Fracture Mechanics and Fatigue Analysis in Engineering

Fracture Stress

Stress at which material fails under load.

Central Crack

Crack located at the center of a material.

Fracture Toughness

Material's ability to resist crack propagation.

Crack Length

Distance from crack tip to opposite side.

Edge Crack

Crack located at the edge of a material.

Critical Crack Length

Crack length at which failure occurs.

Fracture Toughness Value

Measured in MPa√m for materials.

Nominal Stress

Applied stress averaged over a cross-section.

Factor of Safety

Safety margin to prevent failure, typically >1.

Cyclical Loading

Repeated application of load over time.

Stress Amplitude

Difference between maximum and minimum stress.

S-N Curve

Graph showing relationship between stress and number of cycles to failure.

Miner's Principle

Cumulative damage approach for fatigue failure.

Remaining Life

Estimated cycles until failure occurs.

Transverse Force

Force applied perpendicular to the length of a beam.

Bending Moment

Moment causing a beam to bend.

Square Section Beam

Beam with equal width and height dimensions.

Diameter of Holes

Width of circular openings in a material.

Spacing of Holes

Distance between consecutive holes in a row.

Load Direction

Orientation of applied forces on a structure.

Aluminium Alloy

Metallic material known for lightweight and strength.

Yield Stress

Stress at which material begins to deform permanently.

Ultimate Tensile Strength

Maximum stress material can withstand before failure.

Force Amplitude (Fa)

Maximum variation in force applied to a structure.

Modified Goodman

Fatigue failure criterion considering mean and alternating stress.

Gerber Parabola

Fatigue failure criterion using parabolic relationship.

Soderberg Criterion

Fatigue failure criterion based on yield stress.

Cantilever Beam

Beam fixed at one end, free at the other.

Bending Moment (M)

Moment causing bending in a beam, calculated as F times distance.

Bending Stress (σ)

Stress induced in a beam due to bending moment.

Second Moment of Area (I)

Measure of a beam's resistance to bending, calculated as bd³/12.

Fatigue Limit (SD)

Maximum stress level a material can withstand for infinite cycles.

Strain Life Equation

Equation relating strain amplitude to cycles to failure.

True Strain Amplitude

Strain experienced by material during cyclic loading.

Plastic Strain

Permanent deformation occurring after yield point is surpassed.

Paris Law

Describes crack growth rate in materials under cyclic loading.

Crack Growth Rate (da/dN)

Rate of increase in crack length per loading cycle.

Stress Ratio (R)

Ratio of minimum to maximum stress in a loading cycle.

Constants in Paris Law

Parameters determining the relationship between stress intensity and crack growth.

Average Crack Length (a)

Mean length of crack used in calculations.

Error in Cycles to Failure

Difference in predicted cycles due to ignoring plastic strain.

Elastic Term

Component of strain related to reversible deformation.

∆K

Stress intensity factor range during loading.

da/dN

Crack growth rate per loading cycle.

Cycle Counter

Counts loading cycles during crack testing.

Second Moment of Area

Measure of an object's resistance to bending.

Mass Capacity

Maximum weight a structure can support.

Cyclic Loading

Repeated application of load over time.

Surface Flaw

Imperfection on material surface affecting performance.

Radius of Bars

Distance from center to outer edge of bars.

Thickness of Wall

Distance between inner and outer surfaces of a bar.

Loading Cycles

Number of times a load is applied.

Angle of Swing

Maximum angle of deviation from vertical.

AISI 4000 Series Steel

Steel alloy known for strength and toughness.

Necking

Localized reduction in cross-section during deformation.

Log-Log Axes

Graphical representation of data on logarithmic scales.

Integration Limits

Bounds for calculating area under a curve.

Mass of Boxing Bag

Weight of the bag affecting stress on bars.

Lifespan of Implant

Duration before implant failure due to wear.

MRI Monitoring

Imaging technique to detect fractures in implants.

Design Dead Load

Weight of bridge components per unit area.

Design Live Load

Weight of vehicles per unit area on bridge.

Cyclic Loads

Repeated loading and unloading affecting material fatigue.

Safety Factor

Ratio ensuring design can withstand unexpected loads.

Modified Stress Concentration Factor

Factor accounting for stress risers in materials.

Tensile Strength

Maximum stress material can withstand before failure.

Shear Stress

Stress parallel to the surface of a material.

Steel Plates

Structural components connecting cables to bridge deck.

Suspended Bridge

Bridge supported by cables from towers.

Body Weight Transfer

Force exerted by body weight through femur to implant.

Daily Steps

Number of steps taken by an individual daily.

Surface Imperfections

Flaws on material surfaces affecting performance.

Monitoring Sessions

Scheduled checks for implant integrity using MRI.

Tensile Yield Strength

Stress at which material yields under tension.

Fatigue Limit

Maximum stress material can endure for infinite cycles.

Cables in Bridge

Support elements transferring loads to towers.

Structural Bolts

Fasteners used to connect steel plates in construction.

Fracture Mechanics

Study of failure due to crack growth.

Fatigue

Crack growth under cyclical loading conditions.

Brittle Failure

Sudden failure without significant plastic deformation.

Ductile Failure

Failure characterized by significant plastic deformation.

Stress Intensity Factor

Measure of stress concentration at crack tips.

Critical Condition

State where failure occurs suddenly and catastrophically.

Damage Tolerance

Ability to function despite existing cracks.

Crack Propagation

Growth of cracks under applied loads.

Microscopic Cracks

Small cracks resulting from material imperfections.

Design Life

Expected lifespan of a structure before failure.

Monitoring

Regular checks to assess structural integrity.

High Strength Steels

Materials designed to withstand high service stresses.

Oscillatory Loading

Repeated loading that can induce fatigue.

Liberty Ships

Warships that suffered severe fracture issues.

Engineering Knowledge

Understanding of materials and their failure mechanisms.

Material Imperfections

Flaws that can initiate crack growth.

Fracture Cost

Annual economic impact of fracture failures.

Flaws in Materials

Defects that lead to crack formation.

Regular Monitoring

Scheduled assessments to track crack growth.

Remaining Life Prediction

Estimation of how long a component will last.

Service Stresses

Stresses experienced by a structure during use.

Fatigue Crack Growth Laws

Rules predicting how cracks grow over time.

Stress Concentration

Increased stress around geometric features like holes.