Flashcards in Failure Of Materials Deck (31):
Toughness is the energy dissipated per unit volume of the material up to failure.
Uc* = 0.5 x stress x strain (when linear! Otherwise integral for area under curve).
Describe the stress-strain response of a ductile material.
Ductile materials produce a non-linear response. The toughness remains the same, but the strain energy changes when past the elastic limit.
Once a material has plastically deformed, U is the energy recovered when the material is unloaded.
What is ‘inelastic strain energy’?
The energy absorbed by the material through plastic deformation, denoted by U_inelastic.
Define ‘elastic strain energy’ and ‘elastic strain energy density’. How are they related?
Elastic Strain Energy, U:
- The energy input into a system when e.g. loading a bar.
- Area under the curve of a load-displacement plot.
- Can drive a crack to grow.
Elastic Strain Energy Density, U*:
- The elastic strain energy per unit volume material.
- Area under the curve of a stress-strain plot.
U = U* . V
What are the two general classes of fracture seen in engineering materials?
- Brittle (low energy absorption, <5% strain, absorbed by transgranular cleavage fracture).
- Ductile (high energy absorption, absorbed by microvoid coalescence).
What are microvoids? How and where are they formed?
- Microvoids are pockets of air or foreign particles with little to no bond strength.
- Easily formed at inclusions, inter metallic or second-phase particles and grain boundaries.
- Microvoids grow and coalesce as the applied load increases.
Describe how ductile failure under uniaxial tensile force arises and what may be seen at a macro- and microscopic level.
- Necking caused by dislocation movements/polymer chain sliding.
- Atomic deboning and microvoid initialisation.
- Microvoid coalescence to form larger cracks.
- Cracks eventually propagate normal to tensile axis.
- Crack propagation through the periphery along the shear plane at 45o.
- Cup and cone pattern.
Describe microvoid shape for the following:
A) Uniaxial tensile loading
C) Tensile tearing
Uniaxial Tensile Loading:
- Equiaxed dimples
- Elongated and parabolic dimples pointing in opposite directions on matching fracture surfaces.
- Elongated dimples pointing in the same direction on the matching fracture surface.
Describe how brittle failure arises and what may be seen at a micro- and macroscopic level (the three steps of cleavage fracture).
Cleavage fractures have three key steps:
- Plastic deformation to produce dislocation pile-ups.
- Crack initiation.
- Crack propagation to failure.
- Absence of gross plastic deformation.
- Grainy or faceted texture.
- River marking or stress lines.
Describe the two cleavage fracture modes. What strength is each?
Cleavage fracture is the breaking of atomic bonds along crystallographic planes (transgranluar):
- Rough texture with river and feather patterns.
- Moderate to high strength.
This may occur along the grain boundaries (intergranular):
- Sharp and 3D faceted grains.
- Moderate to low strength.
Describe size effects.
Size effects are the change in strength with specimen dimensions. They are induced by flaws and defects, further leading to stress concentrations.
Describe the ductile to brittle transition temperature.
- Plotted as the absorbed energy against temperature behaviour.
- Increasing temperature allows more slip system to operate, yielding plastic deformation to occur prior to failure.
Briefly describe four other key types of failure (not including fracture).
- Fracture by slow crack growth.
- Occurs when material is subject to many repetitions below the static crack growth stress.
- Combined effects of cyclic stress and corrosive environments.
- Fatigue resistance decreases in presence of aggressive chemical environment.
Stress Corrosion Cracking:
- As above, but for non-cyclic stress (but still below yield stress).
- The result of a static load applied over long periods of time.
What is basic view of fracture mechanics?
Elastic stress analyses assume perfectly homogeneous and flawless materials, which is not suitable for designing high-strength materials.
Relationships are established between the material’s inherent resistance to crack growth and the far-field stress.
When a crack reaches a certain critical length, it can propagate catastrophically through the structure.
What is Inglis’s solution?
Stress = R(1+2sqrt(a/rho_r)) Where rho_r = b^2/a
The maximum stress at the tip of a notch. However, as the crack becomes perfectly sharp, the stress tends to infinity.
Describe crack tip singularity. Why is in not found in nature?
Using Inglis’ solution, as the crack becomes perfectly sharp, the stress tends towards infinity (i.e. a singularity).
This is not possible in real materials as it would require impossibly high strength. As such, the material actually undergoes local yielding to blunt the crack tip.
What are the three modes of loading for stress at the tip of a crack?
How does Irwin’s theory improve on Griffith’s theory? What are the three key parameters defined in the modified equation?
Griffith’s theory works on very brittle materials (e.g. glass). This is not typically the case for most metals, which will demonstrate plastic deformation.
As such, Irwin suggest the inclusion of an extra plastic energy. The reformed Griffith equation defines the relationships between:
- critical strain energy release rate, G_c.
- stress level, sigma_s.
- size of the flaw, a.
How might one use Irwin’s theory in a design situation?
By choosing a value of ‘a’ (size of defect) based on the smallest crack that could be easily detected. For a given fracture energy G_c of a material, the safe level of stress ‘sigma_s’ could then be determined.
What is ‘Mode I Fracture Toughness’?
Mode I fracture toughness is the critical stress intensity factor required to extend a crack under an opening model.
What role does specimen thickness play on stress state?
The stress state is dependant on the specimen thickness ‘B’, until the thickness exceeds some critical dimension. The value of ‘K_c’ then becomes relatively constant. This is a true material property known as the ‘plane-strain fracture toughness’, ‘K_ic’.
Describe the plastic zone and when it would occur.
Stated in Inglis’ solution, when a crack is loaded, the stress increases exponentially. However, the material will yield before the stress reaches the singularity. This yield region is known as the ‘plastic zone’ or ‘fracture process zone’.
r_p (plane stress) = 3 . r_p (plane strain)
Describe plane stress and any assumptions.
For thin sheets, it is assumed that no stress exists in the thickness, I.e. sigma_zz = 0. This stress state is known as ‘plane stress’.
However, epsilon_zz still exists! This results in a bi-axial stress state such that the material fractures in a characteristic ductile manner, with a 45o shear lip being formed at each free surface.
Describe plane strain and any key assumptions.
Plane strain occurs when the stress in the thickness direction becomes significant, giving a tri-axial stress state.
The thickness contraction becomes epsilon_zz = 0.
What is a shear lip and where do they dominate?
Shear lips arise as cracks approach the sample surface. They are the dominant failure mechanism in small samples.
What conditions must be fulfilled to allow for the LEFM equations to be valid?
The approximate plastic zone radius ahead of the crack must be:
r_p < a/50
And an additional requirement for plane strain cracks:
r_p < B/50
Define compliance. How is it related to fracture energy?
Compliance ‘C’ is the inverse of stiffness; if something is compliant, it will deform more.
C = delta / P
The strain energy release rate is related to compliance by:
G = P^2 / 2B . dC/da
Same for both fixed displacement and fixed load!
Describe the factors influencing fracture toughness.
1) Extrinsic and intrinsic toughness mechanisms:
- Intrinsic acts predominantly ahead of the crack to promote advance (e.g. microvoid coalescence and cleavage fracture).
- Extrinsic acts predominantly behind the crack to impeded advance (e.g. fibre bridging and grain bridging).
2) Crack tip radius:
- Notching techniques.
Describe ‘Crack Tip Opening Displacement (CTOD)’.
CTOD is a process used to characterise a ductile or very tough material:
- Assumes crack tip plasticity makes the crack behave as if it were longer, a + r_p.
- Calculates the physical displacement of the crack tip.
- Separated into elastic and plastic components of CTOD.
What is an isotopic material?
Anisotropic material has a stress-strain relationship that is independent of orientation of the coordinate system at that point.
- I.e. same elastic properties (E, v) in all directions.