Use Bleach on Relaxed Hair
I also tried to get it done in a color class on my job. A strand test was done and the same thing. It barely lifted and it was very brittle. Now I know that black hair is hardest to lift, so what do you suggest? I myself have left the idea alone.
Using bleach on relaxed hair is "generally safe" as long as the hair has not been damaged by the relaxer and is in reasonably good condition. However, this doesn't mean that you can simply slap a bleaching agent onto the relaxed hair. Performing a chemical service on top of a previous chemical service means you must pay close attention to the hair and how it responds during the service.
Try looking at it this way: The process of relaxing the hair means that the hair's chemical side bonds have been broken permanently. This naturally weakens the hair somewhat. When you then proceed to attempt to bleach the hair from a true black (the darkest possible color) you use a process that disperses the color molecules in the hair shaft.
The lighter you want the hair to be, the more color molecules must be dispersed and obviously the more "substance" of the hair is destroyed. To attempt a dramatic color change all at once, can therefore be catastrophic to the hair.
If you intend to lift the hair color from a true black, it is generally better to do so in stages, using the gentlest chemical formulations possible. In between the chemical services, the hair should be conditioned, nourished and moisturized to help retain as much moisture and condition as possible.
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See also:
Hair coloring
Where does the color go when you bleach dark hair?
What is hair bleach made of? Is bleach harmful to your health?