Fracture mechanisms Ductile fracture Occurs with plastic deformation Brittle fracture Occurs with Little or no plastic deformation Thus they are Catastrophic meaning they occur without warning Ductile vs Brittle Failure Fracture behavior Very Ductile Moderately Ductile Brittle Large Moderate Small Example Failure of a Pipe Ductile failure Brittle failure Moderately Ductile Failure Evolution to failure necking s Resulting fracture surfaces void nucleation void growth and linkage shearing at surface 50 50mm mm steel 100 mm Inclusion particles serve as void nucleation sites fracture Brittle Failure Arrows indicate point at which failure originated Adapted from Fig 8 5 a Callister 7e Brittle Fracture Surfaces Useful to examine to determine causes of failure Intragranular Intergranular between grains 304 S Steel metal within grains 316 S Steel metal 160 mm 4 mm Polypropylene polymer 1 mm Al Oxide ceramic 3 mm Failure Analysis Failure Avoidance Most failure occur due to the presence of defects in materials Presence of defects is best found before hand and they should be determined non destructively Ideal vs Real Materials Stress strain behavior Room Temp s E 10 TSengineering TS perfect perfect mat l no flaws carefully produced glass fiber E 100 typical ceramic 0 1 materials typical strengthened metal typical polymer e materials Considering Loading Rate Effect Increased loading rate increases sy and TS decreases EL s sy TS Why An increased rate allows less time for dislocations to move past obstacles e larger TS e smaller sy e Considering Temperature Effects Increasing temperature increases EL and Kc Ductile to Brittle Transition Temperature DBTT Impact Energy FCC metals e g Cu Ni BCC metals e g iron at T 914 C polymers Brittle More Ductile High strength materials s y E 150 Temperature Ductile to brittle transition temperature Adapted from Fig 8 15 Callister 7e Variation in ductile to brittle transition temperature with alloy composition Design Strategy Build Steel Ships Quickly Pre WWI The Titanic Reprinted w permission from R W Hertzberg Deformation and Fracture Mechanics of Engineering Materials 4th ed Fig 7 1 a p 262 John Wiley and Sons Inc 1996 Orig source Dr Robert D Ballard The Discovery of the Titanic WWII Liberty ships Reprinted w permission from R W Hertzberg Deformation and Fracture Mechanics of Engineering Materials 4th ed Fig 7 1 b p 262 John Wiley and Sons Inc 1996 Orig source Earl R Parker Behavior of Engineering Structures Nat Acad Sci Nat Res Council John Wiley and Sons Inc NY 1957 Problem Used a type of steel with a DBTT Room temp Flaws are Stress Concentrators Results from crack propagation Griffith Crack Model a sm 2so t t 1 2 K t so where t radius of curvature of crack tip so applied stress sm stress at crack tip Concentration of Stress at Crack Tip Engineering Fracture Design Avoid sharp corners s so max Stress Conc Factor K t s w smax r fillet radius o 2 5 smax is the concentrated stress in the narrowed region h 2 0 increasing w h 1 5 1 0 0 0 5 1 0 sharper fillet radius r h Crack Propagation Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip blunting the crack plastic deformed region brittle Energy balance on the crack Elastic strain energy energy is stored in material as it is elastically deformed this energy is released when the crack propagates creation of new surfaces requires this energy When Does a Crack Propagate Crack propagates if applied stress is above critical stress i e sm sc or Kt Kc 1 2 2E s sc a where E modulus of elasticity s specific surface energy a one half length of internal crack Kc sc s0 For ductile materials replace s by s p where p is plastic deformation energy As Engineers we must Design Against Crack Growth Crack growth condition K Kc Ys a Largest most stressed cracks grow first Result 1 Max flaw size dictates design stress Kc sdesign Y amax Result 2 Design stress dictates max flaw size amax 1 K c Ysdesign amax s fracture no fracture fracture amax no fracture Y is a material behavior shape factor s 2 Figure 8 7 Two mechanisms for improving fracture toughness of ceramics by crack arrest a Transformation toughening of partially stabilized zirconia involves the stressinduced transformation of tetragonal grains to the monoclinic structure which has a larger specific volume The result is a local volume expansion at the crack tip squeezing the crack shut and producing a residual compressive stress b Microcracks produced during fabrication of the ceramic can blunt the advancing crack tip Fatigue behavior Fatigue failure under cyclic stress specimen compression on top bearing bearing motor counter flex coupling tension on bottom s Stress varies with time smax key parameters are S stress amplitude sm and frequency sm smin S time Key points when designing in Fatigue inducing situations fatigue can cause part failure even though smax sc fatigue causes 90 of mechanical engineering failures Because of its importance ASTM and ISO have developed many special standards to assess Fatigue Strength of materials Fatigue corresponds to the brittle fracture of an alloy after a total of N cycles to a stress below the tensile strength Fatigue Design Parameters Fatigue limit Sfat no fatigue failure if S Sfat S stress amplitude case for steel typ unsafe Sfat safe Fatigue Limit is defined in ASTM D671 10 3 5 7 9 10 10 10 N Cycles to failure However Sometimes the fatigue limit is zero S stress amplitude case for Al typ unsafe safe 10 3 5 7 9 10 10 10 N Cycles to failure Fatigue Mechanism Cracks in Material grows incrementally da m K dN typ 1 to 6 s a increase in crack length per loading cycle crack origin Failed rotating shaft crack grew even though Kmax Kc crack grows faster as s increases crack gets longer loading freq increases Improving Fatigue Life 1 Impose a compressive surface stresses to suppress surface crack growth S stress amplitude Increasing sm near zero or compressive sm moderate tensile sm Larger tensile sm N Cycles to failure Method 1 shot peening Method 2 carburizing shot put surface into compression 2 Remove stress concentrators C rich gas bad better bad better Other Issues in Failure Stress Corrosion Cracking Water can greatly accelerate crack growth and shorten life performance in metals ceramics and glasses Other chemicals that can generate or provide H or O2 ions also effectively reduce fatigue life as these ions react with the metal or oxide in the material The drop in strength of glasses with duration of
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