Life Cycle Services has just announced in their July 2015 Release that they are releasing the Evaluation version of AX for all Customers and Partners. This follows a similar concept of Dynamics CRM when they offered a 30 day trials for anyone who wanted to try the CRM online.
The details that you would need is a valid LCS account and Azure portal access, some of the other details that you need to select/check are Location, Sizing, LCS project and T&C's. Currently you will only be able to deploy the AX 2012 R3 version, and it aptly seems to pave the way for the AX 7.0 version which is supposed to be fully web based client. You can access the Market place for Dynamics AX Evaluation copy from this link. Have fun with the evaluation versions and make sure your Azure subscriptions don't burn up too quickly by turning off the VM's when not in use.