ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR. MICH. REPORT ON THE INFLUENCE OF SIMULATED COLD FORMING AND ANNEALING ON THE PROPERTIES AT 1600"F OF N-155 SHEET MATERIAL by K. P. MacKay J. W. Freeman Project'2536 February 15, 1957 Curtiss -Wright Corporation Wright Aeronautical Division Wood-Ridge, New Jersey

INFLUENCE OF SIMULATED COLD FORMING AND ANNEALING ON THE PROPERTIES AT 1600~F OF N-155 SHEET MATERIAL Parts made from sheet are commonly formed cold and heat treated to remove the cold work. The process is usually carried out in several steps of cold reduction and intermediate anneals. An investigation was conducted to determine the effect of such treatments on the properties at 1600'F of N-155 sheet material for the Wright Aeronautical Division of the Curtiss-Wright Corporation under Purchase Order FX 39962'1, During cold forming the.sheet is exposed to a range of deformation from those areas which receive' no- deformation to the maximum which can be applied in any one step. These conditions were simulated to obtain basic information by heat treating samples cold reduced by rolling. The effects were studied for material with no reduction to a total of 24 percent reduction in area, In each cases the reduction per pass was one fourth of the total reduction with an anneal between each pass as well as after the last pass. This procedure was used on- the basis that experience had indicated that the maximum reduction per step in cold forming was of the order of 6-percent reduction in area, Two series of experiments were carried out. In one, sample, with no reduction or a total reduction of 8 percent (4 passes df 2-percent reduction) were tested for properties at 1600'F after various annealing treatments, Water quenching or furnace cooling from 2100'F, or reheating to 1850 or 1650~F after furnace cooling from 2100~F were the treatments used. In the other series, samples with total reductions varying from 4 to 24 percent were studied at 1600F with one-type of annealing treatment - heating to 2100~F and furnace cooling. Evaluation of the effects of cold work and annealing was confined to 1600'F because this temperature represented the anticipated service conditions,

Rupture tests were conducted to establish rupture strengths at 20, 80, and 300 hours. Creep data were obtained during the rupture tests to define the time periods for limited deformation under these stresses.

3 TEST MATERIALS Machined specimens of N-155 sheet (AMS 5532) material from Heat M1083 were received. Strips, 24-inches long x 1-1/4 inches wide, had been sheared transverse to the rolling direction of the 0. 078-inch thick sheet. The sheet had been manufactured by Haynes Stellite Company who reported the chemical composition as follows: C Mn Si P S Cr Ni Co Mo W Cb+Ta NZ Fe 0. 10 1.57 0.78.019 0.008 21.67 19.56 19.65 3,10 2.48 0.91 0.15 balo The blanks were cold rolled to the desired reduction at Wright Aeronautical Division on a single stand mill having 4-inch diameter by 6-inch wide rolls. The desired reduction was achieved in four passes equally divided. In the study of the effect of various annealing operations, the individual annealing operation was per - formed after each pass. The specimens used in the reduction study were annealed by furnace cooling from 2100'F to 200'F in a hydrogen atmosphere. Table I tabulates the annealing treatment used, the specimen code, the reduction per pass, the number of passes, and the final reduction. The blanks were machined into specimens with a gage length of 2, 25 inches by 0. 500 inch in width. The gage length was in the center of '1-inch wide strips 22 inches long. PR OCEDURE The objectives of the investigation were attained by evaluation of the following properties at 1600~F: 1. Rupture strengths at 20, 80, and 300 hours were established by three stress-rupture tests for each condition.

4 2, Time-elongation data were taken during each rupture test and creep curves. plotted. 3. Stress -time for total deformations of 0. 2, 0. 5, 1. 0, and 2 percent were derived from the creep curves. These values were plotted as curves and total deformation strengths obtained for the time periods of interest. The deformation included the elastic, and any plastic deformation which occurred during application of the stress to the specimens as well as the subsequent creep. The stress-rupture tests were conducted in single units of the dead weight-beam loaded type, except when low stresses required the use of a.direct load, The following procedure was used to bring the specimens to temperature: 1. The specimens were set up in the units and the heat turned on at 4::0pP. m, to bring the temperature within 50mF of the desired temperature by 5:00 po m, 2, The specimens were allowed to stand overnight, the temperature raised to 1600~F between 8:00 and 9:00 a.m. the next day. 3, Final adjustments to test temperature and for temperature distribution along the length of the specimen were made so that stress could be applied by 1:00 p.m, 4, Time-elongation data were secured by means of extensometers. Collars were fixed on the upper and lower shoulders of the specimens by means of pins inserted through holes drilled in the specimen shoulder, Extension rods were attached to the collars and extended out of the furnace. Rollers carrying a mirror were inserted between each pair of upper and lower extension rods, As the specimen elongated, the mirrors rotated and the rotation was measured by a scale reflected in the mirrors to a telescopeo

5 The readings on both sides of the specimens were taken and averaged, The sensitivity of the extensometer system was 0. 000003 inches per inch in the 2 -inch gage lengtho Inasmuch as the extensometers were attached to the shoulders, the observed deformation included elongation in the fillets and a portion of the shoulders of the specimen as well as the reduced section. A system of correcting the deformation through a calculated "effective gage length" was used. RESULTS The deformation and rupture data obtained at 1600'F are given in Table II and shown as stress versus time curves in Figures 1 through 12, The rupture and total-def ormation strengths derived from Figures 1 through 12 are summarized as Table III and Figures 13 through 23, The data were usually consistent and gave reasonably smooth curves, There were exceptions, however, where the data were somewhat erratic, In such ases either average curves were drawn or the curve was drawn to show 'the probable true behavior of the material, Several. conditions of heat treatment with or without cold work were studied, The properties after the treatments can be summarized as followsInfluence of Conditions of Heat Treatment Treatment at 2100'F, either water quenched or furnace cooled, resulted in the most variation in rupture strength, Figure 13, between material cold reduced 8 percent and material with no cold reduction, These treatments also slightly reduced strength of the material which received no cold reduction, Treatments at 1850oF and particularly at 1650-F after furnace cooling from 21000F brought the two conditions together at strength levels similar to the original material,

6 The differences in rupture strength between as-.received material heat treated and material cold worked to 8-percent reduction and heat treated were at most 1650 psi and in most cases considerably less. The largest deviations from the strength of the original condition was - 1500 psi for the heat treated condition and + 500 psi for cold worked material. In general, these variations are quite small and no more than the variations commonly encountered between different heats (Reference 1). The 8-percent cold reduction prior to heat treatment generally increased short time and slightly reduced long time ductility in the rupture tests, Figure 14, in comparison to the as -received condition when heat treated the various ways, The major exception was the very large increase in ductility at all time periods for the asr eceived material treated first at 2100'F and then at 1650rF. Treatment at 2100~F alone with either water quenching or furnace cooling resulted in about 5-percent less elongation than the as -received material when rupture times were longer than 150 hours, Otherwise elongations were equal to or greater than the astreceived condition0 The lowest elongation measured was 5 percent0 In nearly every case, thee material cold reduced 8 percent had higher deformation strengths, Figures 15 through 18, than the heatr-tretead material with no reduction. The differences generally were less for the treatments involving heating to 2100~F, furnace cooling, and then reheating to 1850' or 1650'F than for a single treatment: at 2100'F, The degree of difference also decreased as the deformation decreased from 2. 0 to 0. 2 percent. In most cases, the difference in strength was considerably less than the largest difference of 2500 psi for 2 -percent total deformation in 5 hours after furnace cooling from 2100@F, The deformation strengths of the as received material decreased in all cases as a result of the heat treatments, Figures 15 through 18, Furnace cooling after heating at 2100'F generally gave the lowest strength of the heat treatments considered, There was little change as a result of subsequently

7 heating to 1850~ or 1650F for deformations of 2. 0 and 1. 0 percent while there was some increase for 0 5 and 0. 2 percent deformation in 80 and 300 hourso The decreases were generally considerably less than the 2600 psi for l-percent deformation in 5 hours after furnace cooling from 2000' and reheating to 1650'Fo The total-deformation strengths of the material cold reduced 8 percent, Figures 15 through 18, were generally closer to that of the as-received material than for the reheated as -received material. Secondly it was- often higher in strength than the as-received condition, except at short-time periods, Inspection of Figures 15 through 18 show that the inter-relationships of total-deformation strengths at 1600'F to 0 or 8-percent cold reduction with the several heat treatments considered were complex,. There were variations in the general trends with both the total deformation and the time period for the de. formation. Thus the "optimum" treatment varied depending on the total deformas tion and time period considered, It should also be recognized that the strength variations were relatively small in most cases. Even the maximum variation in strength of 2600 psi from the as-received condition was no larger, if as large, as is usually expected between heats. Influence of Amount of Cold R eduction The amount of change in rupture strength as a result of varying the cold reduction from 0 to 24 percent, Figure 19, was relatively small when subsequently heated to 2100'F and furnace cooled. Reductions of 4 and 8 percent resulted in the same strength as the as -recrived material. Cold reductions of 16 and 24 percent resulted in strength losses of 500 to 1200 psi from the as 'received condition. Actually simply reheating the as-received materials caused just about as much loss in strength as the larger reductions. Again the variations in strength were seall in comparison to normal scatter in strength for the materialo

8 Cold deformations of 8, 16, and 24 percent and heat treatment at 2100~F and furnace cooling resulted in some loss in rupture test ductility, Figure 20, in comparison to the as-received condition, There was little change from the asreceived condition for cold reductions of 0 and 4 percent.. The maximum decrease in ductility was from 5 to 6 percent for rupture in about 200 hours, Minimum values were around 7-percent elongation, These differences were also small in comparison to normal scatter between heatso The total-deformation strengths generally showed a little change or a slight itr-ease,. Figur es 21 through 24, from the combination of cold reductions of 4 or 8 percent and heating at 2100~F with furnace cooling, The strengths were somewhat reduced by reductions of 16 and 24 percent, Simply reheating the as received material ea us< about as much reduction in deformation strength as coild reductions of 16 and 24 percent, These reductions were no more than 2000 psi and usually less for the deformations and time periods consldered0 The only exceptions were the total. deformation strengths for 1-percent deformation in 5 hours, which were rather poorly establishedo DISCUSSION The most important result of this investigation was the indication that the variations in strength of N-155 sheet at 1600OF as a result of cold work and annealing during fabrication would be small. The variations observed were generally less than the normal heat-to-heat variation for N-155 sheet0 In cold forming parts from sheet there will necessarily be a range in reduction from no deformation to the maximum0 In this investigation the heat treatments used generally reduced strengthat 1600~F of the sheet which received no cold work0 The result was lower or no higher strength values for material with

9 no cold work than for cold worked material. The one study of the effect of percent cold deformation indicated that strengths first increase and then fall off with increasing deformation. The relatively small variations in strength of material cold reduced 8-percent and then heat treated under several conditions suggests that this was probably quite general for the heat treatments considered~ This then indicated that within the rather small range of variations in strength observed, the best treatment would be the one which results in the least loss in strength of the undeformed base metal. There were two treatments which came nearest to meeting this requirement: 1, Water quenching from 2100'F, 20 Furnace cooling from 2100'F and reheating to 1650'F. The second treatment had the further advantage that it avoided reductions in ductility in the rupture tests at 1600'F for cold worked material and considerable increased it.for the undeformed base material. There are a number of limitations to these indicated principles for cold working and annealing during fabrication: lo Considerations of cost, ease of forming to necessary dimensional control, warpage during heat treatment, surface preservation and other practical considerations would control the heat treatment used after cold forming within the range of heat treatments considered since the effects on properties were so small, The only possible exception would be the lowered ductility in the rupture tests for certain reductions and heat treatments. 2o The generalities are based on one sheet. In view of known heat-to-heat variations and probable variations of initial heat treatment and properties within the specification. quite different conclusions might be reached regarding the effects of the annealing treatments during cold forming for sheets with other initial propeties The variations observed were sufficiently small that properties in the initial condition could considerably alter trends indicated by the data.

10 3. The inter-relationships of treatments and cold work to properties varied considerably with. the time period and the measure of strength. Thus, there are particular combinations of rupture or total deformation strength for particular time periods when the results were contrary to the general trends~ If service conditions should be similar to these exceptions, the most favorable treatment might be different than is indicated by general trends. Met~llurgical Considerations A fairly extensive study of the influence of working conditions on the response of N-155 alloy to heat treatment (ref. 2) indicated that the properties of N~155 alloy were relatively independent of prior history for any specific heat treatment. It was recognized, however, that this conclusion was based on condid tions of heat treatments which attained near equilibrum structures for the treatments. The 10-minute treatments at 2100F were probably too short in duration to meet this requirement and some of the variations observed were due to varia - tion of structural change attained as influenced by prior history. Possibly more than 8-percent reduction was necessary to induce recrystallization during heating, The 10-minute period of heating would also be short for solution and diffusion of precipitates0 2. It should be recognized, however, that the conclusion of Reference 2 regarding independence of properties from prior history effects for a given heat treatment actually involved ranges in strength similar.to those found for the sheet in this investigation. Thus, changing temperatures of heat treatment are considerably more influential than the, prior history effects. 3, No microstructural studies were conducted, There is, however,. a definite pos sibility that the particular conditions of working and heat treatment could have caused exaggerataed grain growth when the reduction per pass was small, All alloys are subject to abnormal grain growth when deformed a critical

11 small amount and then reheated to temperatures sufficiently high for grain growth to occur~ The critical deformation is usually between 0. 5 and 2.0 percent0 A temperature of 2100'F should be sufficiently high for abnormal grain growth, althojugh the ten minute heating periods may have been too short. It is also possible that the critical deformationt: was missed in the reductions studied0 It is known that repeated critical deformation and heating greatly increases abnormal grain growth0 It would seem desirable to determine if abnormal grain growth did occur but had little influence on properties at 1600'F, or if it was missed by chance due to the particular reductions considered. If abnormal grain growth were inevitable where a range of reductions occur and it should be detrimental to properties at 1600'F as it often is at other temperatures, it would be well -to know it. CONCLUSIONS The variations in rupture and total-deformation strength at 1600~F found for cold reduced and annealed N-155 sheet were relatively small. The variations were generally less than 1000 to 2000 psi. These variations are no more and generally less than the normally expected heat-to-heat variations for the alloy in sheet form0 The annealing treatments were restricted to 2100'F with or without subsequent heating to 1850' or 1650'F. Some loss in ductility in rupture tests at 1600'F was associated with cold reduction and annealing at 2100'F unless the subsequent treatment at 165.0F was also used. The treatments used reduced the strength of the undeformed sheet as much or more than the cold worked conditions. The results suggest, therefore, two possible generalities regarding heat treatment after cold fabrication of N-155 sheet0

12 1l In view of the relatively small effect of prior cold work on properties after annealing, practical considerations of cost and production ease should control the annealing treatment. 2, Within the limitation of the previous paragraph, better retention of properties over the range of reductions tvolved in cold forming operations can probably be obtained by using the heat treatment which reduces the strength of undeformed sheet material the least. A number of limitations of these two conclusions are present in the report and should be considered in any practical case. REFERENCES al o t"The Stress-Rupture Properties at 1650'F of N-155 Material in Sheet For-m"l K. P. MacKay and J. W. Freeman, Report 2536-8-P. 2, "Influence of Hot —Working Conditions on High-Temperature Properties of a Heat-Resistant Alloy" J. F. Ewing and J., W Freeman, National Advisory Committee for Aeronautics, Technical Note 3727,

Table I Cold Working and Annealing Treatments Used for Sheet Specimens of N-155 Alloy Cold Reduction Total Specimen by Rolling Number Reduction Code per pass (%) of pass:e (%) As -received (AMS 5532) E4B 0 Preheat 1450'F, 5 min. Heat 2100~F, H2 atmosphere, 10 min. - Water Quench C4F 0 C4E 2 4 8 Preheat 1450'F, 5 min. Heat 2100'F, H2 atmosphere, 10 min. - Furnace cool to 200~F B4B 0 B4A 1 4 4 C4A 2 4 8 D4A 4 4 16 E.4A 6 4 24 Preheat 1450'F, 5 min, -Heat 2100eF, H2 atmosphere, 10 min. Furnace cool to 200~F - Heat 1850~F, DNH3 atmosphere, 10 min. - Furnace cool D4B - 0 C4C 2 4 8 Preheat 1450.F, 5 min. - Heat 2100F, H2 atmosphere, 10 min. Furnace cool to 200~F -Heat 1650~F, 2 hours - Air cool C4B - 0 C4D 2 4 8

Table II Stress-Rupture and Stress-Total Deformation Data Obtained at 1600'F for Sheet Specimens of N-155 Alloy after Cold Working and Annealing Def. Total R uptur e Deformation Time for Specified Total Spec. Per pass No. of Def, Stress Time Elong, on Loading Deformation (hours) No. (%) passes (%) (psi) (hrs) (%) (%) 0, 2% 100 5%1.0 2. 0% As. Received E4B I 0 14, 500 27. 5 21,0 0. 110 0. 5 2.9 5.4 9,2 2 0 12,000 66. 9 20. 01) 0. 083 1. 3 7. 7 16.0 (25) 3 0 93,000 402. 9 8. 5 0. 052 20. 0 74. 0 137. 223 Preheat 1450'F, 5 min. - Heat 2100F, H2 atmosphere, 10 min, Water Quench G4F1 0 14, 500 19. 2 20.0(1) 0. 104 00.2 0. 8 1.8 (4.0) 2 0 11,500 114.4 15. 0(1) 0. 709 1. 6 11. 5 25.5 41.9 3 0 9,400 133. 3 13. 0 0. 062 6, 3 20. 2 37.8 (60) C4E1 2 4 8 14, 500 23. 2 33.5.0.096 0. 2 0.6 1.3 4.0 2 2 4 8 11,500 167.4 8.5 0. 078 3. 8 28. 8 60 3 106. 3 2 4 8 9,400 350. 1 5. 0 0. 065 13. 5 70. 0 162. 273. Preheat -1450'F, 5 mm,. Heat 2100'F, H2 atmospherie, 10 min. - Furnace cool to 20-0F B4B2 - - 0 12,000 47, 0 18.0(1) 0. 090 0.9 2. 5 5.7 11.6 3 0 9, 800 179. 9 15. 5(1) 0. 063 6. 0 15. 0 34.5 63.0 1 0 8, 700 290, 5 10. 5 0. 057 10, 7 35, 5 74.5 134.7 B4A 1 1 4 4 14, 500 22,4 17. 0(1) 0. 107 0. 7 2, 9 6.6 9.8 2 1 4 4 11,500 11:3, 8 16. 0 0. 081 1.3 7. 7 19.2 34.6 3 1 4 4 9,400 332, 5 10. 0 0. 052 12, 0.43, 0 101. 178. C4A 1 2 4 8 14,s500 26,4 16,5 0.106 0, 5 1,8 4,2 (9.1) 2 2 4 8 11,500 104, 0 12, 0 0. 085 1, 1 7, 6 27.7 44,4 3 2 4 8 9,400 250, 4 77,0 0, 072 12. 0 38, lOS, 183, D4A2 4 4 16 1,SOO 370 6 10 5 0. 086 0. 1S 2, 65 701 14,4 1 4 4 16 9,400 166, 9 9. 5 0, 065 6, 2 19, 5 47,0 80,5 3 4 4 16 9, 15O 188, 5 10,5 0, 061 3, 25 14, 5 35.!5 715

Table II (continued) Defo Total Rupture Deformation Time for, Specified Total Spec. Per pass Noo of Def, Stress Time Elongo on Loading Def ormation (houros) Noo (%) passes (%) (psi. (hrs}) (%}) (%l} ~00~2% 00.5% -".. 2. E4A2 6 4 24 11,500 44, 4 13 5(1} 0. 085 0, 8 3, 0 6.8 13 5 6 4 24 9, 000 1920 4 80 5(1) 0O 068 6, 5 220 0 47,0 86. 6 4 24 8,000 369, 9 8.0 0o 060 13, 0 50o 109. 199, Preheat 1450'F, 5 mino Heat 2100'F H2 atmosphere,, 10 minO Furnace Cool Heat 1850"F, DNH3 atmosphere, 0 min Furnace Co.o - D4B2 _ _ 0 14,500 15,8 40,5 0, 108 0o 12 0.45 o 0 2,15 1 0- 11,500 94.5 39.0 0,084 0o 65 2,o35 7.0 14.9 3 - 0 9,400 268.6 12,5 0.066 6,5 19,0 41,5 85,5 C4C2 2 4 8 14, 500 16. 0 35O 5 0, 132 0. 1 0, 55 1 3 2,. 1 2 4 8 11,500 74,5 13,9 0.090 0,5 4.0 12,1 24.4 3 2 4 8 9,400 416. 6 10o 0(1) 0.070 11o 0 47, 0 127. 232,0 Preheat 1450'F, 5 min, Heat 2100'F, H2 atmosphere, 10 min. - Furnace cool to 200~F - Heat 1650- F, G hrs, Air Coo1 9 t, *.. *,*,. ' C4B1 0 14,500 240 9 60, 0. 095 0o 1 0.4 0, 8 (2 6) 2 - 0 11, 500 87,4 41,5 0o 080 0, 5 1.9 5.1 11.4 3 0 9,400 384, 5 23, 5 0, 070 50 0 1 7.5 38.5 84,0 C4D1 2 4 8 14,500 31,7 36,5 0,101 0,2 1 0 2.2 4 3 2 2 4 8 11,500 128. 4 18, 0(2) 0. 098 1, 3 7 6 26,0 50 7.3... 2. 4 8 9,400 3660 2 9o 5(1) 0.093 10 0 54, 0 134 0 2220 (1) Broken in gage mark (2) Broken outside gage mark

Table ~II Ruapture and Total Deformation Strengths for Specified Time Periods at 1600'F for N=155 Sheet Material after Indicated Cold Working and Annealing Treatments Rupture Strength for Specified Reduction Time Periods (hours) Heat Treatment Code (%.80 300 As Received (AMS 5532) E4B 0 15,000 12,000 9,600 Preheat 1450-F, 5mino C4F 0 14,50.0 11,250 8,800 Heat 2100'F, H2 atmosphere, 10 min. C4E 8 14, 800 12,500 9,800 Water Quench Preheat 1450'F, 5 min. B4B 0 139500 11,000 8,600 Heat 2100'F, H2 atmosphere, 10 min. B4A 4 15,100 12,000 9,600 Furnace cool to 200'F C4A 8 15,200 12,100 9,000 D4A 16 12,500 10,200 8,500 E4A 24 13,200 10, 300 8,300 Preheat 1450'F, 5 min. D4B 0 14,000 11,800 99200 Heat 2100'F, H2 atmosphere, 10 min. C4C 8 13o900 11,800 9,800 Furnace cool to 200'F Heat 1850-F, DNH3 atmosphere 10 min. Furnace cool Preheat 1450~F, 5 min. C4B 0 14,900 1z,000 9,800 Heat 2100'F, H2 atmosphere, 10 min. C4D 8 16,000 12,500 9,800 Furnace cool to 200'F Heat 1650~F, 2 hrs. Air cool

Table III (continued) 2j% T otal Deformation Str ength Reduction for Specified Time Periods (hours) Heat Treatment Code (%) 5' 20 80 300 As. Received E4B 0 (15. 400) 12,800 10,400 8,600 Preheat 1450'F, 5 mino C4F 0 14,200 11,900 10,000 8,400 Heat 2100-F, H2 atmosphere, 10 min. C4E 8 14,300 13,000 11,800 9,200 Water Quench Preheat 1450'F, 5 min. B4B 0 (1J,500) 11,200 9,400 7,600 Heat 2100'F, H2 atmosphere, 10 min. B4A 4 (15,500) 12, 700 10,500 8 700 Furnace cool to 200'F C4A 8 (15,800) 13,000 10,500 8. 800 D4A 16 (13, 000) 11,00 9,400 8,000 E4A 24 (13,200 11,000 9,100 7, 600 Preheat 1450'F, 5 min. D4B 0 13,200 11,200 9,500 8,200 Heat 2100F, H2 atmosphere, 10 mine, C4C 8 13,600 11,900 10,300 9,100 Furnace cool Heat1850eF9 DNH3 atmosphere, 10 min. Furnace Cool Preheat 1450.F, 5 min. C4B 0 13,000 11,100 9,500 8,200 Heat 210.0F, H2 atmosphere, 10 min. C4D 8 14,300 12,500 10,800 9,000 Furnace cool to 200'F, Heat 1650'.F, 2 hrs. Air cool

Table III (continued) 1%o Total Deformation Strength Reduction for Specified Time Periods (hours) Heat Treatment Code (%} 5 Z 80 300 As Received E4B 0 14,500 11,900 9,700 8,000 Preheat 1450~F, 5 min,, C4F 0 13,000 11,000 9,400 (8,100) Heat 210-0F, H2 atmosphere, 10 min. C4E 8 12,400 12,300 11,000 8,200 Water Quench Preheat 1450~F, 5 min., B4B 0 12,400 10,300 8,600 (6,900) Heat 2100'F, H2 atmosphere, 10 min. B4A 4 14,300 11,800 9,700 8,000 Furnace cool to 200~F C4A 8 14,700 12,'000 9% 800 8,100 D4A 16 12,000 10,100 8, 700 7,500 E4A 24 12,000 10,000 8,400 7,000 Preheat 1450'F, 5 min. D4B 0 12,000 10,200 8,800 (7,700) Heat 2100'F, HZ atmosphere, 10 min. C4C 8 129500 11,000 9,800 8,600 Furnace cool Heat 1850'F, DNH3 atmosphere, 10 min. Furnace cool Preheat 1450'F, 5 min. C4B 0 11,900 10,100 8,700 (-7,600) Heat 2100'F, H2 atmosphere, 10 min. C4D 8 13,400 11,800 10,000 8,500 Furnace cool to 200F Heat 1650'F, 2 hrso Air Cool

Table UII. (continued) 0 o5% Total Deformation Strength Reduction for Specified Time Period (hours) Heat Treatment Code (%) 5 Z 80 300 As: Received E4B 0 13,000 10,8Q0 09,000 (7,500) Preheat 1450'F, 5 min., C4F 0 11,800 10,000 8,600 (7,400) Heat 2100F,. H2 atmosphere, 10 min. C4E 8 (12,800) 11,700 9,100 (6,900) Water Quench Preheat 1450'F, 5 min. B4B 0 11,000 9,400 7,600 (6,200) Heat 2100'F, H2 atmosphere, 10 min, B4A 4 12,900 10,300 8,600 (7,000) Furnace Cool to 200'F C4A 8 12,300 10,300 8,500 (7,000) D4A 16 10,800 9,100 7, 700 (6,600) E4A 24 10,800 9,100 7, 500 (6300) Preheat 1450'F, 5 min. D4B 0 10,700 9,300 (8,2.00) (7,200) Heat 2100F, H2 atmosphere, 10 min. C4C 8 11,200 10,100 9.000 (8,000) Furnace cool He'at 185.0-F, DNH3 atmosphere, 10 min. Furnace cool Preheat 1450'F, 5 min. C4B 0 10,600 9,300 (8,100) (7,200) Heat 2100'F, H2 atmosphere, 10 min. C4D 8 12,000 10,300 9%000 (7,900) Furnace cool to 200'F Heat 1650'F, 2 hrs, Air cool

Table III (continued) 0, 2%o Total Deformation Segth Reduction f or. Specified Time Period (hours) Heat Treatment Code (%) 5 ZO 80 8300 As Received E4B 0 10,500 9,000 7,800 (6,700) Preheat 1450'F, 5 min, C4F 0 10',100 8, 900 7, 700 (6,700) Heat 2l00'F, H2 atmosphere, 10 min. C4E 8 11,300 8,700 (6,700) (5,200) Water Quench Preheat 1450'F, 5 min, B4B 0 9,900 8,200 6,500 Heat 2100'F, H2 atmosphere, 10 min, B4A 4 10,400 8, 800 7,300 Furnace cool toZ00'F C4A 8 10,400 8, 900 7, 600 D4A 16 (9,300) (7,900) 6,700 E4A 24 9,200 7,600 6,v300 Preheat 1450'F,5 min. D4B 0 9,600 8,500 (7, 600) Heat 2100'F,M H2 atmosphere, 10 nin. D4G 8 10. 000 9, 000 (8, 000) Furnace cool Heat 1850'F DNH3 atmosphere, 10 min, Furnace cool Preheat 1450'F, 5 min, C4B 0 9,500 (8,300) (7, 300) Heat 210OOF, H2 atmosphere, 10 min. C4D 8 10, 000 8,900 (7,900) Furnace cool to 200'F Heat- 1650'F, 2 hrs, Air cool

9. _ _ __T _ _ _ _ E~~~~~~~~~~~789I 2 354 Mate6r a: AMS_____K Heat'?;io>,: M. 0 83 5 t4 a.:: Li a - 1 1 1. 2 & A I-~~~~~~~~~~~~~~~~~~~~~~~~I - tx tE-I f;:10 i1 - - _ __-_0 - 10 -i- tt I < t V - |I _ _ _ _ _ _ r z___+e < 0 1 I I 1: Total. Dif ___ _ 1 *jO t zr7 I l I I I I I i~~~~~~~~~~~~~~~~~- _ ___ +_ _,I+_ -- II A~~~~~~~~' 1 -~-7 -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~MN 811 —1 -. _____ ___ _ll --- 1 7 - 9_ 1_ X 3_4 5 6 7 8 9 1 2 3 4 5 6 7 9 1 2 I _____Irne -ho~xrs ______ _ Figtirel, __ _ _ ___ _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o __e cres _ Eire t60 fo __ns~ -~~~~~~~~~~~~ oer~q*3li condition. noed Above, T________tstr ___eomtonec eln - _ _ ~~~~~~~~~~~~~~~~~ 4- K 9 1345

Spec. Nos I T4 I 2 4 — 4 -. __ - - Th ______ - _7 -C %1TptaIl A 4D fprma 5i- r —[ -t --- —~~~ —~ --- 4- ___ _ ~~Total Dafr~tin'i v _~~~~~~~~~~~~~~~~~~~TtlD 2~~~~~~~~~~~~~~~ a L ______________ ______ ____ 1-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1 M. __ 13. ___~~~~~~~~hur 9 -.~~~~~~~~~~~~:r ___ ___________ ss otldo r- ioiti~i ~to - otki e t 0__F r ___ __ __Sp,ite 15.s-etmaeia.i __ __ e- c-ni~:-m pt-iab ___9 _ __ 4__ z The9-_.6 89

=~~:,t:: I 1,, t~ ~t: t:':... a~~~~~~~~~__:i ~ _''.' -Se- I I - I I I I I ' ' I I ~ --- —l I Ankld i___[ i - i f-tt-l~~~~~~~~~~~~~~~ -- i '...... I......... — -i ---t — - --- ---- —......... -- -- r -- [i.... I~~~~~~~~~~~~~~~~~~~~~~~~~~~: ---- -I-..._j...i.....I[ — ll-' -lI Il i~~~~~~ i-. P i I ' i I ----— [- — t-[ 'i jt.......... - i i -......................... --....... i........ ~ ~ [ - If I... -- [ - iI............................. -- ' ~ -. ---~~-~ ---1.- c f~11-1,I-i aI. -- --.... --— [ -- ------- 1~ ~~~~~~~' i ' '. '''i 0'0 rOta:l D~forL~T~tion' ~.q [,, [ i I.~~~~~~ ~ ~~~~~~~~~ i I,:I I [ I C~~~~~~~~4 1 i~~~~~~~~~~~~~~~~. ` _]l~] i::....... i....! i'!i ':.I,... _i:r~:.......!....'~' -: ':I ~ [ I ' [ I s,~~~~~~~~ 5 I III... ~:~ ~~~~~~~[...' ' II if~~~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~ C- III'~'i ]-' I ~ —. o uk~~~~~ I......... -i; j-l..... I I 9~~.... dI:IIIi_ 7 i ~~I 7~~~ 't' ~i —L ---~ --- —- — ~ i ~ ~ ~ ~ ~ ~ ' 1 i i:I i. -i[f~ I~- -. i. — t - - [ -- I I... _._... _1..-.... —.. s — 1~ ~~ - __:_ _ i [ol L__ i i __~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~__Il_____~- _i Il_.....~~~ ---titie:rh- ~'ii-i — 3 ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i: '1'~ '-._.-'I _~ -.... [~~gr I! r I t ' -- ' LI me eat.:sreSoa.le~o in izj u~~~~~n~ L lO'F r e t rp-e'a i rre-n'.1 / / I-'": ' '' '"j'j I j - ~t,! 'i.!:.~~ ~t It.......iiititIiIt-........ i...I -it It: -....... [...i i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~it:I.-.. 7 9 1 2. 3 5 6 7 8 9 I 3 4.5, 6 7 8 9 1 Z.~ 4

' ~ ~ __ _ r T~v"V'_ _ _ _ _ _ _ _ _ __ _ V i -_ _ _ _.._., -—,..... ~.'~....~....:.,: —.n- -,:.~_j 1,u._4_ -.~ _ _F~._ _._ ": I JIi IL _/.'__ __- ~.;'i..__~- _-_'- _-"-'-! '._- ~~,::. %~-~: I~.:'-'T'oTha D~f'-n~-i'ii- - '... _ _._. t ~ ~ ~: — ltb -i -___ '.... —........~........... ~ ---[ —1- — ]- -___ _....................... ]..,.. ~.., t- -~-q-.........!. ~. _~.l___L_ _ __' — ~-. --- —. --- —' __j~ ~~~~~ KW _-& —t-, - - 52 ___' -i' —.4 o.... lb. - ~,~1o -t'I-' -S~t,t '"~ e-....d',"'i -n-aTvi - da...... 3j gur41, -, —, ___t ___. _ + ' _' _ ''I ___ ''e " " ~ ~~ H' __ __ _ ___ _____________~ ~~~~~~ ____ i......' — iL ---.i ____....:L...11 ]~I ~ ____________.:t___ 7. 89... 3 4 't~7 9 4 5 b 7 9

':!'!~.7- 'x —~~~~~~~~~~~~~~~~-4-',.. 8.-....~H~I7%:- -T11 l~~~~~~~eat~~~~~~~~~~~~~w~~' '"i - ' ~K '. ' T i'r~~i I' i- ~ I V ~ ~ _ _I _ _ __ __R_d.C 4_ OAief rn ato r I [ i -_ to ~~~~~~~~~~~~ mill __ -— n-' _ _ __ I t Ii ~~~~~~~~5 Total __ I~~~~ ___ __ t' to:. t!!!..iI.t'.t -'I::..'-'1. —;.,!- - ' 'i'_J._'__L__L__t_t L __~...L............__;..._.._......~.....-..- nN -- --- 7t Nii -t -- t- Tf..T. ___-~__:_. '. ~ _,_ '.' ~ -"': j iI:.~~I:, ~,..:i~-._~.=-,~4-=-~ ---4u~- __ —~ ~~a~v~ao-!...-:-' ______ ~ ~ ~ ~?-:' ___ I' ___=~-,~- __-_ _: —hi......__ __ —:-: ___ -,J~~~~~~~_ - 1~~ o~ __.. _u~_____1____I...___.-.,...-.:.:-..- _'__.__[_-__-L____=_ -..,-'. j~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-i-m._-i-' —{ — "~' --- _ _ - lrs —_.._._ __._' -... _.._._. --- -......-_ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.:. t_,,~~~~~~~~~~~t - F" --- ——.t~ I - t'!'l j-'i~ i ~ ""!"' i",'"t 7+7 i -' t I' r t'-' *... ef' o'e, 'v ':t"'"'e '" -'" - f 71 s'e,! ~~~~I t____ —__-'....I..1 ____.L....iL..~.LtI t...L....1.......t '______ ____-'-'!___ 1...,....LI.'t. t-~-'.!-t.4.....!i.;......i.....:.i ________ '"'i':__ ' I '____ 791. t ' 3.I 4 5 6789 t,.: i.... ~L.! ~, I '.,_LZ_ —L ~.,..1 2..'- 3 45 I 7891 2. 4' i ll 1.. e '!,. ___ 89 1 3 9 1 9 1 2

9 - - -W 1: 1::1 1:f I: I 1 - s -; - - 1 ' 1 _ _:0 _ _ _ _ _, 7~~~~~~~_ _ _r | = - 1X- - i~~ _- 4 1~ lX E3~~~~~~~_ -u-c-I 49;:1101:1 11ii1lii, - — t- -F-t ----i- - l 7-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~5WA o~h mJ +AF - P ee- 4-4t 1 -i! F _ 1dI euI Il++F4 r1t4Ufio -De~~~~~~~~~~~~~__ t-tl — T4m -,:l +:;:Iea:- +:t Z__t i.+_ $ ' e 4 -~ -1 j -- f ----4 - D — f:rn~ -4- - -- 4L I 1-1 -;T -IF^ * -4p~P15 1 _11__-__I - __ ___ _ I_ -1 I - I e r it1 f — A M-1to '4 1 - I ____ __ 1 X < - t -j I - - I - 1 0bRt 5 o 1TotalDiforntior,oTotal DE omito L t L T - f | -D- I DI- VI: 01: LLI -IS- | 0| 0 - -_ L4_ < 1 0.2 To al DLP~R l~ 081 X 4 = 7 L. _ _ _! _._ __ _ ___. _.__ 7tt1< - -:-1.- 4X.......... 1 - 1001:1 -4::1 l| 1 --- —- -1 ~ Vt-1-1:tt l l; —l7- -___ t................................ -t 8s - 77X (XA t +41 t ' 0 L Time ho 7rs 3~~ ___ t7 I__ I__ I_ I_ l rr5- |.11| I__ __ l_ 4 | 0| |i Wguref p..... Wress.-!.u' ure'larldlstre.59sl~d formatio, timei curVes obtai ~ed 4t Ii DO IF' fcr Wheet sp~ecireso -5 1- -- 1 ----.. Iseetrrate igne c h tn~e4 ea ap< — -- y:' l7;l00ii00-' 4 5 6 7 - 9 1 __3 4i5: I - I - - 7 _ 9 I 2C 1 t.1. - -,0.1.Tll 4, t I:: —I I '-p - g-1- - - _ -- - 3 1- - - - 1 -— ' ': 1 _ _ ' _ _ _ _ I - ' 1 1 I'' - -.- - '- ' 1 ' - t- - i _ _ _ _ _: 1 _ _ _ _' 11 7 8 1 23 4 6 78 9 2 3 4 5 7 - 9T12 3e

et N8: 9 82 3 N7 1 _ _ _ __ _ __8_ spec. rlos.:. D y_ 6c RedL1j'ctian- - T. 4~ 4- i -- 1f -I - _ - - I t 7 < 5 ----~~~~~~~~~~~~~~~~~~~~~~4i6L"A.2o~ _ He1 _- A YiL* 1Def~ormai t _ 4~~~ - I -+- -K --- —- - ~ —t An _ 5__ _ _ Total D'for1tio11 3. ___~~~~~~~~~~~~~~~~~~~~~: tV __ I —l —0 1taD f 0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- - -- - _ _.-... - - 4. _ _ I - i 7 1 V I r i V -t - _.-.~~~ __ _. 1 _ _-i T~ 1 ~-j -- - —.iOt-!5To:....~ Wm, MM I 1 - - - __- ii'w'e hoars Fiu __re tlbss- ut e adsrstdfmatiorn time curv'eslobta1ie F. secmes ~fNirb 2 t -g' — nd- "6 --- - k s rt 9_1 1 2 r 4 5 j: 7 8 9 1 2 llfi I ~L J_ _ __ _ __ _ ij { jJ __ __ _ _ _____~t __ __ _ _____________ _______~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~ --- ____ ______ ______ -- -----. ---— ~- ^-T~I --- ~ — -- ______~~~~~_.____1_ ____..- _____ I-III ___ _ _ ___ I i J ' H ] _______ 7891 2 3 4 5 6 78912 3 4 5 57891 2 3

7 912 r 7. 8 9 9 68 StX =C Lt|- 05 t 1 I I I~Ali 4t81 l | S - v tX 1::.1:F. |I(; _t tO4VP - t 5 C 1 I I: - ~ - 1 - = ttt+: t t V ---smationt ---tH __ 717~j~ -_ 4 F S ~I I I I; 1 ~~~I I I 0 W~~- I I I -- t —L- -— t- - -a Anne: __'o: 1V:at.Pih 75t 4 _! 60e he0 — - ____sE0-+t-~~~~~~~~~~~~~~~~~~~~~~~_I.___7- =- -----:.-. - -_.. - i i t - ffi —4, —T-t<X ---l — ^04 4_ L8 Total I 4 1 _ _ - F 0 1 I ~ b I ~ 1 I I _ _ i I 1 i 1! I I 3X;t|- 1 _-_+~l~U-` _ _ — _ -_ 0 - --- - - 4- - I r r: 20 1- -_2-< | 'I t0 0_ - -- ________ ___ ' I ' '__ _, _ ___ - _ _ _ _ 21. _ _ SK t at e. _ _ _ _ _ _ __ _ It_ ______ _____ _ ___ WLrLi n___ __ _t___

"ii ~ ~~~~~~ ~~~~~~~~~~~~~~~~~ - r' T? F + Matieral:A 543 N _S _ | _ _| 7 Weat~: c>' j;exl 8It 4tL 0 | cHeat: I ----- i__ _ 3educiot1 t 1 x LT1 - _ 5 T 7m t 6.3)e: RedO~ f1 __1: __i rn i —f -F~c _ _:.-__ - -1 ---KLr~ - -- -t- -------- 2 I -j -~- 24Olt tt u there m - nA c,.-e 40=1 L --- I — ' —1-11- -|1-1tt1- I5 - 1 5; 1 -H I --- 3 —1-1 —_ -_, = -~~~~~~~~ DQcftrmather n5____13 | > - _ L!5t_ - -1- t1 13 triha tioT 2 ___ t__ TVi ol __ - t Cob 3tt | Ttal Defc 9 I ___ __ -__ ___ __ - _~~~~~~~~~~~~ Ji - -- F 1 o -I _____________ the __gtolroe.loe4T1. 1. 0 ____________; 7 20-tl-4 X 0 -: —1-. I T. l W tXTTI l 0 1;, I 1~~~~~~ -; i I L, I i- rV 7~~~ 8 9 1 Z ____ L -i-,40510t ___~~ — __~- __ I __ __ — ~~~~~~~ ~~~~~~~~ ~ ~~~~~ ~~~~~~~~~~~~~~~~ ____ I li.- -__ — _____ -__ ____ __ I ~ ___ tt ___ 1~~~~~~IJ~~~~~~- pI~e - tota d-ox Lhfs L4 if izi F`ro j~~~ ___ ___ __ ___ I I. _ _ _ arm-~~~~~~~________ I fo__ time i- i I I 'i I 1 t_______ 17. 1.1.....j..A ___ I. ________ ~:-:l ---i a I ~........l ____________ 1 ________-l 1- _______ J~~igur 40 9 SY~ hotr s ru ute ad a" 8 9 1 235 7891 7891

a. _ _...:1;1 1: ~ E;IIIt __ __: 1 ';1,11,1;IW 8t t~~~~-H-'; * -g 6$;1i51 51I> - I~ I__f_Spec- AlA. _ __ __ A K -4 - -| - |I v- - - R -l tj rPi 1-.eha ~-. _-T4f]rain iI - _ _.. I, F. I *c c~o I ___ ___ rLV- - 3-p*4_ -- 0! '- - i__ _ _ _ * % T otal Deforrz iation I o __ 1___ -__ -_ _:01: S 0 | 0 V!: 10 f: — 10: i 1 0 1 _ _ I _: 0 ] i 1 1 A F f o. i%| Total Defor'afon o | <- X: 10 - - 1 t 1 tl 1 1S tX |i I: [ — -t — ---- 4-. 20 1:::: f- f-: i 0-74 I - - ' -1 i! - -,__ _ _ _ _ __ __ _ _ ___, _, I__ ___:1 I -1 j ~ -.>.5hL -t I _ 1 -,;1: 0 10 1 *c F1i 1F 4~~~~~~~ + t t T0 f0 _ _ _ _ _ _ _ _7 -_ _t - — ~ 30~~~ r.zr -+ —~- 3100 | Figure l0 St; -t.. E es$- luptu e nd st e 1total deforn-ition tirre curkres 6bt~in d S.t ~6{0 - ~fromn sh~eet sped~imen$ 1:- |I - 01s; 1 T:1W __0 I _ __ I II.:.: j i..1 1 t' I l3 < < - - -: i- -i --- E ]; A i! L - f l | {. X~~~~~ ~~~~~I I -' xs ---- -. I.-1 — ' ---41- I...ir I —; TT { 1.III.._:,1 i1i _. I 7 9 1 2 3 4 5 6 7 89 12 3 4 S 67 8931 2 3 4

-r ~~~Material: NI I It.. _. - - -~ --- —t OR iiden..~~~~~~ — Heaa Ltno~ '-'7-?-.. C. min., ',i-i:- I ' - ~ - ___ _ __ __ ________B__ __ _ -H~~~~~~~~~~~~~~~ L ___ _ _____* ____ _:_, ho Itr. 'i' ---4 ---: ---t- 11 _____- ~~~~~~~~ I __ ____ 1 1 ____~~~~~~~~~~~~~~~~~~1~~~.~~~ ~~-j. -K — I-0 K51o otl f sl-:1I =. _ I:_L _____.L.,i-~- -, _______li rin - 4~~__ ___ " ____4 __ 1234''.~'' '; ~~~~~~~~~~~~~~~~~~~ 0'....._. _ _: ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~:..............................................MURNN 8. __I_ _ _.110_1____ ___ l- _____ ____- ~__ r __ j ____ M M ____________ _________ ________ 1~~~~~~~~~~~~~~~~~ ~ --- i..i4. ____ l L1 ~~~~~~~~~~~~~~~~~~~~~~~ — -j__ -_ I t I — T ---[ —Y -, 1 ITi I. _____ ___~~~~~~~~~~~~~ I (L 11 1.t en.7., ____ K~~~~~~' ~,!on,4 S:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ti MR -h&( Wi JI5 I It.... -] - —...-n d. _____________ __________ 1 ' 1 _________ L L L ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~I... L....... i. J....... __ _ _ _:__ _ _ _ 7I~91 2 3 4 5 J 7891 2 3 4 5 ~ 7891 2 4 I~~~~~~~~~~~~ I 7 8 9 1 3 4 5 6 7 8 9 1 3 4 5 5 7 8 11 #I 1 J ' J

1 I _ I j i i - ' 1 ~ Material- A 55 2,NI 5 1 - - 4 Heat:- M 083 I ___bpec-~ ~ ~ ~ ~ ~ ~ ~ ~ __ ___oI____ _ 6t~~~~~~ t M sn te l _ReduCtiomn 8'- _ ~, 'a. ed, _ __t i, e ~ ~ e k-I i I — |~~~~- E ---i- -----,_ - I W -4_ _ — "-I I Ai: Coql j De..... i i i -! i --- K T --- —- -— 1 — -- - - ----— h- -~ -t --— l1 — -I + --- —- - i ---l-L;t-~-1 1 __ 4 __.JTia ~eogt~ ~3: H t I id~. _ _-I t!:- -! I Ajir Cec1o ~~i ---l a I L f fl! i 1:i _| X + j jD.#tsl Tcital I~eforr atiOn Ttl ] i:t~ I I: ~ i! i~~ i I I ~I~~ I I I efI: l 2t 0 t ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.. 1 7 t1:- -[ 8 i!- 9: 0lil1i 7 i 2Lo. r~~-~-K-t- ________ ~ ~ 5~~jij~fH] _._ ' 1i —.!.i - i - 1: 6p 1 1 1 - ] + >-, S 1 i!!;! 1 1::: ll -!0 isi i;-i! 4 1z1 01 0J!::" ": '' -!-r i+-:.":':~ 1..i.... ':;::!::'I 5 I-1-V __ -— 1- < --- - -01 -, — t_ ___t___ __-l — -~7-j-tY -0 -:!-ot ---- __ __-: l -;______ *_____ t_ _ _ _ T,i _________ __ _~. t,. _ _. 1 _._. 41 _____ _____ — — ___ _____1 —, ---t ' —t — t l- g — l --- —---- -0 —1- '- --— 7r-r —r ---- — t s 1-i I - ~: i::: I 0 0 1' " -! __, _ _ _ J - I 3tl!1 - 1 1,t I -t. l l -_ _ _ _ _ _ _____ - ~1 -|!!, Figuie 1Z I s~~~~~~~ttess-tuttitrb indstrqs~~~~~~~~deforreatiofitim'e C~~~~~~rve9 lobtainedaq lfoo t from~~~~~~~~-he-1 — IIpejci~ -s _ ji i_*___ ___ _______ _______,_ *-_- _I -_t4-{ *_-_____- __ Ti _ — - e- ho — r ---- - - ___e --- —---- N 1 -du1" i 1 ~~ ~ ~ ~ ~ ~ ~~0 ':, Figuxte __e ian s rq -def or rtxati icte. ate.j I om- -h I~ 7V.! I - I, 155 seietmmCe rbn a10o the condition hed at e vn 'of...!! 4 I _. j i.I '4 I. I 4 I 6 7: _____, ___ L1 i_ l IA4_ ______ _ 1__: ___ ltl _ l _=___ _ i- _,__=,!: 3. 4! 4 78 1 2 3 4 5 8 9 2 3 4!~~~~ 'l -.:::::-!11!E]I;Si: ~::- 4:: IX-1,7 -.-.11... -::-I| 1 1 I, I ^ J _ I I t I i X! t..:I I I ' ".|'.:. 7 8 9 i 2 3 4 5 6 7 8 fi 1 2 3 4 s 6 7 8 9 1 2 3 4~~~~~~~~~~~~'" j~i..

I ' - Iii~ [1_V '"T 1 1 1 e —~-.:,-iw'J-;.:~.-i,.-..-+.-!-.~-i-.......! '...1 ' 1 - 1.... ~ I.-.I. —! *" — ".- 1. --.. -. -',d:; —!.'.....-iC,' C-t~. t — ':1"i' t 'I- 1 tL t tI I I": f t -1t W:- Al' 4: -I:I.. I. I 4M 1 -- 41 — __ _.V.. |r!, 1 1- i l I l: l:: t: i: l! I:!:1 Q:

ANN ARDOR. MICH. R eduction IP - 6ajiI ~I~7f9~~I I K ~ 4i I; i 'I t.. -i _ _ i-. —'- ~-i — ____ 1-..... __ __ _ T i: -7-T~C __ t I:.. _ 1.G I~~~~~~~~~ I: tp ~.t~::i i._ ~~ ~ ' 4 __ _ _-_ 0 fl __ ~414 1 II -- o r f ~ ~ ~ t:... ~ f ~ t ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I. 20111 I- j - I _ I ~~~cl I I —~~~~~~~~~~~~~~~~~~~4- --— ~ —~~~~~~~~~~~~~~~~~~-~~~~~~~~~- __ 1i~ __ ____ ____...2 I I~ 1 ~ ~ ' _______;-4~ ~ ~ ~ ~ ~~~~___ t-.-.- ______i 1k — i -I~_I-_ 1OF 0 T j77.jr i ~, I t Ar i~~iiiriaoaIir.ieo vaILILIZI]1 iiiiil 30 1 i~~~~~~~~111 = i:'Ch-, r,t.1. Tt:U W6Ze 1

-t ~ ~~~~~~~~~~~ -It If T: i i,~~ ~ i: A11 i,t: 'I'i:1-~'f T ( -t '-IIT I1~ i i - —: i. L ~; I t~~~~~~ —a — t -.~~~~~~~~~~~~~~~~~~1.i~~~~~~~~~~~ *1'*I 4,~~~~~~~~~~~~~~1.,4Cfp.t I-,t I. i i-i..i i iI - 2- BL.: i I:-~~~-1.. t:1 i. I: I8%-R d c 'i n..... -f ii..:........ hrs 414 ~ ~VAN -'-.9b..;. i.; ~~~~~~~~~~~~~~~~~~~~~~~~-7 --- -t aI, — -- - _j I. K:: r L 1-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*I i.c. *I-;I.- ~ ~'L ~...K-.K.... 1-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7 -— i ~ - -i I A i1r t e.I.... i ~ t~ 4r -V ---.L: — A-i — -i -:- L 4 ~~~~~~~~~~~~~~~~~~~~~~~~4;-1 1l- -: -: ii[IIALi iLVI[ItiiLK j: r I {~~ II- ____ _I L.. i_ i ~-, ~:,ii:: i: I A ' Dol ' I r e i: i~~~~~~~i r t ~ t f -~ 1 Le V ft tx ft-W ~~~~~~~~~t In' e r 4 -u1L._I:i_

-i i. _~ ii ~,, i~. ~._ _.1.~j I.~ i..; J..I I f F ' 1-~I..: ~-i ~'11 i.!!i '!.'l!!?!'.-j-ii ii~ i ~ ~i. ~ ~''.t~. — I... 1 1 1 4<..... ~.... I. II!; i I [7hi t -1':. -t'. K — — '! 7' '~-i- i i'!- i. t'.:.....~11.- - 1::_: i~~~- i! Uoxak toule, ~~~~~~~~~~~~'DI!", 4:'~- il0i~. -vk!m 04 i~''i~~~~~~~~~~~~!- cr'-,1~ iiP~Ut0 i ii....: 4I -17 t 171i__-a - _ v-n IzI I fi 4 ' Iv1 LI_~ ~ ~ ~ ~ ~ ~ ~ ~~~i~i~~ ~. I.~.,-t ~ -- ia t lr ~~~~~~~~~~~i ~ ~~. IL0.~~ IiIi Cpl i CJ3. fi ~ SI 1=3 I - 3; ~ ~~ -I -t ' i1:: i I Ii.I: ':'4> w~~~~~wL ~ - I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4 --If t ~ t!+.! 1 -~~~ r!~~~i i~~~iii i.1 -: I~~~~~~~i i.: i: ' ~ 1~~~~~~:' ~... Ai%." a 6~~~~~~ -- K —'. — t --- — — [I-'- -I - -i -i i-li — - - - - - - - ~r-i.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- ~ ~ ~ ~::l:..[.:;......~~~lle~~~__:~ i~ --- i'~-t: ---"1-'~mr._ ': ' t.. i... frT~ [. ~ 'i ~~':,i-1 t ~:1 I f-? ' c.. I. —. —~~~~~~~~~~~~~~~~~~~..?.... i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- L:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

777........: ' —; I;,: ';;; ~I I t K.~1:; A ~L:.. Aj.- -x T-K II 4 7ii. -ri -r - I:r~- -. I II.. I_;_._.. I_:_.X... 4 i~ ~ ~ ~-e- - -- - -~- if 7 17Ij 4 I I i.....: i -............: 7 7 f...... - - - A.-4 - - -- - ----- A' g m r,ia i 0 ~~I r- i..I II'.;j~~~~~~~i ~ ~ ~ ~ ~ ~ ~~~~~~~~ t i ~~ ~ tona at tr e t~~~~~~~ I.-K. 4_ __l N -V-I<T-<4 -... i:l -i~~~~~ - -i -- ij4J fi ~~~~~~~~~~i~~~~~~~~i::~~~~~- --- -- ----- - 4 -- ~~:"~- 4.~ -------- ILL -i~~~~~~~~~~~~ -~i -i __ _ -1I ~ 1...L: -- - II

I- - t;; 71:7 _;.....:-:. _ t '_.;: - i: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~-i: 1' - -1: 1''- E:1 '['1f'1 1-1 1 I I -; j i ~ 4':-::: II: 1 1:. - - - j - - -V': j- - 1 t71 _ —.. _ --- —-- — ~ — I A~~~~~~ |: 1:: |- 7 L:!. i i -0 | t 1 | i;: I; |. l,. t ~. | I, 1 *. i |, | i | C '! ' | ' 0' I ' ' |: "_! I' ' i |: ', 1%Reu tic 7n W 0-4^ —t — -t ---- t — - - --— i --- —- _~~ iI 7V [ L -1F _l_;L. - 1i- - -- 7 $-; +: ~;~ i TI'. 1 f ii j:~~~~~~~~~~~~~~N.A Pa 1;:: 1:: 1:: I 1::, -: 1 - L ' M 1 i- 1- f ( ~~~- - 1- i j -o:1~ 1 ~: | i 12:I r l 1 l 1 l i t1 1::: 1: I;! t11 ~~~~~~~~~~~~~~~~ -.- 4~~~~~~~~~~~~~~P 00t~~~~~~~~ 1 —i0 —~~~~~~~~~~~~~:W~~~ 0 — s c~T- -I+ —t- t~~~ t;tt i.;.. X; 1. * - t-< t 1X t Y | W t t -~ --;-.2 I — - ti; t t K 3711 t i L7 t > 1 % - T ' [ 8 ' 0 ' 0 '' I - -; ' - l t l ~ - 0 70 —.- - 2 r - I K -;; ' f i - i- X j 4.:1 N_ E --,. i III eaX-rntnt~ 1l; S- l 1 Pj - f.~~ I iI air ola'd8 e e~ a~~~ry e11:1 0.11 1 _~IX -l~ 1~.~ -- 1 e -— t — I; ' 1 y -..: _:::_ - rt::: 1i. t - i,>,: | i I ~i 1 1:!.:, |: 1:: i~~~~~~~-._- I - t; 1 - -- t. - _ - l::: 4 - -i 77 17:. _ t T 1 i:1: i1 r \| |- ~1-0~|"t- '. I: t j T t;,: 1 _ _ i- I- U:t t dV 17: f * | | * | T f ts | | Z |: | | | |, + | * X t * <,~~~~~~~~~~~~~~~~~~~~~~~~~~~~: i: i..;.|-ew X!1 - k ~i. L. I,, |, I, I I I: I 1 1 I 1 1 - t- 1.; '1 ' '1'S' '-:::i t}h~rSTeattt I I 1'l!;1 tfI - ' s I' L 1 ' -1 t- ',1 t I iI| I; i ~ I ' -::' i.;:: i |;. ' | ''I 1: I - III: ' ' ' I:'I,<ff — -tt' - i < = -- t- I4 l, l;Il I j. I: i -X- -t T — i 1 |;~ *; 1 | A t I. I; | II I. * xI z; | |g- _>-t_4+-? -i | t'-' tX*;I i |; - - -Xst-. -.i t..: *- I I;;|4I; ~; 1-;I;-| ---1;t|*i;l r L tT A4- I i-, F: i. e-t1, #,t, 'tii'|*;| 1 * ~ *: | -;|

-rTZIT.tTii " t I - -.~~~~~~~~~~~~~~~~~~~~~~~~~~ 434 ~ L J L 4 1- t~~~~~~~~~~~~~~in - ~~~~tI t~~~~~Ort.1 I~~~~~~~~~~~~~~ — ln. r*

f-i * i. lS,: - - - I + ~~~~~~~~~~~~~~~~t - *:; i; ';. - '!*._.._,,,|.,._....._..,.,'.1...!~ ~~~~~~~~~~`11 j1 1 1 -1: i f 1. 1;1 - 1;-1!I i]FI-__- - I- -i I, Iii I L.1* I t1t i '; '1-' ' ' 0 '''''e - ' L t0 -'14 i @Ai 1 - '001t _.___,-i -- - - - - 1 -.~.: -'.. ' '' *, '1. -- '-t- - -.-. '-d --.:_- -., - - ^.. ee< —4I j -X I I,, I tTT,- fj;, ~-+ — i ll- SlLT-f> --- -j 5- 'M;l,_ I 1 t I i:1:1 I1; iuil: q>~t-t —I- 14 1i --; 1-:[: - - - t I ' t - t -l - --- -: i - - H -- I i +;1XH4Xff1Xi-. 4Ift-1 -0.1.1 t.... i _:1..r: tt.t... r; 1_,1.:,1 1 7-t > I Il1.1 i / <;[ i:,: - 1 - - I: - tii i 1-X I - 1. I i -. -l l - ' 't44.; l 4 I t "I ia ---,l --- _.:~~I. 1 ~~-I.A — - <- - - -- -1j- -- -FI~ ---X — X-l'-0-1 L*~00- - - ' -- - - -— r 1 l:1: 10 1: i: _1: i 1: 10:'::-; 1f i: '1:: ' t t |: -i,,2 lt: - i 1 S~ ~. 1. 0. t, C1-:Oi,;. 1 I We,.. ~~1 ~i~i~ ~:-i, i 1::: i ~:: 4: P4 41 4I, I I. I I I. I L~~: I -t IT-i-g I. I g~~~~~- 4 - 1.: i; t: 1ti 7; 1: t - -; — 1 1 nlf- - -If I 4 _ - _, <'II r i r r |I | 4i 1 ] ' I i rF:It - - 1- - l - F- - t- - ---- -1I --- Jl T- lr7 -I; C --— I-JX: I; i; -; L ' i;:; 1,1 1: ~:-s'; I:1 --- i 1 1:. l-'>d:*..Lpz9'st fu~ it x T:l l ji I ~~ ~ --;:+1; I ^X I - I ' I ' 1;I' i-I I; I 1; i i' | 1 1,_- r;.-. - K -:I - I, 1 — _.,.tis | 1 j j t,1 1 l r~j; l + t j i l t-;l; t e l - l t F l; f [ T e-. -4.* * l 4 & r t i k rl;,; - 6, t | 'Li —' | 4 ' k - |- ' '; 4 t l T; 1 E 8 - 1 L. - I-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4 - +1 ~~~~~~ 1 4 - r-i-i: ~ ii __i 1<4 -L I —

[ _ I~ --- t L: -.-,ttt,: t,: 1.i _:1 -!,,,, Ot VI, lie~i w~~~~pAW U }joii~~~~~~~~ 143 P44P t ~ *tC-_i4-M - t iJ~~ -O-~T;:: too->Xeini RtptiP Q3 -c-* --- -7 _T — 11 -........... 1 - 4 1~~~~~~~ I If ____ b 4 8 ' S Si-I-[X t t '.:: I. _ _: - I t I — - ----- -----------— ti — i --- —-t —r --- — -- -t! - -p.....5. -. t~ t. I: ' 11 - J I I Ii>t1I~~~t~t2I~ t 1107 [ ~;i~; - _~-I ~; - ~ 1 — l - 1 t- - l I 1 -, i -!-t t- u —;! | il i:t- -!,:.- lit "- - ~~. — 1: -' 1 ' t - I -::, -, 1 - '; -1:-t-l- -1:: ---i t- qQ -::j — l - 1 i~~1t _ 4. _- _ _ _ ___ - -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~ __ __ __ I-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-1 _, l- _ _ _! t - --- l-,t- t-,-.-. -. —. -.-!;,.I: 1 p|...i.it...g.r..I Ij t; -FI- - -i I''5l' 'l't:-,:' 1911:,.li.-':, —t'' 77V 1tF-F I0-Sl 4l8 - *-l-' itft —l'- 'L WT I I < '00'12 f i i t I S; ' 10 r:i ~ 01 t I-,X 1~: 1 1 ~-~-.; 1 - i l -- 7i1:::-1: - 1::f[ -::l it /t:aT 1X 14 i I;i |f::[ -!: 1 +> -2 -_ XA_ t::2v <!|!Js t M t - t- L I ~- - ti~- i - i t! |;: i:1: i:+9 > ^: +: r: z i: i~ ':: |: ttteX 14.: r r,0 i I!-S ~ i; ' tf 0D _ _ i;~~ 0.... 1iX 110 i,:1+ 001:01 td'tf0000 t00000T-I& -y,0.fe

V f [1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1 1 t1;- --— j ----..-.i —t. — i I I -__ II __ __ _ I ~ ~ ~ ~~~ ~~~~ rl --- flt —~i —i __ — ____r-:..__ _..L.~_~~t --- ~t~ ~ ~ ~~::01I- _ -. 1:-i- -~ —_~- i i i --:0::::;!0 r:t: X; 4. t I --- —1i - -.1 +.. [iI~ -,1 1 J.~. m. --- —----- i -— ____________ -~ - t- -i _. _xj. i__ _______ __ ___ __ ___ __ __C-~-~. L -t - - -t-~~ ~ 0 i 1; ' L i. Ip-; Z-)-:i - -I t I t t — iI -.- L- -- T L-: -- - T-0 L ' _ _.:1.__ : t 04l__l _1 4___ -_. ___. __ - - ---- --- -1 t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s.0:L iO 4z;:5:t lU -$.U+i-1 5L4><4s f%- -< L "LA -t --— L._ S i 4 t t d~~~~ ~i t~ 1- r t ----j —t! -~- --— S~ 1 — F_! t -:~ - - b 1, |;, ig I jt i I [0ts, — 4 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -4 *1 m i3!-L < |*i -+1-};X^ - | l y |_I~ tr ~~~ _4 --— L —t-l 1- I__ _ F — 1::1: 1-:::; - - + 1:! 1:::1:: 1: ~:: I:::1 1:!::!::: 1: 1 1:::.: I -: |, ii 1 i t ---t:i.-......T:,: |xpn-u;l 01OX' —,os1Q 3 -- ------— t- 1 l I-~ - bo~o Di-r-W is — r7 "n 1- -— X --- sat~e~ J frp~ ~T '~ —, T --- r ----~ ----I -, 4: ~ ~ I 1, 00: i; _t_:.i tl:-__i __!-<SF i i -= i: 7t!- 1::::| -:!-;: -it: -1:::0,:1 - t — -t:l f- t - it, t 1:! I t-i1 1-i-l -1 l i:i 1:-'^. 11 i —i:-A HA I 1 1< 1 1 1! 1 6 -_ 1: W. iW - | ~ ~ -- -!-_ - -0X —0; } ti _._C - 1: |0 1 -| i00, |-i6 _,+ TL10 i- _t.i-+ — t0- | ~i i; | t -4 t - i — - X-< r W t^ zt iH:~~~~ ~ ~:!:: t,: 1;} 7_ i r::L i,: i L,-:; i - ltt —r-: 1- 1 1 P^09l5 ' l |!,, -1::,l:1 e:1 1:: I ~ --:.-: 0:: i~ ~ ~, 4-W —i- 1X ---.;!::T --- i-WX i i ' -t0i< t - --- [~~ t l.i t i::1 ij::-~1:1: i:: i. -at.:: l: 1: 1-1 1 1-.: i;:i;i -~~ ~ < - -:tt-i, t lf - I.-:L f, —.. Ii:::::, fl:l 1 1:1 j.-:- t7 i - t;- i, 1:T —:1::-l I-, i:: ] i il -' 4 t 1 -1 - -i - ' --,-:: -,;;, 1 —

> 1 +:1r- i - -; ~ 1 1 - i0 i: i f. t; _ - i 1 X 1 1!1:. IfI i __;.t:-; - -_!:_ ITl l 1 i - I I- —; i.j L. i 7 i- 7 - 7 - -...; - { 1 T 1 4.!; 11~~~~~~ 1* ~-* * 1. ___ I, _ _ _ ~ ~ ~ T t: | ii,-. -i:t — 1X x l -l -- t i 10-l — *~t —1 — t r 1jnijj-jjftjj ir; I, I 1 -- t - v I, - i tL t i t v ~~i - ~ ~ ~ L~~4 - -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 7 ir i -I --- -' -i —~ I~~~~~~~~~~~~~i.+:'- ' 1; i 1; 1 1:t:: ' I::.:; Es f. Ii:ll......................... Si:; l _ t: rl O S Il. -: ~ I ~, -. I~iii -: ''. I I 1T IP t -i I!. i217 i;4 v l - ~i _ __ I ii t t t t 1:-: ' 1t- '1 i::1.::1::!:.;'101 i 1 1 -:-I::Ii - iI 't, I 2 1 i-il~~~~~~~i 1::1 1-l; l-:!::: 1. 1:-~ +;l-ltl lrl:7 t-u 1l tt-rxl 1.1 1'5.::1::......... 1- —:l fi:. -. H................: 1';dI 1 i t.. -~-i r LS?' t~~~~1 ~ I, I. 1 *I I. | | |; | 1 1 I I i E 1.-tl~~~~: - 10:l010 't| 0t-l 4|,0!< - - - - k~~~~ ~ 1 1 ': t ': t f _-t I 1I: 1.; t - -+ — i -.. |~~~ '~~: 4.X. '.l9.1 L I I.1;''...1.'..1 1,1 -A..1:.!,.1-.-4. 14 I: 1 -;-|; f.!: 2- L 1: i; 1 -~i _4 4- W e t0 ':! 1,,X:.:b:i r3' 51: 8 i''$-1:.!:,1V.::1 1:1 I r —w..-.i 1..- -; -- -: - —.: 4_ ~.. r o..M _. et, 1t t,: l::r.;: ~ -~ l~ 'I:. l' ~ r l -;-:,E:-l '!E' l.. ',.. l l:. l,l 'i:0,i:. i ' t..0L — 1 i::j. r-.~~~~~~~~~~~~~~~~~~~ 14.1 -, t:loo.G Qt1-Xt aO4=Oetl!!:#: k [;1! I-' ': ',:'-, 'l: ':';:.:: I_-X- I':L ''L I':i~; 1 - t ~i- ~~: ~ ~ l:i — wIIt: ~ ' -,L -:4_ '-, EtT''*'ir.!-vl l- -- '-r —l '-T; —l l: l- '4I-:l';'&:' -':'l'-.' 'l'-' -:;l'';-' i.''*-l'-' ' ':':

~7F{ ft!-' ---t —;:- -I:t-j- — i - 1:-;' — -- -- -l- ' l —' A Al i A-IX0X —lW:-L a~~I~+-l-. ':? 1 ~-~ 'l W — I': ----::'.....1' i~~ '"1' — ~ —;- * — ' t-'. -. 1':- t!?'-01t!'- '-' '~ ~.... 46~~~~~~ I........-.._ * - *:..i.I ' -..-. - t - - ' ' --. -'...::,. t:.- 1 --- I -i - f: I -- - - - I -r 1 -- -'i i. -. 41; =2...: 7....T. -H I - -K I4 e t H- i- 1- t 'T t - l- -l 1 Ft-lF —t 1 X 4, _..:.T 7+ t- i 1 -+:- l;~ t~ — |;it tt 1 ti; t W1!- Ctdd Re~1:ti.- 4- --- - -. — — I''...-"Fi..-'-,e.-.. I..,. =.. * 4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ' tt.. '....,. -!k......"I |..? | e..I A.. R. _____ I k...... A.I':' 1X t".. _ L t... lit~~ ~~~~~~~~~........I.ce -V7V.... 17'~~~~~~~ ~1 yf ___ _ _ ~~~~~~~~~~~~~ f v Ci f - 1 j6rfj;C a c -e C 1 t-...... -.: T - 1 4 ~~~~~~~_=_ __-{ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.....,-:1... I....'' ---~ ~ 'I Ix~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~.JK ________ I.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. i ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I~~~~~~~~~~~~~~~~~~~