Wiring is a technique used to bend and hold branches in a certain position. The technique of wiring has only really been in use for the last 100 years, therefore it is a relatively new technique considering the art of bonsai has been around for thousands of years.
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In most cases, one would leave the wire on the tree for one growing season, although some trees are slower growing and take longer to hold the wired position, in which case the wire will remain on for longer. When wiring one should always be cautious for wire bite- this occurs when the branch grows to the extent that the wire cuts into it. Wire bite can leave ugly scars that may never grow out. If you feel that your wiring is beginning to damage your tree, you should remove it immediately.
Bending thick branches drastically is likely to put a lot of stress on the branch. To aid the process, one should split the branch down the centre in a lengthwise direction. (To do this, use branch-splitters or a sharp knife). Then wrap moist raffia around the branch to protect the new wound. The next step is to wire the branch and proceed as normal. The raffia will also allow for the wire to remain on the branch for a longer period of time.
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I would suggest the use of proper bonsai wire as opposed to copper wire because it is easy to work with, corrosion protected and can be re-used. When selecting the correct wire to bend a branch, keep in mind that the gauge of the wire should be 1/3 of the thickness of the branch. Essentially ones aim is to bend the wire around the branch and not the branch around the wire. Application of the wire is relatively simple. First make sure the wire is anchored to the trunk, the wire is then wrapped around the branch in a spiral at a 45 degree angle. Sometimes in the case of thick branches, a second or even third piece of wire is required. These are applied using the same technique I mentioned above and should mirror your first wires positioning.