IMPERFECTIONSFOR BENEFIT. Sub-topics. Point defects Linear defects dislocations Plastic deformation through dislocations motion Surface

Transcription

1 IMPERFECTIONSFOR BENEFIT Sub-topics 1 Point defects Linear defects dislocations Plastic deformation through dislocations motion Surface

2 IDEAL STRENGTH Ideally, the strength of a material is the force necessary to break inter-atomic bonds 2

3 DEFECTS IN CRYSTALLINE STRUCTURES 3

4 CRYSTALS ALWAYS CONTAIN DEFECTS A vacancy is a site at which an atom is missing while vacancies play a role in diffusion, creep, and sintering, they do not influence strength Total number of atomic sites Energy required for the formation of a vacancy Point defects: 0.1 nm (10-10 m) 4 Temperature

5 SOLUTE ATOMS Substitutional solid solution dissolved atoms replace those of the host Interstitial solid solution dissolved atoms squeeze into spaces or interstices between the host atoms Dissolved atoms rarely have the same size as the host material, so the surrounding lattice is distorted Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

6 SELF-INTERSTITIAL DEFECT Large distortions in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated The formation of this defect is not highly probable, and it exists in very small concentrations, which are significantly lower than for vacancies. 6

7 IMPURITY ATOMS substitutional impurity atom interstitial impurity atom Material properties can be altered significantly through the addition of impurity atoms 7

8 INTERSTITIAL DEFECTS 8

9 SUBSTITUTIONAL DEFECTS 9

10 POINT DEFECTS IN CERAMICS cation interstitial anion vacancy cation vacancy a cation vacancy anion vacancy pair a cation vacancy and a cation interstitial pair. Frenkel defect Schottky defect 10

11 SUMMARY OF POINT DEFECTS vacancy interstitial atom small substitutional atom (c) 2003 Brooks/Cole Publishing / Thomson Learning large substitutional atom Frenkel defect Schottky defect 11 a cation vacancy and a cation interstitial pair. a cation vacancy anion vacancy pair

12 DEFECTS FOR PLASTICITY Crystals all contain line defects known as dislocations Dislocated = out of joint Dislocations act as the main source of plastic deformation in crystalline materials A dislocation is an extra half-plane of atoms in the crystal in the figure, the upper part of the crystal has one more double-layer of atoms than the lower part dislocations distort the lattice and make metals soft and ductile 12

13 ENERGY OF DISLOCATIONS Dislocations distort the lattice The magnitude of distortion decreases with distance away from the dislocation line Elastic energy associated with them If they cost energy, why are they there? All metals initially contain an appreciable number of dislocations produced from the growth of the crystal from the melt or vapour phase. Irregular grain boundaries are believed to be responsible for emitting dislocations. Dislocation can be formed by aggregation and collapse of vacancies. Heterogeneous nucleation of dislocations is possible from high local stresses at second-phase particles or as a result of phase transformation. 13

14 STRESSES AROUND DISLOCATION CORE The atoms above the dislocation line are squeezed together The atoms below are pulled apart The free energy of a dislocation is the sum of a number of terms: (i) the core energy (within a radius of about three lattice planes from the dislocation core); (ii) the elastic strain energy outside the core and extending to the boundaries of the crystal, and (iii) the free energy arising from the entropy contributions 14

15 CHARACTERISTICS OF DISLOCATIONS The magnitude and direction of the lattice distortion is expressed in terms of a Burgers vector For metallic materials, the Burgers vector is in a close-packed crystallographic direction and is of magnitude equal to the interatomic spacing. edge dislocation The Burgers vector is significant in determining the yield strength of a material by affecting solute hardening, precipitation hardening and work hardening. 15

16 BURGERS VECTOR To determine the Burgers vector of a dislocation in a two-dimensional primitive square lattice, proceed as follows: Trace around the end of the dislocation plane to form a closed loop. Record the number of lattice vectors travelled along each side of the loop (shown here by the numbers in the boxes): In a perfect lattice, trace out the same path, moving the same number of lattice vectors along each direction as before. This loop will not be complete, and the closure failure is the Burgers vector: 16

17 DISLOCATIONS AND PLASTICITY The concept of the dislocation was invented independently by Orowan, Taylor and Polanyi in 1934 as a way of explaining two key observations about the plastic deformation of crystalline material: o The stress required to plastically deform a crystal is much less than the stress one calculates from considering a defect-free crystal structure o Materials work-harden: when a material has been plastically deformed it subsequently requires a greater stress to deform further. The existence of dislocations experimentally was verified in 1947 A transmission electron micrograph of a titanium alloy in which the dark lines are dislocations 17

18 DISLOCATIONS IN 2D A 'raft' of equally sized bubbles floating on the surface of a liquid is a good large-scale model of a single plane of atoms in a crystal structure. The forces between the bubbles mimic the forces between atoms in a crystal. The bubbles pack to form a close-packed plane. If the raft is made carefully, it is possible to see a variety of structural features in the raft that also occur in real crystal structures, such as grain boundaries, vacancies, dislocations and solute 'atoms'. 18

19 DISLOCATIONS AND PLASTIC DEFORMATION Plastic deformation corresponds to the motion of large numbers of dislocations. When a shear stress is applied to the dislocation, the atoms are displaced, causing the dislocation to move one Burgers vector in the slip direction Continued movement of the dislocation eventually creates a step The crystal is deformed 19

20 PLASTIC DEFORMATION From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then reforming bonds with new neighbors as large numbers of atoms or molecules move relative to one another 20

21 DISLOCATIONS AND PLASTIC FLOW The edge dislocation is made by cutting, slipping, and rejoining bonds across a slip plane The dislocation line separates the part of the plane that has slipped from the part that has not Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

22 EDGE DISLOCATIONS The formation of a step on the surface of a crystal by the motion ofan edge dislocation Dislocation line moves in the direction of the applied shear stress 22

23 When a dislocation moves it makes the material above the slip plane slide relative to that below (a): Initially perfect crystal (b) (d): the passage of the dislocation across the slip plane shears the upper part of the crystal over the lower part by the slip vector b; when it leaves the crystal has suffered a shear strain γ Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

24 WHY DOES A SHEAR STRESS MAKE DISLOCATION MOVE? Representation of the analogy between caterpillar and dislocation motion In the different loading conditions, dislocations tend to move mainly along different sets of directions. Dislocation motion along a crystallographic direction is called glide or slip. The direction along which dislocations generally move is that with the highest resolved shear stress -the component of an applied stress that acts along a slip direction in a slip plane. 24

25 SCREW DISLOCATIONS The upper front region of the crystal is shifted one atomic distance to the right relative to the bottom portion 25

26 SCREW DISLOCATIONS The formation of a step on the surface of a crystal by the motion of a screw dislocation. The dislocation line motion is perpendicular to the stress direction 26

27 DISLOCATION MOVEMENT For a dislocation to move, only bonds along the line it moves must be broken this is significantly easier than braking all of the bonds in the plane In crystals there are preferred planes and directions for which dislocation movement is easier these are called the slip planes and slip directions Slip displacements are tiny however, if a large number of dislocations traverse a crystal, moving on many planes, the material deforms at a macroscopic level 27

28 DISLOCATION SLIP Slip - The process by which a dislocation moves and deforms a material. Dislocations do not move with the same degree of ease on all crystallographic planes of atoms and in all crystallographic directions. Slip direction - The direction in which a dislocation moves. Slip plane - The plane of preferred dislocation movement. Slip systems - The combination of the slip direction and slip plane makes up the slip system 28

29 SLIP PLANES The crystallographic plane along which the dislocation line moves is the slip plane The slip system depends on the crystal structure For a particular crystal structure, the slip plane is that plane having the most dense atomic packing, that is, has the greatest planar density. 29

30 SLIP SYSTEMS IN FCC How many slip systems are there in FCC cell? There are 12 slip systems: four unique {111} planes and, within each plane, three independent <110> directions. Metals with FCC or BCC crystal structures have a relatively large number of slip systems (at least 12) Three slip directions These metals are quite ductile because extensive plastic deformation is normally possible along the various systems. 30 HCP metals, having few active slip systems, are normally quite brittle.

31 Crystals resist the motion of dislocations with a friction-like resistance f per unit length Dislocations move from an applied shear stress τ as they move the upper half of the crystal shifts relative to the lower half by a distance b Dislocations move if τ exceeds f/b Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

32 INTERACTION OF DISLOCATIONS When metals are plastically deformed, some fraction of the deformation energy (~ 5%) is retained internally; the remainder is dissipated as heat. The major portion of this stored energy is as strain energy associated with dislocations. There are regions in which compressive, tensile, and shear lattice strains are imposed on the neighboring atoms The strains extend into the surrounding atoms, and their magnitudes decrease with radial distance from the dislocation. The atoms near core of dislocation are displaced from their proper places -> higher potential energy -> to keep the energy as low as possible, the dislocations should be as short as possible Lattice strains. Slight displacements of atoms relative to their normal lattice positions, normally imposed by crystalline defects such as dislocations, and interstitial and impurity atoms. Line tension: T ½ Eb 2 32

33 DISLOCATIONS INTERACTIONS: REPULSION The strain fields surrounding dislocations in close proximity to one another may interact such that forces are imposed on each dislocation by the combined interactions of all its neighboring dislocations. Two edge dislocations of the same sign and lying on the same slip plane exert a repulsive force on each other Explain why? C and T denote compression and tensile regions, respectively. 33

34 DISLOCATIONS INTERACTIONS: ANNIHILATION Edge dislocations of opposite sign and lying on the same slip plane exert an attractive force on each other. Upon meeting, they annihilate each other and leave a region of perfect crystal. 34

35 DEFORMATION BY TWINNING In addition to slip, plastic deformation in some metallic materials can occur by the formation of mechanical twins, or twinning A shear force can produce atomic displacements such that on one side of a plane (the twin boundary), atoms are located in mirror image positions of atoms on the other side Open circles represent atoms that did not change position; dashed and solid circles represent original and final atom positions, respectively 35

36 TWINNING twinning occurs on a definite crystallographic plane and in a specific direction that depend on crystal structure 36

37 MECHANISMS OF DEFORMATION For a single crystal subjected to a shear stress, (a) deformation by slip; (b) deformation by twinning. 37

38 WHY MOST OF CERAMICS ARE BRITTLE (NOT PLASTIC)? ceramics Plastic deformation occurs by the motion of dislocations. So, what is the problem? 38

39 When the shear stress acts on an aggregate of crystals, some crystals will have their slip planes oriented favorably with respect to the shear stress In samples that have many grains, the tensile stress required to cause yielding is approximately three times the shear strength of a single crystal

40 GRAIN BOUNDARIES Grain boundaries form when differently oriented crystals meet the individual crystals are called grains, the meeting surfaces are grain boundaries

41 POLYCRYSTALLINE STRUCTURE The grain boundaries is a narrow zone where the atoms are not properly spaced Grain boundaries may be also considered as defects! 41

42 GRAIN BOUNDARIES Boundaries can be described in terms of dislocation arrays The atoms are bonded less regularly along a grain boundary, there is an interfacial or grain boundary energy 42

43 SLIP LINES ON THE SURFACE OF A POLYCRYSTALLINE SPECIMEN Slip lines on the surface of a polycrystalline specimen of copper that was polished and subsequently deformed 43

44 NANOSTRUCTURED SOLIDS Relative to microstructural features of micro-grained metals and alloys, the nano-structured materials contain a higher fraction of grain boundary volume (for example, for a grain size of 10 nm, between 14 and 27% of all atoms reside in a region within nm of a grain boundary); therefore, grain boundaries play a significant role in the materials properties. 44

45 GRAIN BOUNDARIES IN NANOMETALS Crystals contain internal interfacial defects, know as grain boundaries, where the lattice orientation changes The misfit between adjacent crystallites in the grain boundaries changes the atomic structure (e.g. the average atomic density, the nearestneighbor coordination, etc.) of materials. At high defect densities the volume fraction of defects becomes comparable with the volume fraction of the crystalline regions. In fact, this is the case if the crystal diameter becomes comparable with the thickness of the interfaces. Non equilibrium materials DEFECTS!!! 45

46 WHY NANOSTRUCTURED POLYCRYSTALLINE MATERIALS ARE UNSTABLE? Disclinations and grain boundary dislocations form elastically distorted layers (zones) near grain boundaries. High density of defects -> High energy Nature -> seeks to lower energy Grain growth occurs in materials to reduce the overall energy of the system by reducing the total grain boundary energy. Therefore, grain growth in NC materials is primarily driven by the excess energy stored in the grain or interphase boundaries. 46

47 PLASTIC FLOW IN POLYMERS the interactions between lamellar and intervening amorphous regions in response to an applied tensile load. 47

48 MATERIAL SURFACE Surface is also a defect!! 48