Dynamic fracture mechanics with electromagnetic force and its application to fracture toughness testing

Engineering Frucrure Merhonics Prmted in Great Britain.

Vol. 23. No. I. pp. 265-286.

iH313-7944186 $3.00 + .oO Pergamon Press Ltd.

1986

DYNAMIC FRACTURE MECHANICS WITH ELECTROMAGNETIC FORCE AND ITS APPLICATION TO FRACTURE TOUGHNESS TESTING Department

G. YAGAWA and S. YOSHIMURA of Nuclear Engineering, University of Tokyo, 7-3-l Hongo, Bunkyo-ku, Tokyo, Japan

study is concerned with the application of the electromagnetic force to the determination of the dynamic fracture toughness of materials. Taken is an edge-cracked specimen which carries a transient electric current 1 and is simply supported in a uniform and steady magnetic field B. As a result of their interaction, the dynamic electromagnetic force occurs in the whole body of the specimen. which is then deformed to fracture in the opening mode of cracking. For the evaluation of dynamic fracture toughness, the extended J integral with the effects of the electromagnetic force and inertia is calculated using the dynamic finite-element method. To determine the dynamic crack-initiation point in the experiment, the electric potential method is used in the case of brittle fracture, and the electric potential and the J-R curve methods in the case of ductile fracture, respectively. Using these techniques, the dynamic fracture toughness values of nuclear pressure vessel steel A508 class 3 are evaluated over a wide temperature range. Abstract-This

1. INTRODUCTION of the dynamic fracture toughness of engineering materials has become increasingly important for the assurance of the integrity and safety of structural components subjected to dynamic loadings. Various dynamic fracture toughness testing methods using mechanical impact loading (e.g. the instrumented charpy test and the dynamic three-point bending test), which are standardized as in the EPRI test procedure[ I], have been employed in many practical situations[2-71. However, the loading rate of most of them to obtain the reliable dynamic toughness value seems to be limited to the order of about lo4 MN/m3’2.s in terms of i for highly ductile materials such as nuclear pressure vessel steels. One reason for this is that the inertia effects, including the dynamic contact phenomenon at the impacted point of specimen and the stress wave propagated from that point, create difficulties in estimating the fracture toughness under the high-loading-rate condition. For example, the load signal measured with a strain gauge mounted on the hammer always oscillates around the actual load required to deform the specimen at the higher loading rate. Thus, the empirical procedures based on static fracture mechanics, such as the EPRI testing method, require setting an upper limit to the loading rate condition. One of the most important criteria for the restriction is given as follows: THE EVALUATION

t > 37,

(1)

where t is the time to fracture in the elastic fracture or the time to general yield in the postgeneral-yield fracture, and 7 the period of the apparent specimen oscillation related to specimen geometry, dimensions and material properties[l]. However, many investigators have indicated that such a static approach often leads to erroneous Kid and Jld values[8,9]. Dynamic analysis, including the inertia effects and the dynamic contact phenomenon at the impacted point, is required in order to well understand the dynamic fracture behavior of materials[ lo]. The experimental difficulty in detecting the dynamic crack initiation time, especially for ductile fracture with stable crack growth, is another reason for inaccurate dynamic fracture toughness data. The J-R curve technique with multiple specimens, usually used in the quasistatic fracture test which requires one to determine the stable crack growth[l 11, has also been proposed as the JId testing procedure[3, 4, 61. However, it seems difficult in this method to control the loading to give a desired displacement to the specimen in the higher-loading-rate condition over the order of lo4 MN/m3’2.s.

266

G. YAGAWA

and S. YOSHIMURA

For these reasons, the authors, who have been involved in fracture mechanics in relation to the electromagnetic force [ 12-161, have considered that the new dynamic fracture-testing concept with the electromagnetic body force could be one of the most suitable ways for obtaining the dynamic fracture toughness of materials under the actually needed loading-rate conditions. This paper presents the application of the electromagnetic force, which occurs directly in the whole body of the specimen as a body force, to the determination of the dynamic fracture toughness. To show the effectiveness of the proposed method, the dynamic fracture toughness values of the nuclear pressure vessel steel A508 class 3 are evaluated at a stress intensity factor rate K near 1 x IO5 MNlm3’**s in a broad temperature range from lower shelf to upper shelf, and compared with the static and the dynamic toughness values in the literature. 2. PRINCIPLE

OF THE METHOD

Figure 1 shows the basic principle of the present experiment. The test specimen is set between the electromagnet, so that the magnetic field B is given to the specimen in the thickness direction (i.e. the -Z direction). The electric discharge circuit is then opened to induce a transient electric current I in the specimen, flowing from the right to the left in the specimen. As a result of the interaction of the magnetic field and the electric current, the Lorentz force I x B occurs in the specimen in the downward direction (i.e. -Y direction). In the present experiment, the magnetic field is kept steady over time and the current is applied dynamically, so the time variation of the applied force, proportional to that of the current, can be directly and accurately measured. Figure 2 shows the diagram of the electric current discharge circuit with the cracked test

MAGNET

Fig.

1. Edge-cracked

beam

under

DISCHARGE

SCR

switch

electromagnetic

force.

CIRCUIT

Resistance(R)

Inductance(L)

J

Fig. 2. Schematic

S'X~:FORCE

view of body-force-type

VECTOR

loading.

Dynamic fracture mechanics with EMF SCR switch

267

Resistance(R)

Y

J-

X

Z

4 :xi:FORCE Fig. 3. Schematic view of surface-force-type

VECTOR loading.

specimen, where the downward arrows schematically indicate the body force vectors caused by the interaction between the magnetic field B and the electric current I. The electromagnetic force can also be applied to the specimen as a surface force through a conductive metal tape attached to it as shown in Fig. 3. This type of loading appears particularly useful if the specimen is made of nonmetallic materials. Another merit of this method is that no Joule heating occurs at the vicinity of the crack tip, although this does not seem so important in usual situations[ 14- 161.

3. ADVANTAGES OF THE METHOD In order to show one of the differences between the present electromagnetic force method and a conventional one such as the drop-weight-type test for fracture toughness testing, a typical & vs time curve given by K~tho~9~ is taken here (see Fig. 4). The mechanics behavior of the crack under impact loading by drop weight is investigated there by measuring the dynamic stress-intensity factors directly at the crack tip by means of the shadow optical method of caustics. The influences of dynamic effects are evaluated by comparing the dynamic stressintensity factors K?y” with the equivalent static stress-intensity factors Kitat. The latter are determined from the measured hammer load PH utilizing the conventional static stress-intensity factor formula. The times are given in absolute units and also in relative units by normalization with the period of the eigenoscillation of the impacted specimen 7. The Kitat value shows a strongly oscillating behavior as shown in Fig. 4. The actual dynamic stress-intensity factor ZCty”also shows an oscillating behavior, although not so strongly as the ,Pat values. Figure 5 illustrates the schematic representation of loss-of-contact effects observed with a prenotched-bend specimen under drop-weight loading. The loss of contact starts at about t = 0.5~ when the stress wave reaches the anvils from the impacted point. For about t = T, the specimen is completely free and only after this time, i.e. at a time of about t = 1.257, do the specimen ends come into contact with the anvils. With different test conditions this loss of contact can occur later for a second time. It is noted that the early specimen reaction is the same for both the supported and the unsupported specimens. On the other hand, Fig. 6 shows the calculated time variations of the applied electromagnetic load P,, the load at supported points P, and the dynamic J integral JLfyn. which is defined later in this paper. It is noted here that the Jdyn integral takes the maximum value without higher-mode oscillation after the peak point of the electric current transient curve. Namely, the peak value of the electromagnetic force is observed at about 0.5 ms, whereas that of the Jdyn integral is observed after 2 ms. Another interesting feature here is that the dynamic supporting load caused by the electromagnetic force P, oscillates with the period of the natural oscillation of the part of the specimen outside of the supported point. However, as its value is always positive during the

ci 0

STRESS b

INTENSITY b

h,

FACTORS

K, 0

w

, MNrf3’* E b

269

Dynamic fracture mechanics with EMF

L mm

.uu ,,1,*, IxB

...._._.

r'

I

1 TIME, Fig. 6. Electromagnetic

A508 cl Lass 3 steel

I

I

2

3 t (msec)

load P,, reaction load at supported points P, and Jdyn integral vs time.

event, it is expected that the specimen loaded by the electromagnetic force continues to contact the supporting points; this tendency differs from the experimental results shown in Fig. 4 for the fracture phenomenon impacted by mechanical loading[9]. Moreover, the Jdyn integral vs time curve has no higher-mode oscillation; this tendency also differs from the results shown in the mechanical loading cases. The above results can be explained as follows. When the electromagnetic force acts dynamically on the whole body of the specimen, no local high-stress-concentration region is formed in it except at the supported points apart from the crack tip. Although the stress wave propagates more or less from the supported points, the higher-mode oscillations as shown in the cases impacted by mechanical loading are diminished on the way to the crack tip. After all, these characteristics of the dynamic electromagnetic force as a body force may help to reduce the higher-mode oscillation of the dynamically loaded specimen. We summarize here the characteristics of the present dynamic fracture testing method using the electromagnetic force as compared to the conventional mechanical impact-loading methods. As one of the experimental estimation methods for dynamic stress-intensity factors, the simple static formulae are often used with the instrumented impact test. It appears, however, that a static analysis is not adequate to describe the loading condition in the specimen under the proposed conditions except at much later times during the event, and very large times to fracture cannot always be achieved. Therefore, the fully dynamic evaluation procedures by means of the dynamic finite-element methods[Sl or the shadow optical method[9] are developed among others to determine reliable impact fracture toughness data with a freedom of choice of test conditions within the framework of the dynamic fracture testing using the mechanical impact loading. Although these procedures would improve the accuracy of fracture toughness data obtained, there still remains the question of the repeatability or reproducibility of the fracture fracture

270

G. YAGAWA and S. YOSHIMURA

event, since the dynamic behaviors of test specimens depend more or less on the complicated contact condition between the specimen, hammer and anvils, loading rate, geometry of hammer, and so on. The fracture testing method using the electromagnetic body force seems to be an ideal procedure to solve the problem, since J dyn vs time has no higher-mode oscillation as explained above. 4. NUMERICAL ANALYSES As a detailed description of the numerical procedure has been published by the present authors[l4-161, its brief overview and results are summarized in this section. The two-dimensional electric current distribution in the specimen is calculated first to evaluate the electromagnetic force acting in the specimen. (The electromagnetic force in the specimen can often be replaced by the uniform surface force for simplicity even in the body force type (see Fig. 2) if the deformation of the specimen is characterized by the beam mode.) Following this, a two-dimensional dynamic and elastic-plastic analysis based on the Jz flow theory is performed with the dynamic J integral[l7] as a fracture-mechanics parameter, including the effects of the electromagnetic force and the inertia. In our case the J integral can be written as follows: J dyn

=

Wn,

-

Ti$

{pu; - (I X B)i} $ I

I

dA,

(2)

where Ti is the traction force along the integration path I, and W, nl , p, ui and A are the strain energy density, the X1 component of the unit normal vector, the mass density, the displacement and the domain surrounded by r, respectively (see Fig. 7). Figure 8 shows the finite-element mesh and the paths for Jdyn integral calculations. The material properties adopted here are those of Type 304 stainless steel and of A508 class 3 steel presented in Table 1, and the plane stress is assumed as the two-dimensional stress condition. Figure 9 shows the calculated J integrals vs path number at the time of 0.2 ms. The open

Fig. 7. Crack-tip coordinates

for the definition of Jdyn integral.

Fig. 8. Paths for J integral calculation.

Dynamic fracture mechanics with EMF

271

.

s

l

5 r(Wdx,-Ti~ds) ax,

Jstat=

-

0.

123456

PATH NUMBER Fig. 9. Path independency

of calculated Jdyn integral.

Table 1. Material properties assumed for numerical analyses

Young’s modulus Poisson’s ratio Yield stress Strain-hardening rate Mass density (T: Equivalent

Type 304 stainless steel

A508 class 3 steel

1.9 X 10’ MPa 0.3 225 MPa 2700 MPa (225 MPa < Z < 340 MPa) 2100 MPa (340 MPa < C) 7.9 x 103 kg/m3

2.06 x 10’ MPa 0.3 441 MPa 1960 MPa (441 MPa < Z) 8.03

x

l@ kg/m3

stress (= a).

1000 - -196°C 2

800.

-150°C_ 1'gg

E

2%

'". 600-

150°C

_

w & $ 400 -

A508 class3

200

I

0 0 Fig. 10. Temperature-dependent

2

I 4 STRAIN, stress-strain

steel

_

4 12

I

I

I

6

8

10

E (%) relation of A508 class 3 steel for calculations.

272

G. YAGAWA and S. YOSHIMURA

1.2 -

1.0 -

0 A

- 41°C,

105°C 7°C

0 - 41°C v - 74°C 0 - 88°C Q) -196°C

P

EXP

FEM $0.8

-

2 0.6 s -!! 0.4 A508 class3

0

2 LOAD POINT

4 6 DISPLACEMENT,

Fig. 11. J,,,, L’Sload-point displacement

steel

ib 8 6 (mm)

in static three-point

bending test.

and filled circles represent, respectively, the J integral with the body force effect Jdyn and that without the effect JStat. The path independence of the former is apparent from the figure. Figure 10 shows the temperature-dependent stress-strain relations of A508 class 3 steel, which are employed in the calculations. The static numerical results of the J integral vs the load-point displacement are shown in Fig. 11 with the experimental data of the static three-

TIME,

t (msec)

Fig. 12. Various time histories of electromagnetic

force.

273

Dynamic fracture mechanics with EMF

FINITE

0

ELEMENT METHOD

0123456

TIME,

t (msec)

Fig. 13. Calculated time variations of Jdyn integral for the loading conditions given in Fig. 12

point bending tests over the temperature range from - 196 to 105°C. The experimental are evaluated with the estimation method given by Rice et a1.[18]: 2A J= b(W - a)’

J integrals

(3)

where A is the area under the load-displacement curve, b the specimen thickness, and (W a) the remaining untracked ligament. The accuracy of the present numerical procedure with

FINITE

ELEMENT METHOD No. 9

8

0

1

2 3 TIME,

4 5 t (msec)

Fig. 14. Calculated time variations of crack mouth opening displacement loading conditions given in Fig. 12.

6 (COD,,,,,,)

for the

274

G. YAGAWA and S. YOSHIMURA

No. 9

FINITE ELEMENT METUnn

8

0123456

t (msec)

TIME I

Fig. 15. Calculated time variations of deflection at the center of specimen for the loading conditions given in Fig. 12.

respect to static J integral evaluation is guaranteed by the coincidence of their results as shown in this figure. Figure 12 shows nine kinds of time history of the electromagnetic load, which are subsequently employed as input data to calculate the time dependent J+ and so on. Figures 13, 14 and 15 show the calculated time variations of the .I+ integrals, the CODS at crack mouth point and the deflections at the center of the cracked beam, respectively, corresponding to the nine loading conditions in Fig. 12.

Type 304 stainless

steel

1

N& \ 7 ;r_ v =. ‘I

.6

FINITE ELEMENT METHOD

-8 4

.6

-4

. 2

t

1

2

1.5

COD mouth

2.5

[mm)

Fig. 16. Calculated relations between Jdyn integral and COD,,,,, given in Fig. 12.

for the loading conditions

3

Dynamic fracture mechanics with EMF

m

(I 4OIlIll

275

304 stainless

steel

*m~*..~.+L,.~*,,H.,..+* IxB A ao=Z(hrm

T1-&5%%.~J

9 FINITE

ELEMENT

5

METHOD

t

18

15

20

DEFLECTION,

8

25

30

3!

[mm1

Fig. 17. Calculated relations between J+ integral and deflection at the center of specimen for the loading conditions given in Fig. 12.

Figure 16 shows the calculated relations between the Jdyn integral and the CODmouth for the nine loading conditions in Fig. 12, where each point indicated with the number corresponds to the peak point of the time history of the electromagnetic load with that number in Fig. 12. For example, COD,,,ti, and Jdyn for loading case No. 5 take the maximum values 1.5 mm and 0.5 MJ/m2, respectively at the same time. It appears from the figure that the nine curves with various loading rates overlap with each other rather well. Figures 17 and 18 show the similar relations between the Jdyn integral and the deflection at the center of cracked specimen and those between the COD,,,,lr, and the deflection at the center of cracked specimen. These curves also show good coincidences with each other. The reason for the coincidence of the relations among the three parameters, Jdyn, deflecirrespective of the different loading rates, may be explained by the fact tion, and COD,,,,,,, that the deformation of the cracked beam under the dynamic electromagnetic force always behaves in a simple first natural eigenmode. This characteristic of the cracked beam under the dynamic electromagnetic force is very useful for the purpose of fracture toughness evaluation as shown later, because the critical J +,, integral value can be easily obtained from the above unique relation between the Jdyn integral vs deflection or COD mouthand the critical time detected experimentally, once the calibration curve is derived beforehand with the numerical or experimental methods. Incidentally, it should be noted that the Joule heating concentrated around the crack tip due to the singularity of the electric current distribution affects more or less the fracture behavior of the cracked specimen carrying the electric current. Figure 19 shows the time history of the calculated temperature due to the Joule heating at the crack tip of a cracked specimen of Type 304 stainless steel carrying a transient electric current. As shown in previous studies by the present authors[l4-161, the region of important temperature increase is restricted to very near the crack tip. As a result, the thermal stress due to the Joule heating contributes very little to the J integral value as shown in Fig. 20, which is the time variation of the ratio of the J integral value due to the electromagnetic force combined with thermal stress JLT to that due to the electromagnetic force only JL. Therefore, the influences of Joule heating on fracture phenomena subjected to electro-

216

G. YAGAWA

and S. YOSHIMURA

3 Tvpe 304 stainless

steel

“1mj

2.5 E

9

22

FINITE

ELEMENT

METHOD

1.5

5 g1 0 L-l

.5

0

Fig.

I

5

18. Calculated

10

15

20

DEFLECTION,

6

25 (mm1

relations between COD mOuth and deflection at the center for the loading conditions given in Fig. 12.

TEMPERATURE

0

1

2

3 TIME

current

1

4

1

5

6

7

(msec)

as input data and calculated

temperature

at the crack

tip vs time.

__________--___-----____ /

0.98

.

of the specimen

---- CURRENT

p, ’\ I :

Fig. 19. Electric

5

30

JO.96

GO.94 0.92 0

1

2 TIME

3

( msec)

Fig. 20. Time variation of the ratio of J integral value due to electromagnetic force with thermal force JLT to that due to electromagnetic force only JL,

combined

277

Dynamic fracture mechanics with EMF Holes

forCable

Connection

~,

o$

7

512-

-s/z

IF---

H

7

A

L/2-

L/2 S=160mm.

L= 300mm

for static

S =400mm,

L = 428 mrr

for d;rncmlc

test test

Fig. 21. Configuration and dimensions of test specimen made of A508 class 3 steel.

magnetic force, including the thermal stress and some change of material properties near the crack tip, can in practice be ignored in evaluating the J integral value in the present analyses. It should be pointed out here that the strain rate effects on tensile properties of materials are not taken into account in the present numerical analyses. The strain rate in the vicinity of the crack tip is calculated to reach almost the order of lo2 s- ‘. This result suggests that, if the strain rate effect were taken into consideration, it would more or less affect the unique relations between Jdyn integral, deflection, and COD,,,,,, , as shown in Figs. 16-18. Since the effect is considered to be one of the most important problems in fracture mechanics[l9,20], the present authors will discuss it in a forthcoming paper. 5. EXPERIMENTS 5.1 Specimen

The static and dynamic fracture-toughness tests were performed on the nuclear pressure vessel steel A508 class 3, whose chemical compositions and mechanical properties are shown in Tables 2 and 3, respectively. All the test specimens shown in Fig. 21 were taken from a large plate for nuclear reactor pressure vessels keeping the T-L orientation per ASTM E39978. In the test specimen, a mechanical notch was machined and then a fatigue precrack was given a length of up to a/W = 0.5 (a = crack length, W = width of test specimen) based on the JSME standard for elastic-plastic fracture toughness Ji,[21]. The two holes of 6 mm in diameter were machined for connecting electric current wires with the specimen. Also, holes of 3 mm in diameter machined near the crack were used to connect the voltage probes for the

Table 2. Chemical compositions

of A508 class 3 steel in weight percent

C

Si

Cu

Ni

Cr

MO

V

Al

0.18

0.26

0.02

0.76

0.04

0.48

CO.01

0.018

Mn

P

S

1.32 0.003 0.001

Table 3. Mechanical properties of AS08 class 3 steel Tensile strength (MPa)

Elongation (So)

Reduction of area (%I

7 30 110

971 564 531 498 484 462

971 716 701 642 625 615

5.8 29.7 28.7 26.4 27.6 23.6

6.2 67.8 71.5 70.8 73.6 72.4

7 30 110

631 628 584

708 702 661

25.6 24.9 26.0

73.3 70.0 72.4

Temperature (“Cl Static (; < 10-2 s-1)

Dynamic (i - lo2 s-1)

-196 -70 -40

Yield stress (MPa)

FATT = -22°C; I)E,I,~K= 228 J: RTNDT.= -30°C:i =

strain

rate

G. YAGAWA

I

.

.

and S. YOSHIMURA

.

.

.

.

.

.‘..... . .

. .

.

.

. . .

.

~ STATIC Fig. 22. Comparison

. .

. . . .

. .

.

. .

.

. .

.

. .

. .

.

. .

. .

. .

. .

.

.

6mn

-70°c

DYNAMIC

between static and dynamic fracture surfaces of A508 class 3 steel at - 70°C.

measurement of the electric potential to the specimen. Here, the thickness of the specimen of 6 mm was decided upon due to the small Ioad capacity of the present electromagnetic testing machine. 5.2 Test system The conventional static three-point bending tests were performed using the servo-hydraulic MTS machine, and then the dynamic fracture tests were carried out by using the electromagnetic loading machine, the principle of which is shown in Fig. 2. The transient electric current conducting in the specimen was supplied by the LCR discharge circuit, whose capacity, inductance and resistance are 22 mF, 11pH and 45 mR, respectively. The maximum capacity of the electric current was about 18 kA at about 0.5 ms with the voltage of 1000 V. An electromagnet gives a uniform and steady magnetic field of I.7 T to the specimen. As a result of their interaction, the dynamic electromagnetic force is generated in the whole body of the specimen, which is then deformed to fracture in the opening mode of crack. Note that, as A508 class 3 steel is ferromagnetic, a lateral magnetic force acts on the specimen and bends it in the thickness direction. If the specimen touches the face of the magnet, the insulation of the circuit has failed and the friction force acts on the side of the specimen. To reduce these effects of the lateral magnetic force, a slider made of teflon was employed. Both static and dynamic tests were carried out at various temperatures from - 196 to 115°C.

STATIC

DYNAMIC

Fig. 23. Comparison between static and dynamic fracture surfaces of A508 class 3 steel at 7°C

Dynamic

electric

potential

'0

Fig. 24. Diagram

mechanics

with EMF

279

;m

dlfferen<:e

?fqJ

0

.k

fracture

Time

Time

Brittle

Ductile Fracture

of electric

potential

method

Time

tC

I for brittle material

without

stable

Fracture

crack

growth

The following measurements were made in the tests: (a) the electric current profile, (b) the deflection at the center of the specimen, (c) the electric potential difference between both sides of the crack surface, and (d) the crack extension amount after the test. The crack extension amounts were measured using the three-point-average method after the specimens were heat tinted and broken in liquid nitrogen according to the procedure of the JSME Standard[21]. 5.3 Fracture

surfaces of the specimen

Figure 22 shows the fracture surface of the specimen obtained from the static three-point bending test and that of the dynamic test by electromagnetic force, both at a temperature of

2-0 ,s

c

. a

1.

.

.

a

W

0

.

w

TIME, t(msec) Fig. 25. Typical

time variations

of electric potentials obtained 3 steel specimen at -70°C.

for brittle

fracture

of A508 class

280

G. YAGAWA

and S. YOSHIMURA

-70°C. It is seen from the figure that a stable crack of 0.15 mm in length grew ahead of a fatigue precrack in the static fracture phenomenon at this temperature, while the dynamically loaded specimen was fractured perfectly controlled by cleavage. The difference in these fracture surfaces is apparently due to the strain-rate effect. On the other hand, Fig. 23 shows the static and dynamic fracture surfaces obtained at a temperature of 7°C respectively. All the static and dynamic fracture behaviors tested at and over this temperature were controlled by complete ductile tearing, with shear as shown in the figure. However, the shear region in dynamic fracture surfaces seems to be a little smaller than that in static ones. 5.4 Detection of dynamic crack initiation Brittle fracture Gthoat stable crack growth-electric

potential method (1). Below the transition temperature range where the fracture behavior is controlled by cleavage, the electric potential method using the transient electric current carried in the specimen is utilized to detect the crack initiation. Figure 24 shows the procedure of the present electric potential method. Figures 24(a) and 24(c) show schematically the time variation of the electric potential between both sides of the crack surface of test specimen set in the magnetic field, and that of the dummy specimen set out of the field for the purpose of comparison, respectively. It is shown in the figures that the electric potential 4(u) in Fig. 24(c) starts to increase abruptly after assuming a similar time history as that of +(ao) in Fig. 24(a) until the critical time t,, and starts to decrease again after the second peak. The rise of the potential $(a) starting from the time t, presumably corresponds to the crack propagation, because the electric potential between both sides of the crack surface increases in accordance with the increasing electric resistance of the specimen, which is a function of the untracked ligament length. Likewise, the time of the second peak in Fig. 24(c) seems to coincide with the crack arrest time of the specimen. Figure 25 shows the experimental time variations of the electric potentials $(a) and 4(ao) obtained for A508 class 3 steel at a temperature of - 70°C. It can be seen from this figure that the electric potential $(a) shows the sudden rise starting at the time of 1 ms, which may clearly indicate the crack initiation point.

0

Measured Potential

vs.

Crack

m

Time

Length

vs.

Time

'-1

Time

ti

Time

ti U Crack

Experimental Potential

or vs.

( Calibration

Velocity

Theoretical

Crack

Length

Curve

1

a Fig. 26. Diagram

of electric

potential

method

2 for ductile

material

with stable

crack

growth.

= tan

o

281

Dynamic fracture mechanics with EMF

0

2t3 TIME

1

4

5 6ta7 ( msec)

Fig. 27. Time variation of electric potential ratio obtained for A508 class 3 steel at room temperature.

0.8 3 z _I 90

crack arrest 0.7

z

LOKC 0

QI

SE

“00

k2’

P0 o”

y 50.6 - crack gz initiation

4 0.5

Fig. 28. Time variation

0

1

2 3 TIME

4

5 6 (msec 1

7

of nondimensional crack length for A508 class 3 steel at room temperature.

0.6 -

.

. I.’

:.’

,_I’ o,5

,/” 0.6 0.9 1.0 0.5 0.6 0.7 NONDIMENSIONAL CRACK LENGTH 1 QlW (observed

Fig. 29. Relation between estimated and observed crack extensions room temperature.

for A508 class 3 steel at

282

G. YAGAWA

and S. YOSHIMURA

Ductile fracture with stable crack growth-electric potential method (2). In the present electric potential curve, the value of the electric potential varies with the transient electric current history even without any crack extension. Therefore, it is difficult, particularly for ductile fractures, to accurately measure the initiation of the stable crack growth by directly using the electric potential curve as shown in Fig. 24(b), and also hard to measure the crack extension amount by this method. In order to modify the method to make it more accurate for ductile fractures, we measure the electric potential between both sides of the crack surface of the specimens outside of the magnetic field as well as inside it, as shown in Figs. 24(a) and 24(b), to take the time variation of the potential ratio $(a)/+(~,) as shown in the upper left of Fig. 26. The relation between the potential ratio vs time in this figure shows a very clear change of slope at the time li, which presumably corresponds to the crack initiation time for ductile fracture. It is well known in the static or quasi-static fracture test that the measured potential ratio uniquely coresponds to crack length. The lower left of Fig. 26 shows the schematic calibration curve between the crack length and the potential ratio, which is obtained from either numerical analysis or the experiment. Since the crack velocity of the dynamic ductile fracture is not so fast as that of the brittle fracture for which the calibration curve is affected by the crack velocity[22], one can apply the calibration curve without the dynamic effect to the present dynamic ductile fracture subjected to the electromagnetic force. The right part of the figure shows the schematic time variation of crack length, which is derived from the left part of the figure. The crack velocity can also be obtained by taking the slope of the curve in the figure. Figure 27 shows the time variation of the electric potential ratio obtained for A508 class 3 steel at room temperature. It can be seen from this figure that the potential ratio has a clear slope change at t = ti between 2 and 3 ms and becomes constant after t = t, of about 6.5 ms, which may presumably indicate the crack arrest. Figure 28 shows the relation between the nondimensional crack length vs time for this case. Since the final crack length is estimated from the figure to be 14 mm with W = 20 mm and the time interval between the crack initiation and the arest is about 4 ms, the average crack velocity in this case is estimated to be about 3.5 m/s. Figure 29 shows the comparison for eight specimens between the nondimensional crack length at the arrest estimated from the above method and that measured after the test. It can

Potential

vs.

5

Time

tc

n

Deflection

u

vs.

Time

6

C

Jdyn

Vs.

KId UC) = ( =mc

Deflection

FRACTURE

ANALYSIS ( E-EM )

(plane strain) (plane

stress)

Fig. 30. Diagram of K,d determination

for brittle material without stable crack growth (electric potential method 1).

283

Dynamic fracture mechanics with EMF

Deflectio;

vs.

Time

’ ei

ti Jdyn

‘=-

Deflection

Time

5 4

FRACTURE

ANALYSIS

( FEM 1 JId J ICI 6 for ductile material with stable crack growth (electric potential method 2). 6,

Fig. 31. Diagram of Jl,, determination

be seen from the figure that both values agree rather well, showing that this electric potential method seems to be useful for measuring the dynamic ductile crack growth. 5.5 Procedure to determine dynamic fracture toughness Kid determination

potential method (1). below the transition temperature range is illustrated using the transient electric current conducting in the initiation time t, which is then used to determine the brittle fracture toughness of dynamic crack initiation value derived with the calculated Jdyn integral vs de-

for brittle material without stable crack growth-electric

The diagram of the Kid testing procedure in Fig. 30. The electric potential method specimen is applied to detect the crack critical deflection value 6,. Finally, the Kid (.I,) is obtained from the critical J, flection curve.

Jld determination for ductile material with stable crack growth-electric potential method (2). In the case of dynamic ductile fracture with stable crack growth, the potential vs time curve itself gives no clear indication at the stable crack initiation time. So, as explained above, to detect the accurate stable crack initiation point, we take a ratio by normalizing the electric potential $(a) obtained from the test specimen set in the magnetic field with the potential +(a,,) obtained from the dummy specimen set outside of the magnetic field. Thus, one can determine the dynamic stable crack initiation time ti from the clear change of slope in the potential ratio vs time curve as shown in the upper part of Fig. 31. Finally, the ductile fracture toughness of dynamic crack initiation JId is determined from ti by following the same procedure as in the above Kid testing method. JId determination for ductile material with stable crack growth-J-R curve method. Another method proposed here to obtain the JId value for dynamic ductile fracture is based on the multiplespecimen J integral resistance curve technique, the so-called J-R curve technique, usually used in the static fracture test[l 11. As shown in Fig. 32, each specimen is dynamically loaded up to a desired displacement 6, (not to failure) by electrically controlled force and the corresponding .I+ integral, the J, value, is evaluated with the calculated .I+ integral vs deflection curve. The fracture toughness Jld is determined as a cross point of the blunting line and the J-R curve. Figure 33 compares the static and the dynamic J-R curves for A508- class 3 steel at a temperature of 7°C. The blunting line here, recommended for the relevant material by the TS subcommittee organized in the Japan Welding Engineering Society[23], is written as follows:

J = 4aYAa,

(4)

284

G. YAGAWA and S. YOSHIMURA

Deflection

vs. Time

i5)

Jdyn

E -P

VS. Deflection

FRACTURE ANALISIS ( FEM f

JIn
_~ 61” Jm

li vs.

6

I

II

1

b=

ha

Crack

Extension

Amount

Jill .-

JId

~ Aa Fig. 32. Diagram of Jld determination

for ductile material with stable crack growth (J-R curve method).

where uy is the yield stress of the material obtained from the static tensile test, and Aa the crack extension amount. It is seen in the figure that the dynamic resistance at the initial stage of crack extension is smaller than the static one and that their difference decreases with the crack growth. Such a tendency was also observed in the other cases obtained at higher temperature ranges, although the difference between the dynamic and the static curves becomes smaller as the temperature increases. 6. FRACTURE TOUGHNESS OF A508 CLASS 3 STEEL VERSUS TEMPERATURE All the dynamic fracture toughness data vs temperature obtained in the present study are plotted using solid and dashed lines in Fig. 34, where the dynamic initiation toughness KM is converted from the Jrd value by using the following relationship11 11:

1.0

J, 0

0.5 CRACK EXTENSION

1.0

AMOUNT,

A a (mm)

Fig. 33. Comparison between static and dynamic J-Rcurvesfor A508 class 3 steel at 7°C.

285

Dynamic fracture mechanics with EMF

f

1

400 E t E 3

v/d 0 300 - -O-

scattered static dynamic

1

I

I ~508

class

band , Japanese , Present , Present

static

3 data

steel [ 231

* J-R curve method

$50

-2co

-150

-100 -50 TEMPERATURE,

0

50 T (“C)

loo

150

Fig. 34. Fracture toughness of A508 class 3 steel vs temperature.

where E is Young’s modulus and the plane stress is assumed because of the small thickness of specimen of 6 mm. The ASME KIR curve, the Japanese static data (hatched area)[23] and the other dynamic data (dashed line)[6] are also plotted in the figure for the purpose of comparison. The open circles are our static data obtained from the same type of specimens as those used in the dynamic test. According to the finite-element calculation for all of the dynamic experimental results, the loading rate was in the range from 8 x lo4 to 2 x lo5 MN/m3”*s in terms of i. It is also noted that most of our toughness data obtained here fail to meet even the following J1, test size criterion[ 111:

JId

a, b, W - a > -, Uf

where uf is the flow stress; mean value of the material’s yield and ultimate tensile stresses. Nevertheless, as all of the present static and dynamic tests were performed using the specimens with almost a unique configuration, the toughness data obtained here could be used at least for discussing the loading-rate effects. Figure 34 shows that, below the transition temperature range, the dynamic toughness data seem about 30-50% smaller than the static ones, and the transition temperature shifts by 4050 deg to the higher temperature range due to the loading-rate effects. In the upper-shelf temperature range, the dynamic toughness data are also reduced by lo-20% compared with the static data. This tendency appears to be in accordance with the decreased shear rate in the fracture surface for the dynamic cases. It is, however, required to test larger specimens to accurately determine the fracture toughness data in the upper shelf range. 7. CONCLUSIONS The conclusions obtained in this study are detailed as follows. 1. To determine the dynamic fracture toughness of nuclear pressure vessel materials in brittle and ductile temperature regions, the dynamic electromagnetic force method is successfully employed. 2. The main advantages of the method are the easy controlability of the loading rate and load magnitude, the accurate determination of the loading vs time curve, and the compactness of the apparatus for the capacity.

286

G. YAGAWA and S. YOSHIMLJRA

3. Jdyn vs deflection given by the electromagnetic force has a unique curve independent of loading rate. 4. The dynamic crack initiation point is determined by using the electric potential method in the case of brittle fracture, and by the electric potential and the J-R curve methods in the case of ductile fracture. 5. Three kinds of diagram are proposed to determine Kid and J,d. 6. The fracture toughness value of nuclear pressure vessel steel A508 class 3 is reduced at the high loading rate K of the order of IO5 MN/m3’2 .s in the broad temperature range from - 196 to 115°C. Acknowledgmenrs-This work was performed with financial support from the Japan Atomic Energy Research Institute and the Grant-in-Aid for the research of the Ministry of Education, Science and Culture.

REFERENCES [I] W. L. Server, R. A. Wullaert and J. W. Sheckherd, Evaluation of current procedures for dynamic fracture toughness testing. ASTM STP 631, 446-461 (1977). [2] W. A. Logsdon and J. A. Begley. Dynamic fracture toughness of SA533 grade A class 2 base plate and weldments. ASTM S7P 631, 477-492 (1977). [3] W. A. Logsdon, Static and dynamic fracture toughness of ASTM A508 Cl.2 and ASTM A533 Gr.B.Cl. 1 pressure vessel steels at upper shelf temperature, in Proceedings ofthe Winter Annual Meeting ofthe ASME, MPC-8, pp.

149-165 (1979). [4] W. L. Server, Static and dynamic fibrous initiation toughness results for nine pressure vessel materials. ASTM S7P 668, 493-5 14 (1979). [5] L. S. Costin. W. L. Server and J. Duffy. Dynamic fracture initiation: A comparison Trans. ASME, J. Eng. Mater. Tech. 101, 168-172 (1979).

of two experimental

methods.

[6] H. Tsukada, T. Iwadate, Y. Tanaka and S. Ono, Static and dynamic fracture toughness behavior of heavy section steels for nuclear pressure vessels, in Proceedings of the 4th International Conference on Pressure Vessel Technology, Vol. I, C55/80, pp. 369-374. London (1980). [7] T. Kobayashi, Analysis of impact properties of A533 steel for nuclear reactor pressure vessel by instrumented charpy test. Engineering Fracture Mechanics 19, 49-65 (1984). [8] A. S. Kobayashi, M. Ramulu and S. Mall, Impacted notch bend specimens. Trans. ASME, J. Pressure Vessel Tech. 104, 25-30 (1982). [9] J. F. Kalthoff, Time effects and their influences on test procedures for measuring dynamic material strength values, in Proceedings of the International Conference on Application of Fracture Mechanics to Materials and Structures (G. C. Sih, E. Sommer and W. Dahl, eds.), pp. 107-136. Martinus Nijhoff (1984). [lo] J. 0. Hallquist, A numerical treatment of sliding interfaces and impact. ASMEAMD 30, 117-133 (1978). [l I] J. D. Landes and J. A. Begley, Test results from J-integral studies; an attempt to establish a J,, testing procedure. ASTM STP 560, 170-186 (1974). [12] G. Yagawa, M. Masuda and T. Horie, Dynamic fracture analysis of structure under electromagnetic force, in Proceedings of the 1st Symposium on Finite Element Method in Electric and Electronic Engineering, pp. 195206. JSST(l9?9) (in Japanese). 1131 . _ G. Yaeawa. M. Masuda. T. Horie and Y. Ando. Dvnamic fracture of cracked beam under electromagnetic force, in Proieedings of the International Conference on-Analytical and Experimental Fracture Mechanics (G. C. Sih and M. Mirabile, eds.), pp. 757-769. Sijthoff and Noordhoff (1981). [14] G. Yagawa and T. Horie, Cracked beam under influence of dynamic electromagnetic force. Nuclear Engineering and Design 69, 55-59 (1982).

[15] G. Yagawa and T. Horie, Ductile fracture of edge-cracked

beam under dynamic electromagnetic

bending force.

Engineering Fracture Mechanics 20, 23-34 (1984). (161 G. Yagawa and S. Yoshimura, Nonlinear and dynamic fracture of cracked structures under electromagnetic force. Nuclear Engineering and DesignlFusion 2, 53-63 (1985). [17] K. Kishimoto. S. Aoki and M. Sakata, On the path independent integral-j. Engineering Fructure Mechanics 13, 841-850 (1980). [18] J. R. Rice, P. C. Paris and J. G. Merkle, Some further results on J-integral analysis and estimates. ASTM STP 536, 231-245 (1973). 1191 . _ L. B. Freund and A. S. Douglas. Dvnamic growth of an antiplane shear crack in a rate-sensitive elastic-plastic material. ASTM STP 803-1, 5:20’(1983). 1201 M. M. Little. E. Kremnl and C. F. Shih. On the time and loading rate dependence of crack-tip fields at room temperature-A viscopiastic analysis of tensile small-scale yielding. ASTM-STP 803-1, 615-636 il983). [Zl] JSME Standard S 001, Standard Method of Test for Elastic-Plastic Fracture Toughness JI, (1981) (in Japanese). [22] J. Congleton and B. K. Denton, Measurement of fast crack growth in metals and nonmetals. ASTM STP 627, 336-358 (1977). [23] JWES-AE-8301, Report of Atomic Energy Research Committee, Japan Welding Engineering Society (1983) (in Lo

_

Japanese).