4. Weld failure criteria in PAM-CRASH

Spot welds in a body-in-white (BIW) model are rarely represented by solid elements. In PAM-CRASH they are typically condensed into a single PLASTIC or SPOTWELD element, a rigid spider, or a tied contact patch. Because the physical nugget is small and the surrounding sheet metal carries most of the deformation, the weld itself must be judged by a dedicated failure criterion. PAM-CRASH offers three families of criteria — force-based, stress-based, and strain-based — and choosing the wrong one is one of the most common reasons a crash model either tears apart too early or holds together when the physical test shows a pull-out.

What Each Criterion Actually Measures

The three approaches differ in the quantity they compare against an allowable value, and therefore in what they can and cannot capture.

• Force-based: the resultant axial force F and shear force Q transmitted by the weld element are compared with a failure envelope. PAM-CRASH implements this through the weld material card (for example MAT_SPOTWELD / type 100) with normal and shear force limits, often combined as (F/Fn)^a + (Q/Qs)^b ≥ 1. It is cheap, stable, and directly tied to the element's internal force output.
• Stress-based: the criterion evaluates a stress tensor at the weld or at the sheet interface — peel stress, shear stress, or a von Mises equivalent — against a material strength. This is common when the weld is modelled with solid elements or when a PLASTIC shell patch is used and the user wants a stress-based rupture flag.
• Strain-based: failure is declared when an equivalent plastic strain ε_p or a damage variable D reaches a critical value. This is the natural choice for ductile nugget pull-out and for welds embedded in regions that undergo large membrane stretching.

In practice the three are not mutually exclusive. A robust weld model often uses a force envelope for the nugget and a strain limit for the surrounding heat-affected zone (HAZ).

Force-Based Criterion in Detail

The force-based route is the workhorse for full-vehicle crash models because it is numerically inexpensive and its inputs can be calibrated from a lap-shear and a coach-peel coupon test. A typical PAM-CRASH setup uses a weld element with:

MAT_SPOTWELD  id=2001  rho=7.85e-9
  Fn = 4.2 kN      ! normal (peel) force limit
  Qs = 6.8 kN      ! shear force limit
  a  = 2.0         ! normal exponent
  b  = 2.0         ! shear exponent
  dmax = 0.6 mm    ! rupture displacement

The failure index is then

I = (F/Fn)^a + (Q/Qs)^b

and the weld is deleted when I ≥ 1 or when the relative displacement across the weld reaches dmax. The exponent pair controls the shape of the envelope: a = b = 2 gives an elliptical interaction, which matches most steel spot welds reasonably well; a = b = 1 gives a conservative linear envelope suitable for aluminium or for welds with poor nugget quality.

Stress-Based and Strain-Based Criteria

When the weld is discretised with solid elements, or when the surrounding sheet is modelled with a fine shell mesh, a stress-based criterion becomes meaningful. PAM-CRASH evaluates the stress at the integration point and compares it with a user-supplied SIGY or a damage surface. The advantage is that it captures the multiaxiality of the HAZ; the disadvantage is mesh sensitivity — a coarse mesh underestimates the peak stress and delays failure.

Strain-based criteria avoid some of that sensitivity because plastic strain is less mesh-dependent once the element size is below the localisation length. A typical implementation uses a damage accumulation:

D = Σ (Δε_p / ε_f)
failure when D ≥ 1

where ε_f is the failure strain, often taken as 0.15–0.25 for mild steel HAZ and 0.08–0.12 for high-strength steel. This form is well suited to spot welds that fail by nugget pull-out under combined peel and shear, because the strain path in the HAZ is captured directly.

Selecting the Right Criterion

The choice should follow the failure mode you expect and the mesh you can afford. The table below summarises the practical guidance.

A practical rule: start with the force-based envelope for the full-vehicle run, because it is stable and fast. Once the model is running, extract the welds that fail and re-examine them with a strain-based sub-model. If the sub-model predicts failure earlier than the force envelope, tighten Fn and Qs; if later, loosen them. This two-stage workflow keeps the global model robust while still capturing local ductile behaviour.

Worked Example: Lap-Shear Coupon

Consider a 1.5 mm mild-steel lap-shear coupon with a 6 mm nugget, modelled with a single weld element between two shell patches. The coupon is pulled at 5 m/s. The weld element uses Fn = 4.2 kN, Qs = 6.8 kN, a = b = 2, dmax = 0.6 mm. During the run, the shear force Q rises to 6.8 kN at about 4.5 ms, giving I = 1.0; the weld is deleted and the coupon separates. If the physical test shows separation at 5.2 ms, the model is slightly early and Qs should be raised to about 7.5 kN. If the model holds to 6.0 ms, Qs is too high and should be reduced. This calibration loop — run, compare, adjust one parameter — is the standard way to tune weld criteria in PAM-CRASH.

Calibration and Verification Checklist

Whichever criterion you choose, the model is only as good as its calibration. The following points should be checked before a weld criterion is accepted for a full-vehicle run:

1. Coupon tests (lap-shear and coach-peel) are available for the sheet grade and thickness in the model.
2. The weld element size and the surrounding shell mesh are consistent with the coupon mesh used for calibration.
3. The failure index or damage variable is requested in the output (HIST or TH output for the weld element) so that the timing of deletion can be verified.
4. The deletion time in the model is compared with the coupon test separation time; the difference should be within 10–15%.
5. If both force and strain criteria are active, confirm that only one governs the deletion in the expected failure mode.

Force-based criteria remain the default for large BIW models because they are robust and their inputs are easy to obtain. Stress-based criteria are useful when the weld is modelled with solids and the HAZ stress state matters. Strain-based criteria are the most physically faithful for ductile pull-out, but they demand a finer mesh and a reliable failure strain. The most reliable practice is to combine them: use the force envelope for the global model, and use strain or stress checks on the critical welds identified by the global run.