Deformation - Orthopaedic Biomaterials in Research and Practice - page 34

600

σ 0.2% = 205 MPa

E = 193 GPa

500

σ u = 538 MPa

σ
(MPa)

400

ε u = 0.55

300

200

1 cm = 100 MPa
1 cm = 0.08 ε

100

ε u

0.002 0.2 0.4 0.543 0.6

ε

FIGUre 2.10 stress-strain diagram (strain hardening).

σ m = 1.33 MPa (by inspection)
σ u = 0.835 MPa ε u = 1.02 (by inspection or from

Table 2.2)

The value of σ 0.2% (= 1.1 MPa) that occurs at ε = 0.26 predicts that the
total force at yielding was 850 N. This is somewhat greater than the value
we had estimated from the load-deformation curve for the onset of necking
(800 N) (Figure 2.2) but is more accurate, since it is based on true strain.
The imaginary material described by Figure 2.9 is of a type that is
called strain softening. This name comes from the fact that the ultimate
stress is lower than the maximum stress; that is, there is a region of the
curve for which the stress is decreasing despite an increase in strain. This
is characteristic of polymers and some particular metals. The more usual
type of behavior is called strain hardening , in which stress increases
continuously with increasing strain and σ m = σ u . Figure 2.10 illustrates
this more usual type of material behavior.

Structural aspects of deformation

Deformation in response to tensile or compressive loading is easy to
comprehend, since a uniform distribution of stress may be assumed
across the loaded faces perpendicular to the line of action of the applied
forces. Thus, we can write

σ = E ∙ ε

This means that if we know the applied forces, we know the stress
everywhere in the object and also the strain since it is related to stress
by a constant, the elastic modulus. The same is true for shear loading,