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 of 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 = 725 HV Maximum hardness = 712 HV
Example for AISI 1050 steel
Laser Bending Laser Bending ME 677: Laser Material Processing Instructor: Ramesh Singh 1
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 of 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 temperatures • Materials such as stainless steels and the light alloys of aluminum, magnesium and titanium have a high coefficient of 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 ME 677: Laser Material Processing Instructor: Ramesh Singh 3
Principal Mechanisms • Temperature gradient mechanism • The point source mechanism • Buckling mechanism • Upsetting mechanism Upsetting mechanism ME 677: Laser Material Processing Instructor: Ramesh Singh 4
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 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 ME 677: Laser Material Processing Instructor: Ramesh Singh 6
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 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 ME 677: Laser Material Processing Instructor: Ramesh Singh 7
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 s 0 1 Fourierno = 2 z 1 = t interactio n time = t t α α D Beam Dia 2 2 = z s << 0 V Scan Velocity 2 = t s α << 0 t α 1 << 2 s 0 t D / V = D α 1 << ME 677: Laser Material Processing 2 Vs Instructor: Ramesh Singh 0 8
Thermal Gradient Bending • The bending is asymmetric – The restraint is not same at edges and the middle of the sheet – The previously heated region cools and contract – 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 ME 677: Laser Material Processing Instructor: Ramesh Singh 9
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 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 ME 677: Laser Material Processing Instructor: Ramesh Singh 11
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 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 ME 677: Laser Material Processing Instructor: Ramesh Singh 12
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 thickness will occur beyond a particular temperature • The material will be thickened which does not recover even after cooling ME 677: Laser Material Processing Instructor: Ramesh Singh 13
Modeling Thermal Gradient-Trivial or Two Layer Model ME 677: Laser Material Processing Instructor: Ramesh Singh 14
Assumptions • Temperature field is a step function • All thermal expansion is converted to plastic flow • No mechanical strain • No mechanical strain • The bending is purely due to geometry ME 677: Laser Material Processing Instructor: Ramesh Singh 15
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