Materials Science Chapter 7 PDF

CHAPTER 7 Mechanical Properties Of Metals - II 1  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Failure of Materials and Components In selection of materials for various component, the e...

CHAPTER 7 Mechanical Properties Of Metals - II 1  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Failure of Materials and Components In selection of materials for various component, the engineer must always be aware of the possibility of failure. Failure is generally defined as the inability of a component to safely and reliably perform the intended function. From a materials and mechanics point of view failure may take different shapes including yielding, fracture, buckling, wear, and corrosion. Fracture is the most catastrophic type of failure and is defines as formation of new surfaces under stress (see the fracture and newly formed surfaces above) and separation into multiple parts. 2 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fracture of Metals – Ductile Fracture Fracture may be classified into brittle and ductile. Ductile fracture is accompanied by extensive plastic deformation and slow crack propagation. Three stages of ductile fracture in a tensile specimen are: Crack formed by coalescence Ø Specimen forms a neck and of cavities cavities within neck. Note the difference in diameter along Neck the specimen. Change in Ø Cavities form crack and crack direction crack propagates towards surface, perpendicular to stress. Ø Direction of crack changes to 45o resulting in cup & cone Ductile fracture surface – fracture. note dimples due to intergranular void formation and coalescence 3 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fracture of Metals – Brittle Fracture Brittle fracture is accompanied by little or no plastic deformation and very fast crack propagation. Brittle fracture proceeds along cleavage planes (see figure below right) under a stress normal to that plane. Ø Many HCP and BCC metals fracture in a brittle manner at room temperature. Ø Brittle fracture is transgranular or intragranular – propagates across the matrix of the crystal (note ductile fracture is intergranular – propagates between grains at the boundary). 4 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fracture of Metals – Brittle Fracture Brittle fracture also occurs in three stages. Ø Formation and concentration of dislocations along slip planes Ø Shear stress buildup due to dislocation pileup along the planes resulting in nucleation of microcracks Ø Propagation of microcracks and release of stored energy Existing defects in a metal, hydrogen diffusion, corrosion, and geometrical stress risers give rise to brittle fracture. Low operating temperatures and fast loading rates also cause promote brittle behavior. Brittle fractures are very dangerous because they occur with little advanced warning. Usually, a large noise accompanies the fracture. Brittle fracture of a snap ring – note the arrow indicating the initiation point 5 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Comparison of Ductile and Brittle Fractures Ductile fracture Brittle Fracture Class Discussion Topic: Discuss all differences that you observe between the above figures. 6 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Toughness and Impact Testing Dynamic or Impact Toughness is a measure of materials ability to absorb energy before fracture. In situations where impact takes place, Charpy V- notch specimen for instance in collision of mating gear teeth, toughness plays a key role. Dynamic toughness is measured using impact testing machine and a Charpy V-notch specimen In general, ductile materials are tougher than brittle materials. Why? Class Discussion Topic: Discuss how this machine works and what it measures (use the figure). 7 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Ductile to Brittle Transition - DBT The Titanic failure: Titanic’s hull was made up of a type of steel which was sensitive to low temperatures. The steel was ductile at room temperature but became highly brittle at freezing temperatures. On the day of accident, sea temperature was –2oC which made the hull material highly brittle. Impact with the large iceberg and the ductile-to-brittle transition (DBT) of the material resulted I in catastrophic brittle fracture. Class Discussion Topic: Given the impact toughness results, discuss the effect of temperature on the behavior of the metal (focus on the black curves). The difference between red and black 8 curves is the carbon content, what is your Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi conclusion.  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fracture Toughness All materials have small cracks and flaws. Pre-existing cracks and flaws cause stress concentration (amplification). A designer must always consider the possibility of pre-existing cracks and flaws. Note at the crack tip in the figure, the stress is much higher than the far field or nominal stress giving rise to the stress intensity factor, K I. K I = Yσ f πa σaf = Applied or nominal stress = edge crack length (half of the central crack length) Y = geometric constant If the calculated KI exceed the experimental value of critical stress intensity factor, KIC or fracture toughness, the crack extends. 9 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Measuring Fracture Toughness A notch is machined in a specimen of sufficient thickness B. The thickness B must be significantly larger than crack length a. B = 2.5(KIC/Yield strength)2 Specimen is tensile tested to failure. Higher the KIC value, the more ductile the metal is. The KIC value is used in design to find allowable or critical crack size with consideration of a factor of safety. The designed component can operate safely as long as the existing cracks are smaller than the calculated critical crack size. 10 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Cyclic Stresses and Fatigue In real engineering applications, the stresses applied to a component are rarely truly contestant and there are always fluctuations as a function of time. This type of cyclic stress with random amplitude and frequency is often encountered in real life. Cyclic stresses are very dangerous even in low amplitudes. Cyclic stresses, even at low amplitudes below the yield point, when they are elastic, can cause fatigue damage or failure. The damage is almost always internal and hidden and grows slowly over time and with many cycles. The eventual fracture is sudden and catastrophic. 11 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Cyclic Stresses Different types of cyclic or fluctuating stresses are possible (axial, torsional and flexural). In laboratory tests, the cyclic stresses are controlled in amplitude and frequency. The key applied stresses are σmax and σmin. Based on the above applied stresses, four other parameters may be calculated: σ + σ min σ −σ Mean stress, σ m = max ; Stress amplitude, σ a = max min ; 2 2 σ min Stress ratio, R = ; and Stress range, σ r = σ max − σ min 12 σ max Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Cyclic Stresses If σm = 0, σmax = - σmin and the loading is called fully reversed. In a fully reversed case, σr (stress range) = 2σa (stress amplitude) and R (stress ratio)= 1. If both σm ≠ 0, the loading is called repeated. In a repeated loading case, both σmax and σmin may be positive, negative, or different signs. The stress amplitude, σa,plays a key role in fatigue failures. The higher its value, the more extensive the damage. The mean stress, σm, plays a lesser role in fatigue damage. 13 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fatigue Failures Under cyclic loading, components often fail at stress levels well below the yield strength of the material (the stress is elastic). In these situations, cracks nucleate at regions of stress concentration. Fatigue fractured surface of keyed shaft Regions of stress concentrations could be around machined keyways, at locations where shaft diameters change, or around a small internal cracks or inclusions. Fracture started here Cracks continue to propagate with every cycle until the final failure when the remaining cross sectional area of the component is too small. Beach marks 14 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fatigues Testing In a laboratory fatigue test (R. R. Moore test), alternating compression and tension load is applied on metal piece tapered towards center, called. The specimen rotates and each full rotation represents a cycle. The applied stress S is held constant. At each stress, S, the number of cycles, N, needed to cause failure are counted. The S-N points are plotted to form the S-N curve. 15 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Structural Changes in Fatigue Process Crack initiation occurs first. Reversed directions of crack initiation cause surface ridges and groves called slipband extrusion and intrusion. This is stage I and is very slow (10-10 m/cycle). Crack growth changes direction to be perpendi- cular to maximum tensile stress (rate microns/sec). Sample ruptures by ductile failure when remaining Persistent slip bands cross-sectional area is small In copper crystal to withstand the stress. 16 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Factors Affecting Fatigue Strength Stress concentration: Fatigue strength is reduced by increasing stress concentration. Surface roughness: Smoother surface increases the fatigue strength and fatigue life. Surface condition: Surface treatments like carburizing and nitriding increases fatigue life. Environment: Chemically reactive environment, which might result in corrosion, decreases fatigue life. 17 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fatigue Crack Propagation Rate Notched specimen used. Cyclic fatigue action is generated. Crack length is measured by change in potential produced by crack opening. 18 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Stress & Crack Length Fatigue Crack Propagation. When ‘a’ is small, d a/dN is also small. d a/dN increases with inc- reasing crack length. Increase in σ increases crack growth rate. da = fatigue crack growth da dN rate. α f(σ, a) dN ΔK = Kmax-Kmin = stress m = AΔK intensity factor range. A,m = Constants depending on material, environment, frequency temperature and stress ratio. 19 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fatigue Crack Growth rate ΔK ⎛ da ⎞ Log⎜⎜ ⎟⎟ = Log( AΔK m ) ⎝ dN ⎠ = m.Log( ΔK ) + Log( A) Straight line with slope m Limiting value of ΔK below Which there is no measurable Crack growth is called stress intensity factor range threshold ΔKth 20 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fatigue Life Calculation da = AΔK m dN But ΔK = Yσ πa m m Therefore ΔK m = y mσ mπ 2 a 2 m m da Therefore = A( y mσ mπ 2 a 2 ) dN Integrating from initial crack size a0 to final crack size af at number of fatigue cycles Nf af m m Nf m m 2 2 ∫ da = Ay σ π a ∫ dN m m −( ) +1 −( ) +1 a0 0 af 2 − a0 2 Integrating and solving for Nf Nf = m m m m (Assuming Y is independent of crack length) Ay σ π ( − 2 + 1) 21 2 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Creep in Metals Creep is progressive deformation under constant stress. Important in high temperature applications. Primary creep: creep rate decreases with time due to strain hardening. Secondary creep: Creep rate is constant due to simultaneous strain hardening and recovery process. Tertiary creep: Creep rate increases with time leading to necking and fracture. 22 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Creep Test Creep test determines the effect of temperature and stress on creep rate. Metals are tested at constant stress at different temperature & constant temperature with different stress. Creep strength: Stress to produce Minimum creep rate of 10-5%/h At a given temperature. 23 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Creep Test (Cont..) Creep rupture test is same as creep test but aimed at failing the specimen. Plotted as log stress versus log rupture time. Time for stress rupture decreases with increased stress and temperature. 24 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Larsen Miller Parameter Larsen Miller parameter is used to represent creep-stress rupture data. P(Larsen-Miller) = T[log tr + C] T = temperature(K), tr = stress-rupture time h C = Constant (order of 20) Also, P(Larsen-Miller) = [T(0C) + 273(20+log tr) or P(Larsen-Miller) = [T(0F) + 460(20+log tr) At a given stress level, the log time to stress rupture plus constant multiplied by temperature remains constant for a given material. 25 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Larsen Miller Parameter If two variables of time to rupture, temperature and stress are known, 3rd parameter that fits L.M. parameter can be determined. Example: For alloy CM, at 207 MPa, LM parameter is 27.8 x 103 K Then if temperature is known, time to rupture can be found. 26 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display L.M. Diagram of several alloys Example: Calculate time to cause 0.2% creep strain in gamma Titanium aluminide at 40 KSI and 12000F From fig, p = 38000 38000 = (1200 + 460) (log t0.2% + 20) t=776 h 27 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Case Study – Analysis of Failed Fan Shaft Requirements Ø Function – Fan drive support Ø Material 1045 cold drawn steel Ø Yield strength – 586 Mpa Ø Expected life – 6440 Km (failed at 3600 km) Visual examination (avoid additional damage) Ø Failure initiated at two points near fillet Ø Characteristic of reverse bending fracture 28 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Failed Shaft – Further Analysis Tensile test proved yield strength to be 369 MPa (lower than specified 586 MPa). Metallographic examination revealed grain structure to be equiaxed ( cold drawn metal has elongated grains). Conclusion: Material is not cold drawn – it is hot rolled !. Ø Lower fatigue strength and stress raiser caused the failure of the shaft. 29 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Recent Advances: Strength + Ductility Coarse grained – low strength, high ductility Nanocrystalline – High strength, low ductility (because of failure due to shear bands). Ductile nanocrystalline copper : Can be produced by Ø Cold rolling at liquid nitrogen temperature Ø Additional cooling after each pass Ø Controlled annealing Cold rolling creates dislocations and cooling stops recovery 25 % microcrystalline grains in a matrix of nanograins. 30 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi  Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Fatigue Behavior of Nanomaterials Nanomaterials and ultrafine Ni are found to have higher endurance limit than microcrystalline Ni. Fatigue crack growth is increased in the intermediate regime with decreasing grain size. Lower fatigue crack growth threshold Kth observed for nanocrystalline metal. 31 Foundations of Materials Science and Engineering, 6th Edn. Smith and Hashemi