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Computational aspects of steel
fracturing pertinent to naval
requirements
Peter Matic1 , Andrew Geltmacher2 and Bhakta Rath3
Review
Cite this article: Matic P, Geltmacher A, Rath
B. 2015 Computational aspects of steel
fracturing pertinent to naval requirements.
Phil. Trans. R. Soc. A 373: 20140127.
http://dx.doi.org/10.1098/rsta.2014.0127
One contribution of 19 to a theme issue
‘Fracturing across the multi-scales of diverse
materials’.
Subject Areas:
materials science, mechanical engineering,
structural engineering, mechanics
Keywords:
ductile fracture, large strain plasticity,
computational modelling, fracture toughness,
microvoids, image-based modelling
Author for correspondence:
Peter Matic
e-mail: [email protected]
1 Materials Science and Technology Division-Code 6300, 2 Imaging
and Simulation Section-Code 6352, and 3 Materials Science and
Component Technology Directorate-Code 6000, Naval Research
Laboratory, Washington, DC 20375, USA
Modern high strength and ductile steels are a key
element of US Navy ship structural technology. The
development of these alloys spurred the development
of modern structural integrity analysis methods over
the past 70 years. Strength and ductility provided
the designers and builders of navy surface ships
and submarines with the opportunity to reduce ship
structural weight, increase hull stiffness, increase
damage resistance, improve construction practices
and reduce maintenance costs. This paper reviews
how analytical and computational tools, driving
simulation methods and experimental techniques,
were developed to provide ongoing insights into
the material, damage and fracture characteristics
of these alloys. The need to understand alloy
fracture mechanics provided unique motivations to
measure and model performance from structural
to microstructural scales. This was done while
accounting for the highly nonlinear behaviours of
both materials and underlying fracture processes.
Theoretical methods, data acquisition strategies,
computational simulation and scientific imaging were
applied to increasingly smaller scales and complex
materials phenomena under deformation. Knowledge
gained about fracture resistance was used to meet
minimum fracture initiation, crack growth and crack
arrest characteristics as part of overall structural
integrity considerations.
1. Introduction
Ship structural materials have been an important and
enabling technology for US Navy ship and submarine
design. This is particularly true for high strength and
2015 The Author(s) Published by the Royal Society. All rights reserved.
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The work of George Irwin at the US Naval Research Laboratory (NRL) will always be associated
with the science of fracture mechanics, especially for naval steel and aluminium alloys. The start
of NRL’s fracture research efforts occurred when Irwin was hired in 1937 to head the Ballistics
Branch in the Mechanics Division. He quickly became interested in the fracture process through
his work on the ballistic response of steel armour plating. There was a distinct specimen size effect
in armour materials, where penetration testing of large specimens generally exhibited brittle-like
failures but small Charpy and Izod specimens machined directly from the large specimens were
ductile. Irwin investigated several causes for this specimen size effect, which eventually led him
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2. Nonlinear elastic–plastic fracture and crack tip parameters
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high ductility steels used in hulls and superstructures. Progression from HT steels in World War
II to the HY steels in the 1950s and the HSLA steels in the 1980s was driven by the opportunities
provided by enhanced properties and lower-cost fabrication practices [1,2]. Within these broad
developments, the ‘modern ages’ of both structural integrity strategies and the mechanics of
fracture have been closely and continually related.
Ductile fracture in naval steels is a very broad topic. Of particular interest here is to review
the interplay of basic and applied research that addressed some of the important issues involving
naval steels, fracture and structural prediction over the past 70 years. The evolution of theoretical,
analytical and computational tools during this period provided new insights into deformation,
material damage and the fracture characteristics of naval alloys.
Three primary themes emerge in approaching computational aspects of fracture in naval
steels. First, the strong interplay between theoretical concepts and practical applications is
noted. The second theme is the transition from standard material tests (to provide general and
baseline qualification of materials) to customized analysis methodologies (to address specific
and challenging structural performance issues). Third, the advances derived from computational
integration of experiments and simulation methods to enable image-based modelling and
quantitative analysis methods in a field where visual observation is so important.
The focus here will be primarily on fracture from quasi-static large strain deformations,
microstructural damage leading to fracture initiation and elastic–plastic crack growth. The
importance of dynamic and temperature effects will be noted for their importance in motivating
a better understanding of microstructural effects. High cycle fatigue, welding residual stress and
corrosion are also important to naval structure integrity. Their focus, however, is primarily on
small strain deformation and they will not be included in this discussion.
It is important to note that there have been many approaches taken to elastic–plastic fracture
parameters over many years. This has created a rich history for the field, for example global
energy balances, crack tip singularity parameters, crack opening displacement and crack growth
resistance curves [3]. The approaches discussed here highlight some uses of the stress intensity
factor as a crack tip parameter and strain energy density as a local measure of fracture resistance.
They were motivated by the scientific challenges of thin section ductile deformation and fracture
for naval technologies addressed during the 1980s and 1990s. Organizations such as the Ship
Structures Committee brought attention to specific problems and potential solutions in this
area [4].
The 1970s and 1980s were also important eras for the nuclear power, pressure vessel and
general industry sectors. Flaws in base metal and welds were key issues. Work in these areas
culminated in the 1990s fracture mechanics principles and fracture acceptance criteria for nuclear
power plants in the ASME Boiler and Pressure Vessel Code—Section XI in 1993 [5]. Structural
integrity procedures for European industry were addressed by the 1999 SINTAP standard [6].
Welded structure flaw acceptance criteria and methods were also addressed in British Standards
PD6493 [7] in 1991 and 7910 [8] in 1999. Common issues continue to be addressed and refined
in these standards, including crack shape, specimen size effects on fracture parameters and
loading history.
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to develop the theoretical and experimental basis for the new field of fracture mechanics. A few
of Irwin’s efforts in this field are highlighted here. Two significant compilations [9,10] explain the
overall breadth and impact of his research.
In 1948, Irwin published his first seminal paper on the concept of linear elastic fracture
mechanics (LEFM) [11]. In LEFM, he equated elastic energy release rate G to the areal rate of
energy adsorption using the framework of the Griffith theory for the fracture of brittle materials.
This allows for the development of the stress intensity factor K. In that paper, Irwin was able
to derive K (denoted as C in this paper) for a centrally notched plate. His LEFM research was
critical to understand the role of local stress concentrations on the fracture behaviour of materials
and that the limiting velocity of fracture in a material can be used to explain crack branching in
materials with limited ductility. In the following years, Irwin continued his efforts by extending
LEFM to include different states of applied stress and transverse constraint (i.e. plane stress versus
plane strain), specimen geometry, a plastic zone correction to the strain energy release rate and the
basis for subcritical crack growth through various mechanisms, such as fatigue, stress corrosion
cracking and corrosion fatigue [12–15].
Irwin was also integral to the development of fracture surface analysis techniques at NRL [16].
He used these methods to examine limiting crack velocities, crack growth direction and thus
identify the fracture initiation sites in failed components. He was known to be interested in
the development of ‘pin holes’ ahead of cracks in foil specimens and was able to explain
discontinuous fracture through analysis of time under load and the fracture path in the
plastic zone.
William Pellini’s 1976 book titled Principles of structural integrity technology [17] captured
the Navy’s knowledge base and engineering analysis methods developed in NRL’s Metallurgy
Division during the post-World War II decades to design ships, aircraft and missiles resistant
to fracture. Peter Palermo, who directed ship structural design at the US Naval Sea Systems
Command, writes in the book’s foreword that Pellini ‘. . . summariz[es] coherently more than
25 years of groundbreaking research on real problems . . .’ and that he has ‘. . . translat[ed]
the physical phenomena of fracture and crack growth to a format that facilitates engineering
analysis . . .’.
The success of LEFM applied to relatively brittle materials also raised important questions
about design with ductile materials, such as the steels, that are so important to naval ship
structures. The interplay of ductile alloy stress–strain characteristics (quantified by stiffness,
yield stress, strain hardening and failure strain) and fracture characteristics (associated with the
crack stress intensity factors and concept of a local critical value for a material) was increasingly
important, as was the recognition that material quality and service conditions were fundamental
factors. Alloys and weld quality were governed by alloy and weld composition choices and
processing practices.
These factors set the initial conditions for microstructural response to deformation. The
subsequent service temperatures, strain states and dynamic loading rates controlled the relative
brittle versus ductile responses of the naval steel microstructures. This, in turn, affected fracture
initiation, crack growth and the potential for crack arrest and ship damage tolerance. Collectively,
the problem was highly nonlinear and beyond a direct theoretical description.
The interplay between fracture toughness and material strength was recognized as one
important factor and, in particular, the ratio of these two quantities. This was related to the
concept of elastic constraint and the strain state enhancement or inhibition of plastic flow
adjacent to the crack tip and in the far-field bulk material. This was increasingly important
to the relatively thin section ship structures and any cracks, where many components of the
structure were more likely to exhibit ‘low constraint’ affecting crack growth in the base metal,
and ‘high constraint’ near welds and structural detail intersections. As a result, a direct method for
laboratory determination of a unique fracture toughness parameter or behaviour was problematic
for relevant structural dimensions.
The fracture analysis diagram (FAD) was developed to account for the effects of temperature
on crack growth, microstructural mechanisms and large-scale plastic deformation. It addressed
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FAD
0.50
0.25
yc
initiation
small cracks
FTE
initiation
for
TTC
C
TT
CA
T
0.75
NDT
r
fo
arrest
0
TTC
30
NDT
20
60
90
40
120
60
150
80
180 (°F)
100 (°C)
Figure 1. Basic features of FAD relating applied stress and temperature to crack size, elastic–plastic deformation and crack
arrest.
important and complex design issues above the nil ductility temperature by providing practical
information on fracture initiation and the likelihood of sustained crack propagation versus crack
arrest in ductile materials. The FAD combined what worked using LEFM with experimental
methods and analytical insights to overcome what was not theoretically possible to describe based
on theories of micromechanics and ductile fracture. It could also be constructed to account for
higher loading rates, which also suppressed ductility.
The FAD was based on developing and applying careful, rigorous and relatively simple
experimental test procedures to probe the microstructural effects on crack growth and gather
sufficient data on which to base design decisions. The approach is important because it
highlighted and accounted for the effects of microstructural fracture mechanisms without being
able to model or predict them. Physical testing of small laboratory specimens at different
temperatures, crack sizes and applied stress captured the changes in cleavage, quasi-cleavage
and microvoid mechanisms and the subsequent effect on unstable brittle fracture and stable
ductile fracture.
The FAD was constructed by combining the concepts of nil ductility temperature (NDT), crack
arrest temperature (CAT), fracture transition to elastic (FTE) behaviour and fracture transition to
plastic (FTP) behaviour, as shown in figure 1. These concepts were important for understanding
fracture propagation and designing against it. If crack propagation initiated and the material
failed predominantly by cleavage mode of fracture the prospects for crack arrest and limited
damage to the ship structure were decreased. Yielding of the structural cross section ahead of
the crack, on the other hand, could arrest the crack and contain the structural damage. The FAD
generated a practical design space ensuring that structural components loaded to anticipated
levels of applied stress could contain cracks up to a critical size without loss of structural integrity
over a range of service temperatures. Since Pellini introduced the FAD, many researchers have
continued to develop fracture mechanics methods to address specimen size, temperature and
constraint effects on the ductile-to-brittle transition region of material response. These methods
include the development of an ATSM standard (ASTM E-1921) [18] for determination of To , and
the master curve and unified curve analysis techniques, designed for the pressure vessel and
nuclear industries [19,20].
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FTP
plastic
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UTS
sys
4
shelf
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3. Large strain elastic–plastic material responses for ductile fracture
Concern about fracture initiation and crack growth also drove nonlinear fracture mechanics in
the 1980s and 1990s. The increasing ability of non-destructive evaluation to detect both larger
voids and smaller cracks challenged predictive capabilities and structural design guidelines.
Ship structural geometries and welded joints required new methods to account for complex
geometries, material nonlinearity, voids and cracks.
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4. Elastic–plastic fracture of naval steels
rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373: 20140127
In the 1980s, finite-element analysis methods were being applied to the design of steel
components and forming processes in the shipbuilding industry. As these techniques were
developed, they would be applied to a mix of basic and applied research topics, often focused
on specific concerns. In relation to Navy steels, a natural progression was towards better
characterization of large strain behaviour now needed for the simulation techniques.
The elastic–plastic constitutive algorithms and numerical solution strategies of commercial
simulation software were becoming powerful and reliable enough to address problems such as
plate bending where large-scale strains of 100% would be produced. Ductile fracture of highperformance steels would also generate large strains near the crack tip.
In both cases accurate yield, hardening and flow parameters for basic elastic–plastic
constitutive models were really not available. Analytical methods commonly used to estimate
uniaxial strains and stresses from post-yield data of necking ductile uniaxial tension test
specimens pre-dated the finite-element methods. Simulations of simple tension tests of HY and
HSLA steels using conventionally derived stress–strain curves, however, began to diverge at
modest average engineering strains of less than 10%.
NRL’s Materials Science and Technology Division began to look carefully at improving the
quality of elastic–plastic constitutive parameters. The material stress–strain characterization
was approached as an inverse problem using the load–displacement response of multiple
different tensile specimen geometries as input. The objective was to determine the stress–strain
curve that generated the measured load–deformation responses of a parametric set of tensile
specimens [21,22]. HY-100 steel parameters were determined through an interactive sequence
of finite-element analyses that converged to the solution for the uniaxial stress–strain curve. The
set of tensile specimens featured four different lengths and three different diameters, for a total
of 12 length-to-diameter (L/D) aspect ratios that provided a range of deformation constraint
during elongation and necking. Photographic and video imaging methods were developed and
applied to the tension tests to automate the measurement of specimen deformations and profile
shapes. The finite-element simulations replicated each experimental specimen load–deformation
response using the HY-100 steel stress–strain solution parameters derived from this procedure.
The simulation results using the stress–strain parameters generated multiaxial stress state,
strain state and energy density values from the tensile specimens at the locations where local
fracture initiation occurred experimentally. Recognizing the influence of the multiaxial strain
states and the observed microstructural features, the strain energy density values associated
with higher elastic constraint specimens were tabulated for use in subsequent studies of
fracture initiation and crack growth. As one of the first of many subsequent inverse parameter
optimization strategies for nonlinear materials, the method was also used to obtain flow and
local fracture parameters for HY-80, HSLA-80 and HSLA-100 steels [23,24] (figure 2).
A sensitive indicator of the method’s capability was found in the unique and progressive
bifurcation of the strain field and necking predicted in the set of HY-100 tensile specimens.
Physically, the HY-100 data showed the neck moving from the symmetry plane, in low L/D
specimens, to an asymmetric location closer to one of the specimen grip sections, in higher L/D
specimens. These observations were guided by the simulations using the optimum parameters
and then measured in the experimental data.
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6
120
80
HSLA-80
HSLA-100
40
HY-100
HY-80
0
0.3
0.9
0.6
uniaxial log plastic strain e
1.2
1.5
Figure 2. Stress–strain curves with demonstrated computational accuracy at large strains to fracture for HY-80, HY-100,
HSLA-80 and HSLA-100 steels.
The increasing use of finite-element methods further highlighted these issues. In ship
structural design, the plastic deformation predicted by finite-element analysis was often
found to be more prevalent than anticipated by the semi-empirical design guidelines for
the same structural detail. This could include plasticity generated from the deformation
forming of structural components, or operational loads on complex geometries and
welded corners.
Initial investigations at NRL on modelling standard fracture specimens focused on the role
of material nonlinearity and the non-uniform development of plasticity across the crack front.
The strength and ductility of the HY and HSLA steels generated considerable plasticity and
specimen surface deformation, more consistent with lower levels of elastic constraint mentioned
previously. This complicated the interpretation of standard fracture toughness testing and its
application to cracks in the structural section thicknesses comparable to those used in ships
and submarines.
Meshing in the vicinity of the crack tip for all the analyses described below was a balance
between the finite-element mesh refinement and the computational resources available. Crack
tip meshing these elastic–plastic materials relied on eight-noded reduced integration, hybrid
elements. Mesh refinement studies were performed resulting in element sizes less than 1% of the
crack length. Non-uniform meshing was used to reduce element density away from the crack tip.
(a) Predicting the onset of crack growth in compact fracture specimens
A thorough analysis was conducted of a standard compact fracture specimen of HY-100 steel
using two-dimensional plane strain and three-dimensional finite-element simulations [25]. The
specimen had a thickness of 22.9 mm (0.90 inch), width was 50.8 mm (2.0 inch), and the initial
crack depth (i.e. the sum of the initial notch plus fatigue pre-cracking) was nominally 25.4 mm
(1.0 inch), equal to one-half the specimen width. The predicted load and displacement values,
along with the plastic zones and internal strain energy density values along the crack front, were
generated from the simulation results. Physical testing of the compact specimen was conducted
in the laboratory with automated data acquisition of load and displacement data, alternating
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uniaxial Cauchy stress s (103 lb in–2)
200
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A study was also performed on two different geometries of HY-100 three-point bend fracture
specimens [28]. The objective was to determine the effect of reduced specimen thickness with side
grooves on enhancing the effective level of constraint along the crack front. One specimen was
0.98 mm (2.50 inch) thick without side grooves. The other specimen was 11.4 mm (0.45 inch) thick
with 20% side grooves. Two-dimensional nonlinear finite-element analyses of the specimen were
performed for the limiting conditions of plane stress and plane strain. The experimental and plane
strain computational load versus crack-mouth-opening displacement (CMOD) curves for both
specimens were in excellent agreement at lower loads. The divergence from plane strain occurred
at a comparable fraction of load initiating crack growth. Both experimental results were between
the bounds generated by the plane stress and plane strain predictions. The thinner specimen with
side grooves was closer to plane strain, whereas the thicker specimen without side grooves was
closer to plane stress. The side grooves as designed were able to more than compensate for the
reduced thickness of the specimen. The computationally predicted CMOD values corresponding
to crack growth initiation, using the local HY-100 fracture initiation energy density value, were
about 25% less than either measured CMOD value. This again indicated the importance of the
three-dimensional fracture characteristics of HY-100 steel in terms of both the continuum and
crack at these specimen thicknesses.
(c) Simulation of crack growth in compact tension fracture specimens
A computational parametric study was also conducted to simulate stable crack growth in a
modified HY-100 compact tension specimen geometry using two-dimensional finite-element
analyses [29]. The objectives were to numerically model stable crack growth and understand the
relative effects of crack length, material strength and material toughness.
Two modified compact tension specimen models were developed, each with a different
crack length-to-specimen width ratio of 0.136 and 0.250. The holes in the specimen for pin
and clevis loading were deleted, so the specimen was solid in this area. Stress was applied at
the top boundary of the specimen along the axis of the deleted holes to load the specimen.
.........................................................
(b) Simulation of three-point bend fracture specimens
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current potential drop data for detecting crack growth, and visual observation of the specimen
deformation.
The load versus displacement results from the two-dimensional simulations were in excellent
agreement up to approximately 80% of the experimentally observed load at which crack growth
began. Beyond this point, the two-dimensional simulation generated a higher load. This was
consistent with a plane strain model generating too much constraint.
The three-dimensional simulation was in full agreement with the experimental load–
displacement result and within 3.5% of the load at the predicted onset of crack growth. Onset
was taken to occur when the strain energy density associated with the higher constraint tension
specimens near the crack tip.
The simulation results showed the highest values of strain energy density at the centre of the
crack front, in the mid-plane of the specimen. The energy density values along the crack front
decreased for points away from the centre towards the free surfaces. This was consistent with the
appearance of a curved crack front in the physical specimens once crack growth began.
In addition to the load–displacement response and the onset of local crack growth, the
apparent stress intensity factor K fracture toughness values from the computational simulation
were within 3.5% of the experimental result. Both values were determined in accordance with
the ASTM-399 standard [26]. The computational and experimental J integral fracture toughness
values also agreed within 2.5% of each other. Both these values were determined using ASTM
E-813 [27]. Taken together, a more complete understanding of local material, crack tip and global
specimen response associated with fracture was obtained using the compact specimen in a low
constraint test.
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This modification avoided a larger model size and additional computational complexity to place
pin contact on loading holes.
The HY-100 stress–strain curve and local fracture toughness was used as a baseline material
behaviour. The parametric properties were constructed around the HY-100 properties as well
as higher and lower values of both the yield stress and the critical strain energy density to
produce fracture.
Node release, element removal and model remeshing were options considered to model
crack growth. Node release was selected because it was suitable for predicting crack growth in
ductile steels, with the necessary simulation practice to ensure solution convergence and stability.
Element removal was not selected because it was better suited for materials sustaining more
diffuse crack damage over element volumes. Model remeshing was not selected because, at that
time, it was more difficult to implement owing to the computational demands of updating each
new mesh with the prior material plastic deformation history.
Crack growth was implemented by nodal force release using debonding interface elements to
specify the path, but not the time, of growth. This provided a prediction of crack growth based
on the local conditions in the vicinity of the crack tip. Nodal release was triggered when the local
energy density near the crack tip, averaged to account for the discretization of the model, reached
a critical value for HY-100 steel. Nodal release was implemented by reducing the nodal forces at
an essentially constant load.
This approach was different from some common practices at the time. These practices
modelled crack growth by specifying a priori the crack length and the applied forces (or
displacements) as boundary conditions based on the experimentally observed values of both.
Prescribing the crack length by incrementally releasing nodes ahead of the crack tip was
computationally simple to implement. The method cast the crack length as an independent
variable rather than as a dependent variable, and therefore did not require a crack growth
criterion to determine crack tip position as a dependent variable of the analysis. Defining
crack growth from experimental data did facilitate the study of plastic deformation fields,
crack tip parameters and global energy balances as the load and crack length increased in the
specified manner.
The results of the simulations for HY-100 provided insights into the numerical aspects of
implementing crack growth predictive algorithms and the physical influences of crack size,
material strength and local fracture toughness. Crack growth of over 60% of the initial crack size
was achieved for some parameter combinations, and the discrete crack growth of the node release
algorithm was a practical approximation of stable crack growth. The predicted crack growth
rates were consistent with the general trends observed for HY-100, which sustained significant
crack growth in the compact tension specimen geometry prior to gross plasticity and plastic
hinge formation in the area between the crack tip and specimen surface. A direct comparison
would have required a three-dimensional crack growth simulation, not practical at that time, to
account for the higher crack growth rates near the centre of the specimen and the lagging rates
near the surface.
Each node release event produced a partial unloading of the specimen as force equilibrium
was re-established for the new crack length. As the crack grew, the magnitude of the local crack
tip unloading decreased, as quantified by the local-to-critical strain energy density ratio. This
produced conditions moving progressively closer to crack instability with each crack growth
increment. For the cases of longer crack and higher material strength, the rate of growth increased
as more elastic energy was available in the specimen to drive plastic deformations. The influence
of local fracture toughness was more closely related to the interplay between it and the strain
hardening of the material, which again influenced the relative elastic energy available in the
system and the relative ability of the material to sustain greater plastic deformation prior
to fracture.
The results of these three studies demonstrated a range of computational approaches for
fracture initiation, crack growth and material property influences on plastic zone size and
fracture for relevant specimen thicknesses. Given that the HY steels featured very high strength
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and ductility, the methods applied and insights obtained from these studies were also directly
applicable to other materials which would be easier to model.
(a) Submarine bulkhead hydrostatic test panel
A parametric computational study was conducted for a submarine bulkhead design using
candidate steels. Bulkhead test panels were used to evaluate design and material resistance to
deformation and fracture when subjected to hydrostatic pressure from one side. The test panel
was a circular plate with T-stiffeners welded in the pattern of an inscribed square. The panel was
welded at its periphery into a hydrostatic loading chamber. Pressure was applied from the
reinforced side, deforming the plate away from the T-stiffeners.
Physical panel tests conducted by the Naval Surface Warfare Center-Carderock Division
(NSWC-CD) had shown that HSLA-80 steel had produced a desirable and somewhat unexpected
result of higher panel deflections at a given pressure load than the HY-80, HY-100 or
HSLA-100 steels under consideration. The results for HSLA-80 also exhibited corresponding less
deformation near the plate and stiffener intersections. The result meant that more energy was
being dissipated by HSLA-80. The objectives of bulkhead test panel simulations conducted by
NRL [24] were to understand how the properties of fabricating it with either HY-80, HY-100,
HSLA-80 or HSLA-100 steel affected panel deformations; map how plastic flow fields develop in
the test panel; identify locations where cracks may initiate; and predict the structural integrity
with and without small cracks at the panel and T-stiffener welded intersection.
A three-dimensional finite-element shell model of the panel captured the large-scale panel
response, whereas a two-dimensional continuum model was used for the intersection. The
simulations were able to understand the role of the more uniform work hardening in the stress–
strain response of the HSLA-80 in the panel response. The higher yield stress in the 80 and 100 psi
yield steels did produce a stiffer panel response. The more uniform and generally higher strainhardening slope in the HSLA-80 distributed high plastic strains across a larger volume of the plate
and was able to dissipate more plastic energy in resisting the pressure load. Conversely, the rapid
decrease in strain hardening beyond 0.20 uniaxial strain for either HY-80, HY-100 or HSLA-100
steel produced more localized plasticity just inside the stiffener boundary. These influences, along
with a sufficiently high strain energy density to fracture, also indicated the HSLA-80 bulkhead
panel would be comparable to HSLA-100, and exceed that of HY-80 and HY-100, in resisting
crack formation or existing crack growth (figure 3).
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A series of structural design concepts and ship components were analysed to understand new
crack formation or existing crack growth. These analyses, conducted during the late 1980s and
well into the 1990s, included submarine bulkhead test panel material influences on deformation,
ship structure weld flaw criticality, weld metal strength influences on fracture initiation and the
grounding characteristics of a double hull ship concept.
Common themes were the complex geometries; analyses enabled by nonlinear finite-element
simulation with the potential to reduce design or maintenance costs; utilization of the large
strain elastic–plastic local fracture material parameters discussed earlier; and careful decisions
in model development to balance physical detail against model size. The results from these
analyses demonstrated practical application of finite-element simulation to the structural design
and structural integrity processes for naval structures.
It is also noted that the effects of structural fatigue are not explicitly addressed in terms of
N-cycle effects on material fracture. Fatigue was captured implicitly when material specimens
taken from ship structures were tested to obtain local fracture parameters. A separate line of
inquiry in the naval structures community was focused on fatigue loading characterizations,
waveforms, cumulative damage and probabilistic analysis methods at that time.
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5. Naval structural integrity analyses
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50 000
40 000
40 000
30 000
30 000
20 000
20 000
Z
Y
X
10 000
0
HY-80
0
p = 2160 psi
p = 2060 psi
10 000
Z
Y
X
HSLA-80
0
p = 2180 psi
Figure 3. Deformed shape and von Mises stress field showing plastic flow gradients in bulkhead test panel at applied pressure:
(a) HY-100 and 2180 psi, (b) HSLA-100 and 2160 psi, (c) HY-80 and 2060 psi and (d) HSLA-80 and 2180 psi. (Online version in
colour.)
(b) Lack-of-penetration weld flaw integrity in ship structures
In the same time period of the late 1980s, opportunities developed to apply these methods
to assess the integrity of HT steel ship structures with lack of penetration weld flaws.
Two complementary studies were conducted using finite-element simulations on similar
flaw geometries found in surface ship hull T-stiffeners. These flaws were internal, threedimensional, macroscopic, high aspect ratio voids in the butt welds joining the flanges of the
T-stiffeners.
The flaws had not been detected during fabrication when revision of the welds would have
been more practical. Operational experience of the ships had not produced widespread incidents
of crack formation or crack propagation. So, the discovery of the flaws was considered somewhat
of a surprise considering their size.
Initial estimates of flaw criticality were made using simpler analytical approaches based on
application of fracture mechanics to conservative idealizations of the flaws. The projected area
of the three-dimensional flaw was used to create an ‘equivalent crack’. Values of KIC and JIC for
the base and weld materials were used in the fracture mechanics calculations. They predicted
that crack growth would initiate at much lower than expected stress levels, corresponding to the
service loads, which was not observed.
The cost of repairing existing flaws in an operational ship structure was very high. The ship
had to be removed from service and the interior spaces cleared of equipment in order to gain
access to the welds. It was an important factor motivating the use of finite-element methods and
the accurate stress–strain curves for an elastic–plastic analysis.
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In the first of two studies conducted by NRL for the Naval Sea Systems Command [30], two
T-stiffener specimens, one with a weld flaw and one without a weld flaw, were removed from
a ship for physical tension testing. They also provided the dimensions for a three-dimensional
finite-element model of the T-stiffener with the flaw. Some smaller material samples for tensile
specimens were also removed.
The weld flaw in the T-section was modelled as a long internal ‘slot’ 0.100 inch high, 0.025
inch wide and running through the 2.0 inch long transverse (LT) weld joining the two T-frame
flange sections. The net section thickness around the flaw was made comparable to the base metal
plate thickness, owing to local weld crown asymmetry diagonally across the flaw, and justified a
decision to omit the weld crown. The model geometry was then symmetric across both transverse
and longitudinal symmetry planes, which reduced the model size by a factor of four.
HT base metal and associated weld metal stress–strain curves and local fracture toughness
values were developed using the flat tensile specimens from higher-quality welds. The specimens
featured a serial composition of base–weld–base metal along its length, without any large weld
flaws. Tensile testing produced a range of results in specimen load–displacement and fracture
locations, probably owing to smaller scattered voids, but the dominant trend was that the
specimens that failed in the base metal had markedly higher reduction in area than the specimens
that failed in the weld metal.
The stress–strain curves and local fracture toughness values for both the base metal and
weld metal were determined by adapting the procedures discussed earlier. The weld material
overmatched the base metal in yield stress, by about 20%, and was significantly less ductile
compared with the base metal, by a factor of 10. Local critical strain energy density at fracture
in the weld metal was about 7% of the base metal value. No account for a heat-affected zone in
the base metal was made for these analyses.
The T-stiffener finite-element model was subjected to a longitudinal tension load applied at
the boundary. The maximum energy density, relative to the critical material value for fracture,
occurred in the weld material. The location of this point was on the periphery of the flaw at
approximately 80% of the distance from the flange centre to the flange edge. The value increased
monotonically to the predicted load of fracture initiation.
The physical testing of the two T-stiffener sections, one with and one without the weld flaws,
was done after the finite-element analysis of the section with the weld flaw was performed. The
tests were used to compare the load–time plots and identify when the flaw began to fracture and
exhibit crack growth based on the onset of load differences between the two plots. Fractography
was used to identify the location of fracture initiation. The predicted fracture initiation load
was within 5% of the measured load, and the predicted location agreed favourably with the
fractographic assessment.
A supplementary two-dimensional finite-element analysis was performed to understand how
the presence of a weld crown would affect the T-stiffener tension results [31]. A butt-welded HT
plate was modelled featuring a weld crown on both sides of the weld material and an interior
weld flaw. For the early stages of tensile loading, the strain energy density relative to the weld
metal critical value was initially higher at the flaw tip compared with the corresponding relative
maximum in the base metal near the base and weld metal boundary.
As the tensile loading progressed, the base metal cross section yielded, which resulted in
unloading of the of the stronger weld material with the wider net cross section. Continued loading
increased the maximum relative strain energy to the point where the fracture initiation location
shifted from the weld metal to an area near the weld metal and base metal interface. This change
in location was a direct result of the weld and base metal nonlinear material responses and the
presence of the weld crown. This analysis also demonstrated that the defect was a less critical
feature of this system and the base metal would in fact govern fracture initiation.
The analyses provided excellent insights into the role of these weld flaws in fracture initiation
and quantitative input into the ship maintenance decision process. They were based on the
material behaviours and fracture properties, and predicted weld flaw fracture initiation without
an a priori specification of location.
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The standard practice in weld design is to use a weld material that features even- or over-matched
yield stress when compared with the base metal. The technical challenge and cost of developing
higher strength weld materials to keep pace with the increases in base metal yield strength
were considerable. The occurrence of fabrication-related cracking with even- or over-matched
base metal was a major consideration. Cold cracking could be avoided by pre-heating the base
metal. In the late 1980s, the option of using undermatched yield strength weld material was under
consideration for use with the higher strength Navy steels to avoid the cost of pre-heating.
Elastic–plastic finite-element analysis was again an excellent tool to evaluate the influence of
weld geometry, weld material yield stress and applied load on a weld system. General trends
were established in lieu of an experimental test programme for the Naval Sea Systems Command.
Parametric two-dimensional computational studies were conducted for double-V welds joining
two plates of HY-100 base metal [33]. A four region heat-affected zone, with progressively higher
yield stress and lower critical strain energy value for local fracture initiation, was included in the
base metal on each side of the weld. The heat-affected zone parameters were maintained for all
the analyses. The weld geometry parameter was the presence or absence of a weld crown on each
side of the weld. The welded plate was subjected to two loading conditions, one tensile and one
bending load.
Representative parametric material parameter sets were developed for the weld metal
analyses, constructed from representative standard and candidate weld designs. The weld metal
yield stress was even with the base metal, overmatched by 18% or undermatched by 18%. All
three weld materials featured similar strain-hardening elastic–plastic flow curves beyond the
yield point. The strain energy density to initiate fracture was assumed to have a constant value,
generating the lower ductilities observed at higher strengths.
The computational simulations were conducted to determine the load–displacement response
of the weld, the location of maximum local strain energy density in each of the different material
parameter regions of the model, and the predicted fracture initiation point of the weld where the
local maximum strain energy reached the critical value for that material.
The results from the complete set of 12 analyses showed that system nonlinearities would
make the a priori prediction of the fracture initiation location in each case difficult. General
trends showed that initiation shifted from interior to exterior surface locations and from the
weld material to the heat-affected zones when (i) the weld metal strength increased, (ii) the load
changed from tension to bending, and (iii) the crown was added to the weld profile. The effect of
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(c) Parametric simulations of over-, even- and under-matched weld designs
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In the second study of weld flaws, a three-dimensional finite-element analysis was conducted
for similar weld-defect geometries in a T-stiffener flange reinforcing a section of hull plate [32].
The hull plate was subjected to transverse pressure loading. The stiffener flange was 4.0 inches
wide, the web was 10.0 inches tall and both sections were 0.2 inches thick. The weld with
symmetric weld crown geometry was a maximum of 0.4 inches thick. The weld defect was a
slot shape 0.05 inches in width, 0.10 inches in height and ran the width of the flange. The hull was
0.375 inches thick.
To analyse this component, a preliminary analysis was performed using a more economical
shell model of the hull plate and stiffener without the weld and defect. The hull was loaded by
the pressure, and the results of this model used to establish local displacement loading conditions
for the three-dimensional T-stiffener model.
The analysis showed that for the bending generated by the pressure loading, constraint at the
intersection of the flange and the web produced the maximum stain energy density prediction of
fracture initiation at the outer edge of the weld flaw just above the web–flange intersection. This
location was different from that in the first study of the T-stiffener under tension, where fracture
initiation occurred at the flaw edge in the flange, at some distance away from the web. Again, the
analysis provided data for ship maintenance decisions.
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weld strength was most significant for tensile loads, whereas the effect of weld crown was most
significant for bending loads.
6. Image-based modelling of material damage and microstructures
By the late 1980s, a major challenge to modelling material damage and predicting fracture
in naval steels was the geometric complexity of the microstructural features associated with
microvoid initiation, propagation and coalescence. Complex arrays of microvoids could be seen
.........................................................
In the early 1990s, interest in double hull designs returned owing to the Exxon Valdez oil spill and
subsequent legislation, with the damage resistance of the inner hull of paramount importance.
The advanced double hull (ADH) concept for naval and commercial ships, developed at the
NSWC-CD, featured intersecting transverse and longitudinal webs between inner and outer
hulls spaced 79 inches apart. A quarter-scale structural test model to support the overall ADH
programme was designed to evaluate the double hull design performance in stranding and
grounding events [34]. The distance between the inner and outer hull in the quarter-scale model
was 18.5 inches. A conical penetrator was used to simulate an object at the bottom of a harbour or
shallow waterway. The quarter-scale model simulated the stranding event by using the penetrator
to deform the hull structure.
A computational model was developed and analysed by NRL, whereas NSWC-CD fabricated
the physical model for testing at the National Institute of Standards and Technology [35,36]. The
primary objectives were to understand the deformation of the double hull structure, the ability of
the web components to collapse and absorb energy, and the likelihood of inner hull fracture. It was
assumed that the outer hull would probably be breached during such an event. The A36 steel was
characterized by tensile specimen tests and computational simulations to optimize the elastic–
plastic parameters for large strains and fracture. The combination of large strain plastic flow,
penetrator-to-hull contact, structure surface-to-surface deforming contact, and fracture of thin
section components required accurate consideration of material behaviour, complex structural
response and fracture in one large analysis.
The analysis and test showed that the penetrator deformed the hull section globally
and breached the outer hull locally. Complex collapse of the longitudinal and transverse
stiffeners followed, effectively protecting the inner hull. The predicted and measured load
and displacement at outer hull fracture were in good agreement. The subsequent loads were
predicted to be higher in the analysis than in the test, but these differences were traced to
boundary conditions and welds. Deformations of the test model were greater owing to the higher
compliance of its bolted attachments to the test fixtures, compared with the smaller deformations
generated by ideal boundary conditions in the model. Localized weld failures at the longitudinal
webs developed in the test model, whereas the finite-element shell model did not have the
resolution to account for welds.
Both these differences were valuable in highlighting the importance of ADH design
parameters and fabrication quality. In the computational analysis, the inner hull was not predicted
to fracture, meeting the design objective. The test inner hull did fracture owing to the partial loss
of the longitudinal webs, which prematurely initiated penetrator contact with the inner hull and
produced localized deformation. The ability of advanced simulation techniques and structural
integrity methods to add this type of insight and value to the design and testing process was
clear (figure 4).
These analyses of structural components, structural concepts and weld details demonstrated
practical application of finite-element simulations to high strength and high ductility naval steels
in the structural integrity and structural design processes. The simulations were used by the Navy
ship structures community in combination with existing standards, engineering expertise and
cost–benefit considerations to enhance their decision process with new tools.
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(d) Simulation of a double hull ship grounding
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(a)
(b)
in cross sections of ductile tensile specimens loaded to within a few percentage of fracture surface
initiation. Cleavage, quasi-cleavage and microvoids were relatively easy to identify on a twodimensional fracture surface. Predicting the evolution of actual microdamage to understand
how it modulated the evolution of local fracture would ultimately require comprehensive threedimensional visual imaging of material volumes, accurate geometrical models and quantitative
simulation methods able to predict and track damage evolution and coalescence leading to
fracture initiation and crack growth.
(a) Microdamage evolution in ductile fracture
Many naval steels fail by the accumulation of damage through the process of ductile fracture.
It is well known that ductile fracture consists of three stages that occur simultaneously: (i) void
nucleation, (ii) void growth, and (iii) void coalescence. By inhibiting any of these three stages,
the ductility and strength of these alloys can be improved. The process of void nucleation is fairly
well understood by both experiment and theory [37–41]. Void nucleation usually occurs at second
phase precipitates or inclusions. In HY-80 and HY-100 naval steels, voids are nucleated with little
or no loading at the large MnS particles that occur in large stringers that form during processing.
Thus, for these steels, most of the ductility occurs under the void growth and coalescence
stages. The process of strain-induced void growth has been studied both experimentally and
computationally for isolated voids [39,42–45].
As detailed below, NRL has studied the role of void interactions effects when the multiple
voids are closely spaced to better understand the ductile fracture process. Of the three stages of the
ductile fracture process, void coalescence is the least understood. Many studies of the void linking
process use regular arrays of holes (in two dimensions) or voids (in three dimensions) [43,46].
It has been shown that these void geometries overestimate the strains needed for voids to
coalesce [47]. In order to examine the role of void spacing and clustering, NRL has developed
experimental and computational tools to measure these parameters and use them to generate
accurate finite-element meshes of actual microstructures for predictive models in two and
three dimensions.
NRL performed initial two-dimensional experiments and computational modelling to
determine the role of geometrical perturbations, in the form of pairs of through-thickness holes,
in the deformation localization behaviour of sheet specimens [48]. The effect of loading path was
examined considering both uniaxial and equal biaxial tension to initiate localized necking in the
ligament between the hole pairs. While the experiments were performed on sheet specimens
of 3003 aluminium consisting of either 1, 2 or 3 hole diameter spacings, the results provided
insights applicable to ductile steel alloys. Additionally, finite-element models of the hole pairs
were used to examine the influence of matrix strain hardening on ligament localization. It is noted
.........................................................
Figure 4. Quarter-scale double hull test article for grounding simulation: (a) finite-element model of quarter-scale double
hull test article and schematic drawing of stranding event, and longitudinal view from loading plane of predicted test article
deformed shape (b) with outer hull displayed and (c) without outer hull displayed. (Online version in colour.)
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An initial foray into image-based modelling began with videography of a soft elastomer with
submillimetre-scale voids [52,53]. A cross section of the elastomer featured a complex array of
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(b) Image-based simulation of microvoid arrays
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that, while the hole interactions in two dimensions are more pronounced than void interactions
in three dimensions, the results relate to forms of void linking which occur owing to plastic
flow localization. In the two-dimensional study, the strain at the onset of localized necking in
the ligament between the holes was shown to increase with increasing hole spacing and strainhardening exponent, as well as when the biaxiality of the loading path increases. The ligament
localization event was also found to follow the Hill criterion, if the local strain states are properly
accounted for in the analysis.
It is well known that the void linking process usually initiates in regions of local high void
content and clustering. However, many continuum localization models are based on unit cells,
which assume some form of periodic void arrays, and over predict the applied strains for void
coalescence. In order to better understand the role of void clustering, NRL continued the twodimensional analysis of hole linking using randomly spaced arrays of multiple holes in sheet
materials tested under uniaxial or equal biaxial tension [49]. The results indicate that hole linking
owing to flow localization is dependent on stress state in a number of ways. As mentioned above,
the localization strain to initiate hole linking increases as the biaxiality of the applied stress state is
increased. However, when the specimens contain multiple holes, the linking process is accelerated
under stress biaxiality, because the flow localization between the holes is dependent solely on
hole spacing. Under uniaxial tension, the flow localization between holes is dependent on both
the hole spacing and the directionality of the linking path. As a consequence, it was determined
that the flow localization process is more gradual with considerable damage accumulation prior
to specimen fracture.
As mentioned above, voids are thought to nucleate at MnS inclusions at little to no strain in
high strength, low alloy steels such as HY-100. Thus, NRL measured local MnS inclusion densities
on polished sections in three orthogonal directions, the rolling direction (RD), the LT and the short
transverse (ST) [50]. While the RD and LT sections were found to contain uniformly distributed
inclusion arrays, the ST data exhibited banding of the inclusions. Thus, it was determined that
actual inclusion/void distributions with different levels of clustering were needed for accurate
predictive models of void linking in these types of ductile steels.
An examination of subcritical and pre-critical voids in HY-100 using X-ray computed
microtomography (XCMT) was performed [51]. D-notch tensile specimens have been tested by
Penn State University in the LT orientation to fracture and to two levels of strain prior to fracture.
The levels of strain were approximately 80% and 85% of the strain to failure. At the lower strain,
banded clusters of voids elongated in the RD are present. This agrees with the two-dimensional
observations of banded MnS inclusions by metallography. The higher strain specimen shows a
remarkable growth in the level of damage. The growth initially occurs along the RD followed
by void sheeting perpendicular to the RD, as seen in figure 5a. Voids inside the intense strain
localization band grow faster than the voids outside the localization. Using the XCMT data
with image-based computational models of actual void geometries in three dimensions, a new
void linking model for HY-100 was determined. First, the primary long stringer MnS inclusions
nucleate cigar-shaped voids with little or no applied strain. Void growth occurs in the elongated
direction through a field of smaller inclusions. Critical groups of elongated voids coalesce into
bands through flow localization ahead of the crack tip, as shown in figure 5b. Large bands
then combine into large cracks using a void sheeting mechanism and small MnS and carbide
inclusions. Figure 5c shows the results from a finite-element simulation of two three-dimensional
voids under high triaxial conditions, similar to the above experiments. The surface contour
represents the elements that have a plastic equivalent strain of 0.50. The similarity of the contour
to the linking voids in figure 5b suggests that the void linking criterion may have the form of a
strain to failure.
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(a)
(b)
(c)
finite-element model of two interacting voids
under high triaxiality
100 mm
fracture
surface
RD
ST–LT section A–A
showing void sheeting
200 mm
ST
ex = 0.0115, ey = ez = 0
surface contour at epeeq = 0.5
Figure 5. XCMT projection of a three-dimensional crack tip in a D-notch specimen tested to 85% of its failure strain with
(a) linking voids ahead of the crack tip in HY-100 steel, (b) close-up of three individual voids that have linked together ahead
of the crack tip and (c) finite-element simulation of two individual voids (from XCMT data for a specimen tested to 80% of
failure) with a surface contour of the region with a plastic equivalent strain of 0.5 as a void linking criterion. (Online version
in colour.)
voids that intersected with the free surface. The surface of the bulk sample was imaged as it
was subjected to increasing uniaxial compressive deformation. The resulting video images clearly
showed deformation localization and collapse of the voids at the cross section. Two-dimensional
finite-element models of the cross section were constructed from an image of the undeformed
cross section. Nonlinear elastic simulations of compressive loading produced void deformation
and collapse very similar to that observed in the video, even while recognizing the difference
between the three-dimensional physical material and the two-dimensional model.
Because it was shown that the ductile fracture of HY-100 steel occurs by a void sheet
mechanism influenced by the clustering of MnS inclusions, NRL employed image-based models
to examine the deformation localization behaviour within void arrays based on experimentally
measured inclusion microstructures [54]. Treating the elongated voids as through thickness
holes in arrays of over 100 holes determined from standard micrographs in two-dimensional
models of flow localization, critical features such as void size, shape, spacing and clustering have
been evaluated. Examples of the computer models are shown in figure 6. As seen in figure 6,
deformation localization across the specimen was especially sensitive to the presence of a few
large voids that were spaced within the bands of inclusions noted above. The void linking process
was enhanced by voids pairs oriented at 45◦ ± 15◦ . In cases where multiple large voids were
not present near this orientation, smaller voids coalesced in order to generate the required stress
conditions for void sheeting. The results also showed that deformation localized more readily
in specimens tested under multiaxial applied strain. Within microstructures consisting solely of
small voids, high density clusters can cause intense strain localization between closely spaced
voids, but it is normally confined to occur within the scale of the cluster itself. The models
with actual void microstructures were also compared with regular, periodic arrays of voids. As
expected, the periodic arrays greatly increased the applied strain required for flow localization
across the specimen.
NRL also developed novel cellular automaton methods to rapidly quantify initial
microstructural information and simulate the evolution of material damage [55,56]. These imagequality simulations were focused on mesoscale systems of microvoids and microcracks that
span a wide range of engineering materials. The use of cellular automaton methods produced
rapid simulations that cover the full range of damage morphologies. The model is based on an
expanding representative volume element (RVE) in a cellular domain. The state of a cell, which
can be either solid material or void, is determined by mapping existing voids through plastic
convection and creating new damage through the cellular automaton. The cellular automaton
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A
linking
voids
ahead of
crack
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(b)
17
regular
random
image-based
Figure 6. Simulated void pair and void array interactions for (a) a regular array of voids, (b) four experimentally observed void
arrays and (c) a random array of voids. (Online version in colour.)
formulation addresses the effect of damage initiation, propagation and coalescence through the
iterative evaluation of individual cells based on that cell’s current state and the current state of the
eight neighbouring cells. The amount of damage in each time step is controlled by conservation
of mass in the expanding RVE. By modifying the ratio of damage to plastic convection and the
probabilities in the cellular automaton rule table, the model can generate microcrack or microvoid
damage morphologies exhibiting different spatial scales. Very rapid simulations are achieved
using this formulation. Thus, a wide range of material damage morphologies can be rapidly
modelled in a single simulation architecture based solely on local cell geometry.
(c) Macromodel analogues for insight into three-dimensional microvoid interactions
In an initial study on the effect of void–void interactions on the mechanisms of intervoid ligament
failure in three dimensions, NRL developed simple cylindrical specimens with blind macroscale
holes to model the complex void interactions [57]. The goal of the study was to determine
the co-planar cavity arrangements that reproduce the observed ligament failure mechanisms
in ductile materials. In this study, cold-rolled 1018 steel bar stock was used. The specimens
contained blind radial spherical holes with the spacing between the holes equal to the spherical
cavity radius. Two of the specimen geometries produced the typical ligament necking found
during the ductile void coalescence process. The first specimen contained three deep blind holes
spaced 120◦ apart with three shallow holes placed in the middle ligament between the deep
hole pairs. This specimen was effective in generating the Y-shaped intervoid ligaments observed
between microvoids in ductile materials. The second specimen consisted of six radial holes with
a central longitudinal hole. This specimen produced similar void–void interactions with annular
symmetry. The global material response was similar for both specimens. It was noted that the
amount of ligament material plasticity was extremely dependent on the number of interacting
voids and that three voids were required to set up flow instabilities within the intervoid ligaments
in three dimensions.
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(a) serial section three-dimensional reconstruction
of AL6XN stainless steel microstructure
(b)
image-based finite-element modelling of
three-dimensional reconstruction
111
001
101
0.0100
0.0033
–0.0033
–0.0100
–0.0167
–0.0200
uniaxial stretch
y-axis
Figure 7. AL6XN microstructure using serial sectioning techniques. (a) Three-dimensional reconstruction featuring grain
orientation at 10 µm voxel size. (b) Image-based finite-element model of the microstructure under uniaxial stretch conditions
in the x- and y-directions illustrating regions of high stress. (Online version in colour.)
(d) Three-dimensional materials science for naval steels
As part of the Office of Naval Research’s ‘Naval Steels-by-Design’ programme during 2000–
2005, researchers at NRL aimed to develop a computationally based methodology to assist in
the design of advanced naval steels [58]. An additional focus of this research was to integrate
these computational methods with advanced experimental measurement techniques. Both the
computational and experimental tools ranged across length and time scales. Relevant information
about material microstructures was incorporated into simulations, from first-principles models at
the atomistic length scale to continuum response at the mesoscale. The first-principles electronic
structure calculations employing density functional theory were combined with Monte Carlo and
molecular dynamic simulations to query the magnetic and atomistic structure of iron and nickel
alloys. Accurate angular-dependent potentials were developed for calculations of grain boundary
structure, energy and element segregation.
During this programme, NRL also developed three-dimensional reconstruction techniques to
characterize the microstructure, including grain and grain boundary statistics, three-dimensional
boundary plane analysis (i.e. frequency of special grain boundary character), compositional
analysis of second-phase precipitates and matrix phase, and three-dimensional morphology,
connectivity and crystallography of grains. Figure 7a shows the application of these techniques
to the three-dimensional reconstruction of an AL6XN austenitic stainless steel microstructure
using serial sectioning [59]. With the three-dimensional reconstructions, image-based finiteelement modelling was performed to identify critical microstructural features in the mechanical
response of the alloy. NRL developed mesh generation techniques to use the experimental
data reconstructions as direct input into models [60]. Particular emphasis was placed on the
identification of microstructural features that initiate localized plasticity under a range of applied
loading conditions from uniaxial tension to biaxial tension and simple shearing, as shown
in figure 7b. Unique visualization techniques were developed to highlight the regions of the
microstructure where failure and fracture will initiate.
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uniaxial stretch
x-axis
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e, e11
(ave. crit.: 75%)
0.0238
0.0167
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7. Future challenges and trends
Progress in these areas will enable new understanding of persistent problems such as the
evolution of stress corrosion cracks from corrosion pits, another important and costly failure
mechanism for naval ship structures. Scientific challenges include determining the underlying
causes with advanced detection, measurement and prediction capabilities. Integrating new
experimental and computational methods, such as those described above, should produce a more
comprehensive understanding of localized corrosion, pit formation, the transition of growing pits
to short stress corrosion cracks and the fracture processes of naval materials in the near future.
8. Summary
The evolution of fracture mechanics for naval steels was driven by the need to use high strength,
high ductility and high fracture toughness alloys (e.g. HT, HY and HSLA steels) in naval
ships designed using sound principles of structural integrity. The operational requirements for
successive classes of ships and submarines required better understanding of material behaviour
and continuous advancement of fracture mechanics to meet this goal.
The challenge of exploiting small-scale or large-scale plastic strains in relatively thin hull,
stiffener and bulkhead structural components (from the fracture toughness versus yield stress
perspective) was met only through the developments made in nonlinear fracture mechanics.
Methods were needed to predict and avoid new crack formation, minimize existing crack growth
and instability, and rely on large-scale plastic flow to create damage tolerant structures.
Over the past 70 years, progress was made through successive advancements in experimental
observations, theoretical approaches and the application of computational methods to both. At
the more macrocrack level, the theoretical constructs of elastic stress intensity factors preceded
the construction of the FAD to conceptually account for how plasticity, temperature and loading
rate can influence design. Later, computational simulations integrated elastic–plastic analysis
to predict deformation, fracture initiation locations and crack growth in complex structural
.........................................................
— Recent advances in three-dimensional materials science, such as faster imaging, faster
data acquisition and more efficient image segmentation algorithms, enabling larger and
more accurate three-dimensional microstructural reconstructions.
— Advanced application of destructive (e.g. mechanical polishing and focused ion beam
serial sectioning) and non-destructive (e.g. conventional and synchrotron tomography)
imaging techniques will aid in ex situ and in situ measurements of fracture initiation
processes and crack growth evolution.
— High resolution flash X-ray imaging of dynamic material damage and fracture in extreme
environments will help to ensure ballistic and shock resistance.
— Progress in the computational modelling of fracture and fatigue over the past 25 years,
first with the advent of cohesive zone theory [52] and more recently with the extended
finite-element method [53], along with other finite-element techniques will improve the
basic understanding of fracture processes.
— Computational modelling of fracture and fatigue using statistical techniques will
address outlier phenomena, operating from atomistic to bulk scales and governed by
fundamental fracture and fatigue mechanisms. This will build on the recent statistical
methods used to design materials for stiffness and strength based on processing–
microstructure–property linkages in material knowledge systems [54].
rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373: 20140127
The progress in ductile fracture mechanics, as discussed here with a focus on naval relevant alloys
and demonstrative applications, highlighted important changes in experimental data acquisition
strategies, computational methods, material parameter characterization and structural analysis
complexity. Current materials science and technology efforts should impact future understanding
of ductile fracture and the improvement of ductile naval steels. These efforts include
19
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Research Laboratory for their helpful discussions.
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