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 ... 

The two most common specimen types used to measure fracture toughness are (a) the three-point bend specimen shown schematically, and (b) the compact specimen shown mounted in grips with a clip gage extensometer attached. Panel (c) shows a schematic diagram of various types of load vs displacement plots describing the determination of an LEFM test (ASTM, 2013c). 

This assumes a fully plastic ligament and ignores elastic effects hut does allow J to be foimd in the fully plastic case. In fact, this form is true when elastic energy is included, provided thatL/W = 4. This analysis has been widely employed for measuring the toughness of very tough materials since the stress state in the ligament is very close to plane strain for the three-point bend test. Thus, the Jc measured at crack initiation should be the same as Gc in an LEFM test. The specimens may be much smaller and the size criterion is... 

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. 

Secondly, the same rubber-toughened epoxy adhesive as was used for the T-peel tests [45] discussed in Section 3.3 has also been studied [51,57] using a LEFM test specimen, i.e. the standard tapered-double cantilever-beam specimen [58]. At the same rate of test and for the same locus of joint failure, a value of Gc of 2750 100 J/m was determined using the LEFM test, compared with a value 2900 400 J/m from the T-peel tests. Thus, here we have completely different test geometries giving the same value of Gc. So, again, a cross-check indicates the robustness of the above analytical approach for modelling the peel test. 

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 ... 

Broeklehurst [37] has written an exhaustive review of the early work (prior to 1977) on fracture in polyerystalline graphite. Mueh of this work foeused on the fraeture behavior of nuclear graphites. In most investigations eonsidered, conventional fracture meehanies tests and analysis were performed for maeroseopie craeks. LEFM provided an adequate eriterion for failure. Additionally, results on work of fraeture, strain energy release rate, and fatigue eraek propagation were reported. 

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. 

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... 

Figures 19 and 20 summarize the fracture behavior of the previously mentioned PP with MFR 12 dg min 1 in between -30 and 60 °C. Details concerning the experimental procedure, the F-d curves and the data reduction according to the principles of the LEFM are given in [77]. The aim of this section is to correlate the relative capacity of both systems to absorb input energy up to a deformation corresponding to Fmax (Gini) and up to fracture (Gtot Fig. 19) with their deformation maps deduced from their Fd-curves and careful observation of their fracture surfaces (Fig. 20). To take implicitly into account variations in specimen stiffness, arising from variations in temperature and rate dependence of the modulus the test rate was sometimes expressed in terms of the crack tip loading rate, dK/dt, given by ...

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. 

Ductile-brittle transitions are more accurately located by variable temperature tests than by altering impact speed in an experiment at a fixed temperature. This is because a linear fall in temperature is equivalent to a logarithmic increase in straining rate. The ductile-brittle transition concept can be clarified by sketches such as that in Fig. 11-25. In the brittle region, the impact resistance of a material is related to its LEFM properties, as described above. In the mixed mode failure... 

Although material ranking was successful and corresponded to application tests using a conventional LEFM approach, ways to get geometry independent material descriptors have to be found. We will describe in next section the method we used to achieve it. 

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. 

There is a transition in the impact behaviour of both HIPS and ABS at low temperatures. At 20 °C, the entire fracture surface is stress-whitened, indicating a tou fracture which cannot be analysed by LEFM methods. At lower temperatures, however, whitening is confined to a small area near the base of the notch, and experiments have shown that this type of fracture can be described by LEFM. The point is illustrated in Fig. 14, which presents data obtained by Bucknall and Reid in Charpy tests on razor-notched HIPS specimens. At -25 °C, impact strength / is proportional to BWZ, as predicted by Eq. (15). At 40 °C, on the other hand, there... 

For the experimental determination of LEFM parameters, compact tension (CT) and single edge notched (SEN) bending specimens are commonly used. According to the European Structural Integrity Society (ESIS) test protocol (59) and standard practices (60,61), A) under mode I can be determined from the load-displacement curves according to the relationship ... 

---