Biomedical Engineering Reference
In-Depth Information
its penetration is measured as a function of load and time. Special devices, nanoindenters, work with
loads ranging from several tens of μN to N, and penetrations from tens of nm (1 nm
10
9
m) to sev-
eral tenths of a millimeter. The loaded area can be as small as a tiny fraction of a mm
2
. This enables
the study of “macroscopic” properties of a tooth, as well as the properties of its parts and their micro-
structural components
[2,3]
.
This chapter is closely related to Chapter 16, which has explained the basic nanoindentation proce-
dures. In the following text, some of the topics will be treated in more detail, and also other possibili-
ties will be shown, such as the use of elastic and plastic work of indentation, determination of the onset
of permanent deformations and construction of stress-strain curves, or the study of properties in non-
homogeneous materials. Attention will also be devoted to the characterization of materials with time-
dependent load response and evaluation of the resistance against crack propagation. But first, basic
terms will be explained for the readers with only moderate knowledge from mechanics of materials.
The internal response of material to load is characterized by means of
stress σ
(force per unit area,
N/mm
2
MPa) and
strain
ε, which expresses the relative elongation of material (
ΔL
/
L
, nondimen-
sional or expressed in %). For relatively low stresses, the deformations are elastic and reversible, and
the strain is directly proportional to stress, ε
σ
/
E
. The proportionality constant
E
,
elastic modu-
lus
, characterizes the stiffness of material and corresponds to the stress, which would lengthen the
specimen by 100%. If the stress exceeds some limit value, the body either breaks (brittle materials,
after exceeding the
strength σ
U
) or starts to deform faster (ductile materials, after exceeding the
yield
strength σ
Y
). In this case, permanent deformations remain in the body after unloading. Resistance
against plastic deformations can be characterized by hardness
H
, measured by pressing an indenter
into the specimen and calculating the ratio of the load and area of the imprint. Stresses also appear in
the body due to imposed deformations or temperature changes if dilatations are prevented. In
elastic-
plastic materials
, like metals and ceramics, deformations occur nearly simultaneously with the load.
In polymers or biological tissues, deformations depend on the load and also on its duration and time
course. Such materials are called
viscoelastic
. Under constant load, their deformations grow grad-
ually, slower under lower stress. They can be reversible (delayed elastic deforming) or irreversible
(creep). A complementary property of viscoelastic materials is
relaxation
of stresses and forces in
cases of imposed constant deformation.
Two other important phenomena are fracture and fatigue.
Fracture
in a relatively brittle material,
such as enamel, proceeds by propagation of a crack across the body. The crack can be present as an
internal defect, or can be nucleated in a localized contact with a hard body, or in fatigue processes.
Under load, stresses are highly concentrated at the crack tip. The seriousness of a crack is character-
ized by the
stress intensity factor K
I
, which simultaneously considers the effect of stress and the crack
size;
K
I
σYa
1/2
;
σ
is the nominal stress,
a
is the characteristic crack dimension, and
Y
is a nondi-
mensional geometric parameter. The unit of
K
I
is MPa m
1/2
. A crack propagates fast if the crack inten-
sity factor exceeds critical value
K
IC
, called
fracture toughness
.
K
IC
characterizes the resistance to fast
crack growth and is determined experimentally. In some cases, cracks grow (very slowly) even if the
stress intensity factor is lower than
K
IC
. This occurs in
fatigue processes
, which can lead to delayed
fracture (from minutes to years). Here, the crack grows due to the creation and cumulation of sub-
microscopic defects in cyclic loading (especially in metallic materials), or due to chemical action of
the environment at the crack tip in the stressed material (stress-enhanced corrosion, typical of silicate
ceramics and some other materials). The velocity of subcritical crack growth can also be expressed as
a function of stress intensity factor.
