Flexibility can be an important feature for printed-circuit boards (PCBs). Not all circuits are planar; some may need to be bent once to fit a particular product design while some might need to undergo continuous flexing as part of an application. Not all circuit materials are created equal, and some have more mechanical flexibility than others and can survive a certain amount of bending and flexing without damage. Understanding what makes a circuit material capable of bending and flexing, and what happens to it when it is bent or flexed, helps when specifying circuit materials for such uses.

Circuit boards are composites of different materials, such as conductive metals and dielectric materials, each with its own mechanical properties. The material stackup will depend on the type of circuit and the number of circuit layers. As more different materials are combined to form a PCB, especially in multilayer PCBs, the task of predicting the effects of bending and flexing becomes more complex. A key material parameter in determining how well a particular material will bend and flex is the modulus or stiffness of the material, with some of the composite materials of a PCB significantly stiffer, or with much higher modulus values, than others.

For example, the metallization in an RF/microwave PCB, primarily copper, will essentially determine the limits of flexibility in a circuit board since it has the highest modulus value of the material stackup, at 17,000 kpsi. Compare this to the much lower modulus values of dielectric materials, such as polytetrafluoroethylene (PTFE) with ceramic filler, at 300 kpsi, or PTFE with microfiber glass filling, at 175 kpsi. In a typical microstrip circuit, with conductor layer, dielectric, and ground-plane layer, the dielectric layer offers great flexibility but the top and bottom metal layers will set the limits of bending and flexibility for the composite structure.

Since high-frequency circuit boards are composite structures, the differences in flexibility of the component materials must be considered to determine how much bending and flexing a circuit board can withstand without damage to the stiffest of its material components, the metallization layers. This can be done by treating a PCB as if it were a beam being bent, with a certain bend radius depending upon the stiffness of the beam. A rubber beam will bend much more easily than a higher modulus metal beam, and be capable of enduring a much smaller bend radius without cracking. A PCB considered as a beam will also have a certain bend radius depending upon the overall stiffness of the composite group of materials, with the metallization layers setting the limits on the flexibility and minimum bend radius of the circuit board.

As with a beam, when a PCB is bent into a section of an imaginary circle, with a bend radius for that circuit, strain is placed on different parts of the beam and the PCB, with tension on the outer side and compression on the inner side of the bend radius. Between the areas of tension and compression lies an almost infinitely thin transition area or neutral axis with no strain. The strain increases as the distance from the neutral axis to the tension or compression plane increases. In a balanced circuit board, the neutral axis would lie at the geometrically center of the circuit board.

Stress from tension and compression works in different ways on a PCB’s materials, with tension pulling materials apart and compression squeezing them together. For a PCB with microstrip circuitry and copper conductors on the outer bend radius, this means that the stiffest or highest-modulus material in the composite PCB is being subjected to a certain amount of tension that will increase as the bend radius is made smaller. At the same time, the bottom ground plane is also being stressed and subjected to compression. Both forms of stress, if excessive, can lead to cracks in a microstrip circuit’s metallization layers. In addition, stress occurs at the interfaces of materials with different modulus values, such as the intersection of the copper conductor layer and the dielectric layer. Cracks from stress can start at the interface and work through the copper layer. To minimize damage to the metallization layers and ensure reliability in bent and flexed circuit boards, the key is to determine the amount of stress that a particular PCB can endure without cracking the metal layers.

The amount of stress on a PCB from bending and flexing is not simply a matter of knowing the modulus of the stiffest material component but in knowing how the PCB is constructed. For example, in a multilayer circuit board, differences in the thicknesses of the dielectric layers can cause increased amounts of strain when the circuit is bent. Each layer of a multilayer circuit structure will have its own modulus, and the structure will have a modulus as a whole. Since copper is the stiffest material component of most microwave circuits, the thickness of the copper and the percentage of copper in the entire PCB material stackup will contribute a great deal to the overall modulus and flexibility of the PCB as a whole.

Even the type of copper can determine the flexibility of a microwave circuit. Due to differences in the grain structures of rolled copper and electrodeposited (ED) copper, rolled copper is typically better than ED copper for PCBs that must be bent or flexed. For applications that may call for ED copper, some special types of ED copper are available for better bending and flexing than standard ED copper.  In addition, finishes added to copper conductors, such as electroless nickel/immersion gold (ENIG) plating, can add a high modulus to the overall PCB modulus, limiting the amount of bending and flexing that a PCB can safely endure.

Different microwave circuit constructions will present different bending and flexing capabilities. Stripline, with copper conductors sandwiched between upper and lower dielectric layers, is inherently better equipped for bending and flexing than microstrip. The signal conductor layer in a typical stripline construction is at or close to the neutral axis for minimum stress; however, the outer ground planes will typically have high stress.  

General guidelines to avoid damage when bending or flexing circuit materials pertain to single-bend and dynamic flexing situations. When a single bend is required, the bend radius should be at least 10 times the thickness of the circuit so that the strain on the circuit layer is 2% or less. For dynamic flexing, strain should be held to less than 0.2% for more than 1 million flex cycles and less than 0.4% for 1 million or less flex cycles.

Readers wishing to learn more about how to model stresses placed on PCBs from bending and flexing are invited to attend John Coonrod’s MicroApps presentation, “High Frequency Circuits Which Bend and Flex,” scheduled for May 24 at 12:30 p.m at the 2016 IEEE International Microwave Symposium (IMS) in San Francisco’s Moscone Center. The presentation will provide circuit bending prediction models and include a microstrip example using ½-oz. rolled copper on 5-mil-thick RO3003™ laminate material from Rogers Corp.

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