Cmh17 Allowables

CMH-17 Composite Allowables (structures/composites/cmh17-allowables)

Use when the task is statistically based composite material design allowables: A-basis and B-basis values from coupon test samples, one-sided normal tolerance k-factors, coupon pooling across batches and environments, and laminate-level allowables derived from lamina allowables with knockdown factors. This leaf is the composite counterpart of structures/materials/mmpsd-allowables (which treats metals); it is also distinct from structures/composites/laminate-stiffness, which computes the elastic stiffness matrix rather than strength design values.

Domain quick reference

• A-basis: 95% confidence that 99% of the population exceeds the value; B-basis: 95% confidence that 90% exceeds the value.
• One-sided normal tolerance k-factor (Owen/Odeh approximation): z_c = 1.6448536269514722 (0.95 confidence); z_p = 2.3263478740408408 for A-basis content or 1.2815515655446004 for B-basis; a = 1 - z_c^2/(2(n-1)); b = z_p^2 - z_c^2/n; k = (z_p + sqrt(z_p^2 - a*b))/a.
• Allowable = sample mean - k * sample standard deviation.
• Common minimum samples: 10 for A-basis, 6 for B-basis; verify against the current CMH-17 edition.
• Pooling: combine coupon batches (batches, environments) into one effective sample; the pooled mean is the overall mean and the pooled standard deviation is the within-batch pooled value (sum((n_i - 1) s_i^2) / sum(n_i - 1))^0.5. The larger effective sample count lowers the k-factor.
• Knockdown factors: environmental conditioning (hot/wet), barely visible impact damage (BVID), and open hole features reduce the lamina allowable to the laminate allowable; the combined factor is the product of the individual factors, each in (0, 1].
• Where strength data are Weibull distributed, the content quantile eta * (-ln(p))^(1/beta) from a two-parameter Weibull MLE fit is used in place of the normal tolerance method.
• CMH-17 is the Composite Materials Handbook (proprietary, published by SAE); name and paraphrase only, per standards-map.yaml and research/briefs/06-legal-export-control.md. FAR-25 is the public airworthiness context for transport category strength substantiation.

Workflow

1. Gather the coupon test sample per material, batch, environment, and property of interest; record the sample count.
2. Check the sample count against the basis minimum with check_sample_count.
3. For a single batch, compute the k-factor with k_factor_one_sided and the allowable with allowable_from_sample.
4. For pooled data, call pooled_allowable with the batch list to get the pooled mean, pooled standard deviation, effective n, k-factor, and pooled allowable.
5. For Weibull-distributed strength data, fit the two-parameter Weibull with weibull_mle and derive the content quantile or basis value with weibull_content_value / weibull_basis.
6. Apply the environmental, BVID, and open hole knockdown factors to each lamina allowable with knockdown to get the laminate allowable.
7. Assemble the lamina and laminate allowable table with build_allowable_table; each row carries the basis designation and the confidence/content statement from basis_statement.
8. Confirm the deterministic checks with the contract test scripts/test_cmh17_allowables.py.

Basis value statistics

The A- and B-basis design values follow the standard one-sided normal tolerance approach: the allowable sits k sample standard deviations below the sample mean. Because the k-factor grows as the sample shrinks, small coupon samples produce conservative (low) allowables; meeting the minimum sample count is the first validation step.

Pooling is the composite-specific refinement: coupon batches from different panels, batches, or environments are combined into one effective sample. The pooled standard deviation weights each batch by its degrees of freedom, so batch-to-batch scatter is retained without inflating the estimate by between-batch spread, and the larger effective n reduces the k-factor and raises the allowable relative to any single batch alone.

For strength distributions that are not normal, the two-parameter Weibull fit provides the content quantile: with shape beta and scale eta from the MLE, the value exceeded by fraction p of the population is eta * (-ln(p))^(1/beta). The sample-size shrink (1 - 1/n) applied in weibull_basis is a conservative engineering adjustment; the authoritative confidence factors are the published CMH-17 values (referenced, not reproduced).

Knockdown model

Laminate allowables are derived from lamina allowables by multiplying the lamina value by each applicable knockdown factor, in (0, 1]:

• environmental conditioning factor: hot/wet conditioned strength reduction (for example 0.9 for a wet elevated temperature case);
• barely visible impact damage (BVID) factor: compression and shear strength reduction after impact (for example 0.85 for a compression-dominated case);
• open hole factor: strength reduction at fastener holes (for example 0.95 for an open hole tension case).

Combined knockdown = env * bvid * hole; laminate allowable = lamina allowable * combined. Each factor must be strictly between 0 and 1; unit factors leave the allowable unchanged.

Worked example

A tension lamina coupon sample of 7 values is [100, 102, 104, 106, 108, 110, 112] MPa. For B-basis:

• n = 7, mean = 106.0, sample standard deviation about 4.32.
• k_factor_one_sided(7, "B") is between 2.0 and 2.8; the allowable is mean - k * sd, positive and below the sample mean.
• With the environmental factor 0.9, BVID factor 0.85, and open hole factor 0.95, the combined knockdown is 0.9 * 0.85 * 0.95 = 0.72675 and the laminate allowable is about 27% below the lamina allowable.
• The table row carries the statement "B-basis: 95% confidence, 90% content".

If the 7-value sample is split into batches of 4 and 3 across two environments, pooling combines them into one effective sample of 7: the pooled standard deviation stays within the batch spreads, the k-factor is driven by the total n, and the pooled allowable is computed from the overall mean.

Pitfalls

• Using the allowable below the minimum sample count: A-basis needs about 10 coupons and B-basis about 6 (verify against the current CMH-17 edition); smaller samples grow the k-factor and the value loses its statistical meaning.
• Pooling when batches disagree: the pooled standard deviation is the within-batch value sum((n_i - 1) s_i^2) / sum(n_i - 1), so it retains batch scatter only if the batches are genuinely combinable; pooling between-batch spread inflates the estimate.
• Applying the normal tolerance method to Weibull strength data: for Weibull-distributed properties use the two-parameter MLE content quantile eta * (-ln(p))^(1/beta), not the normal k-factor.
• Multiplying knockdown factors outside (0, 1]: each factor must be strictly between 0 and 1; a factor at or above 1 (or at or below 0) breaks the combined knockdown 0.9 * 0.85 * 0.95 = 0.72675 chain.
• Confusing the basis statements: A-basis is 95% confidence / 99% content and B-basis is 95% confidence / 90% content; the table row statement must match the requested basis.
• Forgetting this is lamina-to-laminate: the knockdown path derives laminate allowables from lamina allowables; the elastic stiffness side (not strength design values) belongs to laminate-stiffness, and the metal counterpart is materials/mmpsd-allowables.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_cmh17_allowables.py

The test covers the k-factor bands and monotonicity, minimum sample counts, allowables below the sample mean, pooling behavior (k shrinks with effective n, pooled sd within batch spreads), Weibull content values and basis values, knockdown reduction, the allowable table builder, and invalid-input edge cases.

Compliance

• Standards referenced, not reproduced: CMH-17 (proprietary, SAE publication) name + paraphrase only; mmpsd and far-25 resolve in standards-map.yaml, both reference-only.
• compliance: STANDARDS-REF, gated: false.