Term
Griffith's Law: what does it and does it not consider? What is the basic premise? What is used to determine the equation 

Definition
provides the thermodynamic or energetic criterion for failure but does not consider the mechanism by which failure occurs it states that a ccrack will propagate in a material when the elastic energy released as a result of that propagation exceeds the energy required to propagate the crack Utotal=Usurface+Uelastic minimize to find criterion for stress 


Term
what term is added to allow Griffiths equation to be modelled for a ductile material? 

Definition
the plastic work of deformation 


Term
What is the energy releast rate or crack extension force? What is G_{c} a measure of? 

Definition
G=dU/dA change in potential energy per unit increase of area Crack extension occurs when G=work to fracture
G=G_{c}=2γ_{s}+γ_{p}
G_{c} is a measure of fracture toughness 


Term
What did Obreimoff's experiment show? What equations are used to derive the equilibrium crack length 

Definition
 brittle fracture is reversible under the right circumstances
 whether it occurs or not is governed by balancing stored elastic energy with work of fracture
a0 is found using U_{E} and U_{S} 


Term
For a crack to close, what conditions are necessary? 

Definition
 must be a perfectly clean environment (vacuum)
 only elastic deformation/not plastic



Term
What is the fundamental flaw in linear elastic fracture mechanics?
Why is it okay to continue to use LEFM? 

Definition
the calculations assume elastic behavior, however, for a crack to grow, there must be some plastic flow ahead of the tip
Ultimately, the contribution from the nonelastic bits are a small fraction of the total equation 


Term
What is the principal of superposition
What are the two reasons for why it can be used 

Definition
 all stresses are elastic
 all stresses are small
it suggests you can add two stresses at right angles to each other to produce a 2D hydrostatic tension 


Term
What is R and how is it related to G 

Definition
R=2γ_{S}+γ_{P}
it is known as the resistance to crack growth and is hte maount of energy needed to make a crack grow 


Term

Definition
Acrack area
Bdepth/thickness
2Acrack surface area 


Term

Definition
k_{t}stress concentration factor σ_{max}/σ_{0}
Kstress intensity factor, the extent to which the crack intensifies any stress below the failure stress
K_{IC}the critical stress intensity factor or fracture toughness (minimum stress before propagation begins) 


Term
What is the fact that stress 'goes to infinity' at a crack tip not an issue? 

Definition
the integral is finite. the portion of the graph where the fracture stress is exceeded forms a plastic zone 


Term
describe crack modes 1, 2, 3
What are the equations for total stress with plane stress and plane strain 

Definition
1opening
2shearing front/back
3shearing side/side
EG=K_{I}^{2}+K_{I}_{I}^{2}+(1+ν)K_{I}_{I}_{I}^{2} [stress]
EG=(1ν^{2})K_{I}^{2}+(1ν^{2})K_{I}_{I}^{2}+(1+ν)K_{I}_{I}_{I}^{2} [strain]
Total G is always dominated by Mode I



Term
Why does ductile failure have the appearance it does? 

Definition
 voids nucleate (usually on second phase particles) and grow most rapidly in the center of the sample where triaxial stress state exists
 Voids grow and coalesce to produce a circular internal crack which grows
 the sample fails by shear in plane stress at the outer regions of the sample
where void nucleation is difficult (ie pure metals) much more ductility is observed and the sample can thin almost to a point before failure occurs 


Term
discuss riverlines in ductile materials 

Definition
 this cleavage fracture surface is characterized by a planar intergranular crack which changes plane by the formation of discrete steps
 facets correspond to the individual grains and in single crystals an entire slip plane can consist of one facet
 eventually these facets converge and eventually disappear int eh direction of crack growth
 they form at grain boundaries where the cleavage palne in one grain is not parallel to the plane in teh adjacent grain



Term
what conditions favor brittle fracture 

Definition
 high yield stress
 reduced slip systems (HCP and BCC metals, low temperature)
 high constraint (plane strain) and rapid deformation



Term
what is the relationship between grain size the failure type?
what is the significance of grain size? 

Definition
small grains>>yielding precedes failure
large grains>>yielding and failure at any point
small grain size increases both toughness and strength therefore it is one of the best strengthening mechanisms 


Term
cracks become blunted due to plasticity. what are necessary for the crack to continue propagating? 

Definition
microcracks
these exist to act as stress concentrators
these are limited to the size of a grain because they do not have the energy to cross a grain boundary 


Term
what governs the ductile/brittle transition 

Definition
the macroscopic yield *not what's happening at the crack tip 


Term
what factors may promote cleavage failure? 

Definition
 high yileld stress  large amount of stored elastic energy
 large grain size  large build up of stress from pileups
 coarse carbides  can crack
 deep notches  constraint
 thick specimens (plane strain)



Term
what are two methods of elastic plastic fracture mechanics? 

Definition
 Crack Tip Opening Displacement (CTOD)
 JIntegral



Term
What is the significance of CTOD? 

Definition
It allows for one to understand elasticplastic effects of small components and involves looking at the curvature of a crack tip
curvature is related to the fracture toughness of a material 


Term

Definition
a precracked specimen is put into a threepoint bending test 


Term
What are JIntegrals
What are its three main stages? 

Definition
the rate of energy absorbed per unit area as the crack grows
J=dU/dA
1crack blunting
2 fracture initiation
3steady state crack growth 


Term
describe R curves as a function of crack length and how they differ for brittle and ductile specimens 

Definition
R(Brittle)  these lines are flat and R is not effected by crack length
R(ductile)  shape of Sqrt(a) because as crack length increases, often the plastic zone increases as well 


Term
describe how G varies with crack size for load control and strain control fixed grips 

Definition
G v. a increases for load control
G v. a decreases for strain control fixed grips 


Term
What are the conditions for fast fracture?
stable crack growth? 

Definition


Term
what is the effect of having a plastic zone? 

Definition
 deformation occuring in teh plastic zone greatly increases R, the work to propagate crack
 for small plastic zone size, LEFM can be applied to ductile failure



Term
what is the Irwin method? What equation is it based on? 

Definition
a way of calculating zone size by suggesting there is a virtual crack tip that extends the distance of the actual tip placing it at the center of the plastic zone
based on the equation for K_{IC} and simply involves the rearrangment of variables to find r_{y}
σ=K_{I}/Sqrt[2πr_{y}], r_{y}=a+Δa and r_{p}=Δa+r_{y} 


Term
How can one find the real shape of a plastic zone 

Definition
Use a yield criterion (such as von Mises)
plug in principal stresses then plot r_{p} v. angle 


Term
how does K_{IC} vary wiht speciment thickness 

Definition
thin specimens tend to have higher values of K_{IC} and exhibit plane stress
thick specimens tend to have lower values of K_{IC} and exhibit plane strain 

