1What is Failure?Examining FailuresDuctileNecking or bendingDull, fibrous fractureShear “lips”BrittleLittle or no distortionFlat FractureBright/coarse textureConclusion: ductile and brittle materials fail differentlyCode of Hammurabi (~2000 BC)If a builder build a house for a man and do not make its construction firm, and the house which he has built collapse andcause the death of the owner of the house, that builder shall be put to death.If it cause the death of the son of the owner of the house, theyshall put to death a son of that builder…ASME Code of EthicsThe Fundamental Principles Engineers uphold and advance the integrity, honor and dignity of the engineering profession by: I. Using their knowledge and skill for the enhancement of human welfare; II. Being honest and impartial, and serving with fidelity the public, their employers and clients; and III. Striving to increase the competence and prestige of the engineering profession. The Fundamental Canons 1. Engineers shall hold paramount the safety, health and welfare of the public in the performance of their professional duties.+ 7 moreHow do parts fail? static loading dynamic loading wear corrosion embrittlement temperature effects heat affected zones …In this classStatic Failureparts fail only when stresses are greater than Syor Sut… right??well, it depends…2OK… Here’s the truth…All that we have are HYPOTHESES about why parts fail!and we will discuss these hypotheses over the next few days(your book erroneously calls these THEORIES)*with possible exception of Distortion EnergyDuctile Failurewhere Failure=YieldingDistortion Energy Theoryfailure occurs iff the total strain energy in a unit volume reaches or exceeds the strain energy in the same volume corresponding to the yield strengthDistortion Energy Theory (von Mises-Hencky)()()()2213232221σσσσσσσσ−+−+−=′≥′ySσ/Syσ/Syσ′=ySNDistortion Energy Derivation Cont.¾Von Mises Stress » the uniaxial tensile stress that would cause the same distortion energy as created by the actual stressesσ′()()()()()()()262222222213232221zxyzxyxzzyyxτττσσσσσσσσσσσσσσ+++−+−+−=′−+−+−=′In terms of applied stresses:Distortion Energy: Pure Shearτστmaxmax32max10τσστσ−===()()()()()( )yyyyySSSSS577.033222max2max2max2max2max213232221===++=−+−+−=′=τττττσσσσσσσSyDistortion vs. Max Shear3The Empirical SupportReproduced from Fig. 7.11,p. 252, in Mechanical Behavior of Materials by N. E. Dowling, Prentice-Hall, Englewood Cliffs, NJ, 1993)Ductile Failure Conclusions“Both the distortion-energy theory and the maximum shear theory are acceptable as failure criteria in the case of static loading of ductile, homogenous, isotropic materials whose compressive and tensile strengths are of the same magnitude.”(from Norton, Machine Design, 2ndedition)Brittle Failurewhere Failure=FractureBrittle FailureWhile ductile failure tends to be due to shear stresses and the sliding of atoms in the lattice of the material, normal stresses play some role in the failure of brittle materialsin tension: brittle materials fail due to normal tensile stress alone – what theory is appropriate?in compression: some combination of compressive normal and shear stresses cause failureCoulomb –Mohr & Modified MohrOn Brittle Materials… Many brittle materials are UNEVEN (especially cast brittle materials) Some cast, brittle materials have shear strengths greater than tensile strengthsModified Mohr4Modified Mohr Quadrant I – max normal stress¾ N=Sut/σ1 Quadrant IV – connect with straight lines()311σσσ+−=utucucutSSSSNSutSutSucσ1σ3-Sut-SutEmpirical Support (Brittle)Summary Ductile Material¾Distortion Energy preferred¾Maximum Shear OK Brittle Material¾Modified Mohr
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