2 1 Various Types of Damage
Table 1.1 Various types of damage
Fracture type Volume damage Mixed damage Surface damage
Sudden Cleavage Liquid metal embrittlement
(Hg, Cd, Ga)Cavities (Trans or
Delayed Creep Creep fatigue Fatigue
Hydrogen embrittlement Corrosion fatigue
Wear – Fretting-Fatigue
an increasing deformation takes place without an increase of the applied forces.
Ratcheting is another way to produce excessive deformations. However important
for the stability of structures, we will not deal with these types of collapses.
Nevertheless, plastic instabilities at various scales need to be considered in the
occurrence of damages, so that we will have to account for them in several sections
of this book. The basic treatment of plastic instability can be found in chapter 3 of
the ﬁrst volume.
Damage is due to initiation and development of surfaces, cracks or cavities at
various scales. Their origin lies in microscopic defects of various kinds. They can
be distributed within the volume of the material or on its surface only. They can grow
and coalesce. In this way macroscopic cracks are created. These can propagate more
or less slowly and eventually in a catastrophic fashion. The various types of damage,
which bring up more or less precise notions in the mind of the reader, are listed and
classiﬁed in Table 1.1.
The multiplication or the growth of these defects lead to the development of
cracks and ﬁnally to fracture. We must be able to calculate the loads needed for
the various steps in the evolution of damage and cracking, so as to predict when a
failure would take place.
The ﬁrst step, very often the most critical one, is the initiation of damage. This
requires the production of surface energy, that is the breaking of atomic bonds. This
needs a high local stress. In most cases, homogeneous loading is insufﬁcient. Local
stress raisers must be present. Thus, we need to relate the local stress and strain
ﬁelds at their level to the macroscopic mechanical loadings. Chapter 2 of the ﬁrst
volume gives treatments of this kind of problems.
Damage initiations at various locations leads to a distribution of defects within
the bulk or on the surface, depending on the mechanism. Lazar’ Katchanov and Yurii
proposed, for the treatment of creep rupture, a method to deal with small,
distributed defects within the volume of the material. This is damage mechanics.
Lazar’ Markovich Katchanov (1914–1993) and Yurii Nikolaievich Rabotnov (1914–1985) were
Russian professors in solid mechanics.
1 Various Types of Damage 3
It considers that, owing to the presence of these defects, the effective stress is higher
than the applied stress so that the elastic moduli of a damaged material are lowered.
The effective stress is then introduced in the usual constitutive equations. Some care
is needed in the use of damage mechanics, restricted to the case of distributed defects
within the bulk, avoiding its extension outside of the limits of its basic hypotheses.
We will give some notions about damage mechanics in dealing with creep rupture
and with the fracture of concrete.
The coalescence of distributed defects, or the development of a single one, can
lead to the formation of a crack. When cracks are present, strain concentrations exist
near their tips. The propagation of cracks depends of course on these concentrations.
Their calculation is made possible by the theory of fracture mechanics. It allows
determining of the critical size of cracks resulting in fracture. The next chapter will
be devoted to this most important subject.
The local approach to fracture mechanics consists in relating the macroscopic
critical condition for crack propagation to the microscopic critical conditions near
the crack tip for microscopic defects (cleavages or cavities) to nucleate, grow
and coalesce. This synthesis of fracture mechanics and microscopic treatments
allows better predictions of fracture and understanding of the inﬂuence of the
microstructures of materials.
The elements of microstructure are not uniformly distributed. Precipitates and
inclusions are more or less dispersed within grains, the sizes and orientations of
which are not uniform. For this reason statistical analysis will be needed in many
cases for a sound treatment of damage and fracture. One of the main tools, which
we will use, is based on the weakest link model. It leads to the statistics of Weibull,4
which plays an important role in fracture theories.
To better understand Table 1.1, it is necessary to recall here elements, which are
tackled in chapter 1 of the ﬁrst volume.
Damage of a material results from the development of new surfaces.
On the atomic scale three basic types of damage can be envisaged (Fig. 1.1):
cleavage, slip with formation of surface steps, and creation of cavities resulting from
diffusion of vacancies.
The term cleavage is used only in connection with crystalline materials, but
an analogous mechanism, the breaking of bonds normal to the plane of the crack
(called mode I in fracture mechanics), is responsible for the crazing of polymers,
and for the fracture of concrete and glass. This is also the case for intergranular
fractures, which occur in grain boundaries nearly perpendicular to the crack opening
Slip is responsible for plastic deformation as was studied in Chap. 3 of Volume I.
This can lead to the structural instability of necking or plastic collapse as mentioned
above. Plastic deformation can also lead to the formation of small internal cavities
in the material, which can grow, coalesce and ﬁnally cause fracture. Again, that can
take place within the grains or at the grain boundaries.
Ernst Hjalmar Wallodi Weibull (1887–1979) was a Swedish engineer.
4 1 Various Types of Damage
Fig. 1.1 Atomic scale damage: (a) cleavage; (b) slip; (c) appearance of cavities
Under cyclic loading slip is not perfectly reversible: after a time it can cause
deteriorations, which are most often taking place at the surface, ending with fatigue
Corrosion can interact with slip mechanisms of damage either under static
loading, leading to stress-corrosion, or cyclic loading, producing corrosion fatigue.
A particular kind of aggressive environment is made of liquid metals (Hg, Cd,
Ga), which affect the surface energy and can lead to sudden fractures from liquid
Wear results from mechanical loadings as well in many instances of chemical
The last mechanism at the atomic scale shown in Fig. 1.1 can occur only when
the temperature is high enough for vacancies to diffuse; it is the dominant effect in
creep at high temperatures.
The creation of vacancies occurs also when neutron irradiation creates a large
excess of vacancies over the equilibrium concentration. But irradiation embrittle-
ment results also from the number of other defects created in the atomic structure.
1 Various Types of Damage 5
The diffusion of impurities, in particular to grain boundaries, reducing their
fracture energy, or creating precipitates, can produce impurities embrittlement. This
results in intergranular cracking.
The fast diffusion of hydrogen, faster than the diffusion of other elements, and
also the fact that the coalescence of hydrogen atoms produces gas bubbles and not
solid precipitates, confer speciﬁc characteristics to hydrogen embrittlement.
Chapter 2 of this volume will be devoted to fracture mechanics, introducing
notions such as the strain energy release rate, stress intensity factor, the crack
opening displacement, the energy rate (or J integral) of Rice and Cherepanov.
Chapter 3 will deal with cleavage fracture including a study of the mechanisms
at the microscopic scale as well as the ensuing macroscopic fracture conditions.
It will also include various embrittlement mechanisms: impurities, hydrogen and
Chapter 4 will treat ductile fracture mechanisms of cavities nucleation, growth
The preceding developments will allow us, in Chap. 5, to consider the brittle
ductile transition, an important aspect of the fracture of carbon steels in particular.
Chapter 6 will be devoted to fatigue, once again envisaged both at the micro-
scopic and at the macroscopic levels. It will treat the initiation of fatigue and the
propagation of cracks under cyclic loadings.
Chapter 7 will deal with environment assisted damage. It will include stress
corrosion, liquid metal embrittlement and corrosion fatigue.
Creep-fatigue-oxidation phenomena will be studied in Chap. 8.
Chapter 9 will cover friction and wear. Contact mechanics will ﬁrst be developed
in order to understand the phenomena taking place at the interface between rubbing
Finally, fracture of non-metallic materials such as glass, ceramics, concrete,
polymers and composites will be tackled in Chap. 10.