Barty leaves without trophy but still No.1

Barty plans on celebrating her golden European summer with "maybe a beer or two" before jetting off to Australia to recharge her batteries before the American hardcourt swing.

Naomi Osaka's first-round demise and Monday's fourth-round departure of Karolina Pliskova ensures Barty will extend her stint atop the rankings for at least another two weeks.

That means the 23-year-old's reign will eclipse the fortnight that Evonne Goolagong Cawley - the only other Australian to top the women's rankings since they were introduced in 1973 - spent at No.1 in 1976.

"If we can hold on to the No.1 ranking, it would be great. But if we don't, it's not going to really change anything we do between now and our next event," Barty said after her 3-6 6-2 6-3 loss to American Alison Riske on Monday.

Barty's defeat was her first in 16 matches and only her seventh in the past nine months.

After withdrawing from her scheduled third-round doubles match on Tuesday citing an arm injury, Barty's bigger concern is getting her mind and body ready for the US Open starting on August 26.

"Rest and recover," Barty said when asked of her plans for when she arrived home, no doubt to a hero's reception after becoming Australia's first French Open champion in 46 years.

"I think it's also important to really celebrate what we've been able to achieve over the last eight weeks.

"It's been an extremely positive time for me and my team. Go and rest and recover with the family back home, then switch focus back to the hard courts.

"In the US, which I love that time of year, I love getting back over to the summertime there. I have some really good memories from last year.

"We go back, we knuckle down, train again, then we go again."

Barty will launch her American assault in Montreal from August 5 before winding up her US Open preparations in Cincinnati.

The final grand slam of the year gets underway on August 26.

Australian Associated Press