Chap 8
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Fracture; microscopic aspects
Crack nucleation • Nucleation of a crack in a perfect crystal essentially involves the rupture of interatomic bonds. Stress for crack nucleation = theoretical cohesive stress (~E/30). • Ordinary materials break at stress ~E/104, because of the existence of surface or internal defects and the plastic deformation that precedes fracture. – Fracture stress in whiskers can approach the theoretical value.
• The brittleness of a material is related to the behavior of dislocations in the region of crack nucleation. – In brittle materials, dislocations are practically immobile. – In semibrittle materials, dislocations are mobile, but only on a restricted number of slip systems. – In ductile materials, there are no restrictions on dislocation movement.
• Ductile fracture in metals – Nucleation, growth and coalescence of voids (usually starts at second-phase particles) – Dimple
– Continuous reduction in cross-sectional area (in high purity metals) – Shearing along a plane of maximum shear
Pure metal under uniaxial tension • Dislocations can move on a large number of slip systems. • Crystal deforms plastically until the start of plastic instability (necking). • Then, the deformation is concentrated in the neck until the crystal separates along a line or a point.
•
Cracks can be nucleated by the grouping of dislocations pile up against a barrier – Crack nucleation depends on stress relaxation at the other side of the barrier.
• Lattice rotation associated with the bend plane and intersection of twin boundaries can nucleate cracks.
Cracking or cavitation at high temperature • w-type crack – stress concentration at triple junction due to GB sliding.
• r-type cavitation – Small cavities formed at GBs approximately normal to the tensile stress.
•
Microcavities nucleated at second-phase particles – –
•
break of second-phase particle separation of particle/matrix interface
Generally, the voids nucleate at small plastic strains. The microcavities grow with dislocation slip. The materials between the voids undergoes necking on a microscopic scale.
Fracture by void nucleation, growth and coalesence • •
Nucleation, growth and coalescence of microcavities gives the fracture appearance consisting of small “dimples”. “cup-and cone” fracture in cylindrical tensile specimens
• Voids are nucleated ahead of the crack. • Void grows and eventually coalesces with the main crack.
• The size, separation, and interfacial bonding of particles determine the characteristics of ductile cracks, and the ductility of the materials. • lnAo/Af (reduction of area) – Ao: initial cross-sectional area; Af: final cross-sectional area at fracture point
• • • • •
“Ductility” signifies a material’s capacity to undergo plastic deformation. “Ductility” is not a fundamental property of a material. It depends on the state of stress, strain rate, temperature, environment, and prior strain history of the material. A high temperature (or a low strain rate) leads to high ductility. A low temperature (or high strain rate) leads to low ductility. An increase in the degree of stress triaxiality results in a decrease in the ductility of the material. Stress state depends on external loading, geometry of structure, thermal stress, etc. σ1 > σ 2 > σ 3
εo : the plastic strain at fracture in uniaxial tension ε1: the maximum principal plastic strain at fracture Tensile stress Shear stress
Fracture Plastic strain
Brittle, or Cleavage Fracture •
• • •
Transgranular cleavage occurs by direct separation along specific crystallographic planes by means of a simple rupturing of atomic bonds. – Cleavage along (100) planes in BCC structure (such as Fe) Tendency for cleavage fracture increases with an increase in strain rate or a decrease in temperature. Ductile-brittle transition temperature (DBTT) increases with strain rate. The ductile fracture needs a lot more energy than the brittle fracture.
Cleavage Fracture • • •
Adjacent grains have different orientations. Cleavage crack changes direction at GB. Shinny appearance River markings – Cleavage steps can be initiated by the passage of screw dislocation. – Cleavage step is parallel to the crack propagation direction. – Crack change direction at various points along GB. – As the crack propagates, the steps will group together to form river pattern.
Formation of cleavage steps • River markings – Cleavage steps can be initiated by the passage of screw dislocation. – Cleavage step is parallel to the crack propagation direction. – Crack change direction at various points along GB. – As the crack propagates, the steps will group together to form river pattern.
Cleavage Fracture • Normally, FCC metals do not show cleavage. A large amount of plastic deformation will occur before the stress necessary for cleavage is reached. • Cleavage is common in metals with BCC (Fe, W, Mo, Cr) or HCP (Zn, Be, Mg) structure. • Quasi cleavage: cleavage on a fine scale and on not well defined crystallographic plane. – Seen in quenched and tempered steels. – The real cleavage planes are replaced by small and illdefined “cleavage facets” that initiate at carbide particles. – River markings are not observed
• Intergranular fracture: crack follows GB. – Bright and reflective appearance on a macroscopic scale. – It tends to occur when GBs are more brittle than the crystal lattice. – Examples: sensitized stainless steel, carbide film along GBs in steel, segregation of P or S on GBs in steel
•
•
Failure by cleavage and by ductile means are competing mechanisms. – When cleavage cracks form and propagate at a greater rate than plastic deformation, the material fails in a brittle manner. A reduction in grain size causes a reduction in DBTT. – Both yield stress and fracture stress increase with a reduction in grain size. – Yield stress (σy) decreases with increasing temperature. – Cleavage stress (σc) is not dependent on temperature.
Toughening mechanisms for ceramics •
Addition of fibers –
•
Crack bridging, crack deflection, fiber pullout
Addition of a second-phase that transforms at the crack tip with a shear and dilational component. –
•
Reducing stress concentration at crack tip
Production of microcracks ahead of the crack –
Crack branching, distributing the strain energy over a larger area
•
To eliminate, as much as possible, flaws in the material. K Ic = σ πa For a common ceramic having fracture toughness of 4MPa√m, a reduction in flaw size from 1 to 0.1 mm can increase the tensile strength from 16 to 56 MPa.
Compressive, tensile, flexural strength of ceramics
• It is the inability of ceramics to undergo plastic deformation that is responsible for the different mechanical behavior between metals and ceramics. This makes ceramics much stronger but less resistance to crack propagation. • The compressive strength of ceramics is close to 10 times of their tensile strength. • The low ductility and low resistance to crack propagation are responsible for the great difference between the compressive and tensile strength of ceramics. In metals, the difference is relatively small, because failure is often initiated only after considerable plastic deformation.
• Crack branching (bifurcation) – As the impact velocity increases, the extent of crack branching increases.
Sources of flaws in ceramics • The strength of ceramics is mainly determined by the concentration and size of flaws in it.
Effect of grain size on strength of ceramics • In ceramics, the flaw size (2a) is often related to the grain size (D), 2a = D. K Ic σ= πD 2
Compressive failure in brittle materials by axial splitting
Compressive fracture of brittle materials •
Failure of brittle materials under compression is activated by existing flaws. • It involves the formation of localized regions of tension in the material.
• The compressive failure of brittle materials is strongly affected by lateral confinement (stresses transverse to the loading direction).
Thermally induced fracture in ceramics •
The anisotropic effect of expansion on microcracking affects the strength of ceramics in a manner that is dependent on grain size.
1
D1
=
2
σ = K Ic
(
σ = k K Ic
D2
πa
=
K Ic
D
)
π2
Smaller grain size, higher tensile strength
Crack nucleation • Nucleation of a crack in a perfect crystal essentially involves the rupture of interatomic bonds. Stress for crack nucleation = theoretical cohesive stress (~E/30). • Ordinary materials break at stress ~E/104, because of the existence of surface or internal defects and the plastic deformation that precedes fracture. – Fracture stress in whiskers can approach the theoretical value.
• The brittleness of a material is related to the behavior of dislocations in the region of crack nucleation. – In brittle materials, dislocations are practically immobile. – In semibrittle materials, dislocations are mobile, but only on a restricted number of slip systems. – In ductile materials, there are no restrictions on dislocation movement.
• Ductile fracture in metals – Nucleation, growth and coalescence of voids (usually starts at second-phase particles) – Dimple
– Continuous reduction in cross-sectional area (in high purity metals) – Shearing along a plane of maximum shear
Pure metal under uniaxial tension • Dislocations can move on a large number of slip systems. • Crystal deforms plastically until the start of plastic instability (necking). • Then, the deformation is concentrated in the neck until the crystal separates along a line or a point.
•
Cracks can be nucleated by the grouping of dislocations pile up against a barrier – Crack nucleation depends on stress relaxation at the other side of the barrier.
• Lattice rotation associated with the bend plane and intersection of twin boundaries can nucleate cracks.
Cracking or cavitation at high temperature • w-type crack – stress concentration at triple junction due to GB sliding.
• r-type cavitation – Small cavities formed at GBs approximately normal to the tensile stress.
•
Microcavities nucleated at second-phase particles – –
•
break of second-phase particle separation of particle/matrix interface
Generally, the voids nucleate at small plastic strains. The microcavities grow with dislocation slip. The materials between the voids undergoes necking on a microscopic scale.
Fracture by void nucleation, growth and coalesence • •
Nucleation, growth and coalescence of microcavities gives the fracture appearance consisting of small “dimples”. “cup-and cone” fracture in cylindrical tensile specimens
• Voids are nucleated ahead of the crack. • Void grows and eventually coalesces with the main crack.
• The size, separation, and interfacial bonding of particles determine the characteristics of ductile cracks, and the ductility of the materials. • lnAo/Af (reduction of area) – Ao: initial cross-sectional area; Af: final cross-sectional area at fracture point
• • • • •
“Ductility” signifies a material’s capacity to undergo plastic deformation. “Ductility” is not a fundamental property of a material. It depends on the state of stress, strain rate, temperature, environment, and prior strain history of the material. A high temperature (or a low strain rate) leads to high ductility. A low temperature (or high strain rate) leads to low ductility. An increase in the degree of stress triaxiality results in a decrease in the ductility of the material. Stress state depends on external loading, geometry of structure, thermal stress, etc. σ1 > σ 2 > σ 3
εo : the plastic strain at fracture in uniaxial tension ε1: the maximum principal plastic strain at fracture Tensile stress Shear stress
Fracture Plastic strain
Brittle, or Cleavage Fracture •
• • •
Transgranular cleavage occurs by direct separation along specific crystallographic planes by means of a simple rupturing of atomic bonds. – Cleavage along (100) planes in BCC structure (such as Fe) Tendency for cleavage fracture increases with an increase in strain rate or a decrease in temperature. Ductile-brittle transition temperature (DBTT) increases with strain rate. The ductile fracture needs a lot more energy than the brittle fracture.
Cleavage Fracture • • •
Adjacent grains have different orientations. Cleavage crack changes direction at GB. Shinny appearance River markings – Cleavage steps can be initiated by the passage of screw dislocation. – Cleavage step is parallel to the crack propagation direction. – Crack change direction at various points along GB. – As the crack propagates, the steps will group together to form river pattern.
Formation of cleavage steps • River markings – Cleavage steps can be initiated by the passage of screw dislocation. – Cleavage step is parallel to the crack propagation direction. – Crack change direction at various points along GB. – As the crack propagates, the steps will group together to form river pattern.
Cleavage Fracture • Normally, FCC metals do not show cleavage. A large amount of plastic deformation will occur before the stress necessary for cleavage is reached. • Cleavage is common in metals with BCC (Fe, W, Mo, Cr) or HCP (Zn, Be, Mg) structure. • Quasi cleavage: cleavage on a fine scale and on not well defined crystallographic plane. – Seen in quenched and tempered steels. – The real cleavage planes are replaced by small and illdefined “cleavage facets” that initiate at carbide particles. – River markings are not observed
• Intergranular fracture: crack follows GB. – Bright and reflective appearance on a macroscopic scale. – It tends to occur when GBs are more brittle than the crystal lattice. – Examples: sensitized stainless steel, carbide film along GBs in steel, segregation of P or S on GBs in steel
•
•
Failure by cleavage and by ductile means are competing mechanisms. – When cleavage cracks form and propagate at a greater rate than plastic deformation, the material fails in a brittle manner. A reduction in grain size causes a reduction in DBTT. – Both yield stress and fracture stress increase with a reduction in grain size. – Yield stress (σy) decreases with increasing temperature. – Cleavage stress (σc) is not dependent on temperature.
Toughening mechanisms for ceramics •
Addition of fibers –
•
Crack bridging, crack deflection, fiber pullout
Addition of a second-phase that transforms at the crack tip with a shear and dilational component. –
•
Reducing stress concentration at crack tip
Production of microcracks ahead of the crack –
Crack branching, distributing the strain energy over a larger area
•
To eliminate, as much as possible, flaws in the material. K Ic = σ πa For a common ceramic having fracture toughness of 4MPa√m, a reduction in flaw size from 1 to 0.1 mm can increase the tensile strength from 16 to 56 MPa.
Compressive, tensile, flexural strength of ceramics
• It is the inability of ceramics to undergo plastic deformation that is responsible for the different mechanical behavior between metals and ceramics. This makes ceramics much stronger but less resistance to crack propagation. • The compressive strength of ceramics is close to 10 times of their tensile strength. • The low ductility and low resistance to crack propagation are responsible for the great difference between the compressive and tensile strength of ceramics. In metals, the difference is relatively small, because failure is often initiated only after considerable plastic deformation.
• Crack branching (bifurcation) – As the impact velocity increases, the extent of crack branching increases.
Sources of flaws in ceramics • The strength of ceramics is mainly determined by the concentration and size of flaws in it.
Effect of grain size on strength of ceramics • In ceramics, the flaw size (2a) is often related to the grain size (D), 2a = D. K Ic σ= πD 2
Compressive failure in brittle materials by axial splitting
Compressive fracture of brittle materials •
Failure of brittle materials under compression is activated by existing flaws. • It involves the formation of localized regions of tension in the material.
• The compressive failure of brittle materials is strongly affected by lateral confinement (stresses transverse to the loading direction).
Thermally induced fracture in ceramics •
The anisotropic effect of expansion on microcracking affects the strength of ceramics in a manner that is dependent on grain size.
1
D1
=
2
σ = K Ic
(
σ = k K Ic
D2
πa
=
K Ic
D
)
π2
Smaller grain size, higher tensile strength
