外文原文-基于疲劳失效两个阶段和不同测试的金属强度特性

METAL STRENGTH CHARACTERISTICS AT TWO STAGES OF FATIGUE FAILURE AND DIFFERENT TEST BASES M. Ya. Galperin UDC 539.431.043.3 It has been shown in 1-5 that when the fatigue failure process is divided into two stages it is possible to make a more complete characterization of the strength properties of metals used for making machine com- ponents and supporting elements of structures. The random overloadings occurring in metallic components in operation due to variable loads often lead - in the presence of fatigue macrocracks (even of relatively small size) - to serious fractures and break- downs. Therefore it is necessary in strength calculations to determine the durabilities and strength limits of the metals used not only at the final stage of failure but also at the stage of fatigue macrocracK formation. In order to clarify the difference in the fatigue characteristics of structural metals relative to cycles and failure stresses when the fatigue failure process is divided into two stages the results of large-scale bend- ing tests of rectangular section testpieces of types 45 and St. 3kp steels and type AV aluminum alloy have been used together with data from 6 for round-section testpieces of high-strength nodular graphite cast iron. The mechanical properties of these materials are shown in Table 1. In order to study the fatigue failure relations on full-sized testpieces of noncircular cross section, the tests were carried out using rectangular sectioned beams of width b 24 mm and height h = 90 mm. The dis- tance L between the supports was 700 mm (Fig. la). In the selection of the metal for this part of the investiga- tion static tests were made in axial tension of the testpieces of type 45 steel from five different melts, dH = 10 mm, /working = 5dH) cut along the rolling direction from plates of cross section 25 100 mm. The results obtained showed that as the hardness of the metal changed there was a marked change of the strength and plastic properties (Fig. 2). 800 C -IJ J50- I e f Fig. 1. Sketches of testpieces. Translated from Problemy Prochnosti, No. 5, pp. 22-35, May, 1978. Original article submitted October 18, 1976. 518 0039-2316/78/1005-0518507.50 ?9 1979 Plenum Publishing Corporation TABLE 1. Mechanical Properties of the Materials Investigated* Testpiece material Type 45steel(strip, 25x 100 ram), melt 142 Type 45 steel (strip, 25 100 mm), melt 145 Type 45 steel (sheet, = 11.7 ram), melt 369 TypeSt. 3kp steel(strip, 4 30 ram) melt 6534 Type AV luminum alloy (testpiece cut from com- ponent) High-strength nodular graphite cast iron (bars of diam. 85-90 mm and length 400 ram) Condition of materml kgfnam kgf/mm As supplied The same Formed profile Cast in sand molds 35,5 39,3 39,4 29,4 31,5 $ 52,0 $ 66,0 74,5 73,3 43,9 34,5 83,0 ,% 23,0 19,0 15,5 33,0 I 14,0 2,3 ,% |3,1 9, 18,: 12, t7r Strength limit ofsmh test- t I piece (No- / 10 dH = 7.52 2,9 187 30,0 5,5 217 31,4 4,8 217 33,5 9,4 121 -, 95 13.2 1,32 0,43 277 27,0 *Each value was determined as the mean from five or more testpieces. ?9 *Testpiece cut out transverse to roiling direction. r ield point. “* Pure bending with rotation. 45 J5 i / ,0 b, kgf I mm z I w,.4r -_, kgf/mm2 S f kgf/mm 2 V_ 1, % kg f/mmz S._ 1, kgf/mm z VE_t, % kg f/mmz S 2 ?9 .-1 kgf/mm V_l, % ( s. 1., kg f/mm Sal s. 1 kg f/mm V60 s.L“ % a-t, kg f/mmz S_l, kgf/mm z V_, % _pkgf/mm z SE_, kgf/mm s VF_g % Test bass Nb, cycles ,o. I 4.,o. I ,o, I ,.,o I ,o, ,o, ,o. m B w B 44.0 1,9 4,3 22,5 25,2 0,75 0,8 3,3 3,2 AIuminum alloy AV 14,1 10,8 _ 16,7 1,7 1,0 _ 1,4 12,1 9,3 _ 8,4 w m Type 45 steel, melt 142 24,3“ 23,0 24,8 23,3 0,26 0,30 0,34 0,38 1 ,I 1,3 1,4 1,6 b-24 ram; 21,4 21,6 0,40 0,43 t,9 2,0 h=90mm; r= 120; aa-l,0) 20,8 20,0 21,0 20,2 0,43 0,38 0,44 0,44 2.1 1,9 2,1 2,2 D D Type 45 steel, melt 145 (5=24 ram; h =90ram; r= 120 ram; % 1,0) 26,9 23.0 22. i 21,0 28.2 23,2 22,3 21.3 0.71 0,54 0,50 0.42 0,86 0,48 0,45 0,43 2,6 2,3 2,3 2,0 3,0 2,1 2,0 2,0 Type 45 steel, melt 369 h=5=l 1,7mm ; r=62,5mm aal,0) 43,2 34,9 28,0 25,8 22,7 47,4 38,3 30, I 27, 1 23,7 3,3 3,7 3,3 3,0 2,7 1,9 3,1 3,2 3,1 2,4 7,6 10,6 II.8 11,6 11.9 4,0 8.1 10,6 ll,4 10,1 Type SL 3kpsteelo melt 6534 (h=6=4mm; r=42,Smm; aol,0) 34,0 28,6 22,6 19,7 14,6 40,5 30,5 23, 1 20,2 15,9 1,7 1,3 1,2 0,95 0,8 2,2 “I ,5 0,9 0,85 0,6 5.0 4,5 5.3 4,8 5,5 5.4 4,9 3.9 4,2 3,8 ADaminum alloy AV b=20mm; h=3mm; ore=0; xot,0) 20.0 18,3 16.0 14.5 10,9 10.31“ 21,9 19,7 16,7 15,0 11,5 I0,7 0,8 0,75 0,7 0,75 0,7 0.75 f 0,86 0,85 0,85 0,9 0,8 0,75 4,0 4,1 4,4 5,2 6,4 7,3t“ 3,9 4,3 -5 ,-l-“ 6,0 7,0 7,0 (b=2ffnm; h=3 mm;r=O,5mm; aa=2,1; om=5,0 kg f/mmz) 9,5 8,4 7.7 6,4 5,3 13,2 9,8 8,8 6,8 5,4 0,75 0,57 0,42 0,40 0,22 1,4 0,77 0,62 0,32 0,21 7,9 6,8 5,4 6,2 4,2 10,6 7,9 7,0 4,7 3,9 High-strength cast iro (da=8mm; r=30mm; aol,O ) 50,65 47,2 40,0: 37,8 35,8 51,5 48,0 40,7 38,3 36,0 2,1 2,3 2,6 2,0 1,3 . 2,0 2,2 2,5 1,9 1,2 4,2 4,9 6,5 5,3 3.6 3,9 4,6 6,1 5,0 3,3 High-strength cast iron (da=8mm; r=l,Smm; aa=l,62 ) _ 60,5 48,5 44,5 38,5 62,0 50,4 46,0 39,0 2,1 3,2 3,1 1,I 2, 2,8 2,9 1,2 - w 3,3 6.4 6,7 2,9 4,2 5,6 6,1 3.1 5g0 TABLE 2 (continued) Test basis Nb. cycles Characterttcs I I I I determined 10. 4. lO t 10 4 4.10 j 10 4 IO T 10. High-strength cast iron (d.=8mm; r=0,5mm; ao=2,4) -1, kg f/mmz _ 86,4 77,9 59,5 53,7 42,5 _ 98,2 88,1 64,8 56,3 44,7 S g kgf/mm 2 2,8 4,2 5,5 4,8 3,6 _ - - 2,3 3,4 5,4 4,6 3 i“6 V_I % 3,2 5,4 9,2 8,9 8,5 _ - 2,3 3,9 8,3 8,2 8/I High-strength cast iron (dn=45mm; r=85mm; ao_l,0) - z 42,8 39,4 32,8 31, I 28,6 o, kgf/mm - 43,-“Y 40,4 33,7 31,7 28,8 - 2,3 2,3 2,6 2,1 1,2 S_l, kgf/mm z 2,0 2,1 2,9 2,2 1,1 V._f % _ 5,4 5,8 7,9 6,8 4,2 _ 4,6 5,2 8,6 6,7 3,8 High-strength cast iron (d.=22 mm;r=6mrr ca=l,JA) -I, kgf/m m z _ 50 .0 46,3 37 9 35,0 32:8 _ 53,7 48,9 38,7 35,4 32,2. S i, kgf/mm z _ 1,3 1,8 2,4 1,5 0,8 _ 1,2 1,6 2,5 1,5 0,8 V_C % _ 2,6 3,9 6,3 4,3 2,4 . . . . . 2,2 3,3 6,5 4,2 . 2,5 H igh-strength cast iron (d=8 ram; r=30 ram; aa 1,0), cantilever bending with rotation l, kg f/ram2 _ 31 , _ _ _ . 7 _ 7 30,1 28,0 27,6 27,2 _ 42,8 38,3 29,8 28,2 27,4 _ kgf/mm z 2,1 1,5 1,1 1,0 0,92 _ G-l - 1,8 2,0 t ,- 1,1 0,90 V_C % 6,6 5,0 3,9 3,6 3,4 - 4,2“ 5,2 5,0 3,9 3,3 - *Data in the numerator relate to the stage of beginning to form macrocracks of length 0.1-0.5 mm while data in the denominator relate to the final material failure stage. tTest basis 2.10 7 cycles. .t Test bases 5-104 and 5-105 cycles. (Fig. lb), and from strip (4 x 30 mm) of type St. 3kp steel (Fig. lc). The shape and dimensions of the smooth and cut testpieces of type AV aluminum alloy (see Table 1) were similar to the testpieces of type St. 3kp steel (see Fig. lc) with the exception of testpiece height h = 3 mm and cut-out radius r = 0.5 ram. The latter feature reproduces approximately the stress concentration factor anticipated for the component. The testpieces of height 11.7 mm were tested on a model MUK-100 machine while the testpieces of height 3-4 mm were tested on a model MUP-150 machine with constant displacement amplitude with pure bending in one plane and a symmetrical cycle at a loading frequency of 1500 cycles/rain. In this case the bending moments were determined by elastic dynamometers. For directly monitoring the stresses the testpieces of rectangular cross section were fitted with wire resistance transmitters, and an electronic stress/strain meter was used which provided a means of measuring the stresses during pulsating and sign-alternating stress cycles 7. The -origination and development of the fatigue macrocracks were observed by means of a 20x magnifying lens with graduation lines. Large-scale testing of the ferrous metal testpieces was conducted on a test basis of N b = 107 cycles. The smooth testpieces of AV aluminum alloy were tested using a symmetrical cycle and N b = 2 ?9 107 cycles while the testpieces with lateral cut-outs were tested using asymmetric loading cycles and a constant mean stress a m = 5.0 kgf/mm 2 to N b = 2- 108 cycles. The fatigue curves for the metals investigated were plotted in terms of the failure probability parameters as follows: The original fatigue curves were plotted by the normal method and from them stress levels were selected for the large-scale tests. Each type-size of testpiece was tested at five to seven stress levels selected according to the sloping part of the fatigue curve obtained for the given testpiece type-size and using from 10 to 25 testpieces at each stress level. The test results were subjected to statistical analysis by the method given in 8. 521 90 c = 66 kgf/rnmZ; HB = 183-187 kgf/rnm; I = q00 ram; b = 24 ram; h = 92 turn; r = 120 ram; I 7. I ! # : I O c y c l e . s T j . / J / O e .0 5 I0 d ./0 / / t7 gO 18 19 20 21 2Z 23 2r Z5 a 25 Oa(s.L), kgf/mm 2 o b = 74.5 kgf/mm2; HB = 217 kgf/mmZ; Up l = 700 ram; b = 24 mm; h = 92 rnrn; r = 120 mm; %=l,0;#min/Smal s /y , Z 20 2/ 22 23 2 ZH 26 27 28 Oa(s.L)0 kgf/mm 2 b Fig. 3. Distribution functions for the amplitude of the failure stresses (or strength limits for beams of type 45 steel for different test bases. (Con- tinuous lines represent the stage for the formation of macrocracks of length 0.1-0.5 mm; dashed lines represent the final material failure stage; the chain- dotted lines represent an approximation). The life distribution diagrams obtained in the coordinates P -N were used to plot a family of fatigue curves in the coordinates -N corresponding to equal probabilities of forming macrocracks of length 0.1-0.5 ram or equal probabilities of final failure 2, 5, 10, 20, 30, 50, 70, 90, 95 and 98%. The equal failure probability diagrams in the coordinates P- were used to plot the distribution function of failure stresses (or strength limits) for different test bases. The composite graphs of these functions were replotted on normal probability paper. As an example Fig. 3a shows such graphs for beams of type 45 steel, melt 142, and Fig. 3b for beams of type 45 steel, melt 145. Similar curves were plotted for all the metals in- vestigated and from them the mean failure stresses and their standard deviations S() were found. In accor- dance with 9 the values of were determined at the point corresponding to the quantile Up + 5 = 5 (I n = 50%) while the values of S(a) were determined as the difference between the stresses at the displaced quantiles Up + 5 = 6 and Up + 5 = 5. The coefficients of variation of the failure stresses were found from the expression 522 TABLE 3. Comparison of Data Relating to the Reduction of Strength Limits at the Macrocrack Formation Stage with the Final Failure Stage as a Percentage, at Dif- ferent Test Bases Geometric characteristics of testpiece Failure probabilit P, qo 10 ?9 Test basis, Nb, cycles 4“10 1 10S I 410 I0 10 j b=24 mm i h=90 mm r=120mm L:700mm ao 1,0 b30 IITI h=l 1,7 mm r=62,5 mm a o 1.0 b=20 mm h4 mm r=42,5 mm ao-1,0 b=20 mm h=3 mm r=42,5 mm aa ,0 b=20 mm h=3 mm r=O,5mm aa=2,1 d.=8 mm r=- 30 mm o 1,0 d.=8 mm r=: 1,5 mm aa= 1,02 d,=8 mm r=0,5 mm ao=2,4 Type 45 steel strip(25 100,mm),melt 142 98 2,4 l 1,8 1 50 2,1 1,5 2 1,6 1,0 Type 45steel, strip (2100 mm), melt 145 98 I 5, 1 0,9 0,8 50 4,7 0,9 1,2 2 . 3,8 0,9 1,1 Type 45 steel, sheet (, = 11.7 ram), melt 369 1,0 0,6 1,3 ,0 0,8 0,9 1,0 l,l 0,9 1,2 1,0 l,l 9 I lgL 461 53 52qo8 I 50 8,9 8,9 7,0 4,8 4,2 1,0 17,5 15,4 10,2 3.3 9,9 Type St.Skp. steel, strip (4x30 ram). melt 6534 99 50 1,0 I - . 17,2 I 15,9 I 14,2 Aluminum alloy AV 9,4 8,4 I0,7 8,7 ll,0 8,7 Aluminum alloy AV 5.6 6.1 4,1 7,4 I 7,1 6,2 1,8 1.6 4,8 1,9 2,7 8,2 3,2 5,4 11,8 5,8 5,5 4,1 4,5 3,3 4,8 3,8 1,5 4,9 99 50 1,0 99 50 1,0 High-strength nodular 99 50 1,0 99 50 l,O 99 50 1,0 34,2 35,0 36,7 32,9 28,0 14,8 17,5 14,7 11,6 13,2 II,9 8,2 2,4 5,1 5,9 d.-45 mm r:85 mm ao-_- 1,0 dn=22 mm ?9 6 mm aa= 1,44 Cantilever bending with rotation (d,=8 mm ?9 =30 mm ao 1,0) *Test basts 2.10 T cycles. tTest bases 5.104 and 5“ 10 g cycles. 99 50 1,0 99 50 1,0 99 50 1,0 raphite cast iron 1,3 “f 1,0 1,8 1,7 2,8 2,1 - 1,9 - 2,3 - 2,8 10,1 8,5 12,0 1,6 14,3 I5,8 1,0 1,3 2,3 2,5 4,0 4,0 4,7 3,7 6,9 5,4 9,1 7,4 22,0 21,3 25,9 21,3 30,3 21,0 1,0“f 1,7 2,7 1,6 3,8 6,5 7,3 8,2 10,0 3,5 2,7 1,5 2,2 2,2 2,1 8,5 6,2 3,4 1,7 ,2 t 8 !,2 L4 i,l 1,8 L6 L1 2j 1,4 lfi I ,z 1,3 1,2 2,6 2,0 1,4 0,6 0,7 0,9 1,6 1,3 1,1 4,3 5,0 6,6 0,8 0.9 1.0 1,3 1,2 1,1 0,8 0,9 1,8 D m m m m 1,2 e 3,7 5,7 3,9 2,4 4,0 m m 523 ,B = 217 YjYp -*-“ =:rnm - a h-5In . . . . b “ “c . L v “ 0.0 t )-r 1 0.#- 1.0 1.2 I# 1.5 /.8 ZO/L. 20 30 50 O.kgf/mm“ d e Fig. 4 Nck/Np r =/.0 b M Steel 45 I “ z b = 7mm; a. a L = 500 mm; I “ Z8 r= 120mm; I z3 _j I o I I = . 0 .z u, ta 7,8 /oo),.1. 8 Io =1.0 a8 5 I b Fig. 5 Fig. 4. Relations of Nck/1p - (ri/r-i (or aa/(cra)s.1.) and N/Np - amax for the test- pieces investigated: a) ground from 45 steel; b) with unmachined (black) surface: c) AV aluminum alloy; d, e) high-strength cast iron (continuous lines for plane canti- lever bending, dashed lines for cantilever bending with rotation), s. 1.) Strength limit. Fig. 5. Relations: a) Nck/N p = f(ra/(Cra)s.1.) - a and Nck/N p = f(a)max; and b) for a beam of rectangular section of type 45 steel melt 142: b = 7 mm; h = 90 mm; L = 500 mm, amin/amax = 0.11; r = 120 mm; c a 1.0. s (o) v () = - . O“ The failure stress (or strength limit) dispersion characteristics obtained are shown in Table 2 while the data relating to the reduction in the strength limits, as a percentage, at the stage of forming macrocracks of length 0.1-0.5 mm in comparison with the values at the testpiece final failure stage at various test bases and failure probabilities are shown in Table 3. The fatigue curves were plotted in absolute stress values and the number of cycles as well as in relative (dimensionless) values in the form of relations for the ratio of the mean number of cycles up to the appearance of macrocracks Nck to the mean number of cycles to failure Np as a function of the relative stress level ai/5-_ t (or overloads) in accordance with the data in 9: N ck where ei is an assigned stress, -1 is the mean value of the strength limit fora symmetrical load cycle. In the ease of an asymmetric load cycle the right-hand side of Eq. (1), the relative stress level, is expressed in stress amplitudes as the ratio eai/(a)s.1., where Crai is an assigned stress amplitude and (a)s.1. is the mean amplitude of the strength limit. From Eq. (1) it is possible to estimate the life of a metal at the stage to the appearance of a fatigue mac- rocrack as a function of the relative stres level and also to determine the fraction of the life (in terms of cycles) during the stage of its development from the initial size (0.1-0.5 mm) to testpiece (or component) failure over the whole cross section. Figure 4 shows Eq. (1) for all the investigated metals as relations between the ratios Nck/Np and the maximum failure loads area x for high-strength cast iron: Nck _ (or). (2) p 524 TABLE 4. Scattering Characteristics of the Critical Lengths l cr and Areas (Fy)c r of the Macrocracks, the Fracture Stress Amplitude (aa)D, and the Stress Intensity Fac- tors K c for Beams of Dimensions 24 x 90 x 700 mm of Type 45 Steel, Melt 145 (s.1. = strength limit) Ga (%.1. (ck)cP mrn I a0,90 SD, S(ick)cr mm a0,90 Cocff. of variation I V(Zck)cP qo Scatter inter- I(/ck)max/ val (/ck)min“ i(/cDmin (/ck) max 1,23 1,086 1,045 22,1 24,0 25,6 19,1-25,2 23,5-26,5 22,1-29,2 5,3 4,3 6,1 3,6-8,2 3,0-6,7 4,2-9,6 23,9 17,9 23,8 16,0-33,0 18,0-33,0 17,0-34,0 2,06 1,83 2,00 ?9 % -FU)cr, mm z (%) s.L 1,23 471,6 1,086 529,1 1,045 564,7 % (%) s. L 1,23 1,086 1,045 Critical dimensions ofmacrocrack areas a0,90 Sul er, mmZ V(FU) cr 390,8-552,4 139,4 96,4-217, 29,5 461,4-596,8 116,8 80,8-182,3 22,0 472,6-656,8 158,8 109,8-247,9i 28,1 (Fy)mln- -(Fy)max 338-796 382-770 362-790 Stress amplitudes of final fracture part sections not occupied by cracks (%) D mm- ( kg f/mm a0,90 S(a)D kgf/ Go,9 o V(a)D -(%)D max mm 2 36,3 34,4-38, I 3, I 2, I-4,9 8,5 33,5-42,9 35,3 33,8-36,8 2,6 1,8-4,0 7,4 32,2-41,2 35,9 34,1-37,6 3,0 2,1-4,7 8,3 32,4-40,5 ( F u)m F(/)m|l 2,36 2,02 2,18 ()D max (%) D ml. 1,28 1,28 1,25 ( 1,23 1,086 1,045 Stress intensity factors Kc kg f/rnm3/2 ao,9o 410,4 397,6-423,2 484,5 457,8-511,2 404,4 388,8-480,0 472,3 443,7-495,9 406,0 387,5-424,5 476,0 446,7-505,3 s c, kgrna /2 %.90 22,2 15,3-34,6 46, I 31,8-71,9 26,9 18,6-41,9 40,7 28,1-63,5 31,9 22, I-49,8 50,5 34,9-78,8 % 5,4 9,5 6,6 8,6 7,9 10,6 (Kmin- -(KQmax 376-445 26-558 362-449 411-553 360-459 404-539 (K,)n 1,18 1,31 1,24 1,35 1,25 1,33 Note. The nnmerator shows data with no account of plastic strain in the crack tip and the denominator shows data with this factor taken into account. It is evident from Fig. 4a that for the same relative stress levels the fraction of the life (in cycles) for which the beams of the same full-size dimensions worked with developing fatigue macrocracks was higher for the steel of melt 142 than for the steel of melt 145. This may be related (as will be shown below) to the different characters of the failures of beams of the same type of steel but different melts. Equation (1) for smooth testpieces with rolling scale of type 45 steel (see Fig. 4b) indicates that for the same ratio i/u-i the fraction of the working life (in cycles) of a testpiece with developing macrocracks for this steel is greater than for ground beams with the same hardness (melt 145). But for smooth testpieces with an unmachined surface of type St. 3kp steel (h = 4 mm) and for testpieces of type 45 steel (h = 11.7 mm) with a similar surface condition, as relative stress level increases it is observed that there is a more marked in- crease in the fraction of the working life (in cycles) of the test piece with developing macrocracks than for th