Mechanical Properties

Transcription

1 Mechanical Properties Elastic deformation Plastic deformation Fracture

2 Plastic Instability and the Ultimate Tensile Strength s u P s s y For a typical ductile metal: I. Elastic deformation II. Stable plastic deformation III. Unstable deformation IV. Fracture L L I II III e P At plastic instability necking initiates the supportable load begins to decrease Plastic instability is due to a loss of balance between Increase in strength due to hardening Increase in stress due to thinning

3 Plastic Instability: The Considere Criterion Increase in strength Increase in stress Balance dσ y = dσ dε dε dσ = d P A = P A da A = σdε dσ y > dσ dσ y < dσ Stable deformation necking stops Unstable deformation necking continues dσ dε = σ Considere Criterion for plastic instability

4 Ultimate Tensile Strength plastic instability : ds/de = 0 P s s u L L e P Ultimate strength at plastic instability [ ] dσ dε = σ ds de = 0 ds de = d σe ε d[ e ε 1] = e ε dσ σe ε dε e ε dε Note: Considere condition depends on geometry For sheet samples, θ = σ/2 dσ = e 2ε dε σ

5 Ductility Lost at Nanograin Size Decreasing grain size σ y increases ε u vanishes

6 Cause of Ductility Loss Plastic instability in tension (σ u, ε u ) by Considere criterion: dσ/dε = σ Decreasing grain size Dramatically increases yield strength Has a much smaller effect on work hardening By normal dislocation processes Hence σ u approaches σ y, ductility is lost Need alternate mechanisms of work hardening Example: transformation-induced plasticity (TRIP)

7 Coherent γ α: The Bain Strain

8 TRIP steel: mechanisms The TRIP effect is not primarily transformation strain The fcc-bcc transformation only permits a Bain strain of ~25% Models of current TRIP suggest only a few percent (Bhadesia) The observed >20% strain must come from other mechanisms Unlike shape memory; a bcc flip can give >40% strain The important effect is on work hardening TRIP is, inherently, a softening mechanism TRIP produces a complex microstructure that hardens more rapidly

9 How TRIP enhances ductility For high ductility, need Low work hardening at small strains High and increasing work hardening at high strains But not too high TRIP Transformation strain softens by adding free elongation Complex microstructure hardens by confining ductile material Tune via austenite stability (m) for progressive transformation

10 Mechanical Properties Elastic deformation Plastic deformation Fracture

11 Modes of Failure P ß a ß T L a ß r ßa P ßa buckling necking cracking The root cause of fracture may be Elastic instability (buckling, flutter) Elastic strain creates hinge where stress increases to fracture Plastic instability (necking) Plastic strain creates neck where stress increases to fracture Crack instability (fracture) Flaw or crack creates stress concentration that leads to fracture

12 Flutter Failure (elastic) - The Tacoma Narrows Bridge (1940)

13 Plastic Instability at Su An Exploded Propane Tank

14 Fracture Crankshaft failure in an aircraft engine

15 Crack Tip Stress Field ß a Stress concentrates at crack tip a ß r ß T ßa Assuming elastic behavior a σ T = Qσ a ρ σ a = applied stress σ T = crack tip stress ρ = crack tip radius Q = shape factor (order 1) ßa Note: As ρ 0, σ T increases without bound sharp crack fracture at small σ a brittle behavior

16 Example: Edge Cracked Sheet

17 Crack Tip Stress Increases with Load at Fixed Crack Length 100 lbs 200 lbs 300 lbs 400 lbs 500 lbs 600 lbs 700 lbs 800 lbs stress (ksi)

18 Crack Tip Stress Increases with Crack Length at Fixed Load 0.02 in in in in in in. stress (ksi)

19 Crack Instability and Fracture Toughness a ß ß a ß T r ßa ßa Unstable crack propagation (simple model) Let σ B be inherent fracture strength Crack is unstable when σ T = σ B The critical applied stress is σ a = σ c, where σ σ c = Q 1 B ρ a Fracture toughness σ B and ρ are very difficult to measure The product, σ B ρ is easily measured Fracture toughness test Measure σ c for known crack length and shape Replace σ B ρ by fracture toughness, K c: σ c = Q 1 K c a

20 Plane Strain Fracture Toughness The fracture toughness K c K c = Qσ c a = σ B ρ K c K Ic T plane strain Is not a material property Decreases with sample thickness The reason is ρ is due to plastic deformation at crack tip Thin sample deforms through-thickness ρ ß The plane strain fracture toughness, K Ic Is the asymptotic value of K c Is a material property (test in plane strain) Has built-in safety since K ic K c σ c = Q 1 K c a Q 1 K Ic a ß T 1

21 Using Fracture Toughness ß a ß T Use tough materials Ductile materials have high ρ high K ic Low σ y ordinarily gives ductility Strong materials tend to be brittle High σ y means sharp cracks a ß r ßa ßa Inspect for manufacturing defects Non-destructive testing (NDT) methods Dye penetrant X-ray acoustic Let a* be largest crack that cannot be found Set design stress such that σ a < σ c * = Q 1 K Ic a * If σ c * > σ u, design to σ u

22 The Source and Control of Toughness K IC ßy The fracture toughness, K Ic Decreases with yield strength Decreases with temperature Often dramatically at T B Particularly in bcc metals Decreases with strain rate K Ic brittle T B ductile Source: fracture mode Ductile fracture mode High toughness Brittle fracture Low toughness T

23 Fracture Toughness (K ic ) Fracture mode: 1 st order effect Ensure ductile fracture if possible Toughness in the given mode: 2 nd order effect Strength Purity

24 Brittle Fracture ß Transgranular cleavage: Fracture across grains on selected crystallographic planes ß ß Intergranular fracture: Separation along grain boundaries ß

25 Ductile Rupture: Possibility of High Toughness Ductile rupture material tears at crack tip Large plastic deformation nucleates voids at inclusions Voids grow until they join together Leave ductile rupture dimples on the fracture surface

26 Understanding and Controlling Fracture Toughness K Ic brittle T B T ductile Ensuring a ductile mode High K Ic requires ductile fracture The ductile-brittle transition K Ic drops dramatically at T B Particularly in bcc metals Whenever possible Use at T T B Control T B with microstructure K Ic Property improvement Toughness in the ductile mode K ic decreases with σ y Improve characteristic: K Ic (σ y ) σ y

27 The Ductile-Brittle Transition TB KIc brittle ductile T

28 The Ductile-Brittle Transition K Ic σ brittle T B T B T ductile σ II σ I The Yoffee diagram T > T B : Yield before fracture Crack tip blunts Stress concentration reduced Ductile failure mode T < T B : Fracture before yield Crack tip remains sharp Brittle fracture at small K ic Fracture mode - Mode with least fracture stress σ Y T

29 Controlling the Brittle Transition: Suppress Intergranular Fracture T B Intergranular fracture mode Ordinarily very low K ic K Ic brittle ductile Suppress intergranular fracture Lowers T B T In bcc Changes brittle mode to transgranular T B may drop by > 100K Fe-Mn steels σ σ I σ II In fcc Cleavage does not usually happen Suppressing IG eliminates T B T B σ Y T

30 Intergranular Fracture: Sources and Cures Grain boundaries contaminated Embrittling impurities Cures Purity Heat treatment Gettering gather in stable compound E.g., rare earth sulfides Grain boundaries inherently weak Glue them with surfactants B additive to Fe-Mn, Ni3Al

31 Controlling the Brittle Transition: Inhibit Transgranular Cleavage σt σ TB Refine effective grain size Increases fracture stress 1 σ f = Kf d Increases strength (Hall-Petch) σy T Decrease mean free path 1 σy = σ0 + K y d Balance lowers TB

32 Controlling the Brittle Transition: Inhibit Transgranular Cleavage (large) Grain size (small) DBTT (K) %C -Plain carbon 0.17%C -Nb steels 0.05%C -1.5%Mn steels TMCP steels 0.05%C -2.0%Mn -FP,85% 0.05%C-1.5%Mn -Nb steels 0.05%C -2.0%Mn -M,85% 0.2%-1.6%Mn -M,85% Kotobu Nagai, NRIM, Tsukuba, Japan Yield strength (MPa) Grain refinement is the only mechanism that Increases strength Simultaneously decreases T B