Debond energy

Ti Interface debond energy % Critical stress for interlaminar... 

Debond energy, (J m 2) Permanent strain, ep Residual crack opening, up 0-5... 

Noting that most ceramic fibers have a fracture energy, ry == 20 J m-2, Eqn. (2) indicates that the upper bound of the debond energy T, = 5 J m-2. This magnitude is broadly consistent with experience obtained on fiber coatings that impart requisite properties.20,40" 3... 

Measurements of the sliding stress, t, and the debond energy, T, have been obtained by a variety of approaches (Table 1.1). The most direct involve displacement measurements. These are conducted in two ways (1) fiber push-through7push-in, by using a small-diameter indentor 33 38,39 and (2) tensile loading in the presence of matrix cracks,5,44,45 Indirect methods for obtaining r... 

A traction law crb(u) is now needed to predict rw. A law based on frictional sliding along debonded interfaces has been used most extensively and appears to provide a reasonable description of many of the observed mechanical responses (Eqn. 1). The traction law also includes effects of the interface debond energy, T,.1 For many CMCs, T, is small, as reflected in the magnitude of the debond stress, 2,-. 

Analyses of the plastic strains caused by matrix cracks, combined with calculations of the compliance change, provide a constitutive law for the material. The important parameters are the permanent strain, e0 and the unloading modulus, E. These quantities, in turn, depend on several constituent properties the sliding stress, r, the debond energy, T, and the misfit strain, il. The most important results are summarized below. 

Small Debond Energy. For SDE, when cr< crs, the unloading modulus E depends on r0, but is independent of T, and Cl. However, the permanent strain e0 depends on T, and Cl, as well as r0. These differing dependencies of E and e0 on constituent properties have the following two implications. (1) To simulate the stress-strain curve, both e0 and E are required. Consequently, r0, T, and Cl must be known. (2) The use of unloading and reloading to evaluate the constituent properties has the convenience that the hysteresis is dependent only on tq. Consequently, precise determination of r0 is possible. Moreover, with t0 known from the hysteresis, both T,- and Cl can be evaluated from the permanent strain. The principal SDE results are as follows. 

Large Debond Energy. For LDE (Fig. 1.23), when cr< crs, the unloading modulus depends on both r and T, (Fig. 1.26). There are also linear segments to the unloading and reloading curves. These segments can be used to establish... 

Two representative probe test curves for the detachment of an SIS adhesive from steel and from EP surfaces are shown in Pig. 22.17 while the initial portion of the curve is identical, the force drops rapidly to zero for the EP surface, and never forms the characteristic fibrillar plateau observed on steel surfaces. How does this happen As qualitatively described by Creton et al. [55] for a detachment from a polydimethylsiloxane layer, when the resistance to crack propagation is low, cavities are nucleated (around the peak stress) and then propagate as interfacial cracks at the interface between the probe and the adhesive, and eventually coalesce. This process of crack propagation and coalescence is responsible for the sharp drop in force observed in Fig. 22.17 for the EP surface and occurs at rather low values of nominal strain. In this case no formation of the characteristic foam stracture responsible for the high debonding energy is observed. 

For probe tack, the newly measured debonding energies constitute a new dimension for short duration performance. In addition to the peak force, tack energy should be considered in many high speed applications. Since the peak force and tack energy appeared to have originated from different parts of the viscoelastic spectra, it offered an opportunity to adjust the formulation for optimum performance. 

More direct measures of interface debonding energy are provided by the pull-out or push-out tests shown in Fig. 16.26. When a tensile force is applied to a fiber to extract it from its composite matrix, an interface crack eventually starts to run along the fiber. It is obvious from a simple fracture mechanics argument that the stress on the fiber to propagate the crack, assuming a very compliant matrix, must be given by an expression of the form... 

The occurrence of one or the other of these processes will depend on a delicate balance between the tensile properties of the adhesive and the interfacial parameter, Despite the fact that the level of stress and the maximum extension that these fibrils will achieve often controls the amount of work necessary to debond the adhesive (the external work done during this process can sometimes represent up to 80% of the practical debonding energy), no quantitative analytical treatment of this extension and fracture process exists for such highly non-linear materials. Numerical methods have, however, been successful in predicting at least the extensional behavior if not the point of fracture [29,30]. 

Fig, 9. Debonding energy, W, as a function of temperature for probe tack tests of different acrylic polymers. , Poly(2-ethylhexyl acrylate) o. poly(n-butyl acrylate) , polyfisobutyl acrylate) a, poly(ethyl acrylate) , poly(methyl acrylate). Contact time 0.02 s. Data from [34. ... 

E should be in a window of 0.01-0.1 MPa. Above that level, proper bonding and fibril formation are reduced and below that level, viscoelastic dissipation during the debonding process will be too low. controls the maximum extension of the fibrils and therefore plays a major role in the measured debonding energy. A relatively small e iax is typically desirable for removable PSA, while a larger value is often characteristic of semi-permanent ones. A reasonable idea of the value of iix can, in principle, be obtained by a characterization of the adhesive in elongational deformation. 

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