Dynamic Strain Rate Modeling for Multi Ply Boxboard under Rapid Compression
Dynamic strain rate modeling predicts multi-ply boxboard Z-direction compression and interlayer shear collapse during high-speed converting and package drops.
Cowper-Symonds Model
Deformation Equation
Dynamic stress analysis of packaging materials undergoing high-speed impact requires mathematical formulations that relate yield strength to deformation rates. The cowper-symonds model represents the empirical relationship between the dynamic yield strength of a material and the strain rate to which it is subjected. It is applied to predict how materials behave under rapid loads.
Rate Dependence
When materials deform rapidly, their internal structure resists movement more intensely than under slow loading conditions. The cowper-symonds model calculates a scaling factor based on two material parameters that are determined through laboratory testing. These parameters adjust the static yield strength to account for strain rates across several orders of magnitude.
The model assumes that the plastic flow stress increases non-linearly as the rate of deformation rises, which is critical for simulating drops from high positions. This correction helps in choosing the proper packaging thickness to prevent product damage during sudden transit shocks.
Numerical Calculation
Implementing the formula in finite element simulations allows for the optimization of protective packaging designs. The calculation requires the input of experimental strain-rate data to calibrate the scaling coefficients for a specific board or polymer grade. It uses the ratio of the dynamic strain rate to a reference strain rate to scale the baseline static yield strength.
This numerical approach eliminates the need for endless physical drop testing by isolating the strain-rate sensitivity of the chosen substrate.