Linear-elastic fracture mechanics approach

Mode I fracture tests were performed in three-point bending (SE(B)) at a low (lOmm/min) and a high (Im/s) loading rate according to the testing protocols that were developed by the European Structural Integrity Society - Technical Committee 4 (ESIS TC4) to determine fracture toughness in plastics by a linear elastic fracture mechanics approach, which have become now international standards [15,16]. 

In the Irwin approach, as with the Griffith approach, strength is found to depend on a combination of a material property (intrinsic) and a flaw size (extrinsic). In the linear elastic fracture mechanics approach, however, the material property is T or R and it has a component that depends on the microstructure of the material. Thus, if the mechanisms that increase T for a material can be identified, an approach is available to increase the reliability of brittle materials. It is this philosophy that has been a major driving force in the recent production of ceramics with higher strengths and toughnesses than had previously been considered possible. 

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. 

ISO (2000) Standard test method for the determination of fracture toughness (Gc and Kc) - A linear elastic fracture mechanics approach. ISO Standard ISO 13586... 

ISO 15850 2002 Plastics - Determination of tension-tension fatigue crack propagation -Linear elastic fracture mechanics (LEFM) approach... 

The best approach, however, consists of controlling the defect size and geometry and taking into account the corresponding stress-field inhomogeneity. This is realized in the frame of linear elastic fracture mechanics (LEFM), which was first applied to metals and ceramics and then adapted with success to polymers (Williams, 1984). 

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. 

The fact that thermosets are typically brittle and generally exhibit linear elastic stress-strain behavior suggests that linear elastic fracture mechanics (LEFM) and test methods may be applicable. In fact, these approaches have proven very popular, as is evidenced by the successful use of a number of LEFM-based fracture... 

Polymers which yield extensively under stress exhibit nonlinear stress-strain behavior. This invalidates the application of linear elastic fracture mechanics. It is usually assumed that the LEFM approach can be used if the size of the plastic zone is small compared to the dimensions of the object. Alternative concepts have been proposed for rating the fracture resistance of tougher polymers, like polyolelins, but empirical pendulum impact or dart drop tests are deeply entrenched forjudging such behavior. 

For many engineering applications, impact fracture behavior is of prime practical importance. While impact properties of plastics are usually characterized in terms of notched or un-notched impact fracture energies, there has been an increasing tendency to also apply fracture mechanics techniques over the last decade [1, 2 and 3]. For quasi-brittle fracture, a linear elastic fracture mechanics (LEFM) approach with a force based analysis (FBA) is frequently applied to determine fracture toughness values at moderate loading rates. 

Applications of linear elastic fracture mechanics (primarily) to the brittle fracture of solid polymers is discussed by Professor Williams. For those not versed in the theory of fracture mechanics, this paper should serve as an excellent introduction to the subject. The basic theory is developed and several variants are then introduced to deal with weak time dependence in solid polymers. Previously unpublished calculations on failure times and craze growth are presented. Within the framework of brittle fracture mechanics and testing this paper provides for a systematic approach to the faOure of engineering plastics. 

Linear elastic fracture mechanics studies on toughened brittle plastics at room temperature concentrated on thermosetting resins, which have sufficiently high yield stresses to meet the requirements of Eq. 12.7. There has been increasing emphasis on ductile fracture mechanics in testing the toughened thermoplastics. An alternative approach is to determine the parameter, Jj, which is the quantity corresponding to Gj in linear elastic fracture mechanics, as discussed below. 

Soutis, Fleck, and Smith [22], proposed the use of linear elastic fracture mechanics and the principle of superposition to determine the failure strength of composites with holes, in particular, under compression. This approach essentially models the damage developing at the edge of the hole as a crack with loaded surfaces. This is a one-parameter model as the crack surface stress must be determined by tests. 

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