\nPrincipais conclus\u00f5es<\/strong><\/p>\n\n\n\n
\n
- A bend radius multiplier is not a rule. It is what you get when you fix a stackup, choose an allowable copper strain, and solve IPC-2223’s equations.<\/li>\n\n\n\n
- The standard’s own dynamic worked examples give R\/T of 31 for a 185 \u00b5m single-sided stack and 88 for a 320 \u00b5m double-sided stack, not the 100\u00d7 and 150\u00d7 that circulate in the field.<\/li>\n\n\n\n
- IPC-2223 Figure 5-7 allows rolled annealed copper under 16% deformation and electrodeposited copper under 11%. That five-point gap is why dynamic flex requires RA foil.<\/li>\n\n\n\n
- The 6\u00d7 static rule is roughly an order of magnitude more conservative than the standard’s own installation-bend equation, which returns an R\/T near 0.55 on a thin single-sided stack.<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n
What Is a Bend Radius on a Flex PCB?<\/h2>\n\n\n\n
A flex PCB bend radius is the inner radius of the curved section: the distance from the innermost surface of the bent circuit to the centre of curvature.<\/p>\n\n\n\n
That surface is where the calculation starts, not where the failure happens. Bend a flex circuit and the neutral axis sits somewhere inside the stack. Material outside the axis stretches; material inside it compresses. The outer foil is pulled toward its elongation limit while the inner foil buckles and delaminates from the coverlay adhesive.<\/p>\n\n\n\n
The radius controls strain everywhere in the bend, and the mechanical envelope sets it. In one sentence: the radius scales with total flex thickness, scales with how far the outermost copper sits from the neutral axis, and on a fixed stack the dynamic multiplier lands close to two orders of magnitude above the static one. The standard’s own single-sided example gives R\/T 31 against R\/T 0.45.<\/p>\n\n\n\n
Anatomy of a flex PCB bend. The neutral axis is the surface that neither stretches nor compresses. Copper outside it is in tension; copper inside it is in compression.<\/em><\/figcaption><\/figure>\n\n\n\n How to Calculate the Minimum Bend Radius<\/h2>\n\n\n\n
IPC-2223 gives two equations, split by construction. Both work in micrometres.<\/p>\n\n\n\n
IPC-2223 \u00a75.2.3.4.1, single-sided with coverlay (Eq. 1):\n\n R = (c \/ 2) \u00d7 [(100 - E_B) \/ E_B] - D\n\nIPC-2223 \u00a75.2.3.4.2, double-sided with coverlay (Eq. 2):\n\n R = (d \/ 2 + c) \u00d7 [(100 - E_B) \/ E_B] - D\n\n R = minimum bend radius, \u00b5m\n c = copper thickness, \u00b5m\n d = dielectric thickness in the flexible clad material, \u00b5m\n D = dielectric thickness including adhesive, \u00b5m\n E_B = allowable copper deformation, %\n<\/code><\/pre>\n\n\n\nThese were read from the November 1998 base revision of IPC-2223. The current revision is IPC-2223F, dated May 2026, and the publisher’s current-revision listing<\/a> is where to confirm which edition your fabricator builds to. Clause numbering has changed across revisions, so verify against a licensed copy. This article does not claim the text is identical in F.<\/p>\n\n\n\n
D is subtracted because R is measured at the innermost surface, while D is the dielectric and adhesive between that surface and the copper. Thicker material under the copper puts the foil further out at the same inner radius, so a smaller R produces the same strain.<\/p>\n\n\n\n
E_B takes three values: 16% for a single crease in rolled annealed copper, 10% for installation bending (flex-to-install, tied to the minimum elongation in IPC-MF-150), and 0.3% for repeated motion. Those three numbers are the only thing separating the multipliers.<\/p>\n\n\n\n
Define T first.<\/strong> T is the sum of the base film, every copper foil, every adhesive or bondply layer, and the coverlay on both sides, measured in the bend region. It is not the nominal substrate thickness on the data sheet, and it is not the thickness at the stiffener, which is thicker by design and irrelevant to the bend. Two engineers disagreeing by a factor of two have almost always defined T differently.<\/p>\n\n\n\n
Take the standard’s single-sided example: 50 \u00b5m polyimide base, 25 \u00b5m adhesive, 35 \u00b5m copper, and coverlay with its adhesive. That is T = 185 \u00b5m, c = 35 \u00b5m, D = 75 \u00b5m. At E_B = 0.3%, Eq. 1 returns 5,741 \u00b5m, or 5.74 mm<\/strong>, an R\/T of 31.<\/p>\n\n\n\n
Take the double-sided example: a 50 \u00b5m polyimide core, two adhesive layers, two 35 \u00b5m copper foils, coverlay on both faces. That is T = 320 \u00b5m, d = 100 \u00b5m, c = 35 \u00b5m, D = 75 \u00b5m. At 0.3%, Eq. 2 returns 28,173 \u00b5m, or 28.17 mm<\/strong>, an R\/T of 88.<\/p>\n\n\n\n
Hold that stack fixed and change only the application. At the 10% installation limit, Eq. 1 returns 82.5 \u00b5m, or 0.083 mm<\/strong>, an R\/T of 0.45. The geometry did not move; the answer moved by a factor of 69. A flex-to-install bend and a dynamic hinge are different design regimes.<\/p>\n\n\n\n
That 0.083 mm is below anything you can form and inspect reliably, and the equation does not care. On a thinner stack the first term falls further, and D can exceed it, at which point Eq. 1 returns a negative radius. That is not an arithmetic error: it means the strain limit is no longer binding, because copper that thin tolerates almost any radius the process can produce. Read a negative result as “not the governing constraint” and set the drawing value from what the tooling and the coverlay will survive without creasing.<\/p>\n\n\n\n
Report the diameter with the radius. A 5.74 mm radius is an 11.5 mm minimum bend diameter<\/strong>, and the mechanical engineer sizing the housing thinks in diameter, because that is the gap between two walls. Then add 20% to 30% for production: T varies with adhesive flow and lamination, and the formed radius carries its own tolerance. The 5.74 mm result becomes 6.9 mm to 7.5 mm.<\/p>\n\n\n\n
Run the calculation on the finished stack, not the design intent. Coverlay adhesive flows during lamination, so the finished T sits a few micrometres above or below the nominal sum, and a fabricator quoting a build will give a finished thickness range rather than one number. Use the top of that range for a dynamic part. The radius scales linearly with T, so a 5% thickness overrun is a 5% radius overrun, and on a 28 mm dynamic radius that is well over a millimetre of housing nobody budgeted for.<\/p>\n\n\n\n
Minimum bend radius against allowable copper strain, computed from IPC-2223 Eq. 1 and Eq. 2 for the standard’s own worked stacks. The curve is the relationship; the steepness is why the published multipliers disagree.<\/em><\/figcaption><\/figure>\n\n\n\n projeto de imped\u00e2ncia controlada<\/a><\/p>\n\n\n\n
Why the Multiplier Changes: The Strain Math<\/h2>\n\n\n\n
The equations are not empirical fits. They are the geometry of a bent beam written in the standard’s notation, and the rearrangement is short enough to do on a whiteboard. Bend a layer of thickness c so its inner surface has radius R. The neutral axis sits at R + c\/2, the outer surface at R + c. The outer arc is longer in proportion to the radii, so strain at the outer fibre is (c\/2)\/(R + c\/2), which reduces to c\/(2R + c). Set that equal to E_B\/100 and solve:<\/p>\n\n\n\n
R = (c \/ 2) \u00d7 [(100 \/ E_B) - 1]<\/code><\/pre>\n\n\n\nThis is Eq. 1 with D removed. Add the dielectric offset back, because R is measured at the inner surface rather than at the copper’s inner fibre, and you have the standard’s equation exactly. The familiar relation epsilon = t\/(2R), with t the distance from the neutral axis, is the same statement in approximate form: set t = c and invert, and you get (c\/2)(100\/E_B), which is the standard’s own expression without the small exact-form correction. The derivation belongs to IPC-2223. The point is that the equation is already the strain relation.<\/p>\n\n\n\n
So a multiplier is the factor (100\/E_B – 1) at a chosen strain, scaled by how far the copper sits from the axis and divided by total thickness. For the three limits that factor is 5.25, 9 and 332. Moving from 10% to 0.3% multiplies it by 37 before any geometric term changes.<\/p>\n\n\n\n
The limits come from IPC-2223 Figure 5-7, which gives maximum deformation under 16% for rolled annealed copper and under 11% for electrodeposited copper. That gap answers the question designers ask most often about dynamic flex. RA foil is not preferred because of folklore about grain structure; the standard allows it roughly 45% more deformation before the copper is considered failed, and at 0.3% per cycle that margin separates a hinge that survives qualification from one that cracks.<\/p>\n\n\n\n
Keep those base-foil figures separate from the plated-copper recommendations in \u00a74.3.1.1 and \u00a74.3.1.2, which give 12% and 18% elongation for electrolytically plated copper in through-holes, measured per IPC-TM-650 Method 2.4.18.1. They are different quantities on different features and they are not interchangeable with the RA and ED limits. A bend region contains base foil, not plated barrel, so Figure 5-7 is the figure that governs the radius.<\/p>\n\n\n\n
One inconsistency is worth flagging rather than smoothing over. Figure 5-7 shows about 3% for installation bending, while the \u00a75.2.3.4.1 worked calculation uses 10% for the same case. The two do not agree, and this article does not resolve which is intended. The 10% figure is the more permissive one, so a design built to 10% carries less margin than the number implies. Read 3% as conservative when the bend is formed once and must not crack in the field.<\/p>\n\n\n\n
Layer count enters through the same lever arm. Each added layer moves copper further from the neutral axis and adds stiffness, so strain at the outermost foil rises at an unchanged radius. A 300 \u00b5m four-layer stack with 25 \u00b5m coverlay puts its outermost copper about 125 \u00b5m from the axis. At E_B = 0.3% that requires R = 41.5 mm, an R\/T of 138.<\/p>\n\n\n\n
The neutral axis also does not sit at mid-plane in an asymmetric adhesive-based stack. Adhesive is softer than polyimide and the copper distribution is uneven, so the axis shifts toward the stiffer side. The distance to the outermost copper is larger than a symmetric calculation suggests, and the true strain is higher than the geometry implies.<\/p>\n\n\n\n
Agora, o achado que muda a forma como voc\u00ea interpreta as regras est\u00e1ticas do campo. Em uma estrutura fina de face \u00fanica, com coverlay de 25 \u00b5m, adesivo de 12 \u00b5m, cobre de 18 \u00b5m e filme-base de 25 \u00b5m, T = 80 \u00b5m, c = 18 \u00b5m e D = 37 \u00b5m. A Eq. 1, no limite de instala\u00e7\u00e3o de 10%, resulta em R = 81 \u2212 37 = 44 \u00b5m, ou R\/T de 0,55. A regra de 6\u00d7 aplicada aos mesmos 80 \u00b5m resulta em 480 \u00b5m. Nesse raio, o cobre externo sofre cerca de 1,9% de deforma\u00e7\u00e3o, contra uma toler\u00e2ncia de 10%, aproximadamente um quinto do que a folha suportar\u00e1. Os multiplicadores est\u00e1ticos s\u00e3o regras pr\u00e1ticas conservadoras, n\u00e3o os m\u00ednimos da norma. A margem n\u00e3o \u00e9 desperdi\u00e7ada, porque a conforma\u00e7\u00e3o manual e a varia\u00e7\u00e3o do laminado s\u00e3o fatores reais, mas voc\u00ea deve saber que est\u00e1 escolhendo essa margem.<\/p>\n\n\n\n
propriedades do material-base de poliimida<\/a>]<\/p>\n\n\n\n
Qual multiplicador se aplica ao seu projeto<\/h2>\n\n\n\n
A coluna da direita mostra o R\/T que as equa\u00e7\u00f5es da IPC-2223 produzem para uma estrutura representativa, n\u00e3o uma faixa inventada para esta p\u00e1gina.<\/p>\n\n\n\n
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