Dynamic damage constitutive model of plastic hardening⁃softening process of coal under impacting load

The CO2 gas fracturing has become an effective comprehensive treatment technology for high gassy and out⁃ burst coal mines in China，which is a low⁃frequency，low⁃velocity，long⁃wave，non⁃explosive technology. The mechanism and process of destroying coal are different from the high strain rate impact of explosive，and may be closer to the dam⁃ age mechanism under medium strain rate impact. In order to study the coal failure characteristics under the impact of CO2 fracturing，the separated Hopkinson pressure bar (SHPB) test system was used to conduct the impacting tests on coal samples taken from Xinyuan coal Mine，in Yangquan Mining Area，Shanxi province under the conditions of me⁃ dium strain rate (10-100 s-1). Through the analysis on the characteristics of coal brittle failure to ductile failure and the mechanism of pre⁃peak hardening and post⁃peak softening of the stress⁃strain curve，the dynamic damage con⁃ stitutive model describing plastic hardening⁃softening mechanism was established，including the dynamic elastic modu⁃ lus ED controlled by the strain rate. Moreover，the physical meaning and fitting method of the model parameters were given to verify the correctness of the model. The research results show that 1 the dynamic stress⁃strain curve of coal is approximately the ideal elastoplastic deformation process under the impacting load，which shows the charac⁃ teristics of pre⁃peak strain hardening and post⁃peak softening. The process of internal fracture damage evolution is de⁃ fined in four stages: I⁃no damage，II⁃micro⁃crack evolution，III⁃macro crack nucleation，and IV⁃macro crack propa⁃ gation，collapse failure stage. 2 The constructed equation of model can describe the whole process of plastic hardening and softening of coal，especially developing an accurate description method of the strain softening process in the BCsection of the stress⁃strain curve. 3 The new model contains only five dynamic parameters，which has the advantages of clear mechanical meaning，fewer parameters，and convenient fitting calculation. Among the five parameters，the dynamic elastic modulus E ， ultimate strain ε and post⁃peak strain εB increase with the increase of strain rate ·ε ，DsIwhile the brittleness index n decreases as the strain rate increases. Furthermore，the processes of damage accumulation and macro crack nucleation are controlled by ultimate strain ε and post⁃peak strain εB . 4 Compared with previous re⁃sIsearch，the new model has higher accuracy and stronger universality，and is also suitable for describing the plastic sof⁃ tening damage and failure characteristics of coal under medium and high strain rate impacting conditions.