ENB331 Materials and Manufacturing 2 Week 4.docx

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Course
ENB331
Professor
Prasad Yarlagadda
Semester
Spring

Description
ENB331 Lecture Materials and Manufacturing 2 Fracture Mechanics Most failures in Engineering Structures are due to:  Poor design  Defects introduced during processing and  Poor material selection fabrication  Assembly and service conditions  Imperfections in materials Classifications of Failure Mechanisms 1. Fracture: Failure of materials under static (constant) loading: a. Brittle fracture: breaking of materials following elastic deformation (fracture dominant failure) b. Ductile fracture: Failure due to elongation beyond point of necking (yielding dominant failure) 2. Fatigue: Time dependent failure due to repeated stress/strain (cyclic loading) 3. Creep: Time dependent strain (deformation under static load at high temperatures Ductile Fracture Yielding Dominant Failure: Formation of micro-voids and cavities at grain boundaries and/or interfaces between material and impurities. Coalescence of voids and cavities to form elliptical crack, in doing this, extensive plastic deformation around crack tip until critical crack length. Rapid propagation of crack by shear deformation at ~45° to tensile axis. CUP and CONE fracture Fibrous central region consisting of multiple “dimples” (left over from micro-voids). Shear lip (tearing) of the material at the outer region. Defects in “Yielding dominant failure” are microscopic: dislocations, interstitials, grain boundaries, precipitates. Brittle Fracture Fracture Dominant Failure: Crack propagates rapidly and perpendicular to tensile axis. Little or no plastic deformation around crack tip. Very flat fracture surface (Cleavage). Flaws are macroscopic i.e. weld defects, porosity (holes), inclusions, steel corrosion, cracks etc. Fracture through crystal Cracks propagate along grains transgular. the grain boundaries: intergranular fracture. In polycrystalline materials this can give a faceted e.g. solidification of brittle appearance as different films along grain crystallographic planes are boundaries can lead to exposed. intergranular fracture. Ductile Fracture Brittle Fracture  One piece  Many pieces  Large deformation  Small deformation 1 Week 4 Tuesday, 27 August 2013 ENB331 Lecture Materials and Manufacturing 2 Stress-Strain behaviour DaVinci observed: The longer the wire, the smaller the load for failure. This is because: Flaws cause premature failure, larger samples contain more flaws Stress Concentration The stress ahead of perpendicularly orientated elliptical notich in an infinite plate: The stress is concentrated due to notch and the maximum stresm σ (fracture stress) depends upon the radius of the notch tip, ρ. σm≈ σ * √ where √ Critical Stress Griffith formulated that failure of materials can be occurred beyond a critical crack length (Griffith Crack Length). The theoretical critical stress for crack propagation in a brittle material: ( ) E = modulus of elasticity γ = specific surface energy s 2 Week 4 Tuesday, 27 August 2013 ENB331 Lecture Materials and Manufacturing 2 Geomertical Effect of Cracks Geometrical changes of section, defects, flaws, holes etc concentrate stress differently. e.g. maximum stress at a circular hole in a plate is three times the nominal stress. Whereas an elliptical flaw concentre much higher stresses. Limitation of Stress Concentration Factor As the elliptical notch turns into a crack, ρ goes to m and σ tends to infinity. √ This suggests that the stress at the tip of all cracks is infinite, if stress at crack tip is infinite why don’t all cracks cause fracture at very low stresses? Material at the crack tip yield
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