NASA-TR-R-358-1971 Stress-intensity factor for a cracked sheet with riveted and uniformly spaced stringers《带有铆钉和均匀间隔纵梁裂缝板的应力强度因素》.pdf

1、STRESS-INTENSITY FACTOR FOR A CRACKED SHEET WITH RIVETED AND UNIFORMLY SPACED STRINGERS by C. C, Poe, Jr. Lungley Research Center Humpton, Vu. 23365 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 0 WASHINGTON, D. C. MAY 1971 P I Provided by IHSNot for ResaleNo reproduction or networking permitted wit

2、hout license from IHS-,-,-TECH LIBRARY KAFB, NM 17. Key-Words (Suggested by Authoris) I Illill lllll lllll lllll lllll11111 lllll Ill1 Ill1 18. Distribution Statement 1. Report No. NASA TR R-358 19. Security Clanif. (of this report) Unclassified 3. Recipients Catalog No. I 2. Government Accession No

3、. I 21. NO. of Pages 22. Rice* 20. Security Classif. (of this page) Unclassified 62 $3.00 - 5. Report Date May 1971 4. Title and Subtitle STRESS-INTENSITY FACTOR FOR A CRACKED SHEET WITH RIVETED AND UNIFORMLY SPACED STRINGERS 7. Author(s) C. C. Poe, Jr. 9. Performing Organization Name and Address NA

4、SA Langley Research Center Hampton, Va. 23365 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration Washington, D.C. 20546 8. Performing Organization Report No. L-6826 10. Work Unit No, 1 126-14-15-01 11. qntract or Grant No. I 13. Type of Report and Period Covered 1 T

5、echnical Report 14. Sponsoring Agency Code I 15. Supplementary Notes 16. Abstract The stress-intensity factor and forces in the most highly loaded rivet and stringer were calculated for a cracked sheet with riveted and uniformly spaced stringers. Two sym- metrical cases of crack location were consid

6、ered - the case of a crack extending equally on both sides of a stringer and the case of a crack extending equally on both sides of a point midway between two stringers. The complete results are presented on design graphs for systematic variations of crack length, rivet spacing, stringer spacing, an

7、d stringer stiffness. The results show that the stress-intensity factor for the stiffened sheet is significantly less than that for an unstiffened sheet, except for crack lengths much less than the stringer spacing. Also, the forces in the most highly loaded stringer and rivet asymptotically approac

8、h limiting values for increasing crack length. limiting values of the stringer and rivet forces are smaller for stiffer or more closely spaced stringers or for more closely spaced rivets. The stress-intensity factor and the Stress-intensity factor Crack Stiffened panel * For sale by the National Tec

9、hnical Information Service, Springfield, Virginia 22151 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-STRESS-INTENSITY FACTOR FOR A CRACKED SHEET WITH RIVETED AND UNIFORMLY SPACED STRINGERS By C. C. Poe, Jr. Langley Research Center SUMMARY The stre

10、ss-intensity factor and forces in the most highly loaded rivet and stringer were calculated for a cracked sheet with riveted and uniformly spaced stringers. Two symmetrical cases of crack location were considered - the case of a crack extending equally on both sides of a stringer and the case of a c

11、rack extending equally on both sides of a point midway between two stringers. The complete results are presented as design graphs for systematic variations of crack length, rivet spacing, stringer spacing, and stringer stiffness. The results show that the stress-intensity factor for the stiffened sh

12、eet is significantly less than that for an unstiffened sheet, except for crack lengths much less than the stringer spacing. Also, the forces in the most highly loaded stringer and rivet asymptotically approach limiting values for increasing crack length. The stress- intensity factor and the limiting

13、 values of the stringer and rivet forces are smaller for stiffer or more closely spaced stringers or for more closely spaced rivets. INTRODUCTION The design of a complex structure for maximum residual strength and maximum resistance to fatigue-crack propagation requires quantitative knowledge of the

14、 stresses in stiffened panels containing cracks. In recent years, considerable progress has been made in the stress analysis of cracked bodies by specifying a stress singularity near the crack tips. singular stress field, has been used successfully to estimate fracture strength and fatigue- crack gr

15、owth rates in situations where the assumptions of linear elasticity are valid. However, the stress-intensity factor (or some similar parameter) has been calculated only for simple configurations and panels with one or two stringers (refs. 1 to 10). Existing knowledge of stiffened panels is limited t

16、o experiments with box beams and tension panels (refs. 11 to 15). The stress-intensity factor, a parameter that describes the intensity of the In the present investigation, the stress-intensity factor and the forces in the most highly loaded rivet and stringer were calculated for a cracked sheet wit

17、h riveted and uni- formly spaced stringers. The unknown rivet forces were determined by requiring the Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-displacements at the rivets in the sheet and stringers to be equal. The stress-intensity factor for

18、the cracked sheet was determined by superimposing the stress-intensity fac- tors for the rivet forces and for the applied uniaxial stress. Two cases of symmetrical crack location were considered - the case of a crack extending equally on both sides of a stringer and the case of a crack extending equ

19、ally on both sides of a point midway between two stringers. Although the points of attachment are referred to as being riveted, the results apply equally well to spotwelded attachments. The salient effects of independently varying stringer stiffness, stringer spacing, rivet spacing, and crack length

20、 are discussed in detail. The complete results for sys- tematic variations of stringer stiffness, stringer spacing, rivet spacing, and crack length are presented in the form of design graphs. Aij a Bi b b0 d E F K - K L P SYMBOLS displacement at ith rivet because of force of unity at jth rivet half-

21、crack length displacement at ith rivet because of applied uniaxial stress of unity stringer spacing specific value of stringer spacing rivet diameter Youngs modulus of elasticity maximum force in stringer stress-intensity factor stress-intensity-factor coefficient for rivet forces stringer-load-conc

22、entration factor point force applied to surface of crack 2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-P Q r,d S t V W X,Y X0,YO Z Z (Y rivet spacing rivet force plane polar coordinates applied uniaxial stress thickness y-component of displacemen

23、t stringer width rectangular Cartesian coordinates rivet coordinates Westergaard stress function complex variable stringer-spacing reduction parameter Yi,(Y2,3,a4 r A functions defined on page 17 function defined on page 17 function defined on page 18 ratio of stringer stiffness to total stiffness l

24、J. U Poissons ratio 5 distance from origin to point on crack surface functions defined on page 14 p1 pa “Xx“yy normal-s tress components 3 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- normal stress acting on crack surface shearing-stress componen

25、ts Txy STXZ Jy z lyc$2 51 functions defined on page 14 function defined on page 16 Subscripts: A pertaining to part A of sketch (g) pertaining to part B of sketch (g) B i at ith rivet j at jth rivet lim limiting S stringer Superscript : S stringer FORMULATION OF PROBLEM Unknown Rivet Forces Sketch (

26、a) shows a sheet stiffened by stringers of uniform size and spacing. The stringers are attached to the sheet with equally spaced rivets, and the sheet and stringers are subjected to the uniaxial stresses S and S- respectively, which produce equal longitudinal strains at large distances from the crac

27、k. The sheet contains a crack that is located symmetrically with respect to the stringers; that is, a crack that extends equally on both sides of a stringer or equally on both sides of a point midway between two stringers. The crack is assumed to be coincident with a row of rivets. (The results in r

28、ef. 9 indicate that this is the most critical case.) ES E 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 0 0 0 0 0 0 0 s4 -I Til- I1 -10 0 0 0 0 0 0. 0- Sketch (a) Sketch (b) shows the rivet forces acting symmetrically with respect to the crack

29、 when the crack extends equally on both sides of a stringer. The forces are also sym- metrical for the other crack location. The row of rivets collinear with the crack exert no force because of symmetry. As required by equilibrium, the rivet forces act in oppo- site directions on the sheet and strin

30、gers. All forces acting on the sheet and stringers were assumed to act at the midplane of the sheet. Sketch (b) 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-The equations necessary to determine the unknown rivet forces Qj were obtained by equati

31、ng the displacements at the rivet locations in the sheet and stringers. The dis- placements were written in terms of the following influence coefficients: Aij and Bi, which represent the displacements in the cracked sheet at the ith rivet because of unit values of Qj and S, respectively; and Afj and

32、 Bf, which represent the displacements in the stringers at the ith rivet because of unit values of Qj and S%, respectively. Thus, the displacement at the ith rivet in the sheet and stringers can be written E and (2 1 $= AS;F 2 2 2 Txz = Tyz = 0 6 Provided by IHSNot for ResaleNo reproduction or netwo

33、rking permitted without license from IHS-,-,-where K is the stress-intensity factor, and terms containing higher powers of r have been neglected. B cau - Sketch (c) f symmetry, the uniaxial stress S and the symmetrical rray of rivet forces produce only an opening mode of crack deformation in the sti

34、ffened sheet. By using the principle of superposition, the total-stress-intensity factor can be written as K=SG+ (4 1 j where Sfi is the component due to the uniaxial stress S, and EjQj is the compo- nent due to the symmetrical set of rivet forces Qj. For the case of plane stress, the coefficient is

35、 given (see ref. 17) for the symmetrical set of point forces shown in sketch (d) as - K= EL3 nt + V)Ql - (1 + V)QJ (5) Sketch (d) 7 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-where Y a1 = and (An error in ref. 17 has been corrected in assumption

36、 is made that there are no rivet holes along the row of rivets through which the crack is assumed to advance. or into a hole indicate that the effect of the holes on the stress-intensity factor is negli- gible except when the crack tip is within approximately a diameter of the hole. Thus, equations

37、(4) and (5) will be accurate except when the crack tip is close to a rivet hole. of eq. (5).) In equations (4) and (5), the The results in reference 18 for a crack extending from Stringer- Load- Concentration Factor For convenience, a stringer-load-concentration factor L is defined as the ratio of t

38、he maximum force in the stringer to the remote force applied to the stringer For a stringer that spans the crack, the rivet forces oppose the opening of the crack and, therefore, transfer load from the sheet to the stringer. Thus, the maximum force in a stringer occurs between the crack and the rive

39、t on either side nearest the crack. The force at this location in the stringer is wtsSEs + 1 Qj E F= j By substituting equation (7) into equation (6) (7) L=l+ wtsSEs E CQj j a Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Num erica1 Solution Becaus

40、e the stresses in the sheet at large distances from the crack are unaffected by the presence of the crack, the rivet forces are negligibly small except in the vicinity of the crack. In the present investigation only those rivets within the rectangular region shown in sketch (e) were included in the

41、solution of equations (3). The height of the region L 7 2a -4 Sketch (e) was chosen to be equal to the crack length 2a or to include 20 rivets per stringer, whichever was larger. The width of the region extended beyond the crack tips to include the next stringers. area were actually considered as un

42、knowns in the solution of eqs. (3).) calculations the computed value of the stress-intensity factor was found to be affected by less than 1 percent when the size of this region was increased. (Because of symmetry, only those rivet forces in one quadrant of this From preliminary RESULTS AND DISCUSSIO

43、N Preliminary calculations revealed that a variation in stringer width (for a given value of stringer stiffness) and a variation in rivet diameter had only a small effect on the results. in reference 9. Thus, values of d/p = 1/4 and w/d = 5 were used to represent stringer width and rivet diameter. A

44、lso, a value of v = 0.3 was used for Poissons ratio in both the sheet and stringers. This finding is consistent with that reported previously for a single stringer The parameters that were found to have a significant effect on the results are rivet spacing, stringer spacing, stringer stiffness, and

45、crack length. The following subsections contain discussions of the salient effects of these parameters on the stress-intensity fac- tor and the forces in the most highly loaded rivet and stringer. 9 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-App

46、endix B presents graphs of the stress-intensity factor and the forces in the most highly loaded rivet and stringer for systematic variations of the significant parameters. Thus, these graphs may be used as design graphs. Stress-Intensity Factor Figure 1 shows the effect of stringer stiffness on the

47、relationship between the stress-intensity factor and half-crack length for a crack extending equally on both sides of a stringer and a crack extending equally on both sides of a point midway between two stringers. The stress-intensity factor and the ha1.f-crack length and rivet spacing are made nond

48、imensional by dividing by the stress-intensity factor of an unstiffened sheet S Fa and the stringer spacing b, respectively. The ratio of rivet to stringer spacing is fixed at p/b = 1/6. The stiffness of the stringers is expressed as p, the ratio of total stringer stiffness to total panel stiffness. For stringers of uniform size and spacing The curves show that the stress-intensity factor of the stiffened sheet is essentially equal to that of an unstiffened sheet when the crack length is small compared to stringer spacing. Moreover, for a crack located mid