《纺织复合材料》课程参考文献（Composite Materials Handbook，Volume 3）Chapter 6 Structural Behavior of Joints.pdf_P6-P10

MIL-HDBK-17-3F Volume 3,Chapter 6 Structural Behavior of Joints plateau(i.e.elastic-perfectly plastic response)if the latter is adjusted to provide a strain energy density to failure equal to that of the actual stress-strain curve gives.Test methods for adhesives (see Volume 1, Section 7.6)should be aimed at providing data on this parameter.Once the equivalent elastic-perfectly plastic stress strain curve has been identified for the selected adhesive in the range of the most severe environmental conditions(temperature and humidity)of interest,the joint design can proceed through the use of relatively simple one-dimensional stress analysis,thus avoiding the need for elaborate finite ele- ment calculations.Even the most complicated of joints,the step lap joints designed for root-end wing and tail connections for the F-18 and other aircraft,have been successfully designed(Reference 6.2.1(t))and experimentally demonstrated using such approaches.Design procedures for such analyses which were developed under Government contract have been incorporated into the public domain in the form of the "A4EG","A4EI"and "A4EK"computer codes mentioned previously in Section 6.2.1 and are currently avail- able from the Air Force's Aerospace Structures Information and Analysis Center(ASIAC).Note that the A4EK code permits analysis of bonded joints in which local disbonds are repaired by mechanical fasten- ers. 6.2.2.5 Behavior of composite adherends Polymer matrix composite adherends are considerably more affected by interlaminar shear stresses than metals,so that there is a significant need to account for such effects in stress analyses of adhesively bonded composites.Transverse shear deformations of the adherends have an effect analogous to thick- ening of the bond layer and result in a lowering of both shear and peel stress peaks.(See Section 6.2.3.4.4). In addition,because the resins used for adherend matrices tend to be less ductile than typical adhe- sives,and are weakened by stress concentrations due to the presence of the fibers,the limiting element in the joint may be the interlaminar shear and transverse tensile strengths of the adherends rather than the bond strength(Figure 6.2.2.5(a)).In the case of single lap joints(Figure 6.2.2.5(a),part(A))bending failures of the adherends may occur because of high moments at the ends of the overlap.For metal ad- herends,bending failures take the form of plastic bending and hinge formation,while for composite ad- herends the bending failures are brittle in nature.In the case of double lap joints,peel stress build up in thicker adherends can cause the types of interlaminar failures in the adherends illustrated in Figure 6.2.2.5(a),part(B). The effect of the stacking sequence of the laminates making up the adherends in composite joints is significant.For example,90-degree layers placed adjacent to the bond layer theoretically act largely as additional thicknesses of bond material,leading to lower peak stresses,while 0-degree layers next to the bond layer give stiffer adherend response with higher stress peaks.In practice it has been observed that 90-degree layers next to the bond layer tend to seriously weaken the joint because of transverse cracking which develops in those layers,and advantage cannot be taken of the reduced peak stresses. Large differences in thermal expansion characteristics between metal and composite adherends can cause severe problems.(See Section 6.2.3.4.2)Adhesives with high curing temperatures may be unsuit- able for some low temperature applications because of large thermal stresses which develop as the joint cools down from the curing temperature In contrast with metal adherends,composite adherends are subject to moisture diffusion effects.As a result,moisture is more likely to be found over wide regions of the adhesive layer,as opposed to con- finement near the exposed edges of the joint in the case of metal adherends,and response of the adhe- sive to moisture may be an even more significant issue for composite joints than for joints between metallic adherends. 6-7

MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-7 plateau (i.e. elastic-perfectly plastic response) if the latter is adjusted to provide a strain energy density to failure equal to that of the actual stress-strain curve gives. Test methods for adhesives (see Volume 1, Section 7.6) should be aimed at providing data on this parameter . Once the equivalent elastic-perfectly plastic stress strain curve has been identified for the selected adhesive in the range of the most severe environmental conditions (temperature and humidity) of interest, the joint design can proceed through the use of relatively simple one-dimensional stress analysis, thus avoiding the need for elaborate finite element calculations. Even the most complicated of joints, the step lap joints designed for root-end wing and tail connections for the F-18 and other aircraft, have been successfully designed (Reference 6.2.1(t)) and experimentally demonstrated using such approaches. Design procedures for such analyses which were developed under Government contract have been incorporated into the public domain in the form of the "A4EG", "A4EI" and "A4EK" computer codes mentioned previously in Section 6.2.1 and are currently available from the Air Force's Aerospace Structures Information and Analysis Center (ASIAC) . Note that the A4EK code permits analysis of bonded joints in which local disbonds are repaired by mechanical fasteners. 6.2.2.5 Behavior of composite adherends Polymer matrix composite adherends are considerably more affected by interlaminar shear stresses than metals, so that there is a significant need to account for such effects in stress analyses of adhesively bonded composites. Transverse shear deformations of the adherends have an effect analogous to thickening of the bond layer and result in a lowering of both shear and peel stress peaks. (See Section 6.2.3.4.4). In addition, because the resins used for adherend matrices tend to be less ductile than typical adhesives, and are weakened by stress concentrations due to the presence of the fibers, the limiting element in the joint may be the interlaminar shear and transverse tensile strengths of the adherends rather than the bond strength (Figure 6.2.2.5(a)). In the case of single lap joints (Figure 6.2.2.5(a), part (A)) bending failures of the adherends may occur because of high moments at the ends of the overlap. For metal adherends, bending failures take the form of plastic bending and hinge formation, while for composite adherends the bending failures are brittle in nature. In the case of double lap joints, peel stress build up in thicker adherends can cause the types of interlaminar failures in the adherends illustrated in Figure 6.2.2.5(a), part (B). The effect of the stacking sequence of the laminates making up the adherends in composite joints is significant. For example, 90-degree layers placed adjacent to the bond layer theoretically act largely as additional thicknesses of bond material, leading to lower peak stresses, while 0-degree layers next to the bond layer give stiffer adherend response with higher stress peaks. In practice it has been observed that 90-degree layers next to the bond layer tend to seriously weaken the joint because of transverse cracking which develops in those layers, and advantage cannot be taken of the reduced peak stresses. Large differences in thermal expansion characteristics between metal and composite adherends can cause severe problems. (See Section 6.2.3.4.2) Adhesives with high curing temperatures may be unsuitable for some low temperature applications because of large thermal stresses which develop as the joint cools down from the curing temperature. In contrast with metal adherends, composite adherends are subject to moisture diffusion effects . As a result, moisture is more likely to be found over wide regions of the adhesive layer, as opposed to confinement near the exposed edges of the joint in the case of metal adherends, and response of the adhesive to moisture may be an even more significant issue for composite joints than for joints between metallic adherends

MIL-HDBK-17-3F Volume 3.Chapter 6 Structural Behavior of Joints suspect,since some peel plies leave a residue on the bonding surfaces that makes adhesion poor. (However,some manufacturers have obtained satisfactory results from surface preparation consisting only of peel ply removal.)Low pressure grit blasting (Reference 6.2.2.6(b))is preferable over hand sand- ing as a means of eliminating such residues and mechanically conditioning the bonding surfaces. For joints which are designed to ensure that the adherends rather than the bond layer are the critical elements,tolerance to the presence of porosity and other types of defect is considerable (Reference 6.2.1(t)).Porosity(Reference 6.2.1(z))is usually associated with over-thickened areas of the bond,which tend to occur away from the edges of the joint where most of the load transfer takes place,and thus is a relatively benign effect,especially if peel stresses are minimized by adherend tapering.Reference 6.2.1(z)indicates that in such cases,porosity can be represented by a modification of the assumed stress-strain properties of the adhesive as determined from thick-adherend tests,allowing a straightfor- ward analysis of the effect of such porosity on joint strength as in the A4EI computer code.If peel stresses are significant,as in the case of over-thick adherends,porosity may grow catastrophically and lead to non-damage-tolerant joint performance. In the case of bond thickness variations(Reference 6.2.1(aa)),these usually take place in the form of thinning due to excess resin bleed at the joint edges,leading to overstressing of the adhesive in the vicin- ity of the edges.Inside tapering of the adherends at the joint edges can be used to compensate for this condition;other compensating techniques are also discussed in Reference 6.2.1(aa).Bond thicknesses per se should be limited to ranges of 0.005-0.01 in.(0.12-0.24 mm)to prevent significant porosity from developing,although greater thicknesses may be acceptable if full periphery damming or high minimum viscosity paste adhesives are used.Common practice involves the use of film adhesives containing scrim cloth,some forms of which help to maintain bond thicknesses.It is also common practice to use mat car- riers of chopped fibers to prevent a direct path for access by moisture to the interior of the bond. 6.2.2.7 Durability of adhesive joints Two major considerations in the joint design philosophy of Hart-smith are:(1)either limiting the ad- herend thickness or making use of more sophisticated joint configurations such as scarf and step lap joints,to insure that adherend failure takes precedence over bond failure;(2)designing to minimize peel stresses,either by keeping the adherends excessively thin or,for intermediate adherend thicknesses,by tapering the adherends (see discussion of effects of adherend tapering,Section 6.2.2.2 and 6.2.3.5.).In addition,it is essential that good surface treatment practices(Section 6.2.2.6)be maintained to insure that the bond between the adhesive and adherends does not fail.When these conditions are met,reliable per- formance of the joint can be expected for the most part,except for environmental extremes,i.e.,hot-wet conditions.The Hart-Smith approach focuses primarily on creep failure associated with slow cyclic load- ing (i.e.,1 cycle in several minutes to an hour)under hot wet conditions;this corresponds,for example,to cyclic pressurization of aircraft fuselages.In the PABST program,References 6.2.1(n)-(q)(see also Ref- erence 6.2.1(v)),18 thick adherend specimens,when tested at high cycling rates(30 Hz)were able to sustain more than 10 million loading cycles without damage,while tests conducted at the same loads at one cycle per hour produced failures within a few hundred cycles.Similar conclusions regarding the ef- fects of cycling rate were presented in Reference 6.2.2.7(a).On the other hand,specimens representative of structural joints,which have a nonuniform shear stress distribution that peaks at the ends of the joint and is essentially zero in the middle (see Section 6.2.3.4.3 on ductile response of joints and Figure 6.2.3.4.3(b),part(B)in particular)are able to sustain hot-wet conditions even at low cycling rates if (e, the length of the region of elastic response in the bond layer,is sufficient.Based on experience of the PABST program,the Hart-Smith criterion for avoidance of creep failure requires that blmin,the minimum shear stress along the bond length,be no greater than one tenth the yield stress of the adhesive.But the stress analysis for the elastic-plastic case (Section 6.2.3.4.3)using a bilinear adhesive response model leads to an expression for the minimum shear stress in double lap joints with identical adherends given by Tp Tblmin= 6.2.2.7(a sinh Bpdle/2to 6-9

MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-9 suspect, since some peel plies leave a residue on the bonding surfaces that makes adhesion poor. (However, some manufacturers have obtained satisfactory results from surface preparation consisting only of peel ply removal.) Low pressure grit blasting (Reference 6.2.2.6(b)) is preferable over hand sanding as a means of eliminating such residues and mechanically conditioning the bonding surfaces. For joints which are designed to ensure that the adherends rather than the bond layer are the critical elements, tolerance to the presence of porosity and other types of defect is considerable (Reference 6.2.1(t)). Porosity (Reference 6.2.1(z)) is usually associated with over-thickened areas of the bond, which tend to occur away from the edges of the joint where most of the load transfer takes place, and thus is a relatively benign effect, especially if peel stresses are minimized by adherend tapering. Reference 6.2.1(z) indicates that in such cases, porosity can be represented by a modification of the assumed stress-strain properties of the adhesive as determined from thick-adherend tests, allowing a straightforward analysis of the effect of such porosity on joint strength as in the A4EI computer code. If peel stresses are significant, as in the case of over-thick adherends, porosity may grow catastrophically and lead to non-damage-tolerant joint performance. In the case of bond thickness variations (Reference 6.2.1(aa)), these usually take place in the form of thinning due to excess resin bleed at the joint edges, leading to overstressing of the adhesive in the vicinity of the edges. Inside tapering of the adherends at the joint edges can be used to compensate for this condition; other compensating techniques are also discussed in Reference 6.2.1(aa). Bond thicknesses per se should be limited to ranges of 0.005-0.01 in. (0.12-0.24 mm) to prevent significant porosity from developing, although greater thicknesses may be acceptable if full periphery damming or high minimum viscosity paste adhesives are used. Common practice involves the use of film adhesives containing scrim cloth, some forms of which help to maintain bond thicknesses. It is also common practice to use mat carriers of chopped fibers to prevent a direct path for access by moisture to the interior of the bond. 6.2.2.7 Durability of adhesive joints Two major considerations in the joint design philosophy of Hart-smith are: (1) either limiting the adherend thickness or making use of more sophisticated joint configurations such as scarf and step lap joints, to insure that adherend failure takes precedence over bond failure; (2) designing to minimize peel stresses, either by keeping the adherends excessively thin or, for intermediate adherend thicknesses, by tapering the adherends (see discussion of effects of adherend tapering, Section 6.2.2.2 and 6.2.3.5.). In addition, it is essential that good surface treatment practices (Section 6.2.2.6) be maintained to insure that the bond between the adhesive and adherends does not fail. When these conditions are met, reliable performance of the joint can be expected for the most part, except for environmental extremes, i.e., hot-wet conditions. The Hart-Smith approach focuses primarily on creep failure associated with slow cyclic loading (i.e., 1 cycle in several minutes to an hour) under hot wet conditions; this corresponds, for example, to cyclic pressurization of aircraft fuselages. In the PABST program, References 6.2.1(n)-(q) (see also Reference 6.2.1(v)), 18 thick adherend specimens, when tested at high cycling rates (30 Hz) were able to sustain more than 10 million loading cycles without damage, while tests conducted at the same loads at one cycle per hour produced failures within a few hundred cycles. Similar conclusions regarding the effects of cycling rate were presented in Reference 6.2.2.7(a). On the other hand, specimens representative of structural joints, which have a nonuniform shear stress distribution that peaks at the ends of the joint and is essentially zero in the middle (see Section 6.2.3.4.3 on ductile response of joints and Figure 6.2.3.4.3(b), part (B) in particular) are able to sustain hot-wet conditions even at low cycling rates if Ae , the length of the region of elastic response in the bond layer, is sufficient. Based on experience of the PABST program, the Hart-Smith criterion for avoidance of creep failure requires that τ b | min , the minimum shear stress along the bond length, be no greater than one tenth the yield stress of the adhesive. But the stress analysis for the elastic-plastic case (Section 6.2.3.4.3) using a bilinear adhesive response model leads to an expression for the minimum shear stress in double lap joints with identical adherends given by b min p bd o | = sinh / 2 t τ τ β Ae 6.2.2.7(a)

MIL-HDBK-17-3F Volume 3.Chapter 6 Structural Behavior of Joints where tp is the adhesive yield stress and Bod is given by Bod=[2Gboto/Eotb]1/2 where Gbo is the initial shear modulus,tp the bond thickness and Eo and to the adherend axial modulus and thickness.Because sinh(3)=10,this amounts to a requirement that Bodle/2to be at least 3,i.e.,that the elastic zone length be greater than 6to/Bod.Since ce,is equivalent to the total overlap length,( minus twice the plastic zone length (p,then making use of the expression given in Section 6.2.3.4.3 for (p (p=(Ox/2 Tp-1/Bpd)to where ox is the nominal adherend loading stress,the criterion for elastic zone length reduces to a crite- rion for total overlap length corresponding to a lower bound on which can be stated as 6.2.2.7(b) Equation 6.2.2.7(b)for the joint overlap length is the heart of the Hart-Smith approach to durability of bonded joints for cases where adherend failure is enforced over bond failure for static loading,and in which peel stresses are eliminated from the joint design.This type of requirement has been used in sev- eral contexts.In Reference 6.2.1(s)for example,it becomes part of the requirement for acceptable void volume,since in this case the voids,acting essentially as gaps in the bond layer,reduce the effective length of the overlap.The criterion has to be modified numerically for joints other than symmetric double lap joints with equal stiffness adherends and uniform thickness.For more sophisticated joint configura- tions such as step lap joints,the A4EI computer code provides for a step length requirement equivalent to that of Equation 6.2.2.7(b)for simple double lap joints. In addition to creep failures under hot-wet conditions,the joint may fail due to cracking in the bond layer.Johnson and Mall(Reference 6.2.2.7(b))presented the data in Figure 6.2.2.7(a)which shows the effect of adherend taper angle on development of cracks at ends of test specimens consisting of compos- ite plates with bonded composite doublers,at 10 cycles of fatigue loading;here the open symbols repre- sent the highest load levels that could be identified at which cracks failed to appear,while the solid sym- bols are for the lowest loads at which cracks just begin to appear.The predicted lines consist of calcu- lated values of applied cyclic stress required to create a total strain energy release rate threshold value, Gah,at the debond tip for a given taper angle.The values of Guh for the two adhesives were experimentally determined on untapered specimens.The angle of taper at the end of the doubler was used to control the amount of peel stress present in the specimen for static loading.It is noted that even for taper angles as low as 5(left-most experimental points in Figure 6.2.2.7(a))for which peel stresses are essentially non- existent for static loading,crack initiation was observed when the alternating load was raised to a suffi- cient level.A number of factors need to be clarified before the implications of these results are clear.In particular,it is of interest to establish the occurrence of bond cracking at shorter cycling times,say less than 3x10cycles corresponding to expected lifetimes of typical aircraft.Effects of cycling rate and envi- ronmental exposure are also of interest.Nevertheless,the data presented in Reference 6.2.2.7(b)sug- gests the need for consideration of crack growth phenomena in bonded composite joints.Indeed,a major part of the technical effort that has been conducted on the subject of durability of adhesive joints (see Reference 6.2.2.7(c)-(i)for example)has been based on the application of fracture mechanics based concepts.The issue of whether or not a fracture mechanics approach is valid needs further examination. Apparently,no crack-like failures occurred in the PABST program,which was a metal bonding program, even when brittle adhesives were examined at low temperatures.The amount of effort which has been expended by a number of respected workers on development of energy release rate calculations for bonded joints certainly suggests that there is some justification for that approach,and the results obtained by Johnson and Mall appear to substantiate their need for composite joints in particular. 6-10

MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-10 where t p is the adhesive yield stress and β bd is given by bd b0 o o b 1/2 β = [2G t / E t ] where Gbo is the initial shear modulus, t b the bond thickness and E0 and t0 the adherend axial modulus and thickness. Because sinh(3) ≈ 10, this amounts to a requirement that β bd e A / 2t0 be at least 3, i.e., that the elastic zone length be greater than 6 0t bd / β . Since Ae , is equivalent to the total overlap length, A , minus twice the plastic zone length Ap , then making use of the expression given in Section 6.2.3.4.3 for Ap : Ap = / 2 -1/ d i σ x τ p β bd to where σ x is the nominal adherend loading stress, the criterion for elastic zone length reduces to a criterion for total overlap length corresponding to a lower bound on A which can be stated as A ≥ F H G I K J x p bd + o 4 t σ τ β 6.2.2.7(b) Equation 6.2.2.7(b) for the joint overlap length is the heart of the Hart-Smith approach to durability of bonded joints for cases where adherend failure is enforced over bond failure for static loading, and in which peel stresses are eliminated from the joint design. This type of requirement has been used in several contexts. In Reference 6.2.1(s) for example, it becomes part of the requirement for acceptable void volume, since in this case the voids, acting essentially as gaps in the bond layer, reduce the effective length of the overlap. The criterion has to be modified numerically for joints other than symmetric double lap joints with equal stiffness adherends and uniform thickness. For more sophisticated joint configurations such as step lap joints, the A4EI computer code provides for a step length requirement equivalent to that of Equation 6.2.2.7(b) for simple double lap joints. In addition to creep failures under hot-wet conditions, the joint may fail due to cracking in the bond layer. Johnson and Mall (Reference 6.2.2.7(b)) presented the data in Figure 6.2.2.7(a) which shows the effect of adherend taper angle on development of cracks at ends of test specimens consisting of composite plates with bonded composite doublers, at 106 cycles of fatigue loading; here the open symbols represent the highest load levels that could be identified at which cracks failed to appear, while the solid symbols are for the lowest loads at which cracks just begin to appear. The predicted lines consist of calculated values of applied cyclic stress required to create a total strain energy release rate threshold value, Gth, at the debond tip for a given taper angle. The values of Gth for the two adhesives were experimentally determined on untapered specimens. The angle of taper at the end of the doubler was used to control the amount of peel stress present in the specimen for static loading. It is noted that even for taper angles as low as 5o (left-most experimental points in Figure 6.2.2.7(a)) for which peel stresses are essentially nonexistent for static loading, crack initiation was observed when the alternating load was raised to a sufficient level. A number of factors need to be clarified before the implications of these results are clear. In particular, it is of interest to establish the occurrence of bond cracking at shorter cycling times, say less than 3x105 cycles corresponding to expected lifetimes of typical aircraft. Effects of cycling rate and environmental exposure are also of interest. Nevertheless, the data presented in Reference 6.2.2.7(b) suggests the need for consideration of crack growth phenomena in bonded composite joints. Indeed, a major part of the technical effort that has been conducted on the subject of durability of adhesive joints (see Reference 6.2.2.7(c)-(i) for example) has been based on the application of fracture mechanics based concepts. The issue of whether or not a fracture mechanics approach is valid needs further examination. Apparently, no crack-like failures occurred in the PABST program, which was a metal bonding program, even when brittle adhesives were examined at low temperatures. The amount of effort which has been expended by a number of respected workers on development of energy release rate calculations for bonded joints certainly suggests that there is some justification for that approach, and the results obtained by Johnson and Mall appear to substantiate their need for composite joints in particular