Melbourne - Top seed Ashleigh Barty steps up her bid to end the host country's title drought and Tunisia's Ons Jabeur is chasing more history in the Australian Open quarter-finals on Tuesday.

The world No 1 Barty is under huge pressure to win in Melbourne - the last time an Australian woman triumphed in their home Grand Slam was Chris O'Neil in 1978.

But the 23-year-old, the reigning French Open champion, faces a stern test in 2019 finalist Petra Kvitova, and Barty has not had it all her own way in Melbourne.

She needed three sets to win her opener against Ukraine's 120th-ranked Lesia Tsurenko and was also pushed to three on Sunday against 18th-seeded American Alison Riske.

Barty said conditions play their part in Melbourne, where there has been pollution, heavy rain, wildly fluctuating temperatures and, on Sunday, some breezes.

"It could be cold, raining, roofs closed. All these variables that come into it," said Barty.

"Year in, year out, it's about trying to be consistent every single match, trying to be present every single match, not thinking about what's happened before, not thinking about what's to come."

Two-time Wimbledon champion Kvitova presents a major threat.

The Czech seventh seed and the Australian played five times last year, with Kvitova winning the first three and Barty the last two.

Tellingly, the 29-year-old Kvitova beat Barty in the quarter-finals last year at Melbourne Park, 6-1, 6-4.

"I love Petra, but let's hope she doesn't break my heart on Tuesday," Barty said after getting through against Riske.

But Barty is a better player than 12 months ago. She won her maiden Grand Slam in June at the French Open and topped the world rankings for the first time.

She also defeated Kvitova, the 2011 and 2014 Wimbledon champion, in three sets in the semi-finals on her way to the title at the season-ending WTA Finals in Shenzhen.

Kvitova said she admired the way the younger Barty handled the weight of Australian expectations.

"She's dealing with it like probably nobody else. That's really something why she is deserving to be number one and won a Grand Slam," said Kvitova.

Inspirational Jabeur

It is a different kind of pressure for Tunisia's Jabeur - she is hoping to inspire young people across the Arabic-speaking world.

The unseeded 25-year-old knocked out China's Wang Qiang - who upset Serena Williams in the previous round - and faces American Sofia Kenin in the last eight.

The 14th seed Kenin ended the fairy tale run of 15-year-old Coco Gauff.

Jabeur, the first Arab woman to reach a Grand Slam quarter-final, has got Tunisians getting up in the middle of the night to watch her matches on television.

"I'm receiving a lot of messages, especially people waking up at 5:00 am in the morning to watch my match. I'm really proud," said Jabeur, at 78th in the world Africa's top-ranked player.

"Hopefully they can still watch me and following more, just not in the Grand Slam, but the other tournaments," she added.

"It will be really amazing. I hope really I can give a good example.

"Hopefully I can do more here."