Stress, Strain and Moduli Flashcards
Lectures 2 and 3
What is elastic/plastic deformation?
materials deform in response to load, at a high enough load they break
What is the difference between elastic and plastic deformation?
Elastic deformation is recoverable
Plastic deformation is permanent
What kind of deformation do ductile materials experience (e.g. metals)?
Elastic and plastic deformation
What kind of deformation do brittle materials experience (e.g. glass and concrete)?
Minimal plastic deformation
What is Stress?
Force over area
Measured in Pa (Nm^-2)
What is Strain?
Fractional change in dimensions, dimensionless (may be reported in %)
What is the equation for Normal stress?
What is the equation for Normal strain?
What is the equation for Young’s modulus (also known as Elastic modulus)?
What may Young’s/Elastic modulus be referred to?
also referred to as stiffness
What is the Young’s modulus?
The materials property
What is Poisson’s ratio?
Measure of the contraction in the direction perpendicular to the applied stress
What is the equation for Poisson’s ratio?
What is Poisson’s ratio?
a material property
What are typical values for Poisson’s ratio?
Positive for most materials but theoretical range for isotropic (looks the same in all directions) materials
Materials with negative Poisson ratios tend to have special cellular structures
What is Shear stress, strain and modulus?
If the forces are applied parallel to the surface then it is shear.
What is the equation for Shear Stress?
What is the equation for Shear Strain?
What is the equation for Shear modulus?
What is the equation for the shear modulus of the material being isotopic?
What is the Shear modulus?
a material property
What is the relationship between the Young’s and shear modulus for a typical metal?
What is the equation for Volumetric strain?
How can tension affect the volume of a shape?
Can involve changes in volume, but these are generally small
What does Shear involve?
No change in volume, only a change in shape
What does hydrostatic pressure cause?
Hydrostatic pressure causes changes in volume
What is the equation for Bulk modulus
In the equation B = - P/(deltaV/V) what does the minus sign indicate?
The minus sign indicates compression
What is the bulk modulus?
a material property
What is the equation for the bulk modulus for an isotropic material?
For a typical metal the relationship between the Young’s modulus and the bulk modulus is?
B = E
Applied forces result in?
Stress(es) in a body
Strain(s) or changes in the dimensions of a body
Stress and strain are related by material properties
Moduli
- Young’s modulus (GPa)
- Poisson’s ratio (dimensionless)
- Shear modulus (GPa)
- Bulk modulus (GPa)
What is an isotropic material?
Materials that have uniform properties in all directions (e.g. window glass)
How many moduli do we need to relate stress to strain in isotropic materials?
Only need 2 (out of 4) moduli to relate stress to strain in isotropic materials (i.e. any 2 of E, V, G and B)
What materials can we treat as isotropic?
Can treat many materials as being isotropic (on a large scale)
- e.g. metals, ceramics etc. because they contain many randomly oriented grains
What materials are not isotropic?
Wooden table, Fibre glass fabric, plywood
How many unique components of stress are there?
6 unique components of stress - 3 normal stresses and 3 shear stresses
How many unique components of strain are there?
6 unique components of strain - 3 normal strains and 3 shear strains
how many moduli needed for non-isotropic materials?
If transversely isotropic e.g. wood - 5 independent moduli needed
If orthotopic e.g. plywood - 9 independent moduli needed
What is the graph for young’s modulus?
What are the three equations of normal strain are related to normal stresses?
What are the three equations of shear strain that are related to shear stresses?
How can the 3 normal stresses and 3 shear stresses be presented?
A steel object with E = 210GPa, v = 0.33 is subject to the following stresses σ xx = 100MPa, σ yy = -20MPa, σ xy = 100MPa and σ zz = 50MPa. Is the strain ε xx equal to?
A steel object with E = 210GPa, v = 0.33 is subject to the following stresses σ xx = 100MPa, σ yy = -20MPa, σ xy = 100MPa and σ zz = 50MPa. Is the strain ε xy equal to
What are the equations for plane stress in isotopic materials that applies to thin sections
