02.10 · Three-point bending: span and stiffness
Level 3IntermediateEst. 25 min
All blocks keep the CREATE / DISCOVER / SIMULATE positions, with Equipment below Geometry; unused records remain disconnected. This changes the view only, not the exercise records.
∑ Used models & submodels
Only models assigned to records used by this exercise are listed here. The full-layout option preserves the supplied starter records; no Workbench records are changed.
Euler–Bernoulli beam · Linear static · ASTM D7264 · Three-point flexure · Procedure A load
Beam bending uses effective laminate axial stiffness, the linked section geometry, support span and applied loading. Euler–Bernoulli deflection excludes transverse shear deformation, roller contact and indentation. Ply stress recovery for rectangular laminate coupons is separate from section-level beam stress recovery.
∑ Theory & assumptionsData travelling between blocks
Materials → Laminates
Stored ply stiffness, strength, density and expansion properties.
Mechanical → Simulation
SIMULATION selects this case and its analysis model; the case owns its applicable cycle and input references.
Laminates → Mechanical
Ply angles and thicknesses, stiffness, mass and ply properties.
Geometry → Mechanical
Part shape and dimensions, thickness or section definition, and model-specific geometric inputs. Each selected case consumes only the dimensions its model supports.
Models → Mechanical
Applied model assignment: Euler–Bernoulli beam · Linear static. Model parameters and formulation are used by Mechanical.
Inspect specimen width, laminate thickness, support span and central force.
Models: Euler–Bernoulli beam · ASTM D7264-26-based
Study scope and limitations
Procedure A teaching setup. Transverse shear deformation, roller contact and indentation are excluded.
Where to find it
In the CLT structural response workspace, open Response → Failure → Fatigue. Run the populated connected simulation first. Supply measured effective-ply fatigue calibration for every active source and stress channel. Fatigue is evaluated separately; the ordinary simulation Run does not evaluate cyclic life automatically.
Upstream coupling
Stored material plies and solved Micro plies use their existing elastic properties, angles and individual thicknesses. The laminate recovers bottom, middle and top ply stresses at two mechanical endpoints. The full six-component Load vector is used at one endpoint and Rload times that vector at the other. Progressive-ramp checkboxes are not fatigue amplitude selectors.
Selected saved thermal, cure and moisture histories contribute fixed residual strain at both endpoints. Available cure-conditioned stiffness is reused through the existing process-state pathway. Changed inputs require a new connected run. The fatigue calibration must independently cover the effective composition, orientation, process state, environment and cycling frequency; elastic homogenization does not create fatigue coefficients.
Model conventions
All stresses are in MPa and N is cycles, not reversals. U is a calibrated curve intercept, not an automatically inferred fiber strength. For peak-based curves, S is the dominant signed endpoint magnitude. Compression-dominated channels reverse sign before forming local R; calibrate with that same convention. Basquin uses half the stress range. No automatic Goodman or other mean-stress correction is applied.
| Model | Implemented relation | Inputs |
|---|---|---|
| Kim–Zhang | N = N₀ + U⁻ᵝ [(S/U)¹⁻ᵝ − 1] / [α(β−1)] | U, α > 0, β > 1, N₀ > 0 |
| Sendeckyj | S = U [1 + C(N−1)]⁻ˢ | U, C > 0, s > 0; controls use α=C and β=s |
| Weibull S–N | S = L + (U−L) exp[−α(log₁₀ N)ᵝ] | U, 0 ≤ L < U, α > 0, β > 0 |
| Kohout–Vechet | S = U [(1 + N/B)/(1 + N/C)]ᵇ | U, 0 < B < C, b < 0 |
| Basquin | Sₐ = A Nᵇ | A > 0, b < 0. Convert reversal-based coefficients before entry. |
The Kim–Zhang stress curve is obtained by algebraically inverting the stated life equation with N−N₀, preserving S=U at N=N₀. Weibull uses log base 10 explicitly: coefficients fitted with natural logarithms must be converted. The Weibull S–N curve is not a probability distribution and supplies no reliability percentile.
Calibration and persistence
- Select the effective ply source, σ1, σ2 or τ12 channel, and dominant sign.
- Select a model and enter its coefficients, published/test source, local stress-ratio bounds and tested cycle range. No material-specific coefficients are prefilled.
- Check that the calibration covers the current composition, process, temperature, moisture and frequency. Confirm applicability; changing inputs resets confirmation.
- Use Store fatigue inputs in CASES, then save the database. The setup follows that case record. Re-run the simulation after storing inputs, then Evaluate fatigue.
Reading results without a false pass
The table reports local endpoint stresses and R, estimated cycles when inside the calibrated domain, and requested cycles divided by estimated life. Missing calibration, zero-amplitude creep-only channels or an endpoint that fails the static ply check are not evaluated. Stresses above the fitted range and lives beyond it are reported separately, with no invented numeric life. Completed does not mean passed; no overall pass is issued, even when requested cycles are below estimated life.
Scope and verification
This is intact, in-plane CLT constant-amplitude screening. It does not update progressive fatigue damage or evolve temperature/cure during cycling. It does not assess delamination growth, adhesive/core fatigue, out-of-plane/FSDT shear, multiaxial fatigue interaction, variable-amplitude accumulation, creep or self-heating. The FSDT, sandwich, joint and layerwise solvers are not replaced by this panel. Frequency is a recorded calibration condition, not a numerical life correction.
Implementation checks cover forward/inverse equations, cycle conventions, monotonicity, numerical stability, thickness/load scaling, fixed residual stresses, missing data, static failure guards and saved-input round trips. These checks are not experimental benchmark validation. No existing teaching material is marked fatigue-qualified by adding this module.
Sources
- Burhan & Kim (2018), S–N Curve Models for Composite Materials Characterisation: equations 8, 11 and 22; model conventions and comparison.
- Sendeckyj (1981), Fitting Models to Composite Materials Fatigue Data: equivalent static strength and fitted fatigue data.
- Kohout & Věchet (2001), A new function for fatigue curves characterization and its multiple merits: full-range curve.
- A generalization of the fatigue Kohout–Věchet model: equivalent parameterizations.
- Kim & Zhang (2001), Fatigue Damage and Life Prediction of Glass/Vinyl Ester Composites: original model study.
- Weibull (1961), Fatigue Testing and Analysis of Results: original fatigue-curve reference.
∑ CLT and residual-strain recovery · ∑ Monotonic progressive failure · ∑ Process coupling