4. Material modeling for side impact

Side impact is a short-duration, high-velocity event. In a typical pole or barrier test, the struck door outer panel and B-pillar experience strain rates on the order of 10² to 10³ s^-1, while the far-side rocker and floor tunnel may remain below 10 s^-1. This gradient means a single quasi-static stress–strain curve is insufficient: the material model must reproduce both the rate sensitivity of the base metal and the progressive damage that leads to fracture. This chapter covers how to select and calibrate constitutive and damage models for the three material families most common in body-in-white side structures, and how to combine them in a PAM-CRASH deck.

4.1 Strain-Rate-Dependent Steels

For mild and high-strength steels, the flow stress increase with strain rate is usually described by either a multiplicative rate factor or a coupled constitutive law. In PAM-CRASH, the most common steel card is material type 103 (elastic–plastic with Cowper–Symonds rate hardening) or type 36 (tabulated rate-dependent plasticity). The Cowper–Symonds form scales the dynamic yield stress as:

sigma_d = sigma_0 * [1 + (eps_dot / D)^(1/p)]

where:
  sigma_0  = quasi-static flow stress at the current plastic strain
  eps_dot  = current plastic strain rate
  D, p     = Cowper-Symonds coefficients (material constants)

For a typical DP590 grade, representative values are D = 8000 s^-1 and p = 5.0; for a mild DC04 deep-drawing steel, D ≈ 4000 s^-1 and p ≈ 4.0. These are starting points only. The correct procedure is to fit D and p to split-Hopkinson pressure bar (SHPB) data at 10²–10³ s^-1 and to verify the fit against at least three rate levels. A common error is to calibrate only at one high rate and then extrapolate; the resulting curve may over-predict the dynamic yield at intermediate rates, which softens the predicted intrusion by 5–10 mm in a pole test.

When the steel grade shows a pronounced rate-dependent hardening plateau, a tabulated plasticity card is preferable. In PAM-CRASH this is material type 36, where the user supplies a family of true stress–plastic strain curves, one per strain rate, and the solver interpolates. The table below summarizes the recommended model choice by steel family.

4.2 Aluminum Alloys

Aluminum alloys used in side structures—typically 5xxx (e.g., 5182) for inner panels and 6xxx (e.g., 6061-T6) for extrusions—have lower rate sensitivity than steel but a much lower fracture strain. For 6061-T6, the flow stress increase from quasi-static to 10³ s^-1 is roughly 10–15%, compared with 30–50% for DP590. The Johnson–Cook constitutive model is widely used here because it couples rate and temperature in a single expression:

sigma = (A + B * eps_p^n) * [1 + C * ln(eps_dot / eps_dot_0)] * [1 - T_star^m]

where:
  A, B, n   = quasi-static hardening parameters
  C         = strain-rate sensitivity coefficient
  eps_dot_0 = reference strain rate (usually 1.0 s^-1)
  T_star    = homologous temperature (T - T_room)/(T_melt - T_room)
  m         = thermal softening exponent

For 6061-T6, representative values are A = 324 MPa, B = 114 MPa, n = 0.42, C = 0.002, and m = 1.34. In a side-impact simulation the thermal term is often set to 1.0 (isothermal assumption) because the event is too short for significant heat conduction; however, if the model includes adiabatic heating, the thermal term must be retained. The practical risk with aluminum is not the flow stress but the fracture strain: 6061-T6 fails at approximately 0.08–0.12 equivalent plastic strain, so the damage model must be calibrated carefully. Using a steel-like fracture strain of 0.3 will delay failure and under-predict the risk of extrusion cracking.

4.3 Tailored Blanks and Tailor-Welded Blanks

Tailored blanks introduce a spatial discontinuity in thickness, grade, or coating. In PAM-CRASH, the weld line is usually represented by a shared node set or a tied contact interface. The material model must be assigned per zone, and the heat-affected zone (HAZ) should be modeled as a separate material with reduced yield and ductility. A common simplification is to assign the base metal properties to the HAZ, but this over-predicts the joint strength by 10–20% and can shift the predicted failure location away from the weld. For a DP590/DP780 tailor-welded blank, a practical approach is to define three zones: base DP590, HAZ (yield reduced by 15%, fracture strain reduced by 30%), and base DP780. The weld line itself is modeled with a tied contact and a cohesive zone if weld failure is a concern.

4.4 Damage Model Selection: Johnson–Cook, Cowper–Symonds, and GISSMO

The three models serve different purposes and are not interchangeable. Cowper–Symonds is a rate-hardening law, not a damage model; it describes how the yield surface expands with strain rate but says nothing about when the material fractures. Johnson–Cook damage is a phenomenological fracture criterion that defines the equivalent plastic strain at fracture as a function of stress triaxiality, strain rate, and temperature:

eps_f = [D1 + D2 * exp(D3 * eta)] * [1 + D4 * ln(eps_dot*)] * [1 + D5 * T*]

where:
  eta = stress triaxiality (sigma_m / sigma_vm)
  D1..D5 = calibration constants
  eps_dot* = normalized strain rate
  T* = homologous temperature

GISSMO (Generalized Incremental Stress State Dependent Damage Model) is an incremental damage model that tracks damage accumulation and includes a regularization scheme to reduce mesh sensitivity. It is the preferred choice for side-impact simulations involving press-hardened steels and aluminum extrusions, where fracture initiation and propagation must be captured across a range of stress states. The table below provides a selection guide.

4.5 Practical Calibration Workflow

A reproducible calibration sequence for a side-impact material card is as follows. First, obtain quasi-static tensile data at 0.001 s^-1 and fit the hardening law (Swift or Voce). Second, obtain SHPB data at 100, 500, and 1000 s^-1 and fit the rate parameters. Third, perform notched tensile tests at three triaxiality levels (smooth, R=2.5, R=0.4) to calibrate the fracture locus. Fourth, run a single-element simulation in PAM-CRASH to verify that the calibrated card reproduces the coupon force–displacement curve within 5%. Fifth, run a full side-impact model and compare the predicted intrusion profile at the B-pillar and door inner against the physical test. If the predicted intrusion is too low, check whether the rate parameters are over-predicting the dynamic yield; if fracture occurs too early, re-examine the triaxiality calibration.

The selection map above summarizes the recommended pairing of material family, constitutive model, damage model, and the single most influential calibration parameter. In practice, the choice between Johnson–Cook and GISSMO for a given steel grade depends on the available coupon data: Johnson–Cook requires fewer tests but is more mesh-sensitive, while GISSMO requires a full triaxiality calibration matrix but produces more stable fracture predictions across element sizes. For a side-impact model where the B-pillar mesh is refined to 3–5 mm, GISSMO is the safer choice for press-hardened and DP grades; for aluminum extrusions, Johnson–Cook remains acceptable if the mesh is kept above 5 mm and the fracture strain is calibrated at the relevant triaxiality.