Problems in Fracture mechanics, how to use Mathematica to calculate integrals with singular points?

f1[[CurlyPhi]_Rational, s_Rational, [Theta]_Rational,
a_Rational] = (
Sqrt[s](a - s))/((a - s)^2 + a^2 -
2
a*(a - s)*Cos[[CurlyPhi] - [Theta]])

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NIntegrate[
 f1[\[CurlyPhi], s, 4*Pi/20, 1], {\[CurlyPhi], 0, Pi}, {s, 0, 1}]

When Phi equals 0, it cannot be calculated.
Note: the Rate of convergence of Numerical integration is too slow and the integration value is overflow、Indeterminate or Infinity

When Phi equals 4*Pi/20, the result is 4.10626.
Note: the Rate of convergence of Numerical integration is too slow and cannot converge to the specified accuracy

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Is there anyone who can help solve this problem? Thank you very much
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