Are bond defaults more or less likely to happen when interest rates rise?

I know that Moody’s default forecasting model predicts the number of bonds that default which is related to the percentage of bonds that are speculative grade, real industrial production and the ten-year Treasury yield. However, does this question have something to do with recovery rates, since recovery rates and default rates are inversely correlated

Also, does the relation between default probability and interest rates tend to shorten or lengthen the effective duration of corporate bonds?

Thanks!