Linear-elastic fracture mechanics LEFM test

The figure also shows a schematic diagram of load vs displacement plots describing the procedure for determination of the critical load in a linear-elastic fracture mechanics (LEFM) test (see Fig. 10.1c). The determination of Ki is dependent on testing the material under conditions in which it exhibits essentially linear-elastic behavior indicative of a plastic zone that is very small relative to flaw size and specimen dimensions, the domain of LEFM. The equations for the compact specimen and three-point bend specimen are as follows ... 

Obviously, key questions which now arise are how good are these various analytical and finite element analysis methods at yielding a value of the adhesive fracture energy, Gc, (a) which is independent of the details of the peel test geometry, for example, independent of the peel angle and thickness of the peel arm and (b) which agree with results from other test methods, for example, with values of Gc from standard linear-elastic fracture-mechanics (LEFM) tests. 

The tapered-double-cantilever-beam(TDCB) specimen [11,12] shown in Fig. 2 is a standard linear-elastic fracture-mechanics (LEFM) test specimen and the value of the adhesive fracture energy, Gg, may be deduced from ... 

Linear combination of atomic orbitals (LCAO) method, 16 736 Linear condensation, in silanol polycondensation, 22 557-558 Linear congruential generator (LCG), 26 1002-1003 Linear copolymers, 7 610t Linear density, 19 742 of fibers, 11 166, 182 Linear dielectrics, 11 91 Linear elastic fracture mechanics (LEFM), 1 509-510 16 184 20 350 Linear ethoxylates, 23 537 Linear ethylene copolymers, 20 179-180 Linear-flow reactor (LFR) polymerization process, 23 394, 395, 396 Linear free energy relationship (LFER) methods, 16 753, 754 Linear higher a-olefins, 20 429 Linear internal olefins (LIOs), 17 724 Linear ion traps, 15 662 Linear kinetics, 9 612 Linear low density polyethylene (LLDPE), 10 596 17 724-725 20 179-211 24 267, 268. See also LLDPE entries a-olefin content in, 20 185-186 analytical and test methods for,... 

The analysis of brittle fracture is the very domain of Linear Elastic Fracture Mechanics (LEFM). A comprehensive introduction to its fundamentals and the validity of its application to polymers has been given by Williams [25] and more recently by Grellmann and Seidler [26]. The fracture criteria and relevant test procedures elaborated by the ESIS technical committee TC4 can be found in [27]. 

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... 

In most composites with desirable tensile properties, linear elastic fracture mechanics (LEFM) criteria are violated.30,31 Instead, various large-scale nonlinearities arise, associated with matrix damage and fiber pull-out. In consequence, alternate mechanics is needed to specify the relevant material and loading parameters and to establish design rules. Some progress toward this qbjective will be described and related to test data. This has been achieved... 

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... 

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... 

ESIS Technical Committee 4, A Linear Elastic Fracture Mechanics (LEFM) Standardfor Determining Kc and G Testing Protocol (1990). 

Linear elastic fracture mechanics (LEFM) describes the behaviour of sharp cracks in linear, perfectly elastic materials. Since polymers are neither linear nor elastic, the utility of the theory may, at first sight, seem doubtful. In fact, the deviations from the theoretical assumptions are such that quite minor modifications to the analysis produce a precise description of crack growth in polymers within the framework of the conventional theory. The considerable resources of the subject may thus be utilised in that testing experience on other materials may be employed, together with the available analytical work. 

Our discussion thus far has focused in a rather superficial way on the general evolution of the important area of fracture mechanics. The basic objective of fracture mechanics is to provide a useful parameter that is characteristic of the given material and independent of test specimen geometry. We wUl now consider how such a parameter, such as G (, is derived for polymers. In doing so we confine our discussion to the concepts of linear elastic fracture mechanics (LEFM). As the name suggests, LEFM apphes to materials that exhibit Hookean behavior. 

Plastics - Determination of fracture toughness (Gic and Kic) Linear elastic fracture mechanics (LEFM) approach - Amendment 1 Guidelines for the testing of injection-moulded plastics containing discontinuous reinforcing fibres... 

Plastics—Determination of the Fluidity of Plastics Using Capillary and Slit Die Rheometers Plastics—Determination of Fracture Toughness (Gc and Kq). Part 1 Linear Elastic Fracture Mechanics (LEFM) Approach Methods of Test for Volume Resistivity and Surface Resistivity of Solids Electrical Insulating Materials... 

In the discussion so far we have considered only linear elastic fracture mechanics (LEFM) the term linear elastic means that the cracked specimen obeys Hooke s law to a good approximation. In the context of fracture mechanics, the requirement is that the extent of yielding in the neighbourhood of the crack tip is negligible, so that the force-deflection curves for test specimens are linear. In addition, the value of B must be sufficiently high that the deformation at the crack tip occurs under plane-strain conditions. It is found experimentally that these conditions are met if B, (IV — a), and a are all greater than 2.5(K,c/ffy). Provided these conditions are met, the spatial extent of the plastically deformed zone at the crack tip is less than 2 % of the above dimensions, the specimen fractures in plane-strain and the measured is a true material property. 

Different formulations of fracture mechanics provide different fracture parameters. Linear elastic fracture mechanics (LEFM)(D defines a stress field parameter K which reflects the overall intensity of the stress field around the crack. Failure occurs when K achieves its critical value K. The formula for K depends on the test specimen configuration, but for a central crack of half-length c in a semi-infinite sheet, for example, it is given by... 

The procedure was based on the ASTM Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials (E 399), but takes account of the major difficulties imposed by polymers. Although polymeric materials are not strictly elastic, for many cases of practical significance linear elastic fracture mechanics (LEFM) conditions pertain, and the protocol sets out the same validity criteria as for metals. 

Fracture toughness tests were conducted based on the linear elastic fracture mechanics (LEFM) approach. The single-edge-notch 3-point-bending (SEN-3PB) test, based on ASTM D5045, was performed to obtain the mode-I critical stress intensity factor (Kic) of the neat epoxy and epoxy/a-ZrP nanocomposites. Care was taken to ensure that the initial sharp crack, generated by tapping with a fresh razor blade, exhibited a thumbnail shape crack front... 

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. 

In recent years impact testing of plastics has been rationalised to a certain extent by the use of fracture mechanics. The most successful results have been achieved by assuming that LEFM assumptions (bulk linear elastic behaviour and presence of sharp notch) apply during the Izod and Charpy testing of a plastic. 

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