4. Spot weld and structural joint modeling

In a rollover or roof crush simulation, the body-in-white does not fail as a monolithic shell. It fails at the joints. Roof rails separate from B-pillars, pillars tear away from rockers, and spot welds pull buttons out of thin-gauge sheet metal long before the surrounding steel reaches its forming limit. If the weld model is too stiff, the structure behaves like a continuous beam and the simulation over-predicts roof strength. If it is too soft or fails too early, the roof collapses prematurely and the design is rejected for the wrong reason. This chapter covers how to represent spot welds and structural joints in PAM-CRASH, how to model their failure, and how to validate the connector model against physical coupon and component tests.

Connector Types and When to Use Each

PAM-CRASH offers several ways to join shell meshes. The choice depends on the joint's mechanical role, the mesh topology, and whether failure must be captured.

For roof crush, the joints that matter most are the spot welds connecting the roof rail to the B-pillar and the A-pillar to the roof panel. These carry combined peel and shear loading during the crush event, and they are the first to fail. Rigid ties are acceptable only where the joint is demonstrably stronger than the surrounding metal, which is rarely the case in thin-gauge roof structures.

Representing a Spot Weld in the Mesh

A production spot weld has a nugget diameter of roughly 4–6 mm and a heat-affected zone that extends a few millimeters beyond. Two modeling approaches dominate practice.

PLINK (rigid or elastic-plastic link): A single connector element joins one node on each sheet. It is cheap and stable, but it concentrates all load into one node pair, which can cause artificial stress concentrations and premature failure. Use PLINK when the weld is not the critical failure location and when mesh density is coarse.

Solid element weld: A small cluster of solid elements (typically a 2×2 or 3×3 patch) spans the two sheets, matching the physical nugget footprint. This distributes load realistically and is the preferred choice for joints that must fail. The solid elements share nodes with the shell mid-surfaces, or are tied to them via a tied contact. The weld diameter in the model should match the drawing or the measured nugget, not an arbitrary value.

For a typical 0.8 mm roof rail welded to a 1.2 mm B-pillar, a solid weld patch of 5 mm diameter with two elements through the thickness of each sheet is a reasonable starting point. The mesh around the weld should be refined so that the weld patch is not larger than the surrounding elements; otherwise the weld will dominate the local stiffness artificially.

Failure Modeling

Spot weld failure in PAM-CRASH is usually driven by a rupture criterion applied to the connector or solid elements. The most common formulation combines normal (peel) and shear forces into an interaction equation:

(f_n / F_n)^a + (f_s / F_s)^b >= 1.0  ->  weld rupture

where f_n and f_s are the current normal and shear forces, F_n and F_s are the corresponding ultimate capacities, and a, b are interaction exponents (often 2.0 for a quadratic interaction). When the sum reaches 1.0, the connector is deleted or its stiffness is reduced to zero over a short softening period.

The capacities F_n and F_s are not arbitrary. They come from coupon tests: lap-shear specimens for F_s and coach-peel or cross-tension specimens for F_n. For a 5 mm nugget in 0.8–1.2 mm mild steel, typical measured values are on the order of 4–6 kN in shear and 1.5–2.5 kN in peel. These are example ranges; the actual values must come from the specific material and stack-up being modeled.

For solid-element welds, failure can also be triggered by a plastic strain or damage criterion in the weld material. This is more physically detailed but requires calibrated material data for the weld nugget, which is often unavailable. The force-based interaction criterion remains the practical default for full-vehicle roof crush models.

Validation Against Physical Tests

A connector model is only credible if it reproduces the coupon tests used to calibrate it and then predicts a component-level test it was not tuned on. The validation ladder has three rungs.

1. Coupon level: Simulate the lap-shear and coach-peel specimens with the same weld representation and failure criterion. The predicted peak force should fall within about 10–15% of the measured peak, and the failure displacement should be within a similar band. If the simulation is too stiff, the weld patch is too large or the surrounding mesh is too coarse.
2. Component level: Build a sub-assembly such as a B-pillar-to-roof-rail joint and apply a quasi-static peel or three-point bend. Compare the force-displacement curve and the failure sequence. This catches load-path errors that coupon tests cannot reveal.
3. Full-vehicle level: Run the roof crush per FMVSS 216a or the rollover event and compare the force-displacement plateau and the location of joint separation against the physical test. Weld failure locations should match the tear pattern in the tested body.

If the component test fails at a weld that the simulation predicts will survive, the most common causes are an over-estimated weld capacity, a missing weld in the model, or a mesh transition that artificially stiffens the joint. If the simulation fails too early, check for a single-node PLINK concentrating load, an unrefined mesh around the weld, or a peel capacity that was taken from a different stack-up.

Practical Calibration Workflow

The following sequence is a reliable way to build and validate a weld model without over-fitting to a single test.

1. Extract the weld stack-up from the body drawings: sheet thicknesses, materials, and nugget diameter for each joint class.
2. Run lap-shear and coach-peel coupon simulations with the chosen connector representation. Adjust F_s and F_n until the predicted peak forces match the measured means.
3. Apply the calibrated criterion to a component sub-assembly. If the failure location differs from the test, inspect the mesh transition and the load path before changing the criterion.
4. Run the full-vehicle roof crush. Compare the force-displacement curve and the weld tear pattern. Only adjust the criterion if the coupon and component levels remain valid.

The central lesson is that weld failure is a local phenomenon with global consequences. A 5 mm nugget that is modeled as a rigid tie can add hundreds of newtons to the roof crush plateau, while an over-soft weld can remove them. Calibrating against coupons, verifying at the component level, and confirming at full vehicle is the only way to ensure the joint model is both physically defensible and numerically stable.