Abstract
The mechanical properties of materials are related to the fundamental bonding strengths of the constituent atoms in the solid and any bonding defects which might form. A molecular model is presented so that primary bond formation mechanisms (ionic, covalent, and metallic) can be better understood. How these bonds form and respond to mechanical stress/loading is very important for engineering applications. A discussion of elasticity, plasticity, and bond breakage is presented. The theoretical strengths of most molecular bonds in a crystal are seldom realized because of crystalline defects limiting the ultimate strength of the materials. Important crystalline defects such as vacancies, dislocations, and grain boundaries are discussed. These crystalline defects can play critically important roles as time-to-failure models are developed for: creep, fatigue, crack propagation, thermal expansion mismatch, corrosion and stress-corrosion cracking.
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Notes
- 1.
Classical description is—two bodies cannot occupy the same space.
- 2.
In order that ionic contributions are comprehended from both near and far, the potential for anion-pair is often written as: φ(r) = −αe 2/r, where α is the Madelung constant. In cubic crystalline structures, α = 1 to 2.
- 3.
The classical oscillator will oscillate until all its energy is finally dissipated. The quantum oscillator, however, will dissipate its energy in quantum amounts (n + 1/2)ħω until it finally reaches its ground state. In the ground state, the quantum oscillator will still have zero-point energy oscillation: (1/2)ħω.
- 4.
The stress gradient is given by: \( \overrightarrow {\nabla } \sigma = \left[ {\hat{x}\frac{\partial }{\partial x} + \hat{y}\frac{\partial }{\partial y} + \hat{z}\frac{\partial }{\partial z}} \right]\sigma \left( {x,y,z} \right) \).
- 5.
Atom movement is opposite to vacancy movement. Atoms tend to move from relative compressive regions to relative tensile regions. Such atom movement tends to reduce both the relative compressive stress and the relative tensile stress. Atom (or vacancy) movement due to stress gradients is a stress-relief mechanism.
- 6.
Specific density represents the number of atoms per unit area.
- 7.
Other dislocation types can exist, such as screws dislocations (not discussed here). These can also be important in the mass-flow/creep process.
- 8.
The ramp-to-failure/rupture test is described in detail in Chap. 10.
- 9.
The usefulness of ramp-voltage-to-breakdown test for capacitor dielectrics is highlighted in Chap. 11.
- 10.
Recall from Chap. 8, one expects the relaxation-rate constant to be thermally activated: k = k0 exp [−Q/(KBT)].
- 11.
The load/force is constant. The average stress is only approximately constant during testing due to some expected cross-sectional area changes.
- 12.
Recall, from Chap. 11, that the stress-migration/creep bakes for aluminum were generally done at temperatures above 100 °C.
- 13.
Historically, these localized stresses at crack tips have been referred to as either stress raisers or stress risers. The terms will be used interchangeably.
- 14.
The elastic energy U elastic of the material reduces with crack propagation, thus we have defined ΔU released such that it is always positive, i.e., ΔUreleased = −ΔU elastic.
- 15.
Note that when the crack size a goes to zero, the apparent rupture stress goes to infinity. However, in these situations, where the right-hand side of the equation becomes extremely large, the rupture stress will be limited by the normal crack-free rupture mechanisms and σ rupture will assume the crack-free rupture strength.
- 16.
Recall that specific energy density is the energy per unit area.
- 17.
Historically, this has been referred to as Griffith’s equation which was developed for brittle materials. More recently, Irwin is usually credited for developing the failure in terms of a strain energy release rate G [(Eq. (56)], which incorporates both elastic and plastic deformations when new surfaces or interfaces are formed.
- 18.
Linear coefficients of thermal expansion are listed for several material types (in units of 10−6/°C): α polymers ≅ 50, α metals ≅ 10, α ceramics ≅ 2, α glass ≅ 0.5.
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McPherson, J.W. (2013). Time-to-Failure Models for Selected Failure Mechanisms in Mechanical Engineering. In: Reliability Physics and Engineering. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00122-7_12
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