Fracture, Toughness, Fatigue, and Creep Materials Science & Manufacturing PROCESSES

Why Study Failure In order to know the reasons behind the occurrence of failure so that we can prevent failure of products by improving design in the light of failure reasons

Mechanical Failure ISSUES TO ADDRESS... • How do flaws in a material initiate failure? • How is fracture resistance quantified; how do different material classes compare? • How do we estimate the stress to fracture? • How do loading rate, loading history, and temperature affect the failure stress? Mechanical failure is the change in the structure/material that refrains the specimen to perform its intended operation Flaws include micro-cracks, voids, stress concentrations, etc Ship-cyclic loading from waves. Computer chip-cyclic thermal loading. Hip implant-cyclic loading from walking.

What is a Fracture? Fracture is the separation of a body into two or more pieces in response to an imposed stress that is static and at temperatures that are low relative to the melting temperature of the material. The applied stress may be tensile, compressive, shear, or torsional Any fracture process involves two steps—crack formation and propagation—in response to an imposed stress. (Static stress: constant or slowly changing in magnitude with time). the present discussion will be confined to fractures that result from uniaxial tensile loads

Fracture Modes Ductile fracture Brittle fracture Occurs with plastic deformation Material absorbs energy before fracture Crack is called stable crack: plastic deformation occurs with crack growth. Also, increasing stress is required for crack propagation. Brittle fracture Little or no plastic deformation Material absorb low energy before fracture Crack is called unstable crack. Catastrophic 0. Classification is based on the ability of a material to experience plastic deformation. 1. Ductile materials typically exhibit substantial plastic deformation with high energy absorption before fracture

Ductile vs Brittle Failure • Classification: Very Ductile Moderately Brittle Fracture behavior: Large Moderate (%EL)=100% Small Very ductile: Gold, graphite at room temperature; Polymers, Cu at elevated temp Most of metal alloys, fracture is preceded by necking Ceramics • Ductile fracture is usually desirable! Ductile: warning before fracture, as increasing is required for crack growth Brittle: No warning

Example: Failure of a Pipe • Ductile failure: --one/two piece(s) --large deformation • Brittle failure: --many pieces --small deformation

Moderately Ductile Failure- Cup & Cone Fracture • Evolution to failure: void nucleation void growth and linkage shearing at surface necking s fracture • Resulting fracture surfaces (steel) 50 mm particles serve as void nucleation sites. 100 mm In most cases, crack occurs perpendicular to force applied crack occurs perpendicular to tensile force applied

Ductile vs. Brittle Failure 2. Brittle fracture takes place without any appreciable deformation, and by rapid crack propagation. The direction of crack motion is very nearly perpendicular to the direction of the applied tensile stress and yields a relatively flat fracture surface, as indicated in Figure cup-and-cone fracture brittle fracture

Transgranular vs Intergranular Fracture 1. For most brittle crystalline materials, crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes (Figure a); such a process is termed cleavage. This type of fracture is said to be transgranular, because the fracture cracks pass through the grains. 2. In some alloys, crack propagation is along grain boundaries this fracture is termed intergranular 3. Scanning electron fractograph showing an intergranular fracture surface. 50 magnification Intergranular Fracture Transgranular Fracture

Brittle Fracture Surfaces • Intergranular (between grains) • Transgranular (within grains) 304 S. Steel (metal) 316 S. Steel (metal) 160 mm 4 mm Polypropylene (polymer) Al Oxide (ceramic) 3 mm 1 mm

Stress Concentration- Stress Raisers σm › σo Suppose an internal flaw (crack) already exits in a material and it is assumed to have a shape like a elliptical hole: The maximum stress (σm) occurs at crack tip: where t = radius of curvature so = applied stress sm = stress at crack tip Kt = Stress concentration factor t The measured fracture strengths for most brittle materials are significantly lower than those predicted by theoretical calculations based on atomic bonding energies. This discrepancy is explained by the presence of very small, microscopic flaws or cracks that always exist under normal conditions at the surface and within the interior of a body of material. These flaws are a detriment to the fracture strength because an applied stress may be amplified or concentrated at the tip, the magnitude of this amplification depending on crack orientation and geometry. This phenomenon is demonstrated in Figure. Due to their ability to amplify an applied stress in their locale, these flaws are sometimes called stress raisers. Theoretical fracture strength is higher than practical one; Why?

Concentration of Stress at Crack Tip

Engineering Fracture Design • Avoid sharp corners! s r/h sharper fillet radius increasing w/h 0.5 1.0 1.5 2.0 2.5 Stress Conc. Factor, K t s m o = r , fillet radius w h o s max Kt Explain effect of increasing W/h on Kt

Crack Propagation Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, “blunting” the crack. deformed region brittle Effect of stress raiser is more significant in brittle materials than in ductile materials. When σm exceeds σy , plastic deformation of metal in the region of crack occurs thus blunting crack. However, in brittle material, it does not happen. plastic When σm › σy Blunt -> make less intense Elastic strain energy is also called as Resilience energy

Fracture Toughness: Design Against Crack Growth • Crack growth condition: Kc = • Largest, most stressed cracks grow first! --Result 1: Max. flaw size dictates design stress (max allowable stress). amax no fracture --Result 2: Design stress dictates max. allowable flaw size. amax no fracture Kc is the fracture toughness Y is a dimensionless parameter or function that depends on both crack and specimen sizes and geometries, as well as the manner of load application. Relative to this Y parameter, for planar specimens containing cracks that are much shorter than the specimen width, Y has a value of approximately unity. For example, for a plate of infinite width having a through-thickness crack Y=0; whereas for a plate of semi-infinite width containing an edge crack of length Y=1.1 σc σc

Fracture Toughness Brittle materials do not undergo large plastic deformation, so they posses low KIC than ductile ones. KIC increases with increase in temp and with reduction in grain size if other elements are held constant KIC reduces with increase in strain rate

Design Example: Aircraft Wing • Material has Kc = 26 MPa-m0.5 • Two designs to consider... Design A --largest flaw is 9 mm --failure stress = 112 MPa Design B --use same material --largest flaw is 4 mm --failure stress = ? • Use... • Key point: Y and Kc are the same in both designs. 9 mm 112 MPa 4 mm --Result: Pay off -> Yield a profit or result Answer: • Reducing flaw size pays off!

Impact Tests A material may have a high tensile strength and yet be unsuitable for shock loading conditions Impact testing is testing an object's ability to resist high-rate loading. An impact test is a test for determining the energy absorbed in fracturing a test piece at high velocity Types of Impact Tests -> Izod test and Charpy Impact test In these tests a load swings from a given height to strike the specimen, and the energy dissipated in the fracture is measured 3. Impact energy is a measure of the work done to fracture a test specimen 4. Izod -> (notched or unnotched) 5. The test is particularly useful in showing the decrease in ductility and impact strength of materials of bcc structure at moderately low temperatures

A. Charpy Test (Charpy) Impact energy= Kinetic energy + energy absorbed by specimen final height initial height Energy absorbed during test is determined from difference of pendulum height

b. Izod Test Izod test varies from charpy in respect of holding of specimen It is used more as a comparative test rather than a definitive test … although specimens with no notch as also used on occasion

Effect of Temperature on Toughness • Increasing temperature... --increases %EL and Kc • Ductile-to-Brittle Transition Temperature (DBTT)... Low strength FCC metals (e.g., Cu, Ni) Low strength BCC metals (e.g., iron at T < 914°C) polymers Impact Energy Brittle More Ductile Kc -> fracture toughness A material experiences a ductile-to-brittle transition with decreasing temperature. At higher temperatures the CVN (Charpy V-Notch) energy is relatively large, in correlation with a ductile mode of fracture. As the temperature is lowered, the impact energy drops suddenly over a relatively narrow temperature range, below which the energy has a constant but small value; that is, the mode of fracture is brittle High strength materials ( s y > E/150) Temperature Ductile-to-brittle transition temperature

Fatigue Test Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating loads (e.g. bridges, aircrafts, ships and m/c components) The term Fatigue is used because this type of failure occurs after a lengthy period of repeated stress of strain cycling. Failure stress in fatigue is normally lower than yield stress under static loading. Fatigue failure is brittle in nature even in ductile metals The failure begins with initiation and propagation of cracks

Types of Cyclic Stresses

Types of Cyclic Stresses Random Stress Cycle

Terms Related to Cyclic Stresses Mean stress: Range of stress: Stress Amplitude: Stress Ratio:

4. Creep Creep is defined as time dependent plastic deformation under constant static load/stress (steam turbines blades under centrifugal force, pipes under steam pressure) at elevated temperatures At relatively high temperatures creep appears to occur at all stress levels, But the creep rate increases with increasing stress at a given temperature. 2. Another definition of term “creep” 3. … Measurements of strain are then recorded over a period of time

4. Creep Test A creep test involves a tensile specimen under a Constant Load OR Constant Stress maintained at a constant temperature. Temperature: Greater than 0.4Tm

Stress & Temp Effects on Creep Time to rupture decreases as imposed stress or temperature increases Steady creep rate increases with increase of stress and temperature

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