Exploring the fracture toughness KIE and KIC of a medium-Strength steel plate using the surface-flaw test

EXPLORINGTHEFRACTURETOUGHNESS Km AND& OFAMEDIUM-STRENGTHSTEEL PLATEUSINGTHESURFACE-FLAWTEST CUT ZHEN-YUAN Fracture Mechanics Laboratory, Nosh-Western Engineering University, Xian, China Ah&a&-The fracture toughness of a 30 CrMnSiA steel plate of three thicknesses (lo,8 and 5 mm) and three widths (110.80 and 56 mm) has been investigated by using surface-flaw method under room temperature. It is not easy to compute the value of &_a by the maximum applied load. But the values of &a and Kro could be obtained easily, if the computation of the conditional applied load Pro and Pj based on the relative effective extension Au/a0= 10%and 5% were adopted, together with the conditions of P,,,sl/Pra6 1.2and P,,/Ps s 1.3. The Ka - Au curve,i.e.the resistance-curve described by the parameter K, has been plotted. The values of Klc and KIE are then the resistances corresponding to the real extensions of flaws of Au/as = 2 and 7%, respectively. These values so obtained are in good agreement with the computed values of Klc and Km by using the conditional applied loads. The values of KIc and KIE so obtained are also in agreement with the value of Krc converted from the J-integral and the effective value of i(IE computed by the maximumapplied load, respectively. An approximate relation between K,c and rC, has been found to be: Kro = (0.85- 0.9S)Kra. The requirements for the dimensions of specimens are: Thickness of plate: B 2 l.0(K&,&2 l.25(K&00.2)2];Width of plate: 8 Q W/B c 144 d W/2c s 5; Effective length:13 2W.

or

1. INTRODUCTION THESURFACE-FLAW specimen

can simulate the actual shape of flaws which often occur as surface defects, expecially as the defects occuring in service of the aero-space structures (e.g. thin-walled structure or stressed skin). Therefore the surface-flaw method is widely adopted in the research field of fracture mechanics of aero-space materials. Up to the present time, the surface-flaw method has only been used by previous investigators for testing the fracture toughness of high-stren~h or ext~-high-stren~h materials, i.e. only for the initiation of crack or when the subcritical extension of crack is very small. When the latter could indeed be neglected and certain conditions admitted, the surface-flaw fracture toughness of materials may be found successfully by testing. Since the 30CrMnSiA steel belongs to the medium-strength material, its subcritical extension of crack is usually considerable. Hence, the ordinary surface-flaw method for testing of fracture toughness is unsuitable for this material. But the 30CrMnSiA steel plate is still one of the widely used materials in aerospace structure, so it is pertinent to know its fracture toughness. In this paper we present a new surface-flaw method for testing the fracture toughness of the medium-strength material, 2. PROPERTY OF THE SPECS ~TE~AL The chemical composition of the 30 CrMnSiA steel plate tested is listed in Table 1. The heat treatment process: heating to 900 f lO”C, soaking for 12 - IS minutes, oil quenched; annealing at 4802 10°C for 1 hour, water cooled. The regutar mechanical property obtained of 30CrMnSiA steel plate is listed in Table 2.

Table 1. The chemical composition of the 30 CrMnSiA steel plate (%)

EFM Vol. 13.Na 4-F

Si

Mn

Cr

Ni

S

P

cu

1.00

0.88

0.83

0.15

0.009

0.016

0.121

776

GUI ZHEN-YUAN Table 2. The mechanical property of the 30 CrMnSiA steel plate ah (Kg/mm?

w(Kg/mm’)

125

6r(%)

114

10.7

ti(%‘G) 38

Rr 38

3. PRINCIPLE OF THE TESTING METHOD 3.1 Type of P-V Curve. The recorded P-V curves are divided into types as shown in Fig. 1. During testing the two curves of type II all have a “Pop-In” plateau. When the load reaches the plateau value, an audible click occurs distinctively. However, the case of “Pop-In”, especially of type II, 6, is very rare, and most of the cases belong to type I. 3.2 Determination of the “conditional applied load”. In order to determine the “conditional applied load”, we assign the load relative to a certain degree of the effective extension occuring in the front of flaw. It can be determined by the ratio of the effective extension of flaw Aa to the corresponding initial deepness of flaw ao, i.e. Aa/ao. If the effective extension of flaw Au equals to the dimension of yield-zone at the tip of flaw r, = (1/4d2~) (K,Jao.2)2 and the required deepness of flaw a0 = 0.5 (K,E/ao.2)2 for 30 CrMnSiA, then we have:

’ -m(~)2/o.5(~)2=m%

Aa=rY_ a0

a0

(1)

While the relative effective extension determined by the load at “Pop-In” is ha/a0 = 5%.

(2)

Therefore, for testing the value of KIE of 30CrMnSiA, the conditional load Plo can be determined by using the relative effective extension of flaw ha/a0 = 10%; and for the value of &, the conditional applied load P5 can be determined by using the relative effective extension Aala = 5%. The curves describing the relations between the dimensionless variables WEVlP = EV/(rB and the relative flaw dimension a/B (as shown in Fig. 2) can be plotted from the P-V curves (as shown in Fig. 3). These P-V curves are recorded for other specimens of similar geometric shape but possessing different deepness of flaw. When the function of the curves in Fig. 2 are assumed as

g

=f (;,;).

(3)

The partial derivative of the function f in eqn (3) with respect to a/B and a/C divided by f itself would give: (4) (4a) where

the coefficient

H is given by:

tThe second term on the r.h.s. of eqn (4) can be neglected, 0.45 < a/B < 0.55, 0.45 < a/c < 0.55, Aala,, = 10% (or 5%).

since its value is far le$s than the first term. when

Exploring the fracture toughness KIE and K,c of a medium-strength steel plate

771

No.6 a/B=0.509

No.7 a/B= 0.472

V

Fig. I. Types of P-V curve.

For the specimens of a definite shape and a definite initial flaw deepness a,JB, the coefficient H can be determined by the calibration curve Fig. 2. Therefore the relative increments of the crack opening displacement corresponding to the standard states of Aala,, = 10 and 5% are: du/V = lO%H; and dvlV= 5%H,

(6)

respectively. The slope of the secant line corresponding to Fig. 1 should be equal to l/[l + 10% (or 5%)H] of the initial tangent slope P/V, i.e. the secant line OPlo (or OPs) drawn from the origin of

.

0.45-a/c-0.55

6.0 -

A 5.0 -

Q 4.0 t tl 3.0 -

2.0 -

I.0 -

1 0

1 I 1 1 1 0.1 0.2 0.3 0.4 0.5

1

1

I

I

0.6 0.7 0.6 0.9

a/B

Fig. 2. Calibration curves.

I

1.0

178

CLJIZHEN-YUAN a/B

0

= 0.333

0001

0.002

0.524

0610

0.00s

0.004

0.659

0.008

a/B= 0.642 0.7530.002

0700

0.654

0.006

0.965

2000-

0

0.001

0.002

0.003

0.004 I(

0.005

0.006

0.007

mm

(b)

Fig. 3. P-V curve. (a) 0.45 i a/c ~0.55; (b) 0.55 c a/c < 0.65.

coordinates should be of a slope less than the initial tangent slope of this curve by 10% (or 5%), H. The ordinate of the intersection point of the secant line OPIo (or OP,) with the curve gives the value of the “conditional applied load” PI0 (or PJ. In order to validify the tested value of fracture toughness, the following conditions are to be satisfied: Pmax/P,o s 1.2: Pm,,/P5 d 1.3. 1

(7)

3.3 Selection of formula for the calculation of K,. The approximate solution for the stress intensity factor at the terminal of the minor-axis of the surface-flaw was first given by Irwin[l] in 1962. Henceafter the approximate formulas have been revised by many investigators[2-61 of fracture mechanics including Irwin himself, in order to extend the scope of application. Various revised methods have been introduced and analysed in papers [7,8]. Shah-Kobayashi’s

Exploring the fracture toughness I&

and Klc of a medium-strength

steel plate

179

formula has presently been recognized as one of the best, not only because of its sounder theoretical basis but also of its wider scope of application. The expression for the stress intensity factor at the terminal of the minor-axis of the surface-flaw as presented by ShahKobayashi is:

in which: o-tensile stress applied on two ends of thin plate, perpendicular to the crack surface; a-length of semi-minor axis of the elliptical crack. Q-parameter of flaw shape, which can be found from the diagrams given in [9]; J&-product of revised coefficients of the front and the back surfaces, a function of a/c and a/B. It can be found from diagrams given in [4]. When computing the plane-strain toughness KIE, the average stress UN on net cross section should be adopted for: UN

PO

=

(9)

in which: PQ-conditional applied load PI,-,(or PJ; B and W-thickness and width of specimen, respectively; C-length of semi-major axis of the elliptical crack. 4. DESCRII’TION OF TESTING 4.1 Specimen preparation. The total length and the machining requirements are shown in Fig. 4. The artificially generated flaw (machined crack) on the specimen was notched before heat-treatment. Then the machined crack was preshaped on a high-frequency fatigue machine under three-point bending. During pre-crack the maximum and minimum bending stresses in the specimens were approximately 0.5 uo.2and 0.05 ~0.2respectively, i.e. Pfmin= l/lOPfmaX. For setting the clip-on displacement gage on the pre-cracked specimens, two blind holes were pressed adjacent to the two sides of the crack with distance 2Y (calibration distance), according to the initial calibration distance and the linear calibration range of the clip-on gage. 4.2 Calibration. The specimens are preshaped to various deepness of cracks. The legs of the clip-on gage were inserted into the blind holes on the specimen at an initial load of lOO& 5000 kg. And then the gauge was fixed by a rubber ring as shown in Fig. 5. The load was applied gradually and the output signals of the local transducer and the displacement gage were amplified by Y6D-3 dynamic strain meter. The amplified outputs were recorded by the L23-204 X-Y recorder and the plotted P-V curves are as shown in Fig. 3. The EV/gB - a/B calibration curves based on Fig. 3 are as shown in Fig. 2. The best-fit equations of the calibration curves are: EV=-0255+2529g+4582 uB

’

’

B

*

~=0.085-0.201;+5.9!98(;)2.

a ’ 0.45 < 9 < 0.55; 0li’ 0.55+0.65. Q?

-+-

Fig. 4. Surface-flaw

specimen.

CUIZHEN-YUAN

780

Fig. 5. Clip-on gage and method mounting.

By means of eqns (5) and (lo), the calculated values of coefficients H are listed in Table 3. Table 3. Values of coefficients H (l/C

0.45 - 0.55

0.55 - 0.65

u/n

0.4

0.5

0.6

0.7

H

1.66

1.65

1.65

1.67

0.7 0.8 _____~_~ 1.99

2.00

4.3 Testing. The testing installation was the same as for calibration. The specimen was pulled to fracture in l-3 minutes. The P - V curves during testing are shown in Fig. 1. The maximum load P,,, was recorded and the dimensions of a and 2c measured. The values of PI0 and Ps are determined by the method of reduced-slope secant as described in Section 3.2. The value of K, was calculated thereby. In order to plot the KR - Au curve and to inspect the flaw-front of the specimen for subcritical growth of crack, seven specimens with the same deepness of cracks were tested. During the gradual application of load, P-V curves were plotted and the secants 0P5 were drawn, the tests were interrupted at loads slightly less than, or equal to, or greater than P5, and the load at interruption Pstopwas recorded. The specimens after the interrupted tensile tests were subjected to a second fatigue test. When the crack was extended to a certain degree, the fatigue test was stopped, and the specimens broken by bending. The macroscopic photographs of the cracked flaw are shown in Fig. 6. The dimensions of a 2c and Au were measured therefrom. The cracked flaws were then inspected by a, PSEM-500 scanning electronmicroscope. The extended region of the cracks are as shown in Fig. 7. The general view of the extended region on specimen No. 26 (Fig. 8a) and the microscopic characteristics of the same (Fig. 8b), the final fractured region (Fig. 8c), the pre-cracked region (Fig. 8d) and the refatigued region (Fig. 8e) are as shown in Fig. 8. 5. TEST RESULTS AND ANALYSIS 5.1. The values KIE computed from P,,, were obtained with the following results: For the specimens with B = 10 mm, W = 80 mm, KIE = 414 Kg/mm 3’2, the ratio of valid tests to total number of tests is 50%; for the specimens with B = 8 mm, W = 80 mm, & = 374 Kg/mm3’*,the ratio of valid to total is 67%; for the specimens with B = 5 mm, W = 40 mm, no valid KIE has been obtained. If the value KIE be computed from PI0 for the specimens at rN > 0.9 ~r~.~,together with the value KIE computed from P,,,, the following results were obtained: Z?rE= 416 Kg/mm3”, ratio of valid tests is 100%for specimens with B = 10 mm; Z& = 373 Kg/mm3’*,ratio of valid tests is 100% for specimens with B = 8 mm; Z& = 297 Kg/mm3’*,ratio of valid tests is 60% for specimens with B=5mm. Moreover, for specimens with B = 8 mm and B = 10 mm, the values KIE computed by the latter method are in agreement with the values KIE computed from P,,,.

Exploring the fracture toughness KIE and KIC of a medium-strength steel plate

Fig. 6. The macroscopic photographs of the cracked flaw.

Fig. 7(a).

Fig. 7(b).

781

182

Cl11 ZHEN-YUAN

Fig. 7(c).

Fig. 7(d).

Exploring the fracture toughness K,E and K,C of a medium-strength steel plate

Fig. 7(e).

Fig. 7(f). Fig. 7. Microscopic characteristics of cracked flaws. (a) Specimen No. 9 640x; (b) Specimen No. 10640x; (c) Specimen No. 12 80x; (d) Specimen No. 13 640x; (e) Specimen No. 20 640x; (f) Specimen No. 21 640x.

783

784

CUI ZHEN-YUAN

Fig. N(a)

Fig. N(b).

Exploring the fracture toughness KfE and KIc of a medium-strength steel plate

Fig. 8(c).

Fig. 8(d).

785

‘Xi ZHEN-YUAN

Fig. 8(e) Fig. 8. The microscopic characteristics of eracked flaws (Specimen No. 26). (a) General view of the extended region ,640X;(b) Extended region 1250x; (c) Final fractured region 1250~;(d) Pre-cracked region 1250x; (e) Re-fatigued region 1250x.

Exploring the fracture toughness KjE and I&

of a medium-strength

steel plate

181

100

--e-e+7

t

0

B,mm

Fig. 9. KIE - B curve.

The plotted KfE - B curve is shown in Fig. 9. At B = 10mm, the tangent of the curve is almost horizontal, when ~~(K~~~~~.~~2 = 0.9, r&B - a) = 10.5- 14.5%, which sIightly exceeds the restriction suggested in [lo]. For specimens with B = 8 mm and B = 10 mm, most part of the fractured surface (more than 80%) was planar. Therefore it can be recognized that the fracture of these specimens belong fundamentally to the plane-strain type. The mean value KIEof the material is 416 Kg/mm312,with a scatter of -5.5 - +4.1%. 5.2, The value KJcwas computed from Ps. The plotted K&l curve is shown in Fig. 10. It can be seen that the tangent of curve at B = 10 mm is horizontal. Therefore the value Kfcof the = 1.23. material is equal to 354 kg/mm3’2,with a scatter of - 11.5- t 13%, while B/(K&z,J2 5.3. From the electronmicroscopic fractography of seven specimens, a high-strain region between the two fatigue flaws (Fig. 7) shows the characteristic of dimpled fracture, in contrast to the two regions of fatigue crack extension which are of the “polished” characteristic. From the microscopical characteristics of cracked flaws as shown in Fig. 8, it can be seen that the extended region (Fig. 8b) and the final fractured region (Fig. 8c) are both of the characteristic of dimpled fracture, but the pre-cracked region and the re-fatigued region possess the characteristic of fatigue fracture. Hence, under the action of Psthe cracks of specimens were indeed initiated and extended forward. 5.4. KR - Ahacurve was plotted as shown in Fig. 11, according to the data of KR and Aa. While Au = 2% a0 and Au = 7% uo, the co~esponding resistances are Kfc= 360 Kg/mm3” and KIE= 415 Kglmm3’2, respectively. They are in excellent agreement with the Kfc= 354 Kg/mm3’* and KIE= 416 Kg/mm3” obtained by the method of conditional load. The value Klcis also in agreement with the KIc= 376 Kglmm3’2[1l] converted from the J-integral. 5.5. From the measured data of fracture toughness of 30 CrMnSiA steel plate, it can be seen that there is an approximate relation between the plane-strain fracture toughness I& and the surface-flaw fracture toughness KfE, i.e. Klc = (0.85 - OJO)K,,.

400 r {

JO0

/--•

- 200 G /

‘““t-#-u-0

S

6

8 7 8,mm

Fii. 10. Kfc - B curve.

9

10

(11)

GUI ZHEN-JUAN

0.1

0.2

03 Aa,

04

0.5

0.6

mm

Fig. 11. Kn -Au

curve.

5.6. During the course of testing, it had been observed that there was a severe necking at the flaw located cross section of the specimens with B = 8 mm, W = 56 mm. It is probably due to that the width of these specimens and hence the constraint for deformation were insufficient. Since the ratios g&aO.z are greater than 1 for specimens with B = 8 mm, W = IlOmm, resulting from too large a ratio of width to thickness, the influence of the flaw on the fracture of these specimens is reduced as a consequence. The plotted KQ - W/B curve is shown in Fig. 12. The ratio of the length of flaw to the width of plate has been found to have an influence on the fracture toughness too. Which can be seen from Fig. 13. On the basis of the present test results, the restrictions for the width of specimens are suggested as follows: 8~ W/B
(12)

6. CONCLUSIONS (1) If the “conditional applied loads” of Pro and 4( corresponding to the relative effective flaw extensions of Au/a@= 10% and Augur= 5% are adopted, under the conditions of ~~~~~P,~G 1.2 and Pm,,/P5 d 1.3, the values of KfE and Kfc of 30 CrMnSiA steel plate can be obtained by surface-flaw testing. (2) The values of Klc and KfE can be obtained on the resistance curve KR - .Aa at the specified real extensions of flaws ha = 2% a0 and Au = 7% ao, respectively. (3) There is an approximate relation between Klc and KIE of the 30CrMnSiA steel plate. i.e. K;, = (0.85-

300

N

O.~)K~~.

I-

400

loo t

It 01

7

8

8

10

II

W/E

Fig. 12. KG - W/B curve.

12

I3

Exploring the fracture toughness Km and K,, of a medium-strength steel plate

:

400

789

y&f

mE \

300 -

r” i

200

-

t 100

I

I

0.2

0.3

I 0.1

0

2 c/w Fig. 13. Ko - 2cl W curve.

(4) The requirements for the dimensions of specimens for surface-flaw tests are: Thickness of plate: Width of plate: Effective length:

B 2 l.O(KI,/~,&*[or 1.25&/~~,,2)*1 8~ W/Bc10,4~

W/2c~5;

1a 2 W.

The present investigation of the fracture toughness of the medium-strength steel plate using surface-flaw test is only explorative. Further applications of the present method to other medium-strength steels, as well as some theoretical researches alongside, would be desirable. REFERENCES 111G. R. Irwin, Crack extension force for a part-through crack in a plate. J. Appl. Mech. Ser. E. 29(4),651-654(1%2).

VI A. S. Kobavashi and W. L. Moss, Proc.

2nd Int. Conf. Fracture. 3145 (1%9).

131P. C. Pairsand G. C. Sih, ASTMSTP 381, p. 51 (1985). [41 R. C. Shah and A. S. Kobayashi, On the surface Raw problem. ASME pp. 79-324 (1972). iSI F. W. Smith, The elastic analysis of the part-circular surface flaw problem by the alternating method. ASME p. 141 (1972). [61 G. R. Irwin, Characterization of part-through cracks in tension, ASME p. 4 (1972). [71 Fracture Toughness Group of Peking College of Iron & Steel, Inuestigation of the Fracture Toughness of the High-Strength Steel Plate Using Surface Flaw Test, (In Chinese) (1975). @I Fracture toughness group of Peking materials research institute. The Study of the Fracture Characterization of LDlOCS Aluminum Alloy Using Surface Flaw Method, Fracture 1,24-45,(In Chinese) (1977). [91 J. N. Masters et al., Investigation of deep flaw in thin walled tanks, NASA CR-72606, 37 (1969). UOI T. W. Orange, T. L. Sullivan and F. D. Calfo, Fracture of thin sections containing through and part-through cracks, ASTMSTP 4%, pp.61-68 (1971). HII Cui Zhen-Yuan et al., Tests on fracture toughness Km and Jro of the 30CrMnSiA steel plate, Collected Reports on the Sutface-Flaw Fracture Toughness Tests, Fracture Mechanics Laboratory, North-Western Engineering University pp. 34-51 (In Chinese) (1978). (Received IO January 1980; received for publication 29 February 1980)