MSE 256B Lecture Notes 9-28-23

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University of California, Irvine *

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256B

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Mechanical Engineering

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Oct 30, 2023

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Conventional Tensile Properties Ductile Metal Engineering Stress Strain Ultimate s y P force Tensile Ao inaitieaa I strength Fracture UTS e initia s e Defo length road UTS Y P TA d D Ado to da do five da ive strain hardening geometive softening between Tys and UTS AdoplodA at UTS dP A dot Td A o i Thus UTS has no bearing on fracture of the material Needle Point Failure Not what we would call Fracture

A metal with limited ductility will exhibit Cup and cone Fracture Void Form y o of y Near side need cone to toooo Conclusion Fracture is complex in a tensile test Uts has little to do with fracture process Tensile test not a good way to assess fracture properties

Brittle Material s X Fracture UTS Tys The measured value of Uts is very sensitive to surface condition Little practical e value Uts only works in practice if stresses are extremely low or only in compression To push engineering materials to higher stresses another set of design criteria are needed

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Notable Fractures of the Past 1 Early observation of brittle fracture of steel Paper Nathaniel Barns by 1879 Recent cases have occurred of fracture in bessemer bars they nearly all took place during severe weather Kirk steel plates when cold on being thrown down split right up Pieces from each side stood all of Admiralty tests 2 Titanic 1912 sinking after striking iceberg very quickly 1500 drowned 3 Molasses Tank Explosion 1919 Calc stress I 180 MPa Around rivet holes I 345 MPa UTS 379 MPa stress too high

4 Methane Storage Tank Explosion 1944 Cleveland OH One of most disasterous brittle fractures in history 225 people killed one Sg mile of city distoyed 7 106 damages Plate was not sufficiently heat treated 5 World War II merchant ships sato 5000 were bie It 1000 cracked by 1946 200 Serious damage 9 T 2 tankers and 7 Liberty ships sustained complete fracture Some cause as Titanic 6 Molasses Tank Exposion 1973 Bell view N.J Big mess Still do not have this problem licked 7 Supertanker fractures 197 8,2004 Another repeatin tragedy due to ignorance of fracture behavio

Theoretical Fracture Strength We wish to estimate upper limit of fracture stress in a crystal Pull crystal apart along crystal plane There are two Considerations Elastic resistance and surface energy created by fracture r Assume Model with Th f Ax exp Bx Xo Ntext uses sin funct Ex x atomic separation e DE strain E LE DEF E x dIxlx x

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4 A exp Bx Bax exp Bx Et E to Ex x E Xo A A Ex Now match stress law to surface free energy 28s r dx A Px exp B x dx a Integrate by parts 28 A xexpf.tt J fexp Bx dx L A xexg.tt expfgI g

ZEB x 1 exp Bx 1 28 Az B Fg We want to evaluate tin at day o If A exp BE BA exp 1 Be o 11 B x A exp BH 0 x I Tin Ey Xt exp 1 Eje but I FEI Fu I E FE ITE Ent 0.5 ME I E Eh 10

Almost all materials fail under stresses that are much lower than Th because of stress concentrations associated with notches cracks There are some i Unless the geometry is extremely limited a notable exceptions defect must reduce of from Tn Inglis Approach For Determining 1913 Consider elliptical hole through a plate under tension 44 4 Y t a g Lat th E stress I k k k r Elastic solution Tmax T i 4 r I 28 For an ellipse Radius ftp.purrature p h Fa

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