2. Forming-induced property changes

When a stamped metal component is formed, it does not enter the vehicle body in a neutral, as-received state. The forming process permanently alters the material: it distributes plastic strain, thins the sheet, locks in residual stresses, and raises the yield strength through work hardening. In a one-step crash simulation, the part is typically modeled with nominal thickness and virgin material properties, so these histories are ignored. The consequence is a systematic mismatch between simulated and physical crash behavior — particularly in energy absorption, fold initiation, and failure timing. This chapter explains what each forming-induced change is, how it is quantified, and how it propagates into the crash model.

The Four Forming Legacies

Forming leaves four coupled signatures in the part. They are not independent: plastic strain drives thickness reduction and work hardening, and the non-uniform through-thickness stress state after unloading is what we call residual stress.

  • Plastic strain (effective/equivalent plastic strain, EPS): the accumulated irreversible deformation at each integration point. In a deep-drawn corner it can exceed 0.3; on a flat web it may be below 0.02.
  • Thickness reduction: under the constant-volume assumption of metal plasticity, thinning is approximately t/t₀ ≈ exp(−ε₁ − ε₂) for in-plane principal strains, or more simply t ≈ t₀·exp(ε₃) where ε₃ is the through-thickness strain. A 20% thinning in a draw wall is common and directly reduces bending stiffness and axial crush resistance.
  • Residual stress: the self-equilibrated stress field remaining after the forming tools are removed. It arises from non-uniform plastic flow and elastic springback. Magnitudes of 50–250 MPa are typical in high-strength steel draw walls.
  • Work hardening: the increase in flow stress with plastic strain. For a power-law material, σ = K·εⁿ, so a region with ε = 0.15 can have a flow stress 30–60% above the annealed yield point, depending on n.
Reference convention used throughout this course: strains are reported as true (logarithmic) strains, with ε₁ the major in-plane principal strain, ε₂ the minor in-plane principal strain, and ε₃ the through-thickness strain. Positive values denote tension. Thickness is measured normal to the sheet mid-surface. All stress values are Cauchy (true) stress unless stated otherwise.

How Forming History Enters the Crash Model

The standard industrial workflow is a two-stage chain: a forming simulation (implicit or explicit) produces a dynain file, and the crash model is initialized from it. The *INITIAL_STRESS_SHELL keyword imports the through-thickness stress resultants and the effective plastic strain, while thickness is updated either by remeshing the shell with the formed thickness or by mapping t per element. The mapping is the critical step — if the forming mesh and crash mesh differ, an interpolation error is introduced that can be larger than the physical effect you are trying to capture.

A practical check is to compare the imported thickness field against the forming result. If the crash model shows a uniform t₀ after import, the mapping silently failed. If thickness is imported but EPS is zero, the work-hardening state is lost and the material will yield too early in the crash.

Forming History → Crash Model: Property Transfer Chain Forming Simulation Blank → Draw → Springback Outputs per element: EPS, t, σ_res, ε_p dynain file (implicit or explicit) map Mapping / Initialization *INITIAL_STRESS_SHELL *INITIAL_FOAM_REFERENCE thickness remap interpolation error risk mesh mismatch init Crash Model State Non-uniform t(x,y) Pre-strained material (EPS) Residual stress field Elevated initial yield → realistic crash response Effect on Crash Response Metrics Plastic Strain Pre-strained zones yield earlier Fold location shifts Energy path changes ε_p up to 0.3+ Thickness Reduction Lower bending stiffness Reduced axial crush load Earlier local buckling Failure strain margin ↓ t/t₀ ≈ 0.8 typical Residual Stress Biases fold direction Alters springback Affects crack initiation Small effect on global 50–250 MPa Work Hardening Higher flow stress More energy absorbed Delayed necking Stiffer local response σ = K·εⁿ

Quantifying the Effect: A Worked Example

Consider a B-pillar inner made from DP780 sheet, t₀ = 1.6 mm, with a power-law hardening curve K = 1200 MPa, n = 0.14, and initial yield σ_y0 = 450 MPa. After forming, a draw-wall element carries ε_p = 0.12 and has thinned to t = 1.32 mm.

The flow stress at that point is σ = 1200 × 0.12^0.14 ≈ 1200 × 0.744 ≈ 893 MPa, compared with σ_y0 = 450 MPa for the virgin material. The section's axial crush resistance scales roughly with σ · t, so the formed element is about (893 × 1.32) / (450 × 1.6) ≈ 1.64 times stronger than a naive one-step model would predict. Ignoring forming therefore underestimates local strength in heavily worked regions — but the same thinning reduces the failure strain margin, so the net effect on fracture is not simply conservative.

Common pitfall: Importing EPS without updating thickness, or vice versa, produces a non-physical combination. A pre-strained element at nominal thickness will appear both strong and thick, over-predicting energy absorption. Always verify that EPS, t, and the residual stress field come from the same forming result and the same mesh mapping.

What to Check Before Running the Crash

A short verification pass catches most mapping errors before they contaminate the crash result:

  1. Plot the imported thickness field. It should be non-uniform and match the forming contour. A flat field means the remap failed.
  2. Plot EPS. High-strain bands should coincide with draw walls and corners, not with flat webs.
  3. Check the residual stress resultants. They should be self-equilibrated — the sum over the section should be near zero. A large net resultant indicates an unconverged springback step.
  4. Confirm the material card uses the same hardening curve in both stages. If the forming used a different K, n, or a tabulated curve, the imported EPS will not correspond to the crash model's flow stress.
  5. Run a single-element or small-patch check: apply a small displacement and confirm the initial yield load matches the expected pre-strained value, not the virgin yield.

When the Effect Can Be Neglected

Forming history is not always worth the mapping cost. It can be reasonably omitted when the part is lightly formed (ε_p < 0.03 over most of the gauge area), when the crash mode is dominated by global bending rather than local folding, or when the material is a low-hardening alloy where the flow-stress shift is small. Conversely, it is essential for deep-drawn closed sections, tailor-welded blanks with steep thickness gradients, and any component where fold initiation location determines the crash mode. The decision should be made per component, not per vehicle.

The practical takeaway is that forming history is a state transfer problem, not a material-model problem. The crash material card stays the same; what changes is the initial condition of every integration point. Getting that transfer right — thickness, plastic strain, and residual stress together — is what makes a one-step crash model behave like the real stamped part.

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