Cleavage Direction Risk Checker

Resolve signed normal traction on independently measured cleavage planes under caller applied stress/tensile limit; compressive traction remains negative and this idealized screen does not predict fracture or handling safety.

Description

Normal traction on a plane depends on both plane orientation and applied stress.

Normal traction on a plane depends on both plane orientation and applied stress. Signed compressive traction must remain negative rather than becoming tensile magnitude.^[1]

When to use Cleavage Direction Risk Checker

Use this tool to resolve signed normal traction on independently measured cleavage planes under caller applied stress/tensile limit; compressive traction remains negative and this idealized screen does not predict fracture or handling safety.

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.

How to use Cleavage Direction Risk Checker and understand its results

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
Enter appliedSymmetricStressTensorPa, measuredCleavagePlaneNormals, callerTensileTractionLimitPa using the field table and calculation rules, then run the tool.
Read planeNormalTractionsPa, aboveCallerTensileTractionFlags. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
appliedSymmetricStressTensorPa	Applied symmetric stress tensor Pa	list of list of number	Required
measuredCleavagePlaneNormals	Measured cleavage plane normals	list of list of number	Required
callerTensileTractionLimitPa	Caller tensile traction limit Pa	number	Required

Enter an exactly symmetric finite 3×3 Cartesian stress tensor in Pa and nonzero three-component plane normals. Normalize each normal, compute signed traction and flag strict exceedance of a nonnegative caller tensile limit.

plane traction=unit normalᵀ × stress tensor × unit normal

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
planeNormalTractionsPa	Plane normal tractions Pa	list of number
aboveCallerTensileTractionFlags	Above caller tensile traction flags	list of number

json

{
  "input": {
    "appliedSymmetricStressTensorPa": [
      [
        10,
        0,
        0
      ],
      [
        0,
        -5,
        0
      ],
      [
        0,
        0,
        0
      ]
    ],
    "measuredCleavagePlaneNormals": [
      [
        1,
        0,
        0
      ],
      [
        0,
        1,
        0
      ]
    ],
    "callerTensileTractionLimitPa": 8
  },
  "output": {
    "planeNormalTractionsPa": [
      10,
      -5
    ],
    "aboveCallerTensileTractionFlags": [
      1,
      0
    ]
  }
}

Limitations and assumptions

This idealized screen omits flaws and fracture mechanics. It does not predict breakage or certify handling safety.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Matrices are limited to 128 rows and 128 entries per row; other numeric lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Parting Plane Warning Checker: Compare measured parting-plane normals to declared cut-plane normal with sign-invariant acute angles; parallelism warning is geometry only, not cleavage probability or safe cutting advice. For a complementary task, use Thermal Shock Sensitivity Checker: Screen caller measured temperature contrast with a fully constrained isotropic thermoelastic stress proxy and caller strength limit; geometry, anisotropy, defects and transient heat transfer omitted, no safe heating/cleaning advice.

References

Cleavage Direction Risk Checker — tool.io

Similar or alternative tools

Parting Plane Warning Checker
Compare measured parting-plane normals to declared cut-plane normal with sign-invariant acute angles; parallelism warning is geometry only, not cleavage probability or safe cutting advice.
Thermal Shock Sensitivity Checker
Screen caller measured temperature contrast with a fully constrained isotropic thermoelastic stress proxy and caller strength limit; geometry, anisotropy, defects and transient heat transfer omitted, no safe heating/cleaning advice.