Modes of loading

In the case of rubbery adhesives values of the adhesive fracture energy measured under different modes of loading are shown [69,70] in Table 7.4. As expected the order of values for Gc is mode I mode II mode III. 

In the case of structural adhesives then joint fracture under mode II, combined mode I/II and mode III has been conducted by several groups [41,42,95-102,125-127] and some typical values are shown in Table 7.5. 

For the brittle DGEBA-TEPA adhesive the mode I value is the lowest with mode II being the highest and the mode II value may even be an underestimate since failure of the shear specimen employed did not occur by pure mode II. Indeed, it is usually extremely difficult to obtain crack growth under pure mode II conditions and, in practice, the fracture is locally in mode I. 

Commercial rubber-toughened epoxy-film adhesive 2.30 0.18 0.90 0.20 99,127 

DGEBA = diglyicdyl ether of bisphenol A epoxy resin. 

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Lack of accepted stress intensity factors for internally pressurized components has, until recently, limited this appHcation. The factors are a function of the size and shape of both cracks and high pressure components as well as modes of loading (91). Stress intensity factors can be derived analytically for some simple geometries, but most require the appHcation of advanced numerical methods (105—107). Alternatively they may be deterrnined experimentally (108). 

During filling, the catalyst is distributed uniformly to avoid the possibility of channeling that coiild lead to poor heat transfer, poor conversion, and harm to the catalyst because of hot spots. During startup, sudden surges of flow may disturb the bed and are to be avoided. For instance, in a study of a hydrodesulfuiizer by Murphree et al. (Ind. Eng. Chem. Proc. Des. size unit varied between 47 and 80 percent with different modes of loading and startup. 

Naturally, in most cases, we cannot neglect 8L/ , and must derive more general relationships. Let us first consider a cracked plate of material loaded so that the displacements at the boundary of the plate are fixed. This is a common mode of loading a material - it occurs frequently in welds between large pieces of steel, for example -and is one which allows us to calculate 8Lf quite easily. 

The study on commercial HDPE samples could not provide a correlation of the izod impact test with the field performance test, i.e., drop impact resistance on moulded products [113]. It was found that the sample of highest density and lowest izod impact strength passed the drop impact test, but other samples of lower density and higher izod impact strength could not withstand shock loading by drop impact and failed in brittle manner. This may be due to the fact that velocities and modes of loading vary widely in different impact tests. It has been reported that even the qualitative agreement between the different impact tests is poor because the test bars and moulded products often have different orientation characteristics, particularly near the surface [115]. 

Mechanical testing was conducted on samples 25 mm in length, 10 mm in width and 0.1 mm in thickness, Because of the high compliance of the films, it was difficult to mount an extensometer on the samples to measure E. A DMA was therefore used to assess the elastic properties of the composite samples in the tensile mode of loading. A 5 N static tensile load and displacement amplitude of 16 /tm at a frequency of 1 Hz were applied. Nine measurements for each sample were made and the average values are reported here. 

In Charpy-like tests, a severe triaxial stress state prevails at the sample crack tip. Softer modes of loading can be of interest for specific applications. Biaxial tests like impact falling weight are therefore often used. Plaques of defined dimensions are impacted with a hemispherically tipped dart of given diameter at selected test speed(s) (often 3 ms-1 and more). 

Hydrogen embrittlement in steels can be manifested under different modes of mechanical loading, i.e., static, monotonically increasing, or cyclic. The severity of hydrogen embrittlement can depend on the specific mode of loading, e.g., static vs. monotonically increasing, as well as variations in one type of loading. 

Xu G., Argon A. S. and Ortiz M., Nucleation of Dislocations from Crack Tips under Mixes Moded of Loading Implications for Brittle vs Ductile Behavior of Crystals, Phil. Mag. 72, 415 (1995). Xu G., Argon A. S. and Ortiz M., Critical Configurations for Dislocation Nucleation, Phil. Mag. 75, 341 (1997). 

Thus, the development of brittle fracture does not occur on a counter mechanism (as opposed to the start of brittle fracture), and is directly related to the growth of the main crack (macrocrack). By this means the possibility exists to use the concept of fracture mechanics, which reduces to the solution of the left-hand side of the formulas (3.9) and (3.10) (the parameters K, G, depending on the mode of loading design), and the right—the critical values that characterize the material s properties. 

The stresses at the crack tip for forward shearing (mode 11) and longitudinal shearing (mode 111) modes of loading may be similarly obtained [1]. The stresses for mode II are given by Eqn. (3.30) as follows ... 

Figure 3. The three modes of loading near a crack tip.

Note of the author That is why center-point loading is the most severe one among the three modes of loading, and ultimate load (break-point load) for center-point... 

As it was shown above, center-point loading is the most severe among the three modes of loading—center-point, third-point, and quarter-point loading. Theoretically, ultimate load (break-point load) for center-point load should be 1.5 times lower compared to third-point load, when the same materials and profiles are fesfed. In reality, there might be some slight deviations from this coefficient due to anisotropicity of materials, too short support span (i.e., a noticeable effect of shearing compared to flexural), nonflat position of a specimen, and so forth. 

In addition to the continuous loading and unloading procedure, a stepwise mode of loading was also applied. 

Detailed derivations of the relationship similar to Eq. 14 can be found in the literature [16.54.55]. Double-torsion specimens [56.57] are convenient, because of their geometry and the mode of loading, for the study of crack growth rates under a fixed load, where G and K remain constant, i.e., independent of the crack length. 

The mode III toughness has been shown to be as important as the other two modes for delamination between angle plies [152]. Test method development for this mode of loading... 

Typical values for the fracture toughness 0 of various adhesives under dilTerent modes of loading are given in the literature [179.180] including fatigue fracture data [180], The references also provide data on work of adhesion for various interfaces and environments. 

The failure of adhesive joints depends on the combination of peel and shear loading. In fracture mechanics, three basic modes of loading (Fig. 6.10) are the following ... 

Figure 6.10 Basic modes of loading on cracks (left to right Mode I, Mode II, Mode ni).

For certain simple specimen geometries and modes of loading, there are analytical solutions for the stress intensity factor. For a central crack of length la in an infinitely wide sheet, subjected to a distant tensile stress [Pg.270]

Blackman BRK, Kinloch AJ, Rodriguez-Sanchez FS, Teo WS. The fracture behaviour of adhesively-bonded composite joints effects of rate of test and mode of loading. Int J Solids Struct 2012 49 1434-52. http //dx.doi.org/10.1016/ j.ijsolstr.2012.02.022. 

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