Interfacial shear moduli

Figure 1.9 Interfacial shear moduli (elastic = solid lines viscous = dotted lines) for protein alone (P) and protein + surfactant (P + S) at the oil/water interface.

Extending the analogy with bulk rheology, for linear shear deformation of an interface it is possible to define a surface (or interfacial) shear viscosity rj° and a surface (or interfacial) shear modulus G°. In a Cartesian co-ordinate system, with again the z-axis normal to the interface... 

Shear deformations. In these tests the Interface Is deformed in shear to a certain extent or at a certain rate and the shear stress required is measured as a function of the shear strain and/or time. The interfacial shear modulus G or the Interfaclal shear viscosity t]° cem be calculated using [3.6.17] or [3.6.16], respectively. By analogy to the technique described above, stress relaxation experiments can also be carried out from these one Ccm obtain an interfacial shear stress relaxation modulus G ] ) = y(t)/(Ax/Ay). For solld-llke interfacial layers fracture can be studied as a function of time by deforming the interface at various shear rates and measuring the required shear stress as a function of the shear strain. 

Interfacial shear properties can be determined either by steady state or by oscillatory measurements (see sec. 3.6f). In the latter case dynamic shear moduli are obtained in the former the interfacial shear modulus or the interfacial shear viscosity is obtained. 

Moreover, this model can also involve parameters that refer to the interfacial rheological properties, such as the interfacial dilation modulus and the interfacial shear modulus (Jacobs et al. 1999). Consequently, quantitative measurements of... 

The influence of compatibilizer concentration on the two relaxation times also was analyzed by Van Hemelrijck et al. (2004). They have fitted the Palierne model with an interfacial shear modulus by introducing a concentration gradient of the block copolymer along the interface. Figure 1.3 presents the dynamic moduli of compatibilized blends—polydimethylsiloxane (PDMS)/polyisoprene (PI)—at various ratios of compatibilizers versus angular frequency (Van Hemelrijck et al. 2005). 

The ratio (p/G) has the units of time and is known as the elastic time constant, te, of the material. Little information exists in the published literature on the rheomechanical parameters, p, and G for biomaterials. An exception is red blood cells for which the shear modulus of elasticity and viscosity have been measured by using micro-pipette techniques 166,68,70,72]. The shear modulus of elasticity data is usually given in units of N m and is sometimes compared with the interfacial tension of liquids. However, these properties are not the same. Interfacial tension originates from an imbalance of surface forces whereas the shear modulus of elasticity is an interaction force closely related to the slope of the force-distance plot (Fig. 3). Typical reported values of the shear modulus of elasticity and viscosity of red blood cells are 6 x 10 N m and 10 Pa s respectively 1701. Red blood cells typically have a mean length scale of the order of 7 pm, thus G is of the order of 10 N m and the elastic time constant (p/G) is of the order of 10 s. 

For effective demulsification of a water-in-oil emulsion, both shear viscosity as well as dynamic tension gradient of the water-oil interface have to be lowered. The interfacial dilational modulus data indicate that the interfacial relaxation process occurs faster with an effective demulsifier. The electron spin resonance with labeled demulsifiers suggests that demulsifiers form clusters in the bulk oil. The unclustering and rearrangement of the demulsifier at the interface may affect the interfacial relaxation process. 

In the macrocomposite model it is assumed that the load transfer between the rod and the matrix is brought about by shear stresses in the matrix-fibre interface [35]. When the interfacial shear stress exceeds a critical value r0, the rod debonds from the matrix and the composite fails under tension. The important parameters in this model are the aspect ratio of the rod, the ratio between the shear modulus of the matrix and the tensile modulus of the rod, the volume fraction of rods, and the critical shear stress. As the chains are assumed to have an infinite tensile strength, the tensile fracture of the fibres is not caused by the breaking of the chains, but only by exceeding a critical shear stress. Furthermore, it should be realised that the theory is approximate, because the stress transfer across the chain ends and the stress concentrations are neglected. These effects will be unimportant for an aspect ratio of the rod Lld> 10 [35]. 

Stress/strain behaviour in the elastic region, i.e. below the yield stress, as a function of volume fraction, 4>, contact angle, 0, and film thickness, h, was examined [51]. The yield stress, t , and shear modulus, G, were both found to be directly proportional to the interfacial tension and inversely proportional to the droplet radius. The yield stress was found to increase sharply with increasing <(>, and usually with increasing 6. A finite film thickness also had the tendency to increase the yield stress. These effects are due to the resulting increase in droplet deformation which induces a higher resistance to flow, as the droplets cannot easily slip past one another. 

Imposing a shear stress parallel to the fiber axis of a unidirectional composite creates an interfacial shear stress. Because of the disparity in material properties between fiber and matrix, a stress concentration factor can develop at the fiber-matrix interface. Linder longitudinal shear stress as shown by the diagram in Fig. 13, the stress concentration factor is interfacial. The analysis shows that the stress concentration factor can be increased with the constituent shear modulus ratio and volume fraction of fibers in the composite. Under shear loading conditions at the interface, the stress concentration factor can range up to 11. This is a value that is much greater than any of the other loadings have produced at the fiber-matrix interface. 

Two different polyacrylonitrile precursor carbon fibers, an A fiber of low tensile modulus and an HM fiber of intermediate tensile modulus were characterized both as to their surface chemical and morphological composition as well as to their behavior in an epoxy matrix under interfacial shear loading conditions. The fiber surfaces were in two conditions. Untreated fibers were used as they were obtained from the reactors and surface treated fibers had a surface oxidative treatment applied to them. Quantitative differences in surface chemistry as well as interfacial shear strength were measur-ed. 

G denotes the shear modulus and a is the specific interfacial energy. In the sense of Eqn. (6.8), we can use Eqn. (12.5) to calculate the activation energy for the nucleation of martensite. Normally, AGtr >RT, which implies that martensite nucleation is unlikely to be induced by thermal fluctuations. We conclude that the nucleation is heterogeneous and dislocation arrays are the nucleation sites. 

Here we have conducted experiments to develop an understanding of how the commercial size interacts with the matrix in the glass fiber-matrix interphase. Careful characterization of the mechanical response of the fiber-matrix interphase (interfacial shear strength and failure mode) with measurements of the relevant materials properties (tensile modulus, tensile strength, Poisson s ratio, and toughness) of size/matrix compositions typical of expected interphases has been used to develop a materials perspective of the fiber-sizing-matrix interphase which can be used to explain composite mechanical behavior and which can aid in the formulation of new sizing systems. 

The fiber modulus and matrix shear modulus are also required for the analysis. The fiber s coordinates are recorded directly from the stage controllers to the computer. The operator begins the test from the keyboard. The x and y stages move the fiber end to a position directly under the debonder tip the z stage then moves the sample surface to within 4 yum of the tip. The z-stage approach is slowed down to 0.04 jan/step at a rate of 6 steps/s. The balance readout is monitored, at a load of 2 g the loading is stopped, and the fiber end returned to the field of view of the camera. The location of the indent is noted and corrections are made, if necessary, to center the point of contact. Loading is then continued from 4 g in approximately 1 g increments. Debond is determined to have occurred when an interfacial crack is visible for 90-120° on the fiber perimeter. The load at which this occurs is used to calculate the interfacial shear stress at debond. 

The strength of adhesion between the fiber and matrix could also be expected to play a role in this change in failure mode. The interfacial testing system (ITS) provides comparative data on the interfacial shear strengths of the bare and sized E-glass fibers in real composites. A handbook value of 76 GPa [19] was used for the tensile modulus of E-glass fibers and the matrix shear modulus was previously determined as 1.10 GPa. Table 4 lists the mean interfacial shear strength, standard deviation (SD), and number of fiber ends tested for the two fiber types. 

The increase in fiber-matrix interfacial shear strength can be predicted from a purely mechanistic viewpoint. Rosen [20], Cox [21], and Whitney and Drzal [22] have shown that the square root of the shear modulus of the matrix appears explicitly in any model of the interfacial shear strength. It has been demonstrated experimentally [23, 24] that the fiber-matrix interfacial shear strength has a dependence on both the product of the strain-to-failure of the matrix times the square root of the shear modulus and on the difference between the test temperature and Tg when the interfacial chemistry is held constant. 

In (15.36) rm is the matrix fracture energy, t is the interfacial shear strength, and Ex is the axial modulus of the composite. In (15.37) e refers to the effective properties of the composite, which, for unidirectional fiber reinforcement, can be calculated with good approximation by the rule of mixtures. 

Experimental load deflection curves (Fig. 3.) illustrate the large difference in crack propagation observed in each case. A difference in stiffness between both bonded specimens is observed and results from either a difference in the bond line quality or from interfacial conditions. For both specimens, adherends were made from the same sample of wood. Both wood substrates contained no apparent defects and had the same longitudinal Young s modulus (14500 MPa). Both also had the same growth characteristics (oven dry specific density, annual growth rings), and as a consequence very close values of transverse and shear modulus adjacent to the bond line. Thus, any difference in stiffness is likely to be due to... 

---