Chapter 8. Failure

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Chapter 8. Failure

  1. Introduction
    1. Failure of materials may have huge costs. Causes included improper materials selection or processing, the improper design of components, and improper use.

  2. Fundamentals of Fracture

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

  Ductile Brittle
deformation extensive little
track propagation slow, needs stress fast
type of materials most metals (not too cold) ceramics, ice, cold metals
warning permanent elongation none
strain energy higher lower
fractured surface rough smoother
necking yes no
  1. 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.

  1. 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.

    1. 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 raisers.

    3. 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 notch toughness.

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.
    1. Cyclic Stresses

      These are characterized by maximum, minimum and mean stress, the stress amplitude, and the stress ratio (Fig. 8.20).

    1. The S—N Curve

      S—N curves (stress-number of cycles to failure) are obtained using apparatus like the one shown in Fig. 8.21. Different types of S—N 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 S—N 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 S—N curve continues to fall with N.

      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).

    1. 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

  • slow
  • 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. 8.25.)

    1. . Crack Propagation Rate (not covered)
    1. . 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)
    1. . Environmental Effects
  • Thermal cycling causes expansion and contraction, hence thermal stress, if component is restrained. Solution:
  • 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.

    1. . 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 region. Characteristics:

  • Creep rate: de/dt
  • Time to failure.
    1. . 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 exp(-Qc/RT)

    1. . Data Extrapolation Methods (not covered.)
    1. . 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 materials).

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