The Dynamic Impact Experiments Under Active Confining Pressure and the Constitutive Equation of PP/PA Blends at Multi‐Axial Compressive Stress State

Summary : A special active hydraulic confining pressure installation matched with Φ14.5 mm SHPB apparatus was developed. A series of active confining pressure impact experiments for PP/PA blends are performed in this special SHPB system under two kinds of axial strain rate: 8.0*10 2 , 1.4*10 3  s −1 and the active confining pressure of 0 MPa, 4 MPa, 8 MPa, 12 MPa, 15 MPa, 20 MPa. The axial strain‐time profile, the axial stress‐time profile and the hoop strain‐time profile of the specimen are recorded online respectively. According to the equilibrium equation, the complete state of principal stress and principal strain of PP/PA blends under multi‐axial stress state is analyzed. The experimental results reveal that the axial stress‐strain curves all are related to the confining pressure and the strain rate. It can also be seen that under a constant effective strain rate the effective stress‐ effective strain curves at different confining pressures are coincident basically. This manifests that under a certain effective strain rate there is only one unique effective stress‐ effective strain curve. The multi‐axial constitutive equation for PP/PA blends is suggested finally as:$\underline \sigma = ({\rm \sigma }_{{\rm conf}{\rm .}} + {\rm \sigma }_{{\rm eff}} /3)\underline {\bf I} + \underline {\bf A} {\rm \sigma }_{{\rm eff}} $ where σ conf is the confining pressure value.$$\sigma _{eff} (\varepsilon _{eff},\dot \varepsilon _{eff} ) = E\varepsilon _{eff} + \alpha \varepsilon _{eff}^2 + \beta \varepsilon _{eff}^3 + E_2 \int_0^t {\dot \varepsilon _{eff} (\tau )\exp \left( { - {{t - \tau } \over {\theta _2 }}} \right)} d\tau $$For 113 PP/PA blends, E  = 2.98 GPa, α = −31.15 GPa, β = 93.31 GPa, θ 2  = 8.54 µS, E 2  = 0.82 GPa.