a crack tip in a linear elastic material are related to the applied stress intensity factor K. In some materials, non-linear deformation behavior may occur in the high-stress zone at the crack tip. The effect of this process zone will be to change the stresses at the crack tip. These stresses can often described by a local stress intensity factor K. If the stresses are reduced and the... 

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. 

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