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NBSIR 84-3012

NAT'L INST. OF STAND & TECH

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Second Interim Progress Report:

MATERIALS SELECTION CRITERIA FOR

CRACK ARRESTER STRAKES IN NAVAL

VESSELS

National Bureau of Standards

U.S. Department of Commerce

Boulder, CO 80303

October 1984

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34-3012

1934

NATIONAL BUREAU OF STANDARDS UBRARY

NBSIR 84-3012

Second Interim Progress Report:

MATERIALS SELECTION CRITERIA FOR

CRACK ARRESTER STRAKES IN NAVAL

VESSELS

R.B. King

T. Teramoto

D.T. Read

Fracture and Deformation Division

Center for Materials Science

National Bureau of Standards

U.S. Department of Commerce

Boulder, CO 80303

October 1984

Sponsored by:

Naval Sea Systems Command (SEA05R25)

Directed by:

David Taylor Naval Ship R&D Center

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Materials Selection Criteria for Crack Arrester Strakes in Naval Vessels:

Second Interim Progress Report

R. B. King, T. Teramoto, and D. T. Read

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

The phenomenon of crack arrest, in which a crack propagates through a brittle material, encounters a high toughness material, and stops has been

studied. This phenomenon is of practical importance in understanding crack

arrest in ship structures. Laboratory experiments have been conducted under

conditions intended to simulate those in a structural situation.

These experiments were designed to include two key features of ship

structural behavior: 1) Crack arrest occurs specifically because a step in

toughness is encountered; 2) the load on the specimen, simulating dead load

in the structure, is transferred to the uncracked ligament after arrest, thus

introducing the possibility of reinitiation. A spring-loaded double-cantilever-beam (DCB) specimen has been used in these experiments. An electronbeam weld is made along the crack propagation line, producing a brittle crack

propagation path with a step in toughness at its end.

The dynamic run-arrest portion of these experiments has been modeled

using a modification of Kanninen's DCB model that includes the effect of the

loading spring, and using -a finite element model. The elastic-plastic

reloading portion has been modeled quasistatical ly using J integral and

tearing instability theory. In addition, a simplified dynamic viscoelasticplastic model has been developed to analyze the reloading portion of the

experiments.

Results of this program are intended to indicate quantitatively whether

a candidate arrester material will arrest a crack at service temperatures and

subsequently prevent reinitiation.

Key words: crack arrest; crack propagation; dynamic fracture; dynamic

toughness; elastic-plastic fracture; toughness

1
INTRODUCTION

This report describes progress on the research program "Materials Selection

Criteria for Crack Arrester Strakes in Naval Vessels." This is the second

interim progress report covering this program. In the first report, results

of an extensive literature survey on research relevant to this program were

presented, and research plans were described [1]. In the period described by

the present report, progress has been made in several areas: 1) A specimen

design has been developed that permits laboratory simulation of the key

features of crack propagation and arrest in ships. 2) Analytical models

sufficient to characterize the specimen have been developed. 3) Extensive

experimental results have been obtained using EH36 steel and HY80 steel. In

this report, crack propagation and arrest, as are likely to occur in ships,

are described; the specimen design and analytical models are discussed; and

the procedures and experimental results are presented.

In a worst case fracture event in a ship, the crack may propagate long

distances before encountering an arrester. Dynamic effects become important

in such a "long crack jump" event [2]. A large percentage of the service

stress driving the crack in the ship is likely to result from dead loading,

and thus from a quasistatic analysis it would be expected that the crack would

be propagating under severely growing stress intensity conditions. However,

inertia effects tend to offset the expected growth of stress intensity,

because of large and rapid compliance increases resulting from crack

propagation. These compliance changes necessitate significant structural

motion to maintain load; this motion cannot occur instantaneously.

Nevertheless, crack arrest does not occur because of decaying stress intensity

in the actual ship; instead it occurs specifically because a step increase in

material toughness is encountered at the arrester interface.

2
After arrest, the uncracked ligament is reloaded to a higher stress than

before cracking. The possibility exists of overloading the ligament because

of the large area loss caused by a long crack jump. This was alluded to in

[2], where it was pointed out that "another concern is the possibility that

the arrester, after temporarily stopping a crack, will fail in gross yielding

as the loads on the ship hull are redistributed. " In addition to gross

yielding, however, there is the possibility that the crack, which after load

redistribution is likely to be surrounded by a large plastic strain field,

will reinitiate and propagate through the arrester in ductile tearing.

Successful performance in the arrester application consists of two steps:

1) The crack propagation through the hull steel will be largely in the

cleavage mode, with some accompanying ductile ligaments [3, 4] and shear lips

[5]. In order to cause arrest, the arrester steel must be sufficiently tough

and have a low enough ductile to brittle transition temperature to force a

fracture mode change from cleavage to tearing. 2) The arrester must be able

to resist failure by reinitiation in tearing. This necessitates a high

tearing modulus, to prevent unstable tearing and to provide high resistance

to stable tearing, so tearing cannot propagate through the finite-width

arrester strake.

The experiments described in this paper were designed to incorporate the

features described above of crack propagation and arrest in ships. Before

describing the experiments, a review is made of relevant theory on dynamic

crack propagation, and previous experimental work on crack arrest at a high

toughness interface is described.

THEORETICAL BACKGROUND

A literature review of research relevant to the current program was

described in [1], where an extensive review of the theory of dynamic crack

3
arrest was presented. Key results from the theory are summarized here for

completeness. In crack propagation and arrest in both ships and in the

experiments described in this paper, the crack propagates through a brittle

material and then encounters a higher toughness material, whereupon arrest may

occur. The extent of the plastic deformation accompanying propagation through

the brittle material is considered to be sufficiently small to permit the use

of dynamic linear-elastic fracture mechanics (LEFM). More widespread

plasticity may occur after the crack has encountered the ductile material,

however, so that the final stage of the run-arrest event requires description

by elastic-plastic fracture mechanics (EPFM).

Dynamic LEFM theory is based on a generalization of the Griff ifth-IrwinOrowan fracture criterion [2]. The condition for crack propagation is

G is the dynamic energy-release rate, a is the instantaneous crack length, B

is the thickness at the crack tip, and W, U, and T represent the work done by

the applied loads, the specimen's stored strain energy and the total kinetic

energy, respecti vely . The dynamic toughness of the material is characterized

by the parameter R. To account for possible strain-rate effects in the high

strain-gradient region near the crack tip [5], R is taken to be a function of

the crack speed. A near-tip evaluation of G establishes the relation between

G and the dynamic stress-intensity factor, K [6]:

G > R ( 1 )

where

G

= - 1/B (-dW/da + dU/da + dT/da) ; ( 2 )

G = [(l-v2)/E]A(a) K2 (3)

4
where A(a) is a geometry-independent function of crack speed a» v is Poisson's

ratio, E is Young's modulus, and K, the stress intensity factor, is the

coefficient of the singular term of an expansion of the mode I elastic stress

field in the near-tip region of the moving crack. Making use of eg (3), the

crack propagation criterion eg (1) may be replaced by the eguivalent

condition

K > Kp (a) (4)

A schematic plot of Kj^, the dynamic material fracture resistance, as a

function of a is shown in figure 1. Except at very high crack speeds, the value

of Kp is less than the static initiation toughness, K^, so that less driving

force is reguired to maintain continued crack propagation than to initiate

crack extension.

From a dynamic solution for propagation of a semi-infinite crack in an

infinite body, Freund [6] has shown that the value of the stress intensity

factor after arrest is egual to the statically computed value for the same

body. This result will also be true for finite bodies if the duration of the

run-arrest event is short enough that wave reflection from the boundaries does

not have time to occur. This explains the experimental results of Kihara

et al [7], who found that a static computation of K was sufficient to predict

the results of a crack arrest test as long as the crack propagation length was

short. For longer crack jumps, however, serious discrepancy arose between the

static calculation and experimental results. This phenomenon was studied in

detail by Kanazawa et al [8], who in successive experiments systematically

varied the distance from the crack plane to the specimen boundaries where

significant wave interaction was occurring. Crack propagation lengths in a

5
ship may be long, and structural details are present from which wave reflections

are likely to occur. Specimens intended to simulate crack propagation in

ships should therefore be designed so that significant wave interaction with

the boundaries of the specimen does occur during testing.

The value of K as a function of time during a test can be calculated from

a dynamic LEFM analysis of the specimen. From this and the crack growth

history a(t), the resistance can be inferred, if it is assumed that the

equality in eg (4) holds.

If, when the propagating crack encounters the tough material of the

arrester, significant plastic deformation occurs during the arrest process,

then dynamic LEFM may be invalidated. This portion of the run-arrest event

may therefore require EPFM analysis. This is a difficult problem because

dynamic elastic-plastic analysis is significantly more complicated than

elastic analysis. In addition, it has not been established which driving

force parameter is most suitable for characterizing crack propagation under

elastic-plastic conditions. Several candidate parameters, such as the J

integral. Crack Opening Displacement (COD), and Crack Opening Angle (COA), may

be general izabl e to the dynamic crack propagation case, but this has not yet

been proven. At present, it appears most likely that a near-tip deformation

parameter such as COD or COA will be suitable for the dynamic running crack

case [9].

The difficulty of EPFM analysis is alleviated somewhat for the

application in the current program, because the experimental results in this

paper appear to justify a simplified theoretical approach: The initial

run-arrest event occurs at a high speed but is accompanied by relatively

little plastic deformation; thus it can be characterized by LEFM. After

arrest, the plastic deformation is extensive but occurs relatively slowly, and

6
thus from quasistatic reasoning, parameters like the J integral and tearing

modulus are appropriate to characterize the reinitiation portion of these

tests. Because, as will be demonstrated under Experimental Results, a

relatively large amount of stable tearing (40 to 50 mm) typically occurs in

the reinitation phase of these tests, the rigorous validity of J and T as

characterizing parameters is in question [10]. Nevertheless, these parameters

provide at least a good qualitative basis for assesssing the driving-force

conditions in these tests in the reinitiation phase.

SPECIMEN AND APPARATUS DESIGN

Before designing a specimen configuration, a literature review was

performed of experimental work relevant to crack arrest by high toughness

arresters in ship structures. Results of this literature survey are presented

in [1] and are summarized here for completeness. Most of the recent work

directed towards studying crack arrest at a high toughness interface under

conditions similar to those in ships has been conducted in Japan [7,8,11,12].

Large duplex specimens, typically of the "double-tension" type (fig. 2) have

been employed. Crack propagation is initiated in a brittle starter section.

This section is welded to the arrester material under study. The main tensile

load applied in these tests simulates service stresses in a structure. Load

drop during the run-arrest event in these tests has been found experimentally

to be minimal [12] and arrest does occur under rising stress intensity

conditions. However, significant load drop will occur after arrest because

the large testing machines used are effectively under fixed-grip conditions.

Thus, dynamic load redistribution to the uncracked ligament is not present 1'^

these tests. Another drawback to the use of large duplex specimens of the

type described is that it is difficult to channel crack propagation. ^

and branching often occur in the starter section resulting in arrest w: - i

not caused by the arrester material [11].

7
The specimen design used in the tests described in this paper was intended

to eliminate some of the drawbacks cited for the large-scale duplex specimens.

A spring-loaded double-cantilever beam (DCB) configuration was chosen

(fig. 3). The DCB configuration is desirable because high crack propagation

lengths can be achieved under relatively low loads. However, this specimen

undergoes large compliance changes during crack propagation, thus the spring

in the load train is necessary to prevent severe load drop. The loading

spring was constructed using Belleville disk washers. It has a stiffness of

2.04 kN/mm per washer (the number of washers used varied between 8 and 16) and

a load capacity of 410 kN.

To prevent the problem of turning or branching in the starter section a

duplex configuration was not used. Instead, the specimens were machined

entirely of ductile material. A brittle crack propagation path was provided

by placing an electron-beam weld along the crack line. This relatively

brittle weld tends to channel the crack propagation along a straight line, and

a step in toughness is present at the end of the weld.

A key feature of the double-tension specimen was provided in this specimen

by machining a pocket into which a hydraulic jack is placed. The jack loading

is very stiff, effectively fixed grip. It decays very rapidly as crack

propagation occurs and has essentially vanished by the time the crack has

propagated to the end of the weld. Desired conditions at arrest can thus be

provided by adjusting the main load applied through the loading spring, while

initiation conditions are independently controlled by adjusting the jack load.

The following instrumentation was used on the specimen: load was monitored

using the testing machine's load cell output, after amplification by a signal

conditioner. Crack position as a function of time was detected using

resistive trip-wire gages. In the first two tests reported here, these gages

8
were made using conductive paint lines. In subsequent tests commercial crack

detector gages were used. The latter approach was more satisfactory. Typical

locations of the trip-wire gages are shown in figure 4. To study the

evolution of the plastic deformation in the ligament as a function of time,

strain gages were also placed at selected locations in this region (i^ig. 4).

Since the uncracked ligament is loaded primarily in bending, a Green and Hundy

[13] type slip-band pattern was expected. This was confirmed using a

quasi-static finite element model of the specimen. The strain gages were

intended to be placed in the path of the slip band development.

Transient data from all instruments were collected using several digital

oscilloscopes. Digitizing rates ranged from 10 microseconds per point for the

slowest signals studied to 0.5 microseconds per point for the fastest.

Triggering was achieved using a trip-wire gage located approximately 10mm from

the crack tip. Prior to initiation, temperatures in the specimen were

monitored using two thermocouples, one placed in the vicinity of the starter

notch tip in the electron beam weld and the other near the end of the weld in

the base metal

.

The experiments on EH36 were used for test method development. Three

different specimen configurations were used in the tests on EH36. The specimen

dimensions are shown in figure 5, Several considerations affected specimen

dimensions. The loading spring used was capable of applying 410,000 N. The

beam arm heights were chosen so that they would not yield under this load

during crack propagation. This was intended to reduce the possibility of

crack turning. The length of the specimen was determined by choosing a

desired crack jump length, estimating the starter notch length needed to reach

the initiation toughness value, and sizing the uncracked ligament width. In

the first two tests, this width was chosen so that the load at at net section

9
yield would be equal to the applied load at arrest computed quasistatical ly.

In all subsequent tests the ligament widths was chosen so that the net section

yield load was significantly less than the applied load at arrest computed

quasistatical ly. As discussed in the section on analysis, the value of the J

integral in the specimen after arrest was computed statically and the ligament

width was chosen such that significant ductile tearing would occur after

arrest.

In estimating the applied load at arrest, unloading of the load spring

was accounted for quasistatically by calculating the compliance change in the

specimen between the initial and final crack lengths. The quasistatic calculation predicted load drops of 5-10% in the geometries tested. Based on the

considerations described, the tapered design of specimen 1 resulted in smaller

specimen dimensions for a given crack jump length. It was later decided that

this advantage was outweighed by the additional analytical complexity caused

by the nonprismatic beam arms. Two different rectangular specimen sizes were

tested in the EH36 series to achieve different crack jump lengths. Because

the results of the EH36 tests indicated that sufficient dynamic effects could

be obtained using specimens with relatively small crack lengths (125 mm or

greater), a single smaller specimen design (fig. 4) was used for all of the

HY80 tests.

PRESENT ANALYTICAL APPROACH

The behavior of the DCB specimens used here should ideally be modeled

using dynamic, elastic-plastic fracture mechanics for two reasons: 1. The

crack propagation length is sufficiently long that significant wave

interaction occurs with the boundaries of the specimen during propagation. 2.

The uncracked ligament after arrest reaches net-section yield upon load

redistribution. While some preliminary attempts have been made to perform

10
elastic-plastic modelling of dynamic crack propagation [14], this remains a

difficult problem.

Fortunately the experimental results justify significant simplification

of the analysis of these tests. The dynamic crack propagation through the

weld is accompanied by relatively little plastic deformation. After arrest,

the load begins to redistribute and the plastic deformation becomes extensive,

but this deformation takes place an order of magnitude more slowly than the

elastic straining during crack propagation. Thus, the overall event may be

approximately analyzed in two stages: an initial dynamic, linear elastic

stage, followed by a quasistatic elastic-plastic stage.

DCB Model

The dynamic linear elastic portion of these tests has been modelled using

a modification of Kanninen's model of the DCB specimen, in which the specimen

is treated as a Timoshenko beam on a generalized elastic foundation [15]. The

modification was made to permit analyzing the effect of the loading spring

( ig. 6). The jack was treated as being infinitely stiff, so that

displacement is prescribed at the jack point. However, the specimen arm is

permitted to pull away away from the jack, in which case the jack load falls

to zero. The spring is included at an intermediate point on the beam, and

displacement is prescribed on the spring. The mass of the spring and other

masses (e.g. the mass of the clevis attached to the spring) are included as a

lumped mass between the spring and specimen.

Before performing a dynamic analysis on the actual tests, two checks were

made to provide confidence in the model. First, a static analysis of the

stress intensity factor was made using the DCB model. This analysis was

compared to the predictions of the stress intensity factor from a finite

element model of the specimen; the result is shown in figure 7. It is seen that

11
despite the fact that the arms of the DCB specimen used in the tests reported

in this paper are short and deep, Timoshenko beam theory is adequate for

modelling them. As an additional check, a dynamic calculation of K as a

function of time under specified load was performed using the DCB model. The

same analysis was performed using the two-dimensional finite element program

reported in [16]. The mesh used in the finite element analysis consisted

of constant strain triangle elements and is shown in figure 8. The results for

K as a function of time using both models are shown in figure 9. The results of

the one dimensional DCB model are considered satisfactory for the time range

of interest. The discrepancy between the DCB model calculations and the

finite element model results is less than 15% for the first 0.25 milliseconds.

The elastic run-arrest portion of all the experiments conducted lasted less

than 0.25 milliseconds.

After performing the above checks, the DCB model was used exclusively to

model the DCB tests. Only "generation phase" [17] computations were performed,

that is, the model was forced to propagate the crack so that the experimentally

observed crack growth history a(t) was followed. The value of the stress

intensity factor, K, as a function of time was then calculated. The values of

jack load and spring displacement measured at initiation were input to the

model. Results are presented below in the sections on experimental results.

Plastic Hinge Model

Post-arrest calculations of the J integral and tearing modulus were made

using quasi-static elastic-plastic analyses. A simple post net-section-yield

model, called the plastic hinge model, for calculating the J integral was

derived by assuming that a plastic hinge develops at the uncracked ligament.

The derivation is presented in the Appendix; the result is:

12
J = + Jn ( 5 ) e p

Jg and Jp are the elastic and plastic parts of J, respectively. is given by

Je

= ( 6 )

where K is calculated from a static application of the DCB model at the load

corresponding to net section yield. Since the specimen arms are relatively

long after arrest and this is a static calculation, the simpler Euler-Bernoul 1

i

beam model of Kanninen [18] may be used for this purpose. The value of K from

this model is [18]:

K = [(2/3)P/(xBh^'^^)][xa(sinh^xb+sin^Xb)

2 2 sinhxbcoshxb-sinxbcosxb]/(sinh xb-sin xb)

(7)

where x = b = ligament width = W-a and P is the applied load. In

evaluating (7), the applied load is set equal to the limit load, the

expression for which is given in the Appendix. Equation (7) is only valid for

prismatic beam arms. Therefore, for test EH36-1 a numerical solution for a

nonprismatic beam on an elastic foundation was used instead.

From the Appendix, the plastic part of J, Jp, is given by:

Jp = 0p[l + (-2W+2b) {(2W-b)2 - b2}‘*](a-Af|5y) ( 8 )

where A is the total deflection at the load point (i.e. on the specimen side

of the spring), and Aj^^y elastic deflection at the load point evaluated

at This is given by the Euler-Bernoul 1 i DCB model as [18]:

%Y " ^limit ^

13
where

333322 9 9 0=2{x h )[2x a +{6x a (sinhxbcoshxb+sinxbcosxb) +6xa(sinh^ b+sin'^ b) +

3(sinhxbcoshxb-sinXbcosxb)}/(sinh^Xb-sin^Xb)] ( 9 )

for long crack lengths, eq (8) for Jp reduces to the expression for a deeply

cracked specimen with remaining ligament in pure bending.

To apply the model for calculating post-arrest Jp in the DCB specimens,

the applied load after arrest was first computed quasi statically by accounting

for unloading of the spring caused by compliance changes in the specimen

during crack propogation. If this calculated applied load, Papp-j-jed*

greater than it was assumed that plastic deformation of the specimen

would occur until the load dropped to P, . ... Thus, the value of A-A.,cv in

limit NbY

eq (8) is given by

A-A

NSY

= (Pappl ied

- Pt1 imi t' (10)

where K is the stiffness of the loading spring. Maximum values of the J

integral calculated using this model are shown in Tables I and II for the EH36

tests and HY80 tests, respectively.

The DCB model, of course, does not account for all possible wave modes.

Because reflected waves can contribute to crack propagation, the model might

be inadequate for a material in which an unaccounted-for wave mode noticeably

affected crack propagation. This is not believed to be the case in the

present study.

Lumped-Mass Model

A second post-arrest model was developed that accounts for dynamic

effects after arrest in a simplified manner. The lumped-mass visco elastic14
plastic model shown in figure 10 was used for this purpose. This model is

referred to as the lumped-mass model. All external mass and elastic stiffness

of the load train (including those of the loading spring) are included in the

parameters M and K. The specimen's mass, is lumped at a single point. A

spring of constant represents the elastic stiffness of the specimen at the

load point, a sliding frictional device represents the static limit load of

the specimen (the device is rigid when the load applied to it is less than

P, . .. and slides freely when the load reaches P,. . + ), and a dashpot

represents the strain-rate elevation of yield stress in the specimen. The

applied displacement, elastic specimen crack mouth opening displacement (CMOD),

and plastic CMOD are given by U., U, and U , respectively, within the lumped-mass

R P model, the CMOD and the load point displacement A are equal and are given by U.

The value of is computed using the static Eul er-Bernoul 1 i model for the DCB

specimen, eq (7). The dashpot's viscous damping coefficient was computed as

follows: A linear relation was assumed to exist between flow strength of the

material and strain rate, specifically.

The value of c^ was taken to be 0.002/MPa, a typical value for structural

steel [5], for both EH36 and HY80. Next, the hinge point in the specimen was

found from a static limit-load analysis. Using this hinge point, the cracktip opening displacement was related to the load-line displacement:

( 11 )

CTOD = Ad/(W-b+d) ( 12 )

where

(13)

15
is the distance from the crack tip to the hinge point. Finally, an effective

"gage length" equal to the specimen thickeness was introduced so that the

strain at the crack was approximated by

e = CTOD/B (14)

Using (11-14), the result for the dashpot coefficient is

The differential equations governing the two degree-of-f reedom system in figure

10 are

(K+K^) U + MU - Kg Up = KUg (16)

(17)

When the load in the specimen does not exceed the static limit load, eqs (16)

and (17) reduce to the single expression

(K + Kj)U + m3 = KU^ (18)

When the model is used solely for post-arrest calculations with a stationary

crack, then (16-18) are linear and may be solved in closed form. When a

running crack is analyzed, and , depend inplicitly on time in

a complicated, nonlinear fashion, and the model must be solved numerically.

After solving (16-18), the J integral as a function of time can be calculated.

The plastic displacement. Up, from the lumped-mass model is equal to

eq (8), thus Jp can easily be calculated. Given U(t) and Up(t), the elastic force.

16
P, acting on the specimen can be calculated, and can be evaluated using

eqs (6,7).

Dynamic effects in the lumped-mass model are too simplified to properly

represent the elastic run-arrest portion of the tests. For example, wave

motion along the specimen arms (which act as waveguides) is not present in the

lumped-mass model. For this reason, for modeling the pre-arrest portion of a

test, where the details of dynamic effects are more important but plasticity

is negligible, the one-dimensional Kanninen model was used. Calculations with

this model were carried out until the instant of arrest. The solution to the

Kanninen model at the time of arrest permitted the calculation of U and L), to

be used as initial conditions for the lumped-mass model. (The initial values

of U and U are zero because at the instant of arrest the specimen has not

P P yielded .

)

In addition to permitting estimates for the post-arrest J integral, the

lumped-mass model is attractive because it qualitatively represents the

situation in a ship: The external mass and external stiffness, M and K,

represent the "effective global mass" and "global stiffness" of the structure,

while all other parameters represent the cracked section of the structure.

As will be seen in table II, below, the J-integral values calculated

using these approximations high, on the order of 2 MN/m ( 11,000 1 b/i n) . These

high values are hard to believe, and so the simplified analytical procedure

outlined above must be questioned. In Results and Discussion below, results

calculated according to the present procedure will be listed. Other results,

calculated using a different version of the lumped-mass model, will be given

also. These results will show that J rises rapidly with time during the crack

arrest-reinitiation time period. This implies that obtaining correct crack

length values for correlation with J values to form a dynamic J-R curve may be

17
difficult. The other results will also allow an estimate of the degree of

uncertainty present in these calculations of dynamic J during the crack

arrest-reinitiation event, which are believed to be the first such

calculations ever reported.

Post-Arrest Tearing Modulus

A static post-arrest calculation was used to estimate the applied tearing

modulus, Tgpp for this specimen. The procedure presented in Appendix I of

ref. [19] was used to derive an expression for a deeply-cracked double cantilever beam specimen under spring loading. The result is:

Tgpp = 2b2(2W-b)/h3+(EB/K)(l+(2b-2W)/[{2W-b)2+b2]hb/(2W-b) (19)

where b is the uncracked ligament width after arrest.

MATERIALS

Crack arrest tests were performed on two steels: EH36 and HY80. The

tests of EH36 were used to refine the experimental procedures; HY80 was tested

because it is used as a crack arrester material in ships.

EH36 is a tough carbon-manganese steel used in ships and other large

engineering structures. Its flow strength, increases from about 430 MPa to

about 520 MPa as temperature decreases from 0 to -70®C. It has a sharp

ductile-brittle transition at around -75°C, Fig. 11.

HY80 is a low carbon, nickel -chromium-molybdenum alloy steel with

excellent toughness and ductility. Its flow strength at 0°C is about 670 MPa,

rising to about 750 MPa at -100°C. Its nil-ductility temperature is in the

range -60 to -100°C. Its room temperature static tearing modulus, for crack

extensions of the order of 1 mm, is about 70.

18
EXPERIMENTAL PROCEDURES AND RESULTS

The EH36 specimen material was used to develop experimental procedures,

which were then applied to HY80. Therefore, the procedures and results for

these two specimen materials will be discussed separately.

Experimental Procedure-EH36 Specimens

A ductile-to-brittle transition curve obtained from Charpy tests [20] for

EH36 steel is shown in figure 11. Before testing the crack arrest specimens,

static fracture toughness testing was performed on the electron beam welds. A

plate of EH36 base metal was electron beam welded with the weld parallel to

the rolling direction. Three point notched bend bars, 25 mm square, were cut

from the specimen with the notch oriented so that crack growth would be in the

plane of the plate (fig. 12). A starter notch of aoDroximatel v 10 mm in

length was cut and then fatigue sharpened to 12 mm. Five specimens were tested

at temperatures ranging from -40 to -100 °C. The lower shelf of the material

was reached at approximately -50°C, and the lower shelf toughness was

approximately 80 MPa/M.

This toughness value was used to estimate the starter notch length

required in the specimens. The relation between applied load and K was

calculated as discussed above in the analysis section. Starter notches were

sawed into the specimens approximately 5 mm shorter than the desired length,

and the notches were then fatique sharpened to reach the final length.

Fatiguing was performed in a 980 kN servo-hydraul ic testing machine at 5 Hz.

Typically 20,000 cycles were required. Fatigue crack growth rates were slower

than expected for the aK levels applied. This was due to the presence ot

compressive residual stress in the crack arrest specimens. For the sane

reason higher than expected loads were typically needed to cause initiation of

unstable crack propagation. The residual stress was estimated to ef f ecf i ve’’

y

19
reduce the applied value of K by approximately 40 Mpa/m. After this effect was

discovered it was offset by increasing the final fatigued notch length by

approximately 20 mm. The starter crack lengths used in each of the tests are

shown in figure 5.

Cooling of the specimens was performed using a box, made of polystyrene

foam in which copper cooling coils were placed. The coils were in contact

with the specimen over a large region; liquid nitrogen was cycled through

them. In addition, liquid nitrogen was injected against the specimen at the

starter-notch tip. The goal was to achieve a low enough temperature at the

notch tip to assure lower shelf behavior of the weld, while maintaining the

desired test temperature in the remainder of the specimen. Nylon pins were

used during cooling to reduce the heat sink effect of the clevis grips. These

were replaced by steel pins before loading.

In the first test a specimen temperature of 0°C was used. This was

intended to assure upper shelf behavior of the base metal at the instant the

crack propagated to the end of the weld. The test temperature in the second

test was -70°C. This test was intended to show that arrest would not occur in

the specimen if the arrest material were brought sufficiently down from the

upper shelf. The third specimen was tested at 0°C. Arrest was intended to

occur in this test as in the first test. However, as discussed above under

specimen design, the uncracked ligament width of the specimen was chosen so

that severe ductile tearing of the ligament would occur upon load

redistribution.

After cooling the specimens to the desired temperature, a main load of

410 kN was applied through the loading spring shown in figure 3. The starter

notch length was chosen such that unstable crack propagation should occur at

this load level. However, because of scatter in initiation toughness values

20
and the residual stress effect mentioned above, typically higher K values were

needed than that corresponding to 410 kN. The loading jack was then used to

apply additional load until the specimen failed. In the third test on EH36, a

large ratio of jack load to main load was needed (main load 410 kN, jack load

160 kN). The stiffen jack tended to make the fracture process more stable,

which caused a pop-in of approximately 5 mm in length to occur in this test.

The jack load was then reapplied and unstable crack propagation took place at

a jack load of 180 kN.

Experimental Results For EH36 Steel

In the first experiment the temperature in the arrest section of the

specimen was approximately 0°C. Dynamic crack propagation occurred until the

end of the electron beam weld was reached where upon the crack arrested

abruptly. In the second experiment the arrest material was at -70°C.

Referring to figure 11, this material has a very sharp ductile-brittle

transition at approximately -70®C. In this test arrest did not occur. In the

last test the ligament width had been chosen so that after arrest the net

section yield load was exceeded. This caused a significant amount of stable

ductile tearing to occur.

Transient data are shown for the first and third tests in figures 13-15.

Due to a power supply failure the transient data were lost in the second test.

Crack length as a function of time for the first test is shown in figures 13a. The

crack tip quickly accelerated to a speed of approximately 750 m/sec and propagated

at this speed for 120 microseconds until the end of the weld, after which

arrest occurred abruptly. Applied load as a function of time for this test is

shown in figure 14. A load drop of approximately 16% occurred during crack

propagation. After arrest, the load dropped further and then recovered.

21
strain gages were placed near the end of the weld at the location shown

in Fig. 4. These were intended to be in the point of the slip-band pattern

for studying the evolution of plastic deformation. The trace from the strain

gage farther from the end of the weld was lost. Strain in the near gage as a

function of time is shown in Fig. 15. The strain at this point increased

rapidly but remained below yield until after arrest. After arrest, upon load

return (Fig. 14) yield occurred. The plastic deformation increased at a rate

approximately an order of magnitude smaller than the elastic strain rate

during the crack run. This experimental observation, which was repeated in

the third test, is felt to justify the analytical approach presented above:

the dynamic crack propagation event was accompanied by relatively little

plastic deformation but occurred rapidly, and so it can be treated by dynamic

LEFM analysis; the post-arrest deformation and reinitiation involved extensive

plastic strain, but developed slowly, and so can be treated by quasi-static

EPFM analysis.

The plots of the stress intensity factor, K, as a function of time

inferred from the crack speed data using the DCB model described in the

analysis section are shown in Fig. 16. It is seen that the stress intensity

factor remained above for EH36 during both tests. Because the crack

propagation toughness, Kjp(a) , should be lower than Kj^, the static-initiation

toughness, arrest did not occur because of load drop but instead occurred

because the step in toughness at the end of the weld was encountered. The

dynamic K values at the instant the end of the weld was encountered, given in

Table 1, were obtained from the plots of Fig. 16, by using the trip wire data

to get the time at which the crack encountered the end of the weld.

Crack length as a function of time for the third test is shown in

Fig. 13b. In this test the crack tip reached a high speed of approximately

22
1,000 m/s during the early stage of crack propagation but decelerated to 167

m/s prior to arrest. The applied load as a function of time is shown in

Fig. 14b. In this more massive specimen a larger compliance change occurred

during crack propagation so load drop was more severe. The load had dropped

approximately 45% at arrest. The value of stress intensity K as a function of time

calculated using the DCB model is shown in figure 16b. The stress intensity factor

remained above throughout crack propagation, so that arrest would not have

occurred without the step in toughness at the end of the weld. However,

because of the relation between a and applied K the crack did decelerate

considerably during crack propagation. Strain in the vicinity of the end of

the weld as a function of time for the nearer-tip location shown in fiqure 4 is

plotted in figure 15b. As for the first test it is seen that rapid elastic

straining of this region took place during crack propagation, followed by more

slowly developing plastic deformation after arrest.

The crack propagation gages indicated that reinitiation occurred during

the third test. The last gage was placed in the base metal approximately 5 mm

from the end of the weld. The next to last gage was located 12.5 mm from this

gage. An interval of 1.5 m occurred between the breaking of the next to

last and last gages indicating arrest followed by reinitiation. From

examining the fracture surfaces it appears that approximately 40 mm of stable

tearing occurred after reinitiation. Using the plastic hinge model, the

quasistatical ly calculated value of the J integral was 0.86 kN/m in this

specimen. The upper shelf value of the static-initiation toughness, J , is

approximately 0.3 kN/m [20] for this material so tearing was expected. As

discussed above, the applied tearing modulus did not exceed T ^ so unstable

mat

tearing did not occur.

For the specimen in which reinitiation occurred (test EH36-3), the

tearing modulus was calculated statically using eq(19) with the result

23
T,^„=37. Based on results for a similar C-Mn steel [21], this is less than

app

the tearing modulus, EH 36, which should be greater than 50, so

unstable tearing was not expected, and, in fact, did not occur.

The series of tests on EH36 permitted development of the test method. It

was demonstrated that, using the modified DCB specimen design, arrest does not

occur if the material is not tough enough to force a fracture mode change from

cleavage to tearing, but does occur if it is, and that reinitiation in ductile

metal is possible upon load redistribution to the uncracked ligament.

Experimental Procedure- HY80 Specimens

As discussed in the section on EH36 specimens, before testing the specimens

of HY80, the fracture toughness of the electron-beam weld in HY80 was first

measured using static three-point bend bar tests. Five specimens were tested

at temperatures ranging from -20°C to -50°C. The lower shelf temperature of

the weld material was approximately -50°C, and the lower shelf toughness was

(formally invalid, indicated by subscript q) = 7Q Mpa/m. The starter notch

lengths in the DCB specimens were chosen so that the initiation toughness should

be reached at a load of 410 kN in the loading spring with no jack load. The

entire jack load was then available as reserve. To account for the residual

stress effects in the electron-beam weld in the DCB specimen, the starter notch

length was increased slightly, to 55 mm, for each of the HY80 specimens. The

notches were saw cut with a root radius of approximately 0.11 mm. Fatigue precracking was not used in the HY80 tests for two reasons: 1) Using a blunt

starter notch permits the initiation toughness, K^, to exceed K^, so that the

crack has more of a tendency to propagate unstably [22]. 2) In the EH36 specimens

it was found that the fatigue cracks had a tendency to turn out of the weld.

Cooling of the specimens was accomplished using the device discussed in

the section on EH36. The main load of 410 kN was then applied through the

24
loading springs. If this load was insufficient to cause initiation, the main

load was then supplemented with the jack load.

Experimental Results-HY80 Specimens

The experimental results are summarized in Table II and described and

discussed in detail below. The first test was a failure because an

insufficiently high energy electron-beam weld was used. The weld was not

brittle enough and the crack turned out of the weld before the end of the weld

was encountered. This was remedied by locating a higher energy electron-beam

welder (50 KV, 170 mA), capable of welding the 25 mm thick specimens in one

pass. In all subsequent tests the crack ran straight along the weld until the

end of the weld was encountered. The highest temperature at which arrest

first failed to occur because the crack ran straight into the HY80 in cleavage

was found to be -70±10°C. This falls in the range of nil -ductil ity

temperatures reported for HY80, approximately -60 to -100 C [23].

The stress intensity, K, values reported in column 5 of Table II, for the

instant the running crack encountered the end of the weld, do not represent

specific values of crack arrest toughness for HY80. It is claimed that, for

those specimens in which arrest was observed, the crack arrest toughness must

have been higher than the K value at which arrest actually occurred (specimens

HY80-2, and 4-7). For the specimens in which arrest did not occur, the crack

arrest toughness must have been lower than the K value used (specimens HY80-3

and 8).

In tests HY80-2, HY80-4, and HY80-5 the fracture mode changed from

cleavage to tearing and arrest occurred at least momentarily. Reinitiation in

ductile tearing then occurred in each of these tests. The pause time between

arrest and reinitiation was typically approximately 1.5 m, or an order

magnitude longer then the initial run-arrest time. Typical fracture surfaces

25
are shown in Fig. 17. In test HY80-2 the reinitiation was stable and a

ductile tearing "thumbnail" of approximately 40 mm in length appears on the

fracture surface. In tests HY80-4 and HY80-5 the reinitiation was stable at

first, but became unstable after 40-50 mm of tearing. The unstable tearing

was in a macroscopic tearing (shear lip) mode. Thus the tearing modulus of

HY80 appears to be strongly temperature-dependent in this temperature range.

Tests HY80-2, HY80-7, and HY80-8 form another series. By varying the

number of washers the applied tearing modulus was varied from approximately 28

to 53. At -35°C HY80 is on the upper shelf so the material resistance to

tearing is the same as at room temperature. Room temperature J integral

resistance curve data for HY80 were reported in Ref. [24]. The tearing modulus

is initially approximately 100, but, because of the "roundhouse" nature of the

resistance curve, drops off to approximately 40 after several millimeters of

tearing. In each of tests HY80-2, HY80-7, and HY80-8 at least 40 mm of stable

tearing occurred. In tests HY80-7 and HY80-8 this was followed by instability

in the shear lip mode. From these results, it was concluded that the tearing

modulus of HY80 on the upper shelf under the dynamic conditions of these

modified DOB tests is approximately 35 ± 6. The driving force values reported

in Table II were inferred from the test parameters by using the models

discussed in the analysis section.

Detailed plots of the data recorded in each of the HY80 tests are shown

in Figs. 18 to 20. The plots of crack position as a function of time. Figs.

18a-f, show that typically the crack ran at high speed (on the order of 500

m/s) through the weld. In tests HY80-3 and HY80-8 the crack did not arrest.

The transient data was lost from test 8 because a slight pop-in immediately

prior to initiation caused premature triggerring. The plot from test HY80-3

(Fig. 18b) shows that the crack continued at high speed past the end of the

26
weld. In each of the tests in which arrest occurred (HY80-2,4,5,6, and 7) a

pause of approximately 1.5 ms is evident in between the time at which the

last crack gage across the weld was broken and the first gage in the base

metal (approximately 5 mm from the end of the weld) was broken. In tests

HY80-7 and HY80-8 in which unstable reinitiation occurred, the crack speed in

the tearing mode varied from 5 to 30 m/s.

The plots of load as a function of time are similar for each of the

tests. From Fig. 19 it is evident that a relatively small amount of load drop

occurred up to the instant of arrest. The load then dropped precipitously as

the beam arms in the specimen continued to move apart at a high speed while

the mass of the loading spring prevented immediate load recovery. The load

then recovered after approximately 1-2 ms. The period of the oscillations

in the load trace corresponds to the transit time of a wave along the beam

arms from the crack tip to the loading point and back.

In test HY80-2, a strain gage was placed in the vicinity of the end of

the weld along the slip-band path (Fig. 20) and shows fast elastic straining

up to instant of arrest, followed by yielding and slower plastic deformation

as the load returns and is distributed to the uncracked ligament.

Using the initial applied load and the crack growth history as input, the

modified DCB model was used to calculate K as a function of time prior to

arrest (Fig. 21a-f). The dynamic K values at the instant the weld was

encountered, given in Table II, were obtained from the plots of Figs. 21a-f,

by using the trip-wire data to get the time at which the crack encountered the

end of the weld.

Load-line displacement and velocity at the instant of arrest were used as

initial conditions to predict J as a function of time up until the instant of

27
reinitiation, using the lumped-mass viscoelastic-plastic model discussed

above; the results for J at the instant of reinitiation are also shown in

Table II.

Application of the J-integral to dynamic crack reinitiation in crack

arrest tests constitutes an extension of the J-integral beyond its known range

ov validity and into a range where even its correct definition is unknown.

Another report [26] examines the definition and evaluation of fracture mechanics

parameters in crack arrest tests. In that report, a different implementation

of the lumped-mass model described above was used to calculate J as a

function of time after arrest. The results for two specimens are shown in

Figs. 22 and 23. The time axis on these figures corresponds to the oscilloscope

time reference. Re-initiation is believed to have occurred in both these tests

at about 1.5 ms. These results indicate that J at reinitiation was in the

range 0.4 to 0.8 MN/m, more than twice the room-temperature static Jj^ value

but less than the values given in Table II. But the plots clearly show that

small errors in the reinitiation time could lead to large errors in J at

reinitiation.

It is believed that the J levels at reinitiation are larger than the static

J, values, by an unknown amount. The present uncertainty in J should be

attacked by seeking a proper definition of J applicable to both specimens

and structures, by searching for accurate methods to evaluate J, and by

attempting to make use of all existing data and to get better data in future tests.

CONCLUSIONS

A new test method has been devised to simulate conditions under which

cracks propagate long distances and arrest at high toughness interfaces in

ships. Results on EH36 ship steel and HY80 were described. Successful crack

arrest in these experiments, when it occurred, consisted of two phases;

28
1) Arrest occurred when the crack encountered the step in toughness between

the brittle weld and the arrester material. The arrest material was on the

upper shelf and had sufficient toughness to force a fracture mode transition;

In the tests in which this condition was not met, because the arrest material

was below its ductile/brittle transtion temperature, arrest did not occur.

2) After arrest the loading spring reloaded the uncracked ligament causing

severe plastic straining. The arrest material had a sufficiently high tearing

modulus to prevent reinitiation in unstable tearing. In the test in which

this condition was not met, because of high loading system compliance, unstable

tearing followed by specimen failure occurred.

Both of the above phases are believed to be present in the run-arrest

event in ship structures. The first phase is addressed by existing tests,

such as the hybrid double tension test [12], but the second phase is not.

In the HY80 series of tests it was possible to use the test method to

quantitatively evaluate the arrest performance of a steel under conditions

simulating those in a ship. It was found that the temperature below which a

fracture mode transition from cleavage to tearing will not occur is approximately -70°C. This value provides a valuable basis for comparison of the

arrest performance of other steels to HY80. In addition, it was found that

the value of applied tearing modulus at service temperature above which the

arrester steel was unable to prevent failure by unstable reinitiation in

tearing was approximately 34.

This test method provides the basis for quantitative materials

selection criteria for the crack-arrester strake application. It can be

applied in two manners; 1) The relative performance of candidate steels for

the arrester application can be assessed. For this purpose the results

already obtained on HY80 steel will serve as a useful comparison. 2) The

29
abso1 ute suitability of a steel for the arrester application in a specific

ship can be determined. The test method described qualitatively simulates

conditions in a ship. To make the simulation quantitative will necessitate

proper choice of the experimental parameters: the loading spring and total

external mass must properly represent the "global" compliance and inertia of a

ship, while specimen parameters (specimen size, crack jump length, ligament

width) represent "local" conditions in the cracked section of a ship.

These parameters can only be chosen properly by using analytical modeling of

hypothetical run-arrest events in specific ships .

30
Appendix: Static J Integral Solution for DCB Specimen After Net Section Yield

Following the approach of Rice, Paris and Merkle [25], the J integral

after net section yield is expressed as a sum of elastic and plastic parts:

0 = Jg + Jp ' (20)

The elastic part is determined from a stress intensity factor solution.

The Kanninen beam-on-elastic foundation model was used for this purpose as

described in the text. The plastic part is derived from a plastic hinge

analysis:

-d/B)

A 3P

dA ( 21 )

where P is the load applied to the specimen, B is specimen thickness, and a is

load-point deflection. The material is assured to be perfectly plastic, and

after net section yield P is equal to Equation (21) then reduces to

Jp (^-'^NSy) (22)

Plimit determined by assuming that a plastic hinge has developed at the

cracked section, and is given by

[-(2W-b) + {(2W-b)2+b2}^] (23)

where W is the total width of the specimen measured from the load line to the

end and b is the uncracked ligament width.

the

31
By differentiation, one obtains:

9P,,.^,-t/3a = -op[H-(-2W+2b){(2W-b)2+b2}‘^] (24)

Substituting (24) into (22), the expression for Jp presented in the text

(Eq.8) is obtained.

32
ACKNOWLEDGMENT

The authors would like to express their appreciation to David McColskey,

Daniel Vigliotti and John Moulder for valuable assistance in performing the

experiments described in this paper.

This report was prepared as part of the Fracture Control Technolgy

Program under the sponsorship of Dr. H. H. Vanderveldt, Naval Sea Systems

Command (SEA 05R25). The effort was directed by Mr. John P. Gudas, David

Taylor Naval Ship R&D Center, under Program Element 62761N, Task Area

Sf. 61-544-504.

33
REFERENCES

1. R. B. King, "Interim Progress Report: Materials Selection Criteria For

Crack Arrester Strakes in Naval Vessels", NBSIR 83-1681, Jan. 1983.

2. Hahn, G. T., Rosenfield, A. R., Marshall, C. W., Hoagland, R. G., Gehler,

P. C., and Kanninen, M. F., "Crack Arrest Concepts and Applications", in

Fracture Mechanics , eds N. Perrone et. al . , University of Virginia Press,

Charlottesville, Va., 1978, pp. 205-227.

3. Hoagland, R. G., Rosenfield, A. R., and Hahn, G. T., "Mechanisms of Fast

Fracture and Arrest in Steels", Met. Trans

.

, V. 3, 1972, pp. 123-136.

4. Ogura, N., "A study on the Ductile Arrest of a Brittle Crack", J. Soc.

Naval Arch. Japan , V. 110, 1961, pp. 443-453.

5. Krafft, J. M., and Irwin, G. P., "Crack Velocity Considerations", Fracture

Toughness Testing and Its Applications, STP 381, ASTM, Philadelphia, Pa.,

1965, pp. 114-129.

6. Freund, L. B., "Dynamic Crack Propagation", The Mechanics of Fracture , ed. F. Erdogan, ASME AMD, V. 19, ASME, N. Y., 1975, pp. 105-134.

7. Kihara, H., Kanazawa, T., Ikeda, K., Okage, H., Nakajima, T. , and Lajima,

A., Study on Welded Type Crack Arrester , IIW Doc. No. X-618-71, 1971.

8. Kanazawa, T., Machida, S., and Teramoto, T. "Study on Fast Fracture and

Crack Arrest", Exp. Mech

.

, V. 21, 1981, pp. 78-88.

9. Freund, L. B., private communication.

10. Hutchinson, J. W., and Paris, P. C., "Stability Analysis of J-Controlled

Crack Growth", Elastic-Plastic Fracture , ASTM STP 668, J. D. Landes, J.

A. Begley, and G. A. Clarke, Eds, ASTM, Philadelphia, Pa., 1979, pp.

37-64.

11. Kawaguchi, Y., Tsukamoto, M., Maruyama, K. , Bessyo, K. , and Kato, Y., "Crack

Arrestebi 1 i ty of Ni Steel Plates for Low Temperature Service to the

Extremely Long Brittle Crack", in Proceedings, International Conference

on Fracture Toughness Testing, the Welding Institute, Cambridge, U. K.,

1982.

12. Machida, S., Kawaguchi, Y., and Tsukamoto, M. , "An Evaluation of the

Crack Arrestabi 1 i ty of 9 % Ni Steel Plate to an Extremely Long Brittle

Crack", J. Soc. Nav. Arch. Japan, V. 150, 1981, pp. 569-575 (in Japanese).

13. Green, A. P., and Hundy, B. B., "Initial Plastic Yielding in Notched Bend

Tests", J. Mech. Phys. Solids, V. 4, 1956, pp. 128-144.

34
14 . Dahl berg, L., "Plastic Effects in Dynamic Crack Propagation", Advances in

Fracture Research , Proceedings of the Fifth International Conference on Fracture, Pergamon, Oxford, 1981, pp. 2195-2203.

15. Kanninen, M. F., "A Dynamic Analysis of Unstable Crack Propagation and

Arrest in the DCB Test Specimen", Int. J. Fract., V. 10, 1973, pp.

415-430.

16. Malluck, J. F., and King, W. W., "Fast Fracture Simulated By Conventional

Finite Elements: A Comparison of Two Energy-Release Rate Algorithms",

Crack Arrest Methodology and Applications , ASTM STP 711, G. T. Hahn and

M. F. Kanninen, eds., ASTM, Philadelphia, Pa., 1980, pp. 38-53.

17. Kanninen, M. F., "Critical Appraisal of Solution Techniques in Dynamic

Fracture Mechanics", Numerical Methods in Fracture Mechanics , eds. A.

Luxmoore and R. Owen, University of Swansea Press, Swansea, U. K., 1978,

pp. 612-633.

18. Kanninen, M. F., "An Augmented Double Cantilever Beam Model for Studying

Crack Propagation and Arrest", Int. J. Fract. , V. 9, 1973, pp. 83-91.

19. Paris, P. C., Tada, H., Zahoor, A., and Ernst, H., "The Theory of Instability of the Tearing Mode of Elastic-Plastic Crack Growth", Elastic-Plastic

Fracture , ASTM STP 668, J. D. Landes, J. A. Begley, and G.A. Clarke,

eds., . ASTM, Philadelphia, Pa., 1979, pp. 5-36.

20. Anderson, T., and McHenry, H. I., "Fracture Toughness of Steel Weldments

for Arctic Structures", NBSIR 83-1680, Jan. 1983.

21. Pitman, S. "An Investigation of the Toughness Transition of a C-Mn-Cb

Steel for Static and Dynamic Loading", Master's Thesis, Colorado School

of Mines, 1978.

22. Hahn, G. T., Hoagland, R. G., Kanninen, M. F., Rosenfield, A. R., and

Sejnoha, R., "Fast Fracture Resistance and Crack Arrest in Structural

Steels", Ships Structures Committee Rept. No. SSC-242, 1973.

23. Babecki, A. J., and Puzak, P. D., "Explosion Test Performance of Smallscale Submarine Hull Weldments", NRL Memo Rep. 996, 1^59.

24. Vasilaros, M. G., Gudas, J. P., and Joyce, J.A., "Experimental Evaluation

of Tearing Instability Phenomena for Structural Materials", Rept. No.

NURGE/CR-2570, U.S. Nuclear Regulatory Commission, Washington, DC, 1982.

25. Rice, J. R., Paris, P. C., and Merkle, J. G., "Some Further Results of

J-Integral Analysis and Estimates", Progress in Flaw Growth and Fracture

Toughness Testing, ASTM STP 536, ASTM, Philadelphia, Pa., 1973, dd.

231-245.

26. Teramoto, T. , Read, D. t., and King, R. B., "Fracture Mechanics Parameters

in Crack Arrest Specimens," NBSIR, to be published.

35
m

m zc. :r

U) CO I I CO roI o o

00 00

COro

00 VO

vD ro

*< 3

ro o

Ln

ro^ I cn O I 33 O • 00o>

OO 1 "*«J I 0 ro o -s ' o»

CO 2

TO

C ^ 3

-*•

O cr 3 -h ro

(/)

a> 3

r+ 7^

o> o> a>

Z.

O' ro 7^ • t/i 3

Cl Qi

ro I -5

roQ-

—I 3>

ro 3 3

Qj

O -*• O

r+ -5 3 O OJ o ro 3

a; c 3 3

36

TABLE I

Results

for

tests

of

EH36

steel
TABLE

II

Results

for

tests

of

HY80

steel.

KO

O 4-i C ^ fD •-> fO

4-1 rO 3

</>•«“ U

c ^ e

•I- ‘r- <0 c u :

fO O) u

U •!- ^ E

H- fO o c

CSJ 00 00

CM

00o•<d*

3

B QJ U

i- X u

:

<0 OJ *r- s; s- -M O to

CM

CM

CO CO

CM

CM

CM

O 4-

•r- O

4-» 01

4-> C

•r- C *f- 4^ 3 S.

•r- O fO CEO •r- < I— o

QO

O) o

to to to to

(/)(/) l/)U) (/)(/) (/)(/) oic oc oc oc >^3 >>3 >>3 >,3

o

>» o o O)>> o>» oo

4-1 s- c o o

to 4-1

4-1 o c

lA 3

c o s: u'^ o c to 4^ O Om

fO •D z C «/) >—

'

o fO

o

COo

00

to to

•I- Q.

4-> r" o

COo

CO

a\

iA

i- CT O C

-Q O T- £ s. 3 CL z uo

fO - s- C-) O) o E

0)

otD o00

o

o. oCO o00 oCO o00>- o00>- o00

37
LU

cro

< 2

u. ^

O Q = ^

2 CO

>- lU Q 2

o

O

LU

QC

O

CRACK SPEED/RAYLEIGH WAVE SPEED

Figure 1. Schematic plot of as function of a.

38
Figure 2. Double-tension specimen.

39
Figure 3 Modified double-cantilever beam specimen.

40
Figure 4. DCB Specimen used for HY80 tests.

41
0

45.7

Figure 5. DCB Specimen dimensions for EH36 tests.

42
Figure 6. Modified one-dimensional model for DCB specimen.

43
250

200

k 100

60 -

OL

0

o

o

A

O

A

O

A

e

static Calculation

A Finite element solution

o DCB Model

J J I I I 50 100

CRACK LENGTH, mm

Figure 7. Comparison of static results for the stress intensity factor from

one-dimensional beam model and two-dimensional finite element

model

.

44
Figure 8. Finite element mesh used for dynamic analysis ot DCB specimen.

45
TIME, ms

Figure 9. Comparison of results for K as a function of time from one- dimensional beam model and two-dimensional finite element model.

46
Figure 10. Lumped-mass visco-elastic-plastic dynamic model of DCB specimen.

47
CHARPY

IMPACT

ENERGY,

Joules

TEMPERATURE, ®C

Figure 11. Ductile-to-brittle transition curve for EH36.

48
Figure 12. Three-point bend bars for static fracture

electron beam welds. toughness testin'; : f

49
RELATIVE

CRACK

LENGTH,

a-a*.

mm E

E

o

Figure 13. Crack speed as a function of time in EH36 tests.

(a) Test EH36-1 (b) Test EH36-3

(Individual crack detector gage breaks were not detectable in test

EH36-1. Fig. 13(a) is inferred from calibration curve for crack

gage circuit).

50
TIME, ms TIME, ms

Figure 14. Applied load as a function of time in EH36 tests

(a) Test EH36-1 (b) Test EH36-3.

51
(a) Test EH36-1 • (b) Test EH36-3

Figure 15. Strain in the vicinity of the end of the electron-beam weld in EH36

tests.

52
K/INITIAL

K

TIME, ms

a b

Figure 16. Dynamic stress intensity K as a function of time, calculated from

the DCB model using observed crack velocity data, for specimens

EH36-1 and EH36-3.

53
80-6

Figure

17.

Typical

fracture

surfaces

for

HY80

DCB

specimens.
s- CD c 00

4-5 U

CD -o

4-5 c

CD to "O JO00

c_> f—t to

S- • o 1/5 C75 E •1— o Li- s_ 4--o

CD

s- -o3

CD to

<4-C • cn

•r— >5 (— C/5 CD CD 4-5 > c/5 •rTM •r- CD

4-5 4-5 1— U

14- . (D

C c tr> P £Z OJ QJ >> o E S- 1/1

LLI 2

+-) o o O O) I c C CLCVJ 3 1/5 1/5 4- O ITD o 00 5

to 00 >-

1/5 or OJ

fO t/5 Cl

S- -t-5 -t-> • C O t/5 3 ^ O 4- (U C "O

t— CU +J (/5 CD +-> r- CD C75 to

1/5 c_) to E O to CT5 tCL S- 4-5

4-5 ^1/5

-iC I O O) J CD to

rz C05-— S- CD

S- to to c_) lc_- to

00

CT5

•r“

LL.

avon TviiiNi/avoi

55
LOAD/INITIAL

LOAD

d e f

TIME, ms

Figure 19. Applied load as a function of time in HY80 tests,

(a) - (f) Tests HY80 2-7 respectively.

56
STRAIN

X

1000

Figure 20. Strain in the vicinity of the end of the electron-beam weld along

slip-band path in test HY80-2.

57
o

d

'A IVlilNI/X

58

Figure

21. K

asa

function

of

time

calculated

from

crack

velocity

data

for

HY80

tests,

(a)

-

(f)

Tests

HY80

2-7

respectively.
E

E

Figure 22. J-interval vs. time for HY80-4.

59
E

Z

2 4 6 8

TIME, ms

Figure 23. J-integral vs. time for HY80-6.

60
NBS-114A REV. 2-8CI

U.S. OEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. TIBSIR 84-3012

2. Performing Organ. Report No. 3. Publication Date

October 1984

4 . TITLE and subtitle

Materials Selection Criteria for Crack Arrester Strakes in Naval Vessels:

Second Interim Progress Report

5. AUTHOR(S)

R. B. King, T. Teramoto, D. T. Read

6. PERFORMING ORGANIZATION (If joint or other than MBS. see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8 . Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Naval Sea Systems Command SEA05R25

David Taylor Naval Ship Research and Development Center

Annapolis, MD 21402

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

The phenomenon of crack arrest, In which a crack propagates through a brittle material, encounters a high toughness material, and stops has been studied. This phenomenon

is of practical importance in understanding crack arrest in ship structures. Laboratory

experiments have been conducted under conditions Intended to simulate those in a structural situation.

These experiments were designed to include two key features of ship structural behavior: 1) Crack arrest occurs specifically because a step in toughness is encountered;

2) the load on the specimen, simulating dead load in the structure, is transferred to the uncracked ligament after arrest, thus Introducing the possibility of reinitiation. A spring-loaded double-cantilever-beam (DCB) specimen has been used in these experiments.

An electron-beam weld is made along the crack propagation line, producing a brittle crack

propagation path with a step in toughness at its end. The dynamic run-arrest portion of these experiments has been modeled using a modification of Kanninen's DCB model that Includes the effect of the loading spring, and using

a finite element model. The elastic-plastic reloading portion has been modeled quaslstatically using J integral and tearing instability theory. In addition, a simplified

dynamic viscoelastic-plastic model has been developed to analyze the reloading portion of

the experiments.

Results of this program are Intended to indicate quantitatively whether a candidate

arrester material will arrest a crack at service temperatures and subsequently prevent

reinitiation.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by se-'^-.co crack arrest; crack propagation; dynamic fracture; dynamic toughness; elasticplastic fracture; toughness

13.

AVAILABILITY

Unl imited

I I For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED pa64

15. P c

10 .


I