《纺织复合材料》课程参考文献（Composite Materials Handbook，Volume 3）Chapter 6 Structural Behavior of Joints

MIL-HDBK-17-3F Volume 3.Chapter 6 Structural Behavior of Joints CHAPTER 6 STRUCTURAL BEHAVIOR OF JOINTS 6.1 INTRODUCTION It would be difficult to conceive of a structure that did not involve some type of joint.Joints often oc- cur in transitions between major composite parts and a metal feature or fitting.In aircraft,such a situation is represented by articulated fittings on control surfaces as well as on wing and tail components which require the ability to pivot the element during various stages of operation.Tubular elements such as power shafting often use metal end fittings for connections to power sources or for articulation where changes in direction are needed.In addition,assembly of the structure from its constituent parts will in- volve either bonded or mechanically fastened joints or both. Joints represent one of the greatest challenges in the design of structures in general and in compos- ite structures in particular.The reason for this is that joints entail interruptions of the geometry of the structure and often,material discontinuities,which almost always produce local highly stressed areas, except for certain idealized types of adhesive joint such as scarf joints between similar materials.Stress concentrations in mechanically fastened joints are particularly severe because the load transfer between elements of the joint have to take place over a fraction of the available area.For mechanically fastened joints in metal structures,local yielding.which has the effect of eliminating stress peaks as the load in- creases,can usually be depended on;such joints can be designed to some extent by the "P over A"ap- proach,i.e.,by assuming that the load is evenly distributed over load bearing sections so that the total load(the"P")divided by the available area(the"A")represents the stress that controls the strength of the joint.In organic matrix composites,such a stress reduction effect is realized only to a minor extent,and stress peaks predicted to occur by elastic stress analysis have to be accounted for.especially for one- time monotonic loading.In the case of composite adherends,the intensity of the stress peaks varies with the orthotropy of the adherend in addition to various other material and dimensional parameters which affect the behavior of the joint for isotropic adherends. In principle.adhesive joints are structurally more efficient than mechanically fastened joints because they provide better opportunities for eliminating stress concentrations;for example,advantage can be taken of ductile response of the adhesive to reduce stress peaks.Mechanically fastened joints tend to use the available material inefficiently.Sizeable regions exist where the material near the fastener is nearly unloaded,which must be compensated for by regions of high stress to achieve a particular re- quired average load.As mentioned above,certain types of adhesive joints,namely scarf joints between components of similar stiffness,can achieve a nearly uniform stress state throughout the region of the ioint. In many cases,however,mechanically fastened joints can not be avoided because of requirements for disassembly of the joint for replacement of damaged structure or to achieve access to underlying structure.In addition,adhesive joints tend to lack structural redundancy,and are highly sensitive to manufacturing deficiencies,including poor bonding technique,poor fit of mating parts and sensitivity of the adhesive to temperature and environmental effects such as moisture.Assurance of bond quality has been a continuing problem in adhesive joints;while ultrasonic and X-ray inspection may reveal gaps in the bond,there is no present technique which can guarantee that a bond which appears to be intact does, in fact,have adequate load transfer capability.Surface preparation and bonding techniques have been well developed,but the possibility that lack of attention to detail in the bonding operation may lead to such deficiencies needs constant alertness on the part of fabricators.Thus mechanical fastening tends to be preferred over bonded construction in highly critical and safety rated applications such as primary aircraft structural components,especially in large commercial transports,since assurance of the required level of structural integrity is easier to guarantee in mechanically fastened assemblies.Bonded construction tends to be more prevalent in smaller aircraft.For non-aircraft applications as well as in non-flight critical aircraft components,bonding is likewise frequently used. 6-1

MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-1 CHAPTER 6 STRUCTURAL BEHAVIOR OF JOINTS 6.1 INTRODUCTION It would be difficult to conceive of a structure that did not involve some type of joint. Joints often oc￾cur in transitions between major composite parts and a metal feature or fitting. In aircraft, such a situation is represented by articulated fittings on control surfaces as well as on wing and tail components which require the ability to pivot the element during various stages of operation. Tubular elements such as power shafting often use metal end fittings for connections to power sources or for articulation where changes in direction are needed. In addition, assembly of the structure from its constituent parts will in￾volve either bonded or mechanically fastened joints or both. Joints represent one of the greatest challenges in the design of structures in general and in compos￾ite structures in particular. The reason for this is that joints entail interruptions of the geometry of the structure and often, material discontinuities, which almost always produce local highly stressed areas, except for certain idealized types of adhesive joint such as scarf joints between similar materials. Stress concentrations in mechanically fastened joints are particularly severe because the load transfer between elements of the joint have to take place over a fraction of the available area. For mechanically fastened joints in metal structures, local yielding, which has the effect of eliminating stress peaks as the load in￾creases, can usually be depended on; such joints can be designed to some extent by the "P over A" ap￾proach, i.e., by assuming that the load is evenly distributed over load bearing sections so that the total load (the "P") divided by the available area (the "A") represents the stress that controls the strength of the joint. In organic matrix composites, such a stress reduction effect is realized only to a minor extent, and stress peaks predicted to occur by elastic stress analysis have to be accounted for, especially for one￾time monotonic loading. In the case of composite adherends, the intensity of the stress peaks varies with the orthotropy of the adherend in addition to various other material and dimensional parameters which affect the behavior of the joint for isotropic adherends. In principle, adhesive joints are structurally more efficient than mechanically fastened joints because they provide better opportunities for eliminating stress concentrations; for example, advantage can be taken of ductile response of the adhesive to reduce stress peaks. Mechanically fastened joints tend to use the available material inefficiently. Sizeable regions exist where the material near the fastener is nearly unloaded, which must be compensated for by regions of high stress to achieve a particular re￾quired average load. As mentioned above, certain types of adhesive joints, namely scarf joints between components of similar stiffness, can achieve a nearly uniform stress state throughout the region of the joint. In many cases, however, mechanically fastened joints can not be avoided because of requirements for disassembly of the joint for replacement of damaged structure or to achieve access to underlying structure. In addition, adhesive joints tend to lack structural redundancy, and are highly sensitive to manufacturing deficiencies, including poor bonding technique, poor fit of mating parts and sensitivity of the adhesive to temperature and environmental effects such as moisture. Assurance of bond quality has been a continuing problem in adhesive joints; while ultrasonic and X-ray inspection may reveal gaps in the bond, there is no present technique which can guarantee that a bond which appears to be intact does, in fact, have adequate load transfer capability. Surface preparation and bonding techniques have been well developed, but the possibility that lack of attention to detail in the bonding operation may lead to such deficiencies needs constant alertness on the part of fabricators. Thus mechanical fastening tends to be preferred over bonded construction in highly critical and safety rated applications such as primary aircraft structural components, especially in large commercial transports, since assurance of the required level of structural integrity is easier to guarantee in mechanically fastened assemblies. Bonded construction tends to be more prevalent in smaller aircraft. For non-aircraft applications as well as in non-flight critical aircraft components, bonding is likewise frequently used

MIL-HDBK-17-3F Volume 3.Chapter 6 Structural Behavior of Joints This chapter describes design procedures and analytical methods for determining stresses and de- formations in structural joints for composite structures.Section 6.2 which follows deals with adhesive joints.(Mechanically fastened joints will be the subject of a future revision of the Handbook.) In the case of adhesive joints,design considerations which are discussed include:effects of adherend thickness as a means of ensuring adherend failure rather than bond failure;the use of adherend tapering to minimize peel stresses;effects of adhesive ductility;special considerations regarding composite ad- herends;effects of bond layer defects,including surface preparations defects,porosity and thickness variations;and,considerations relating to long term durability of adhesive joints.In addition to design considerations,aspects of joint behavior which control stresses and deformations in the bond layer are described,including both shear stresses and transverse normal stresses which are customarily referred to as "peel"stresses when they are tensile.Finally,some principles for finite element analysis of bonded joints are described. Related information on joints in composite structures which is described elsewhere in this handbook includes Volume 1.Chapter 7.Section 7.5(Mechanically Fastened Joints)and 6.3(Bonded Joints)to- gether with Volume 3,Chapter 2,Section 2.7.8 on Adhesive Bonding. 6.2 ADHESIVE JOINTS 6.2.1 Introduction Adhesive joints are capable of high structural efficiency and constitute a resource for structural weight saving because of the potential for elimination of stress concentrations which cannot be achieved with mechanically fastened joints.Unfortunately,because of a lack of reliable inspection methods and a re- quirement for close dimensional tolerances in fabrication,aircraft designers have generally avoided bonded construction in primary structure.Some notable exceptions include:bonded step lap joints used in attachments for the F-14 and F-15 horizontal stabilizers as well as the F-18 wing root fitting,and a ma- jority of the airframe components of the Lear Fan and the Beech Starship. While a number of issues related to adhesive joint design were considered in the earlier literature cited in References 6.2.1(a)-6.2.1(h),much of the methodology currently used in the design and analysis of adhesive joints in composite structures is based on the approaches evolved by L.J.Hart-Smith in a series of NASA/Langley-sponsored contracts of the early 70's (References 6.2.1(i)-6.2.1(n))as well as from the Air Force's Primary Adhesively Bonded Structures Technology (PABST)program (References 6.2.1(o)-6.2.1(r))of the mid-70's.The most recent such work developed three computer codes for bonded and bolted joints,designated A4EG,A4EI and A4EK(References 6.2.1(s)-6.2.1(u)),under Air Force contract.The results of these efforts have also appeared in a number of open literature publica- tions (Reference 6.2.1(v)-(z)).In addition,such approaches found application in some of the efforts tak- ing place under the NASA Advanced Composite Energy Efficient Aircraft(ACEE)program of the early to mid 80's (Reference 6.2.1(x)and 6.2.1(y)). Some of the key principles on which these efforts were based include:(1)the use of simple 1-dimensional stress analyses of generic composite joints wherever possible;(2)the need to select the joint design so as to ensure failure in the adherend rather than the adhesive,so that the adhesive is never the weak link;(3)recognition that the ductility of aerospace adhesives is beneficial in reducing stress peaks in the adhesive;(4)careful use of such factors as adherend tapering to reduce or eliminate peel stresses from the joint;and(5)recognition of slow cyclic loading,corresponding to such phenomena as cabin pressurization in aircraft,as a major factor controlling durability of adhesive joints,and the need to avoid the worst effects of this type of loading by providing sufficient overlap length to ensure that some of the adhesive is so lightly loaded that creep cannot occur there,under the most severe extremes of humid- ity and temperature for which the component is to be used. Much of the discussion to follow will retain the analysis philosophy of Hart-Smith,since it is consid- ered to represent a major contribution to practical bonded joint design in both composite and metallic 6-2

MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-2 This chapter describes design procedures and analytical methods for determining stresses and de￾formations in structural joints for composite structures. Section 6.2 which follows deals with adhesive joints. (Mechanically fastened joints will be the subject of a future revision of the Handbook.) In the case of adhesive joints, design considerations which are discussed include: effects of adherend thickness as a means of ensuring adherend failure rather than bond failure; the use of adherend tapering to minimize peel stresses; effects of adhesive ductility; special considerations regarding composite ad￾herends; effects of bond layer defects, including surface preparations defects, porosity and thickness variations; and, considerations relating to long term durability of adhesive joints. In addition to design considerations, aspects of joint behavior which control stresses and deformations in the bond layer are described, including both shear stresses and transverse normal stresses which are customarily referred to as "peel" stresses when they are tensile. Finally, some principles for finite element analysis of bonded joints are described. Related information on joints in composite structures which is described elsewhere in this handbook includes Volume 1, Chapter 7, Section 7.5 (Mechanically Fastened Joints) and 6.3 (Bonded Joints) to￾gether with Volume 3, Chapter 2, Section 2.7.8 on Adhesive Bonding. 6.2 ADHESIVE JOINTS 6.2.1 Introduction Adhesive joints are capable of high structural efficiency and constitute a resource for structural weight saving because of the potential for elimination of stress concentrations which cannot be achieved with mechanically fastened joints. Unfortunately, because of a lack of reliable inspection methods and a re￾quirement for close dimensional tolerances in fabrication, aircraft designers have generally avoided bonded construction in primary structure. Some notable exceptions include: bonded step lap joints used in attachments for the F-14 and F-15 horizontal stabilizers as well as the F-18 wing root fitting, and a ma￾jority of the airframe components of the Lear Fan and the Beech Starship. While a number of issues related to adhesive joint design were considered in the earlier literature cited in References 6.2.1(a)- 6.2.1(h), much of the methodology currently used in the design and analysis of adhesive joints in composite structures is based on the approaches evolved by L.J. Hart-Smith in a series of NASA/Langley-sponsored contracts of the early 70's (References 6.2.1(i) - 6.2.1(n)) as well as from the Air Force's Primary Adhesively Bonded Structures Technology (PABST) program (References 6.2.1(o) - 6.2.1(r)) of the mid-70's. The most recent such work developed three computer codes for bonded and bolted joints, designated A4EG, A4EI and A4EK (References 6.2.1(s) - 6.2.1(u)), under Air Force contract. The results of these efforts have also appeared in a number of open literature publica￾tions (Reference 6.2.1(v) - (z)). In addition, such approaches found application in some of the efforts tak￾ing place under the NASA Advanced Composite Energy Efficient Aircraft (ACEE) program of the early to mid 80's (Reference 6.2.1(x) and 6.2.1(y)). Some of the key principles on which these efforts were based include: (1) the use of simple 1-dimensional stress analyses of generic composite joints wherever possible; (2) the need to select the joint design so as to ensure failure in the adherend rather than the adhesive, so that the adhesive is never the weak link; (3) recognition that the ductility of aerospace adhesives is beneficial in reducing stress peaks in the adhesive; (4) careful use of such factors as adherend tapering to reduce or eliminate peel stresses from the joint; and (5) recognition of slow cyclic loading, corresponding to such phenomena as cabin pressurization in aircraft, as a major factor controlling durability of adhesive joints, and the need to avoid the worst effects of this type of loading by providing sufficient overlap length to ensure that some of the adhesive is so lightly loaded that creep cannot occur there, under the most severe extremes of humid￾ity and temperature for which the component is to be used. Much of the discussion to follow will retain the analysis philosophy of Hart-Smith, since it is consid￾ered to represent a major contribution to practical bonded joint design in both composite and metallic

MIL-HDBK-17-3F Volume 3,Chapter 6 Structural Behavior of Joints structures.On the other hand,some modifications are introduced here.For example,the revisions of the Goland-Reissner single lap joint analysis presented in Reference 6.2.1(k)have again been revised ac- cording to the approach presented in References 6.2.1(z)and 6.2.1(aa). Certain issues which are specific to composite adherends but were not dealt with in the Hart-Smith efforts will be addressed.The most important of these is the effect of transverse shear deformations in organic composite adherends. Although the main emphasis of the discussion is on simplified stress analysis concepts allowed by shear lag models for shear stress prediction and beam-on-elastic foundation concepts for peel stress pre- diction,a brief discussion will be provided on requirements for finite element modeling of adhesive joints Similarly,although joint failure will be considered primarily from the standpoint of stress and strain energy considerations,some discussion of fracture mechanics considerations for adhesive joints will also be in- cluded. 6.2.2 Joint design considerations 6.2.2.1 Effects of adherend thickness:adherend failures vs.bond failures Figure 6.2.2.1(a)shows a series of typical bonded joint configurations.Adhesive joints in general are characterized by high stress concentrations in the adhesive layer.These originate,in the case of shear stresses,because of unequal axial straining of the adherends,and in the case of peel stresses,because of eccentricity in the load path.Considerable ductility is associated with shear response of typical adhe- sives,which is beneficial in minimizing the effect of shear stress joint strength.Response to peel stresses tends to be much more brittle than that to shear stresses,and reduction of peel stresses is desirable for achieving good joint performance. 1 BONDED DOUBLER DOUBLE-STRAP JOINT UNSUPPORTED SINGLE-LAP JOINT (a) ■■ TAPERED STRAP JOINT SINGLE-STRAP JOINT TAPERED SINGLE-LAP JOINT STEPPED-LAP JONT DOUBLE-LAP JOINT SCARF JOINT FIGURE 6.2.2.1(a)Adhesive joint types (Reference 6.2.1(n)and 6.2.2.1(a)). From the standpoint of joint reliability,it is vital to avoid letting the adhesive layer be the weak link in the joint;this means that,whenever possible,the joint should be designed to ensure that the adherends fail before the bond layer.This is because failure in the adherends is fiber controlled,while failure in the adhesive is resin dominated,and thus subject to effects of voids and other defects,thickness variations, environmental effects,processing variations,deficiencies in surface preparation and other factors that are not always adequately controlled.This is a significant challenge,since adhesives are inherently much weaker than the composite or metallic elements being joined.However,the objective can be accom- plished by recognizing the limitations of the joint geometry being considered and placing appropriate re- strictions on the thickness dimensions of the joint for each geometry.Figure 6.2.2.1(b),which has fre- quently been used by Hart-Smith(References 6.2.1(n).6.2.2.1(a))to illustrate this point,shows a pro- 6-3

MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-3 structures. On the other hand, some modifications are introduced here. For example, the revisions of the Goland-Reissner single lap joint analysis presented in Reference 6.2.1(k) have again been revised ac￾cording to the approach presented in References 6.2.1(z) and 6.2.1(aa). Certain issues which are specific to composite adherends but were not dealt with in the Hart-Smith efforts will be addressed. The most important of these is the effect of transverse shear deformations in organic composite adherends. Although the main emphasis of the discussion is on simplified stress analysis concepts allowed by shear lag models for shear stress prediction and beam-on-elastic foundation concepts for peel stress pre￾diction, a brief discussion will be provided on requirements for finite element modeling of adhesive joints. Similarly, although joint failure will be considered primarily from the standpoint of stress and strain energy considerations, some discussion of fracture mechanics considerations for adhesive joints will also be in￾cluded. 6.2.2 Joint design considerations 6.2.2.1 Effects of adherend thickness: adherend failures vs. bond failures Figure 6.2.2.1(a) shows a series of typical bonded joint configurations. Adhesive joints in general are characterized by high stress concentrations in the adhesive layer. These originate, in the case of shear stresses, because of unequal axial straining of the adherends, and in the case of peel stresses, because of eccentricity in the load path. Considerable ductility is associated with shear response of typical adhe￾sives, which is beneficial in minimizing the effect of shear stress joint strength. Response to peel stresses tends to be much more brittle than that to shear stresses, and reduction of peel stresses is desirable for achieving good joint performance. FIGURE 6.2.2.1(a) Adhesive joint types (Reference 6.2.1(n) and 6.2.2.1(a)). From the standpoint of joint reliability, it is vital to avoid letting the adhesive layer be the weak link in the joint; this means that, whenever possible, the joint should be designed to ensure that the adherends fail before the bond layer. This is because failure in the adherends is fiber controlled, while failure in the adhesive is resin dominated, and thus subject to effects of voids and other defects, thickness variations, environmental effects, processing variations, deficiencies in surface preparation and other factors that are not always adequately controlled. This is a significant challenge, since adhesives are inherently much weaker than the composite or metallic elements being joined. However, the objective can be accom￾plished by recognizing the limitations of the joint geometry being considered and placing appropriate re￾strictions on the thickness dimensions of the joint for each geometry. Figure 6.2.2.1(b),which has fre￾quently been used by Hart-Smith (References 6.2.1(n), 6.2.2.1(a)) to illustrate this point, shows a pro-

MIL-HDBK-17-3F Volume 3,Chapter 6 Structural Behavior of Joints gression of joint types which represent increasing strength capability from the lowest to the highest in the figure.In each type of joint,the adherend thickness may be increased as an approach to achieving higher load capacity.When the adherends are relatively thin,results of stress analyses show that for all of the joint types in Figure 6.2.2.1(b),the stresses in the bond will be small enough to guarantee that the adherends will reach their load capacity before failure can occur in the bond.As the adherend thicknesses increase,the bond stresses become relatively larger until a point is reached at which bond failure occurs at a lower load than that for which the adherends fail.This leads to the general principle that for a given joint type,the adherend thicknesses should be restricted to an appropriate range relative to the bond layer thickness.Because of processing considerations and defect sensitivity of the bond material,bond layer thicknesses are generally limited to a range of 0.005-0.015 in.(0.125-0.39 mm).As a result,each of the joint types in Figures 6.2.2.1(a)and 6.2.2.1(b)corresponds to a specific range of adherend thicknesses and therefore of load capacity,and as the need for greater load capacity arises,it is preferable to change the joint configuration to one of higher efficiency rather than to increasing the adherend thickness indefinitely. OUTSIDE FAMURES JOINT SHEAR STEPPED-LAP JOWNT FAILURES FAILURES SHOWN REPRESENT THE LMMIT ON EFFICIENT DESIGN FOR SHEAR FAILURES EACH GEOMETRY OINT UTSIDE TAPERED-STRAP JOINT DOUBLE-STRAP JOINT tEND STRENGTH PEEL FAILURES BENDING OF SINGLE-LAP JOINT ADHERENDS DUE TO ECCENTRIC LOAD PATH ADHEREND THICKNESS FIGURE 6.2.2.1(b)Joint geometry effects(Reference 6.2.1(n)). 6.2.2.2 Joint geometry effects Single and double lap joints with uniformly thick adherends(Figure 6.2.2.1(a)-Joints(B),(E)and(F)) are the least efficient joint type and are suitable primarily for thin structures with low running loads(load per unit width,i.e.,stress times element thickness).Of these,single lap joints are the least capable be- 6-4

MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-4 gression of joint types which represent increasing strength capability from the lowest to the highest in the figure. In each type of joint, the adherend thickness may be increased as an approach to achieving higher load capacity. When the adherends are relatively thin, results of stress analyses show that for all of the joint types in Figure 6.2.2.1(b), the stresses in the bond will be small enough to guarantee that the adherends will reach their load capacity before failure can occur in the bond. As the adherend thicknesses increase, the bond stresses become relatively larger until a point is reached at which bond failure occurs at a lower load than that for which the adherends fail. This leads to the general principle that for a given joint type, the adherend thicknesses should be restricted to an appropriate range relative to the bond layer thickness. Because of processing considerations and defect sensitivity of the bond material, bond layer thicknesses are generally limited to a range of 0.005-0.015 in. (0.125-0.39 mm). As a result, each of the joint types in Figures 6.2.2.1(a) and 6.2.2.1(b) corresponds to a specific range of adherend thicknesses and therefore of load capacity, and as the need for greater load capacity arises, it is preferable to change the joint configuration to one of higher efficiency rather than to increasing the adherend thickness indefinitely. FIGURE 6.2.2.1(b) Joint geometry effects (Reference 6.2.1(n)). 6.2.2.2 Joint geometry effects Single and double lap joints with uniformly thick adherends (Figure 6.2.2.1(a) - Joints (B), (E) and (F)) are the least efficient joint type and are suitable primarily for thin structures with low running loads (load per unit width, i.e., stress times element thickness). Of these, single lap joints are the least capable be-

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. 6-5

MIL-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