ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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Fatigue Testing of Brittle Solids
J.A. Salem, Glenn Research Center at Lewis Field; M.G. Jenkins, University of Washington
Summary
Fatigue testing of ceramics and glasses is performed by either indirect or direct methods. Indirect or strength
methods employ smooth tensile or flexure specimens and infer the fatigue parameters from strength
measurements without crack length measurements. Direct methods employ either long cracks or short cracks,
and the crack length is measured by observation of the crack or by inference from devices such as strain gages
and electrical resistance grids. Long crack test specimens include fracture mechanics specimens such as the DT,
DCB, CT, and SEPB. Short crack methods employ surface cracks formed by indentation, or surface cracks that
develop naturally on the surface of a smooth test specimen. Structural ceramic and glass components that are
designed to have long lives will fail from small cracks developed over long periods of time. The cracks will
develop from either inherent processing flaws or from damage generated in component machining and handling
(e.g., machining cracks). Cyclic loading, though not required to induce growth in glasses and many ceramics,
tends to accelerate fatigue crack growth. Thus the measurement of fatigue parameters should be done with tests
employing realistic crack sizes, environments, and the applicable load histories. As a result, the development of
standardized static and cyclic fatigue test methods has revolved around the use of small, inherent flaws.
Fatigue Testing of Brittle Solids
J.A. Salem, Glenn Research Center at Lewis Field; M.G. Jenkins, University of Washington
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Multiaxial Fatigue Testing
Yukitaka Murakami, Kyushu University, Japan
Introduction
TESTS for combined-stress fatigue and multiaxial fatigue have been conducted since the early stages in the
history of fatigue testing. In particular, the combined-stress fatigue test for cylindrical specimens has been used
by many researchers. The main objective for classical studies of combined-stress fatigue was to obtain fatigue
data for axles and to find the criterion for the fatigue limit under combined stress. Although recent studies still
use essentially the same testing method, the main objective is to elucidate the factors that control the fatigue
mechanism and particularly the behavior of small fatigue cracks.
The influence of loading history and phases is also a topic of recent studies. Cylindrical specimens or tubular
specimens are mostly used for these studies. Perhaps the most important recent topic in multiaxial fatigue
studies is the behavior of cracks. The threshold condition of macrocracks and crack propagation paths in large
structures have been investigated by many researchers.
Although cracks mostly propagate by mode I (the opening tension mode), even under mixed mode loading, the
propagation behavior is affected by mixed mode loadings due to various factors such as the size of the yield
zone at the crack tip, crack closure, and friction between crack surfaces.
On the other hand, a crack seldom grows by pure mode II (sliding or shear mode) or mode III (tearing mode) in
real structures. Some examples of mode II fatigue are contact fatigue damage in rolls of steelmaking mills,
contact fatigue of rails and bearings, and fretting fatigue. In these cases, the criteria for the threshold condition
for mode II cracks and the resistance to mode II crack growth are needed. Crack growth by mode III is the form
studied in the torsional fatigue test of circumferentially notched specimens. Thus, the fatigue testing method,
specimen geometries, and stress intensity factors are all important factors in the study of multiaxial fatigue.
Many factors of multiaxiality make the testing method more complicated than mode I fatigue testing, and,
accordingly, many researchers, working independently, have developed their own original methods. This article
first explains stress states of combined stress and stress fields near crack tips and then describes various
multiaxial fatigue testing methods.
Multiaxial Fatigue Testing
Yukitaka Murakami, Kyushu University, Japan
Stress States
Most engineering designs and/or failure analyses involve three-dimensional combinations of stress and strain
(multiaxiality) in the vicinity of surfaces and notches, which can be limiting in fatigue applications. This section
provides a brief review of these stress states. Additional information is provided in the article “Multiaxial
Fatigue Strength” in Fatigue and Fracture, Volume 19 of Asm Handbook.
Two dimensional stress states without cracking are defined in Fig. 1, where the basic relations are:
(Eq 1)
where σ
1
, σ
2
are the principal stresses. σ
x
= σ
0
and σ
y
= -σ
0
in Fig. 1(d), and this is equivalent to the case shown
in Fig. 1(b) if τ
xy
= σ
0
.
Fig. 1 Two-dimensional stress states without cracking
The yield criterion or yield stress, σ
Y
, is:
Tresca: σ
1
- σ
2
= σ
Y
(Eq 2)
Von Mises: − σ
x
σ
y
+ + =
(Eq 3)
Stress states at the tip of a crack in combined mode I and mode II are defined by stress-intensity factors. K
I
is
the mode I stress intensity factor, and K
II
is the mode II stress intensity factor. Radial stress (σ
r
), normal stress
(σ
θ
, and shear stress (τ
rθ
) in polar coordinate (r, θ) in the vicinity of the crack tip are given as follows (Fig. 2):
(Eq 4)
(Eq 5)
(Eq 6)
Fig. 2 Stress state near a crack in a polar coordinate
The direction (θ
0
) where σ
θ
has the maximum value is given by:
K
I
sinθ
0
+ K
II
(3 cosθ
0
- 1) = 0
(Eq 7)
(Eq 8)
This equation gives θ
0
= ± 70.5° for pure mode II (K
I
= 0).
The stress intensity factor that prescribes σ
θ
is defined by:
(Eq 9)
The maximum value (K
θmax
) of K
θ
for pure mode II is derived, substituting θ
0
= ±70.5° into Eq 9. Thus:
K
θmax
= 1.155K
II
(Eq 10)
Stress State at the Tip of a Crack in Mode III. If there is a semielliptical surface crack and the crack is subjected
to pure shear (Fig. 3), the condition at the deepest point of crack front, A, is pure mode III, and the condition at
surface corner points, B and C, is pure mode II, which means the branching angle at B and C by mode I crack
growth is 70.5° under reversed torsion (Ref 1). (There have been some discussions among researchers about the
irregular singularity close to the corner point where a crack meets the free surface. It is known that a mode I
stress component in tension has a singularity different from - . If K
III
≠ 0 at the surface point, it means that
there exists a shear stressb τ
yz
on the free surface. Therefore, K
III
must be zero at points B and C.)