Basic Science

Bone biomechanics - stress, strain and fatigue

Basic science overview plus stress-strain behaviour, viscoelasticity and fatigue failure of bone

31 questions 5 source pages

Images appear with the first question taken from each source page — tap a question to open it.

Q1What is the scope of this introductory basic science page?▸

Not covered in the speaker notes
the source image is the only source for this section

Q2Which basic science topics should be revised from this section?▸

Not covered in the speaker notes
No topic list is provided in the notes

Q3Describe the axes of a stress-strain curve.▸

Y axis = stress = force/area (N/m2)
X axis = strain = change in length over original length (no unit/%)
Graph measures tensile stress, but compressive and bending forces relate more to daily use

Q4Describe the elastic phase of the stress-strain curve.▸

Proportional change of stress and strain
Slope is Young's modulus, measuring material stiffness
Behaviour follows Hook's law

Q5What is Young's modulus and what does it measure?▸

Slope of the elastic phase of the stress-strain curve
Measures material stiffness

Q6Differentiate the proportionality limit, elastic limit and yield stress.▸

Proportionality limit: stress at which Hook's law is no longer obeyed
Elastic limit: stress at which deformation stops being entirely reversible (end of elastic phase)
Yield stress: stress needed to induce 0.2% permanent strain (start of plastic phase)

Q7What happens during the plastic phase of a stress-strain curve?▸

Yielding represents material bond breakage
The kink: upper and lower yield point due to grain dislocations and relocations, usually in ductile materials
Strain hardening increases resistance to further deformation
Highest point is the ultimate tensile strength (UTS), then necking and breakage

Q8What is strain hardening and how does cold working relate to it?▸

Plastic deformation increases a material's resistance to further deformation
Lattice defects become too numerous and restrict each other's movements
Cold working increases the yield point and ultimate tensile strength
At the expense of lower ductility and toughness

Q9What is necking and what causes it?▸

Dislocation of molecules after the UTS
Leads to reduction in the cross sectional area
Followed by breakage of the material

Q10What does the area under the stress-strain curve represent?▸

Toughness of the material
Energy absorbed per unit area before fracture

Q11Why is annealing performed and what are its three stages?▸

Heating above the recrystallisation temperature after cold working, to restore original properties
Stages: recovery, recrystallisation, grain growth
Reduces hardness, making it more workable for further work hardening, and relieves internal stresses
Increases ductility and enhances toughness

Q12Give the sequence of Young's modulus of materials.▸

Ceramic, cobalt chrome, stainless steel, titanium, matrix polymers
Then cortical bone, PMMA, PE, cancellous bone, tendon, cartilage

Q13What is special about the stress-strain behaviour of tendon and ceramic?▸

Tendon: initial toe phase when collagen fibres align longitudinally to take up stress; fails in a stepwise manner as fibres break sequentially
Ceramic: high Young's modulus with a very short/no plastic phase

Q14Define stiffness, hardness and rigidity.▸

Stiffness: ability of a material to resist deformation (slope of a load-displacement curve)
Hardness: resistance of a localised surface to deformation; takes into account stiffness and UTS; not a basic mechanical property
Rigidity: a structure's ability to resist deformation

Q15Define ductility, toughness and strength.▸

Ductility: degree of plastic deformation a material can undergo before failure
Toughness: energy per unit volume a material can absorb before failure (from ductility and the UTS)
Strength: maximal stress a material can withstand before fracture

Q16Define notch sensitivity, endurance limit and fatigue life.▸

Notch sensitivity: sensitivity to fracture from a surface inhomogeneity (do not mix up with scratch profile)
Endurance limit: stress withstand after 10 million cycles without fatigue failure
Fatigue life: number of cycles needed to cause failure at a specific stress level

Q17Draw and label a stress-strain curve (page task).▸

Label the elastic phase (slope = Young's modulus) and plastic phase
Mark proportionality limit, elastic limit, yield stress, UTS and breakage
Show area under the curve = toughness
page asks to draw the curve and give the sequence of Young's modulus, plus tendon and ceramic

Q18Define a viscoelastic material.▸

Materials sensitive to the time and rate at which the load is applied

Q19Compare the behaviour of an elastic solid and a viscous liquid.▸

Elastic solid: stores all the energy used to deform it
Viscous liquid: dissipates all the energy used to deform it by flow
Viscoelastic materials are intermediate in properties between the two

Q20Define creep.▸

Constant stress
Strain increases with time

Q21Define stress relaxation.▸

Constant strain
Stress decreases with time

Q22What is the effect of loading rate on stiffness in viscoelastic materials?▸

Strain behaviour is time dependent
Stiffness increases with increased rate of loading

Q23What is hysteresis?▸

Different stress-strain behaviour upon loading vs unloading
Due to heat dissipated when micromolecules move against each other

Q24What does an S-N curve show?▸

Number of cycles leading to fatigue fracture at a specific stress
Left side = low cycle fatigue; right side = high cycle fatigue

Q25What do the X and Y axes of the S-N curve represent?▸

X axis = number of cycles (N)
Y axis = stress (S)
Plots the number of cycles leading to fatigue fracture at a specific stress

Q26Define the endurance limit and what it divides.▸

Stress a material can withstand after 10 million cycles without fatigue failure
Divides finite-life fatigue from infinite-life fatigue

Q27Differentiate brittle fracture, fatigue fracture and creep fracture.▸

Brittle fracture: stress > UTS, single load
Fatigue fracture: below UTS, above endurance limit, repetitive load
Creep fracture: below UTS, above yield strength, constant load with time; fails when stretched out

Q28Define fatigue strength/limit.▸

Stress at which fracture occurs after a specified number of loading cycles
Contrast with the endurance limit, defined at 10 million cycles

Q29List the 3 zones of a fatigue fracture.▸

1. Crack initiation zone
2. Fatigue zone (beach marks)
3. Instantaneous zone

Q30What are ratchet marks and how do they form?▸

Formed when multiple fatigue origins are near each other
A crack starts at each origin; as cracks meet, a ridge or step is formed
Ratchet marks are not origins, but the location where cracks meet

Q31What are beach marks and when are they absent?▸

Alternating stripes of lighter and darker colour in the fatigue zone
Colours result from different loading levels or environmental conditions
Absent when cracks grow under uniform loading and environmental conditions

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Bone biomechanics - stress, strain and fatigue