These are general mechanics explanations and CDS model limits. They do not reproduce ASTM procedures or establish compliance. Obtain the licensed current standard for its mandatory specimen, fixture, calibration and reporting requirements.
Tension and axial stiffness
σ = F/(b t), ε = ΔL/Lg, and E = dσ/dε in an appropriate elastic range. The loaded cross-section and local gauge length must be known. Machine displacement includes compliance that a local strain gauge may not measure.
Beam bending and fixture span
For a slender, simply supported rectangular beam with one center force P, σmax = 3PL/(2bt²) and the elastic center compliance is δ/P = L³/(4Ebt³). These are Euler–Bernoulli formulas, with negligible shear compliance. Four-point loading has different moment and compliance expressions governed by load positions and whether P denotes total force or force at each nose. Short-beam and sandwich tests need shear and local-contact assessment.
Shear and coordinate transformation
Under ideal uniaxial loading of a ±45° laminate, the material-axis shear magnitude follows |τ12| = |σx|/2 and |γ12| = |εx − εy|. A nominal fixture shear stress F/A is a different idealization. Check field uniformity, loading and the selected model before interpreting a shear modulus or strength.
D7136-25 · Elastic center impact
Physical reduction
Initial impact energy = ½ m v²; work W = ∫ F dδ; elastic Hertz contact F = K_H δc^(3/2).
Plate bending and local indentation contribute separately to displacement and compliance. The reduced model needs plate dimensions, laminate bending stiffness, impactor properties, support conditions and contact calibration. An elastic solution stores and returns energy. Damage thresholds, degradation and residual strength require measured calibration; loading work alone is not irreversible absorbed energy.
Scope of this CDS model
First plate mode with CLT bending stiffness and Hertz elastic contact. Symmetric specially orthotropic thin plate, center strike, supplied density and indentation coefficient. Force, displacement and energy histories; higher modes, membrane stiffening, permanent indentation and damage are excluded. ASTM D7136 is a method reference, not a compliance claim.
Model or method source ↗ · Open the matching exercise guide ↗
D7136-25 · Calibrated center impact damage
Physical reduction
Initial impact energy = ½ m v²; work W = ∫ F dδ; elastic Hertz contact F = K_H δc^(3/2).
Plate bending and local indentation contribute separately to displacement and compliance. The reduced model needs plate dimensions, laminate bending stiffness, impactor properties, support conditions and contact calibration. An elastic solution stores and returns energy. Damage thresholds, degradation and residual strength require measured calibration; loading work alone is not irreversible absorbed energy.
Scope of this CDS model
Two-mass Hertz contact with irreversible calibrated scalar plate stiffness loss and explicit energy accounting. Supplied damage coefficients are illustrative until measured calibration. No damaged area, failure-mode map, penetration or residual CAI strength is predicted.
Model or method source ↗ · Open the matching exercise guide ↗
D6264-23 · Quasi-static center indentation
Physical reduction
Initial impact energy = ½ m v²; work W = ∫ F dδ; elastic Hertz contact F = K_H δc^(3/2).
Plate bending and local indentation contribute separately to displacement and compliance. The reduced model needs plate dimensions, laminate bending stiffness, impactor properties, support conditions and contact calibration. An elastic solution stores and returns energy. Damage thresholds, degradation and residual strength require measured calibration; loading work alone is not irreversible absorbed energy.
Scope of this CDS model
Elastic CLT first-mode plate compliance plus Hertz indentation. Symmetric specially orthotropic thin plate and supplied contact coefficient. Total displacement is plate deflection plus contact indentation. Fixture compliance, permanent indentation and damage propagation are excluded.
Model or method source ↗ · Open the matching exercise guide ↗
D6641-23 · Compression coupon
Physical reduction
σnom = F/Aref; tangent stiffness = dσ/dε within a justified elastic range.
Specify gross or net reference area and the actual gauge definition. Coupon alignment, end constraints and buckling can dominate a compression result. A measured open- or filled-hole comparison needs matching geometry and calibration; smooth-coupon strength is not the notched strength.
Scope of this CDS model
Uniform small-strain compression using linked laminate Ex and thickness. Measured compressive strength supplies a screening ratio; fixture, tabs, buckling and failure evolution are not simulated.
Model or method source ↗ · Open the matching exercise guide ↗
D5379-19(2026) / D7078-20(2025) · Shear coupon
Physical reduction
τnom = F/A_shear; for ideal uniaxial ±45° loading, |τ12| = |σx|/2 and |γ12| = |εx − εy|.
The area and strain transformation depend on the specimen and loading idealization. A rail or notched specimen does not guarantee a uniform shear field. The ±45° transformation belongs to that laminate loading case and must not be substituted for a fixture-specific stress reduction.
Scope of this CDS model
Uniform nominal shear between notches using linked laminate Gxy and thickness. Not a notch/fixture stress field or nonlinear shear solution. Gauge length is the effective shear deformation length, not crosshead travel.
Model or method source ↗ · Open the matching exercise guide ↗
D5528-21 · DCB opening
Physical reduction
G = P²/(2b) · dC/da, where C = δ/P.
For a linear-elastic cracked beam, energy release depends on the change in compliance with crack length. Specimen thickness, arm stiffness, root rotation and the chosen calibration affect the reduction. Force–deflection alone is insufficient without crack length and the applicable calibration.
Scope of this CDS model
Ideal Euler–Bernoulli DCB with equal homogeneous 0° arms, each half the linked laminate thickness. No root rotation, shear, large displacement or cohesive growth. Critical load is an initiation estimate from supplied GIc.
Model or method source ↗ · Open the matching exercise guide ↗
D7905-19e1 · ENF sliding
Physical reduction
G = P²/(2b) · dC/da, where C = δ/P.
For a linear-elastic cracked beam, energy release depends on the change in compliance with crack length. Specimen thickness, arm stiffness, root rotation and the chosen calibration affect the reduction. Force–deflection alone is insufficient without crack length and the applicable calibration.
Scope of this CDS model
Ideal equal-arm, homogeneous 0° ENF beam; support span is twice the half-span. Crack must be shorter than the half-span. No shear/root correction or unstable crack growth. GIIc is supplied, not fitted automatically.
Model or method source ↗ · Open the matching exercise guide ↗
D6671-22 · Mixed-mode fracture envelope
Physical reduction
G = GI + GII; Gc = GIc + (GIIc − GIc) [GII/(GI + GII)]^η.
This mixed-mode energy envelope requires independently measured mode-I and mode-II toughness and a fitted interaction exponent. It is an initiation criterion under its calibrated assumptions, not a universal crack-growth or fatigue law.
Scope of this CDS model
Benzeggagh–Kenane envelope from calibrated GIc, GIIc and exponent. Supplied GI/GII are energy-release rates from a separate test reduction or analysis. This does not resolve the MMB lever fixture or propagate a crack.
Model or method source ↗ · Open the matching exercise guide ↗
D5229-20 · Moisture uptake calibration
Physical reduction
∂c/∂t = ∂/∂z (Dz ∂c/∂z); diffusion time scale t ∝ h²/Dz.
A Fickian uptake model uses measured diffusivity, equilibrium content and appropriate surface activity. Fit the uptake history rather than treating one final mass as sufficient. Resin degradation, swelling-dependent diffusion and non-Fickian behavior require additional evidence.
Scope of this CDS model
Homogeneous slab, initially dry, both faces held at equilibrium moisture. Fits diffusivity from two early uptake measurements (both ≤50% saturation) using the square-root-time approximation. Edge ingress and temperature dependence are excluded. Does not overwrite material properties.
Model or method source ↗ · Open the matching exercise guide ↗
D5961-23 · Bearing / bypass screening
Physical reduction
Nominal bearing stress = F_bearing/(d t).
d is the reference hole/fastener diameter and t is thickness. Bearing and bypass loads must be identified separately. Nominal bearing stress is a reporting convention; local contact, clearance, load sharing and progressive damage need a validated joint model or measurements.
Scope of this CDS model
Single-pin nominal bearing, net-section and shear-out checks with independent measured allowables. Bypass tension is added to net-section load only. No contact, bolt preload, load redistribution or validated bearing–bypass interaction envelope.
Model or method source ↗ · Open the matching exercise guide ↗
D6484-23 · Open-hole compression
Physical reduction
σnom = F/Aref; tangent stiffness = dσ/dε within a justified elastic range.
Specify gross or net reference area and the actual gauge definition. Coupon alignment, end constraints and buckling can dominate a compression result. A measured open- or filled-hole comparison needs matching geometry and calibration; smooth-coupon strength is not the notched strength.
Scope of this CDS model
Nominal gross/net stress and demand relative to measured open-hole compressive strength for this geometry and layup. This is test-data screening, not an uncalibrated notch-strength prediction. No local buckling or kink-band simulation.
Model or method source ↗ · Open the matching exercise guide ↗
D6742-23 · Filled-hole comparison
Physical reduction
σnom = F/Aref; tangent stiffness = dσ/dε within a justified elastic range.
Specify gross or net reference area and the actual gauge definition. Coupon alignment, end constraints and buckling can dominate a compression result. A measured open- or filled-hole comparison needs matching geometry and calibration; smooth-coupon strength is not the notched strength.
Scope of this CDS model
Compares user-measured open- and filled-hole compressive strengths using gross-section stress. Use matched layup, hole, environment and fastener condition. Filling a hole does not automatically recover strength; no fastener contact/preload model is applied.
Model or method source ↗ · Open the matching exercise guide ↗
D7136-25 / D7137-23 · Impact & CAI assessment
Physical reduction
Residual nominal compression strength = maximum measured force / reference area.
An impact event and a later compression test are separate measurements. Relate residual strength to a documented damage state and specimen geometry. A nominal stress reduction does not predict damage area or compression-after-impact strength from impact energy alone.
Scope of this CDS model
Incident energy from measured impact velocity; residual compressive strength from measured peak CAI force. Rebound energy estimates energy not returned to the striker, NOT damage energy. No impact/contact solver, damage-area prediction or energy-to-strength extrapolation.
Model or method source ↗ · Open the matching exercise guide ↗
D5766-23 · Open-hole tension
Physical reduction
σnom = F/Aref; εnom = ΔL/Lg; E = dσ/dε in the selected elastic range.
Use the appropriate loaded area and gauge length. Flatwise, in-plane and core tests measure different material directions and failure mechanisms. Crosshead travel includes fixture and machine compliance and cannot automatically replace a local strain measurement. Report the model’s stated scope and calibration.
Scope of this CDS model
Gross/net nominal tension and demand relative to measured open-hole tensile strength for the same geometry and layup. No uncalibrated notch-strength prediction, local hole stress or damage evolution.
Model or method source ↗ · Open the matching exercise guide ↗
D3479-19(2023) · Tension–tension fatigue
Physical reduction
Nf = f(σmax, R, temperature, material state); R = σmin/σmax.
Life and retained properties require calibrated cyclic data under matching stress ratio, temperature and loading mode. A fitted tension-fatigue curve is not a prediction of multiaxial spectrum life. Distinguish crack initiation, stiffness loss and final failure.
Scope of this CDS model
Constant-amplitude Basquin S–N interpolation using stress AMPLITUDE, calibrated at one exact tensile R ratio. Coefficients and limits are hypothetical defaults: replace them and document the measured source/environment in Parameter basis. No damage growth, scatter, self-heating or extrapolated life.
Model or method source ↗ · Open the matching exercise guide ↗
D7291-22 · Flatwise laminate tension
Physical reduction
σnom = F/Aref; εnom = ΔL/Lg; E = dσ/dε in the selected elastic range.
Use the appropriate loaded area and gauge length. Flatwise, in-plane and core tests measure different material directions and failure mechanisms. Crosshead travel includes fixture and machine compliance and cannot automatically replace a local strain measurement. Report the model’s stated scope and calibration.
Scope of this CDS model
Circular coupon loaded normal to its plane through bonded thick metal end-tabs. Uniform stress uses actual circular area, supplied through-thickness Ez and linked stack thickness. In-plane E2 is not Ez. Block/bond restraint and interlaminar failure evolution are excluded.
Model or method source ↗ · Open the matching exercise guide ↗
C273-20 · Core shear
Physical reduction
τnom = F/A_shear; for ideal uniaxial ±45° loading, |τ12| = |σx|/2 and |γ12| = |εx − εy|.
The area and strain transformation depend on the specimen and loading idealization. A rail or notched specimen does not guarantee a uniform shear field. The ±45° transformation belongs to that laminate loading case and must not be substituted for a fixture-specific stress reduction.
Scope of this CDS model
Bare-core nominal shear between bonded loading plates. Stress is force / bonded plan area; shear strain uses explicit core G and relative plate displacement across linked core thickness. Use a core-only stack. End effects, adhesive slip and cell-scale fields are excluded.
Model or method source ↗ · Open the matching exercise guide ↗
C365-22 · Core flatwise compression
Physical reduction
σnom = F/Aref; tangent stiffness = dσ/dε within a justified elastic range.
Specify gross or net reference area and the actual gauge definition. Coupon alignment, end constraints and buckling can dominate a compression result. A measured open- or filled-hole comparison needs matching geometry and calibration; smooth-coupon strength is not the notched strength.
Scope of this CDS model
Uniform flatwise compression of a core-only stack between platens. Supplied core Ez gives elastic strain and shortening. Nominal stress uses the full plan area including cells. No crush plateau, densification, platen friction or automatic 2%-deflection strength inference.
Model or method source ↗ · Open the matching exercise guide ↗
C297-16(2024) · Sandwich flatwise tension
Physical reduction
σnom = F/Aref; εnom = ΔL/Lg; E = dσ/dε in the selected elastic range.
Use the appropriate loaded area and gauge length. Flatwise, in-plane and core tests measure different material directions and failure mechanisms. Crosshead travel includes fixture and machine compliance and cannot automatically replace a local strain measurement. Report the model’s stated scope and calibration.
Scope of this CDS model
Uniform flatwise tension of equal-faced sandwich bonded to loading blocks. Compare nominal stress with independent measured core, bond and facesheet through-thickness strengths. Explicit Ez values give series compliance; bondline/block compliance is neglected. Core + two faces must equal linked stack thickness.
Model or method source ↗ · Open the matching exercise guide ↗
C393-20 · Sandwich core flexure
Physical reduction
Face stress estimate σf ≈ M/(b tf d); core shear estimate τc ≈ V/(b c).
M and V are bending moment and shear force, b is width, tf is face thickness, d is face-centroid separation and c is core thickness. These are first-order balanced-sandwich estimates. Include shear compliance when appropriate; core crushing, face wrinkling and debonding are separate limits.
Scope of this CDS model
Symmetric three-point sandwich nominal core shear and mean facesheet stress from actual core/face dimensions. Equal thin faces, negligible axial core load. Core + two faces must match linked stack. Screening only: no indentation, wrinkling, debond growth or predicted displacement.
Model or method source ↗ · Open the matching exercise guide ↗
D7249-20 · Sandwich facesheet flexure
Physical reduction
Face stress estimate σf ≈ M/(b tf d); core shear estimate τc ≈ V/(b c).
M and V are bending moment and shear force, b is width, tf is face thickness, d is face-centroid separation and c is core thickness. These are first-order balanced-sandwich estimates. Include shear compliance when appropriate; core crushing, face wrinkling and debonding are separate limits.
Scope of this CDS model
Symmetric four-point long-beam sandwich with equal thin faces and support span/total thickness >20. Nominal face/core stress plus ideal elastic midspan displacement from supplied face Ex and core G. Ignores axial core stiffness, indentation, wrinkling, adhesive compliance and damage. Not a D7250 stiffness reduction.
Model or method source ↗ · Open the matching exercise guide ↗
D7078 · Rail shear mechanics
Physical reduction
τnom = F/A_shear; for ideal uniaxial ±45° loading, |τ12| = |σx|/2 and |γ12| = |εx − εy|.
The area and strain transformation depend on the specimen and loading idealization. A rail or notched specimen does not guarantee a uniform shear field. The ±45° transformation belongs to that laminate loading case and must not be substituted for a fixture-specific stress reduction.
Scope of this CDS model
Nominal shear response uses the loaded gauge area and the supplied effective shear properties. It does not resolve the rail fixture stress field or establish uniform shear. The standard is a method reference, not a compliance claim.
Model or method source ↗ · Open the matching exercise guide ↗