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Failure of Engineering Materials Failure

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					                 Failure of Engineering Materials
(Callister: Chapter 8)
• After completing this section, you should understand the
   principles and application of the following concepts used to
   characterize engineering materials:
    – Ductile vs. Brittle Fracture
    – Fracture Toughness
         • concepts and equations
         • stress intensity factor, fracture toughness, plane strain fracture
           toughness
    – Impact Tests
    – Fatigue Test
    – Creep Test




ES 021                             Chap 8 - Failure                             1




                                     Failure
• The fracture of any material occurs in two steps:
    – Crack formation
    – Crack propagation

• The failure of engineering materials is classified in terms of being:

    – Ductile: significant plastic deformation prior to fracture

    – Brittle: little or no plastic deformation prior to fracture




ES 021                             Chap 8 - Failure                             2
                              Ductile Fracture
  • Ductile fracture of many
    engineering metals results in a
    “cup and cone” fracture
    surface.
  • This is created by a process
    known as microvoid
    coalescence.




  ES 021                          Chap 8 - Failure     3




                               Brittle Fracture
• Brittle fracture involves very little plastic
  deformation
    – The fracture surface is usually flat and
      perpendicular to the applied stress.

• A brittle fracture surface often shows
    – Chevron markings, or

    – A series of fan-like ridges or “river pattern”




  ES 021                          Chap 8 - Failure     4
                           Brittle Fracture
• Crack propagation in brittle fracture
  can be either:

    – Transgranular: through the grains
      (Also called cleavage)




    – Intergranular: along the grain
      boundaries



In both cases, the surface usually appears
shiny because the facets reflect light.


ES 021                         Chap 8 - Failure    5




                      Stress Concentrations

• When a “perfect” solid is loaded in
  tension, the normal stress is the same               F
  in any part of the specimen.                    σ=
                                                       A
• If a flaw (e.g. a small crack) exists
  inside the specimen, the free surfaces
  cannot transmit any load.

• The material adjacent to the crack must
  carry the additional load.


   The stress is concentrated at the
   edges of the crack.



ES 021                         Chap 8 - Failure    6
                         Stress Concentrations

• The degree of concentration of the stress depends on:

   – the size of the crack, a
   and,
   – the radius of the crack tip, ρt.

                             1
                       a       2
           σ m ≈ 2σ 0  
                      ρ 
                       t
• The stress concentration factor
  is the ratio of the maximum
  stress to the average stress
                                     1
                σ      a               2
           K t = m = 2 
                      ρ 
                σ0     t
  ES 021                                     Chap 8 - Failure   7




                           Fracture Toughness

  • A crack will propagate when the stress reaches some
    critical value.

  • A more convenient approach to describing the
    behaviour of a material that contains a crack is to use
    the Stress Intensity Factor, K

                        K = Yσ πa

  • Y is a geometric factor that depends on crack and
    specimen size
  • σ is the average stress (i.e. F/A)
  • a is the crack size


  ES 021                                     Chap 8 - Failure   8
                           Fracture Toughness

• There are four uses of the variable, K, that are intimately related
  and you must not confuse:

    Kt – the stress concentration factor
         • the ratio of the maximum stress to the average stress

    K – the stress intensity factor
         • Associated with the geometry of the component

    KC – the critical stress intensity factor (Fracture Toughness)
         • For a given applied stress, this is the stress intensity factor that will
           cause a crack to propagate.
         • For a given flaw size, KC is geometry dependent

    KIC – the Plane Strain Fracture Toughness
         • This is reported as a material property. It is the minimum value of
           Fracture Toughness for the material


ES 021                              Chap 8 - Failure                                    9




                         Crack-Opening Modes

• Mode I is the most common




ES 021                              Chap 8 - Failure                                   10
                Fracture Toughness




                                                 a


                                                           t
                                             w
ES 021                Chap 8 - Failure                11




  Plane Strain Fracture Toughness of Some Materials




ES 021                Chap 8 - Failure                12
                 Fracture Toughness: Example 1
An aluminum alloy is subjected to a constant stress of 150 MPa. What is
the maximum tolerable flaw size that will avoid fast fracture?
(KIC=30 MPa m1/2, σy=375 MPa, Y=1)


         K IC = Yσ πa
                                                 amax = 1.27cm
                   2
         K  1
     a =  IC 
          Yσ  π                      • Edge Crack: amax = 1.27cm
                       2
            30  1
          =       
            1×150  π
                                       • Internal Crack amax = 2.54cm
          = 1.27 ×10 −2 m
          = 1.27cm

ES 021                        Chap 8 - Failure                            13




                Fracture Toughness: Example #2
What is the minimum value of KIC needed to ensure that a plate with a
yield strength of 300 MPa and external flaws as large as 0.5 mm will
plastically deform before fast fracture can occur when subjected to a
tensile load? (Y=1.1)


            K IC = Yσ πa

            a = ? .5mm = 5 × 10 −4 m
                0

           σ = ? MPa
               300

          K IC > 1.1× 300 π × 5 ×10 −4

          K IC > 13MPa m


ES 021                        Chap 8 - Failure                            14
                          The Impact Test

 • The Impact test measures a materials ability to absorb kinetic
   energy.
 • This quality is often referred to as the Toughness of the material.




                                                 Charpy




                                                      Izod

                               ∆E = ρg (h0 − h f )


 ES 021                       Chap 8 - Failure                     15




                          The Impact Test

•Impact Test Data: Energy absorbed and/or % shear fracture




 ES 021                       Chap 8 - Failure                     16
                       The Ductile-to-Brittle Transition

   • Temperature has a significant influence on the toughness of
     BCC metals. (Steel is the most important example)
           – At low temperatures, they are brittle while at higher temperatures
             they are more ductile.

   • One approach to designing
     structures is to define a
     Transition Temperature,
     below which the material
     should be considered brittle

   • This is the Ductile-to-Brittle
     Transition Temperature
     (DBTT)



   ES 021                            Chap 8 - Failure                             17




                       The Ductile-to-Brittle Transition
   •      There are three accepted methods of determining the DBTT
           – ½ ∆T                  – ½ ∆E               – T for minimum energy




         ED
Energy




         Eavg

         Emin

         EB
                       TB          DBTT DBTT                  TD
   ES 021
                                   Temperature
                                     Chap 8 - Failure                             18
                            The Fatigue Test

• When a component is subjected to a cyclic stress, it may fail by
  a process known as fatigue.

• From a designer’s point of view, fatigue can be a particularly
  dangerous form of failure because:

    – it occurs over time

    – it occurs at stress levels that are not only lower than the UTS, they
      can even be lower than the yield strength.


• The cyclic stress causes small cracks to form and grow until
  they are large enough to cause fast fracture.

                        K IC = Yσ πa

ES 021                         Chap 8 - Failure                           19




                            The Fatigue Test

• Fatigue tests are conducted
  by subjecting a series of
  samples to an alternating
  stress.



• To approximate the in-service
  conditions, one can control
  the:
    – maximum stress
    – minimum stress
    – frequency




ES 021                         Chap 8 - Failure                           20
                                The Fatigue Test

• Calculated test variables are:

    – The mean stress
                  σ max + σ min
           σm =
                            2
    – The stress range
           σ r = σ max − σ min

    – The stress amplitude
                  σ max − σ min
           σa =
                            2
    – The fatigue ratio
                σ min
           R=
                σ max
ES 021                             Chap 8 - Failure                     21




                                The Fatigue Test

• A single fatigue test subjects a specimen to a specified stress
  profile and measures the number of cycles to failure.

• The results of a series of tests are plotted as Stress Amplitude
  vs. log(cycles to failure) on an S-N curve.

                  S
              400

              300

              200

              100

                  0

                      102        103     104          105   106   107   N
ES 021                             Chap 8 - Failure                     22
                  Reading Logarithmic Scales

• Locate the following numbers on the scale
    –    5
    –    90
    –    15
    –    35
    –    2.5




     1                              10                       100




• Where is zero?


ES 021                        Chap 8 - Failure                     23




                            S–N Curves

• Fatigue failure is a statistical event.

• S-N curves are really showing the probability of failure




ES 021                        Chap 8 - Failure                     24
                             The Fatigue Test
• Many ferrous (iron-based) materials
  exhibit a Fatigue Limit (Endurance
  Limit)
   – below this stress amplitude, they will
     not fail by fatigue




• Most non-ferrous materials do not have
  a fatigue limit.

   – Their fatigue strength is usually
     expressed as the maximum stress for
     no failure after some specific number of
     cycles.



   ES 021                         Chap 8 - Failure                    25




                             Fatigue Failures

   • Fatigue failures often leave tell-tale features called “beach marks”
     on the fracture surface.




   ES 021                         Chap 8 - Failure                    26
                        Factors in Fatigue Life

  • Fatigue failure is controlled by “how difficult it is to start and
    propagate a crack”.
  • Anything that makes this process easier will reduce a
    components fatigue life.

        Good Things                                  Bad Things
  • Smooth surfaces                         • Rough surfaces (deep
                                              scratches, dents…)
  • “Hard” surfaces
                                            • Stress concentrations
  • Residual compressive
    stresses (a compressive                 • Corrosive environments
     stress helps to keep a crack
     closed)


  ES 021                        Chap 8 - Failure                           27




                            Fatigue Failure.
  • De Havilland Comet: G-ALYP/6003
      – January 10th 1954




Crashed from 25,000ft                              1290 flights
Further crashes occurred                           Total flying time: 3681 hours

  ES 021                        Chap 8 - Failure                           28
                           Fatigue Failure.

 • De Havilland Comet
     – The Investigation




   Cyclic pressure testing of a grounded aircraft
 ES 021                       Chap 8 - Failure              29




                           Fatigue Failure.

 • De Havilland Comet
     – The Cause of Failure
                            Corner of Hatch         Fatigue Cracks




          Hatch
                                                    Rivet Hole

Fatigue crack propagation from rivet holes



 ES 021                       Chap 8 - Failure              30
                              Fatigue Failure.



 • Improvements following Comet disasters
            • improved design
            • improved inspection
            • improved materials




          Fatigue cracking of fuselages is still relatively common

                                        BUT
             Catastrophic failure of fuselages is not common


 ES 021                             Chap 8 - Failure                        31




                              Fatigue Failure.

 • Aloha Airlines Flight 243
     – April 28th1988                                           90,000 flights
                                                                19 years old


                                                                  All required
                                                                 safety checks
                                                                had been done


                                                                The Problem
                                                               of Old Aircraft
“..at 24,000ft, both pilots heard a load ”clap” or “whooshing” sound, followed by
a wind noise behind them……The captain observed that… there was blue sky
where the first class ceiling had been..”


 ES 021                             Chap 8 - Failure                        32
                       Creep of Materials

• Creep is the time dependent deformation of a material
  subjected to a constant stress. (usually less than the yield stress)



• It is generally only significant when the temperature is greater
  than 0.4×Tm (Tm =melting temperature on an absolute scale)



• A creep test measures strain as a function of time at a
  constant stress and temperature.




ES 021                       Chap 8 - Failure                        33




                         The Creep Test

• The data from a creep test is plotted as strain vs. time




•   Secondary creep is characterized by a constant creep rate.
                                    ∆ε
                             εs =
                             &
                                    ∆t
ES 021                       Chap 8 - Failure                        34
               Stress and Temperature Effects

• Remember that, at any temperature, dislocations will move if a
  large enough stress is applied.

• During the recovery phase of the annealing process:
    – Dislocations were able to rearrange themselves due to the
      increased thermal energy.


• Similarly,
   – increasing the deformation temperature allows
     dislocations to move under a lower applied stress.




ES 021                       Chap 8 - Failure                      35




                         The Creep Test

• Increasing the stress or the temperature has the same general
  effect on the creep behaviour:
    – initial strain increases
    – steady-state creep rate increases
    – rupture life is decreased




ES 021                       Chap 8 - Failure                      36
                           The Creep Test
• Empirical relationships are commonly used to describe the
  steady-state creep rate:

• For a specific temperature:
                                                  ε = K1σ n
                                                  &
   – K1 and n are material constants

• For any temperature:                                        − Qc  n
    – K2 and Qc are constants
                                                  ε = K 2 exp
                                                  &                 σ
                                                              RT 
    – Qc is called the activation energy for creep




ES 021                         Chap 8 - Failure                           37




                           The Creep Test

• The results from a series of creep tests can be plotted on a
  stress-rupture curve.
                                  Find the time to rupture at 538°C if
                                  the stress is 80 MPa.
                                                  ≈ 4 × 103
                                                  ≈ 4000 hrs

                                       What is the maximum service
                                       temperature of a component that
                                       must last 10,000hrs at 50 MPa?

                                             649o C > T > 538o C
                                                  T ≈ 590o C

ES 021                         Chap 8 - Failure                           38
         Mechanisms for Creep Deformation in Metals

• Thermal Activation of Dislocations
    – Increasing the temperature can provide the additional energy
      required to move pinned dislocations



• Diffusion of Atoms
    – Atoms physically move in response to the applied stress




ES 021                       Chap 8 - Failure                        39




                 Improving Creep Resistance




ES 021                       Chap 8 - Failure                        40
                                 Summary

• How do materials fail?
    – Plastically deform:
          • accumulate damage,
          • reduce in area,
          • fracture
    – Fracture due to existing defects
    – Cyclic loading
          • Propagate cracks by fatigue processes,
          • fracture
    – Deform by creep at elevated temperatures,
          • accumulate damage,
          • reduce in area,
          • fracture




ES 021                           Chap 8 - Failure                       41




                                 Summary

• In Chapters 7 and 8, we have covered the types of tests used to
  determine the material properties used by engineers to design
  load bearing components.

• These are the issues that you will have to consider in your
  designs.
    –    Static Loads – Tensile (compressive) properties
    –    Dynamic Loads – Impact, Fatigue
    –    Detectable or known flaws – Fracture Mechanics
    –    Temperature Effects – Tensile properties, Impact, Creep



    – Environmental Aspects – corrosion, abrasion, chemical reactions




ES 021                           Chap 8 - Failure                       42

				
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