2. Heat Flow, Arc Physics and Metal Transfer

Introduction and Context

Welding is a localized thermal–electrical–metallurgical process. The quality of a welded joint depends not only on the nominal current and voltage shown on a power source, but also on how energy is generated, transported through the arc, transferred by molten metal, and dissipated into the workpiece. These phenomena determine penetration, bead geometry, dilution, distortion, residual stress, solidification structure, and defect formation.

The welding arc is a conducting plasma established between an electrode and the workpiece, or between two electrodes. Within this plasma, electrical energy is converted into heat, light, and electromagnetic effects. At the same time, droplets may detach from the electrode and enter the weld pool through mechanisms controlled by gravity, surface tension, electromagnetic force, plasma drag, and arc pressure. The weld pool then undergoes a transient thermal cycle involving heating, melting, solidification, and cooling.

A useful understanding of welding therefore requires three linked descriptions: arc physics, metal transfer, and heat flow. This chapter develops these descriptions and shows how they guide process selection, parameter control, thermal analysis, and industrial troubleshooting.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Explain the electrical and physical behavior of welding arcs and plasmas.

2. Relate power-source characteristics to arc length, stability, and process response.

3. Distinguish the principal modes of electrode metal transfer.

4. Apply heat-source models to estimate weld-pool dimensions and thermal fields.

5. Interpret thermal cycles, cooling rates, heat-affected-zone behavior, and solidification effects.

6. Diagnose instability, spatter, lack of fusion, burn-through, and distortion using heat-flow principles.

7. Evaluate the role of sensing, waveform control, simulation, and automation in advanced welding.

The Arc as an Electrical Plasma

An arc is sustained when the gas between the electrode and workpiece becomes sufficiently ionized to conduct current. Electrons, positive ions, and neutral atoms coexist in a high-temperature plasma. Electrons generally carry current toward the anode, while positive ions move toward the cathode. The voltage across the arc is commonly represented as

V_a = V_c + V_p + V_a

where the terms represent voltage drops in the cathode region, plasma column, and anode region respectively. The repeated symbol is conventionally distinguished in detailed treatments by subscripts for cathode, column, and anode; physically, the important point is that the arc voltage consists of localized electrode drops and a distributed plasma-column drop.

The cathode region supplies electrons through thermionic emission, field emission, or combined mechanisms. The anode receives electrons and is heated by their kinetic energy and recombination effects. The plasma column is approximately electrically neutral overall, although strong gradients of temperature, species concentration, and electrical potential exist within it. Arc temperature may reach several thousand kelvin, but the workpiece does not attain a uniform temperature because heat transfer is strongly localized and continuously modified by electrode motion and fluid flow.

Arc voltage is influenced by arc length, shielding-gas composition, current, electrode material, and pressure. In many practical conditions, increasing arc length increases voltage. A long arc generally spreads heat over a wider area and can increase spatter or atmospheric exposure, whereas an excessively short arc may cause electrode sticking, unstable transfer, or short circuits. Shielding gases containing argon, helium, carbon dioxide, or oxygen additions alter ionization behavior, plasma conductivity, surface tension, and arc shape.

The arc also produces electromagnetic forces. Current flowing through the plasma generates a magnetic field, and the interaction between current density and magnetic field produces a body force often called the pinch force. In a sufficiently concentrated current path, this force constricts the arc and assists droplet detachment. Arc pressure acts on the weld-pool surface and can deepen penetration, particularly when the arc is constricted or strongly focused.

Electrical Characteristics of Welding Power Sources

A welding power source does not merely supply a fixed voltage or current. Its external characteristic describes the relationship between output voltage and current under changing load conditions. Constant-current sources are designed so that current changes relatively little when arc length changes. They are widely used in processes in which the operator or mechanism controls electrode feed independently, such as shielded metal arc welding and gas tungsten arc welding. Constant-voltage sources maintain approximately constant voltage; when arc length changes, current changes substantially, producing a self-regulating response in continuously fed wire processes.

For a constant-voltage process, a small reduction in arc length tends to reduce voltage. The power source responds by increasing current, which melts wire more rapidly and restores the arc length. Conversely, a longer arc tends to reduce current and wire melting, allowing the electrode to advance toward the workpiece. This interaction is known as arc self-regulation. Its effectiveness depends on inductance, control response, wire-feed speed, electrode extension, and the dynamic behavior of the arc.

The total electrical power supplied to the arc is approximately

P = VI

and the net heat input per unit length is commonly estimated as

H = ηVI/v

where H is heat input per unit length, η is thermal efficiency, V is voltage, I is current, and v is travel speed. This relation is useful but incomplete. It does not fully describe heat distribution, arc pressure, droplet energy, preheating, or losses to shielding gas and radiation. Two welds with equal nominal heat input may therefore have different penetration and cooling behavior if their heat-source shapes and process efficiencies differ.

Power-source inductance and waveform control are particularly important in short-circuiting transfer. Inductance limits the rate of current rise, controlling the intensity of the short-circuit pinch and reducing violent current spikes. Modern inverter sources can regulate current at high speed and produce pulsed, controlled-short-circuit, tandem, or customized waveforms. Such control changes droplet size, transfer frequency, spatter, arc pressure, and heat input without necessarily changing average current greatly.

Metal Transfer from the Electrode

Metal transfer describes the movement of molten electrode material across the arc into the weld pool. Transfer mode affects deposition rate, penetration, spatter, shielding requirements, bead shape, and suitability for different positions and thicknesses. The mode is governed by current density, electrode diameter, polarity, wire extension, shielding gas, arc length, surface tension, and waveform.

Short-Circuiting Transfer

In short-circuiting transfer, the molten electrode tip periodically touches the weld pool. The arc extinguishes during contact and reignites as the wire separates. This mode operates at relatively low current and heat input, making it suitable for thin materials, root passes, and positional welding. Its limitations include possible spatter, incomplete fusion when parameters are too cold, and sensitivity to inductance, stick-out, and gas composition.

Globular Transfer

Globular transfer produces relatively large droplets that detach irregularly, often under the combined influence of gravity and electromagnetic forces. It commonly occurs at intermediate current ranges, especially with carbon-dioxide-rich shielding gases. The droplets may wander and strike the pool with considerable momentum, producing spatter and a rough bead. Although useful in some high-deposition applications, uncontrolled globular transfer is generally less desirable where appearance and positional control are important.

Spray Transfer

Spray transfer consists of a stream of small droplets moving axially across a relatively stable arc. It usually requires current above a transition value and an argon-rich shielding gas. The process provides high deposition rate, good fusion, low spatter, and a relatively smooth bead. However, its high average heat input and fluid pool make it less suitable for thin sections and out-of-position welding unless specialized pulsed control is used.

Pulsed-Spray Transfer

Pulsed current alternates between a peak level, which detaches a droplet, and a background level, which sustains the arc while limiting average heat input. Properly controlled pulsed transfer can provide spray-like droplet transfer at a lower average current. It is therefore valuable for aluminum, stainless steel, thin sections, positional welding, and applications requiring controlled penetration and reduced spatter. Poor synchronization between pulse parameters and wire-feed speed can instead produce irregular transfer and arc instability.

Controlled Short-Circuit and High-Deposition Modes

Modern power sources manipulate current rise, current decay, arc length, and droplet detachment to control short-circuiting transfer. These systems reduce spatter and heat input while preserving productivity. Tandem-wire and multi-electrode systems increase deposition rate, but they introduce interactions among arcs, magnetic fields, molten pools, and synchronization controls. Their successful use requires coordinated waveform design and accurate wire positioning.

Heat Flow and Heat-Source Models

Heat entering a workpiece is transported by conduction through the solid, convection within the weld pool, radiation, and fluid flow driven by electromagnetic forces, surface-tension gradients, buoyancy, and droplet impact. In the molten pool, convection may dominate the shape of the fusion zone; in the solid workpiece, conduction is usually the primary mechanism.

A moving heat source creates a nonuniform and time-dependent temperature field. The general heat-conduction equation is

ρc(∂T/∂t) = ∇·(k∇T) + Q

where ρ is density, c is specific heat, k is thermal conductivity, T is temperature, and Q represents internal heat generation. In welding, material properties may vary strongly with temperature, and latent heat must be considered during melting and solidification. Boundary conditions include convection and radiation from exposed surfaces and heat loss through fixtures.

The classical point or line heat-source solutions are useful for qualitative analysis, but they do not accurately represent the finite width and depth of real arcs. The double-ellipsoidal heat-source model is widely used in numerical welding simulations. It divides the source into front and rear ellipsoids with different energy fractions, allowing the model to represent the typically steeper leading thermal gradient and more extended trailing thermal field. Parameters describing source width, depth, length, and front-to-rear energy partition are calibrated against measured fusion-zone dimensions.

Gaussian surface and volumetric heat sources are also used. A Gaussian distribution places maximum heat intensity near the arc axis and reduces it radially. Keyhole processes may require a conical or hybrid volumetric model because energy is deposited below the surface through a vapor cavity. The choice of model must correspond to the physical process; a mathematically convenient heat source is not automatically a physically valid one.

Heat input is affected by travel speed, current, voltage, polarity, electrode efficiency, preheat, interpass temperature, and arc efficiency. Increasing travel speed generally reduces energy per unit length and narrows the thermal field. Increasing current usually increases melting and penetration, although the result depends on transfer mode and arc distribution. Preheating reduces the temperature gradient and cooling rate but increases the total thermal exposure of surrounding material.

Thermal Cycles, Cooling Rates and Metallurgical Consequences

A material point near a weld experiences a thermal cycle rather than a single temperature. The cycle includes heating to a peak temperature, a period above critical transformation temperatures, and cooling through solidification and transformation ranges. The peak temperature decreases with distance from the fusion boundary. Regions that melt form the fusion zone; adjacent regions that experience significant solid-state thermal alteration form the heat-affected zone (HAZ).

Cooling rate is often expressed over a selected temperature interval, such as 800 to 500°C for steels. It depends on heat input, plate thickness, joint restraint, preheat, interpass temperature, geometry, and thermal properties. A high cooling rate can refine some structures but may also promote hard, brittle transformation products in susceptible steels and increase hydrogen-cracking risk. A low cooling rate can reduce hardness and cracking tendency but may produce coarse grains, excessive distortion, or reduced productivity.

The weld thermal cycle influences grain growth, precipitation, dissolution, tempering, sensitization, and phase transformation. In low-alloy steels, the cooling path may be interpreted using continuous-cooling-transformation concepts. In precipitation-hardened alloys, excessive thermal exposure may overage the HAZ and reduce strength. In stainless steels, improper thermal exposure may promote sensitization or undesirable phase formation. Aluminum alloys may experience local softening even when the weld metal itself is sound.

The weld pool solidifies from partially melted grains at the fusion boundary. Heat flow direction and solidification rate influence dendrite orientation, segregation, porosity retention, and weld-metal anisotropy. The ratio of temperature gradient to solidification rate is often associated with the morphology of the solidification structure, while their product influences the scale of the structure. These relationships are useful in interpreting cracking and mechanical-property variations.

Process Stability and Defect Formation

A stable welding process produces a repeatable arc length, predictable transfer, consistent pool dimensions, and manageable spatter. Stability is not identical to low noise or visual smoothness; it must be evaluated through electrical signals, bead geometry, defect frequency, and process capability.

Arc instability may result from contaminated surfaces, inadequate shielding, excessive stick-out, unsuitable polarity, incorrect inductance, poor wire alignment, unstable voltage, or interaction between arcs. Shielding failure permits oxygen, nitrogen, or hydrogen to enter the molten metal, increasing porosity and altering surface tension. Excessive arc length can broaden the bead and reduce penetration, while insufficient length can cause sticking or repeated short circuits.

Common thermal defects have identifiable causes. Lack of fusion may arise from insufficient heat input, excessive travel speed, incorrect torch angle, or inadequate cleaning. Burn-through is associated with excessive local energy, a large root gap, thin material, or insufficient support. Undercut can result from excessive current, voltage, or travel speed. Excessive distortion reflects unbalanced heating and cooling, restraint, and joint sequence. Spatter often indicates unstable short-circuiting, unsuitable transfer conditions, poor shielding, or excessive current rise.

Measurement, Modelling and Digital Control

Industrial welding systems increasingly combine current and voltage monitoring with wire-feed measurement, travel-speed sensing, thermal cameras, laser profilometry, and acoustic or optical arc signals. Statistical analysis of these signals can identify drift before defects become visible. Digital weld procedure qualification systems can record parameter histories, interpass temperatures, and operator or robot actions for traceability.

Finite-element thermal models predict temperature fields, cooling rates, phase changes, distortion, and residual stress. Their reliability depends on validated material properties, realistic boundary conditions, calibrated heat sources, and appropriate mesh refinement. Machine learning can classify arc signatures or predict bead geometry from process data, but it should complement rather than replace physical understanding. Models trained on a narrow range of alloys or joint designs may fail when transferred to new conditions.

Automation also changes the meaning of process stability. A robot may reproduce an unstable parameter set very consistently; repeatability does not guarantee quality. Closed-loop systems should therefore monitor both control variables, such as current and voltage, and outcome variables, such as penetration, bead profile, temperature, and defect indicators.

Illustrative Case Study: Controlling HAZ Hardness in a High-Strength Steel Joint

Background

A fabrication plant produces structural components from a high-strength low-alloy steel. A gas metal arc welding procedure gives acceptable bead appearance, but hardness measurements in the HAZ vary significantly between shifts. Several joints develop delayed hydrogen-assisted cracks during inspection after cooling.

Situation and Analysis

The investigation finds that average current and voltage are within the nominal procedure range, but travel speed varies. Interpass temperature is also uncontrolled. Some operators use a short arc with high current, while others use a longer arc at lower current. Although nominal electrical power is similar, the heat-source distribution and energy per unit length differ. During cold production periods, the plate begins at a lower temperature, increasing cooling rate. Moisture in consumables and inadequate surface cleaning add hydrogen.

The problem is therefore not simply “insufficient heat.” It is a combined thermal-cycle and hydrogen-control problem. High cooling rates promote hard HAZ transformation products, while diffusible hydrogen and restraint provide conditions for delayed cracking.

Approach and Solution

The plant establishes a qualified range for current, voltage, travel speed, heat input, preheat, and interpass temperature rather than controlling only current and voltage. A calibrated infrared sensor records interpass temperature. Consumables are stored and handled under controlled conditions, and joint surfaces are cleaned before welding. A short data-logging trial correlates thermal-cycle indicators with HAZ hardness.

The procedure is revised to use controlled preheat and a maximum interpass temperature, with a travel-speed window that maintains the required heat input. Operators are trained to maintain electrode extension and torch position. Cooling-rate estimates are checked against hardness results, and delayed inspection is retained for critical components.

Outcome

Hardness variation is reduced, delayed cracking is eliminated in the production trial, and the process becomes less dependent on individual operator technique. The principal improvement comes from controlling the complete thermal cycle and hydrogen condition rather than treating arc voltage and current as sufficient quality indicators.

Learning Points

1. Equal nominal power does not guarantee equal weld thermal cycles.

2. Cooling rate depends on preheat, geometry, thickness, restraint, and travel conditions.

3. Process qualification should define ranges and monitoring methods, not only target values.

4. Thermal control and hydrogen control must be considered together in susceptible steels.

Limitations, Professional Practice and Best Practices

Heat-input equations and analytical heat-source models are engineering approximations. They may not capture arc wandering, droplet impact, fluid convection, phase-dependent properties, or changing surface conditions. Numerical results should therefore be validated using macrosections, thermocouples, hardness mapping, bead geometry, and mechanical testing.

Professional practice requires compliance with applicable welding procedure, qualification, inspection, electrical-safety, ventilation, and material-handling requirements. Arc radiation, fumes, electric shock, hot metal, compressed gases, and fire hazards require engineered controls and trained personnel. Ethical engineering judgment is important when a process appears visually acceptable but lacks evidence of penetration, thermal control, or mechanical performance. Production pressure must not replace qualification and traceability.

Best practice is to control the complete process chain: select a suitable transfer mode; match the power-source characteristic to the electrode-feed system; establish validated current, voltage, speed, extension, gas, and waveform ranges; control preheat and interpass temperature; monitor actual signals; verify bead and fusion geometry; and periodically confirm the procedure through inspection and testing. Parameter changes should be treated as changes to the thermal and metallurgical process, not merely as adjustments in machine settings.

Current Developments and Emerging Directions

Recent development is directed toward low-spatter waveform control, high-speed sensing, hybrid laser–arc welding, tandem and multi-wire systems, digitally connected power sources, and model-based adaptive control. Hybrid processes combine the deep, concentrated heat source of a laser with the gap-bridging and deposition capability of an arc. Digital twins are being developed to connect parameter histories with predicted thermal fields and distortion. Advanced monitoring may eventually support real-time detection of incomplete fusion and penetration variation, although calibration, data quality, and explainability remain important concerns.

Chapter Summary

Welding quality is governed by the interaction of arc physics, power-source behavior, metal transfer, heat flow, and metallurgical response. The arc is a conducting plasma whose voltage, current density, electromagnetic forces, and shielding environment determine energy distribution and droplet behavior. Constant-current and constant-voltage sources produce different forms of arc response and self-regulation. Short-circuiting, globular, spray, pulsed-spray, and controlled-transfer modes offer different combinations of heat input, deposition rate, spatter, and positional capability.

Heat input per unit length is useful for comparison but cannot fully describe a weld because heat-source shape, efficiency, fluid flow, and boundary conditions also matter. Analytical and numerical heat-source models help predict temperature fields, while thermal cycles and cooling rates explain HAZ transformations, hardness, cracking, and distortion. Modern sensing, waveform control, simulation, and automation improve consistency, but they must be supported by physical validation and professional engineering judgment.

Key Terms

Arc plasma: Ionized gas containing electrons, ions, and neutral particles that conducts welding current.

Arc voltage: Electrical potential difference associated with the cathode region, plasma column, and anode region.

Arc efficiency: Fraction of electrical power effectively transferred as heat to the workpiece.

Constant-current source: Power source designed to maintain nearly constant current as arc length changes.

Constant-voltage source: Power source designed to maintain approximately constant voltage and support wire-feed self-regulation.

Self-regulation: Automatic tendency of a wire-feed arc to restore arc length through changes in melting current.

Pinch force: Electromagnetic force that constricts current-carrying liquid metal or plasma.

Short-circuiting transfer: Transfer mode in which the electrode repeatedly contacts the weld pool.

Globular transfer: Irregular transfer of relatively large droplets across the arc.

Spray transfer: Axial transfer of small droplets at a current above the transition level.

Pulsed-spray transfer: Spray-like transfer produced by alternating peak and background current.

Heat input: Energy supplied per unit length of weld, commonly estimated from voltage, current, efficiency, and speed.

Heat source model: Mathematical representation of the spatial and temporal distribution of welding energy.

Thermal cycle: Temperature–time history experienced by a material point during welding.

Cooling rate: Rate at which a material cools through a specified temperature interval.

Heat-affected zone: Base-metal region altered by welding heat without being melted.

Fusion zone: Region melted during welding and subsequently solidified.

Interpass temperature: Temperature of a joint immediately before depositing the next weld pass.

Process stability: Consistency of arc behavior, transfer, pool geometry, and resulting weld quality.

Residual stress: Stress remaining in a component after nonuniform heating and cooling.

Review Questions

Short Answer Questions

1. Why is a welding arc classified as a plasma?

2. What is the difference between constant-current and constant-voltage power sources?

3. State two characteristics of spray transfer.

4. Define heat input per unit length.

5. What is meant by a welding thermal cycle?

Long Answer Questions

1. Explain the electrical regions of an arc and discuss the factors affecting arc voltage.

2. Compare short-circuiting, globular, spray, and pulsed-spray transfer with respect to current, heat input, spatter, and applications.

3. Derive and discuss the practical significance of the heat-input relationship H = ηVI/v.

4. Explain how cooling rate and thermal cycle influence HAZ properties and weld cracking.

5. Discuss the use and limitations of double-ellipsoidal and Gaussian heat-source models.

Analytical / Application Questions

1. A weld has acceptable average current and voltage but develops variable HAZ hardness. Identify the likely thermal and process variables requiring investigation and justify your choices.

2. A thin sheet application requires low spatter, controlled penetration, and positional welding. Select an appropriate transfer mode and explain the power-source and waveform considerations.

3. Two welds have equal calculated heat input but different penetration profiles. Explain, using arc physics and heat-source concepts, why their results may differ.

22. Multiple Choice Questions with Answers

Question 1

Which power-source behavior supports self-regulation in a continuously wire-fed arc process?

A. Constant-voltage output causing current to respond to arc-length changes

B. Constant-current output preventing any current variation

C. Zero inductance at all operating conditions

D. A fixed heat-source width independent of arc length

Correct Answer: A. Constant-voltage output causing current to respond to arc-length changes

Question 2

Which transfer mode is generally characterized by small droplets moving axially across the arc at relatively high current?

A. Short-circuiting transfer

B. Globular transfer

C. Spray transfer

D. Explosive transfer

Correct Answer: C. Spray transfer

Question 3

If travel speed is increased while voltage, current, and efficiency remain constant, the calculated heat input per unit length will generally:

A. Increase

B. Decrease

C. Remain exactly unchanged

D. Become independent of arc efficiency

Correct Answer: B. Decrease

Question 4

What is the principal purpose of the background-current period in pulsed-spray transfer?

A. To sustain the arc while limiting average heat input

B. To extinguish the arc permanently

C. To increase droplet size indefinitely

D. To eliminate the need for shielding gas

Correct Answer: A. To sustain the arc while limiting average heat input

Question 5

Which force assists constriction of a current-carrying arc or molten droplet?

A. Electromagnetic pinch force

B. Hydrostatic buoyancy only

C. Radiation pressure from the workpiece

D. Mechanical restraint alone

Correct Answer: A. Electromagnetic pinch force

Question 6

Why may two welds with equal calculated heat input produce different fusion-zone shapes?

A. Heat input has no relationship to welding

B. Heat-source distribution, arc pressure, efficiency, and fluid flow may differ

C. The cooling rate must always be identical

D. Electrical current cannot affect penetration

Correct Answer: B. Heat-source distribution, arc pressure, efficiency, and fluid flow may differ

Question 7

Which condition generally increases cooling rate in a steel weld?

A. Higher preheat temperature

B. Lower heat input and a cold, thick workpiece

C. Higher interpass temperature

D. Reduced thermal conductivity

Correct Answer: B. Lower heat input and a cold, thick workpiece

Question 8

The region next to the fusion zone that is thermally altered but not melted is called the:

A. Arc column

B. Heat-affected zone

C. Transfer cone

D. Cathode spot

Correct Answer: B. Heat-affected zone

Question 9

What is a major limitation of an unvalidated numerical heat-source model?

A. It cannot use temperature-dependent properties

B. Its predictions may not represent the actual energy distribution or boundary conditions

C. It always predicts excessive cooling rates

D. It eliminates the need for experimental inspection

Correct Answer: B. Its predictions may not represent the actual energy distribution or boundary conditions

Question 10

In the illustrative high-strength-steel case, why were preheat and interpass-temperature control important?

A. They controlled the thermal cycle and helped reduce excessive cooling-rate variation

B. They eliminated the need for clean surfaces

C. They converted globular transfer into laser welding

D. They guaranteed zero residual stress

Correct Answer: A. They controlled the thermal cycle and helped reduce excessive cooling-rate variation