Mechanical properties of Solids Mechanical properties

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Mechanical properties of Solids Mechanical properties Powered By Docstoc
					DC Levendis                                                                                    15 February 2010




              Mechanical properties of Solids
               Mechanical properties

               Compressive or tensile stress
               Hardness
                 Other properties:-
                 Impact energy
                 Fracture toughness
                 Fatigue
                 Creep (used in the field of tribology)


               READ (i) Section from Shackelford “Introduction to materials science
               for engineers” (ii) Section on BN: Inorganic Chemistry by Shriver &
               Atkins
               and www.doitpoms.ac.uk/tlplib/mechanical-testing/index.php



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              Mechanical properties
                While it is very common to associate properties with a metal, it is possible
                to produce a wide range of properties from the same material, by varying
                the composition slightly, or by varying its processing. The different ways
                of processing a metal include how it has been cooled and worked, and any
                heat treatments it has been subjected to.
                These processes and compositional changes affect the microstructure of
                the material, in particular the grain shape and size and the dislocation
                density, as well as phase structure and precipitates.




                Use the www.matter.org.uk/glossary links for definitions


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DC Levendis                                                                     15 February 2010




              Factors used to measure mechanical
              properties:

                    •E.g
                    •Bulk modulus


                    •Young’s modulus




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              Bulk Modulus

               Compressibility and Bulk modulus
                               •response to stress is given by
                               coefficients of proportionality (‘moduli’)
                               •The bulk modulus (K) of a substance
                               measures the substance's resistance to
                               uniform compression. It is defined as
                               the pressure increase needed to cause a
                               given relative decrease in volume. (Units
                               in Pa or GPa)



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DC Levendis                                                                            15 February 2010




                  Bulk Modulus

                        Examples of bulk modulus for
                        selected materials

                •Bulk modulus (K) is the inverse of compressibility (κ) and is a
                measure of hardness:                             1
                                                          κ             ∂V
                •C (diamond)              442 GPa
                                                              =− V (       )T
                •C (nanorods)             491 GPa                       ∂P
                •Au (fcc metal)           220 GPa
                                                                    κ       1
                •Cu (fcc metal)           140 GPa                       =
                                                                            κ
                •W (bcc metal)            310 GPa
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                  Bulk Modulus of Elements

                        Bulk modulus of elements in the periodic
                        table

                •C (diamond) 442.3 GPa
                •C (nanorods) 491 GPa
                •B           320 GPa
                •Au (fcc metal) 220 GPa
                •Cu (fcc metal) 140 GPa
                •W (bcc metal) 310 GPa


              www.webelements.com/


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DC Levendis                                                           15 February 2010




              Stress and Strain in Materials
                Types and definitions
                Stress strain curves
                Alloys
                Calculations at the atomic scale
                Examples: Precipitation hardening
                Heat treatment




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              Mechanical properties
                  Responses to stress (various types of stress:
                tensile, compressive, uniaxial, isotropic)
                   – Qualitatively, consider: rubber (elastic?)
                   –           glass rod, ceramic (brittle)
                   –           copper metal, plastic (ductile)




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DC Levendis                                                                                        15 February 2010




              Mechanical properties
                                                  Definitions
                    Tensile stress
                                      (σ
                      –tensile stress (σ) σ = Force/(cross section area)
                           σ = F/A                        (units?)




                             Look up the difference between nominal stress and true stress
                             www.doitpoms.ac.uk/tlplib/mechanical-testing/stress-strain.php    9




              Mechanical properties
                                                  Definitions
                                                                                   strain.
                   There are two main types of strain - elastic strain and plastic strain.
                                                                            reversible.
                   Elastic strain is the stretching of atomic bonds, and is reversible.
                   Elastic strain can be related to the stress by Hooke's law : σ = Y ε


                   Tensile strain (ε) :
                      distortion of the sample
                      ε = (change in length)/(original length)
                                            ε = Δl/l

                      strain,
              Plastic strain, or plastic flow, is irreversible deformation of a material.
              There is no equation to relate the stress to plastic strain.


                             Look up the difference between nominal strain and true strain
                             www.doitpoms.ac.uk/tlplib/mechanical-testing/stress-strain.php   10




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DC Levendis                                               15 February 2010




              Experimental measurement of stress
              and strain




                                tensometer



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              Interpretation at the atomic vs. the
              microscopic levels (vs. macroscopic)




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DC Levendis                                                                                            15 February 2010




              Interpretation at the atomic level:
              elastic deformation: stretching of
              atomic bonds




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              Interpretation at the atomic level:
              Plastic deformation: Slip planes (ductility,
              assuming no defects)




                                                                In general ccp metals (Cu, Au)
                                                                are more ductile than hcp metals
                                                                     Cd)
                                                                (Zn, Cd)
                                                                The modulus of elasticity often
                                                                depends on the direction along
                                                                which the stress is applied (i.e. it
                                                                                            (i.e.
                                                                is anisotropic)

              Slip in CCP metals differs to HCP metals

                      www.doitpoms.ac.uk/tlplib/slip/slip_in_ccp.php                           14




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DC Levendis                                                                15 February 2010




              Grain boundaries shown using HRTEM




                          SrTiO3 grain boundaries.




                     www.doitpoms.ac.uk/tlplib/slip/slip_in_ccp.php   15




              Stress-strain curves
                strength, ductility and toughness




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DC Levendis                                                                                   15 February 2010




               Stress-strain curves
                 strength, ductility and toughness




              A - limit of proportionality
              B - yield stress
              E - final instability point / failure point
              F - fracture stress


                         •Look up definitions of Hooke’s law, Young’s modulus
                         •See www.doitpoms.ac.uk/tlplib/mechanical-testing/theory1.php
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                         •See Shackleford handout




               Hooke’s law is obeyed at small strain. The material is
               elastic in this region

                                              σ=Yε

                       where Y (or E) is Young’s modulus, or the modulus of
                       elasticity, for the solid (gives a measure of ‘stiffness’)

                      The ratio of an applied normal stress, σ to the resultant
                            normal strain, e in the direction of loading
                                               Y = σ/ε
                     The relation applies only for strains up to an elastic limit,
                         which is of order of 0.1-1.0% for most materials.

                    Values of Y range from ~0.01 GPa for rubbers, through ~1-
                     10 GPa for ceramic (fibres) and 1000 GPa for diamond.




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DC Levendis                                                                                 15 February 2010




                 Example: The interatomic distance along the <111>
                 direction in α-Fe (bcc) (i.e. along the body diagonal) is
                 2.480Å (measured crystallographically). When a tensile
                 stress of 1000MPa is applied along the <111> direction,
                 this interatomic distance increases to 2.489Å.
              Calculate the modulus of elasticity (Young’s modulus)
              along the <111> direction of α-Fe
                 σ=Yε

                              (2.489-
                Therefore ε = (2.489-2.480)/2.480 = 0.00363
               Y = 1000MPa/(0.00363) = 275GPa

              Note that 275GPa is the maximum Y for Fe. The minimum
              is 125GPa along the <100> direction.
                                            atom-
              Exercise: (i) Calculate the atom-atom distance along the <100> direction
                        a-                      Fe.                    atom-
              (i.e. the a-axis) in unstressed α-Fe. (ii) Calculate the atom-atom distance
              along the <100> direction under a tensile stress of 1000MPa.
                                                                  [Ans: 2.864Å; 2.887Å]
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                 Stress-strain curves
                   strength, ductility and toughness




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DC Levendis                                                15 February 2010




              Stress-strain curves
                high- and low- strength materials




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              Tensile test data for selected alloys




              Al2O3     380       ~1000
              SiC       470       170

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DC Levendis                                                                                 15 February 2010




                  Steel
                 In metallurgy, stainless steel is defined as a steel
                 alloy with a minimum of 10% chromium content by
                 mass.[1] Stainless steel does not stain, corrode, or
                 rust as easily as ordinary steel (it stains less), but it is
                 not stain-proof

                 Stainless steel differs from carbon steel by amount of
                 chromium present. Carbon steel rusts when exposed
                 to air and moisture.




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              Example: Precipitation hardening in alloys:
              Al with 4%wtCu




                    http://www.doitpoms.ac.uk/tlplib/mechanical-testing/results1.php   24




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DC Levendis                                                                                15 February 2010




              Example: annealed copper




                   http://www.doitpoms.ac.uk/tlplib/mechanical-testing/results2.php   25




              Example: annealed copper compared with
              work hardened copper


                See videoclips




                   http://www.doitpoms.ac.uk/tlplib/mechanical-testing/               26




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DC Levendis                                                                                                15 February 2010




                       Other mechanical properties

                   Hardness
                   Impact energy
                   Fracture toughness
                   Fatigue                  Aluminium Crank Arm.
                                            Dark area: slow crack growth. Bright
                   Creep                    area: sudden fracture.

                   Wear ( used in the field of tribology




              Gas turbine            Failed blade
                                                  thermal mechanical failure                         27
              compressor blade failure                                         creep           oxidation




                       Creep
                       Creep is the tendency of a solid material to slowly move or deform
                       permanently under the influence of stresses. It occurs as a result of long
                       term exposure to levels of stress that are below the yield strength of the
                       material.

                       When a material is subjected to a stress that is greater than or equal to
                       its yield stress, the material deforms plastically. When the stress is
                       below this level, then in principle it should only deform elastically.

                       However, provided the temperature is relatively high (see later for the
                       meaning of this), plastic deformation can occur even when the stress is
                       lower than the yield stress. This deformation is time-dependent and is
                       known as creep.




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DC Levendis                                                                         15 February 2010




               Hardness
                A measure of a material's resistance to localised plastic
                deformation. A number of different hardness tests are widely
                used, including:

                    •the Vickers (diamond pyramid) test

                    •the Brinell test

                    •the Rockwell test.




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               Hardness
              Abrasive hardness as a function of lattice
               enthalpy density
                    OsB2 and AlMgB14




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DC Levendis                                                                                         15 February 2010




                                Hardness: indentation

              MOHS
              HARDNESS
              SCALE
              (of little use
              to Materials
              Scientists)


              Brinell hardness number is approximately
                 proportional to tensile strength
                 Vickers
                 Knoop
                 Rockwell
                 Nano-
                 Nano-indentation (AFM)


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                     Fatigue


                 In materials science, fatigue is the progressive and localized structural
                 damage that occurs when a material is subjected to cyclic loading.

                 The failure of a structure subjected to repeated loading at stress levels below
                 those required to cause general yielding. The process of fatigue may involve
                 the initiation and growth of cracks from stress concentrations. However, the
                 initiation stage is often by-passed since micro-cracks are usually introduced
                 into a structure during processing.




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DC Levendis                                                                                     15 February 2010




                  Fracture toughness


              A measure of the resistance offered by a material to the propagation of crack
              within it.

              Fracture toughness is denoted KIc and has the units of                   .

              Material                                      KIc (MPa-m1/2)
              Aluminium alloy                               24
              Steel                                         50
              Ti alloy                                      44-66

              Aluminium oxide                               3-5
              SiC                                           3-5
              Soda-lime glass                               0.7
              Concrete                                      0.2-1.4

              Polymers (polystyrene)                        ~1.0

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              Carbon nanotubes




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DC Levendis                                                                               15 February 2010




                Carbon nanotubes



              Material Young's Mod (TPa) Tensile strength (GPa) Elongation at break (%)
              SWNT     ~1 (from 1 to 5)      13–53                   16(#)
              Stainless Steel ~0.2           ~0.65–3                 15–50
              Kevlar   ~0.15                 ~3.5                    ~2


              •Can hold ~5000 kg on a cable with cross-section of 1 mm2.
              •Low density: specific strength of up to 48,000 kN·m·kg−1
              (best of known materials). cf high-carbon steel 154 kN·m·kg−1.

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                Space elevators




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