Heat Flow, Residual Stress and Distortion

Introduction

Welding joins materials by creating a localized molten region and then allowing it to solidify. The weld pool may occupy only a small fraction of a component, yet the thermal disturbance spreads through the surrounding metal and can alter its microstructure, dimensions, stress state, and service performance. Heat flow therefore provides the physical basis for understanding weld penetration, cooling rate, the heat-affected zone (HAZ), residual stress, distortion, and several forms of cracking.

A sound welding procedure does more than establish an acceptable bead shape. It controls the thermal cycle so that the weld and its surroundings achieve adequate fusion without excessive hardening, softening, shrinkage, distortion, or cracking. This requires coordinated control of heat input, travel speed, preheat, interpass temperature, joint restraint, welding sequence, and—when appropriate—post-weld heat treatment (PWHT).

Learning Objectives

After completing this chapter, the student should be able to:

• describe heat transfer during welding and interpret a weld thermal cycle;
• calculate nominal arc energy and net heat input under stated assumptions;
• explain the effects of material properties, thickness, joint geometry, and welding parameters on cooling rate;
• distinguish weld-metal, fusion-zone, HAZ, residual-stress, and distortion phenomena;
• predict the likely effects of preheating, interpass-temperature control, and PWHT;
• select practical methods for reducing distortion and cracking;
• analyze a welding problem using thermal, mechanical, and metallurgical evidence.

1. Heat Flow in Welding

Heat moves through a welded component mainly by conduction, while convection and radiation transfer heat from exposed surfaces to the environment. The welding arc, resistance source, laser, electron beam, or friction process supplies energy locally. The temperature field is transient: a point in the workpiece heats rapidly as the source approaches, reaches a peak temperature, and cools after the source passes.

The three modes of heat transfer are:

1. Conduction: energy moves through the solid or liquid because of a temperature gradient.
2. Convection: energy is transported by moving liquid or gas, especially within the weld pool and in shielding gas or cooling water.
3. Radiation: energy is emitted from hot surfaces; it is usually less important than conduction inside the workpiece but contributes to surface losses.

For conduction, Fourier’s law is commonly written as:

Here, q is heat-transfer rate in watts, k is thermal conductivity in W/(m·K), A is the area normal to heat flow in m², and dT/dx is the temperature gradient in K/m. The negative sign indicates that heat flows toward lower temperature. The equation assumes a continuum and a locally defined temperature gradient; it does not by itself describe the moving heat source or phase changes.

A useful thermal property is thermal diffusivity:

where α is thermal diffusivity in m²/s, ρ is density in kg/m³, and c is specific heat capacity in J/(kg·K). High diffusivity allows temperature changes to spread rapidly. Low diffusivity tends to concentrate heat near the weld and can produce steep thermal gradients.

Thermal conductivity, specific heat, density, electrical resistivity, and emissivity vary with temperature. Consequently, simple calculations using constant properties are engineering approximations. They are useful for comparison and preliminary procedure design, but detailed prediction may require temperature-dependent numerical thermal analysis.

Moving Heat Source and Thermal Cycle

In arc welding, the heat source moves relative to the workpiece. A location on the plate experiences a thermal cycle with four characteristic stages:

• initial heating;
• rapid heating near the heat source;
• a peak temperature, which depends on distance from the fusion boundary;
• cooling, often through transformation-sensitive temperature ranges.

The peak temperature determines whether metal melts, partially transforms, recrystallizes, softens, or remains essentially unaffected. Metal immediately outside the fusion boundary may be heated above critical transformation temperatures without melting; this is the HAZ.

Figure: Idealized thermal cycle experienced by a point near a moving weld heat source.

2. Heat Input and Thermal Efficiency

Heat input is a measure of the energy delivered per unit length of weld. For an arc process, the nominal electrical power is:

where P is power in watts, V is arc voltage in volts, and I is current in amperes. If travel speed is v in mm/s, the nominal arc energy per unit length is:

The units are J/mm because J/s divided by mm/s gives J/mm. If travel speed is given in mm/min, the equivalent expression is:

with H_a in J/mm and v in mm/min.

Not all electrical energy enters the workpiece. The net heat input is commonly approximated by:

where η is the process thermal efficiency, dimensionless and between zero and one. Efficiency depends on process, polarity, arc characteristics, joint geometry, shielding, and measurement method. Reported efficiency values should therefore be treated as process-specific estimates rather than universal constants.

Worked Example 1: Net Heat Input

A gas metal arc welding operation uses 24 V, 180 A, and a travel speed of 6 mm/s. Assume a thermal efficiency of 0.80.

Thus, the estimated net heat input is 576 J/mm, or 0.576 kJ/mm. This estimate assumes steady parameters and a constant efficiency. It does not include heat losses that vary substantially during starting, stopping, weaving, or changes in joint geometry.

Heat input affects penetration, weld-pool size, cooling rate, HAZ width, distortion, and productivity. Increasing current or voltage generally increases energy delivery, while increasing travel speed reduces energy per unit length. However, voltage changes can also alter arc length and bead shape, and current may change melting rate. Heat input must therefore be interpreted together with current, voltage, travel speed, process, and joint design.

3. Cooling Rate and Thermal Severity

Cooling rate is the rate at which temperature decreases with time:

where R_c is cooling rate in K/s or °C/s, T is temperature, and t is time. In welding practice, the cooling rate is often evaluated over a specified temperature interval, such as 800–500 °C for steels:

This average is not identical to the instantaneous cooling rate. The temperature interval must always be stated.

Cooling rate is affected by:

• net heat input;
• preheat and interpass temperature;
• plate thickness and joint geometry;
• thermal conductivity and diffusivity;
• ambient temperature and heat loss;
• heat sinking through fixtures;
• weld-pass sequence and multipass reheating.

A thick plate or a highly conductive copper fixture can remove heat rapidly, increasing cooling rate. Preheating raises the initial temperature and reduces the temperature gradient between the weld region and surrounding material. It commonly lengthens the time available for diffusion and transformation, although its exact influence depends on geometry and heat input.

For hardenable steels, a high cooling rate can promote martensite formation in the HAZ. Hard martensite, combined with diffusible hydrogen and tensile stress, increases the risk of hydrogen-assisted cold cracking. Carbon equivalent is often used as a screening indicator of hardenability. One widely used expression is the International Institute of Welding form:

All composition terms are in mass percent. This expression is primarily a comparative weldability indicator for steels; it is not a complete crack prediction model. The actual risk also depends on hydrogen level, restraint, plate thickness, cooling time, consumable condition, and preheat.

4. Weld Zones and Metallurgical Consequences

A fusion weld contains several physically and metallurgically distinct regions:

In carbon and low-alloy steels, the coarse-grained HAZ can develop adjacent to the fusion boundary when peak temperatures are high and cooling is rapid. Grain coarsening may reduce toughness. A softened HAZ can occur in precipitation-hardened aluminum alloys or previously heat-treated steels when strengthening precipitates dissolve or coarsen. Thus, increasing heat input does not have the same metallurgical consequence for every alloy.

The weld pool solidifies under a thermal gradient and a solidification rate. These conditions influence dendrite orientation, segregation, porosity, and susceptibility to hot cracking. Hot cracking occurs at elevated temperature during solidification or immediately afterward, whereas hydrogen-assisted cold cracking occurs after cooling, often with a delay.

5. Origin of Residual Stress

Residual stresses are self-equilibrating stresses that remain after external loads and temperature gradients have disappeared. They arise because different portions of the component undergo unequal thermal expansion, plastic deformation, phase transformation, and contraction.

During heating, the hot weld region tends to expand but is restrained by cooler surrounding material. Compressive stress can develop in the heated region. If the local temperature is sufficiently high, yielding may occur. During cooling, the weld metal and HAZ tend to contract. The surrounding colder metal restrains this contraction, producing tensile longitudinal stress near the weld and balancing compressive stress farther away.

A fully restrained, purely elastic thermal stress can be approximated by:

where σ_th is thermal stress in pascals, E is Young’s modulus in pascals, α_T is the coefficient of thermal expansion in K⁻¹, and ∆T is the temperature change in K. This relation assumes elastic behavior, uniform temperature change, and complete restraint. It is not a direct prediction of welding residual stress because welding involves temperature-dependent properties, yielding, phase changes, and three-dimensional geometry.

Residual stress is commonly categorized as:

• Longitudinal stress: parallel to the weld axis; often large in long welds.
• Transverse stress: perpendicular to the weld axis; associated with transverse contraction and joint restraint.
• Through-thickness stress: varying across thickness; important in thick sections and restraint-sensitive cracking.

Residual stresses can approach the yield strength locally, even without an external load. They may reduce fatigue life, promote stress-corrosion cracking, cause distortion, and influence fracture behavior. Conversely, compressive surface stress can sometimes improve fatigue resistance, as in certain peening treatments.

6. Distortion Mechanisms and Control

Distortion is permanent dimensional change caused by nonuniform heating, cooling, and plastic strain. Common forms include:

• Transverse shrinkage: contraction across the weld;
• Longitudinal shrinkage: contraction along the weld;
• Angular distortion: rotation caused by unequal contraction through thickness;
• Bowing or bending: curvature along a member;
• Buckling: unstable out-of-plane deformation in thin panels;
• Twisting: rotation resulting from asymmetric weld placement.

Distortion is governed by heat distribution and restraint. A narrow weld with deep penetration may produce less total heated width than a broad, high-deposition weld, but the final result depends on joint geometry and pass arrangement. Excessive restraint can reduce visible distortion while increasing residual stress and cracking risk.

Effective control methods include:

1. Reduce unnecessary heat input. Use an appropriate process, current, voltage, and travel speed.
2. Balance welds. Place welds symmetrically about the neutral axis where possible.
3. Use a planned sequence. Skip welding, back-step welding, and alternating sides can distribute contraction.
4. Use presetting. Components may be intentionally positioned opposite to expected distortion.
5. Apply controlled restraint. Fixtures should prevent unacceptable movement without creating excessive stress concentration.
6. Use intermittent welds where design codes permit. This reduces total deposited metal and heat.
7. Minimize unnecessary weaving and oversized fillets. Both can increase heat and shrinkage.
8. Correct distortion safely. Mechanical straightening, controlled thermal straightening, or localized heating must respect material properties and specification limits.

The best strategy is prevention at the design and planning stage. Straightening after welding adds cost and may introduce new residual stresses or local property changes.

7. Preheating and Interpass Temperature

Preheating raises the temperature of the base metal before welding. It reduces the initial thermal gradient, slows cooling, lowers the likelihood of hard HAZ formation, and assists hydrogen diffusion before the joint reaches low temperature. Preheat may be especially important for thick, highly restrained, or hardenable steels.

Preheat should be measured at the correct location and over a sufficiently large area. A hot-air gun or torch may heat the surface unevenly; temperature-indicating crayons, contact thermometers, or calibrated infrared instruments can be used subject to procedure requirements. The specified temperature must be maintained through tack welding and the complete weld sequence.

Interpass temperature is the temperature of the weld area immediately before depositing the next pass. A minimum interpass temperature prevents excessively rapid cooling. A maximum interpass temperature limits excessive accumulation of heat, grain growth, loss of toughness, or undesirable precipitation effects. The correct range is material- and procedure-specific.

Preheat is not automatically beneficial in every situation. Excessive preheat can enlarge the HAZ, reduce productivity, lower strength in some alloys, increase distortion, and impair toughness. It must be selected through a qualified welding procedure, relevant code, material data, and—where necessary—thermal or hardness testing.

8. Post-Weld Heat Treatment

PWHT is a controlled thermal cycle applied after welding. Its purposes may include:

• reducing residual stress through stress relief;
• tempering hard microstructures;
• reducing hydrogen-assisted cracking risk by allowing hydrogen diffusion;
• stabilizing dimensions;
• restoring or modifying material properties.

Stress-relief PWHT generally involves heating at a controlled rate to a specified temperature, holding for a specified time, and cooling under controlled conditions. The acceptable temperature and holding time depend on alloy, thickness, code, and service requirements. A generic stress-relief concept cannot replace a qualified procedure.

PWHT has limitations. It may reduce residual stress but cannot guarantee its complete elimination. It can cause grain growth, over-tempering, loss of precipitation hardening, dimensional change, or reheat cracking. Some alloys require solution treatment and aging rather than conventional stress relief. Local PWHT also creates thermal gradients; temperature uniformity and heating-band width must be controlled.

Distortion, Stress, and Cracking: A Necessary Trade-off

Reducing distortion by increasing restraint may increase residual stress. Increasing heat input may slow cooling but enlarge the HAZ and increase shrinkage. Increasing preheat may reduce hydrogen cracking while increasing distortion. These competing effects demonstrate why welding engineering is a process optimization problem rather than a search for one universally best parameter.

9. Cracking Mechanisms Related to Thermal History

Hot Cracking

Hot cracking occurs during solidification or at high temperature when a weak, partially solidified structure cannot accommodate contraction. It is promoted by unfavorable composition, segregation, a wide solidification temperature range, high restraint, and unsuitable bead shape. Prevention includes selecting compatible filler metal, controlling dilution, avoiding excessive concavity or high depth-to-width ratios, reducing contamination, and improving joint design.

Hydrogen-Assisted Cold Cracking

This form of cracking generally requires three conditions:

1. diffusible hydrogen;
2. a susceptible hard or brittle microstructure;
3. tensile stress or restraint.

Risk reduction includes low-hydrogen consumables, proper storage and baking where specified, clean and dry joint surfaces, suitable preheat and interpass control, adequate heat input, and delayed inspection when required. Postheating may be specified to promote hydrogen escape, but it is not a substitute for low-hydrogen practice.

Lamellar Tearing

Lamellar tearing is a through-thickness cracking problem in rolled plate, commonly near highly restrained fillet or T-joints. It is associated with nonmetallic inclusions arranged in planes parallel to the plate surface and tensile strain through thickness. Measures include improved through-thickness material quality, joint redesign, buttering, reduced restraint, and controlled welding sequence.

10. Applied Case: Distortion and Cracking in a Stiffened Steel Panel

This is an illustrative industrial case. A fabrication shop welds longitudinal stiffeners to a 16 mm low-alloy steel panel. After welding, the panel bows by 8 mm over its length, and delayed cracks appear near several tack welds.

Background and Problem

The original procedure uses high restraint, dry but poorly controlled electrodes, no documented preheat measurement, and a large fillet weld deposited in one direction. The steel has moderate hardenability, and the panel is attached to a massive fixture that acts as a heat sink.

Analysis

The high heat sink and lack of preheat produce rapid cooling. The large fillet creates substantial transverse and longitudinal shrinkage. One-direction welding concentrates contraction on one side of the panel, causing bowing. High restraint prevents free movement and raises tensile stress. Moisture-contaminated consumables provide a hydrogen source. The combination of susceptible HAZ microstructure, hydrogen, and tensile stress explains the delayed cracks.

Approach

The engineering team takes the following actions:

• verifies material certificates and carbon-equivalent information;
• introduces the specified minimum preheat and records it at the joint;
• uses properly controlled low-hydrogen consumables;
• reduces the oversized fillet to the design size;
• changes the sequence to alternate stiffeners and weld directions;
• uses balanced, segmented welds where permitted by design;
• revises tack-weld size and removes defective tacks;
• applies a qualified postheating or hydrogen-diffusion treatment if required;
• inspects after an appropriate delay using visual and nondestructive methods;
• measures panel flatness before and after welding.

Outcome

The revised procedure reduces the thermal gradient and total deposited metal, distributes shrinkage more evenly, and lowers hydrogen and restraint risk. The panel remains within dimensional tolerance, and no delayed cracks are detected during the specified inspection interval. The result is not attributed to preheat alone; it follows from simultaneous control of hydrogen, cooling rate, restraint, heat input, and welding sequence.

Learning Points

• Distortion and cracking can share the same thermal and mechanical causes.
• A fixture can improve dimensional control while increasing heat extraction and restraint.
• Procedure qualification must include measurable variables, not informal instructions such as “weld slowly.”
• Correct diagnosis requires evidence from material certificates, consumable control, thermal records, weld size, sequence, and inspection.

11. Measurement, Modeling, and Contemporary Practice

Temperature crayons, thermocouples, infrared instruments, hardness surveys, dimensional gauges, and residual-stress methods provide complementary evidence. Infrared measurement may be unreliable on shiny surfaces unless emissivity is controlled. Thermocouples provide local data but can disturb the surface or miss steep gradients. X-ray diffraction and hole-drilling methods can estimate residual stress, but each has depth, access, and calibration limitations.

Finite-element thermal–mechanical models can predict temperature fields, plastic strain, residual stress, and distortion. Reliable models require valid material properties as functions of temperature, realistic heat-source calibration, phase-transformation data, boundary conditions, and validation measurements. Artificial intelligence can assist parameter optimization, weld-image inspection, and prediction of distortion from historical data, but it does not remove the need for qualified procedures, physical validation, traceability, and human engineering judgment.

Professional practice must follow applicable welding codes, safety rules, qualified welding procedures, and inspection requirements. Thermal treatments can create fire, fume, electrical, and burn hazards. Records of preheat, interpass temperature, consumable exposure, PWHT charts, and inspection results support quality assurance and accountability.

Best-Practice Checklist

• Define material grade, thickness, joint type, restraint, and service requirements.
• Select heat input limits from qualified procedure data rather than isolated calculations.
• Control consumable storage, surface cleanliness, shielding, and hydrogen sources.
• Measure and record preheat and interpass temperatures.
• Use balanced geometry, suitable sequence, and only necessary weld size.
• Plan fixtures to control movement without excessive restraint.
• Consider cooling rate, HAZ hardness, toughness, and transformation behavior.
• Specify PWHT only when its metallurgical and dimensional effects are understood.
• Validate predictions with dimensional checks, hardness tests, NDT, or residual-stress measurements as appropriate.
• Treat codes and qualified procedures as controlling documents.

Chapter Summary

Welding creates a moving, localized thermal field whose effects extend into the base metal. Heat input is estimated from voltage, current, travel speed, and process efficiency, while cooling rate depends on heat input, material properties, thickness, geometry, preheat, interpass temperature, and heat sinking. The resulting thermal cycle determines weld-metal solidification, HAZ transformations, hardness, toughness, and cracking susceptibility.

Unequal expansion and contraction produce plastic strain, residual stress, and distortion. Longitudinal and transverse shrinkage can cause angular distortion, bowing, buckling, or twisting. Preheat and interpass control can reduce rapid cooling and hydrogen-assisted cracking, but excessive temperatures may enlarge the HAZ or reduce properties. PWHT may relieve stress and temper hard structures, yet it must be designed for the alloy and may introduce new risks.

Effective welding engineering balances thermal, metallurgical, mechanical, dimensional, safety, and code requirements. The most reliable solutions combine suitable heat input, low-hydrogen practice, controlled thermal measurements, balanced sequence, appropriate restraint, qualified procedures, and evidence-based inspection.

Key Terms

Heat input: Energy supplied to a weld per unit length.

Net heat input: Heat entering the workpiece after accounting for process efficiency.

Thermal cycle: The temperature history experienced by a point during welding.

Thermal diffusivity: A material property describing the rate at which temperature changes spread.

Cooling rate: Rate of temperature decrease over time or over a specified temperature interval.

Heat-affected zone: Base metal heated by welding without melting, whose structure or properties are changed.

Fusion boundary: Interface between melted weld metal and unmelted base metal.

Residual stress: Self-equilibrating stress remaining after external loads and thermal gradients are removed.

Longitudinal stress: Residual stress parallel to the weld axis.

Transverse stress: Residual stress perpendicular to the weld axis.

Distortion: Permanent dimensional change caused by nonuniform thermal and mechanical effects.

Angular distortion: Rotation caused by unequal contraction through the thickness.

Preheat: Temperature established in the base metal before welding.

Interpass temperature: Weld-area temperature immediately before depositing the next pass.

Post-weld heat treatment: Controlled heating and cooling after welding to modify stress or properties.

Hydrogen-assisted cracking: Delayed cracking requiring hydrogen, susceptible microstructure, and tensile stress.

Hot cracking: Cracking during solidification or at elevated temperature.

Restraint: Resistance to free movement or contraction of a welded component.

Carbon equivalent: Composition-based indicator used to compare steel hardenability and weldability.

Thermal efficiency: Fraction of source energy transferred effectively to the workpiece.

Review Questions

Short Answer Questions

1. Define net heat input and identify the variables used to estimate it.
2. Why can a thick plate cool faster than a thin plate under otherwise similar welding conditions?
3. Distinguish the HAZ from the fusion zone.
4. Name three forms of welding distortion.
5. State the three conditions generally associated with hydrogen-assisted cold cracking.

Long Answer Questions

1. Explain how a moving heat source produces a thermal cycle and how that cycle affects weld-metal and HAZ properties.
2. Discuss the origin of longitudinal and transverse residual stresses in a restrained welded joint.
3. Explain how preheat and interpass temperature influence cooling rate, cracking, and distortion.
4. Compare hot cracking, hydrogen-assisted cold cracking, and lamellar tearing.
5. Describe a systematic procedure for controlling distortion in a welded structure.

Analytical / Application Questions

1. A weld is deposited at 22 V and 160 A with a travel speed of 5 mm/s and an estimated efficiency of 0.75. Calculate the net heat input in J/mm and explain two limitations of the estimate.
2. A highly restrained low-alloy steel joint shows delayed cracks after welding. Identify the thermal, metallurgical, and mechanical evidence you would collect before changing the procedure.
3. A thin panel meets strength requirements but bows severely after welding. Propose a revised joint-design, sequence, restraint, and heat-control strategy, and explain the trade-offs involved.

Multiple Choice Questions with Answers

Question 1

Which expression gives the estimated net arc heat input when travel speed is in mm/s?

A. H_n = VI/v

B. H_n = ηVI/v

C. H_n = ηv/(VI)

D. H_n = V/(ηIv)

Correct Answer: B. H_n = ηVI/v

Question 2

What is the principal effect of increasing preheat on a susceptible steel joint?

A. It always increases cooling rate.

B. It generally slows cooling and reduces hardening risk.

C. It eliminates all residual stress.

D. It prevents weld-metal solidification.

Correct Answer: B. It generally slows cooling and reduces hardening risk.

Question 3

Which region is heated but not melted during welding?

A. Weld pool

B. Fusion boundary

C. Heat-affected zone

D. Solidification centerline

Correct Answer: C. Heat-affected zone

Question 4

A welding operation uses 20 V, 150 A, 5 mm/s travel speed, and efficiency 0.80. What is the estimated net heat input?

A. 300 J/mm

B. 400 J/mm

C. 600 J/mm

D. 750 J/mm

Correct Answer: B. 400 J/mm

Question 5

Which combination is generally required for hydrogen-assisted cold cracking?

A. Hydrogen, susceptible microstructure, and tensile stress

B. High oxygen, soft microstructure, and compression

C. Low heat input, low restraint, and no hydrogen

D. Radiation, porosity, and compressive stress

Correct Answer: A. Hydrogen, susceptible microstructure, and tensile stress

Question 6

What commonly produces angular distortion?

A. Equal contraction through the thickness

B. Unequal contraction through the thickness

C. Zero thermal gradient

D. Complete absence of restraint

Correct Answer: B. Unequal contraction through the thickness

Question 7

Why can excessive restraint be undesirable?

A. It always eliminates residual stress.

B. It can reduce movement but increase residual stress and cracking risk.

C. It prevents heat conduction entirely.

D. It lowers the melting temperature of the filler metal.

Correct Answer: B. It can reduce movement but increase residual stress and cracking risk.

Question 8

Which statement about PWHT is most accurate?

A. It completely eliminates every residual stress.

B. It can reduce stress or temper hard structures but must be matched to the alloy and procedure.

C. It is required for every weld.

D. It always improves toughness regardless of temperature.

Correct Answer: B. It can reduce stress or temper hard structures but must be matched to the alloy and procedure.

Question 9

A high thermal diffusivity generally means that heat

A. spreads through the material relatively rapidly.

B. cannot leave the weld pool.

C. causes no thermal stress.

D. always produces martensite.

Correct Answer: A. spreads through the material relatively rapidly.

Question 10

Which practice most directly reduces distortion before welding begins?

A. Increasing the fillet size beyond design requirements

B. Using balanced joint design and planned welding sequence

C. Maximizing restraint without qualification

D. Allowing consumables to absorb moisture

Correct Answer: B. Using balanced joint design and planned welding sequence