Scarfed adherends

The design analysis of a scarf may be considered similar to a single lap bonded joint, detailed analysis of which can be found in MIL-HDBK 17-3E 3. The analysis of a bonded joint is made complex, however, by the modulus difference of the adhesive compared to the adherends and the relative thicknesses of both which causes a non-linear distribution of the shear forces in a lap joint with peak stresses at the ends [1]. Scarf repairs provide a more uniform stress distribution however, to achieve this an adequate scarf angle is required [24] shown in Eigure 14.6. 

Recent theoretical studies have become much more complex. New computer-assisted techniques permit the use of finite-element matrix-theory type approaches. The effects of important variables are being determined by parametric studies. More complex joints are also being studied. New adherend materials, including advanced filamentary composites, are also being evaluated. The elastic, low-deflection, constant temperature behavior of scarf and stepped-lap joints has been replaced by elastic-plastic, large-deflection behavior, combined with thermal expansion differences, or curing shrinkage-induced residual stresses. 

Feathering—The tapering of an adherend on one side to form a wedge section, as used in a scarf joint... 

Joint, scarf—A joint made by cutting away similar segments of two adherends at an angle less than 45° to the major axis of two adherends and bonding the adherends with the cut areas fitted together to be coplanar. 

In the case of laminate thicknesses below 5 mm the use of scarf and step-lap configurations shall be considered with care, as producing the required shapes on the adherends may become complicated. Also the bonding may become impossible if adequate jigging cannot be provided, see 5.3,5,11. 

P(7) Knife edges are not allowed in scarf joints. The adherend ends should have a minimum thickness of 1.0 mm. 

P(2) Instead of butt joints a strap, scarf or lap joint configuration shall be used (see Figure 5.41). The joint design is then undertaken according to the procedures for strap or scarf joints respectively. When using strap configurations the adherend ends shall also be bonded. 

P (10) If scarf Joints or step lap Joints are used with adherend thicknesses of less than 5 mm, proper Jigging shall be used during bonding to guarantee an adequate bondline quality. 

Although the joggle lap joint allows shear stresses to be in the same plane as the bonded parts, it does not combine tensile and shear stresses in line with adherends. The double-butt lap joint, the recessed and landed-scarf joint, and the tongue-and-groove butt joint combine both types of stresses in line and, therefore, are recom-mended ... 

Flexible plastics and elastomers. Thin or flexible polymeric substrates may be joined using a simple or modified lap joint. The double strap joint is best, but it is also the most time consuming to fabricate. The strap material should be made out of the same material as the parts to be joined or at least have approximately equivalent strength, flexibility, and thickness. The adhesive should have the same degree of flexibility as the adherends. If the sections to be bonded are relatively thick, a scarf joint is acceptable. The length of the scarf should be at least four times the thickness sometimes, larger scarfs may be needed. 

The second point to be established is the joint configuration — doublelap, single-lap, stepped-lap, or scarfed, as indicated in Fig. 37. The thicker the adherends, the more complicated the joint design needs to be and, conversely, the thinner the adherends, the simpler the joint configuration can be. 

THE EFFECT OF ADHEREND SHAPE—SCARFED, BEVELLED AND STEPPED ADHERENDS... 

It may be useful to the reader to consider as an example the work by Adams et al (1978c) and some of their hitherto unpublished results. They used finite-element methods to examine the stresses in high-performance composites in symmetrical lap joints with parallel, bevelled, scarfed and stepped adherends. The composite adherends were assumed to be linearly elastic type II carbon fibre reinforced epoxy composites with a 60% fibre volume fraction. The mechanical properties of this material are given in Table 3. 

If we now allow for non-linear adhesive behaviour, the high adhesive stress concentrations predicted by the linear elastic analysis will be relieved to some extent. Figure 54 shows the predicted spread of the yield zone of adhesive at the tension end of a double-lap joint as the load is increased. As would be expected, plastic flow begins near the adherend corner and the load corresponds to a joint efficiency of 21%. Each subsequent load increment represents an increase in joint efficiency of 4 4%. When elastic perfectly-plastic behaviour is assumed for the adhesive, a maximum strain criterion for failure seems appropriate. In Fig. 55 the joint efficiency is plotted against the maximum principal strain in the adhesive at each end of a double-lap joint. Assuming a failure strain for the adhesive of 5%, the analysis predicts a joint efficiency of 31% for a double-lap joint compared with 16% predicted by the linear elastic analysis. Similarly, the non-linear analysis predicts an efficiency of 39% for the double-scarf joint compared with 20% predicted by the linear elastic analysis. Although the predicted efficiencies are almost doubled by allowing for non-linear behaviour in the adhesive, failure in the adhesive is still predicted to be more probable than failure in the adherends (Table 5). 

Although the adhesive fails in tension at the end of the joint, most of the load is transferred in the overlap region. It is, therefore, instructive to examine the effect of non-linear behaviour on the adhesive shear stress distribution. The shear stress distributions corresponding to maximum adhesive strains of 10% and 20% in a double-lap joint are shown in Fig. 56(a). The shear stress distributions are only modified significantly at high values of maximum adhesive strain, by which time the joint is likely to have failed. The adherend cTx stress concentrations are reduced, but not significantly, by plastic flow in the adhesive. For a double-scarf joint, the elastic shear stress distributions are similarly modified by yielding of the adhesive (see Fig. 56(b)). 

The effect of scarfing the adherends (Fig. 60) is to unbalance the stress concentrations to such an extent that they are much higher at the compression end than at the tension end of the joint. Although the maximum shear stress is about 7% less than in a double-lap joint, the adhesive fillets of the scarf joint are much smaller, giving a 9% higher stress concentration (Table 6). 

Adams and Peppiatt (1977) used the finite-element technique to determine the stresses in tubular lap joints loaded in tension or torsion and were able to obtain realistic results for stress concentrations by allowing for the stress-relieving effect of the fillet. They showed that, in the axial load case, the stress concentrations predicted from the finite-element models with the fillet have been shown to be greater than those predicted by the Lubkin and Reissner theory. This is because the closed-form solution does not evaluate the true stress concentrations, i.e. those caused by end effects. The influence of the adhesive fillet on the stress concentrations in the torsional case is shown to be less significant, as the stress concentration values from the closed-form theory are of similar size to those predicted by the finite-element models. They also investigated the effects of partial tapering of the adherends to form a scarf joint. It was concluded that the reductions in stress concentration obtained with this form of joint do not make its manufacture for this reason alone worthwhile, and in the axial case the reductions in the stress concentration were not found to be significant. 

---