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experimental investigation was conducted to examine how the upper stress intensity factor in parallel shear KrrrQ(similar to KrQfor Mode I) is affected by increasing the tensile strength of a material. Round notched and precracked bar specimens, fabricated from 4340 steel were used for the investigation. Based on results from four different heat-treatments of this steel it was found that the stress intensity factor KrIm increases as the tensile strength increases. Values of I&Q obtained for high strength 4340steel are in a~eement with those found by other investigators.

INTRODUCTION Although some authors[l, 21 have approached the determination of the stress intensity factor in anti-plane shear theoretically, literature survey indicates that no effort has been made so far to study and determine the value of KI1,,,for a given material. Expressions for Km have been derived from either the Westergaard stress functions or Neuber’s stress concentration factors, An excellent discussion of the plasticity aspects of KI,, is given by McClintock and Irwin[3]. Shah[4], used round notched and precracked bars to determine the combined effect of K,[[ and K1 on high strength 4340 steel. In the present work, the analytical expression as listed by Tada I.51has been adopted to calculate Kllf. The expression is:

(1) where: T = torque; P = ligament radius = r. - a; r. = specimen radius; and a = crack length; the factor F is given by:

+~.(Plro)4i0.208(Plr,)5]

* [l -(P/r#“.

(2)

MATERIAL AND SPECIMEN PREPARATION Specimen blanks were cut from l/2 in. diameter bar of 4340 steel. The chemical composition of this material is given in Table 1. Some blanks were preheated to 800°F and then annealed in salt bath at 1525°F for 25 min. These blanks were then quenched in oil and then separated into three groups. All three groups were then tempered for one hour and then air cooled to room temperature. Tempering temperatures and resulting tensile strengths are given in Table 2. The specimen blanks were then machined to dimensions given in Fig. 1. All specimens were precracked by growing fatigue cracks from the circumferential notch under rotating bending. The maximum nominal cyclic stress levels used were from 37 to 47 ksi.

Table I. Composition of 4340 steel, wt % C: Ni:

0.41 Mn: 0.73 P: I.66 Cr: 0.82 MO:

0.004 0.25 569

S: Al:

0.014 0.05

Si:

0.24

Cu:

0.15

N. TSANGARAKIS

570

TESTPROCEDURE Tests were run in an MTS 20,000 lbs. capacity mechanical testing machine. The parameters measured were torque and angular displacement. During testing, the angular displacement rate was maintained at l”/min and axial tensile loading was kept between 0 and 5 lbs. This small tensile load was necessary to avoid rubbing of the cracked surfaces against each other. Axial eccentricity in loading was less than 0.001 in. The machine instrumentation provided direct outputs for torque and angular displacement. Thus, plots of torque vs angle of rotation were made during each test on an X-Y recorder. After fracturing the specimen, the precrack depth was determined as the average of four measurements made at points 90” apart circumferentially. Specimens showing incomplete precracking circumferentially were discarded. Interpretation of the test record and calculation of KIIIa involved a construction on the test record. Referring to Fig. 2, ihe secant OT, is drawn with a slope of 95% of the slope of tangent OA. A torque T, is then determined as follows: if the torque at every point on the test record which proceeds T5 is lower than T,, then T, is T5 (Fig. 2, Type I); if, however, there is a maximum torque preceeding T5 which exceeds it, then this maximum torque is T, (Fig. 2, Types II and III). This T, value is then used to calculate the KIIIo value via eqns (1) and (2).

Table 2. Tempering temperatures and mechanical properties

Group

Condition

Tempering temperature, “F

1

As received Heat treated Heat treated Heat treated

175 550 400

2 3 4

Hardness 226BHN 45 HRC 50 HRC 52.5HRC

Tensile strength 102ksi 214ksi 255ksi 280ksi

E Sym

I

c

concentric within 0.001

Expanded

Fig. 1. Specimen

details

of

configuration

sections

“A”

and dimensions.

Shear yield stress 65 ksi 120

ksi 175ksi 186ksi

571

Fracture behavior of 4340 steel under mode III loading

TESTRESULTSANDDISCUSSION The test results are depicted in Fig. 3. The bottom curve represents the data from nine specimens of group 1 (Table 2). With increasing (U/C,)the stress intensity factor KrrIo increases rapidly. At approx. 0.49 value for (a/rO) the slope of the curve drastically increases indicating the effect of plastic zone on Krrro[3]. Between 0.31 and 0.49 for the ratio (a/r,,), K, varies from 19 to 27 ksi.-\/in. The second depicts data from 17 specimens of group 2 (Table 2). The effect of (a/~~)on K, is the same as before. Between 0.31 and 0.49 for the ratio (u/r& KIIIQvaries from 42 to 47 ksi.v’in. Here the effect of plastic zone on KIIlo becomes evident for a value of 0.56 for (u/r,,). The third curve was based on five specimens of group 3 (Table 2). Again, the same effect of (u/r,J on K, is observed. For values of (u/rO)between 0.31 and 0.49, K,IIQvaries from 50.5 to 56 ksi.din. The top curve resulted from eight specimens of group 4 (Table 2). Between 0.31 and 0.49 values for varies from 58 to 62 ksi.din. Shah[4] tested 4340 steel specimens of the same the ratio (u/r& K, strength. He found similar results with respect to K, value. The fractured surfaces of all specimens were flat with shear rubbing marks similar to those observed by Shah[4]. For the higher strength steel, the precracked area exhibited some macrofacets similar to those described by Hourlier et u1.[6] for the Ti-5Al-25 Sn alloy. In most of the tests, stable crack growth was evident by the shape of the torque vs angular displacement curves. Stable crack growth was followed by unstable crack growth which lead to fracture.

A

I Torque

Fig. 2. Principal types of torque-angular displacement records.

60 r

101

I

I

I

I

0.2

0.3

0.4

0.5

0.6

(Crack

depth / specimen

radius)

Fig. 3. Mode III stress intensity factors for 4340 steel.

I 07

I 0.9

512

2. I‘SANGARAKIS

Only in two tests on 4340 steel 45 HRC, unstable crack growth was observed to lead to fracture. ‘The plastic strain to fracture drastically decreased from group 1 to group 2 (Table 2). The decrease was less evident for further increase in strength (groups 3 and 4). The slope of the curves in Fig. 3 is decreasing with increase strength. From the data for 4340 steel-52.5 HRC, the stress intensity factor seems to approach the limiting value of 58 ksi.y’in. Assuming that this is true, KIIrc= 58 ksi.l/in. CONCLUSIONS The stress intensity factor in parallel shear for 4340 steel depends upon the strength of this material. Increasing the strength of the steel by an appropriate heat treatment wiil result, for the same crack size, in an increase in the value of the stress intensity factor KffIQ (similar to Kro in Mode I). Increasing the strength of the steel, the amount of plastic deformation leading to unstable crack growth as well as the slope of the J&o -(u/r,,) curve decreases. This may lead, for high strength values, to a lower limiting value of Krrra which may be considered critical (K& as to unstable crack growth (similar to KIc in Mode I).

1. P. C, Paris and G. C. Sih, Stress analysis of cracks. ASTMSpeciul Techn. Pub. No. 381,30-81 (1965). 2. D. 0. Harris, Stress intensity factors for hollow circumferentially notched round bars, J. Basic Engng, Trans. Am. Sot. Mech. Engrs, Series D, 89,49-54 (1967). 3. F. A. McClintock and G. R. Irwin, Plasticity aspects of fracture mechanics, ASTM Special PubI. STP 381 (196.5). 4. R. C. Shah, Fracture under combined modes in 4340 steel. STP 560, pp. 2%X2(1973). 5. H. Tada, The Stress Analysis of Cm&s ~undb~~ Del Research Corporation, Hellertown, Pennsylvania (1973). 6. F. Honrlier, D. McLean and A. Piieau, Fatigue crack growth behavior of Ti-Sal-Z.5Sn alloy under complex stress (I&de I + steady Mode III). Metals Technology, pp. 154-158(May 1978). (Received 17 June 1981; received for publication I6 July 1981)

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