Stress, strain and more on peak broadening. Learning Outcomes By the end of this section you should: be familiar with some mechanical properties of solids understand how external forces affect crystals at the Angstrom scale
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By the end of this section you should:
What happens to solids under different forces?
The lattice is relatively rigid, but….
Note: materials properties will be considered mathematically in PX3508 – Energy and Matter
Tensile strength– tensile forces acting on a cylindrical specimen act divergently along a single line.
Compressive strength– compressive forces on a cube act convergently in a single line
Shear strength– shear is created by off-axis convergent forces.
Slipping of crystal planes
Thus can resolve into tensile and shear components:
Strain ()Plastic region
In the plastic region, under plastic deformation, the material is permanently deformed/damaged as a result of the loading.
In the plastic region, when the applied stress is removed, the material will not return to original shape.
The transition from the elastic region to the plastic region is called the yield point or elastic limit
Structural failure point
At the onset of yield, the specimen experiences the onset of failure (plastic deformation), and at the termination of the range of plastic deformation, the sample experiences a structural level failure – failure point
Maximum possible engineering stress in tension.
The slope of the linear portion of the curve describes the modulus of the specimen.
Young’s modulus (E) – slope of stress-strain curve with sample in tension (aka Elastic modulus)
Shear modulus (G) - slope of stress-strain curve with sample in torsion or linear shear
Bulk modulus (H) – slope of stress-strain curve with sample in compression
Hooke’s law: = E
Higher values of modulus (steeper gradients of slope in stress-strain curve) relates to a more stiff/brittle material – more difficult to deform the material
Lower values of modulus (shallow gradients of slope in stress-strain curve) relates to a more ductile material.
X-ray diffraction patterns can give us some information on strain
Scherrer formula where k=0.9
Take the Scherrer equation and the strain effect
So if we plot Bcos against 4sin we (should) get a straight line with gradient and intercept 0.9/t
0.138 = 0.9/t
Halfwidth: as before
Can give misleading results