Chapter 8. Failure
Fundamentals of Fracture
Failure of materials may have huge costs. Causes included improper materials selection
or processing, the improper design of components, and improper use.
Fracture is a form of failure where the material separates in pieces due to stress, at
temperatures below the melting point. The fracture is termed ductile or brittle depending
on whether the elongation is large or small.
Steps in fracture (response to stress):
- track formation
- track propagation
Ductile vs. brittle fracture
||slow, needs stress
|type of materials
||most metals (not too cold)
||ceramics, ice, cold metals
- Ductile Fracture
Stages of ductile fracture
- Initial necking
- small cavity formation (microvoids)
- void growth (elipsoid) by coalescence into a crack
- fast crack propagation around neck. Shear strain at 45o
- final shear fracture (cup and cone)
The interior surface is fibrous, irregular, which signify plastic deformation.
- Brittle Fracture
There is no appreciable deformation, and crack propagation is very fast. In most
brittle materials, crack propagation (by bond breaking) is along specific crystallographic
planes (cleavage planes). This type of fracture is transgranular (through
grains) producing grainy texture (or faceted texture) when cleavage direction changes from
grain to grain. In some materials, fracture is intergranular.
- Principles of Fracture Mechanics
Fracture occurs due to stress concentration at flaws, like surface scratches,
voids, etc. If a is the length of the void and r the
radius of curvature, the enhanced stress near the flaw is:
sm » 2 s0 (a/r)1/2
where s0 is the applied macroscopic stress.
Note that a is 1/2 the length of the flaw, not the full length for an internal
flaw, but the full length for a surface flaw. The stress concentration factor is:
Kt = sm/s0 » 2 (a/r)1/2
Because of this enhancement, flaws with small radius of curvature are called stress
- Impact Fracture Testing
Normalized tests, like the Charpy and Izod tests measure the impact energy
required to fracture a notched specimen with a hammer mounted on a pendulum. The energy is
measured by the change in potential energy (height) of the pendulum. This energy is called
Ductile to brittle transition occurs in materials when the temperature is
dropped below a transition temperature. Alloying usually increases the
ductile-brittle transition temperature (Fig. 8.19.) For ceramics, this type of transition
occurs at much higher temperatures than for metals.
Fatigue is the catastrophic failure due to dynamic (fluctuating) stresses. It can
happen in bridges, airplanes, machine components, etc. The characteristics are:
- long period of cyclic strain
- the most usual (90%) of metallic failures (happens also in ceramics and polymers)
- is brittle-like even in ductile metals, with little plastic deformation
- it occurs in stages involving the initiation and propagation of cracks.
- Cyclic Stresses
These are characterized by maximum, minimum and mean stress, the stress
amplitude, and the stress ratio (Fig. 8.20).
- The SN Curve
SN curves (stress-number of cycles to failure) are obtained using
apparatus like the one shown in Fig. 8.21. Different types of SN curves are
shown in Fig. 8.22.
Fatigue limit (endurance limit) occurs for some materials (like some
ferrous and Ti allows). In this case, the SN curve becomes horizontal at
large N . This means that there is a maximum stress amplitude (the fatigue limit)
below which the material never fails, no matter how large the number of cycles is.
For other materials (e.g., non-ferrous) the SN curve continues to fall
Failure by fatigue shows substantial variability (Fig. 8.23).
Failure at low loads is in the elastic strain regime, requires a large number of
cycles (typ. 104 to 105). At high loads (plastic regime), one has
low-cycle fatigue (N < 104 - 105 cycles).
- Crack Initiation and Propagation
Stages is fatigue failure:
I. crack initiation at high stress points (stress raisers)
II. propagation (incremental in each cycle)
III. final failure by fracture
Nfinal = Ninitiation + Npropagation
Stage I - propagation
- along crystallographic planes of high shear stress
- flat and featureless fatigue surface
Stage II - propagation
crack propagates by repetive plastic blunting and sharpening of the crack tip. (Fig.
- . Crack Propagation Rate (not covered)
- . Factors That Affect Fatigue Life
- Mean stress (lower fatigue life with increasing smean).
- Surface defects (scratches, sharp transitions and edges). Solution:
- polish to remove machining flaws
- add residual compressive stress (e.g., by shot peening.)
- case harden, by carburizing, nitriding (exposing to appropriate gas at high temperature)
- . Environmental Effects
- Thermal cycling causes expansion and contraction, hence thermal stress, if component is
- eliminate restraint by design
- use materials with low thermal expansion coefficients.
- Corrosion fatigue. Chemical reactions induced pits which act as stress raisers.
Corrosion also enhances crack propagation. Solutions:
- decrease corrosiveness of medium, if possible.
- add protective surface coating.
- add residual compressive stresses.
Creep is the time-varying plastic deformation of a material stressed at high
temperatures. Examples: turbine blades, steam generators. Keys are the time dependence of
the strain and the high temperature.
- . Generalized Creep Behavior
At a constant stress, the strain increases initially fast with time (primary or
transient deformation), then increases more slowly in the secondary region at a steady
rate (creep rate). Finally the strain increases fast and leads to failure in the tertiary
- Creep rate: de/dt
- Time to failure.
- . Stress and Temperature Effects
Creep becomes more pronounced at higher temperatures (Fig. 8.37). There is essentially
no creep at temperatures below 40% of the melting point.
Creep increases at higher applied stresses.
The behavior can be characterized by the following expression, where K, n and Qc
are constants for a given material:
de/dt = K sn
- . Data Extrapolation Methods (not covered.)
- . Alloys for High-Temperature Use
These are needed for turbines in jet engines, hypersonic airplanes, nuclear reactors,
etc. The important factors are a high melting temperature, a high elastic modulus and
large grain size (the latter is opposite to what is desirable in low-temperature
Some creep resistant materials are stainless steels, refractory metal alloys
(containing elements of high melting point, like Nb, Mo, W, Ta), and superalloys (based on
Co, Ni, Fe.)
- Brittle fracture
- Charpy test
- Corrosion fatigue
- Ductile fracture
- Ductile-to-brittle transition
- Fatigue life
- Fatigue limit
- Fatigue strength
- Fracture mechanics
- Fracture toughness
- Impact energy
- Intergranular fracture
- Izod test
- Stress intensity factor
- Stress raiser
- Thermal fatigue
- Transgranular fracture