MIL-HDBK-17-3F Volume 3.Chapter 6 Structural Behavior of Joints cause the eccentricity of this type of geometry generates significant bending of the adherends that magni- fies the peel stresses.Peel stresses are also present in the case of symmetric double lap and double strap joints,and become a limiting factor on joint performance when the adherends are relatively thick. Tapering of the adherends (Figure 6.2.2.1(a)-Joints (D)and (G))can be used to eliminate peel stresses in areas of the joint where the peel stresses are tensile,which is the case of primary concern. No tapering is needed at ends of the overlap where the adherends butt together because the transverse normal stress at that location is compressive and rather small.Likewise,for double strap joints under compressive loading,there is no concern with peel stresses at either location since the transverse exten- sional stresses that do develop in the adhesive are compressive in nature rather than tensile;indeed, where the gap occurs,the inner adherends bear directly on each other and no stress concentrations are present there for the compression loading case. For joints between adherends of identical stiffness,scarf joints (Figure 6.2.2.1(a)-Joint(I))are theo- retically the most efficient,having the potential for complete elimination of stress concentrations.(In prac- tice,some minimum thickness corresponding to one or two ply thicknesses must be incorporated at the thin end of the scarfed adherend leading to the occurrence of stress concentrations in these areas.)In theory,any desirable load capability can be achieved in the scarf joint by making the joint long enough and thick enough.However,practical scarf joints may be less durable because of a tendency toward creep failure associated with a uniform distribution of shear stress along the length of the joint unless care is taken to avoid letting the adhesive be stressed into the nonlinear range.As a result,scarf joints tend to be used only for repairs of very thin structures.Scarf joints with unbalanced stiffnesses between the ad- herends do not achieve the uniform shear stress condition of those with balanced adherends,and are somewhat less structurally efficient because of rapid buildup of load near the thin end of the thicker ad- herend. Step lap joints(Figure 6.2.2.1(a)-Joint(H))represent a practical solution to the challenge of bonding thick members.These types of joint provide manufacturing convenience by taking advantage of the lay- ered structure of composite laminates.In addition,high loads can be transferred if sufficiently many short steps of sufficiently small "rise"(i.e.,thickness increment)in each step are used,while maintaining suffi- cient overall length of the joint. 6.2.2.3 Effects of adherend stiffness unbalance All types of joint geometry are adversely affected by unequal adherend stiffnesses,where stiffness is defined as axial or in-plane shear modulus times adherend thickness.Where possible,the stiffnesses should be kept approximately equal.For example,for step lap and scarf joints between quasi-isotropic carbon/epoxy (Young's modulus=8 Msi(55 GPa))and titanium(Young's modulus 16 Msi(110 GPa)) ideally,the ratio of the maximum thickness(the thickness just beyond the end of the joint)of the compos- ite adherend to that of the titanium should be 16/8=2.0. 6.2.2.4 Effects of ductile adhesive response Adhesive ductility is an important factor in minimizing the adverse effects of shear and peel stress peaks in the bond layer.Figure 6.2.2.4(a)reconstructed from Reference 6.2.2.4(a)shows the shear stress-strain response characteristics of typical adhesives used in the aerospace industry as obtained from thick adherend tests(Volume 1,Section 7.3).Figure 6.2.2.4(a),part(A)represents a relatively duc- tile film adhesive,FM73,under various environmental conditions,while Figure 6.2.2.4(a),part(B)repre- sents a more brittle adhesive (FM400)under the same conditions.Similar curves can be found in other sources such as Reference 6.2.2.4(b).Even for the less ductile material such as that represented in Fig- ure 6.2.2.4(a),part(B),ductility has a pronounced influence on mechanical response of bonded joints, and restricting the design to elastic response deprives the application of a significant amount of additional structural capability.In addition to temperature and moisture,effects of porosity in the bond layer can have an influence on ductile response.Porosity effects are illustrated in Figure 6.2.2.4(b)(Reference 6.2.1(s))which compares the response of FM73 for porous(x symbols)and non-porous(diamond sym- bols)bond layers for various environmental conditions.This will be further discussed in Section 6.2.2.6. 6-5MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-5 cause the eccentricity of this type of geometry generates significant bending of the adherends that magni￾fies the peel stresses. Peel stresses are also present in the case of symmetric double lap and double strap joints, and become a limiting factor on joint performance when the adherends are relatively thick. Tapering of the adherends (Figure 6.2.2.1(a) - Joints (D) and (G)) can be used to eliminate peel stresses in areas of the joint where the peel stresses are tensile, which is the case of primary concern. No tapering is needed at ends of the overlap where the adherends butt together because the transverse normal stress at that location is compressive and rather small. Likewise, for double strap joints under compressive loading, there is no concern with peel stresses at either location since the transverse exten￾sional stresses that do develop in the adhesive are compressive in nature rather than tensile; indeed, where the gap occurs, the inner adherends bear directly on each other and no stress concentrations are present there for the compression loading case. For joints between adherends of identical stiffness, scarf joints (Figure 6.2.2.1(a) - Joint (I)) are theo￾retically the most efficient, having the potential for complete elimination of stress concentrations. (In prac￾tice, some minimum thickness corresponding to one or two ply thicknesses must be incorporated at the thin end of the scarfed adherend leading to the occurrence of stress concentrations in these areas.) In theory, any desirable load capability can be achieved in the scarf joint by making the joint long enough and thick enough. However, practical scarf joints may be less durable because of a tendency toward creep failure associated with a uniform distribution of shear stress along the length of the joint unless care is taken to avoid letting the adhesive be stressed into the nonlinear range. As a result, scarf joints tend to be used only for repairs of very thin structures. Scarf joints with unbalanced stiffnesses between the ad￾herends do not achieve the uniform shear stress condition of those with balanced adherends, and are somewhat less structurally efficient because of rapid buildup of load near the thin end of the thicker ad￾herend. Step lap joints (Figure 6.2.2.1(a) - Joint (H)) represent a practical solution to the challenge of bonding thick members. These types of joint provide manufacturing convenience by taking advantage of the lay￾ered structure of composite laminates. In addition, high loads can be transferred if sufficiently many short steps of sufficiently small "rise" (i.e., thickness increment) in each step are used, while maintaining suffi￾cient overall length of the joint. 6.2.2.3 Effects of adherend stiffness unbalance All types of joint geometry are adversely affected by unequal adherend stiffnesses, where stiffness is defined as axial or in-plane shear modulus times adherend thickness. Where possible, the stiffnesses should be kept approximately equal. For example, for step lap and scarf joints between quasi-isotropic carbon/epoxy (Young's modulus = 8 Msi (55 GPa)) and titanium (Young's modulus = 16 Msi (110 GPa)) ideally, the ratio of the maximum thickness (the thickness just beyond the end of the joint) of the compos￾ite adherend to that of the titanium should be 16/8=2.0. 6.2.2.4 Effects of ductile adhesive response Adhesive ductility is an important factor in minimizing the adverse effects of shear and peel stress peaks in the bond layer. Figure 6.2.2.4(a) reconstructed from Reference 6.2.2.4(a) shows the shear stress-strain response characteristics of typical adhesives used in the aerospace industry as obtained from thick adherend tests (Volume 1, Section 7.3). Figure 6.2.2.4(a), part (A) represents a relatively duc￾tile film adhesive, FM73, under various environmental conditions, while Figure 6.2.2.4(a), part (B) repre￾sents a more brittle adhesive (FM400) under the same conditions. Similar curves can be found in other sources such as Reference 6.2.2.4(b). Even for the less ductile material such as that represented in Fig￾ure 6.2.2.4(a), part (B), ductility has a pronounced influence on mechanical response of bonded joints, and restricting the design to elastic response deprives the application of a significant amount of additional structural capability. In addition to temperature and moisture, effects of porosity in the bond layer can have an influence on ductile response. Porosity effects are illustrated in Figure 6.2.2.4(b) (Reference 6.2.1(s)) which compares the response of FM73 for porous (x symbols) and non-porous (diamond sym￾bols) bond layers for various environmental conditions. This will be further discussed in Section 6.2.2.6