I found some websites for free graphics like icons. But, they require attribution. to the website. Is there any website that provide free graphics for research purpose without the need of attribution?
phylopic.org has some great animal and plant silhouettes which can be used in your graphics under a Public Domain or Creative Commons license. For instance, silhouettes from phylopic are used in figures in these papers (sorry they might be paywalled):
Neither of these studies acknowledged or attributed any image to phylopic.org, but some images may need to be acknowledged depending on the license - which can be seen on each image.
Benjamin provides some suggestions for graphics that do not require attribution, but I gotta ask - why not just attribute the ones you already have appropriately?
In all sites that my students use it is completely acceptable to add a single sentence to the acknowledgements ("Icons in figures 3, 4 and 7 have been produced by user XYZ on ABC"). As long as you clarify copyright questions, this seems substantially easier (and gives you a lot more options) than limiting yourself to visual elements that don't require any sort of attribution.