A bend-strain calculation can show where a stated layer model places the neutral axis and what longitudinal strain that model predicts at selected copper locations in one prescribed bend state. It cannot establish a safe radius, repeated-motion life, manufacturing acceptance, or finished-product qualification by itself. Before using a result in a design release or supplier discussion, verify the complete layer inputs and radius reference, then define the movement, materials, test evidence, and acceptance owner that the calculation leaves open.
Use this page to audit that calculation boundary and prepare a review package. For a broader design review of bend geometry and release decisions, see flex PCB bend-radius rules. For a page focused on repeated-motion design and cycle-life planning, see dynamic flex life-cycle design. Those topics require application-specific inputs and evidence beyond the local calculation shown here.
What must be fixed before calculating local strain?
A neutral-axis result is only interpretable when the cross-section and its coordinate system are explicit. Start with the released construction and the bend definition rather than a nominal total thickness or an assumed geometric mid-plane.
| Input to freeze | What the reviewer needs | If it is missing |
|---|---|---|
| Layer construction | Every layer in order, its thickness, material designation and controlled revision, including coverlay, bondply or adhesive, core, copper, shield, and local additions | The total thickness and stiffness distribution cannot be reconstructed reliably |
| Layer coordinates | Inner and outer reference faces and each layer boundary measured from the stated inner face | Copper location and neutral-axis distance cannot be checked |
| Mechanical properties | The longitudinal modulus and applicable source, temperature, direction, and material state for each modeled layer | The stiffness-weighted neutral-axis estimate is unresolved |
| Copper representation | Copper thickness, location, continuity or pattern, and relevant trace geometry | A continuous-sheet calculation may not represent patterned conductors |
| Width and model form | Whether all layers share the modeled width and whether a beam-like local strip is a defensible simplification | Width may not cancel, or a one-dimensional model may omit important behavior |
| Bend definition | Inside radius or another explicit reference, bend orientation, prescribed state, and temperature | A radius cannot be converted to neutral-surface radius consistently |
| Local geometry | Flex-zone boundaries and nearby cutbacks, vias, pads, stiffeners, shields, and rigid-flex transition features | The local strip result says nothing about those features |
| Source control | Drawing, stackup, material, and analysis revisions, plus who approved each | The result cannot be tied to the design being quoted or released |
Record unknown entries as open inputs. Do not replace an unknown construction with a familiar product family, a supplier default, or a symmetric-stack assumption unless the responsible parties explicitly approve that substitution.
What does a local neutral-axis model calculate?
For a straight, homogeneous-layer strip under the assumptions below, the longitudinal stiffness-weighted neutral-axis position measured from the inner face is
where Ei is the layer's longitudinal modulus, bi its modeled width, ti its thickness, and yi the centroid coordinate of that layer. If every layer has the same width, the common width cancels from numerator and denominator. Do not drop width when the modeled widths differ.
When the specified bend radius is the inside radius, the neutral-surface radius in this model is
With the coordinate increasing from the inner face toward the outer face, the signed local longitudinal strain at coordinate y is
Negative values indicate compression and positive values indicate tension for the bend orientation defined here. A percent value is the dimensionless strain multiplied by 100. State whether a number is a copper-center value or a copper-surface value: a copper centroid at zero strain does not mean that the copper's two surfaces have zero strain.
These equations are used below only for two hypothetical input sets. Both describe a 1 mm-wide, continuous-copper, initially straight local strip with homogeneous layers, perfect bonding and no slip, plane sections, no axial resultant, a common prescribed cylindrical curvature and temperature, and small-strain linear-elastic longitudinal properties. The example moduli are PI 3.5 GPa, adhesive 1.2 GPa, and copper 110 GPa. They are mathematical inputs only; they do not identify a stocked material, an APT construction, or a tested board.
What do the two complete hypothetical stacks show?
Both examples use a stated inside radius of 4000 µm. Their layer sequences close exactly to their declared total thicknesses. The table gives all layer boundaries from the inner face; it allows a reviewer to reproduce the centroid positions and check that the same radius convention is used throughout.
| Case | Layer sequence from the inner face (µm) | Declared and summed thickness |
|---|---|---|
| A | PI 0–25; adhesive 25–40; copper 40–58; adhesive 58–73; PI 73–98 | 98 µm |
| B | PI coverlay 0–25; adhesive 25–40; inner copper 40–58; PI core 58–102; outer copper 102–120; adhesive 120–135; PI coverlay 135–160 | 160 µm |
For Case A, the model’s weighted calculation places y0 at 49 µm from the inner face. The neutral-surface radius is therefore 4049 µm. The copper spans 40–58 µm, so its centroid is at 49 µm and its modeled center strain is zero. At the two copper faces, the signed values are −0.2222771054581378% and +0.2222771054581378%; the maximum absolute copper-surface value in this prescribed state is 0.2222771054581378%.
For Case B, the model calculation places y0 at 80 µm and the neutral-surface radius at 4080 µm. The inner copper centroid is at 49 µm and the outer copper centroid is at 111 µm. Their modeled center strains are −0.7598039215686274% and +0.7598039215686274%, respectively. Across both copper layers, the largest absolute surface value is 0.9803921568627451% in this prescribed state.
The comparison demonstrates a limited geometric point: with these exact hypothetical inputs, the copper locations relative to the calculated neutral axis differ between the two stacks. It does not show that any real single-layer design is acceptable, that any real multilayer design is unacceptable, or that changing the layer count will produce a particular service life. The listed values are model outputs, not measured strains, test results, pass/fail limits, or recommendations for a production radius.
Which behaviors does this calculation leave out?
This arithmetic uses a straight local strip with homogeneous layers, continuous copper, a perfect bond, no slip, plane sections, no axial resultant, common cylindrical curvature and temperature, small strain, and linear-elastic longitudinal properties. It does not include Poisson or plate effects, transverse or interfacial shear, residual stress, plasticity, viscoelastic response, free edges, patterned-copper details, variable width, twist, assembly constraints, or rigid-flex transition behavior.
Those omissions matter. Actual material properties and response depend on the identified material, processing, orientation, temperature, and construction. A drawing may include geometry that changes local load transfer. Motion may reverse direction, vary in radius or speed, combine bending with twist, or change with assembly and environment. The single prescribed state here contains no motion history, strain range or amplitude, specimen data, or matched fatigue results.
Therefore, neither example produces an allowable strain, a minimum qualified radius, a safe/unsafe disposition, a cycle count, a fatigue-life prediction, IPC compliance, or system qualification. Do not turn the arithmetic into any of those outcomes by comparing it with an unverified universal percentage.
Which evidence answers each release question?
Use the handoff below to separate what a local calculation can answer from what must be confirmed through design, materials, manufacturing, application, test, and product-level review. The named owner should be assigned for the specific project; the rows do not imply that a particular supplier provides a test or document by default.
| Review decision | Information available or to submit | Question the evidence can answer | Still open / responsible confirmation |
|---|---|---|---|
| Local section calculation | Controlled layer stack, coordinates, material-property sources, copper locations, radius convention, and analysis assumptions | Can another reviewer reproduce the neutral-axis and single-state strain values for this model? | Design owner confirms the released construction and acceptable model simplification |
| Material and process state | Exact laminate, copper foil designation and thickness, orientation, adhesive system, processing condition, and applicable data sheets or records | Do the modeled properties and construction correspond to the specified material state? | Materials and manufacturing owners confirm actual supplied and processed construction; no named material is inferred from the example |
| Layout and transition | Gerber or ODB++, flex-zone definition, trace geometry, coverlay, shields, vias, pads, stiffeners, and rigid-flex transition details | Which features require separate DFM or local analysis? | Design and supplier CAM/DFM reviewers determine feasibility for the released files and stackup |
| Movement and environment | Assembly constraints, path and direction of motion, radius reference and tolerance, motion sequence or history, temperature, and other relevant environment | What deformation history and conditions should a representative evaluation reproduce? | Mechanical/system owner defines the actual use condition; a single static state cannot supply it |
| Test article and monitoring | Agreed specimen or assembly definition, fixture, conditioning, load/motion profile, monitoring method, interruption or damage criteria, sample plan, and record format | What result was observed for the agreed specimen under the agreed procedure? | Quality, design, and supplier agree in advance on method, responsibilities, acceptance, and reporting; no experimental results are provided here |
| Product qualification and changes | Applicable procurement specification, intended product use, qualification plan, acceptance authority, and revision/change controls | Does the completed evidence satisfy the purchaser's specified requirement for the product and revision? | The purchaser and qualification authority decide acceptance and system suitability; local strain arithmetic does not grant approval |
IPC documents have distinct roles that should stay attached to their scope. The public scope of IPC-2223D (September 2016) identifies a sectional design-standard role for flexible and rigid-flexible printed boards. The public scope of IPC-6013E (September 2021) identifies qualification and performance requirements for flexible and rigid-flexible printed boards, with application requirements specified in procurement documentation. These dated public scope documents do not establish that this example complies, do not provide a universal allowable strain or radius, and are not a statement about the latest revision. Check the contractually applicable edition and full requirements for a real project.
A published IPC-TM-650 2.4.3.2 Rev C method describes a bending test for flexible printed wiring materials and measurement of electrical discontinuities under its specified specimen and test conditions. A method is not a result for the board being designed, and it does not supply a life prediction for a different construction or motion history. Select any test method and acceptance criteria with the responsible quality and design parties for the actual application.
What should a supplier discussion or RFQ package include?
Send a controlled package that lets the supplier identify the design being reviewed and lets both sides state what the review will cover. Ask for a written response to the scope and evidence requested; do not assume an analysis, qualification test, or report is included until the quotation or agreement says so.
- Released Gerber or ODB++ data, fabrication drawing, assembly constraints, revision identifiers, and any existing DFM questions.
- A controlled rigid-flex stackup with every layer, thickness, copper location and pattern, coverlay, adhesive or bondply, shield, stiffener, and local transition feature identified.
- Material and copper designations, property sources and applicable conditions, foil orientation requirements if any, and the records needed to confirm the supplied construction.
- Bend definition: inside or other radius reference, tolerances, direction, flex-zone limits, assembly state, motion path/history, temperature, and other specified environmental conditions.
- The exact question requested of each party: calculation review, manufacturability/DFM review, material confirmation, test planning, test execution, or product qualification support.
- If testing is in scope, the agreed article, fixture, conditioning, motion profile, monitoring and failure criteria, sample plan, report contents, acceptance authority, and change-control process.
- A clear list of deliverables, exclusions, responsible reviewers, quotation assumptions, and the point at which a revised stackup or design requires renewed review.
For complex HDI microvia integration or a manufacturing-scope discussion, the APTPCB rigid-flex capabilities page and rigid PCB capabilities page are related resources. Their links do not establish that a particular stackup, calculation, test, or qualification is available or included in a quote. For complementary power-routing context in rigid sections, see the heavy-copper PCB design and sizing page.
FAQ
If the copper center is at the neutral axis, is the copper strain zero?
The center strain is zero at that coordinate in the stated model. The copper extends on both sides of its center, so its two surfaces can have nonzero tensile and compressive strain. Review the layer faces as well as the centroid.
Can I substitute the inside radius for the neutral-surface radius?
Not in the equations used here. The model defines the neutral-surface radius as the inside radius plus the neutral-axis distance from the inner face. Keep the radius reference explicit when comparing calculations.
Does one bend-state result give cyclic strain range or fatigue life?
No. It describes the local strain in one prescribed state under the stated assumptions. Cyclic range and life require the actual motion and material/test evidence relevant to the construction and application.
Do matching strain values mean two constructions have the same life?
No. This model does not account for all material, process, geometry, loading, or environmental factors that affect a real assembly. It contains no matched fatigue data from which to infer life.
Who approves the calculation, test, and product requirement?
The design owner confirms the construction and model scope; the purchaser and supplier agree on quotation and evidence responsibilities; the applicable quality or product authority sets and accepts qualification requirements. A local calculation does not replace those approvals.
What does IPC-2223 establish for this example?
The cited public scope identifies IPC-2223D as a sectional design standard for flexible and rigid-flexible printed boards. It does not establish that these hypothetical calculations meet a universal radius, strain, cycle-life, or product-acceptance requirement. Confirm the edition and full contractual requirements for the project.
Public references
- IPC, IPC-2223D: Sectional Design Standard for Flexible/Rigid-Flexible Printed Boards, September 2016 public scope / table of contents: ipc.org/TOC/IPC-2223D.pdf.
- IPC, IPC-6013E: Qualification and Performance Specification for Flexible/Rigid-Flexible Printed Boards, September 2021 public scope / table of contents: ipc.org/TOC/IPC-6013E-EN_TOC.pdf.
- IPC, IPC-TM-650 2.4.3.2, Rev C, March 1991, flexible printed wiring material bending test method: ipc.org test-method document. It is cited for method scope, not as evidence of a test result for either hypothetical example.