Deformation - Orthopaedic Biomaterials in Research and Practice - page 43

Thus, in summary, strain hardening increases yield strength at the
expense of lower ductility and toughness, while leaving intrinsic stiff-
ness (modulus) unchanged. This effect is sometimes used deliberately in
fabrication of implants and surgical instruments (see Chapter 7) and is a
necessary result of any plastic deformation in a metallic device.
PROBLEM 2.8
Suppose that the experiment described in Figure 2.16 was continued
until the material failed. Find the ultimate strength, ductility, and work
of failure of the material represented by the stress-strain curve from
the point of reapplication of load after the initial load-unload cycle and
compare the answers with those obtained in Problem 2.5.
ANSWER:
Ultimate strength = σ u = 538 MPa (unchanged)
Ductility = 100 × (0.55 - 0.11) = 44% (vs. 55%)
Work of failure: Again, using the method of squares, the answer is
23 × 8 = 184 J/m 3 (vs. 208 J/m 3 ). Thus, prestressing 316L stainless steel
to 350 MPa leaves its ultimate strength unchanged, but reduces its duc-
tility by 100 × (1 - 0.44/0.55) or 20% and its toughness by 100 ×
(1 - 18.4/20.8) or 11.5%.
Initiation of fracture
When materials fracture, it is because the chemical bonds between
their atomic constituents have been stretched beyond their cohesive
ability. This process may be thought of as either a critical stress (σ u )
being exceeded or an energy storage (work of failure) capacity being sur-
passed. The former (critical stress) view is instructive in that it predicts
the position and orientation of the initial crack.
Fracture will occur when either the maximum tensile or shear strength
of a material is exceeded. In either case, the initial crack occurs in the
plane of the maximum resolved stress. In Figure 2.15, it would be clear,
even without the presence of the force vectors, that the transverse fail-
ures were tensile, since they occur in a plane of maximum tensile stress.
Initial crack patterns in simple loading of the other types discussed
are more complex (Figure 2.17) and may depend on surface constraints.
In compression, when the ends of a short cylinder are free to move, shear
failure occurs. However, if the ends are restrained by friction or other forces,
the rod “barrels” and a large circumferential tensile stress, called a hoop
stress, results, leading to the formation of a vertical tensile failure. This mode
of failure is often seen in incomplete burst fractures of vertebral bodies.
In shear, a simple “delamination” failure occurs. This is difficult to dis-
tinguish from a tensile failure; careful stress analysis is needed to identify it.
In bending, the initial failure is a tensile failure of the outer fiber
under maximum tensile stress, on the convex surface of the beam.