MATLS3MO3: Final Exam Prep

Modules 3, 4 and 5

Examples of flaws/imperfections of materials

1) Casting defects: formed as a result of shrinkage of metal during solidification and/or release of gases dissolved in the liquid metals. Can be controlled by x-ray.

2) Machining: control using fluorescent dye inspection

3) Operational: visual control/inspection

How do defects impact the stress concentration of materials? How does this impact the yield stress of the material?

• Defects in the material are obstacles for the flow. Lines get denser in a region near the defect. The local stress concentration increases.

• As the tip radius decreases, the stress concentration at the tip increases significantly

• If the size of the crack is less than the tolerable crack size, the nominal stress at fracture is greater than the yield stress and fast fracture is not a concern. If it is greater than the tolerable crack size, the plate can fracture at stresses less than the yield strength.

Griffith’s Criterion

Energy associated with the advancement of a crack per unit area of the crack.

Region of material within a semicircle of radius a can be considered crack free. When the crack advances by delta a, the new volume shown in red becomes stress free.

Applicable for brittle materials only since metals range in a Griffiths criterion of 100-1000 J/m^2, whereas glass is a constant 10 J/m^2.

Irwin-Orowan Modification

They realized there is a plastic region of size rp at the tip of the crack that contributes to the high value of Gc in metals. When the crack advances by delta a, the plastic region also has to follow and the new region of the material has to undergo plastic deformation.

Size of the plastic zone (rp) is linked to the materials yield strength.

Design Principles

1. Design Space and Safety Factor SFk

2. Fracture Modes - only focus on Mode 1

3. Shape Factor - for an infinite plate, stress fields are not constrained (Y=1), for a final plate stress field is confined by the finite size (Y>1)

4. Orientation of Crack - largest crack opening stress when the crack is positioned at the normal angle to the stress, no stress when parallel to the stress

Toughening Definition (in terms of Toughening Mechanics)

Increase the work required for crack propogation

Requirements for high fracture toughness (high Gc)

Large flow stress and size of the plastic region at the same time (even though size of the plastic region decreases as the material strength increases)

Which types of materials have a larger plastic zone (rp)?

Stronger, brittle materials are less tough and weaker, more ductile materials are more tough. Stronger materials have a smaller plastic zone and tougher materials have a larger plastic zone.

How does size of plastic zone (rp) contribute to fracture toughness of materials?

Size of the plastic zone is proportional to Gc, inversely proportional to the yield strength in the second power.

Rp and Gc decrease due to higher material strength and lower fracture toughness.

Microscopy and SEM

Resolution is limited by the wavelength of light (500nm). You cannot see any features smaller than that.

Uses energetic electrons and the wave particle duality principle.

SEM (scanning electron microscopy): constructs an image from secondary electrons emitted from the surface of a specimen

Chemical information is obtained from characteristic x-rays

Fracture Modes

1. Microvoid Coalescence/Dimple Fracture (for ductile materials only): the fracture looks like mashed potatoes

2. Trans-Granular Clevage (for brittle materials): fracture surface is shiny and flat within each grain. River pattern present on the surface that indicates the direction of crack propogation.

3. Decohesive (Intergranular) Fracture (for brittle materials): Fracture looks like a collection of rocks. Indicative of embrittlement of grain boundaries (due to hydrogen). This mode is undesired and indicates material problems

4. Fatigue Failure (for cyclic loads): Macroscopic view reveals benchmarks that spread from the crack nucleation site. Possible to see striations at high magnification SEM.

What is Creep

Permanent deformation below the yield stress based on the time and Temp/Melting Temp ratio > 0.4

Engineering Applications of Creep

1. Displacement Limited Design: radial clearance is limited, high temp conditions leads to failure as gap closes

2. Rupture Time Limited Design

3. Stress Relaxation: preload is required for bolts. Preload decreases due to creep over time which could cause failure

Stages of Creep

1. Transient Creep: dislocation density increases, similar to work hardening, creep rate gradually decreases

2. Steady State Creep: no change in dislocation density, balance between dislocation creation and annihilation

3. Tertiary Creep: voids form at grain boundaries, microcracks begin to form, leads to eventual failure

Creep Design Parameters

1. time to rupture

2. creep rate at stage 2

Creep rate increases with T in a super linear character

Self Diffusion mass transfer is the primary mechanism responsible for creep deformation

Creep Mechanisms

1. Nabarro Herring Creep: T/Tm is high, stress is low. Mass transfer takes place through the body of the grains. n=1

2. Dislocation Creep: T/Tm is moderate, stress is high. Thermal energy helps overcome an energy barrier associated with the dislocation glide. Diffusion of vacancies promote dislocation climbing and help to overcome obstacles. n=3-7

3. Coble Creep: T/Tm is moderate, stress is moderate. Diffusion takes place through the grain boundaries. n=1

Factord Influencing Creep Resistence

1. Activation Energy: Increasing Qa leads to a higher creep resistance. Melting point is proportional to activation energy

2. Diffusivity: F.C.C and H.C.P materials have a closely packed lattice, reduced diffusivity and higher creep resistance. B.C.C materials have a loosely packed lattice, increased diffusivity and lower creep resistence

3. Grain Size: Increasing grain size (fewer boundaries, especially oriented perpendicular to the stress) improves creep resistance. Grain boundaries are diffusion pathways.

4. Second Phase Precipitates: presence of secondary phase in the form of coherent precipitates enhances creep resistance (widely used in aerospace technology)

What conditions are maintained in a creep test

Constant stress and temperature over time

How does applied stress impact strain rate

As applied stress increases, the strain rate increases significantly (often nonlinearly)

Parametric Dependencies of Creep

1. Larson-Miller Parameter (temp must be in kelvin): to estimate the lifespan of a material in creep, strain determined is independent of stress and temperature

2. Safety Factors

   1. stress

   2. time

   3. temperatures

What is used in strain limited design and estimating stress relaxation?

Isochronous stress/strain curves

Most common kind of failure of structural materials

Material fatigue

Low vs. High Cycle Fatigue

• Low cycle fatigue is accompanied by a plastic deformation every cycle, evident from hysteresis loop

• High cycle fatigue occurs exclusively in the elastic region

Materials can fail at stress < yield strength even in the absence of high temperatures

Two types of fatigue tests

1. Rotating bending fatigue tests: repeated bending loads while rotating

2. Axial fatigue: specimen is subjected to tensile or compressive loads under its axis

What indicates a higher fatigue resistence?

High tensile strength and low exponent b

Extrinsic Factors that Influence Fatigue Resistence

1. Specimen Size: larger probability of finding a flaw in a larger volume of the material

2. Surface Finish: the rougher the surface, the lower the fatigue strength

3. Residual Stresses: any type of machining produced residual stresses at the surface, tensile stresses reduce the fatigue strength, while compressive stress improves the fatigue strength. Special methods such as shot peening are used to created compressive stresses at the surface.

What is used to improve surface conditions to improve fatigue resistance?

Shot Peening creates compressive residual stresses at the surface. Surface tensile crack-opening stress is reduced when combined with an external load

Why is fracture mechanics needed instead of just tensile properties?

Because real materials contain flaws (cracks, pores), and failure is controlled by crack growth, not just bulk strength.

What does the stress intensity factor (K) represent

Describes the stress concentration at a crack tip and predicts whether a crack will grow.

When does fracture occur in fracture mechanics

When K = Kic (crack becmoes unstable and propogates)

What is fracture toughness (Kic)

Material property representing resistance to crack growth. Higher Kic = more resistant to fracture

Why is the geometry factor (Y) used?

To account for crack shape and location since real components are not idea (edge vs. center cracks)

Purpose of the 3-Point Bending Test

To measure the fracture toughness by loading a pre cracked specimen until fracture

What is Pq and how is it determined

Pq is the critical load at crack instability, found using the 95% secant line on the force displacement curve

What condition must be satisfied for valid fracture toughness results?

Pmax/Pq <= 1.1

How do heat treatments affect strength and fracture toughness

Annealed: low strength, high toughness. Lowest pq, lowest Kic due to no material development (as-recieved), highest crack size due to elasticity

Quenched (martensite): high strength, low toughness (brittle). Medium pq, medium kic, lowest tolerable crack size (quenched sample is brittle, heating is not controlled)

Tempered: balance strength and toughness. Highest pw, highest kic, medium crack size (improved elasticity due to tempering process)

How does deformation at high temperature differ from room temperature?

Room temperature: strain mainly depends on stress

High temperature (creep): strain depends on stress, time and temperature

Why is creep rate vs. time useful?

It makes it easier to identify creep stages compared to strain vs. time

What is the relationship between creep rate and strain in tertiary creep?

Creep rate increases linearly with strain. Higher strain means faster deformation.

How do stress and temperature affect creep?

Higher stress and temperature both mean faster creep