A test method and corresponding fixture design are provided which enable loading a circular test coupon (made, e.g., of ceramic matrix composite material) to failure under biaxial loading conditions while recording strain and temperature. Biaxial loading requires approximately equal loads to be applied in two directions concurrently. The disclosed method uses liquid coolant (e.g., liquid nitrogen) to cool a ring made of metal alloy (e.g., aluminum alloy) that is disposed radially outward from and surrounds the outer edge of the test coupon. The cooled metal alloy ring contracts and compresses the test coupon until failure occurs.