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REFERENCE PUBLICATIONS

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NBSIR 83-1681

Interim Progress Report:

MATERIALS SELECTION CRITERIA FOR

CRACK ARRESTER STRAKES

IN NAVAL VESSELS

R.B. King

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

January 1983

Research Information Center

rsational Bureau of Standards

Gaithersburg, .Maryland 20899 '> x

'

1 NBSIR 83-1681 M

Interim Progress Report:

MATERIALS SELECTION CRITERIA FOR

CRACK ARRESTER STRAKES

IN NAVAL VESSELS

R.B. King

Fracture and Deformation Division

National Measurement Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

January 1983

Sponsored by:

Naval Sea Systems Command (SEA 95R15)

Directed by:

David Taylor Naval Ship R&D Center

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Interim Progress Report: MATERIALS SELECTION CRITERIA FOR CRACK ARRESTER

STRAKES IN NAVAL VESSELS

R. B. King

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

Research has been conducted on the problem of developing

quantitative criteria for materials selection for crack arrester

strakes in naval vessels. Quantitative analysis of material performance in service requires application of dynamic elastic-plastic

fracture mechanics. Results of an extensive literature survey in

the area of dynamic fracture mechanics with specific attention given

to the crack arrest application are presented. The research program

that has been developed is described in detail.

Key words: crack arrest; crack propagation; dynamic fracture

mechanics; elastic-plastic fracture mechanics; materials selection;

toughness.
1. Introduction

In structures where the initiation of crack extension cannot be prevented,

crack arrest becomes a vital line of defense for the prevention of catastrophic

failure. In naval vessels the design strategy for ensuring crack arrest is to

provide high toughness strakes at key locations in the ship's hull. After an

event occurs which causes initiation of a running crack in the hull, the crack

will propagate until it encounters an arrest strake. The high toughness of

the strake is intended to cause the crack to arrest. Criteria for selection

of materials for arrester strakes are needed.

Existing criteria for materials selection, based on experimental procedures

such as the drop weight test [1] and the explosion-bulge test [2], are qualitative in nature. They provide a means for assessing the performance of a steel

relative to that of other steels, and were the basis for selection of HV80 for

use in crack arrester stakes. Quantitative criteria for materials selection

are desirable because they would potentially permit substitution of others

steels for HY80 while still giving assurance of adequate crack arrest performance in service. The overall objective of the NBS research program is to

develop such quantitative materials selection criteria for crack arrester

strakes.

Development of materials selection criteria for crack arrester strakes

requires an understanding of the phenomenon of rapid crack propagation and how

it is terminated when the crack encounters a ductile material (i.e. the

arrester strake). Fracture in high-toughness steels is accompanied by extensive plastic deformation. In fact, such deformation likely contributes

substantially to the dissipation of crack energy which accompanies arrest..

Thus, it is outside the realm of linear elastic fracture mechanics (LEFM) and

must be studied using elastic-plastic fracture mechanics (EPFM) . As will

become apparent, the application of elastic-plastic fracture mechanics to

2
the dynamic phenomenon of rapid crack propagation is in its infancy, and there

is a need for combined experimental and analytical approach to the problem.

Extensive instrumentation will be used to provide adequate characterization of

the arrest event, and finite element analysis techniques will be used to model

the tests. The specific objectives of the research program are: 1) develop a

test method for studying the crack propagation and arrest event under

conditions simulating those actual ship structures, 2) develop instrumentation

capability to permit thorough experimental investigation of dynamic elasticplastic crack propagation and arrest, 3) develop an analytical capability for

modelling dynamic elastic-plastic crack propagation, 4) formulate materials

selection criteria to ensure adequate performance in the arrester strake

appl ication.

This is a progress report on this program. First, the results of a

literature survey that has been conducted on material relevant to crack arrest

in high- toughness steels and the results of a literature survey on dynamic

instrumentation are summarized. Then specific plans that have been developed

for the NBS research program are discussed.

2. Literature Survey on Crack Arrest

An extensive survey has been conducted of literature concerned with crack

arrest and the experimental techniques applicable to the crack arrest problem.

Attention was limited to research that is relevant to the specific problem of

crack arrest that occurs when a crack propagates in a relatively low toughness

plate, and then through a weld into a high- toughness arrester plate.

Research, both experimental and theoretical, on the problem of dynamic

fracture dates back to the 1950s, and it is difficult to categorize the

considerable effort in this area. However, research relevant to the engineering problem of ensuring crack arrest by high- toughness strakes can be divided

3
into two broad categories, which will be referred to as the "small scale

approach" and the "large-scale approach".

Small Scale Approach

An overview of the "small-scale approach", which has largely been

followed in the United States, is given in [3]. Application of this approach

to crack arrester strake design is discussed in [4], In this approach, a

parameter that represents a material property governing arrest is identified,

and its value is measured from tests on relatively small specimens. (Typical

specimen designs used in crack arrest studies are shown in fig. 1). To provide

confidence in the approach, it is attempted to demonstrate that the critical

value of the arrest-governing parameter is a geometry- independent material

property by making measurements on different specimen configurations.

Research to date has been conducted within the framework of linear

elastic fracture mechanics. The Griffith- Irwin-Orowan energy balance

criterion is extended to the dynamic case as follows [3]: The total energy

release rate associated with crack growth is

G

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

where B is thickness at the crack tip, a is crack length, and U, W, T

represent the potential energy of applied loads, strain energy, and kinetic

energy, respectively. All irreversible processes (e.g., creation of new

surfaces and plastic deformation) are assumed to occur in a small zone at the

crack tip and to be characterized by a single parameter, R, which represents

the resistance of the material to crack extension. The criterion for

continued crack propagation is

G 2: R (2)

4
and arrest will occur when the value of G becomes less than R. To account for

high-strain-rate effects in the crack-tip region [5], R is assumed to be a function of crack speed. An equivalent fracture criterion can be expressed in

terms of the stress intensity factor, K, which characterizes the singular

deformation fields in the vicinity of the crack tip: crack propagation occurs

when

(3)

and ceases when K < K

Q

. The equivalence between eq (1) and (2) can be established

by a near tip evaluation of G [6], which results in

1-v 2 G = E A ( v ) K

2 (4)

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

ratio, and E is Young's modulus. Material toughness can thus be expressed by

R or Kp. To completely characterize the arrest event, it is necessary to

measure the functional dependence of R or on velocity. A conservative

simplification which is introduced is to characterize a material's toughness

by the minimum value in a plot of Kn versus time, referred to as K .

A subset of the dynamic LEFM approach is a quasi-static approach based on

the "arrest toughness," K which is defined as the statically computed value of

the stress intensity factor after arrest. Whether a quasi-static approach on

the basis of K or a dynamic approach is superior is a controversial issue in

a the literature. The K approach has been advocated by Crosley and Ripling [7,8]

a based on their original experimental observation that the value of appeared

to be a reproducible material property. These authors present a great deal of

experimental evidence that K is a material property that is independent of

a

5
specimen geometry and loading conditions [8]. On the other hand, experimental

evidence also exists that shows that the predictions of a quasi-static theory

are inaccurate in some circumstances [9], An attempt has been made by Hahn et

al to put this issue in perspective [3]. They argue that a significant amount

of strain energy is converted to kinetic energy during crack propagation, and

that the important factor is how much of this energy is reflected back from

the boundaries of the body to be available for driving the crack. In a large

structure or under short crack jumps, there is little time for kinetic energy

return and K approaches K . In an infinite body, which has no kinetic energy

m a return [10],

Km

(5)

Eq (5) can be shown, in general, to give a lower bound estimate for Km

. The

other extreme is a body that utilizes all of the kinetic energy as driving

force. This extreme would be more closely approached in a small body or long

crack jump. In this case it can be shown that the approximate relation

K

a K

2 /K

m q

( 6 )

holds [3], where is the value of the stress intensity factor at initiation

of fast fracture, which gives an upper bound estimate for K . The true situation will be intermediate between the static prediction of equation (5) and

the fully dynamic prediction of eq (6).

Much research has been conducted towards measuring the toughness governing

crack arrest, whether characterized by K or K . Small scale tests have been m a devised that employ a decaying stress field (induced by wedge loading) to

6
cause arrest, including the double cantilever beam (DCB) specimen [11] and the

wedge-loaded compact- tension specimen [8]. In all toughness tests, the

parameter K or K is not measured directly but must be inferred. (Exceptions

are optical techniques that have been developed for measuring K, which are

discussed below under instrumentation). The value of K can be computed from

a static analysis of measurements of load-point displacement (which is the

same for crack initiation and arrest for wedge loading) and final crack

length. K^, and hence K , is calculated from a fully dynamic analysis of the

specimen using load-point displacement at initiation and final crack length as

input. Dynamic analysis of the crack propagation process is extremely

complicated. Although for some geometries, such as the double cantilever beam

specimen, it is possible to develop a simplified one dimensional theory [12]

in general it is necessary to solve the two-dimensional el astodynamic

equations numerically.

Several drawbacks exist to the small scale approach described. The first

is the lack of large-scale verification in tests that closely simulate actual

service conditions. If the theory is correct, then knowledge of the arrest

toughness of material used in arrester strakes will be sufficient to predict

performance in service. A simplified procedure for applying dynamic LEFM to

crack arrester strake evaluation is presented in [4], but to date the accuracy

of dynamic LEFM predictions has not been verified. Other drawbacks are the

problems associated with the restriction to LEFM. For the high toughness

steels needed to ensure arrest in service, the crack propagation and arrest

event is likely to be accompanied by a large amount of plasticity, thus

invalidating LEFM or rendering it inaccurate. Evidence for the inadequacy of

LEFM is presented in [13]:

7
1. Experimental results on direct evaluation of by optical techniques show a significant geometry dependence.

2. Values of obtained from a dynamic analysis under static loading

gave incorrect predictions under impact loading.

Dahlberg et al . [14] have concluded that the specimen size conditions for

validity of LEFM are more restrictive in the dynamic case than in the static

case, and have shown numerically using finite element modeling that the

plastic zone size accompanying rapid crack propagation can be quite

large [15]. Another problem associated with the restriction to LEFM is the

difficulty of measuring valid arrest toughness in high-toughness steels [1],

Large-Scale Approach

The "large scale approach" was followed in earlier work in the United

States and has been extensively pursued in Japan. Typical specimen

configuratons used in this approach are shown in figure 2. This differs from

the small scale approach, apart from specimen size, in that test conditions

more closely resemble actual service conditions.

Early work in the United States was motivated by brittle fracture of

storage tanks [16]. Arrest can occur in storage tanks when initiation occurs

in a locally embrittled zone and the crack propagates into tough surrounding

material. There is a more gradual gradient in toughness in this application

than in the case of crack arrester strakes in ships. This gradual gradient is

simulated in the laboratory by using a temperature gradient in tests, such as

the ESSO and Robertson tests.

A review of research on crack arrest in Japan was presented by

Kanazawa [17]. Large scale tests have been used in that country primarily for

two reasons. The first is for direct experimental development of design

curves, such as stress as a function of temperature at arrest in various

materials [18]. To simulate the conditions of arrest in a structure when a

8
crack encounters an arrester strake, the "hybrid double-tension" test has been

employed [9,18-20]. In this test a brittle starter material is welded to a

ductile arrester material. Initiation in the starter material is caused by a

secondary loading fixture. The crack propagates out into a main stress field

intended to simulate service stresses applied by the primary testing machine.

There are drawbacks to the use of large-scale tests for direct design in this

fashion. First, a substantial number of expensive tests are required.

Second, there is a tendency to overgeneral ize the results of these tests.

Although they do simulate actual service, the conditions in these tests are

not identical to those in an actual structure. Thus, for example, it may

be reported on the basis of a large scale test that a given material at a

certain temperature and stress level will arrest a running crack that has

traveled a certain length [19]. It is not evident that these parameter values

are geometry independent and therefore cannot be transferred directly to a

structure, although the test results are used precisely in that fashion in

design. The second purpose for large-scale tests has been verification of

fracture mechanics predictions under conditions intended to simulate actual

structural conditions, and it is this purpose that is directly relevant to the

present study. An example is the study in reference 9: The toughnesses of

various candidate materials for crack-arrester strake application were evaluated

using a quasi-static analysis of ESSO test results. The performance of these

materials was then predicted and compared with data obtained from large-scale

tests in which a base starter material was butt welded to the arrester material.

It was found from a static anlaysis that K was significantly lower in the

large-scale tests than in the ESSO tests. It was necessary to introduce an

empirically determined effective crack length to reduce the discrepancy

between the predictions and experimental results. This may have been due to

the neglect of dynamic effects in the analysis. This interpretation is

9
supported by the fact that quasi-static predictions were found to be accurate

for relatively short crack-jump lengths, (less than approximately 200 mm) and

inaccurate for larger lengths which agrees with the "kinetic energy returned"

arguments discussed above. More recent work in Japan has taken dynamic

effects into account in the analysis of experimental data. In reference 20 it

was found that a reasonably geometry- independent K^- vs. -velocity curve could

be obtained for the materials studied, with good agreement between l<D from

small-scale (DCB) test results and large-scale (double- tension type) results.

This appears to provide verification of small- scale testing, at least for the

specimen geometries and materials considered. Contradictory evidence

concerning the validity of small-scale test results based on LEFM was

presented above, however. Various other effects, including the influence of

residual stresses, specimen length, and loading conditions on crack arrest

have also been studied [17].

The large-scale approach has the advantage of providing verification of

fracture mechanics predictions of crack-arrest behavior in specimen configurations, which simulate actual structural configurations. The drawbacks

associated with restriction to LEFM have been present in the research

conducted to date, as well as the additional problems discussed above caused

by quasi-static analysis.

Research On Dynamic Elastic-Plastic Fracture

Relatively little research has been conducted on elastic-plastic dynamic

crack propagation. This is mainly because, as pointed out in reference 13,

the static problem of elastic-plastic, slow, stable crack growth is not yet

fully understood, and the generalization to the dynamic problem is difficult.

Most of the contributions have been theoretical in nature. Several authors

have investigated elastic-plastic effects using relatively simple modeling.

10
In strip-yield-type solutions, yielding is assumed to be confined to a line in

front of the crack, and the physical crack is modeled as a longer crack with

closure stresses acting on its faces in the yield zone. The strip-yield model

was first proposed by Dugdale [21] for the static case and has been applied by

Goodier and Field [22] and Kanninen [23] to the case of rapid crack propagation.

This type of model has the advantage of being relatively simple, mathematically

while still accounting for some of the main features of plasticity. For

example, as a propagating crack approaches the interface with an arrester

strake, the plastic zone in front of the crack will enter the strake, and the

difference in flow properties between the material in the strake and the base

metal may contribute to arrest. This effect could be accounted for in a

strip-yield model. The notion of closure stresses, as used in the strip-yield

models, has been applied to other plasticity effects. Hoagland, et al , [24]

modeled the phenomenon of unbroken ductile ligaments behind the tip of a

running brittle crack by placing closure forces on the faces of the crack in

the model. Ogura [25] explained the apparent lowering of crack driving force

for propagating cracks in ductile materials in which a significant amount of

shear lip area is present by modeling the presence of shear lips as equivalent

to closure stresses on the face of the crack.

Because of the mathematical complexities involved, more exact analytical

treatment has so far been confined to the antiplane strain (mode III)

case [26,27]. Mode III solution may permit qualitative conclusions to be

drawn for the in-plane case by analogy and may provide guidance for numerical

modeling, for example, by giving information about the nature of the

singularity at the crack tip. An elastic-plastic finite-element calculation

of dynamic crack propagation was presented by Dahl berg [15]. In his numerical

simulation of an edge-cracked panel in tension, he found a significant plastic

zone exists in the crack tip region as well as a large plastic wake.

11
Accounting for plastic energy dissipitation outside the crack-tip zone by

including an additional term in equation (1) reduced the crack driving force

approximately in half. The results of the modeled experiment for toughness as

a function of crack velocity were in serious disagreement with results for the

same material from a valid LEFM experiment when the dissipation effects were

neglected. Including the plastic energy dissipation term explained the

discrepancies.

Little experimental work has been done in the area of elastic-plastic

dynamic fracture of metals. However, the problem has been simulated on model

photoelastic materials. A. Kobayashi studied crack propagation in a tough

polymer (Polycarbonate 80) using transmission photoelasticity [28]. He found

that the crack speed range in the polymer was sufficiently low that a

quasi-static analysis was sufficient, and an extensive plastic zone of the

strip-yiel d- type was observed in his experiments. Dally and T. Kobayashi

studied crack arrest at a bimaterial interface by bonding a brittle polymer to

a tough polymer [29]. They found the adhesive toughness, analogous to the

weld toughness in a metal, dominated the arrest event.

Research Needs Identified

It is apparent from reviewing the literature in this field that a

considerable amount of useful research has been conducted that is relevant to

the problem of crack arrest by high toughness strakes, but areas on which

further work is needed have been identified:

1. Elastic-plastic effects in high-toughness arrester materials must

be specifically addressed.

2. Some potentially useful theoretical work has already been done,

including elastic- plastic effects in dynamic crack propagation, but

insufficient experimental evidence is available to confirm the

theory.

12
3. More research is needed on confirming fracture mechanics predictions

of arrest behavior on specimens designed to simulate actual structural conditions. More large-scale experimental work of the type

performed by Kihara et al. [9] is essential. Extensive

instrumentation is necessary in order that dynamic and elasticplastic effects can be properly accounted for in these tests.

The NBS research program is intended to address the identified needs.

III. Literature Survey on Dynamic Instrumentation

Providing sufficient instrumentation to characterize the arrest event in

ductile materials is a challenging problem. A 1 iterative survey has been

conducted on experimental procedures that have been used in dynamic fracture,

and on other experimental mechanics procedures that are potentially

applicable. The discussion of experimental procedures is divided into two

areas: what will be referred to as "conventional" procedures and optical

techniques for characterizing full-field strain patterns.

Conventional Instrumentation

Conventional instrumentation includes trip wires or similar devices for

measuring crack position and strain gages. This type of instrumentation is

used routinely [11,20,30], and its application is relatively straightforward.

The main difficulty is that all circuitry involved (e.g. strain gage bridges

and amplifiers) must be sufficiently fast, and the data must be recorded at

high speeds. This was accomplished in earlier studies [30] using storage

oscilloscopes, but this requires manual data processing. More convenient

high-speed digital recording devices are now available.

Because energy exchange with the surroundings of a specimen is an

important factor in the energy balance criterion (eq 1), it will also be

13
necessary to monitor load-point displacement under other than fixed-grip

conditions. This can be done by using a variation of clip-on gages used for

making displacement measurements.

Optical Techniques

Various optical techniques exist that either have been applied or have

the potential for application to dynamic fracture. These include holography

laser speckle interferometry , photoelasticity, the method of caustic (shadow

optics), and the moir£ method. Of these, the moir£ method or similar gridtype method seems to be the most suitable for this project. Holography is an

extremely sensitive deformation measurement technique [31], which is ideally

suited for measuring small elastic deformations. It is a relatively complicated and expensive method to apply and the high sensitivity is not essential

for this project where the strains of interest are not extremely small.

Speckle interferometry [32], which is also expensive, can be thought of as a

special case of the moir£ method, and the use of moir£ method is more

straightforward in this application.

The method of caustics [33] has proven quite useful for direct measurement of stress intensity factors in dynamic fracture experiments. Extension

of the technique into the elastic-plastic fracture mechanics domain has not

yet been accomplished, however. This technique is best suited for measuring

deformation in the crack-tip region. In principle, it could be applied to

full-field strain measurement, but it is sensitive to out-of-plane deformation,

only and the patterns would be difficult to interpret.

Photoelastic analysis has been applied extensively to dynamic fracture

mechanics [28, 29, 34, 35]. This method is most conveniently used in transmission with transparent model materials. This can yield useful information

because by choosing suitable polymers, the model material can be made brittle

or ductile [29]. To use photoelasticity for measurements directly on the

14
material of interest, photoelastic coatings must be employed [35]. Several

drawbacks exist to the use of photoelastic coatings for dynamic applications.

Coatings tend to be viscoelastic, thus the strain in the coating can lag

behind the strain in the base material to which it is bonded, and the stressoptical coefficient varies with velocity. A more severe drawback for the

application to crack propagation studies is the reinforcement effect of

coatings. This is insignificant under normal circumstances but becomes

important if the crack tends to run under the coating. This was overcome by

Kobayashi and Dally [35] by employing a split coating and using side grooves

to force the crack to run straight. However, it is desired to avoid the use

of side grooves in this study so that the experimental configuration more

closely simulates conditions in an actual structure.

Besides not having the disadvantages of the other optical techniques, the

moir£ method has the advantage that complete information about the in-plane

strain fields may be obtained. A review of the application of the moir£

method to fracture mechanics was presented by Liu and Ke [36]. In the moir£

technique, a fine rectangular grid is applied to a specimen. When the specimen

is deformed, light passing through the specimen grid and an undeformed reference

("Master") is reflected only where spaces between grid lines on the specimen

grid coincide with transparent spaces on the Master grid, resulting in two

fringe patterns. One pattern represents the horizontal displacement component,

u, and the other the vertical displacement component, v. The mixed fringe

pattern is difficult to interpret and, usually, must be separated. Or, a line

reference grating may be used instead of a crossed grid, so that only one set

of fringes is formed. Alternatively, instead of forming the fringe pattern

directly, the deformed specimen grid itself may be photogrpahed and the

fringes formed optically at a later time [32].

15
In static testing, the moir£ method has been used to measure crack

opening displacement [37-41] and strains in the near-tip region of a

crack [37, 38, 40-46]. Crack opening displacement, strain, and displacement

in specimens with rapidly propagating cracks were made by Kobayashi et

al [47-49]. In these experiments only the v fringes (corresponding to the

displacement component normal to the crack) were recorded, and a single

dynamic shot was taken. To capture the strain pattern corresponding to

several crack positions the experiment was repeated thus relying on the

reproducibi 1 i ty of the phenomenon.

Moir£ Method Implementation

There are several difficulties associated with applying the moir£ method

to transient dynamic problems, such as rapid crack propagation. These include

high-speed data acquisition ( i . e . , high-speed photography) , interpretation,

and sensitivity.

Various techniques of high-speed photography have been tried, including a

static camera with a microflash unit [47], a Q-switched laser light

source [48], and an image-converter camera [49]. All of these techniques work

well for capturing a single frame. The only technique that appears to have

adequate dynamic spatial resolution when used to capture several frames is a

Cranz-Schardin type camera [50]. The principle of a Cranz-Schardin camera is

described in [51], and the application of this type of camera to high- speed

photography of dynamic fracture experiments is discussed in [52] and [53].

As discussed above, two techniques may be used in applying the moire

method: the fringes may be photographed directly or the deformed grid may be

photographed and the fringes formed later. Advantages and disadvantages are

associated with either of these choices. Photographing the fringes directly

places a less stringent spatial resolution demand on the camera but requires

16
more intense illumination. Separation of the u and v fringes is more difficult with this approach. If the camera has sufficient resolution to capture

the image of the reference grid as well as the fringes, then it is possible to

separate u and v by the spatial filtering method described by Chiang [54].

The resulting separated fringes are discontinuous, however, which would cause

problems in attempting to digitize the data. Alternatives to separating the

fringes are: 1) using a line grating to capture one set of fringes only,

2) assuming symmetry about a plane and capturing one set of fringes above this

plane and one set below it, or 3) assuming reproducibil ity and repeating the

experiment, capturing the u fringes in the first trial and the v in the

second. Another disadvantage of photographing the fringes directly is that

most of the optical enhancement techniques described below for improving

strain sensitivity will not be applicable. This is offset by the advantage

that the fringes produced by relatively high-frequency grids (which give

higher strain sensitivity) can be captured photographically, whereas the grids

themselves cannot.

If the deformed grid is photographed directly, then the fringes may be

readily separated using spatial filtering. Alternatively, one set of fringes

may be formed and then the other by changing the orientation of a line

grating. This latter technique has the disadvantage that slight misalignment

of the grating can introduce significant errors [55]. In addition, by placing

the photograph of the deformed grid in an optical bench, such as the one shown

in figure 3, various enhancement techniques can readily be applied. The

disadvantage of photographing the deformed grid is that a coarser grid must be

used than when fringes are photographed directly: deformed grids as fine as, 4

17
lines per mm can be readily photographed, but finer grids than this may be

difficult to capture [56],

A major drawback of the moir£ method over other optical techniques is

that it is relatively difficult to obtain adequate strain sensitivity.

Sensitivity increases as finer grids are used. Specimen gratings as fine as

600 lines per mm have been successfully employed [57]. Such high frequency

grids are relatively difficult to apply, and their use would rule out the

option of photographing the deformed grid. The alternative is to use coarser

grids in conjunction with various enhancement techniques. These techniques

must be divided into those that can be applied when directly photographing the

fringes and those that can only be applied when the deformed grid is photographed. In the former category are the use of mismatch [58] and the directfringe multiplication technique developed by Post [59]. Mismatch is an

additive technique in which the effective strain level is boosted by adding

fictitious strains through use of a reference grid of slightly different pitch

than the specimen grid (linear mismatch), rotating the reference grid slightly

with respect to the specimen grid (rotational mismatch), or both. Post's

fringe multiplication technique involves use of a coarse specimen grid and a

fine reference grid and illuminating at non-normal incidence. Higher diffraction orders form the image detected by the camera, resulting in a fringe

density that is a multiple of that which would be produced by equal grids as

coarse as the specimen grid. By this approach, fringe multiplication by a

factor of 20 has been achieved with transparent specimens [60]. The technique

is applicable in reflection but somewhat less straightforward [61]. When the

deformed grid is photographed, optical techniques may be used for enhancement.

Fringe multiplication may be accomplished through spatial filtering by only

allowing selected higher diffracted orders to pass through the diffraction

plane of an optical bench [54]. Fringe multiplication by a factor as high as

18
10 has been obtained using this approach by Chiang et al . [62]. Fringe

shifting can also be achieved by optical means [61, 63], which permits

interpolation in between fringes. A final enhancement technique may be used

as a replacement for or in addition to the above methods. This utilizes

the gray levels of light intensity between fringes to interpolate the

displacement values [64, 65]. If a geometrical optics approximation is used

to evaluate the light intensity of a moir£ fringe pattern, displacement is

predicted to be linearly related to intensity in between fringes [66]. A

physical optics derivation by Sciamerella [64] for the case where only the

zeroth and first diffraction orders are passed by the optical system predicts

an arc-cosine relation between displacement and intensity. The latter

derivation is perhaps a more accurate approximation for practical purposes and

can be made exact by placing a suitable aperture in the optical system [64].

The human eye is not sufficiently sensitive to light intensity changes

to apply this approach advantageously, so a photo-detection system is needed.

This was accomplished by Ross, et al . [65] by using a scanning photodensitometer. A video camera and video digitizer could also be used.

Digitizing of moir£ fringe patterns permits digital processing and

computation of strains, alleviating a drawback shared by all optical techniques, manual interpretation is tedious. Through digitization, a matrix of

light intensity versus position is presented to the computer. The computer

can locate fringes by finding light intensity extrema. Unambiguous automated

numbering of the fringes by the computer is usually difficult. This can

possibly by alleviated through the use of mismatch which can eliminate

re-entrant fringe shapes and produce more predictable fringe patterns.

The results of the above survey indicate that the moir£ method is the

most suitable for application to this project. Experience by previous

19
researchers indicates that if the high-speed photography problem is overcome,

the moir£ technique will be relatively straightforward to apply to the

measurement of plastic strains. Measurement of elastic strains will be more

difficult and require application of some of the various enhancement

techniques described above.

IV. NBS Research Plans

The objective of developing quantitative criteria for materials selection

for crack arrester strakes must be met by first identifying the material parameter or parameters that govern arrest and then developing laboratory techniques for evaluating these parameters. A final step is to verify fracture

mechanics predictions of crack arrest by using large-scale tests simulating

actual structural conditions. The approach to meeting this objective will be

to develop the required experimental and analytical capabilities for performing the above steps.

The extensive plastic deformation accompanying arrest in high-toughness

strakes likely invalidates the use of LEFM parameters (K or G). Other

candidate parameters must first be identified and systematical ly tested.

Candidate parameters include total plastic energy dissipation and dynamic

generalizations of parameters that have proved useful in quasi-static

elastic-plastic fracture mechanics (such as the J integral, the tearing

modulus, crack opening displacement and crack opening angle).

The candidate crack arrest parameters will be evaluated using the

"generation -phase, application phase" approach referred to by Kanninen [13].

This approach has proven highly successful both in testing the validity of

dynamic LEFM [13], and in critically evaluating governing parameters for slow,

stable crack growth and elastic-plastic deformation [67, 68]. In this approach

20
the value of a parameter is first determined for a given material on one

specimen type. This is typically not a direct measurement; enough quantities

must be measured to permit inference of the parameter using numerical

computations. The usefulness of the parameter is then evaluated by using its

value in numerical computations for predicting the fracture behavior of a

different specimen configuration and comparing the experimental results for

the second configuration with the analytical predictions.

A difficulty with this approach is that one has access only to the

"endpoints" for performing the evaluation. If the prediction of the behavior

of the second specimen is in poor agreement with the observed behavior, then,

in principle, the candidate parameter is not useful. In practice, however,

many other things could have gone wrong, such as problems with the measurement

technique or inaccuracies in the numerical computations. This problem will be

aggravated in the present work because measurement techniques for crack

propagation are relatively difficult, and numerical modeling of elasticplastic dynamic crack propagation requires development of new analysis

capabilities. To overcome this difficulty, it is important to be able to

provide "intermediate" information. For this purpose, extensive

instrumentation will be used, including conventional instrumentation (strain

gages and crack velocity gages) and moir£ grids for measuring strain patterns

over a large region. This will permit checking of the parameter-evaluating

methodology at various stages. For example, confidence is provided if the

numerical predictions of elastic-plastic deformation throughout a region in a

specimen agree with experimental observations. Another important reason for

the use of extensive instrumentation (in particular the use of moir£ grids) is

that it may permit direct experimental evaluation of certain parameters such

as the J integral and plastic energy dissipation. This not only permits

21
checking of numerical calculations of the values of these parameters, but

potentially could lead to a laboratory technique for evaluating critical

parameter values directly.

A systematic framework has been described for developing materials

selection criteria for crack arrester strakes. The NBS research plans will

specifically address development of the necessary experimental and analytical

capabilities for making use of this framework.

Experimental Research

The eventual goal of providing the experimental capability for adequate

characterization of dynamic crack propagation and arrest must be reached by

carrying out the following steps concurrently: selection of a suitable

specimen configuration, development of "conventional" dynamic instrumentation,

performance of preliminary dynamic experiments, and development of moir£

strain analysis capabilities.

Specimen Design

The specimen design chosen for use in crack arrest experiments must be

capable of arresting a crack under conditions simulating those in service. To

date, study of the propagation behavior of a crack as it runs from a brittle

material into a ductile material has been done using so-called "duplex"

specimen geometries in with a brittle starter section that is welded to a

ductile arrest section. This approach has the disadvantage that the weld

material must be chosen carefully or it may dominate the test. The weld must

be sufficiently brittle so that it does not arrest the crack but not too

brittle or it will absorb the energy of the crack by shattering. The

wedge-loaded double-cantilever beam specimen has been used in this application

22
[11]. This geometry has the drawback that arrest occurs under severe load

drop conditions.

Tensile geometries, such as the hybrid double- tension test [9, 19], are

conmonly used in Japan. This design also arrests the crack under falling load

conditions but to a lesser extent than in the DCB design, and more closely

simulates service stresses in a vessel than does the DCB design.

Disadvantages of this design include the need for a large capacity testing

machine to be able to achieve large crack propagation lengths and the tendency

for crack turning and branching [19], which obscures interpretation of

results. Both of the above designs will be used in the current program with

modifications to minimize the disadvantages. The first modification

considered is to achieve a brittle starter section by locally heat-treating

along a line in a ductile plate. This can be accomplished using an electronbeam weld. The second modification is the introduction of a spring in the

load train to minimize load drop during propagation.

Conventional Dynamic Instrumentation

As discussed in the literature review, use of conventional instrumentation, such as strain gages and crack velocity gages, is relatively straightforward. The main difficulties are providing necessary circuitry with fast

response and providing a high speed digital data recording capability so that

computerized data reduction may be carried out at a later time. Devices

meeting these needs are commercially available. Measurement of applied load

is difficult in dynamic experiments, because the response of conventional load

cells is too slow. This can be overcome by using remote strain gages to permit

evaluation of remote stress and inference of the value of applied load. Conventional displacement transducers are too slow for recording remote displacement,

but clip-on gages may be used for this purpose by using extension arms.

23
Preliminary Dynamic Experiments

Preliminary dynamic experiments are needed to provide qualitative (and

some quantitative) understanding of propagation and arrest under elasticplastic conditions. This will be useful for later specimen design. In

addition, information from these experiments will provide information needed

in other areas. For example, as discussed below, a critical step in applying

moir£ strain analysis to dynamic experiments will be developing a high-speed

photography capability. It is not readily apparent exactly what speeds are

needed. Crack propagation rates in both brittle and ductile steels are known,

but the situation is less clear in duplex specimens. The photoelasticity

study of Dally and Kobayashi [28] suggests that very high-speed photography

(submicrosecond exposure times) is required to capture the initial stages of

crack propagation through the brittle part of the specimen, but that the crack

speed (and accompanying deformation rates) decreases dramatically as the

interface is approached. It is possible that the most interesting aspects of

the experiment (e.g., evaluation of plastic deformation in the ductile portion

of the specimen as the crack approaches the interface) occur relatively

slowly, thus relaxing photography requirements somewhat.

Moir£ Analysis

Development of the moir£ strain analysis capability is the most

challenging part of the experimental work. The eventual goal is to be able to

use high-speed photography to capture moire fringes or the image of the

deformed grid at several instants of time, then to apply whatever enhancement

methods are needed to attain adequate strain sensitivity, and finally, to.

digitize the fringes and use a computer for data reduction. Three steps are

required to reach this goal:

24
1. A static moir£ capability must be developed. This entails the

assembly of optical and digital equipment required for processing moir£ data,

and performing preliminary static experiments. The feasibility of applying

this setup to dynamic experiments can then be evaluated in two ways: by using

moir£ results obtained under photographic conditions (e.g., illumination and

aperture size) and simulating those that will be present in a dynamic

experiment, and by using a single-shot dynamic experiment.

2. A multiframe high-speed photograph capability must be developed

concurrently with the first step. As discussed in the literature review, the

most feasible approach appears to be the use of a Cranz-Schardin multiplespark-gap camera. Development of the necessary photographic technique for

applying moir£ to crack- arrest experiments will be carried out in a

collaborative effort with Professor R. J. Sanford of the University of

Maryl and.

3. The moir£ method must be applied in a dynamic experiment by

photographing several frames and processing the data.

Analytical Research

A cooperative program with C. F. Shih and L. B. Freund at Brown

University is underway to develop the capability of finite-element modeling of

dynamic elastic-plastic crack propagation and arrest. Finite-element

modeling will be based upon modification of the dynamic elastic-plastic

computer code ABAQUS [69]. The development will be carried out in three

phases. The first, a preliminary phase, involves installation of the program,

modification of the code to permit dynamic crack propagation modeling,

computation of relevant parameters, such as the J integral; and preliminary

verification. In the second phase, dynamic elastic-plastic analysis of crack

propagation and arrest in homogeneous materials will be undertaken.

25
Preliminary screening will be done on candidate parameters governing ductile

crack propagation, and comparison will be made with experimental results

available in the literature. In the final phase, modeling of duplex specimens

of the type used in the experimental part of this program will be done and

comparison made with experimental results.

This report was prepared as part of the Fracture Control Technology

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

Command (SEA 05R15). 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.

26
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27
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28
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,

V. 9., 1969, pp. 296-384.

29
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v

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30
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[69] ABAQUS, Hibbit & Karlsson, Inc., Providence, Rhode Island.

31
Wedge Driven

Between Load Pans

Optional Welds

Between Brittle & Ductile Materials

CDuplex' Specimen)

Figure 1. Typical Snail Scale Crack Arrest Specimens.

32
Starter

NotchFig. 2. Large Scale Crack Arrest Specimens.

33
Collimated

Light Source

Photograph

of

Deformed

Grid

Fourier

Transform

Lenses

Spatial

FUter(s)

Moire

Master

Figure 3. Optical Bench For Moire Enhancement.

34
M BS-1 14A -REV. 2-8CI U.S. DEPT. OF COMM. 1 . BIBLIOGRAPHIC DATA

SHEET (See instructions)

PUBLICATION OR 2 REPORT NO.

. Performing Organ. Report No.

NBSIR 83-1681

Publication Date

January 1983

4. TITLE AND SUBTITLE

Interim Progress Report:

Materials Selection Criteria for Crack Arrester Strakes in Naval Vessels

5. AUTHOR(S)

R. B. King

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s) 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

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

U.S. Navy

David Taylor Naval Ship R&D Center

Annapol is , MD 21 402

10.

SUPPLEMENTARY NOTES

_ 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)

Research has been conducted on the problem of developing quantitative criteria

for materials selection for crack arrester strakes in naval vessels. Quantitative

analysis of material performance in service requires application of dynamic elasticplastic fracture mechanics. Results of an extensive literature survey in the area of dynamic fracture mechanics with specific attention given to the crack arrest

application are presented. The research program that has been developed is descibed

in detail

.

—

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by sem colons

crack arrest; crack propagation; dynamic fracture mechanics; elastic-plastic

fracture mechanics; materials selection; toughness.

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PRINTED PAGES

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