Layerwise processing and local thermal history

A printed layer experiences a sequence

In fusion-based metal additive manufacturing, a small region heats, melts or partially melts, solidifies and may be reheated by later passes. Position, scan strategy and heat removal affect the path. Other additive processes use different bonding mechanisms and should not inherit the same thermal story.

For laser powder bed fusion, first spread a thin powder layer, then scan selected paths with the laser. Where enough energy is absorbed, a small liquid region forms and joins material as it solidifies. A later track can heat its neighbour, and a later powder layer can reheat material already below it. The geometric layer is therefore not an isolated thermal experiment that finishes when the laser leaves.

A local history follows one fixed material location, not the moving hottest point in successive images. A melt pool is the liquid region associated with the moving heat input. Tracking the pool maximum can combine readings from different material locations; it is not automatically the temperature–time record of one point that eventually becomes part of the component.

Identify the bonding mechanism before applying this account. A cured resin forms a polymer network through reaction; a binder-held powder can require later consolidation; a material-extrusion track may develop contact and bonding as a deposited polymer cools. Those routes have their own histories and do not all melt and resolidify a metal. Powder consolidation and polymer processing develops these distinctions.

The same machine setting need not create the same local path

Absorbed energy is partitioned among heating the material, changing its phase and energy leaving the region. A liquid-to-solid transformation releases latent heat that must be transported away. Conduction into connected solid and the build plate, exchange with nearby material and surface losses all influence cooling. A region near a support and a region over loose powder need not have the same heat-removal paths. The actual geometry, contact, temperature field and material state determine the difference.

A nearby track scanned shortly afterward can encounter material that is still warm. Changing scan order changes the distance and elapsed time from earlier heat inputs even if the listed power and speed are unchanged. In one primary bare-plate experiment, constant power and speed still produced a spatially varying melt-pool image area; this supports the need to account for previous passes. It does not establish a universal correction or a final property for a three-dimensional build.

An input summary is useful only on its own basis. For a straight scan at constant delivered laser power P and speed v, the nominal energy per path length is e_line = P/v: over distance ℓ, elapsed time is ℓ/v and delivered energy Pℓ/v, giving P/v after division by ℓ. Its SI unit is J/m. It is not absorbed energy per material mass or the temperature of a location. Absorption, spot shape, surrounding state and heat loss remain unspecified.

For example, 200 W at 1000 mm/s and 400 W at 2000 mm/s both give 0.200 J/mm = 200 J/m. With a nominal 0.100 mm spot diameter, the geometric crossing times d/v are 0.100 and 0.0500 ms. Multiplying by P gives the same 0.0200 J over that crossing time, but one delivers it at twice the power over half the time. This is a geometric input comparison, not a top-hat absorbed pulse or an explanation of the particular thermal records below. Equal e_line has not removed the different clocks or boundary conditions.

Read a complete local temperature record before naming an outcome

Use two entirely fictional local records A and B for a fusion-based metal process. They describe fixed material points at different positions, on a common clock for the first heating event and a nearby-track revisit. T is actual local temperature in °C, and t is elapsed time in milliseconds; 1 ms = 0.001 s. Between the listed points, take T to vary linearly. These are resolved stipulated histories, not raw camera signals, sparse measurements asserted to be complete, or outputs calculated from the preceding P/v example.

For this exercise alone, use a supplied solidus T_s = 1200 °C and liquidus T_l = 1500 °C. Below T_s the point is solid; above T_l it is fully liquid; between them a solid–liquid mixture is possible. Neglect kinetic shifts of those temperature boundaries in this classification. No relation between liquid fraction and temperature is supplied. Real rapid solidification can require phase/kinetic information beyond an equilibrium temperature diagram, and a temperature trace alone does not measure a phase fraction.

Both points start at 300 °C and reach 1700 °C at t = 1 ms. They then cool differently. At the nearby-track event, A reaches only 900 °C at 11 ms, while B reaches 1600 °C. Both are back at 300 °C by 20 ms. In this dossier they remain at 300 °C until a later-layer event begins at 20.000 s: its local times 0, 1 and 2 ms have temperatures 300, 1100 and 300 °C at both points. The late event has its own labelled time origin; it is not a third peak at t = 21 ms.

The table records a material history. It does not identify why A and B differ. A proposed cause such as reduced heat conduction, residual warmth or changed scan timing would need matching geometry/process and spatial thermal evidence. The purpose of the supplied record is to establish what paths can be distinguished before inferring a mechanism or final property.

Separate first formation, solid-state reheating and remelting

In the supplied phase classification both locations first pass above the liquidus, then return below the solidus. Material must solidify as the liquid region cools. In an alloy, the advancing solid can accept a different solute concentration from the adjacent liquid. Rejected solute enriches that liquid, and limited redistribution during later cooling can preserve chemical variation within the solid. Cells or dendritic branches can form as the interface develops; their spacing is not the same quantity as grain size. Solidification, nucleation and growth develops the interface mechanism.

A cooling rate is a temperature change per elapsed time over a declared interval. For A’s first descent, T = 1500 °C occurs between 1 ms at 1700 and 2 ms at 1400: t = 1 + (1700 − 1500)/(1700 − 1400) = 1.667 ms. T = 1200 °C occurs at t = 2 + (1400 − 1200)/(1400 − 600) × 2 = 2.500 ms. Thus the mean cooling-rate magnitude from liquidus to solidus is 300 K/0.0008333 s ≈ 3.60 × 10⁵ K/s. Celsius and kelvin temperature differences have the same size; the millisecond-to-second conversion still matters.

For B, the same first-descent band begins at 2.000 ms and ends at 3.200 ms, giving 2.50 × 10⁵ K/s. Compare matching temperature bands rather than taking one rate near the peak and another near room temperature. A single mean rate is not an instantaneous rate at every point, a spatial temperature gradient or a complete solidification model.

At 11 ms, A’s 900 °C peak is below the supplied solidus. This is subsolidus reheating: heating while remaining solid in this classification. Diffusion, precipitation, dissolution, recovery or another solid-state change can occur if the material state and available time permit it. Crossing an arbitrarily chosen temperature alone does not establish that any one of these completed. Temperature, time and structural change develops the needed rate-versus-clock reasoning.

B’s nearby-track peak at 1600 °C exceeds the liquidus, so its history includes another fully liquid interval. It then crosses the solidification range again. Remelting can replace an earlier local solidification structure in the remelted region, while neighbouring unmolten material follows a heat-affected path. It does not imply complete chemical homogenisation or removal of every defect. The later 1100 °C event at 20 s is subsolidus for both, and could modify the subsequently retained structure if its kinetics permit.

Heating/cooling can also produce incompatible deformation between hot and cooler connected regions. Plastic flow, phase changes or other changed preferred strains can leave stress after the build cools; a purely elastic homogeneous free body returning to its original state is a different case. A local temperature trace supplies neither the full three-dimensional compatibility nor a residual-stress map. Residual stress and processing variability treats that mechanical account.

Local history builds local structure

Grain growth, segregation, defects and stress evolve with this path. Two parts with the same external design can differ because machine state, placement or feedstock changed. Retain actual process records rather than only a machine recipe name.

The dossier makes the ambiguity concrete. Both locations have the same maximum 1700 °C and the same final 300 °C, but A has one fully liquid episode and B has two. Their first cooling rates also differ. Equal endpoint or peak readings have therefore not established equal formation and reheat paths. The layer count in a digital design is not a count of grains, melt-pool boundaries or thermal cycles at a point.

Even those resolved paths do not uniquely predict the final grain size, phase fraction, hardness or strength. Chemistry and initial structure, the spatial thermal field, nucleation/growth and solid-state kinetics matter. A plausible explanation must specify which feature changed and which step in the local history could change it, then compare with suitable structural evidence. Defects, texture and anisotropy develops those distinct final-state features.

For example, a difference in solute distribution associated with solidification calls for composition-sensitive spatial evidence, while a claim of different phases needs phase-sensitive evidence. A change attributed to subsolidus precipitation needs particle/phase and timing evidence rather than just an image of track boundaries. These are causal tests of the proposed explanation; the thermal record is not itself a measured mechanical property.

Keep the clock, position and measurement meaning with the history

Real observations must resolve the changing field. A surface thermal camera senses radiation; calibration and emissivity assumptions are needed to infer actual temperature. Saturation can hide the hottest part, a finite frame interval can miss a short peak, and a surface observation is not automatically the subsurface point later being discussed. The exact temperatures in this exercise were stipulated specifically to isolate path-reading from those measurement problems.

Sampling A only at 0, 2 and 4 ms would report 300, 1400 and 600 °C. Its largest sampled value is 1400 °C, although the resolved history peaks at 1700 °C at 1 ms. The three readings alone cannot justify a claim that it never reached the 1500 °C liquidus. Connecting sparse readings by straight lines is an additional model, not evidence that an unobserved peak did not occur.

Time and spatial rates also differ. If two simultaneously observed positions 0.100 mm apart have temperatures 1000 and 600 °C, the mean gradient magnitude along their line is 400 K/0.000100 m = 4.00 × 10⁶ K/m. That is a different observation from A’s 3.60 × 10⁵ K/s cooling rate. One fixed-point time trace cannot locate the heat-flow direction or the moving interface speed by itself.

Retain point/location registration, layer and track identity, pass order, elapsed times, local boundary/support state and the temperature inference with the record. A model should be checked against the quantity actually measured, while structural and mechanical conclusions need their own evidence. Process models, data and validation develops model verification/fitting/validation; this lesson’s calculation interprets a declared history rather than validating a printer or selecting a production recipe.

Worked examples

Try the reasoning

1. Does every additive process melt feedstock?

   Show the answer and reasoning

   No.

   Some use bonding or curing by other mechanisms.

2. Why retain pass sequence?

   Show the answer and reasoning

   Later passes can reheat earlier regions.

   The final state reflects the whole sequence.

3. Change only B’s nearby-track peak at 11 ms from 1600 °C to 1400 °C, leaving its neighbouring 600/900 °C values. Under the same supplied boundaries, what changed classification is justified?

   Show the answer and reasoning

   The second event no longer reaches the fully liquid region, but it enters the 1200–1500 °C mixed-phase range; it is not wholly subsolidus.

   At 1400 °C the point lies above solidus but below liquidus. A liquid fraction or complete remelted volume cannot be calculated without additional phase/kinetic information.

4. For A’s first event, find the upward 1200 °C crossing on 0–1 ms and the downward crossing. What is the time above the supplied solidus?

   Show the answer and reasoning

   Upward ≈ 0.642857 ms, downward 2.500 ms; time above solidus ≈ 1.85714 ms.

   The upward temperature rise to 1200 is 900 K out of 1400 K in 1 ms. Subtract that crossing time from 2.500 ms. This includes mixed and fully liquid portions; it is not the duration of 100% liquid or a measure of transformed fraction.

5. A new input comparison uses 150 W at 750 mm/s and 300 W at 1500 mm/s with a 0.120 mm nominal spot diameter. Find each P/v and geometric spot crossing time. Do equal values of P/v establish the same thermal history?

   Show the answer and reasoning

   Both are 0.200 J/mm; crossing times are 0.160 and 0.0800 ms. No equal thermal history is established.

   Divide power by speed, then diameter by speed. Each nominal crossing delivers 0.0240 J before absorption/loss interpretation, but power/time, spot profile, surroundings and the evolving material state can differ.

6. A camera samples A only at 0, 2 and 4 ms and reports no value above 1400 °C. Can it establish that A stayed below the 1500 °C liquidus throughout this event?

   Show the answer and reasoning

   No. The supplied resolved record has a 1700 °C peak at 1 ms, which those samples miss.

   A largest sampled value is not an upper bound on an unresolved continuous history. A changed sampling/interpolation model would need independent justification.

7. A note labels the later common peak “1 ms”. Another analyst plots it at 1 ms after the first event and merges it with the 1700 °C initial peak. Find the error and the correct absolute time.

   Show the answer and reasoning

   The note uses elapsed time from the later event beginning at 20.000 s. Its peak is at 20.001 s, not 0.001 s after the first event.

   Keep the event origin with every local clock. The dossier holds both locations at 300 °C between 20 ms and 20 s; moving the later peak removes that long intervening history.

8. A further pair of simultaneous positions separated by 0.200 mm differs by 300 K. Calculate the mean gradient magnitude. May it be compared numerically as the same quantity as a 300000 K/s cooling rate?

   Show the answer and reasoning

   1.50 × 10⁶ K/m. It is a spatial rate, not a temporal cooling rate.

   Use 0.200 mm = 0.000200 m. The two observations have different denominators; predicting an interface speed or structure from them needs a supported spatial/time model.

9. A digital build uses 100 layers each 20 µm thick. Does the nominal 2.00 mm height establish 100 grains through the thickness or exactly 100 reheats at every point?

   Show the answer and reasoning

   No. It establishes the summed nominal layer increments only.

   Grains and local thermal cycles are material-state/path observations. Track overlap, position and later heat inputs are not one-to-one labels for geometric layers; actual height can also differ after processing.

10. Two locations show different particle populations after the build. A report calls the difference proof of a colder first peak, using only equal final temperatures and a build recipe name. What comparison would discriminate a thermal-history explanation?

    Show the answer and reasoning

    Register the locations and actual pass/timing/boundary records, resolve the relevant heating/reheat windows, and compare composition/phase/particle evidence under matched material and post-build history.

    Particles may form, dissolve or grow during later solid-state exposures as well as after initial solidification. Final temperature and a recipe label do not select one mechanism or identify an unobserved first peak.

What to carry forward

• Identify the actual bonding process.
• Track local history through the build.
• Follow one material location and keep all clock origins; a moving melt-pool maximum is another quantity.
• Pass order, residual warmth and available heat-removal paths can change the response at equal nominal settings.
• Compare cooling rates over the same temperature interval, and distinguish K/s from a spatial gradient in K/m.
• Separate subsolidus reheating, partial melting and fully liquid excursions under explicitly applicable phase boundaries.
• Equal peak, endpoint or nominal energy per length does not establish equal history, structure or performance.
• A resolved thermal path constrains an explanation; kinetics, spatial/structural evidence and material state are needed for the final claim.