In most particle acceleration or propagation theories, the characteristic features of the cosmic ray spectra due to acceleration limits or propagation phase changes are charge-dependent^1-4 . Alternatively, the interaction scenario would expect mass-dependent spectral features in general. The observational verification of which relation takes effect in nature is still lacking because of the difficulty in measuring the spectra of individual particles up to very high energies. Here we report direct measurements of the carbon, oxygen and iron spectra from about 20 gigavolts to around 100 teravolts (60 teravolts for iron) with 9 years of on-orbit data collected by the Dark Matter Particle Explorer. Distinct spectral softenings have been directly detected in these spectra for the first time, to our knowledge. Combined with the updated proton and helium spectra, the spectral softening appears universally at a rigidity of about 15 teravolts. A nuclei-mass-dependent softening is rejected at a confidence level of >99.999%. Possible interpretations of these results, including a nearby cosmic ray source^5-7 and other models such as the propagation effect⁸ , are discussed.