BENG 186A Lecture 2: Mechanical Properties

What are the mechanical properties of materials?

• Tensile/compressive

• Torsion/shear

• Strength

• Hardness

• Resilience/toughness

What is the formula for stress?

What is the formula for strain?

What is the difference in direction of force for tensile or normal stress, and shear stress?

Tensile is when force is perpendicular and shear stress is when force is parallel.

What is the formula for shear stress?

How to convert between nominal strain and true strain?

When would you expect the nominal strain to be very different than the true strain?

When the material undergoes large deformations.

What are the equations for Young’s modulus, Shear modulus, and Bulk Modulus?

What is the equation for Poissons ratio?

What is the difference between positive and negative Poisson’s ratio?

Most materials have a positive Poisson ratio and contract perpendicular to stress, while materials with a negative Poisson ratio stretch perpendicular to stress.

How does directionality of a material change its properties of deformation?

Anisotropic materials vary with orientation while isotropic materials deform the same way in all directions.

What is a property of the constants for isotropic materials?

What are the properties of elastic deformation?

• Elasticity or Young’s Modulus E is resistance by interatomic forces

• Stronger bonds are less easily deformed, and have a higher Young’s modulus

• E is typically larger for ceramics and metals compared to polymers

• Ceramics and metals are typically isotropic

• Many polymers are anisotropic

What is the “yield strength” point of a stress strain curve?

The point at which the response is no longer linear

What is plastic deformation?

• Plastic deformation is irreversible deformation, rearrangement of atoms and molecules. It commonly occurs in metals and polymers and only rarely in ceramics.

• Plastic deformation is permanent

• It is a non-linear response of stress-strain

• Sample never returns to original shape

What does a stress- strain curve graph look like?

What is plastic deformation in metals?

• Deformation is due to dislocation motion along a slip plane

• Single crystal: when enough stress is applied in an orientation that coincides with a slip plane (high atomic density)

• Most metals are polycrystalline with many grains

• Deformation of individual grains rather than alterations or opening of grain boundaries

• Deformation occurs when a high enough stress is applied to deform the less favorably arranged grains

• Polycrystalline materials usually stronger due to constraints by neighboring grains

What is plastic deformation in polymers?

• A neck forms after passing yield strength, where polymer chains become oriented with the direction of the load

• Increased strain with increased growth in neck

• Before fracture, increase in stress required

What is hardness?

• Hardness is a measure of how much a material is resistant to plastic deformation

• It is characterized by both yield strength and ultimate tensile strength

• Hardness measurements are frequently used to estimate strength because it is a cheap and simple test

How to measure hardness?

• Apply a known load to a small indenter, either a pyramid or sphere shape, to a surface for a known time and the size of the impression indicates the hardness

• Can create calibration curves to convert hardness to yield strength and ultimate tensile strength

What is resilience?

Resilience is elastic energy that can be stored in the material, springiness

What is toughness?

Toughness is energy required to break a material. Toughness is total amount of energy a material can absorb before fracture

What is strength?

Strength is the maximum amount of stress a material can withstand to stay in the elastic region

What is stiffness?

Stiffness is described by Young’s modulus, stress/strain

What is failure?

Point where there is plastic deformation, certain amount of plastic deformation, or material fractures

What are the three main modes of failure?

Fracture, fatigue, and creep

What is ductile fracture?

• Ductile fracture is when material undergoes plastic deformation before breaking

• Crack propagation occurs fairly slowly

• No further elongation unless stress is applied

• Occurs in metals and some ductile polymers

What is brittle fracture?

• Little evidence of plastic deformation

• Proceeds quickly

• Can lead to catastrophic failure

• More common in ceramics and certain types of polymers

What is ductility?

• Amount of plastic strain required to break the material

• Low ductility materials, or brittle materials, fracture with very little plastic deformation

What is the stability level of cracks for brittle materials and ductile materials?

• Cracks are unstable in brittle materials and can propagate without increase in stress

• Cracks in ductile materials are stable and can resist crack propagation with applied stress

What mode of fracture is preferred, ductile or brittle?

Ductile, as there is warning

What is fatigue?

• Mechanical materials that are used in the body will have some sort of lifetime and therefore will be under repeated loading

• Failure that occurs in structures with cyclic stresses

• Failure can occur at stress levels much lower than the tensile or yield strength

• Responsible for 90% metallic failures, but can also occur in polymers and ceramics

• Dangerous as it can occur suddenly, caused by crack propagation

What is fatigue failure?

Crack initiation, crack propagation, and then final failure

How is fatigue graphically represented?

• S-N curve, maximum stress v. Log number of cycles N

• Fatigue life is estimated as the number of cycles for crack initiation plus the number of cycles for propagation to the critical size that leads to failure

• Fatigue failure is a stochastic process

• A high cycle fatigue life is considered as greater than 10^4 cycles

What are some designs to avoid fatigue?

• Avoid notches and sharp discontinuities and treat surfaces to have added hardness since fatigue propagates as cracks

How does the environment affect fatigue?

Thermal fatigue and corrosion fatigue

What is creep?

Time dependent plastic deformation that occurs when sample is under constant load for along period of time. A certain amount of plastic deformation can occur and will not return to 0

What are some characteristics of creep? What materials does it occur in? What temperatures does it occur at? How is it tested?

• Can occur in all materials

• Usually only a concern for > 0.4Tm for metals, and even higher for ceramics

• Can occur around room temperature with polymers

• Tested by exerting a constant load at a fixed temperature and measuring strains as a function of time

Creep in polymers: What temperature does it occur at? What does it depend on?

• Can occur at low temperature and stress

• For biomaterials, need to know if it demonstrates creep at body temperature

• Depends on the movement of polymer chains in the amorphous regions via viscous flow

• Increased crystallinity usually means less creep

• Creep increases with temperature above the glass transition temperature

What is stress relaxation?

• Decrease in stress over time with constant strain

• Often found in polymeric materials

• Related to reordering of molecular bonds, also related to sample crystallinity and temperature

• Measured by loading a material with enough stress to create a small strain, and then monitoring the stress to maintain constant strain over time

How does temperature influence elastic modulus?

As temperature decreases, elastic modulus increases and material becomes more brittle

What is an application where you may want an anisotropic material? Why?

Tissue engineering, cardiac patches, and bone implants. Useful when the goal is to replicate directional structure and function of native tissues, improve mechanical properties and mimic natural cell behavior.

The cup of a hip implant can be lined with plastic, ceramic, or metal. Which

material has the largest Young’s modulus?

Ceramic

What mode of fracture is preferable – ductile or brittle fracture? Why?

Most biomaterial applications – ductile fracture generally preferred over brittle

fracture. Ductile fracture provides warning before failure undergoing significant plastic

deformation and absorb more energy prior to fracture, safer for implants to avoid

catastrophic failure

For increasing strain rates, would the curve shift 1 to 3 or 3 to 1?

3 to 1 – Curve 3 represents a material deformed at a low strain rate meaning lower

stiffness. Curve 1 represents a high strain rate with a steeper initial slope

How would the curve shift if the temperature was lowered?

The curve shifts in the same direction as increasing strain rate to Curve 1. As temperature decreases elastic modulus increases (steeper initial slope),

ductility decreases (lower strain before failure), and the material becomes

more brittle

Which sample would likely undergo the most creep?

3 – would likely exhibit the most creep behavior. Undergoes the largest strain and has a long plastic deformation region –behaving like a ductile or polymer material which is material type most prone to

creep under a sustained load

Which sample is an example of brittle fracture?

Sample 1 – fractures after very little strain, steep nearly linear stress-strain curve

and fails suddenly, almost no plastic deformation before breaking