A 3d Effect in the Wedge Adhesion Test: Application of Speckle Interferometry

Abstract

The wedge test is of considerable use for evaluating adhesion between two bonded rigid substrates. In its (usual) static form, release of elastic strain energy is equated to effective adhesion energy during crack growth. However, the test is usually treated as two-dimensional. In fact, it is really three-dimensional due to anticlastic bending effects of the bent beam(s) during crack propagation.We studied a composite material=epoxy=aluminium alloy system and observed a curved crack front during propagation. This leads to doubt as to the value of crack length to be inserted in the adhesion energy formula. In addition, by using the highly sensitive technique of speckle interferometry, it was possible to study anticlastic bending effects in a quantitative manner. Far from the crack front, agreement between theory and experimental is good, yet work remains to be done to understand the zone near the fracture zone.

Pre-cracking behaviour in the single cantilever beam adhesion test

“…However, in the case of the wedge test, in which the adherend(s) is (are) initially forced to curve, it is the strain energy associated with this curvature which is the direct source of energy required to propagate fracture (Kanninen 1973;Cognard 1986;Sener et al 2002;Blackman et al 2003;Popineau et al 2004;Sargent 2005;Budzik et al 2009). In the latter case, two rectangular sheets of material are bonded together and a 'wedge' inserted at one end of the structure, in order to force apart the two adherends over a short initial distance.…”

Crack Front Curvature in the Wedge Test

“…The process of minimisation of strain energy is regarded purely as a static, elastic effect. Although an increase of separation rate can either increase or decrease fracture energy, G c , the former is more usual and would tend to fit in better with the type of experiment under consideration [23,32,33]. (Decreasing fracture energy with increasing fracture speed tends to be associated with ''stick-slip'' behaviour.)…”

“…In the 3D version, the principle is, of course, the same, but we must also allow for elastic energy associated with curvature in the y direction. Although this effect was taken into account for the shape of the separated beam and crack length, it was overlooked in the earlier paper as far as fracture energy is concerned [23]. Using beam theory and invoking anticlastic bending in a straightforward manner, we may assimilate the transverse bending (direction y) to a moment mðyÞ ¼ ÀnMðxÞ and curvature w yy ¼ Ànw xx .…”

“…Comparison is made between the simple long beam and short beam [with pre-factor (1 À n 2 ) À1 ] models (both without crack front curvature), the finite element (FEA), and semi-analytic (semi-analytic) calculations. Whilst discussing fracture energy, it is instructive to compare Equation (16) with the earlier model, which assumed anticlastic bending directly [23]. In the elementary analysis of the wedge test, the adhesive fracture energy, G c , is obtained by equating this quantity to the rate of energy release which is a function of x and, therefore, a [see Equations (4) to (6)].…”

“…However, in many cases, such as Figure 1, the effect is certainly more widespread than being confined to the edges, passing across the entire joint width, from y ¼ þ b=2 to y ¼ À b=2. The effect shown in Figure 1 was studied in more detail using speckle interferometry [23]. Undoubtedly, a curvature effect was shown to be present and this was attributed to anticlastic bending [24] of the separated bending beam.…”