Mixed-mode deformation

The friction of polymers or CMP processes can be attributed to two major sources in mixed modes deformation involving the dissipation of energy in quite a large volume around the local area of contact, and adhesion originating from the interface between the wafer and the pads (brush). The details of the deformation and adhesion will be discussed in Chapter 5, along with a clear schematic illustration. 

The mixed mode of sorption of the dye l,l -dioctadecyl-3,3,3, 3 -tetramethylindocar-bocyanine pechlorate (Dil) at the interface of an ODS stationary phase and ACN-water mobile phase was studied by single-molecule resolution and fluorescence imaging techniques. The measurements indicated that minimally four types of adsorption sites are present on the surface of the ODS stationary phase. The desorption times of the dye are different at the different adsorption sites resulting in a deformed peak shape [152],... 

Comprehensive structural study of Ti-3Al-5Zr-Si-alloys, as-cast and deformed, confirmed the features found with the binary Ti-Si-system described above. The transition from polygonal to dendritic structure takes place between 2- and 4-wt.% Si. Alloy with 2-wt.% Si fails with intergranular (but ductile) mode whereas alloys with 4- and 6-wt.% fail with mixed mode where dendritic structure may be recognized. In any case, eutectic areas, in contrast to dendrite or polygonal bodies, which are of a-phase failing with cleavage microcracking, fail with ductile mode - with voids coalescence (Fig. 8). Hot plastic deformation transforms the alloys studied into ductile or semi-ductile materials, which fail only with ductile void coalescence mode [1],... 

Protein Structure. In the IR spectrum, the absorption bands due to the proteiu backbone, consisting of amide groups R—CON—R and side-chain modes, are distinguishable. The amide A band at 3300 cm is due to N—H stretching. The absorption bands in the 1600-1700, 1510-1580-, and 1200-1350-cm regions are labeled amide I, II, and III (marked with a prime in the case of deuteration), respectively. Normal coordinate analysis [801, 802] has revealed that amide I is primarily (76%) the v C=0 mode with some contribution from CN (14%) and CCN (10%) deformation. In contrast, amide 11 and amide 111 are heavily mixed modes. The amide II is an out-of-phase combination of 5 pnH (43%) and v CN (29%) with minor contributions from 5 PC=0, v,yC—C, and v,fN—C. The amide III is an in-phase combination of 5 pN-H (55%) with some contributions from v C—C (19%), v C—N (15%), and 5 pC=0. The amino acid side-chain absorption (due to groups such as C—H, COOH, C=0, —NH2, and —NH3+) overlaps in many cases with amide I and II absorption. 

A mixed-mode criterion for failure of the cohesive zone under different extents of mode-mixedness is also required. Under pure mode-I and pure mode-Il conditions, the failure criterion appears to be simple it is given by the conditions at which the tractions of the relevant cohesive law are reduced to zero ( i = / and ii = /lio, respectively). Mixed-mode criteria are much less obvious since the two modes of deformation may both contribute to failure together. An empirical relationship that has some physical appeal, and appears to capture some of the characteristics of experimental observations in this area is given by Wang and Suo [52]... 

Fracture tests on adhesive joints are always more complex than tests on bulk adhesive specimens and a G rather than a K approach is invariably followed for their analysis. The adhesive is present as a thin layer, it may be constrained by the presence of nearby substrates and the failure paths may be influenced by the poor adhesion with the substrate. Fracture tests on adhesive joints are commonly conducted in mode I (tensile opening mode), mode II (inplane shear mode), and mixed-mode I/n (combinations of mode I and n). The key to success in all LEFM fi"acture mechanic tests is to ensure that the substrates do not deform plastically during loading. Plastic deformation of the substrates would violate the assumptions of LEFM and invahdate the results. In mode I, the DCB and TDCB test specimens are almost universally employed and these tests have been standardized. Either test maybe used for the determination of Gic- The choice of which to use is likely to depend upon factors such as the toughness of the adhesive, the properties of the substrate material employed, and whether or not crack length... 

Liechti KM, Freda T (1989) On the use of laminated beams for the deformation of pure and mixed mode fracture properties of structural adhesives. J Adhes 29 145-169... 

The fatigue crack growth behavior of a structural adhesive is very sensitive to the mixed mode I/n conditions. The fractographic analysis revealed that energy dissipation mechanisms due to inelastic phenomena like bulk plastic deformation and crazing are more pronounced in... 

Step 3. The set of fracture properties G(t) are related to the interfaee structure H(t) through suitable deformation mechanisms deduced from the micromechanics of fracture. This is the most difficult part of the problem but the analysis of the fracture process in situ can lead to valuable information on the microscopic deformation mechanisms. SEM, optical and XPS analysis of the fractured interface usually determine the mode of fracture (cohesive, adhesive or mixed) and details of the fracture micromechanics. However, considerable modeling may be required with entanglement and chain fracture mechanisms to realize useful solutions since most of the important events occur within the deformation zone before new fracture surfaces are created. We then obtain a solution to the problem. 

The stored strain energy can also be determined for the general case of multiaxial stresses [1] and lattices of varying crystal structure and anisotropy. The latter could be important at interfaces where mode mixing can occur, or for fracture of rubber, where f/ is a function of the three stretch rations 1], A2 and A3, for example, via the Mooney-Rivlin equation, or suitable finite deformation strain energy functional. 

IR differences key on frequencies of band maxima and band widths, whereas VCD varies in terms of band shapes associated with those IR transitions, thus being secondarily influenced by frequency and width as well. Two strong bands, the amide I and II, dominate the mid-IR, whereas the amide III is weak and mixed with local CaH deformation modes, spreading its small intensity over a broad region (Diem et al, 1992 Baello et al., 1997 Asher et al., 2001). 

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