PFANF8 (2002) 6:68-79 © ASM International

Modeling Creep Damage Based on Real Microstructure

Modeling Creep Damage Based (continued)
on Real Microstructure
Y. Prawoto and T. Aizawa

(Submitted 16 August 2002; in revised form 3 October 2002)

This paper outlines a method to model creep failure of polycrystalline materials based on a real
microstructure taken from an optical microscope. The creep failure is simulated in 304 stainless steel and
the simulation is based on Norton’s creep law. By treating the grain boundaries and the grains differently
and adopting the void nucleation process proposed by Shewmon, the creep strain energy density can be
used as a failure criterion. The result of the simulation confirmed the results of conventional methods
used in a high-temperature remnant life assessment. The intermediate results of the simulation process
allow calculation/monitoring of stiffnesses degradation as the material undergoes creep failure.

Keywords: creep failure, high-temperature RLA (remnant life assessment), stiffness degradation

Introduction the influence of the stress state on the microstructural

From the reliability maintenance point of view, evolution and creep damage processes.
measuring creep damage and using that measure- Although not comprehensive, research on the
ment to predict residual service life is essential. In mechanism of the void nucleation and growth has
order to optimize maintenance and to safely extend been done by several researchers.[2] It is not the
service life beyond the initial design lifetime, it is intention of the authors to explore in a detailed
necessary to predict accurately the residual life of mechanism the creep rupture, but simply to use
the main components of an industrial plant and/or modeling to obtain appropriate solutions for damage
the plant equipment. Routine evaluation of the assessment and to compare the results of that
microstructures of materials in service may be assessment with the experimental data on 304 stain-
accomplished either by replica technique or through less steel. A further aim is to clarify the stress states
the removal of a boat sample. Quantitative metal- associated with void nucleation and growth. The 304
lography, which relies on the image comparison stainless steel was chosen because of its wide use in
method with Parameter A and TRD-508 standard, engineering applications at elevated temperature.
is one of the standard methods for making this In this study, a simple analysis to simulate creep
assessment.[1] Its simple principle is thought to be failure is performed. The model simulates failure
the reason why this method remains in use. by starting with the development of creep strain in
The basic idea of the image comparison methods the material. This strain is then followed by the
is evaluating the changes in the microstructure of formation of creep damage, including void
materials, for example, the formation and growth of nucleation, coalescence, and cracking. In this text
cavities. Based on data related to the observed micro- the term coalescence involves the development of a
structural evolution, the remnant life assessment is crack by junction of isolated creep voids. The
usually performed. It is, therefore, very important coalesced voids (microcracks) then propagate mainly
to simulate creep void nucleation and growth on due to high stress states, which lead to high creep
polycrystalline materials based on metallographic strain and, eventually, fracture.
samples taken from real microstructure. By doing
so, the evaluation will provide additional confidence, Fundamental Concept and
and the stress state causing the microstructural Methodology
changes may become apparent. Qualitatively, it is
well known that there is a reduction in the load- Basic Creep Equation
carrying capability of materials during creep Creep phenomena and constitutive models appli-
evolution, but there is little knowledge regarding cable to a class M material exposed to various

Y. Prawoto, NHK International Co., 50706 Varsity Court, Wixom, MI 48393. Contact e-mail: Prawoto66@hotmail.com. T. Aizawa,
Research Center for Advanced Science and Technology (RCAST)—The University of Tokyo, 4-6-1 Komaba, Meguro-ku Tokyo 153-
8904, Japan.

68 Volume 2(6) December 2002 Practical Failure Analysis

temperature/stress regimes are shown in Fig. 1.[3] of the activation energy for self diffusion. Thus, the
In most engineering applications, the service load/ creep power may be expressed in term of Qsd instead
temperature regime exposes the materials to condi- of in Qc:
tions where power law creep with n≅5 is observed. .  Q 
ε ssc = A2 exp − sd (σ ss )
n ≈5
The applicable temperature/stress area for such (Eq 2)
exposures is shown as area B in Fig. 1. In this
 kT 
operating regime the class M material does not where the subscript ss stands for steady state. In
experience Nabarro-Herring or Coble creep.[4] engineering application, Eq 2 is further rewritten
as:
In this study, the equation used to describe the
creep behavior for class M materials is:[5,6] .
εec = Bσ en (Eq 3)
n
 b   D Gb  σ e 
p
.  Qc  where σe is the equivalent stress (or, in the case of
εec = A   0 
 d   kT  G   exp −  (Eq 1)
 RT  uniaxial stress, the stress refers to stress in the loading
direction), B is a constant of B = A2 exp (–Qsd/kT),
where b is the Burger vector of the mobile dis- and n is the stress exponent. In the case of 304
locations; d is the grain size; D0 is the frequency stainless steel, these constants are readily available
factor; G is the shear modulus; k is Boltzmann’s in previously published data bases.[10]
constant; Qc is the activation energy for creep; R is
the universal gas constant; T is the absolute Failure in Creep
temperature; and A, p, and n are the dimensionless The failure process of a material subjected to a
constants. In Eq 1, the activation energy for creep, service usually is linked to the consumption of
Qc, is essentially the same as the activation energy energy. Work performed by external forces leads to
for self-diffusion, Qsd. Figure 2 illustrates that over the accumulation of strain energy in the elastic
20 metals show excellent correlation between Qc and medium, and failure of the material occurs by the
Qsd.[5,7] Other supportive experiments are also found sudden release of the accumulated energy. This
in other publications,[8,9] showing that additions energy criterion is based on current fracture
of solute affecting self-diffusion also have identical mechanics concepts. From the continuum mechanics
effects on the creep rate. point of view, Argon[11] was among the first to say
that the void nucleation takes place when the sum
In summary, this work assumes that the activation
of the mean stress and the effective stress reaches a
energy for steady-state creep is approximately that

Fig. 1 Approximate deformation map for class M material. A:

Dislocation glide, B: Five-power law creep (diffusion +
dislocation), C: Coble creep, D: Nabarro-Herring creep, Fig. 2 The activation energy for self-diffusion versus the
and E: elastic deformation. Source: Ref 3 activation energy for creep. Source: Ref 7

Practical Failure Analysis Volume 2(6) December 2002 69

 Modeling Creep Damage Based on Real Microstructure (continued)

critical value. Since then, several other failure criteria Although it is difficult to directly apply the criterion
have been developed. in Eq 4 to void nucleation, the equation can be used
However, for the case of creep failure and creep indirectly to establish a void nucleation sequence,
void nucleation and growth, an approach based solely as discussed later. In the equation, γS is the surface
on stress and strain was proved to be unsuccessful. energy, Sr is the remote average stress normal to the
Experiments reveal that grain boundaries are the grain boundary, P is an internal gas pressure in the
important regions for creep failure. It is accepted void (this pressure may assist the expansion of the
widely that creep-induced void nucleation and void), f(α) is the geometric factor, and f(α)(r*)3 gives
cracking at grain boundaries are controlled by the the volume of a critical nucleus. For example, the
grain boundary diffusion. Numerous authors have radius of curvature of the spherical segment making
analyzed the growth of an array of voids on a grain up the void is related to the radius of the void on
boundary oriented normal to applied stress.[12,13] the grain boundary, a, by a = r sin α. Thus, the void
These models, to a certain extent, allow calculation volume in terms of radius a is a 3 fv1/sin 3 α.
of the time to fracture, or at least illustrate that the Discussion of the details of these relationships is
time to fracture depends on both the void spacing presented in Ref 16. Figure 3 illustrates how the
and the grain boundary diffusion coefficient, Db. value of α was determined. The value of the geo-
The question of how the array of voids originates, metric factor is f(α) ≅ fv1 = (2π/3)(2–3 cos α +
however, is not well understood. cos3 α) for the plain boundaries (two-grain junction)
and fv3 for the triple-point (three-grain junction).
Riedel[14] concluded that: “As a result of stress The complete description of the relationships
analyses it appears that the stress concentrations described by the equation is given in Ref 17.
cannot be exceedingly large, and hardly sufficient Clemm[17] also has proved that the energy density
to reach the theoretical nucleation stresses. Thus the for void nucleation at the grain interiors is much
problem of cavity nucleation cannot be regarded as more than the energy for nucleation at the grain
being quantitatively understood.” Argon et al.[11] boundaries. Using this concept, one can rationalize
even argue that the only place where adequate stresses why the triple-point is the preferred location for
can develop in a metal undergoing creep is around void nucleation. The value of f(α) at the triple-point
grain boundary inclusions that lie on a sliding grain is smaller than that on a two-grain junction, as
boundary. This argument implies that the grain illustrated in Table 1. From the table, it is clear that
boundary must be diagonal to the applied stress or for any typical value of α, the value of fv3 is signi-
else no shear could develop and no sliding could ficantly smaller than the value of fv1, thus
take place. If boundary sliding persists, the stress at suggesting that creep void nucleation at the triple-
the inclusion-boundary junction may reach the level points requires less energy than nucleation at a two-
required to cause void nucleation near the inclusion. grain junction.
However, the theory gives no satisfactory explanation
for the development of a uniform array of voids on Riedel[18] observed that the starting size of an
boundaries normal to the applied stress, which is ex- incipient void nucleus α is 0.2–1 µm, which is
perimentally demonstrated to be a preferred location, consistent with the value of 2a equals 0.46 µm
along with triple-point junctions, for void formation. determined in this investigation (Fig. 4). The
variations fv shown in Table 1 may be used to
In this article, a void nucleation model that de-
scribes the effect of grain boundary orientation
relative to the loading direction is presented.
Shewmon and Anderson [15] cited that void
nucleation takes place when the critical energy for
forming a nucleus is reached. This critical value
depends on position and can be approximated by:

4γ S3 f (α )
G ≈
*
(Eq 4)
(S r + P) 2 Fig. 3 Void shape on the grain boundary

70 Volume 2(6) December 2002 Practical Failure Analysis

indicate the relative favorability of void nucleation. displacement modes, as shown in Fig. 6, where situa-
A lower fv value leads to a lower nucleation barrier. tion (a) simulates the uniaxial constant load test,
while situation (b) simulates the uniaxial constant
Creep Strain Energy displacement test. Although the term used here is
The creep strain energy density is defined as:[19] constant load, the simulation actually was performed
εc
. .c by a little manipulation. The manipulation was done
W = ∫ σ e dεεe (Eq 5) to maintain the calculation stable and to make the
0
model approach reality. In the model, the right side
where the superscript c refers to the creep and the of the model shown in Fig. 6 represents a slab with
strain rate value related directly to power-law creep high D xx and D xy, but extremely low D yy was
described in Eq 3. Equation 5 usually is used for attached. On the surface of this slab a constant
calculation of the C*-integral, which is associated negative pressure was then applied. This simulates
with creep crack propagation.[20] Based on Eq 5, the constant stress condition. For all conditions of
the energy density is then calculated and compared analyses here, the temperature was 550 °C.
with the critical energy density to nucleate voids.
Defining the Failure Criteria
Modeling of Creep Damage As discussed previously, the stress alone is in-
Generation of Finite Element Model capable of causing void nucleation, and the void
The microstructure used in this model was nucleation concept outlined by Shewmon is em-
obtained by tracing the grain boundaries seen on a braced and combined with the creep strain energy
metallographically prepared sample examined in an
optical microscope. The traced picture was then
digitized and meshed to obtain node and element
information. The finite element mesh representing
the grain interiors was rough, while the grain
boundaries were represented by a continuous layer
with the approximate area of 4.8 × 10–13 m2 per
element. This value corresponds to the radius of 390
nm in circle (assuming that the voids are spheres).
Compared with the experimentally verified radius
of 300 nm, the size of the elements was a little large.
However, because the model is based on density, the
size difference should not be a major issue. The
meshing scheme OOF outlined in Ref 21 was used.
Once the elements and nodes are obtained, the data
can then be transferred to a readable format using
commercial packages, for example, ANSYS,[22] as
the tool. The computational condition is shown in
Table 2. The constants used were adopted from Ref
10 and were verified experimentally. A simplified Fig. 4 Typical shape and size of the earliest detectable void of 304
flowchart is shown in Fig. 5. The simulations were steel at the plain-grain boundary (in this particular case
the temperature was 550 °C with constant strain of 0.5%)
performed both on constant stress and constant

Table 1 The Value of ƒ(α) at the Triple-point and Plain Grain Boundaries
α(o) ƒ(α) at grain boundaries; ƒv1 ƒ(α) at triple-point; ƒv3 ƒv1/ƒv3
45 0.4864 0.0974 5.0
50 0.7063 0.2164 3.3
55 0.9801 0.4038 2.4
60 1.3090 0.6718 1.9
Source: Ref 16

Practical Failure Analysis Volume 2(6) December 2002 71

 Modeling Creep Damage Based on Real Microstructure (continued)

density concept. Shewmon has proved that the value

of the critical energy needed to nucleate a creep void
at the triple-point differs from that at a two-grain
junction. To institute the sequence in which the
nucleation takes place, the groupings outlined in
Table 3 are applied. For simplicity, it is assumed
that the value of a is constant at the grain boundary
and varies at the triple-point depending on the grain
boundary angle composing the junction. This system
was established based on the notion that the plane

Fig. 6 Overview of two cases of simulations, constant loading

Fig. 5 Simplification of the modeling flowchart and constant displacement

Table 2 Important Elastic-Plastic and Creep Constants of 304 Stainless Steel at 538 °C and the
Computational Condition
Ramberg-Osgood constants (ε = σ/E + Aσm):
Young’s Modulus (E) 121 GPa
Poisson’s ratio (ν) 0.3
Plasticity coefficient (A) 2.78 × 10-17 MPa-m
Plasticity exponent (m) 6.56
These values were used to model a multilinear elasto-plastic material.
.c
Norton’s power law constants (ε e = Bσ en )
Creep coefficient (B) 4.20 × 10-19 MPa-n/h
Creep exponent (n) 6.05
These values were used to model the creep computation.
Other important information:
Element type 6-node triangular structural solid
Element size (area) 4.8 × 10-13 m2 at grain boundaries
Knock-down multiplier 1 × 10-3 (the value to be multiplied with original modulus to
simulate voids)
Convergence tolerance 0.5% in Force
Max. creep ratio (1 step) 0.25 (ratio of increment between two consecutive steps)
Constant load mode 70 MPa (negative pressure on slab attached on the right side)
Constant displacement mode Displaced the right side 0.4%, 0.3%, 0.2%, 0.165%, 0.16%
Boundary conditions Axis symmetry for both left and bottom
Source: Ref 10

72 Volume 2(6) December 2002 Practical Failure Analysis

perpendicular to the loading direction possesses the almost perpendicular to the loading direction re-
lowest fv1. Because the only component that con- quires the least energy density to nucleate the void
tributes to the void nucleation is the one perpen- provides some justification for the decision to cluster
dicular to the grain boundaries, it is assumed that the nucleation barrier based solely on the geometry.
the value of the nucleation barriers depends on fv1/ In reality, from the point of view of practical failure
sin β, where β is the angle of the grain boundary analysis, engineers can establish their cluster method
and the loading direction. With the same notion, to agree with in-service and experimental obser-
the triple-point is assumed to have four clusters. The vations. Clearly, further experiments and analysis are
classification for the triple-point junction was done needed; however, the focus of this article is simply
by adding the sine of each component composing to establish a model that determines a reasonable
the junction. Although this system of cluster evalu- void nucleation sequence under conditions of grain
ation is not accurate and has little scientific basis, boundary sliding. Conventionally, the modeling of
the fact that the experiments show that the plane creep void nucleation is done only for grain boun-

Fig. 7 Approximate condition of fracture crept with constant stress. The simulation was performed based on the full lifetime of 90,000 h,
and the G* of 4.0e4 J/m3 and the applied stress of 70 MPa were used.

Table 3 One Way of Grouping the Position to Organize the Sequence of Nucleation
Sum of sines of angles
composing the point
Position ID ƒv (factor of difficulty) Value of the factor w.r.t. loading direction Nucleation barrier
A ƒv3(45°) 0.0974 2.26-3 G*
B ƒv3(50°) 0.2164 1.51-2.25 2.2 × G*
C ƒv3(55°) 0.4038 0.76-1.50 4.1 × G*
D ƒv3(60°) 0.6718 0-0.75 6.9 × G*
Plain G.B ƒv1(50°)/sin β 0.7063~ ... 7.2~× G*
Note: β is the angle to the loading direction

Practical Failure Analysis Volume 2(6) December 2002 73

 Modeling Creep Damage Based on Real Microstructure (continued)

daries oriented perpendicular to the loading direc- trial, the void nucleation barrier G* was assumed to
tion and thus is not compatible with grain boundary be 4.0 × 10 4 J/m 3 .This value was chosen to
sliding. The present model uses a model grain boun- accommodate the fact that experiments with 304
dary structure that is based on the real micro- stainless steel show that, in a constant displacement
structure and is therefore capable of establishing a test, the first nucleation takes place after 200 h; a
sequence for creep void nucleation in a real material. 4.0 × 104 J/m3 nucleation barrier is compatible with
The value of β, which is assumed to be constant, that observation.
is typically 50° as shown in Fig. 4. For the initial During calculation, any element accumulating

Fig. 8 The situation of stress redistribution as the void develops during creep. The simulation was performed based on the full lifetime of
90,000 h.

74 Volume 2(6) December 2002 Practical Failure Analysis

strain energy that exceeds the critical energy for void fit—a reduction in load-carrying capacity that
nucleation barrier was “knocked down.” The knock- simulates the measured effects of void development
down process simulates void nucleation. The while maintaining reasonably stable.
analytical results were normalized to the experi-
mental results by reducing the stainless steel Numerical Result
modulus using a multiplier of 1e-3. By trial and Constant Load
error, this value was found to provide an optimal
Figures 7 through 9 show the results of the con-
stant load simulation. Figure 7 shows that the
nucleation begins as early as 25% of the typical creep
lifetime. The void nucleation process leads to stress
redistribution and causes the system to lose its homo-
geneity. This stress inhomogeneity eventually leads
to an increased creep strain rate and, subsequently,
failure. The typical stress redistribution is shown in
Fig. 8. As the creep voids develop and coalesce, the
stress inhomogeneity becomes so severe that plastic
yielding adds significantly to the creep factor. Con-
tinuation of loading changes the coalesced voids to
microcracks, and the system becomes unstable before
Fig. 9 Void volume fraction as a function of creep lifetime for the finally rupturing.
analysis using constant loading

Fig. 10 Approximate condition of fracture crept with constant displacement (relaxation). The simulation was performed based on the
displacement constants of 0.05% and 0.25%, and the G* of 4.0e4 J/m3 were used.

Practical Failure Analysis Volume 2(6) December 2002 75

 Modeling Creep Damage Based on Real Microstructure (continued)

Analysis of residual lifetimes in systems under- Constant Displacement

going creep commonly use a void area fraction to Although in Fig. 10 only two conditions are shown,
express damage evolution. Figure 9 shows that under the analyses were performed systematically, starting
constant load, the void area fraction increases logarith- with the highest displacement of 0.4% and ending
mically as the end of system lifetime is approached. with displacements that caused little or no creep
damage. Unlike the constant load case, the constant
displacement analysis allows for stress relaxation. If
the displacement is high enough to supply the energy
necessary to overcome the critical energy (nucleation
barrier), the nucleation will take place. On the other
hand, if the displacement is small and the critical
energy is not obtained, then the nucleation will never
happen. Figure 11 shows the void volume fraction
developed for various amounts of displacement.
With displacement of 0.175% and above, void
nucleation will occur. Below this value no void will
nucleate. It can be seen also that the higher the
Fig. 11 Void volume fraction as a function of creep lifetime for the displacement, the faster the nucleation takes place.
analysis using constant displacement For example, with the displacement of 0.4%, the

Table 4 Qualitative Void Assessment

76 Volume 2(6) December 2002 Practical Failure Analysis

nucleation begins at approximately 300 h, while the were drawn for the purpose of evaluation. The
same thing happens after 1000 h if the displacement number of the grain boundaries crossed by the line
is 0.165%. For the particular microstructure, is then counted as an overall grain boundary number.
temperature, and material used in this analysis, the By counting the damaged grain boundaries and
critical displacement was approximately 0.16%. calculating its fraction with the overall number, the
value of Parameter A can then be obtained. Having
Discussions the parameter, the lifetime can be estimated using:
Parameter A and TRD-508 t rem 1
= −1 (Eq 6)
The Parameter A and the TRD-508 analysis
methodologies are the most used field techniques,
ts {
{1 − (1 − A) nλ /(λ −1)} }
and, therefore, the comparison was made based on where trem and ts are the remnant life and used times,
these two methods. The TRD (TRD-508) standard respectively. The constants n and λ are creep rate
applies for general failure stage of creep. During the exponent and ratio of rupture strain to secondary
creep process, materials are classified into six stages, strain, respectively. The result is shown in Fig. 14.
ranging from 0 to 5. Table 4 shows the comparison The result also agrees with evaluation of typical steel
of the simulation results with the TRD and also used in the field. It is regrettable, however, that the
illustrates how the voids coalesce and develop into constants in Eq 6 were not available publicly.
cracks. Figure 7 also shows that model predictions
after approximately 25% of the creep lifetime Stiffness Degradation
correspond to level 1 of the TRD-508 standard. The asymptotic homogenization method is be-
After 25-30% of the total lifetime, level 2 was coming one of the standard methods to obtain
attained. According to the standard, this level was average engineering values. The discussion on the
not considered as damage. Levels 3 and 4 of the issue of asymptotic homogenization is beyond the
damage are achieved at approximately 70 and 90% scope of this article and readers are advised to refer
of the total lifetime, respectively. These facts agree elsewhere.[2] Important equations used are:
well with field results.
∂u k( 0)
The evaluation method using Parameter A is u i(1) = χ ikl + u~i(1) ( x) (Eq 7)
∂xl
outlined in Fig. 12. Parameter A is the fraction of
damaged grain boundaries to the total grains. It is where u~ i( 1 ) ( x ) is a constant of integration inde–
usually done by drawing a line the same direction pendent of yi , and χ ikl is the solution of auxiliary
as the loading direction. The number of the grain variational problem, where in this case:
boundaries crossed by the line is then counted. The
fraction of the damaged ones and the overall grain
boundaries is then calculated as the parameter.
To use this method to evaluate the simulation
results, several lines need to be determined. Figure
13 illustrates an example of the graphical represen-
tation on how the data can be obtained. Five lines

Fig. 12 Parameter A; the fraction of the damaged grain

boundaries to the overall grain boundaries Fig. 13 Five lines drawn for evaluation using Parameter A

Practical Failure Analysis Volume 2(6) December 2002 77

 Modeling Creep Damage Based on Real Microstructure (continued)

• The model simulation gives assurance that the

∂χ klp ∂v i ( y ) ∂v ( y ) popular methods used in the field are correct and
∫E
Y
ijkl
∂y q ∂x j ∫
dY = E ijkl i
Y
∂x j
dY (Eq 8)
acceptable.
• Stress redistribution as a result of the void
By solving Eq 8, the following can be calculated:
formation is clarified by the model.
1 ∂χ klp • The asymptotic homogenization method can be
= ∫ ( E ijkl − E ijpq (Eq 9)
H
E ijkl )dY
Y ∂y q used to calculate the stiffness degradation as an
Y
alternative to the conventional methods.
H
with E ijkl being homogenized elastic constant. These
equations are then implemented to the system to Acknowledgment
get the stiffness degradation in the loading direction. This study was partially supported by Japan
Together with the conventional CDM (continuum Nuclear Cycle Development Institute ( JNC).
damage mechanics) an averaging was also performed
References
using the finite element model (FEM), which
1. S. Journaux, P. Gouton, and G. Thauvin: J. Mater. Process.
averages the stress based on constant strain. Figure Tech., 2001, 117, p. 132.
15 shows the comparison of the results. It must be 2. H.E. Evans: Mechanisms of Creep Fracture, Elsevier Applied
noted that because the size of the element was Science Publishers, 1985.
slightly large compared with the real void, the 3. H.J. Frost and M.E. Ashby: Deformation Mechanisms Maps,
stiffness degradation presented here is somewhat an The Plasticity and Creep of Metals and Ceramics, Pergamon
overestimation. The value of the homogenization Press, Oxford, 1982.
method gives better upshot compared with the 4. H. Oikawa and T.G. Langdon: Creep Behavior of Crystalline
Solids, B. Wilshire and R.W. Evans, Ed., Pineridge Press,
conventional CDM that was not capable of describ- 1985, p. 33.
ing the degradation neatly. 5. S.V. Raj: Mat. Sci. Eng. A., 2002, 322, p. 132.
6. A.K. Mukherjee: “An Examination of the Constitutive
Conclusion Equation for Elevated Temperature Plasticity,” Mat. Sci.
An example of simulations for creep failure has Eng. A., 2002, 322, pp. 1-22
been demonstrated. Each module of the simulation 7. W.D. Nix and B. Ilschner: Strength of Metals and Alloys, P.
can be changed according to the material type and Haasen and V. Gerold, Ed., Pergamon Press, Oxford, 1980,
p. 1503.
the conditions to meet the object evaluation. For
8. A.N. Campbell, S.S. Tao, and D. Turnbull: Acta. Metall.
this particular analysis, using 304 stainless steel, the
Mater., 1987, 35, p. 2453.
conclusions are: 9. P. Keblinski, D. Wolf, and S.R. Phillpot: Interface Sci., 1998,
• Combination of the creep strain energy criterion 6, p. 205.
and the nucleation sequence can be used to simu- 10. C. Hahn and K.S. Kim: “Time-Dependent Crack Growth
late the creep damage. in Stainless Steel 304 in the Plasticity-Dominant Field,”Eng.
Fract. Mech., 2001, 68, pp. 39-52.
• The result of the simulation agrees well with the 11. A.S. Argon, J. Im, and N.R. Moody: Metall. Trans. A.,
standardized methods such as TRD-508 and 1975, 6, p. 825.
Parameter A.

Fig. 14 Parameter A versus creep lifetime Fig. 15 Normalized stiffness as a function of creep lifetime

78 Volume 2(6) December 2002 Practical Failure Analysis

12. M.W.D. Van Der Burg, E. Van Der Giessen, and R.C. 18. H. Riedel: ASTM STP700, ASTM, W. Conshohocken,
Brouwer: “Investigation of Hydrogen Attack in 2.25Cr- PA, 1980, p. 112.
1Mo Steels with a High-Triaxiality Void Growth Model,” 19. Y.J. Kim: Int. J. Pres. Ves. Pip., 2000, 78, p. 661.
Acta. Metall. Mater., 1996, 44, pp. 505-518.
20. T.L. Anderson: Fracture Mechanics, CRC Press, Inc., 1995.
13. E.D. Giessen and V. Tvergaard: Mech. Mater., 1994, 77, p.
47. 21. W.C. Carter, S.A. Langer, and E.R. Fuller: “OOF Manual,”
NISTIR 6256, 1 Nov 1998.
14. H. Riedel: Material Science Technology, vol. 6, R.W. Cahn,
P. Haasen, and E.J. Cramer, Ed., VCH Verlag, New York, 22. “Theory Reference—ANSYS Release 6.0,” ANSYS, Inc.,
1993, p. 565. Canonsburg, PA, 2000.
15. P. Shewmon and P. Anderson: Acta. Mater., 1998, 46, p. 23. D. Cioranescu and P. Donato: An Introduction to Homogen-
4861. ization, Oxford Lecture Series in Mathematics and Its Appli-
16. A.S. Argon: Recent Advances in Creep and Fracture of Engi- cations, Oxford University Press, New York, 1999.
neering Material and Structures, B. Wilshire and D.R.J. 24. Q.M. Li: Int. J. Solids Struct., 2000, 37, p. 4539.
Owen, Ed., Pineridge Press, Swansea, 1982, p. 1. 25. B. Hassani and E. Hinton: “A Review of Homogenization
17. P.J. Clemm and J.C. Fisher: Acta. Metall. Mater., 1955, 3, p. and Topology Optimization,” Comput. Struct., 1998, 69, p.
70. 707.

C • A • L • L F • O • R P • A • P • E • R • S

Materials & Processes

for Medical Devices Conference
8-10 Sept 2003 • Anaheim Hilton Hotel, Anaheim, CA
This event will provide an ideal opportunity to take a look at state-of-the-art in science and technology
pertaining to medical device materials, as well as examine ways to apply those to products and applications.
Papers are solicited for, but not limited to, the following areas:
• Fatigue life and durability of medical implants • Corrosion resistance of medical implants
• Surface engineering of medical device • Joining methods for medical devices
• Forming processes used in medical devices • Heat treatment methods used in medical transplants
• Effect of materials on surgical techniques • Biocompatibility of implant materials
• Materials for imaging devices (such as MRI and related device heating or magnetic pulling)
The conference will cover materials including, but not limited to: Stainless Steels, Titanium Alloys, Co-
Cr Alloys, Nitonol, and Noble Metals.
This event is sponsored by ASM International and co-sponsored by ASTM International Committee
F04 on Medical and Surgical Materials and Devices and the American Academy of Orthopaedic Surgeons.

Abstract Submission Deadline: 15 January 2003.

For more information, or to submit your abstract, contact: Conference Coordinator, ASM International,
9639 Kinsman Road, Materials Park, OH 44073; ph: 440/338-5151; fax: 440/338-4634; e-mail: vroberts@
asminternational.org; web: www.asminternational.org.
Sponsored by: Co-sponsored by:

Practical Failure Analysis Volume 2(6) December 2002 79