Thermomechanical- Mechanics of Metalworking Flashcards
What varies from point to point in forming processes?
Temperature, strain, stress, strain rate
What is slab analysis?
Aka equilibrium analysis. Use of analytical methods employing equilibrium of forces
Name 8 metal forming processes
Forging
Rolling
Extrusion
Wire drawing
Deep drawing
Stretch forming
Bending
Shearing
Describe the forces and pressures involved when a square block (billet) is compressed
As it is compressed it flows in a transverse direction parallel to the die surface. This sliding along a surface under normal pressure (p) leads to friction (f) which tends to restrain the flow of material. This frictional shear stress leads to the generation of an internal pressure (q) in the lateral direction (acting inwards?)
Rate of change of internal pressure in x direction for compressing square block
dq/dx=-2f/h
Where q is internal pressure
x is horizontal direction when compression is vertical.
f is friction
h is height of block
How can friction be expressed?
As a fraction of the material’s shear yield strength.
Use f=mk
m is interface friction factor between 0 and 1.
k denotes the material’s yield strength in pure shear
Deriving formula for internal pressure q at any point along the square block from dq/dx=-2f/h
Use f=mk so dq/dx=-2mk/h
Integrate for q=-2mkx/h +c
Boundary condition is q=0 when x=L/2 (edge of block, free surface)
Means c=mkl/h
Also k=Y/rt(3) where Y is normal yield strength
Finally q=(Y/rt(3))(ml/h)(1-2x/L)
Formula for vertical pressure in terms of normal yield strength and internal pressure
p=Y+q
Formula for average forming pressure
p bar=Y+(Y/2rt(3))(mL/h)
What does a friction hill plot?
Normal pressure p over yield strength or internal pressure q over yields strength vs x. q is always 0 beyond x=L/2. From there is diagonal up to the y-axis. p=Y at x=L/2 so p/Y=1. From there is diagonal up to y-axis. Slope of diagonal is increasingly steep for higher values of mL/h
2 cases for friction in plane strain compression
- Constant friction equal to fraction of shear yield strength, f=mk.
- Coulomb friction, f=μp where μ is coefficient of sliding friction and p is normal pressure
When f=mk, what difference does plane strain compression make?
Vertical is z, horizontal x and y into page. There is no strain in y. Means that p=2Y/rt(3)+q instead of Y+q.
2/rt(3) is plane strain effect.
This has an effect on subsequent rearrangements for p and p bar.
Friction hill now plots p or q over 2Y/rt(3).
How to calculate average pressure for plane strain compression
Calculate total force by integrating expression for p over contact length.
F=2Spdx between 0 and L/2.
Divide this force by contact area (L) to give average pressure p bar.
Difference for finding formula for p when f=μp for plane strain compression
dq/dx is now -2μp/h.
Still p=2Y/rt(3) +q and differentiate means dq/dx=dp/dx.
Sub in and dp/dx=-2μp/h (in terms of p)
Separate variables and integrate means p=cexp(-2μx/h).
Use normal boundary condition.
Final formulae for p and q long and on slide 13
What happens to friction hill when using f=μp for plane strain compression?
Diagonal lines now exponential decay curves. Get higher for increasing μ. When μ=0 is just a horizontal line at p/2Y/rt(3)=1
