Processing Prowess 2

I hope the sweet, merciful touch of death releases me from this godforsaken class

Steps for a deformation process

1. Flow or Plastic deformation

2. Shape definition by a tool

3. Shape retention

Which materials classes can undergo solid processes

• Metals

• Plastics

Why can’t ceramics under solid processes

Can’t undergo plastic deformation which is how solid processing works

Thermoforming

Thermoplastic polymers are heated to rubbery state and deformed

6 Types of solid processes

• Wire Drawing

• Extrusion

• Forging

• Rolling

• Bending

• Thermo forming

What area of plastic deformation on the stress strain curve are we interested in?

Plastic deformation before necking

When is the equations for converting engineering and true stress invalid

After necking

Engineering vs true stress

Elastic deformation

Reversable deformation by stretching of the bonds

Plastic deformations

Permanent deformation where slip occurs (planes shear).

Yield stress

The onset of plastic deformation

UTS

maximum engineering stress and onset of necking

2 ways to quantify ductility

• Percent elongation

• Reduction in area

Which curve (true or engineering) provides more information on how a material deforms plastically in the uniform plastic flow regime (pre necking)

true stress true strain curve

strain hardening

Where materials get stronger as they get plastically deformed, thus more stress is needed to continue plastic def.

How does the structure of a metal changes during plastic deformation

• dislocation density increases and these dislocations interfere with each other which hinders plastic def

• The grains become elongated due to stresses applied in a specific direction relative to the microstructure

Average Flow Stress

average true stress needed to cause deformation to reach a final value of strain

Calculating work done per unit volume

Average flow stress * max strain, (area under true curve)

Yield point for polymer

Same point as necking, marks localized deformation, though some polymers experience permanent deformation before this point.

Is there uniform plastic deformation in polymers

No, because the yield point is where necking occurs

Steps of Plastic deformation for a semi crystalline polymer

1. amorphous regions elongated (yields)

2. crystalline regions rotate and align

3. crystalline regions slide (local minima)

4. Forms fibular structure and thins more until failure.

Steps of tensile test for amorphous polymers

1. Yields (necks)

2. Chains align towards tensile stress and stretch and slide

3. Neck grows and consumes the gauge length (cold drawing)

4. Neck stretches elastically until failure

Is the modulus for polymers always linear?

No, need to use secant or tangent to define modulus

Deformation of elastomers

Experience brittle failure, do not plastically deform

Effect of temperature

increases modulus and ductility. Yield strength and strain hardening exponent decreases. Leads to structural changes

Why does heating a plastically deformed metal lead to structural changes?

Heating reduces the Gibbs free energy by transforming the structure to a more stable state through recovery, recrystallization, and grain growth.

Recovery

does not change microstructure and properties much but reduces residual stresses in a metal by increased dislocation motion such as cross slip and climb.

Recystalization

involves nucleation and growth of new, equaxed, less defective grains in the matrix of deformed grains. Decreases dislocation density which decreases strength

Cold working

below crystallization temp (T<0.3 T_m)

Hot working

Deformation and recrystallization occur at the same time (0.5>Tm,T<0.75Tm)

What are the advantages and disadvantages of cold working?

Advantages: Produces stronger metals and better dimensional control.

Disadvantages: Requires higher forces and limits deformation per cycle.

Pros and cons of hot working

Pros: more deformation usin less force

Cons: More expensive (need tools that work at high T) and get weaker metals

Common way of deformation forming a metal

Hot woking stage followed by cold working

Are metal sensitive to strain rate?

Yes, the degree they are sensitive is defined by the strain rate sensitivity exponent (m)

Is yield point affected by strain rate?

Yes

What happens to the mechanical properties of a polymer as temperature increases from below Tg to Tm

• Below Tg: The polymer is glassy with a high modulus, less sensitive to temperature.

• Through Tg : The modulus drops, and for semicrystalline polymers, the drop is less than for amorphous polymers due to crystallites' influence. The material becomes viscoelastic, sensitive to temperature and strain rate, and is termed "leathery" (tough and flexible).

• Rubbery Plateau: At higher temperatures, extensive elastic deformation occurs, similar to a rubber band.

• Then modulus drops as it melts

Effect of strain rate fpr polymers

faster strain rate decreases the yield point, no time for relaxation

What’s the radius of Mohr’s Circle

Assumptions when yielding under triaxial stress state

• material is assumed to be isotropic

• plastic deformation is uniform (no volume change on deformation)

• Yield is not affected by the hydrostatic or mean normal stress [σm=1/3(σ1+σ2+σ3)]

Shear yield stress under triaxial state

k = Y/2

Von Mises Criterion

yielding occurs when the shear strain energy reaches a critical value - yielding will occur when the shear (distortion) stress on octahedral planes reaches a critical value:

Tresca’s criterion

yields when the maximum shear stress at a point reaches the maximum shear stress in a uniaxial tension specimen at yield. Only max and min stress matter

Sticking

As normal forces increase, the shear stress required for motion reaches the material's shear yield strength, causing the material at the interface to yield and flow by shear.

Why is deformation not 100% efficients

• Plastic deformation can frequently lead to an increase in the temperature of the workpiece

• Small amount of the energy expended to create a new shape is stored as elastic energy or in dislocations and other defects

• Friction losses

Bulk deformation

• starting material is a billet, block, or slab with a low surface area to volume ratio.

• process involves a large reduction in thickness or diameter under compressive or combined stresses, resulting in a new 3D shape.

Sheet deformation

• Sheet starting material

• Sheet is formed into shape

Which yield criteria is more conservative

Tresca’s

Which yield criteria are we more likely to use in processing

Von Mises because it is more accurate.

What type of force does shear stress cause

causes shear stresses

wire drawing

reduces the diameter of a metal wire or rod by pulling the wire or rod through a die.

Why do we want the drawing stress lower than the yield point

So we don’t deform our wire when its out of the die

effective strain for wire drawing

Equal to ε_x because ε_y and ε_z are equal

Is deformation asymmetric in wire drawing

Yes

Goal of wire drawing

find the force needed to pull the wire through a given die and also to design the process that produces the required diameter reduction most efficiently

Ideal Deformation

energy dissipated in plastic deformation per unit volume, u, is the area under the true stress-true strain curve,

Ideal Work on a wire

How to account for strain hardening materials

Replace Y with Y_bar (average flow stress)

How to account wire deformation in spherical coordiates

The wire is pulled (tension) radially and experiences compression tangentially

Is axial or tangential stress larger in wire drawing

axial

Three main stresses in in wire drawing with friction

1. Stresses from draw force

2. Axial component of pressure

3. Axial component of fritction

Area of contact of ring like surface

Yielding criteria for wire drawing process

σ_x + p = Y

Redundant deformation

additional energy used to create internal distortions in the metal due to nonuniform deformation.

What main assumption is made in our drawing stress equations (both friction and ideal)

All deformation is uniform plastic deformation

How does friction affect the draw stress?

To get the same reduction of area, you need a larger draw stress where the coefficient of friction is higher

Non uniform deformation

Strains are not uniform and leads to redundant work

Effect of increasing α (angle) on draw stress

Decreases at first because there’s less contact on the die wall (less friction) but then increases because redundant work in now occurring

Extrustion

Bath process where solid billet is deformed by pushing it through a die to create a constant cross-section shape or profile

3 types of solid extruders

1. Forward/Direct

2. Backwards/indirect

3. Impact

How does friction affect extrusion

There’s a large contact area between the billet and chamber. Design strategies are used to reduce the contact

Dead zone

region in the extrusion chamber where the material remains stationary due to low stress and strain. It helps channel the flowing material toward the die exit. The dead zone is in sticky conditions

Sign of pressure in extrusion

Its positive, but its still a compressive stress. The force pushing on the billet

Limitations of extrusion

• The strength of the chamber to withstand radial forces due to plastic deformation of the billet

• The maximum force that can be generated by the ram

• Long billets may buckle

How does friction affect extrusion pressure?

At the start of the extrusion process, friction causes the extrusion pressure to rise as the billet is compressed. The pressure peaks at the point where the extrudate emerges from the die and drops until the end when the last silver is pushed out

How does extrusion pressure change during the process?

Extrusion pressure drops as the ram moves, because the interfacial area causing friction decreases. The pressure increases again at the end when the final section of the billet must squeeze through the die.

Why is extrusion typically halted before all the metal exits?

The process is halted before all metal exits to avoid disruption in flow when the metal squeezes between the ram and the end of the chamber to the die exit.

Properties of hot extrusion

• More deformation and higher extrusion rates

• complicated by the transient nature of the temperature

• average flow stress drops with temperature but the strain rate

  sensitivity exponent increases

Limitations of hot extrusion

• There's a maximum speed beyond which the press can't provide the necessary force.

• surface cracks at a given temperature limit the extrusion speed or the extrusion ratio.

• Both decrease at higher temperatures

Forging

deformation of a workpiece by compressive forces to form a new shape

Open die forging

• the workpiece is compressed between parallel plates with no restrictions in the deformation.

• Material is free to “flow” out between the open edges.

• Reduces specimen height

Closed die forging

involves a series of shaped dies. Multiple deformations progressively shape the metal from a crude form to a more detailed shape.

Main assumptions in open die forging

• Plane strain in the z direction has no strain

• x direction is free to expand, so under plane stress in the x direction (no stresses)

• Thus only forces in the y and z directions, but only deformation in the x and y directions

Yielding for forging

When the effective stress is equal to Y

In an open die forge with friction, where is the local max pressure

In the middle of the workpiece

In an open die forge with friction how does coefficient of friction affect magnitude of the maximum local pressure?

Maximum local pressure will be higher for higher coefficient of friction

How does σ_y change where there’s friction?

σ_y is no longer constant, it varies with lateral position (x)

Y’

Plane flow stress

Sticking in open forging

• material near the platen is stationary, shearing rather than sliding.

• Interfacial shear stress is equal to shear yield stress (k) rather than μp

Axisymmetric Open Die Forging

• No longer under plane strain when compressing cylinder

• Now axisymmetric

• Converted to cylindrical coordinates

Impression die forging

• Only Hot forging

• Pressed between two platens with shaped

  die cavities.

• Flash forms

Precision Die forging

Same as impression, but without the flash, however needs very high deformation

How is the force for closed die forging predicited?

Mostly empirical.

Rolling

thickness reduction by the application of compressive forces applied through a set of rolls

When is the plane strain condition applied in rolling

When the width is at least 5 times greater than the thickness of the workpiece

Limitation of rolling

• Roll separating force must be within the limits of the equipment

Which solid processes go through multiple passes

Wire drawing, rolling, closed die forging

Can there be shaping in rolling?

Yes, can make I beams and other shapes by using special rolls

Does friction hinder or help during rolling

Helps, friction pulls the work piece in

What is the neutral point in rolling

its where the velocities of the workpiece and the roll are the same

What conditions are needed for the max possible reductions

• Unaided entry (friction pulls forward)

• friction force must overcome the reaction force provided by the roll/workpiece interaction