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38 The PCB Design Magazine • June 2015 circuit that is made from different layers of ma- terials. One property critical to understanding bending is modulus; in this case, modulus is the measurement of how stiff the circuit is. A high modulus is stiff, and low modulus is soft. When bending a circuit, softer material will generate less stress within the circuit and when there is less stress, the different layers are less likely to fracture. Bend radius is another very important issue. A simple way to think about this: If it is necessary to bend a metal sheet that is 1/8" thick without frac- turing the metal, then having a large bend radius will be advantageous and, of course, a small, tight bend radius is more likely to cause metal fractur- ing. The small bend radius causes more internal stress on the metal and is prone to fracturing. Another concept to consider is the neutral axis of the composite beam (or the circuit). The neutral axis is the plane within the circuit with no stress. Consider bending the 1/8" metal sheet again and try to imagine the stresses at differ - ent thicknesses within the metal sheet. First, the metal at the inside of the bend radius and those layers of the metal sheet will try to compress and will thus have stress due to compression. Then, consider the outside layers of the metal sheet; those layers of metal will try to rip apart or will suffer stress due to tension. Somewhere in the bend area, there is a transition in the metal, from stress as compression to stress as tension. That small transition area that has no stress is called the neutral axis. Ideally, when a circuit is formed, if there is a conductor on the neutral axis it would not fracture, even considering a circuit with a very tight bend radius, because there would be no stress within the conductor. The neutral axis is usually considered while modeling bending, forming and flexing circuits; the idea is to keep the critical copper layers as close to the neutral axis as possible. In the case of the microstrip circuit shown in Figure 1, the neu - THE ART OF BENDING AND FORMING PCBS continues lightning speed laminates Figure 1: Double-sided PCB used to demonstrate mechanical beam composite theory.

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