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CHAPTER 11

CHAPTER 11. Mechanical Properties ： Failure and Fracture Mechanics Mechanical Properties of Ceramics. 11-I. Failure and Fracture Mechanics A. Fundamentals of Fracture.

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CHAPTER 11

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  1. CHAPTER 11 Mechanical Properties： Failure and Fracture MechanicsMechanical Properties of Ceramics

  2. 11-I. Failure and Fracture Mechanics A. Fundamentals of Fracture ◎ Simple fracture (斷裂): separation of a body into two or more pieces in response to an imposed stress (tensile, compressive, shear, or torsional; the present discussion : uniaxial(單軸) tensile loads.) ◎ two fracture modes (模式) : ductile and brittle. (based on the ability of a material to experience plastic deformation.) F 6-13

  3. ◎Any fracture process involves two steps---crack formation (裂痕生成) and propagation (裂痕擴張) A-1. Ductile fracture (1) extensive(大幅度地) plastic deformation with high energy absorption before fracture; (2) proceeds relatively slowly; such a crack is often said to be stable: (3) evidence(證據) of appreciable(明顯地) gross deformation at the fracture surfaces(斷裂面) F 6-11 F8.3

  4. A-2. Brittle fracture • may proceed extremely rapidly; • very little or no plastic deformation with low energy absorption; • such cracks may be said to be unstable : once started, will continue spontaneously without an increase in magnitude of the applied stress. • ◎ Ductile fracture is almost always preferred : • First, presence of plastic deformation gives warning (警告) • Second, more strain energy is required to induce(引發) fracture. • ◎ most metal alloys : ductile • ceramics : brittle • polymers: may exhibit both types of fracture. T 8-1 F 6-13 F8.3

  5. B. Fracture Phenomena B-1. Ductile Fracture F 8-1 • ◎ extremely soft metals, e.g., pure gold and lead at room • temperature; other metals, polymers, and inorganic glasses • at elevated temperatures.(高溫) • ˙neck down to a point • ˙showing virtually100% reduction in area. • ◎ common ductile metals • ˙only a moderate amount of necking • ˙fracture process (several stages) : • (1) after necking begins, small cavities(孔洞), or • microvoids (微小之孔隙), form; F 8-2

  6. (2) microvoids enlarge(變大), come together, and coalesce(聚合) to form an elliptical (橢圓形) crack, (3) fracture by shear deformation at an angle of about 45° (the shear stress is a maximum.) ˙cup-and-cone fracture ˙interior region : irregular(不規則的) and fibrous (纖維狀的) appearance (外觀) ˙studies of this type : fractographic (using scanning electron microscopy) ˙“dimples”(半圓凹洞), each dimple : one half of a microvoid, spherical or elongated (C-shaped) : indicative (顯示) of shear failure. F 8-3 F 8-4

  7. B-2. Brittle Fracture F 8-5 ◎ in some steel pieces : a series of V-shaped “chevron” markings (痕跡) ◎ Other brittle fracture surfaces : lines or ridges(線痕) that radiate from the origin of the crack in a fanlike (風扇型的) pattern ◎ amorphous materials (e.g. ceramic glasses) : shiny and smooth surface. ◎ most brittle crystalline materials : breaking bonds along specific crystallographic planes (cleavage).

  8. ◎ Fracture of polycrystalline material F 8-6 ˙transgranular (or transcrystalline(穿晶斷裂)) : the fracture cracks pass through the grains (a grainy or faceted texture) ˙ Intergranular(沿晶斷裂): crack propagation is along grain boundaries. three-dimensional nature of the grains may be seen. F 8-7 C. Principals of fracture mechanics (破斷力學)： Stress Concentration(應力集中) ： Experimentally measured fracture strengths are significantly lower than theoreticalcalculations (based on bonding energies): existance of very small, microscopic flaws or cracks an applied stress is amplified(放大) or concentrated at the trip(端點)： Stress Concentration 51

  9. ◎ flaws or cracks： stress raisers ◎ The maximum stress, : (8.1) : magnitude of the nominal applied tensile stress, : radius of curvature of the crack tip a : length of a surface crack, or half of the length of an internal crack. F 8-8

  10. (8.2) ˙effect of a stress raiser is more significant in brittle than in ductile materials. (a ductile material, plastic deformation causes more uniform distribution of stress in the vicinity of the stress raiser) ◎ stress concentration factor Kt :

  11. 11-II. Mechanical Properties of Ceramics The principal drawback: fracture in a brittle manner with very little energy absorption. A. Brittle Fracture Of Ceramics ◎ The brittle fracture process consists of the formationand propagation of cracks: through the grains (i.e., transgranular ) and along specific crystallographic (or cleavage) planes, planes of high atomic density.

  12. ◎ The measured fracture strengths are substantially lower than predicted by theory from interatomic bonding forces: explained by very small and omnipresent flaws that serve as stress raisers according to Equation 8.1, minute surface or interior cracks(microcracks), internal pores, and grain corners. For example, even moisture and contaminants in the atomosphere can introduce surface crracks in freshly drawn glass fibers. ◎ The measure of a ceramic material’s ability to resist fracture when a crack is present is specified in terms of fracture toughness. The plane strain fracture toughness KIC (12.2) Y: dimensionless that depends on both specimen and crack geometries,: applied stress, a: length of a surface crack or half of the length of an internal crack. Crack propagation will not occur as long as the right-hand side of Equation 12.2 is less than the plane strain fracture toughness of the material. KIC for ceramic materials are smaller than for metals. F12-28

  13. ◎ Under some circumstances, specifically when moisture is present in the atmosphere, fracture of ceramic materials will occur by the slow propagation of cracks: static fatigue, or delayed fracture. ◎ Considerable variation and scatter in the fracture strength for many specimens of a specific brittle ceramic material: dependence of fracture strength on the probability of the existence of a flaw that is capable of initiating a crack, depending on fabrication technique, subsequenttreatment and specimen aize ◎ For compressive stresses, there is no stress amplification associated with any existent flaws: brittle ceramics display much higher strengths in compression than in tension (on the order of a factor of 10)

  14. B. Stress-Strain Behavior ：FLEXURAL STRENGTH F12-29 F6-2 F6-3 F6-3 ◎ The stress-strain behavior of brittle ceramics is not usuallyascertained by a tensile test as outlined in section 6.2, for three reasons: ˙It is difficult to preapare and test specimens having the required geometry. ˙ it is difficult to grip brittle materials without fracturing them; ˙Ceramics fail after only about 0.1% strain, specimens must be perfectly aligned to avoid the presence of bending stresses. ◎ A more suitable transverse bending test is most frequently employed: a rod specimen is bent until fracture using a three or four- point loadingtechnique: flexure test.

  15. ◎ The stress at fracture using this flexure test is known as the flexural strength, modulus of rupture, fracture strength, or bend strength, an important mechanical paramenter for brittle ceramics. ◎ For a rectangular cross section, the flexural strength fs is equal to (12.3a) 12.29 Ff: load at fracture, L: distance between support points, when the cross section is circular T12.5 (12.3b)

  16. ◎ During bending, a specimen is subjected to both compressive and tensile stresses, fs will depend on specimen size; with increasing specimen volume (under stress ) there is an increase in the probability of the existence of a crack-producing flaw and, consequently, a decrease in flexural strength C. ELASTIC BEHAVIOR F12-30 ◎ Elastic stress-strain behavior: using flexure tests a linear relationship exists between stress and strain; the slope: modulus of elasticity. ◎ Most ceramis: do not experience plastic deformation prior to fracture D. Mechanisms of Plastic Deformation At room temperature, most ceramic materials suffer fracture before the onset of plastic deformation. Plastic deformation is different for crystalline and noncrystalline ceramics

  17. E. CRYSTALLINE CERAMICS F7-1 F7-2 F7-3 f2-4-5 ◎ Plastic deformation occurs, as with metals, by the motion of dislocations(Chapter7). One reason for the hardness and brittleness: difficulty ofslip (or dislocation motion). ◎ For bonding predominantly ionic, there are very few slip systems. This is a consequence of the electrically charged nature of the ions, ions of like charge are brought into close proximity to one another. For bonding highly covalent, slip is also difficult and they are brittle (1) the covalent bonds are relatively strong, (2) there are also limited numbers of slip systems, and (3) dislocation structures are complex.

  18. F. NONCRYSTALLINE CERAMICS Does not occur by dislocation motion: noncrystalline ceramics have no regular atomic structure , these materials deform by viscous flow, same manner in which liquids deform. Atoms or ions slide past one another by the breaking and reforming of interatomic bonds . There is no prescribed manner or direction . Viscoity: a measure of a noncrystalline material’s resistance to deformation. The viscosity  shear stress  and change in velocity dv with distance dy: F12-31 (12.4) As the temperature is raised, an attendant decrease in viscosity.

  19. G. Miscellaneous Mechanical Considerations ◎ INFLUENCE OF POROSITY F13-13 F13-14 F13-15 ˙Subsequent to compaction or forming of ceramic powders into the desired shape, heat treatment, and sintering: some resiural porosity will remain (Figure 13.15), any residual porosity will havea deleterious influence on mechanical properties (and also on thermal, electrical and optical properties.) (G-1) Effects on elastic properties and strength Modulus of elasticity E decreases with volume fraciton porosity P: F12-32 (12.5)

  20. Eo: modulus of elaticity of the nonporous material. Porosity is deleterious to the flexural strength for two reasons; (1) pores reduce the cross-sectional area (2) they also act as stress concentrators – for an isolated spherical pore, an applied tensile stress is amplified by a factor of 2 . For example, 10 vol%porosity will decrease the flexural strength by 50% Flexural strength decreases exponentially with volume fraction porosity (p): (G-2) Effects on flexural strength (12.6) F12-33 0 and n are experimental constants

  21. H. HARDNESS T12.6 One beneficial mechanical property of ceramics is their hardness, the hardest known materials are ceramics I. CREEP A result of exposure to stresses (usually compressive) at elevated temperatures. Similar to that of metals (Section 8.14)

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