Diffusion model Developing diffusion model: kinetic strength of the - - PowerPoint PPT Presentation

Diffusion model

Developing diffusion model:

• kinetic strength of the heat cycle
• The transformation of pearlite to austenite
• The homogenization of austenite
• Volume fraction of martensite
• Hardness of transformed surface layer
• Hardness of transformed surface layer

• kinetic strength of the heat cycle:
• Structural changes are diffusion controlled. Transformation of pearlite

to austenite , homogenization of carbon in austenite and the decomposition of austenite to ferrite and pearlite.

• Extent of changes depends on kinetic strength of heat cycle.
• Kinetic strength of the heat cycle is given by,

Where Q = activation energy for transformation, R = gas constant.

Simplifying we get where

Where Tp = peak temperature, = thermal time constant

• The transformation of pearlite to austenite
• austenization process is conducted rising the temperature of bulk

material 50-90 C above Ac3 temperature

• Pearlite colonies first transform to austenite. Carbon diffuses outward

from these transformed zones into surrounding ferrite. Ferrite (BCC) Austenite (FCC) Austenite (FCC) Martensite(BCT)

• Formulation
• If the pearlite spacing within a colony is λ , carbon

required sufficient time for lateral diffusion. This time is given by,

• In heat cycle the quantity Dt is replaced by,
• In heat cycle the quantity Dt is replaced by,

= D0

So that, D0

where D0 is pre-exponential C-diffusion in austenite.

• The homogenization of austenite
• Modeling carbon redistribution in austenite.
• Carbon diffuses from the high to the low concentration

regions, which depends on temperature and time.

• The boundary region where carbon % increased is given by,
• The boundary region where carbon % increased is given by,

Where Ce = austenite C %(0.8% ), Cc = ferrite C % (0.05%)

• Volume fraction of martensite:
• Extent of the martensite which forms when the

surface layer is quenched.

• Volume fraction of martensite depends on grain size

and volume fraction of pearlite colonies.

• Maximum volume fraction permitted by the phase diagram

is, is,

• Volume fraction of martensite

Where fi = volume fraction of pearlite = C/0.8

• Hardness of transformed surface layer
• The Vickers hardness of treated surface varies with

depth.

• It is also depends on volume fraction of martensite

and its carbon content and hardness given by rule

• f mixtures

Also from carbon content and martensite volume hardness is given by,

Where Hm = hardness of martensite, Hf = hardness of ferrite.= 150MPa.

Example

• Material and process variables:

Material : AISI 4140 steel. Laser power : 1000 W Beam and distribution: rectangular(12 x 8 mm) with uniform distribution Velocity: 2 mm/s Thermal conductivity : 42.7 W/mk Diffusivity : 11.24 mm2/s Diffusivity : 11.24 mm2/s Specific capacity : 473 J/kgk

Result

• Temperature profile along depth:
• 1. At 1mm temperature above AC3

2.At 1.3mm temperature above AC1 Hardness depth = 1.3mm

• Hardness profile along depth:
• Hardness profile along depth:

Maximum hardness = 712 HV Maximum hardness = 725 HV

Example for AISI 1050 steel

Laser Bending

ME 677: Laser Material Processing Instructor: Ramesh Singh

Laser Bending

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Outline

• Process Descriptions
• Mechanisms of Laser Bending
• Applications

ME 677: Laser Material Processing Instructor: Ramesh Singh 2

Introduction

• Deformation can be induced in a controlled manner in

sheets and plates by tracking the laser beam across one side

• f the material
• Temperature gradients are developed through the material

thickness which induce stresses because of the differential expansion of adjacent layers that are at different temperatures

ME 677: Laser Material Processing Instructor: Ramesh Singh

temperatures

• Materials such as stainless steels and the light alloys of

aluminum, magnesium and titanium have a high coefficient

• f thermal expansion such sheet materials can deform

significantly when laser heated

• The most important beam variables are the energy absorbed

per unit length, the configuration of the heating source and the treatment sequence

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Principal Mechanisms

• Temperature gradient mechanism
• The point source mechanism
• Buckling mechanism

Upsetting mechanism

ME 677: Laser Material Processing Instructor: Ramesh Singh

• Upsetting mechanism

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Mechanism of Bending

ME 677: Laser Material Processing Instructor: Ramesh Singh 5

Thermal Gradient Mechanism

• The material is heated by the laser such that there is

a steep thermal gradient through the thickness

• The material will be under compression due to

restraint caused by the material underneath which is

ME 677: Laser Material Processing Instructor: Ramesh Singh

still cold

• Plastic flow will occur in the surface region provided

the temperature is high enough to cause thermal strain

• The plastic strain will not be recovered during cooling

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Thermal Gradient

• Due to cooling the rest of material will heat up a little via

conduction, causing a reduction in tensile stresses in the cooler region

• Finally, the area over which the stresses operate during

cooling are redistributed to the whole sheet as opposed to

ME 677: Laser Material Processing Instructor: Ramesh Singh

cooling are redistributed to the whole sheet as opposed to the small zone

• The plastic deformation due to heating is not recovered and

the piece bends towards laser on cooling

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Thermal Depth in Bending

• To create this thermal gradient implies that a laser beam must

traverse the workpiece moving at such a speed that the thermal depth, z, is small compared to the workpiece depth s0

1 1

2

= = t z Fourierno α

n time interactio = t

ME 677: Laser Material Processing Instructor: Ramesh Singh 8

1 / 1

2 2 2 2 2

<< = << << << Vs D V D t s t s t s z t α α α α

Velocity Scan V Dia Beam D = =

Thermal Gradient Bending

• The bending is asymmetric

– The restraint is not same at edges and the middle

• f the sheet

– The previously heated region cools and contract

ME 677: Laser Material Processing Instructor: Ramesh Singh

– The previously heated region cools and contract causing a bend at that location while the beam is heating at some other location

• The amount of bending per pass is not very

great, 1-3 deg

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Bending Angle

ME 677: Laser Material Processing Instructor: Ramesh Singh 10

Point Source Mechanism

• If the beam source is stationery then the heated zone is a spot

rather than a line

• For a brief pulse thermal gradient will be created and the

mechanism is similar to thermal gradient

• The mechanical bend differs due to the shortened spot

resulting in pucker on the surface and finally bend along the

ME 677: Laser Material Processing Instructor: Ramesh Singh

resulting in pucker on the surface and finally bend along the line of least resistance (smallest width)

• If the pulse width is longer then it could result in buckling

mechanism

• It is used for micro-components and bending angle is 1/10 -

1/100 of a degree

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Buckling Mechanism

• If there is little thermal gradient through the depth of the

sheet then the gradient mechanism will not work

• Expansion resulting from through heating will result in a

bulge

• This bulge can move upwards or downwards

– initial bend; residual stress, applied stress

The center of bulge is hotter than the edges: the edge

ME 677: Laser Material Processing Instructor: Ramesh Singh

• The center of bulge is hotter than the edges: the edge

deformation will be elastic but center will plastically deform

• On cooling the plastic bend remains
• The rate of bending is 1-15 deg per pass
• The direction of bending could be ensured by introducing a

bias

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Upsetting Mechanism

• If the material geometry does not allow for buckling

due to its thickness or section modulus the no buckling is restrained

• The laser treatment produces a thermal field with no

significant gradient, plastic deformation through the thickness will occur beyond a particular temperature

ME 677: Laser Material Processing Instructor: Ramesh Singh

thickness will occur beyond a particular temperature

• The material will be thickened which does not

recover even after cooling

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Modeling Thermal Gradient-Trivial or Two Layer Model

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Assumptions

• Temperature field is a step function
• All thermal expansion is converted to plastic

flow

• No mechanical strain

ME 677: Laser Material Processing Instructor: Ramesh Singh

• No mechanical strain
• The bending is purely due to geometry

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