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DOBSON+CH9 - FAILURE •  Fracture •  Fa)gue ...

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Unformatted text preview: FAILURE •  Fracture •  Fa)gue •  Creep Duc)le Failure/Fracture The degree of plas)city (e.g. necking in the presence of tensile stress) is used to classify the form of facture. Significant deforma)on before fracture is consistent with duc$le fracture (see (a) right). Duc)le Moderately BriLle Duc)le FRACTURE- separa)on of a body into two or more parts in response to a sta)c stress, at temperatures low with respect to the mel)ng point. Duc)le Failure/Fracture A variety of common forms of fracture have been recognized in metals and alloys and classified in terms of the shapes and paLerns. As such, the field relies heavily on microscopic inves)ga)on of fractured surfaces. Tensile Stress Shear Stress Duc)le Failure/Fracture • Failure Stages: necking σ • Resulting fracture surfaces void nucleation shearing void growth and coalescence at surface fracture 50 mm 50 mm (steel) 100 mm particles serve as void nucleation sites. Fracture surface of tire cord wire loaded in tension. BriLle Fracture •  Li+le plas0c deforma0on •  Rapid crack propaga0on •  Rela)vely flat fracture surface •  Crack mo)on perpendicular to direc)on of tensile stress www.youtube.com/watch?v=i1bk5LwM- JM BriLle Fracture •  Fracture may occur through transgrannular or intergrannular pathways. •  Composi)onal modifica)on of grain boundary structures plays an obvious role in influencing the opera)ve pathway. 4 mm Moderately duc)le vs. briLle failure cup-and-cone fracture - Al brittle fracture - Steel void nucleation Principles of fracture mechanics Maximum Stress Fracture is oUen nucleated at defect structures. Such structures serve to concentrate applied stress on a local region of material. Maximum stress is experienced at the “crack )p” and is a func)on of the crack length (a) and curvature (ρ ). t 1/ 2 ⎛ྎ a ⎞ྏ σm = 2σo ⎜ྎ ⎟ྏ ⎜ྎ ρ ⎟ྏ ⎝ྎ t ⎠ྏ = K t σo ρt = radius of curvature σo = applied stress σm = stress at crack )p Principles of fracture mechanics STRESS CONCENTRATION The amplifica0on of stress is oUen related through the stress concentra0on factor (Kt), ra)o of maximum stress to applied stress. 1/ 2 Where: ⎛ྎ a ⎞ྏ σm σm = maximum tensile stress Kt = = 2⎜ྎ ⎟ྏ σ0 = applied tensile stress σ o ⎝ྎ ρt ⎠ྏ CRITICAL STRESS (CRACK PROPAGATION) It can be shown that the cri)cal stress (σc) required to propagate a crack in briLle material is given by € 1/ 2 ! 2 Eγ s $ σ c = 2# & " πa % Where: E=modulus of elasticity γs = specific surface energy a = ½ the length of an internal crack Principles of fracture mechanics FRACTURE TOUGHNESS A measure of a material’s resistance to bri+le fracture when a crack is present The fracture toughness (Kc) of a material can be expressed in terms of the cri)cal stress (σc). c c Y is a dimensionless parameter dependent on crack and specimen size as well as geometry. K = Yσ πa Design using fracture mechanics The maximum allowable flaw size (a) is given by 1 ⎛ྎ K Ic ⎞ྏ ac = ⎜ྎ ⎟ྏ π ⎝ྎ σY ⎠ྏ € 2 Principles mpact Tes$ng echanics I of fracture m www.youtube.com/watch?v=WNl5NhBRcnQ&feature=related www.youtube.com/watch?v=aywBYH25CV4&feature=related (Izod) *Qualita0ve (Charpy) final height initial height Impact energy: Computed form the difference in the ini)al and final height Duc)le- to- BriLle Transi)on Temperature (DBTT) One of the primary func)ons of Charpy and Izod tests is to determine whether or not a material experiences a duc0le- to- bri+le transi0on with decreasing temperature and, if so, the range of temperatures over which it occurs. Impact Energy FCC metals (e.g., Cu, Ni) BCC metals (e.g., iron at T < 914ºC) polymers Brittle More Ductile High strength materials ( σ y > E/150) Temperature Ductile-to-brittle transition temperature Design Strategy: Stay above the DBTT! • Pre-WWII: The Titanic • WWII: Liberty ships • Problem: Steels were used having DBTT’s just below room temperature. Cyclic Stress: Fa)gue FATIGUE: a form of failure resul)ng from dynamic or fluctua)ng stresses. It is usually catastrophic, sudden, and briLle- like. Cyclic Stresses Cyclic stresses occur in a variety of forms: Reverse stress involves stresses of equal magnitude but opposite sign. Repeated stress involves stresses oscilla)ng between a max and min value. Random stress involves irregular amplitude and frequency fluctua)ons. Cyclic Stress: Fa)gue Cyclic Stresses Cyclic stresses are characterized through the following defined quan))es: σ max + σ min Mean stress σm = 2 σ r = σ max − σ min Range of stress Stress amplitude σ = σ r = σ max − σ min a 2 2 σ min Stress ra0o R= σ max The S- N Curve Fa)gue is oUen evaluated by subjec)ng samples to repeated cyclical loading (stress), monitoring the number of cycles to failure. The analysis involves a plot of the stress amplitude (S) versus cycles (N) to failure. Two characteris)c behaviors are observed: *No fatigue if S < Sfat Lower stress amplitude limit, below which failure does not occur - fa)gue limit. Mainly iron and Ti alloys For some materials, there is no fa0gue limit! Con)nuously increasing number of cycles with decreasing amplitude case for steel (typ.) unsafe Sfat safe 10 3 5 7 9 10 10 10 N = Cycles to failure S = stress amplitude Fatigue limit: Sfat S = stress amplitude The S- N Curve case for Al (typ.) unsafe safe 10 3 5 7 9 10 10 10 N = Cycles to failure www.youtube.com/watch?v=q02AjT5cEgc www.youtube.com/watch?v=P0Fi1VcbpAI&feature=related Crack ini)a)on and propaga)on Fa)gue failure occurs through- 1)  Crack ini0a0on 2)  Crack propaga0on 3)  Final failure Cracks associated with fa)gue failure almost always nucleate at the surface of a component. Crack nuclea)on sites include surface scratches, sharp fillets, keyways, threads, dents… Benchmarks (macroscopic) Stria)ons (microscopic) Improving fa)gue life Many factors can influence fa)gue life. 1) Environment, 2) Geometry, 3) Surface finish, 4) Mean stress 1. Surface Treatments --Method 1: shot peening shot put surface into compression 2. Remove stress concentrators bad bad better better --Method 2: Polishing --Method 3: carburizing C-rich gas Creep The mode of failure experienced at elevated temperatures under which a sta0c stress produces 0me dependent and permanent deforma0on. Primary Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state i.e., constant slope (Δε/Δt). Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate. Adapted from Fig. 8.28, Callister & Rethwisch 8e. Creep: Temperature Dependence • Occurs at elevated temperature, T > 0.4 Tm (in K) tertiary primary elastic secondary ...
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