thermo-mechanical-fea

name	thermo-mechanical-fea
description	Thermo-mechanical FEA — coupled thermal-structural analysis, sequential (one-way) vs. fully coupled formulation, thermal strain ε_th = α×ΔT, temperature-dependent material properties, creep (Norton power law), fatigue life from thermal cycling (Coffin-Manson), mesh requirements for thermal gradients, transient heat conduction FEA, contact thermal resistance, and ANSYS/Abaqus workflow for turbine blades, engine components, and electronics.
metadata	{"priority":7,"promptSignals":{"phrases":["thermo-mechanical FEA","thermal-structural analysis","thermal stress FEA","coupled thermal mechanical","thermal cycling fatigue","creep FEA"],"minScore":3}}

Thermo-Mechanical FEA — Complete Skill

Problem Classification

Coupling Types

One-way (sequential) coupling: thermal → structural; temperature field does not depend on deformation Most common for structural problems: solve thermal first → map temperatures → structural solve Valid when: deformations are small; no significant frictional heating; no contact conductance depending on pressure

Two-way (fully coupled) coupling: simultaneous solution of thermal and structural equations Required when: large deformations change heat flux path; frictional heating is significant; contact conductance pressure-dependent Much more expensive: 3–10× computational cost; use only when necessary

Sequentially coupled procedure (ANSYS/Abaqus): Step 1: Transient/steady-state thermal analysis → solve T(x,t) field Step 2: Map temperatures to structural mesh (identical or interpolated) Step 3: Apply thermal loads ε_th = α×ΔT + mechanical loads → solve σ, u

Thermal Analysis (FEA)

Governing Equation

Transient heat conduction (matrix form): [C] × {Ṫ} + [K_c] × {T} = {Q} [C] = capacitance matrix: Cᵢⱼ = ∫_V ρ × cₚ × Nᵢ × Nⱼ dV [K_c] = conductivity matrix: K_c,ij = ∫_V k × (∇Nᵢ × ∇Nⱼ) dV {Q} = load vector: heat flux BC + convection BC + radiation BC + internal generation

Steady-state: [K_c] × {T} = {Q} [no time derivative]

Time integration: Backward Euler (fully implicit): θ = 1; unconditionally stable; first-order accurate Crank-Nicolson: θ = 0.5; second-order accurate; may oscillate for sharp gradients Δt criterion for stability: Δt < h² × ρ × cₚ / (2k) for explicit; no limit for implicit

Boundary Conditions

Prescribed temperature: T = T_specified on surface Γ_T Heat flux: q_n = q_specified on surface Γ_q [q_n = −k × ∂T/∂n] Convection: q_conv = h × (T_surface − T_fluid) [h = convection coefficient in W/(m²·K)] Radiation: q_rad = ε × σ_SB × (T_surface⁴ − T_surr⁴) [ε = emissivity; σ_SB = 5.67×10⁻⁸ W/(m²·K⁴)] Contact conductance: q_contact = h_c × (T_A − T_B) at interface [h_c = 1,000–100,000 W/(m²·K) for metals in contact]

Mesh Requirements for Thermal FEA

Mesh density near thermal gradients: Rule: minimum 4–6 elements through thermal boundary layer or high-gradient region Biot number at surface: Bi = h × L_element / k → if Bi > 1, element size too large For film coefficient h = 1,000 W/(m²·K) and steel k = 50 W/(m·K): L_e < k/(h × Bi_limit) = 50/(1,000×1) = 50 mm max element size

Element types: ANSYS: SOLID70 (3D 8-node hexahedral thermal); SOLID90 (20-node); SHELL131 (shell thermal) Abaqus: DC3D8 (8-node hexahedral); DC3D20 (20-node); DS4 (4-node shell thermal) For thermal-structural: match thermal element topology to structural element

Structural Analysis with Thermal Loads

Thermal Strain

Total strain decomposition: ε_total = ε_mechanical + ε_thermal + ε_creep + ε_plastic ε_thermal = α(T) × ΔT = α(T) × (T − T_ref) [T_ref = stress-free reference temperature; typically room temperature]

Thermal stress (fully constrained): σ_thermal = −E × α × ΔT [compressive if ΔT > 0 and constrained; E × α ≈ 200,000 × 12e-6 = 2.4 MPa/K for steel] Example: Steel bar constrained at both ends; ΔT = +100°C: σ = −200,000 × 12×10⁻⁶ × 100 = −240 MPa (compressive) → potential buckling

Temperature-dependent properties: E(T), α(T), σ_y(T), k(T), ρ(T), cₚ(T) — must be tabulated over full temperature range Abaqus/ANSYS accept tabular data: define at 10–20 temperature points Ni superalloy: E drops from 207 GPa at 20°C to 150 GPa at 800°C; α increases from 12.5 to 16 ppm/K

FEA Workflow (Abaqus Sequentially Coupled)

Step 1: Define thermal model

• Same geometry as structural
• Assign material thermal properties: k(T), ρ, cₚ(T)
• Apply BCs: convection h(T), radiation, heat flux, temperature
• Request: nodal temperature T at each time step

Step 2: Define structural model

• Same mesh (or compatible for interpolation)
• Assign mechanical properties: E(T), ν(T), α(T), σ_y(T), hardening
• Apply predefined field: temperature from thermal analysis (PREDEFINED FIELD → TEMPERATURE in Abaqus)
• Apply mechanical loads/BCs (pressure, displacement)
• Activate: thermal expansion using *EXPANSION, ZERO = T_ref

Step 3: Solve and post-process

• Extract: von Mises stress σ_vM; plastic strain ε_p; creep strain ε_cr; displacement u
• Compare with: material yield σ_y(T); fatigue limit; creep limit

Creep in Thermo-Mechanical FEA

Norton Power Law

Steady-state creep rate: ε̇_cr = A × σⁿ × exp(−Q_cr / RT) [A, n = material constants; Q_cr = activation energy; R = 8.314 J/(mol·K)]

Typical n: 3–8 for metals (lower n → more linear creep behavior; high n → power-law breakdown) Typical Q_cr: 150–300 kJ/mol (diffusion-controlled)

Larson-Miller Parameter: LMP = T × (C + log t_r) [T in Rankine or Kelvin; t_r = rupture time [h]; C ≈ 15–25 for steels] Master curve LMP vs. σ: determines t_r at any T/σ combination Example: 316 SS at σ = 200 MPa, T = 600°C = 1,112°F: LMP = 1,060 × (C_LM + log(t_r)) → read t_r from curve

Creep FEA (Abaqus): *CREEP, LAW=STRAIN / TIME: define A, n, m, (m for time hardening) Coupled with plasticity: large-deformation step; NLGEOM = YES; small time increments

Creep-Fatigue Interaction

Robinson's rule: D_total = Σ(n/N_f)_fatigue + Σ(t_h/t_r)_creep ≤ D_allowable D_allowable typically 0.1–0.3 for high-temperature components (conservative)

Thermal Fatigue Analysis

Coffin-Manson (Low-Cycle Fatigue from Thermal Cycling)

Plastic strain range from thermal cycling: Δε_p = Δε_total − Δε_elastic = (α × ΔT_cycle − σ/E) [estimated; FEA gives actual Δε_p directly]

Coffin-Manson: Δε_p / 2 = ε_f' × (2N_f)^c [ε_f' = fatigue ductility coefficient; c = fatigue ductility exponent] Typical: c = −0.5 to −0.7; ε_f' = 0.2–1.0 for ductile metals

Morrow (mean stress correction): Δε_total / 2 = σ_f'/E × (2N_f)^b + ε_f' × (2N_f)^c FEA extracts Δε_p at critical location → use Coffin-Manson to estimate N_f

Thermal cycle N_f example: Turbine start-stop cycle: ΔT = 500°C → Δε_p = α × ΔT − σ_y/E = 12e-6 × 500 − 300/200,000 = 0.006 − 0.0015 = 0.0045 Coffin-Manson (IN-718: ε_f' = 0.35; c = −0.55): 0.00225 = 0.35 × (2N_f)^(-0.55) 2N_f = (0.35/0.00225)^(1/0.55) = 155.6^1.818 = 10,200 → N_f = 5,100 cycles

Electronics/Power Electronics Thermo-Mechanical FEA

Solder Joint Fatigue (IGBT, PCB)

Solder joint shear strain: γ = ΔCTEeff × L_chip / h_solder × ΔT [ΔCTEeff = CTE mismatch between chip and board] Typical: CTE_Si = 2.6 ppm/K; CTE_FR4 = 17 ppm/K; ΔCTEeff = 14.4 ppm/K L = 15 mm chip; h_solder = 0.1 mm; ΔT = 80°C → γ = 14.4e-6 × 15 / 0.1 × 80 = 0.173 (17.3%)

Engelmaier model: N_f = 0.5 × (γ_max / (2 × ε_f'))^(1/c) [c = −0.442 − 6e-4×T_s + 1.74e-2×ln(1+f); f = cycling frequency; T_s = mean solder temperature] Standard Sn-Ag-Cu (SAC305): ε_f' = 0.325; c depends on temperature and rate

PCB FEA

Element type: solid3D or shell; temperature applied as predefined field or direct gradient Critical locations: solder joint corners; via barrel stress; component leads Post-process: equivalent plastic strain PEEQ at solder corners; compare Engelmaier criterion

Turbine Blade Thermo-Mechanical FEA

Analysis Setup

Cooling channels: model internal cooling channels explicitly or via convective BC Blade metal temperature gradient: 50–200 K from pressure side to suction side

Centrifugal loading: rotational body force; ω² × r × ρ × dV contribution At 10,000 RPM: ω = 1,047 rad/s; centrifugal stress at root ≈ ρ × ω² × A_blade / A_root × r̄ For IN-738: ρ = 8,100 kg/m³; r̄ = 0.15 m; centrifugal σ ≈ 150–300 MPa

Hot section blade life: Creep: LMP gives rupture life; target blade life > 25,000 h Thermal fatigue: start-stop cycles; target > 1,000 cycles before inspection

Software Implementation

ANSYS Workbench Workflow

1. Thermal analysis system → solve T(x,t)
2. Static structural → import temperature as "Thermal Condition"
3. Thermal expansion coefficient α entered with T_ref (ANSYS calculates ε_th internally)
4. Nonlinear material models: bilinear isotropic hardening; Chaboche kinematic; Norton creep
5. Contact: define bonded/frictional pairs; thermal contact conductance TCC = h_c
6. Postprocessing: σ_vM vs. σ_y(T); NLGEOM for large-deflection creep; PEEQ for fatigue

Abaqus Workflow

1. *HEAT TRANSFER, STEADY STATE or DELTMX (transient time increment control)
2. *STATIC or *VISCO (creep) or *COUPLED TEMPERATURE-DISPLACEMENT
3. *EXPANSION, ZERO = T_ref → specify α(T) tabularly
4. *CREEP, LAW=STRAIN → A, n, m constants for Norton
5. *OUTPUT, HISTORY → request: S (stress), E (strain), PEEQ, NT (temperature)

Standards and References

Standard	Scope
ASME VIII Div. 2 Appendix 5	Fatigue design curves for pressure vessels
API 579-1/ASME FFS-1	FFS assessment including creep
ASTM E606	Strain-controlled fatigue testing (for Coffin-Manson parameters)
ASTM E139	Creep, creep-rupture, and stress-rupture testing
IPC-SM-785	PCB solder joint reliability guideline

Output

Provide: component description (geometry; material; T_range [°C]; mechanical loads; cycling: N cycles per year), coupling strategy (one-way vs. fully coupled; justification — presence of frictional heating or pressure-dependent contact), thermal analysis (BCs: h [W/m²K] and T_fluid; heat flux [W/m²]; temperature distribution T_max and T_min [°C]; time constant τ = ρcₚL²/k [s]; transient or steady-state), structural loads (thermal ε_th = α×ΔT [%]; mechanical σ_mech [MPa]; combined σ_vM at critical location [MPa]; vs. σ_y(T) [MPa]; margin [%]), creep (if T > 0.4 T_m: Norton law parameters A/n; creep strain after t_service [h]; Larson-Miller rupture life t_r [h]; creep life fraction used [%]), thermal fatigue (Δε_p from thermal cycle [%]; Coffin-Manson N_f [cycles]; comparison with design life; pass/fail), mesh sensitivity (element size at gradient zones [mm]; min 4 elements through gradient; convergence check: Δσ < 5% on mesh refinement), and applicable standard (ASME VIII App. 5 for fatigue; API 579 for creep-FFS; ASTM E606 for material data source).