No, ISS crew members do not really have the flexibility to take a consistent mid-day nap. Pretty much every moment of their day is scheduled down to the 5 minute increment.

Shown below is the OPTIMIS Viewer, which details each crew member's schedule for the day. You have the Day/Night tracking bands at the top, GMT/Huntsville time next, TRDS coverage (orange is voice, green is video), then all 5 crew members' schedules. Not shown are dozens upon dozens of system resource and ground commanding bands that are synchronized with many of the crew's activities.

(Image Source)

• Activities with a blue box around them are time critical and MUST be done exactly as scheduled. There are likely critical Station resources needed for those activities that are only available at those times.
• Activities with black titles are hard scheduled and often have other coordination required from flight controllers or payload developers on the ground. Even if no ground coordination is required, often science experiments require certain time durations between related activities. For example, all the orange colored activities are related and need to be performed in that specific order shown. Note that the activity involves both FE-10 and FE-11.
• Activities with magenta titles are flexible activities, and may be completed at any time by the crew member.

It is possible that FE-11 in the schedule shown above could complete some of his flexible activities in his postsleep allocation and take a nap after midday meal since he has most of his day scheduled as flexible. However, I'd say that's the exception to the norm - most of the time crew members don't have that much flexibility in their schedule.

These schedules are generically planned by entire teams of long term planners, then as execution gets down to a month out, Increment Leads for each flight control discipline work with the planners to make a draft of the schedule to the level of detail as shown below. It's like piecing together a jigsaw puzzle to ensure every activity makes it on the schedule and doesn't conflict with another activity's requirements. Many, many man hours go into getting it right before it's handed to the front room for execution.

It would be prohibitively difficult to plan for individual preferences of crew members who wanted to take a break in the middle of the day. Their work schedule would have to extend into the rest of the crew's postsleep or presleep, when mission control is generally radio silent on Space to Ground voice loops to give the crew a break during off work hours.

No, ISS crew members do not really have the flexibility to take a consistent mid-day nap. Pretty much every moment of their day is scheduled down to the 5 minute increment.

Shown below is the OPTIMIS Viewer, which details each crew member's schedule for the day. You have the Day/Night tracking bands at the top, GMT/Huntsville time next, TRDS coverage (orange is voice/video, green is voice only), then all 5 crew members' schedules. Not shown are dozens upon dozens of system resource and ground commanding bands that are synchronized with many of the crew's activities.

(Image Source)

• Activities with a blue box around them are time critical and MUST be done exactly as scheduled. There are likely critical Station resources needed for those activities that are only available at those times.
• Activities with black titles are hard scheduled and often have other coordination required from flight controllers or payload developers on the ground. Even if no ground coordination is required, often science experiments require certain time durations between related activities. For example, all the orange colored activities are related and need to be performed in that specific order shown. Note that the activity involves both FE-10 and FE-11.
• Activities with magenta titles are flexible activities, and may be completed at any time by the crew member.

It is possible that FE-11 in the schedule shown above could complete some of his flexible activities in his postsleep allocation and take a nap after midday meal since he has most of his day scheduled as flexible. However, I'd say that's the exception to the norm - most of the time crew members don't have that much flexibility in their schedule.

These schedules are generically planned by entire teams of long term planners, then as execution gets down to a month out, Increment Leads for each flight control discipline work with the planners to make a draft of the schedule to the level of detail as shown below. It's like piecing together a jigsaw puzzle to ensure every activity makes it on the schedule and doesn't conflict with another activity's requirements. Many, many man hours go into getting it right before it's handed to the front room for execution.

It would be prohibitively difficult to plan for individual preferences of crew members who wanted to take a break in the middle of the day. Their work schedule would have to extend into the rest of the crew's postsleep or presleep, when mission control is generally radio silent on Space to Ground voice loops to give the crew a break during off work hours.