Structural Integrity and Durability
1.6 Structural Integrity and Durability
Bela I. Sandor
The engineer is often concerned about the long-term behavior and durability
of machines and structures. Designs based just on statics, dynamics,
and basic mechanics of materials are typically able to satisfy only minimal
performance and reliability requirements. For realistic service conditions,
there may be numerous degradations to consider. A simple and common
approach is to use safety factors based on experience and judgment.
The degradations could become severe and require sophisticated analyses
if unfavorable interactions occur. For example, fatigue with corrosion or high
temperatures is dif?cult to predict accurately, and much more so when
corrosion is occurring at a high temperature.
There are many kinds of degradations and interactions between them,
and a large (and still growing) technical literature is available in most
of these areas. The present coverage cannot possibly do justice to the
magnitude of the most serious problems and the available resources to
deal with them. Instead, The material here is to highlight some common
problems and provide fundamental concepts to prepare for more serious
efforts. The reader is encouraged to study the technical literature
(including that by technical societies such as ASM, ASME, ASNT,
ASTM, SAE), attend specialized short courses, and seek consulting
advice (ASM, ASTM, Teltech) as necessary.
Finite Element Analysis. Stress Concentrations
The most common problem in creating a machine or structure with
good strength-to-weight ratio is to identify its critical locations and the
corresponding maximum stresses or strains and to adjust the design
optimally. This is dif?cult if a members geometry, including the geometry
and time-dependence of the loading, is complex. The modern analytical tool
for addressing such problems is ?nite element analysis (FEA) or ?nite
element modeling (FEM).
Finite Element Analysis
The ?nite element (FE) method was developed by engineers using
physical insight. In all applications the analyst seeks to calculate a ?eld
quantity: Í stress analysis it is the displacement ?eld or the stress ?eld;
in thermal analysis it is the temperature ?eld or the heat ?ux; and so on.
Results of the greatest interest are usually peak values of either the ?eld
quantity or its gradients. The FE method is a way of getting a numerical
solution to a speci?c problem. An FEA does not produce a formula as
a solution, nor does it solve a class of problems. Also, the solution is
approximate unless the problem is so simple that a convenient exact formula
is already available. Furthermore, it is important to validate the numerical
solution instead of trusting it blindly.
The power of the FE method is its versatility. The structure analyzed may
have arbitrary shape, arbitrary supports, and arbitrary loads. Such generality
does not exist in classical analytical methods. For example,
temperature-induced stresses are usually dif?cult to analyze with classical
methods, even when the structure geometry and the temperature ?eld are
both simple. The FE method treats thermal stresses as readily as stresses
induced by mechanical load, and the temperature distribution itself can be
calculated by FE. However, it is easy to make mistakes in describing
a problem to the computer program. Therefore it is essential that the
user have a good understanding of the problem and the modeling so
that errors in computed results can be detected by judgment.
Stress Concentrations
Geometric discontinuities cause localized stress increases above the
average or far-?eld stress. A stress raisers effect can be determined
quantitatively in several ways, but not always readily. The simplest
method, if applicable, is to use a known theoretical stress concentration
factor, Kt, to calculate the peak stress from the nominal, or average, value,
? max = Kt ?ave
This is illustrated in Figure 1.6.1. The area under the true stress
distribution always equals the area under the nominal stress level,
Mynd 1.6.1 Stress distribution (simplistic) in a
notched member under uniaxial load.
The factor Kt depends mainly on the geometry of the notch, not on the
material, except when the material deforms severely under load. Kt
values are normally obtained from plots such as in Figure 1.6.2 and are
strictly valid only for ideally elastic, stiff members. Kt values can also
be determined by FEA or by several experimental techniques.
There are no Kt values readily available for sharp notches and cracks,
but one can always assume that such discontinuities produce the highest
stress concentrations, sometimes factors of tens. This is the reason for brittle,
high-strength materials being extremely sensitive even to minor scratches.
In fatigue, for example, invisible toolmarks may lead to premature,
unexpected failures in strong steels.
Mynd 1.6.2 Samples of elastic stress concentration factors.
(Condensed from Figures 10.1 and 10.2, Dowling, N. E. 1993.
Mechanical Behavior of Materials. Prentice-Hall, Englewood Cliffs,
NJ. With permission.)
There are many other factors that may seem similar to Kt, but they should
be carefully distinguished. The ?rst is the true stress concentration factor
K? , de?ned as
which means that K? = Kt (by Equation 1.6.1) for ideally elastic materials.
K? is most useful in the case of ductile materials that yield at the notch tip
and lower the stress level from that indicated by Kt. Similarly, a true strain
concentration factor, K?, is de?ned as
where ?ave = ?ave/E.
Furthermore, a large number of stress intensity factors are used in fracture
mechanics, and these (such as K, Kc, KI, etc.) are easily confused with Kt
and K? , but their de?nitions and uses are different as seen in the next section.
Fracture Mechanics
Notches and other geometric discontinuities are common in solid materials,
and they tend to facilitate the formation of cracks, which are in turn more
severe stress raisers. Sharp cracks and their further growth are seldom
simple to analyze and predict, because the actual stresses and strains
at a crack tip are not known with the required accuracy. In fact, this is
the reason the classical failure theories (maximum normal stress,
or Rankine, theory; maximum shear stress, or Tresca, theory;
distortion energy, or von Mises or octahedral shear stress, theory),
elegantly simple as they are, are not suf?ciently useful in dealing with
notched members. A powerful modern methodology in this area is
fracture mechanics, which was originated by A. A. Fúslega?th**
Í 1920 and has grown in depth and breadth enormously in recent decades.
The space here is not adequate to even list all of the signi?cant references
in this still expanding area. The purpose here is to raise the engineers
awareness to a quantitative, practically useful approach in dealing with
stress concentrations as they affect structural integrity and durability.
Brittle and Ductile Behaviors. Embrittlements
Brittleness and ductility are often the ?rst aspects of fracture
considerations, but they often require some quali?cations. Simplistically,
a material that fractures in a tension test with 0% reduction of area (RA)
is perfectly brittle (and very susceptible to fracture at stress raisers),
while one with 100% RA is perfectly ductile (and quite tolerant of
discontinuities). Between these extremes fall most engineering materials,
with the added complication that embrittlement is often made possible by
several mechanisms or environmental conditions. For example, temperature,
microstructure, chemical environment, internal gases, and certain geometries
are common factors in embrittlement. A few of these will be discussed later.
** The Grif?th criterion of fracture states that a crack may propagate when
the decrease in elastic strain energy is at least equal to the energy required
to create the new crack surfaces. The available elastic strain energy must
also be adequate to convert into other forms of energy associated with
the fracture process (heat from plastic deformation, kinetic energy, etc.).
The critical nominal stress for fracture according to the Grif?th theory is
proportional to 1/ . ?crack length. This is signi?cant since crack length,
even inside a member, is easier to measure nondestructively than stresses
at a crack tip. Modern, practical methods of fracture analysis are
sophisticated engineering tools on a common physical and
mathematical basis with the Grif?th theory.
Linear-Elastic Fracture Mechanics (LEFM)
A major special case of fracture mechanics is when little or no plastic
deformations occur at the critical locations of notches and cracks.
It is important that even intrinsically ductile materials may satisfy this
condition in common circumstances. Modes of Deformation. Three basic
modes of deformation (or crack surface displacement) of cracked members
are de?ned as illustrated schematically in Figure 1.6.3. Each of these modes
is very common, but Mode I is the easiest to deal with both analytically
and experimentally, so most data available are for Mode I.
Mynd 1.6.3 Modes of deformation.
Stress Intensity Factors. The stresses on an in?nitesimal element near
a crack tip under Mode I loading are obtained from the theory of
linear elasticity. Referring to Figure 1.6.4,
Mynd 1.6.4 Coordinates for fracture analysis.
There are two special cases of ?z:
?z = 0 for plane stress (thin members)
?z = v(?x + ?y) for plane strain, with ?z = 0 (thick members)
The factor K in these and similar expressions characterizes the intensity
or magnitude of the stress ?eld near the crack tip. It is thus called the
stress intensity factor, which represents a very useful concept,
but different from that of the well-known stress concentration factor.
KI is a measure of the severity of a crack, and most conveniently
it is expressed as
KI = ???a ?(geometry)
where a is the crack length and f is a function of the geometry of the
member and of the loading (typically, f ? 1 ? 0.25). Sometimes f
includes many terms, but all stress intensity factors have the same
essential features and units of stress In any case, expressions of K
for many common situations are available in the literature, and numerical
methods are presented for calculating special K values.
Differential thermography via dynamic thermoelasticity is a powerful,
ef?cient modern method for the measurement of actual stress intensity
factors under a variety of complex conditions (Section 1.6,
Experimental Stress Analysis and Mechanical Testing;
Figure 1.6.12; Color Plates 8 and 11 to 14).
Fracture Toughness of Notched Members
The stress intensity factor, simply K for now, is analogous to
A stress-strain curve, as in Figure 1.6.5. K increases almost linearly
from 0 at ? = 0, to a value Kc at a critical (fracture) event. Kc is
called the fracture toughness of a particular member tested. It does
depend on the material, but it is not a reliable material property because
it depends on the size of the member too much. This is illustrated in
Mynd 1.6.6 for plates of the same material but different thicknesses.
length.
Mynd 1.6.5 Kc = fracture toughness of a particular member.
Mynd 1.6.6 KIc = plane strain fracture toughness of
material.
At very small thickness, Kc tends to drop. More signi?cantly,
Kc approaches a lower limiting value at large thickness (>A).
This worst-case value of Kc is called KIc, The
plane strain fracture toughness in Mode I. It may be considered
a pseudomaterial property since it is independent of geometry at least
over a range of thicknesses. It is important to remember that
the thickness effect can be rather severe. An intrinsically ductile metal
may fracture in an apparently brittle fashion if it is thick enough and has
a notch.
Fracture Toughness Data. Certain criteria about crack sharpness
and specimen dimensions must be satis?ed in order to obtain reliable
basic KIc data (see ASTM Standards). KIc data for many engineering
materials are available in the technical literature. A schematic overview
of various materials KIc values is given in Figure 1.6.7. Note that
particular expected values are not necessarily attained in practice.
Poor material production or manufacturing shortcomings and errors
could result in severely lowered toughness. On the other hand,
special treatments or combinations of different but favorably matched
materials (as in composites) could substantially raise the toughness.
Besides the thickness effect, there are a number of major in?uences on
a given materials toughness, and they may occur in favorable
or unfavorable combinations. Several of these are described here
schematically, showing general trends. Note that some of the actual
behavior patterns are not necessarily as simple or well de?ned as indicated.
Mynd 1.6.7 Plane strain fracture toughness ranges (approximate).
Mynd 1.6.8 Yield strength effect on toughness.
Yield Strength. High yield strength results in a low fracture toughness
(Figure 1.6.8), and therefore it should be chosen carefully, understanding
the consequences. Temperature. Two kinds of temperature effect on
toughness should be mentioned here.
They both may
appear, at least for part of the data, as in Figure 1.6.9, with high
temperature causing increased toughness. One temperature effect is
by the increased ductility at higher temperature. This tends to lower
the yield strength (except in low-carbon steels that strain-age at
moderately elevated temperatures, Um 100 to 500?C), increase
the plastic zone at the notch tip, and effectively blunt the stress
concentration. Another effect, the distinct temperature-transition
behavior in low-carbon steels (BCC metals, in general; easily
shown in Charpy tests), is caused by microstructural changes
in the metal and is relatively complex in mechanism.
Mynd 1.6.9 Temperature effect on toughness.
Loading Rate. The higher the rate of loading, the lower the fracture
toughness in most cases. Note that toughness results obtained in
notch-impact or explosion tests are most relevant to applications
where the rate of loading is high.
Microstructural Aspects. In some cases apparently negligible variations
in chemical composition or manufacturing processes may have a large
effect on a materials fracture toughness. For example, carbon, sulfur,
and hydrogen contents may be signi?cant in several embrittling
mechanisms. Also, the common mechanical processing of cold or hot
working (rolling, extruding, forging) Í?uences the grain structure
(grain size and texture) and the corresponding toughness.
Neutron radiation also tends to cause microscopic defects,
increasing the yield strength and consequently lowering
the ductility and toughness of the material.
Overview of Toughness Degradations. There is a multitude of
mechanisms and situations that must be considered singly and
in realistic combinations, as illustrated schematically in
Mynd 1.6.10 (review Figure 1.6.6 for relevant toughness de?nitions).
Mynd 1.6.10 Trends of toughness degradations.
