4. Material characterization for frontal impact

In a full vehicle frontal impact simulation, the accuracy of the predicted deformation pattern is bounded by the accuracy of the material models assigned to the front-end structures. A crash pulse that looks plausible can still be wrong if the bumper beam yields at the wrong stress, if the rail's strain-rate sensitivity is ignored, or if the failure strain of a cast component is set too high. This chapter covers how to characterize elastic-plastic metals, incorporate strain-rate dependence, define failure criteria, and validate the resulting material cards against coupon tests before they are used in a full vehicle model.

4.1 Elastic-Plastic Metal Behavior in Crash

For frontal impact, the relevant regime extends well beyond the yield point. Mild steel, high-strength steel (HSS), advanced high-strength steel (AHSS), and aluminum alloys all exhibit elastic-plastic behavior with hardening, but their hardening curves and failure strains differ substantially. The material card must capture:

  • Elastic modulus (E) and Poisson's ratio (ν) — typically 210 GPa and 0.3 for steel, 70 GPa and 0.33 for aluminum.
  • Initial yield stress (σy) — the onset of plastic flow.
  • Hardening curve — true stress vs. true plastic strain, usually derived from a uniaxial tensile test up to necking, then extrapolated.
  • Failure strain or damage initiation — the point at which the material can no longer carry load.

In PAM-CRASH, the elastic-plastic material is typically defined with material law 1 (elastic-plastic) or law 103 (elastic-plastic with damage). The hardening curve is entered as a table of true stress versus true plastic strain. A common mistake is to use engineering stress-strain data directly; the conversion is:

ε_true = ln(1 + ε_eng)
σ_true = σ_eng * (1 + ε_eng)

For a typical DP590 steel, the true stress at 10% plastic strain might be around 850 MPa, while the engineering value is closer to 780 MPa. Using the engineering value underestimates the energy absorbed by roughly 8–10% in a rail crush.

4.2 Strain-Rate Dependence

Frontal impact involves strain rates from 100 to 103 s-1 in the crush zones. Most steels and aluminum alloys show a positive strain-rate sensitivity: yield stress increases with strain rate. For mild steel, the yield stress at 1000 s-1 can be 1.5–2.0 times the quasi-static value. For AHSS, the sensitivity is lower but still non-negligible.

PAM-CRASH supports strain-rate-dependent plasticity through material law 1 with a rate-dependent yield function, or through law 103 with a Cowper-Symonds or Johnson-Cook formulation. The Cowper-Symonds model is widely used:

σ_y(ε̇) = σ_y0 * [1 + (ε̇ / D)^(1/p)]

where D and p are material constants. For mild steel, typical values are D = 40 s-1 and p = 5. For DP590, D = 800 s-1 and p = 3.5. These constants must be calibrated from split Hopkinson pressure bar (SHPB) tests or high-speed tensile tests.

Practical note: If strain-rate data are unavailable, do not simply omit rate dependence. A conservative approach is to use the quasi-static curve and apply a global dynamic amplification factor (e.g., 1.2–1.3 for mild steel) to the yield stress, but this must be documented as an assumption and validated against a coupon-level simulation.

4.3 Failure Criteria

Failure in frontal impact can be triggered by several mechanisms: ductile fracture, shear fracture, and in some castings, brittle fracture. PAM-CRASH offers several failure models:

  • Plastic strain failure — element deletion when equivalent plastic strain exceeds a threshold. Simple but mesh-sensitive.
  • Johnson-Cook damage — accounts for stress triaxiality and strain rate. Suitable for ductile metals.
  • GISSMO — generalized incremental stress state dependent damage model. Requires calibration of a damage curve and a instability curve.
  • Maximum principal stress — for brittle materials such as cast aluminum or magnesium.

For a typical frontal rail made of DP590, a plastic strain failure threshold of 0.35–0.45 is common, but this must be calibrated. The failure strain depends on element size; a 5 mm element will fail at a different strain than a 2 mm element. Mesh regularization or a GISSMO-based approach is recommended when mesh sizes vary across the model.

4.4 Validation Against Coupon Tests

Before a material card is used in a full vehicle model, it must be validated against coupon tests. The standard workflow is:

  1. Tensile coupon test — quasi-static (0.001 s-1) and high-rate (100–1000 s-1). Record force-displacement and derive true stress-strain.
  2. Coupon simulation — build a single-element or small mesh model of the coupon, apply the same boundary conditions, and run with the candidate material card.
  3. Compare — force-displacement curve, necking point, and failure displacement. A good match is typically within 5% on peak force and 10% on failure displacement.
  4. Adjust — if the simulation fails too early, increase failure strain or refine mesh; if it fails too late, reduce failure strain or check rate constants.

The following SVG illustrates the validation loop and the key parameters that must be checked at each stage.

Material Card Validation Loop for Frontal Impact 1. Coupon Test Quasi-static + high-rate Force–displacement data True stress–strain curve 2. Material Card E, ν, σ_y, hardening curve Cowper-Symonds D, p Failure strain / GISSMO 3. Coupon Simulation Single-element / small mesh Same BCs as test Run with candidate card 4. Compare Peak force ±5% Failure disp. ±10% Necking onset 5. Decision Match? → Accept card Mismatch? → Adjust (failure strain, D, p, mesh) iterate re-test Key parameters to verify at each iteration: • Elastic modulus E and yield stress σ_y — check against quasi-static test • Hardening curve — compare true stress at 5%, 10%, 15% plastic strain • Strain-rate constants D, p — validate against high-rate coupon • Failure strain — mesh-size dependent; document element size • Energy absorption — integrate force–displacement curve • Necking and failure displacement — visual + numerical check

4.5 Practical Example: DP590 Front Rail

Consider a front rail made of DP590, 1.8 mm thick, modeled with 5 mm shell elements. The quasi-static tensile test gives σy = 380 MPa, ultimate true stress = 850 MPa at 12% plastic strain, and failure at 0.38 plastic strain. High-rate tests at 500 s-1 show a yield stress of 520 MPa. Using Cowper-Symonds with D = 800 s-1 and p = 3.5, the predicted yield stress at 500 s-1 is:

σ_y(500) = 380 * [1 + (500/800)^(1/3.5)] ≈ 380 * [1 + 0.625^0.286] ≈ 380 * 1.37 ≈ 521 MPa

This matches the test within 0.2%. The coupon simulation with these parameters should reproduce the experimental force-displacement curve within 5% on peak force. If the simulation fails at 0.30 plastic strain instead of 0.38, the failure strain is too low; if it fails at 0.45, it is too high. Adjust and re-run until the failure displacement matches.

Common pitfall: Using a single failure strain for all mesh sizes. A 5 mm element and a 2 mm element will fail at different strains. If the full vehicle model has mixed mesh sizes, use GISSMO or apply a mesh regularization factor. Document the element size used during calibration and ensure consistency in the full model.

4.6 Summary of Material Card Checklist

Parameter Source Typical Value (DP590) Validation Check
E, ν Quasi-static tensile 210 GPa, 0.3 Elastic slope
σy Quasi-static tensile 380 MPa Yield point
Hardening curve Tensile test (true stress–strain) 850 MPa @ 12% Force–displacement
D, p High-rate tensile / SHPB 800 s-1, 3.5 High-rate yield stress
Failure strain Coupon test + simulation 0.38 (5 mm mesh) Failure displacement

Once the material card passes coupon-level validation, it can be used in the full vehicle frontal impact model. The same card should be applied consistently across all components made from that material, and any deviation in mesh size or forming history must be accounted for. The next chapter will build on this foundation to assemble the full vehicle model and define the impact boundary conditions.

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