| name | thermal-shock |
| description | Thermal shock resistance of ceramics and metals — Hasselman thermal shock parameters (R, R', R''), Kingery's first crack criterion, severity of quench (Biot number), thermal stress in constrained members (α×E×ΔT), edge cracking of ceramic tiles, thermal fatigue (cyclic thermal stress), coatings and functionally graded materials for thermal shock resistance, and ASTM standards for thermal shock testing. |
| metadata | {"priority":7,"promptSignals":{"phrases":["thermal shock","thermal shock resistance","Hasselman parameter","quench crack","thermal fatigue","ceramic thermal shock"],"minScore":3}} |
Thermal Shock — Complete Skill
Thermal Shock Fundamentals
Thermal Stress Mechanism
Thermal stress in constrained member (no ends free to move):
σ_th = −E × α × ΔT / (1 − ν) [σ_th = thermal stress; E = Young's modulus; α = CTE; ΔT = temperature change; ν = Poisson's ratio; negative → compressive if heating; tensile if cooling]
For rapid cooling (quench): surface cools first → contracts → tension at surface → possible fracture if σ_th > σ_f (fracture strength)
Thermal strain mismatch at interface (bimetallic/composite):
ε_mismatch = (α₁ − α₂) × ΔT [strain incompatibility → stress if bonded; must accommodate]
σ_interface = E_eff × (α₁ − α₂) × ΔT [elastic; in practice relaxed by creep or interface debonding]
Hasselman Thermal Shock Parameters
R-Parameters for Ceramics
Hasselman (1969) theory: defines material figures-of-merit for thermal shock resistance
R (resistance to crack initiation — first crack):
R = σ_f × (1−ν) / (E × α) [σ_f = fracture stress; higher R = more ΔT before first crack]
Interpretation: maximum ΔT tolerable before fracture = R × Bi_correction / kth_factor
For alumina: σ_f = 300 MPa; E = 380 GPa; α = 8.2×10⁻⁶/K; ν = 0.22
R = 300×10⁶ × (1−0.22) / (380×10⁹ × 8.2×10⁻⁶) = 2.34×10⁸ / 3116 = 75,100 K ≈ critical value (this is a material index)
Practical critical ΔT for thermal shock (Kingery criterion):
ΔT_c = σ_f × (1−ν) / (E × α) × f(Bi) [Bi = Biot number; f(Bi) = surface heat transfer correction]
For infinite heat transfer rate (Bi → ∞): f = 1; ΔT_c = R
For finite Bi: ΔT_c = R × (1 + 1/Bi) [approximately; reduces severity]
R' (thermal shock resistance allowing for crack propagation):
R' = R × k_thermal [k = thermal conductivity; W/m·K]
High k → rapid temperature equalization → reduced thermal gradient → lower thermal stress
Materials with high R': SiC (R' = 26,000 W/m), Si₃N₄ (R' = 19,000 W/m), vs. Al₂O₃ (R' = 5,000 W/m)
R'' (damage resistance — energy absorbed by stable crack growth):
R'' = E × G_Ic / (σ_f² × (1−ν)) [G_Ic = critical strain energy release rate]
High R'' → material can absorb more energy through crack extension before catastrophic failure
PSZ (partially stabilized zirconia): high R'' due to transformation toughening
Biot Number
Bi = h × L / k_thermal:
h = convective heat transfer coefficient at surface [W/m²K]; L = characteristic dimension [m]; k = thermal conductivity [W/mK]
Bi << 1: temperature uniform through specimen (no thermal gradient → no thermal stress → excellent thermal shock resistance despite quench)
Bi >> 1: surface temperature changes rapidly; interior lags → large ΔT through thickness → high stress
Practical Bi for common cases:
Still air: h ≈ 10 W/m²K → Bi for 10 mm ceramic: Bi = 10×0.01/30 (SiC) = 0.003 (uniform T; low stress)
Water quench: h ≈ 10,000 W/m²K → Bi = 10,000×0.01/30 = 3.3 (severe gradient; high stress)
Furnace cool: h ≈ 50 → Bi = 0.017 (mild)
Thermal Shock Testing
Water Quench Test (ASTM C1400)
Standard method: heat ceramic bar to T; quench into 25°C water; measure retained strength
Quench temperature: varies (e.g., 300°C, 400°C, 500°C steps)
Critical ΔT_c: temperature drop at which retained strength drops to 50% of original (interpolated)
Retained strength method:
After thermal shock: bend test (3-point or 4-point); retained σ_f (%) vs. ΔT_quench plotted
Inflection point = ΔT_c (critical thermal shock temperature)
Microwave/rapid heating:
For refractory materials: heat with torch or induction; quench immediately
Measure acoustic emission during quench → detect first crack formation
Thermal Cycling Fatigue (ASTM E2368)
Cyclic thermal stress (thermal fatigue):
N_f (cycles to failure) = σ_th_range / (E × ε_f') — Coffin-Manson based:
Δε_th = α × ΔT (each cycle); damage per cycle from thermal strain range
For metallic materials: apply standard Coffin-Manson: Δε_th / 2 = ε_f' × (2N_f)^c
Thermal cycling test parameters:
Heating/cooling rate: controlled (typical 5–50°C/min for ceramic; faster for thermal shock test)
Hold time at T_max and T_min: allows creep and oxidation to contribute
Number of cycles: 100–10,000 cycles depending on application life
Materials and Thermal Shock Resistance Ranking
Ceramics
| Material | ΔT_c [°C] | k [W/mK] | α [10⁻⁶/K] | σ_f [MPa] | Application |
|---|
| SiC (dense) | 350–500 | 120 | 4.3 | 400 | Turbine, nuclear |
| Si₃N₄ | 300–500 | 30 | 3.2 | 700 | Bearing, turbocharger |
| Al₂O₃ (99%) | 150–200 | 30 | 8.2 | 300 | General purpose |
| ZrO₂ (PSZ) | 100–300 | 2.5 | 10.5 | 500 | TBC, medical |
| Cordierite | 800–1200 | 2.5 | 1.5 | 100 | Catalyst substrate (low α → high ΔT_c despite low k) |
| Fused silica | 1000+ | 1.4 | 0.55 | 50 | Optical, lab ware |
Note on fused silica and cordierite: extremely low CTE → very high ΔT_c despite modest strength and k
Metals
Metals generally better than ceramics (ductility → plastic deformation instead of fracture):
Low-alloy steel: ΔT_c not a concern in normal use; embrittlement at low T is bigger concern
Stainless 316L: excellent thermal shock (ductile); quench from red heat OK
Invar (Fe-36Ni): α = 1.5×10⁻⁶/K → near-zero thermal stress; for precision instruments
Titanium: moderate α = 8.6×10⁻⁶/K; low k = 6.7 W/mK → higher thermal gradient → watch during rapid heating
Protective Strategies
Functionally Graded Materials (FGM)
FGM concept: composition gradient from metal (base) to ceramic (surface) eliminates sharp mismatch
CTE gradient: no sudden step change → no stress concentration at interface
Example: plasma-sprayed NiCrAlY/YSZ FGM TBC (5 layers, each 20% more ceramic)
Thermal stress at interface: ≈0 (vs. discrete bi-layer: σ_interface = E_eff × Δα × ΔT)
Coating Approaches
Porous ceramic coatings:
Thermal spray YSZ: low k (2.5 W/mK) + high strain capability (porosity → compliant) → better thermal shock than dense YSZ
Columnar TBC (EB-PVD): columns deflect laterally → accommodate CTE mismatch through column separation
Pre-cracked/micro-cracked ceramics:
Intentional micro-cracking (controlled by composition/heat treatment) → existing cracks accommodate thermal expansion without propagating catastrophically
Example: β-eucryptite ceramics (negative CTE component) self-crack to achieve near-zero effective CTE
Standards and References
| Standard | Scope |
|---|
| ASTM C1145 | Thermal shock testing terminology |
| ASTM C1400 | Thermal shock testing of ceramics (water quench) |
| ASTM E2368 | Thermal fatigue testing of metals and alloys |
| ISO 10545-9 | Ceramic tiles — resistance to thermal shock |
| ASTM C1199 | Thermal shock resistance of ceramics (stacked method) |
| DIN 51068 | Refractory products thermal shock resistance |
Output
Provide: material (ceramic/metal/composite; σ_f [MPa]; E [GPa]; α [μm/mK]; k [W/mK]; ν; G_Ic [J/m²]), thermal shock parameters (R = σ_f(1−ν)/(E×α) [K]; R' = R×k [W/m]; R'' = E×G_Ic/(σ_f²×(1−ν)) [m]; rank vs. competing materials), thermal environment (ΔT [K]; exposure time; frequency if cyclic; heating/cooling medium: water/air/gas; h [W/m²K]), Biot number (Bi = h×L/k; severity: Bi < 0.1 uniform T; Bi > 1 severe gradient), critical ΔT (ΔT_c = R × f(Bi) = σ_f(1-ν)/(E×α) × (1+1/Bi) [K]; compare to applied ΔT; safety margin [%]), thermal stress (σ_th = E×α×ΔT_surface/(1−ν) [MPa]; vs. σ_f [MPa]; factor of safety = σ_f/σ_th), thermal fatigue (if cyclic: Δε_th = α×ΔT per cycle; Coffin-Manson N_f from test data; inspection interval), protective measures (FGM if metal-ceramic; porous TBC; columnar EB-PVD if engine; low-α material substitution), and applicable standard (ASTM C1400 for ceramic quench test; ASTM E2368 for metal cyclic; ISO 10545-9 for tiles).
