Weld Fatigue: Nominal, Hot-Spot, Structural and Notch Stress

Why Welded Joints Are Fatigue-Critical

Welded joints are the most fatigue-critical details in steel structures for three compounding reasons. First, the weld toe is a severe stress concentration — the transition from the weld face to the parent material is a sharp geometric change, with a small toe radius (0.1–1 mm typical) and a high weld angle (30–45°). The stress concentration factor at the toe is typically 2–4, and for a sharp toe it can be higher. Second, the welding process leaves tensile residual stress at the weld, up to the yield strength of the material. The residual stress is superimposed on the applied stress, and at the weld toe the total stress can reach yield even under moderate applied load. The tensile residual stress means that the fatigue crack initiates and propagates under tensile conditions even if the applied stress is partly compressive — the residual tension keeps the crack open. Third, the weld contains local imperfections — undercut at the toe, cold laps, slag inclusions, porosity, lack of fusion — which are crack initiation sites. The combination of stress concentration, tensile residual stress and imperfections means that the fatigue life of a welded joint is much shorter than the fatigue life of the same material without a weld. The fatigue strength of a welded detail at 2 million cycles is typically 20–40% of the material fatigue strength at the same life — the weld reduces the fatigue capacity by more than half.

Welded joints are fatigue-critical because the weld toe is a severe stress concentration (Kt = 2–4), the residual stress is tensile (up to yield), and the weld contains imperfections (undercut, inclusions, porosity). The fatigue strength of a welded detail is typically 20–40% of the unwelded material fatigue strength.

The Four Stress-Based Assessment Methods

The fatigue assessment of welded joints uses one of four stress-based methods, each with its own definition of the stress at the weld and its own set of S-N curves (fatigue classes). The nominal stress method uses the nominal stress in the plate at the weld location — the stress that would be computed by a simple beam or plate theory, away from the weld. The stress concentration of the weld itself is included in the S-N curve (the fatigue class is for a specific detail category). The nominal stress method is the simplest and is used for standard details that are classified in the code (IIW, Eurocode 3, BS 7608, AWS D1.1). The hot-spot stress method uses the structural stress at the weld toe — the stress that includes the stress concentration from the global geometry (the attachment, the stiffener, the cut-out, the plate transition) but not the local notch of the weld toe itself. The hot-spot stress is obtained by extrapolation from the FE model at defined distances from the toe. The hot-spot method is used for details that are not classified in the code and for which the global geometry gives an additional stress concentration beyond the standard detail. The structural stress method (also called the structural stress or the Dong method) uses a through-thickness integration of the stress at the weld, which is mesh-insensitive and captures the structural stress including the bending. The notch stress method uses the local stress at the weld toe with a defined toe radius (typically 1 mm) — the notch stress includes the local notch effect, and a single generic S-N curve is used for all details. The notch method is the most detailed and is used for complex geometries and for optimisation studies.

The four methods use different stress definitions and different S-N curves. Nominal stress uses the plate stress and detail-specific classes. Hot-spot stress uses the structural stress at the toe (extrapolated) and a few classes. Structural stress uses a through-thickness integration and a master curve. Notch stress uses the local stress with a 1 mm toe radius and a single curve. The methods are not interchangeable — match the method to the detail and the FE model.

S-N Curves and Fatigue Classes

The S-N curve (Wöhler curve) is the relationship between the stress range (the double amplitude of the cyclic stress) and the number of cycles to failure. For welded joints, the S-N curve is typically a straight line on a log-log plot: log(N) = log(a) − m × log(Δσ), where N is the number of cycles, Δσ is the stress range, a is the intercept and m is the slope (typically 3 for welded joints in steel, above the fatigue limit). The S-N curves for welded joints are classified by detail category — the fatigue class — which is the stress range at 2 million cycles (the reference life). The IIW and Eurocode 3 system uses classes from 160 down to 36 (MPa at 2 million cycles), and BS 7608 uses classes from A to W. The class is determined by the detail geometry: a full-penetration butt weld ground flush is a high class (90 or 112), an as-welded butt weld is a moderate class (71 or 80), a fillet-welded attachment is a lower class (50 or 56), and a fillet-welded cover plate or a sudden section change is the lowest class (36 or 40). The class reflects the stress concentration and the imperfection severity of the detail. The S-N curve for each class includes the effect of the residual stress (high tensile) and the typical imperfections — the curves are for the as-welded condition. Below the fatigue limit (the knee point, typically at 5–10 million cycles for steel), the curve flattens — the fatigue life is very long (but not infinite, particularly under variable amplitude loading). The constant amplitude fatigue limit (CAFL) is the stress range below which fatigue failure does not occur under constant amplitude loading.

  S-N curve (log-log, welded steel):

  log(N) = log(a) − m × log(Δσ)

  where  N    = number of cycles to failure
         Δσ   = stress range
         m    = slope (typically 3 for welded steel above CAFL)
         a    = intercept (determines the fatigue class)

  Fatigue class = stress range at N = 2 × 10⁶ cycles

  Example classes (Eurocode 3 / IIW):
    112  →  ground-flush butt weld, NDT-tested
    90   →  full-pen butt weld, good quality
    71   →  as-welded butt weld
    56   →  fillet-welded attachment
    40   →  fillet-welded cover plate
    36   →  sudden section change

The S-N curve is a straight line on log-log axes: log(N) = log(a) − m × log(Δσ), with m ≈ 3 for welded steel. The fatigue class is the stress range at 2 million cycles. The class is determined by the detail geometry — from 160 (best) to 36 (worst). The curves assume high tensile residual stress and typical imperfections (as-welded condition).

The Nominal Stress Method

The nominal stress method is the standard method for classified details. The engineer identifies the detail category (the fatigue class) from the code, based on the geometry and the weld type. The nominal stress range is computed from the applied loads using beam theory or a coarse FE model — the stress in the plate at the weld location, away from the local stress concentration of the weld. The fatigue life is read from the S-N curve for the detail class at the computed stress range. The nominal stress method is simple, transparent and well-established — it is the basis of most structural fatigue design codes. The limitation is that it requires the detail to be classified — if the detail does not match a code category, the engineer must either select a conservative lower class or use a different method (hot-spot, structural, notch). The nominal stress method also does not capture the effect of the global geometry on the stress concentration — if the attachment, the stiffener or the cut-out produces an additional stress concentration that is not included in the detail category, the nominal stress method underestimates the actual stress and overestimates the fatigue life. The method assumes that the detail is a standard configuration — a plate with a transverse attachment, a plate with a longitudinal attachment, a butt weld in a plate — and the S-N curve includes the stress concentration for that configuration. For non-standard geometries, the hot-spot or structural stress method is more appropriate.

The nominal stress method uses the plate stress and the detail-specific S-N curve from the code. It is simple and well-established for classified details. The limitation: the detail must match a code category, and the global geometry stress concentration must be included in the category. For non-standard details, use the hot-spot or structural stress method.

The Hot-Spot Stress Method

The hot-spot stress method extends the fatigue assessment to details that are not classified in the code. The hot-spot stress is the structural stress at the weld toe — the stress that includes the stress concentration from the global geometry (the attachment, the stiffener, the plate transition) but not the local notch of the weld toe itself. The local notch is included in the S-N curve (the hot-spot S-N curves are for the weld toe notch, independent of the global geometry). The hot-spot stress is obtained by extrapolation from the FE model: the stress is read at two points at defined distances from the weld toe (0.5t and 1.5t for a type-a hot-spot, or 0.4t and 1.0t, depending on the code), and the hot-spot stress is the linear or quadratic extrapolation to the toe. The extrapolation avoids the stress singularity at the sharp toe — the stress at the extrapolation points is finite and mesh-independent, and the extrapolated hot-spot stress is a well-defined quantity. The hot-spot stress method requires a refined FE model — the mesh at the extrapolation points must be fine enough to capture the stress gradient (element size of 0.5t or smaller near the toe). The hot-spot S-N curves (IIW, DNV) have a few classes — typically two or three, for different weld types (fillet, butt, full penetration). The hot-spot method is used for offshore structures, ship hulls, bridges and other structures with complex welded details that do not match the standard code categories.

The hot-spot stress is the structural stress at the weld toe, obtained by extrapolation from the FE model at defined distances (0.5t and 1.5t). It includes the global geometry stress concentration but not the local weld toe notch. The hot-spot S-N curves are for the weld toe notch. The method requires a refined FE model (element size ≤ 0.5t near the toe) and is used for non-standard details.

The Structural Stress and Notch Stress Methods

The structural stress method (the Dong method, or the Battelle structural stress method) computes the structural stress at the weld by through-thickness integration of the FE stress field. The structural stress is a mesh-insensitive quantity — it is based on the balanced forces and moments at the weld, not on the local stress at a point. The structural stress captures the membrane stress and the bending stress through the thickness, and it is extrapolated to the weld toe. The method uses a single master S-N curve for all weld types and geometries — the scatter band is narrower than the nominal stress classes because the structural stress normalises the geometry effect. The structural stress method is particularly useful for complex geometries where the nominal stress is difficult to define and the hot-spot extrapolation is ambiguous. The notch stress method is the most detailed of the four methods. The weld toe is modelled with a defined radius — typically 1 mm (the "effective notch" or the "worst-case notch") — and the local stress at the rounded toe is computed from a very fine solid FE model. The notch stress includes the local notch effect — the stress concentration of the weld toe itself — and a single generic S-N curve (the notch S-N curve) is used for all details. The notch method is used for the most complex geometries, for optimisation studies, and for the assessment of weld toe improvement (grinding, TIG dressing) — the improved toe radius is modelled, and the notch stress is reduced. The notch method requires the finest mesh (element size of 0.1 mm or smaller at the toe radius) and the most modelling effort, but it gives the most local and the most transferable result.

The structural stress method uses a through-thickness integration of the FE stress — it is mesh-insensitive and uses a single master S-N curve. The notch stress method models the weld toe with a 1 mm radius and uses a single notch S-N curve. The notch method is the most detailed and is used for complex geometries, optimisation, and weld toe improvement assessment.

Load Direction, Weld Orientation and Mean Stress

The fatigue life of a welded joint depends on the direction of the load relative to the weld and the mean stress of the loading. The load direction affects the stress at the weld toe: a load perpendicular to the weld (transverse loading) produces a higher stress concentration at the toe than a load parallel to the weld (longitudinal loading). The fatigue class for a transverse attachment is lower than for a longitudinal attachment of the same geometry. The weld orientation also affects the fatigue life: a weld parallel to the load direction (a longitudinal weld) has a different stress concentration than a weld perpendicular to the load (a transverse weld). The S-N curves for each detail class are for a specific load direction — the engineer must select the curve that matches the load direction at the detail. The mean stress — the average of the maximum and minimum stress in the cycle — has a complex effect. For unwelded material, a tensile mean stress reduces the fatigue life (the Goodman or Gerber correction), and a compressive mean stress increases it. For welded joints, the mean stress effect is largely masked by the residual stress: the tensile residual stress at the weld (up to yield) means that the total stress at the weld toe is tensile even if the applied mean stress is compressive. The S-N curves for welded joints in the major codes (IIW, Eurocode 3) assume high tensile residual stress — the curves are for the worst-case mean stress. This means that stress relief (post-weld heat treatment) does not improve the fatigue class in most codes — the benefit is small and uncertain because the residual stress is difficult to eliminate completely. The exception is for joints loaded in compression (the applied load is compressive and the residual stress is tensile) — stress relief can be beneficial because it allows the crack tip to close under the compressive load.

The load direction and the weld orientation affect the fatigue class — transverse loading is more severe than longitudinal. The mean stress effect is largely masked by the tensile residual stress at the weld. The S-N curves assume high tensile residual stress (worst case), so stress relief does not improve the fatigue class in most codes — except for joints loaded in compression.

Variable Amplitude Loading and Cumulative Damage

Real structures are subject to variable amplitude loading — the stress range varies from cycle to cycle, with a spectrum of amplitudes determined by the load environment (traffic, waves, wind, manoeuvres). The fatigue assessment under variable amplitude loading uses the Palmgren-Miner linear cumulative damage rule: the damage from each stress range level is the number of cycles at that level divided by the fatigue life at that level, and the total damage is the sum over all levels. Failure occurs when the total damage reaches 1.0 (Miner sum = 1.0). The damage sum is: D = Σ(n_i / N_i), where n_i is the number of cycles at stress range level i and N_i is the fatigue life at that level from the S-N curve. The Palmgren-Miner rule is linear — it assumes that the damage from each cycle is independent of the sequence and the history. In reality, the sequence effect can be significant: a high stress cycle can initiate a crack that subsequent low cycles propagate, and the Miner sum at failure can be less than or greater than 1.0 depending on the sequence. The codes account for this by using a Miner sum at failure of 0.5 (conservative, for sequences where high cycles precede low cycles) or 1.0 (for random sequences). Below the constant amplitude fatigue limit (CAFL), the S-N curve is horizontal — no damage under constant amplitude. Under variable amplitude, however, the high cycles can propagate cracks that the low cycles (below the CAFL) then extend — the CAFL is not a true limit under variable amplitude. The codes use a modified S-N curve with a continued slope (m = 5 for the second slope, or a cut-off at a very high life) to account for the damage from cycles below the CAFL. The variable amplitude assessment requires the stress range spectrum (the histogram of stress ranges from the load environment) and the S-N curve for the detail.

  Palmgren-Miner linear cumulative damage:

  D = Σ (n_i / N_i)

  where  n_i = number of cycles at stress range level i
         N_i = fatigue life at level i (from S-N curve)

  Failure when D ≥ D_limit  (typically 0.5 or 1.0 per code)

  Under variable amplitude, cycles below the CAFL contribute damage:
    S-N curve continues with slope m = 5 (or cut-off at very high life)

  →  Linear rule — sequence effects not captured
  →  Miner sum at failure varies with sequence (codes use 0.5 or 1.0)

Variable amplitude loading is assessed with the Palmgren-Miner linear damage rule: D = Σ(n_i / N_i), failure at D = 0.5 or 1.0 per the code. The rule is linear and does not capture sequence effects. Under variable amplitude, cycles below the CAFL contribute damage — the S-N curve continues with a shallower slope.

Crack Initiation and Propagation

The fatigue life of a welded joint has two phases: crack initiation and crack propagation. In the initiation phase, the cyclic loading produces local damage at the stress concentration (the weld toe) — microcracks form, grow, and coalesce into a dominant crack. In the propagation phase, the dominant crack grows macroscopically, following the Paris law: da/dN = C × (ΔK)^m, where da/dN is the crack growth rate, ΔK is the stress intensity factor range, and C and m are material constants. For welded joints, the initiation phase is very short — the weld toe imperfections (undercut, inclusions, cold laps) are effectively pre-existing cracks, and the fatigue life is dominated by the propagation phase. This is why the S-N curve for welded joints has a slope of m = 3 — this is the same m as the Paris law, because the life is propagation-dominated. The crack typically initiates at the weld toe (the stress concentration) and propagates through the plate thickness, then along the plate. The crack path depends on the stress field — a crack at a transverse attachment propagates through the plate thickness and then across the plate width. The propagation can be modelled with fracture mechanics (the Paris law and the stress intensity factor) — this gives the residual life of a joint with a known crack, which is the basis for inspection intervals. The inspection interval is set so that a crack detected at the previous inspection cannot grow to critical size before the next inspection — the "detectable crack" to "critical crack" interval, divided by a safety factor. The fracture mechanics approach is complementary to the S-N approach: the S-N curve gives the total life, and the fracture mechanics gives the propagation life and the inspection interval.

The fatigue life of a welded joint is propagation-dominated — the weld toe imperfections are effectively pre-existing cracks, and the initiation phase is very short. The S-N slope (m = 3) matches the Paris law slope. The crack propagation can be modelled with fracture mechanics (Paris law) for residual life and inspection intervals.

Fatigue Improvement Methods

The fatigue life of a welded joint can be improved by modifying the weld toe geometry or the residual stress state. The improvement methods fall into two categories: geometry improvement and residual stress modification. Toe grinding — grinding the weld toe to a smooth radius with a burr tool — removes the sharp toe and the imperfections (undercut, inclusions) and creates a smooth transition. The fatigue class can be improved by one or two classes (a factor of 1.3–2.0 on life). The grinding must be controlled — the depth is typically 0.5–1.0 mm below the toe, and the grinding marks must be transverse to the stress direction (not parallel, which would create crack initiation sites). TIG dressing — remelting the weld toe with a TIG torch — smooths the transition and removes the imperfections by remelting the surface layer. The dressing gives a similar improvement to grinding. Hammer peening — striking the weld toe with a pneumatic hammer — introduces compressive residual stress at the toe and plastically deforms the toe to a smoother geometry. The compressive residual stress shifts the mean stress and delays crack initiation — the improvement can be a factor of 2–4 on life. Shot peening — blasting the toe with small shot — also introduces compressive residual stress, with a similar improvement. The improvement methods are most effective for details in the lower fatigue classes (high stress concentration) and less effective for details in the higher classes (the toe is already smooth). The improvement is only valid if the method is properly executed and inspected — a poorly executed toe grinding (too shallow, grinding marks parallel to the stress) can reduce the fatigue life. The codes (IIW) give guidance on the improvement factor for each method and the conditions for its application.

Fatigue improvement methods modify the weld toe geometry (grinding, TIG dressing) or the residual stress (hammer peening, shot peening). Toe grinding and TIG dressing improve the class by one to two classes; peening improves by a factor of 2–4. The methods must be properly executed and inspected — a poorly executed improvement can reduce the life. The codes give the improvement factors and the conditions.

A Warning on Reading the Peak FE Stress

A common mistake in weld fatigue assessment is to read the peak von Mises stress at the weld toe from an FE model and compare it with an S-N curve. This is not a valid weld-fatigue method, for two reasons. First, the peak stress at a sharp weld toe is a stress singularity — the theoretical stress at a sharp re-entrant corner is infinite, and the FE stress depends on the element size, not on the physics. As the mesh is refined, the peak stress increases without bound — there is no converged value. Comparing a mesh-dependent stress with an S-N curve gives a mesh-dependent fatigue life, which is meaningless. Second, the von Mises stress is not the correct stress for fatigue — fatigue is driven by the stress range (the cyclic amplitude), not by the von Mises equivalent of the peak stress. The fatigue assessment requires the stress range (the difference between the maximum and minimum stress in the cycle) at the correct location (the weld toe for the hot-spot method, the plate for the nominal method) and in the correct direction (the principal stress perpendicular to the weld, or the structural stress). The valid methods — nominal, hot-spot, structural, notch — each define the stress at the weld in a mesh-independent way: the nominal stress is away from the singularity, the hot-spot stress is extrapolated from non-singular points, the structural stress is an integrated quantity, and the notch stress is at a defined radius (not a sharp corner). The engineer must use one of these methods, not the raw peak stress. If in doubt, the engineer should perform a mesh convergence study — if the stress changes with the mesh, the stress is not valid for fatigue.

Simply reading the peak von Mises stress at the weld toe from an FE model is generally not a valid weld-fatigue method. The peak stress at a sharp toe is a singularity — it depends on the mesh, not on the physics. Use a defined method (nominal, hot-spot, structural, notch) that gives a mesh-independent stress. If in doubt, perform a mesh convergence study — if the stress changes with the mesh, it is not valid.

Key takeaways

• Welded joints are fatigue-critical because the weld toe is a severe stress concentration, the residual stress is tensile (up to yield), and the local geometry contains imperfections (undercut, cold laps, inclusions). Most fatigue cracks in welded structures initiate at the weld toe.
• The four stress-based methods — nominal, hot-spot, structural and notch — use different definitions of the stress at the weld. Each has its own S-N curves (fatigue classes). The method must be matched to the detail and to the FE model — the methods are not interchangeable.
• Simply reading the peak von Mises stress at the weld toe from an FE model is generally not a valid weld-fatigue method. The peak stress at a sharp toe is a singularity — it depends on the mesh, not on the physics. A defined method (nominal, hot-spot, notch with a defined radius) must be used.
• Residual stress from welding is tensile at the weld (up to yield strength) and it shifts the mean stress. The S-N curves for welded joints assume high tensile residual stress — the curves are for the worst case, and stress relief does not improve the fatigue class in most codes (the benefit is small and uncertain).