# Shared Flashcard Set

C15
Fracture
30
Science
Undergraduate 3
06/04/2011

## Cards Return to Set Details

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 occursit 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 crackUtotal=Usurface+Uelasticminimize 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 Gc 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=Gc=2γs+γp   Gc 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 UE and US
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=2γS+γP it is known as the resistance to crack growth and is hte maount of energy needed to make a crack grow
Term
 What is A, B, 2A
Definition
 A-crack area B-depth/thickness 2A-crack surface area
Term
 What is kt, K, KIC
Definition
 kt-stress concentration factor σmax/σ0 K-stress intensity factor, the extent to which the crack intensifies any stress below the failure stress KIC-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
 1-opening 2-shearing front/back 3-shearing side/side EG=KI2+KII2+(1+ν)KIII2 [stress] EG=(1-ν2)KI2+(1-ν2)KII2+(1+ν)KIII2 [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 inter-granular 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 pile-ups 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) J-Integral
Term
 What is the significance of CTOD?
Definition
 It allows for one to understand elastic-plastic 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
 How is CTOD measured
Definition
 a pre-cracked specimen is put into a three-point bending test
Term
 What are J-Integrals What are its three main stages?
Definition
 the rate of energy absorbed per unit area as the crack grows J=-dU/dA   1-crack blunting 2- fracture initiation 3-steady 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
 dG/da>dR/da dG/da=dR/da
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 KIC and simply involves the rearrangment of variables to find ry σ=KI/Sqrt[2πry], ry=a+Δa and rp=Δa+ry
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 rp v. angle
Term
 how does KIC vary wiht speciment thickness
Definition
 thin specimens tend to have higher values of KIC and exhibit plane stress thick specimens tend to have lower values of KIC and exhibit plane strain
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