shock-impact

name	shock-impact
description	Shock and impact — impact factor, strain rate effects, energy methods for impact stress, DBTT, Charpy/Izod testing, drop weight, shock spectrum, fragility.
metadata	{"priority":6,"promptSignals":{"phrases":["impact","shock","impact factor","strain rate","Charpy","drop weight","DBTT","ductile brittle"],"minScore":4}}

Shock & Impact — Complete Skill

Impact Loading — Energy Method (Shigley 6-14)

Conservation of energy: KE_impact = U_strain For weight W dropped height h onto spring k:

Dynamic load factor (impact factor) n: n = 1 + √(1 + 2h/δ_st) δ_st = W/k [static deflection under W]

For h = 0 (sudden load, no velocity): n = 2 For large h: n ≈ √(2h/δ_st)

Impact stress: σ_max = n × σ_st = n × W/A (axial case) σ_max = n × W×L/S (bending case, S = section modulus)

Impact deflection: δ_max = n × δ_st

Energy absorbed: U = σ²_max × V / (2E) [for axial impact, uniform stress] For bending: U_beam = σ²_max × V / (6E) [roughly, for cantilever with tip load]

Velocity Impact (Moving Mass m, Velocity v)

KE = ½mv² Equivalent static force: P_eq = √(2 × k × KE) = v × √(km) Max deflection: δ_max = v/ω_n [undamped, mass strikes spring] Max stress: σ_max = v × √(Eρ) [stress wave in long bar — wave speed c = √(E/ρ)]

Stress wave propagation: c = √(E/ρ) — longitudinal wave speed c_steel = 5,000 m/s; c_Al = 5,100 m/s; c_Cu = 3,800 m/s σ_wave = ρ × c × v_impact [stress at wave front] Duration: pulse = 2L/c (round-trip in bar)

Strain Rate Effects

High strain rate (ε̇ > 10² s⁻¹): material strengthens Dynamic yield strength: S_yd = S_y × (1 + C × ε̇^m) Cowper-Symonds: S_yd/S_y = 1 + (ε̇/D)^(1/q) D = 40 s⁻¹, q = 5 (mild steel) D = 6,500 s⁻¹, q = 4 (aluminum)

At ε̇ = 10⁴ s⁻¹: S_yd can be 2-3× S_y for mild steel

Consequence: do NOT use static Sy in high-rate impact design — brittle fracture more likely even in ductile materials

Ductile-Brittle Transition (DBT)

BCC metals (ferritic steels, Fe): undergo DBT FCC metals (austenitic SS, Al, Cu): no DBT — remain ductile at cryogenic temperatures

DBTT (Ductile-Brittle Transition Temperature): Below DBTT: brittle fracture (low energy, KIC drops sharply) Above DBTT: ductile tearing (high energy absorbed)

Factors raising DBTT (embrittlement):

• High sulfur/phosphorus content
• Radiation damage (nuclear)
• Hydrogen embrittlement
• Cold working (reduces ductility)
• High constraint (thick section, triaxial stress)
• High strain rate

ASTM A36 (structural): DBTT ≈ -20°C typical (varies by heat) A572 Gr50: similar to A36 Low-temperature service (API 5L for pipelines): charpy required, notch toughness specified

Charpy V-Notch (CVN) Test

Standard: ASTM E23 Specimen: 10×10×55mm, 2mm deep V-notch Pendulum energy absorbed [J or ft·lb]

CVN to KIC conversion (approximate, Barsom-Rolfe): For σ_ys < 1400 MPa (upper shelf): K_IC² = 5 × CVN × σ_ys (MPa·m^0.5 units when CVN in J, σ_ys in MPa) Or Rolfe-Novak: K_IC/σ_ys = 0.54(CVN/σ_ys - 0.01)^0.5

AWS/AISC requirements: AWS D1.1 Zone III (Arctic), Zone II (cold climate): CVN ≥ 20 ft·lb at -20°F or -40°F ASTM A709 Grade 50W: CVN ≥ 15 ft·lb at +10°F (bridges)

Drop Weight Test (ASTM E208)

NDT (nil ductility transition temperature): temperature at which 100% cleavage fracture Pellini drop weight test: small brittle crack starter weld bead TNDT = reference temperature for pressure vessel (ASME BPVC App. G) Design rule: operating T ≥ TNDT + 60°F (shifts toughness into upper shelf)

Shock Spectrum

Shock Response Spectrum (SRS): plot of peak SDOF response vs. natural frequency Generated from: acceleration time history a(t) using Duhamel integral for each ω_n Used to: characterize shock severity, qualify equipment (MIL-STD-810, IEC 60068)

Half-sine shock pulse (amplitude g_pk, duration T_d): SRS peak ≈ 1.7 × g_pk at f_n ≈ 1/T_d Frequency: peak around 1/(2T_d) for undamped system

Fragility / Equipment Qualification

Equipment survives shock if: SRS(f_n) < Fragility(f_n) at natural frequency Seismic: response spectrum (RS) vs. required response spectrum (RRS) for qualification IEEE 693 (seismic), ICRU (nuclear): define RS; equipment must survive RS without damage

Output

Provide: impact factor n, dynamic stress σ_max [MPa], energy absorbed U [J], CVN requirement [J/ft-lb], DBTT concern, wave speed c [m/s].